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Ph.D. DISSERTATION

ADVANCED SIGNAL PROCESSINGFOR AUTOMOTIVE RADAR

SYSTEMS

차량용레이더시스템을위한신호처리기법

BY

SEONGWOOK LEE

AUGUST 2018

DEPARTMENT OF ELECTRICAL ANDCOMPUTER ENGINEERING

COLLEGE OF ENGINEERINGSEOUL NATIONAL UNIVERSITY

ADVANCED SIGNAL PROCESSINGFOR AUTOMOTIVE RADAR

SYSTEMS

차량용레이더시스템을위한신호처리기법

지도교수김성철

이논문을공학박사학위논문으로제출함

2018년 8월

서울대학교대학원

전기컴퓨터공학부

이성욱

이성욱의공학박사학위논문을인준함

2018년 8월

위 원 장:부위원장:위 원:위 원:위 원:

Abstract

Recently, as automobile safety has been receiving considerable public attention,

sensors devised for automobiles, such as sonar, vision, lidar, and radar systems, have

become significant. Among these sensors, the radar is robust to harsh environmental

conditions, such as no-light conditions or bad weather. The automotive radar systems,

mounted on automobiles, perform special functions such as adaptive cruise control,

autonomous emergency braking, and blind spot detection for driver safety and conve-

nience.

In this dissertation, advanced signal processing techniques for automotive radar

systems are proposed. In general, frequency-modulated continuous wave (FMCW)

radar systems are widely used for automotive radars. The main purpose of using the

automotive FMCW radar is to extract the information of targets, such as relative dis-

tances, relative velocities, and angles. In automotive radar systems, estimating the an-

gle of the target is a challenging problem because the number of receiving antenna ele-

ments is limited. Therefore, an enhanced target angle estimation method using signal-

to-noise (SNR) compensation or array interpolation is proposed in this dissertation.

In addition to basic target detection, automotive radar systems aim to perform more

advanced functions. For example, the automotive radar should be able to classify the

detected targets. Thus, a method to classify the targets, such as pedestrians, cyclists,

and vehicles, is proposed in the dissertation. In addition, target detection performance

of the automotive radar can be degraded in road structures, such as iron tunnels and

soundproof walls. Therefore, this dissertation proposes a method to recognize such

road structures and to suppress their adverse effects. Moreover, as the number of radar-

equipped vehicles increases in the near future, mutual interference among automotive

radars can cause a serious problem because it degrades the target detection perfor-

mance. Therefore, a method for mitigating the mutual interference is also proposed in

i

this dissertation.

keywords: Automotive radar, target detection, target classification, clutter suppres-

sion, mutual interference mitigation

student number: 2013-20849

ii

Contents

Abstract i

Contents iii

List of Tables vii

List of Figures ix

1 FUNDAMENTALS OF AUTOMOTIVE FMCW RADAR SYSTEMS 1

2 TWO-STAGE DIRECTION OF ARRIVAL ESTIMATION METHOD FOR

LOW SNR SIGNALS 4

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.2 DOA Estimation in Array Antenna . . . . . . . . . . . . . . . . . . . 6

2.2.1 Signal Model for Array Antenna . . . . . . . . . . . . . . . . 6

2.2.2 Subspace-Based DOA Estimation Algorithms . . . . . . . . . 7

2.3 Proposed Two-Stage DOA Estimation . . . . . . . . . . . . . . . . . 8

2.3.1 Stage 1: Coarse DOA Estimation . . . . . . . . . . . . . . . . 9

2.3.2 Stage 2: Fine DOA Estimation . . . . . . . . . . . . . . . . . 10

2.4 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.5 Measurement Results . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

iii

3 LOGARITHMIC-DOMAIN ARRAY INTERPOLATION FOR IMPROVED

DIRECTION OF ARRIVAL ESTIMATION 23

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.2 Conventional Array Interpolation Method . . . . . . . . . . . . . . . 25

3.3 Logarithmic-Domain Array Interpolation . . . . . . . . . . . . . . . 27

3.3.1 Proposed Array Interpolation Method . . . . . . . . . . . . . 27

3.3.2 Enhanced Received Signal Interpolation . . . . . . . . . . . . 29



3.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

4 TARGET CLASSIFICATION USING FEATURE-BASED SUPPORT VEC-

TOR MACHINE 42

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.2 Introduction of Root Radar Cross Section (RRCS) . . . . . . . . . . . 45

4.3 Data Measurement with FMCW Radar . . . . . . . . . . . . . . . . . 49

4.3.1 Measurement Campaign . . . . . . . . . . . . . . . . . . . . 49

4.3.2 Statistical Characteristics of RRCS . . . . . . . . . . . . . . 52

4.4 Feature Extraction Based on RRCS . . . . . . . . . . . . . . . . . . . 53

4.4.1 Magnitude of RRCS . . . . . . . . . . . . . . . . . . . . . . 53

4.4.2 Moving Pattern along RRCS . . . . . . . . . . . . . . . . . . 54

4.4.3 Slopes around RRCS . . . . . . . . . . . . . . . . . . . . . . 56

4.4.4 Extracted-Feature Space . . . . . . . . . . . . . . . . . . . . 56

4.5 Human-Vehicle Classification Using SVM . . . . . . . . . . . . . . . 57

4.5.1 Training and Validation of Data . . . . . . . . . . . . . . . . 57

4.5.2 Classification Results . . . . . . . . . . . . . . . . . . . . . . 58

4.5.3 Real-Time Target Classification . . . . . . . . . . . . . . . . 60

4.6 Application to More Practical Situation . . . . . . . . . . . . . . . . 61

4.6.1 Other Types of Targets . . . . . . . . . . . . . . . . . . . . . 61

iv

4.6.2 Target Classification in Real Road Environment . . . . . . . . 61

4.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

5 STATISTICAL CHARACTERISTIC-BASED ROAD STRUCTURE RECOG-

NITION AND CLASSIFICATION 64

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

5.2 Beat Frequencies in Periodic Road Structures . . . . . . . . . . . . . 67

5.3 Measurement of Radar Signals in Actual Road Environments . . . . . 69

5.3.1 Specifications of Automotive FMCW Radar Used in Measure-

ments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

5.3.2 Received Radar Signal Analysis Method for Measured Data . 71

5.4 Proposed Road Structure Recognition Method . . . . . . . . . . . . . 75

5.4.1 Distribution Fitting of Frequency Components . . . . . . . . 75

5.4.2 Parameters Representing Statistical Characteristics . . . . . . 77

5.4.3 Road Structure Recognition Using SVM Method . . . . . . . 81

5.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

6 PERIODIC CLUTTER SUPPRESSION IN IRON ROAD STRUCTURES 88

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

6.2 Received Signal Analysis in Iron Road Structures . . . . . . . . . . . 90

6.3 Periodic Clutter Suppression in Iron Road Structures . . . . . . . . . 92

6.3.1 Proposed Periodic Clutter Suppression Method . . . . . . . . 92

6.3.2 Clutter Suppression Results . . . . . . . . . . . . . . . . . . 95

6.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

7 MUTUAL INTERFERENCE SUPPRESSION USING WAVELET DENOIS-

ING 103

7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

7.2 Effect of Mutual Interference on Beat Frequency Estimation . . . . . 106

v

7.3 Proposed Mutual Interference Suppression Method Using Wavelet De-

noising . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

7.3.1 Decomposition of Low-pass Filter Output Using Wavelet Trans-

form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

7.3.2 Thresholding for Extracting Wavelet Coefficients of Interfer-

ence Signal . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

7.3.3 Reconstruction of Interference Signal . . . . . . . . . . . . . 114

7.3.4 Subtracting Reconstructed Interference Signal from Original

Low-pass Filter Output . . . . . . . . . . . . . . . . . . . . . 114



7.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

Abstract (In Korean) 139

vi

List of Tables

3.1 Resolution probabilities and root mean square errors for two adjacent

targets located at [−3.5 ◦, 2.5 ◦] . . . . . . . . . . . . . . . . . . . . 35

3.2 Resolution probabilities and root mean square errors for two target

vehicles located at [−1.7 ◦, 4.6 ◦] . . . . . . . . . . . . . . . . . . . . 40

4.1 Body sizes of four human subjects . . . . . . . . . . . . . . . . . . . 50

4.2 Mean values of three extracted features . . . . . . . . . . . . . . . . 57

4.3 Confusion matrix resulting from SVM . . . . . . . . . . . . . . . . . 58

4.4 Classification accuracy for each feature . . . . . . . . . . . . . . . . 59

4.5 Average classification accuracy as increasing the number of features . 59

4.6 Mean values of three extracted features . . . . . . . . . . . . . . . . 61

4.7 Confusion matrix resulting from SVM . . . . . . . . . . . . . . . . . 62

5.1 K-S statistic for distributions in a normal road and an iron tunnel . . . 76

5.2 Average values of five parameters of five road structures . . . . . . . 78

5.3 Confusion matrix derived from SVM with a linear classifier . . . . . . 83

5.4 Confusion matrix derived from SVM with a Gaussian kernel . . . . . 84

5.5 Recognition accuracy when only one parameter is used . . . . . . . . 85

5.6 Recognition accuracy obtained by increasing the number of suggested

parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

5.7 Confusion matrix derived from decision tree learning . . . . . . . . . 86

vii

5.8 Confusion matrix derived from SVM . . . . . . . . . . . . . . . . . . 86

viii

List of Figures

2.1 A conceptual diagram for proposed signal calibration method. . . . . 11

2.2 RMSE values versus SNR values for Root-MUSIC and resolution prob-

ability versus SNR values for Root-MUSIC. . . . . . . . . . . . . . . 16

2.3 Estimated DOA values for 200 trials and calculated RMSE values for

200 trials. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.4 Estimated DOA values in the first and the second stages. . . . . . . . 18

2.5 RMSE values versus SNR values for MUSIC and for TLS ESPRIT. . 19

2.6 Normalized pseudospectrums for conventional MUSIC, MUSIC with

proposed signal calibration, and beamspace MUSIC. . . . . . . . . . 19

2.7 Actual measurement environment on the testing ground. . . . . . . . 21

2.8 Normalized MUSIC pseudospectrums of the first and the second stage

DOA estimations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.1 Two types of interpolation errors from T∗ and V∗. . . . . . . . . . . 33

3.2 Normalized Bartlett pseudospectrums for two adjacent targets located

at [−3.5 ◦, 2.5 ◦]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.3 Resolution probabilities and root mean square errors versus SNR (N =

4). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.4 Resolution probabilities and root mean square errors versus the num-

ber of time samples (SNR is 10 dB). . . . . . . . . . . . . . . . . . . 36

3.5 Normalized pseudospectrums for three targets located at [−8 ◦, 1.5 ◦, 7.5 ◦]. 37

ix


5). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38


3). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.8 Measurement environment of two target vehicles located at [−1.7 ◦, 4.6 ◦]. 39

4.1 A block diagram for operation principle of an FMCW radar sensor. . . 50

4.2 A measurement scenario used for a human-vehicle classification: a

conceptual illustration and an actual photograph. . . . . . . . . . . . 51

4.3 RRCS distributions for human subjects and vehicles (R = 15). . . . . 52

4.4 Accumulated FFT results for a human subject (upper) and a vehicle

(lower). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

4.5 Instantaneous FFT results for a human subject and a vehicle. . . . . . 55

4.6 Three-dimensional spatial distribution of three features for human sub-

jects and vehicles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

4.7 A measurement in a practical road environment (a conceptual illustra-

tion). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

5.1 Distance difference between Rp and Rp+1. . . . . . . . . . . . . . . . 68

5.2 Block diagram for the FMCW radar sensor: signal processing in digital

signal processor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

5.3 Automotive FMCW radar sensor mounted in the front bumper. . . . . 71

5.4 Accumulated Sm for a radar-equipped vehicle entering an iron tunnel. 73

5.5 Snapshots for m = 100 (on a normal road, region A) and m = 460 (in

an iron tunnel, region B). . . . . . . . . . . . . . . . . . . . . . . . . 74

5.6 Instantaneous magnitude responses (Sm) for m = 100 (on a normal

road, region A) and m = 460 (in an iron tunnel, region B). . . . . . . 74

5.7 Distributions of frequency components for a vehicle traveling on a nor-

mal road and in an iron tunnel. . . . . . . . . . . . . . . . . . . . . . 76

x

5.8 Changes in values of the five parameters over 600 radar scans. . . . . 79

5.9 Overlapping areas between two parameters. . . . . . . . . . . . . . . 80

5.10 Conceptual diagram of the fourfold cross-validation method. . . . . . 81

5.11 Block diagram for the proposed method. . . . . . . . . . . . . . . . . 83

6.1 Accumulated Sm for a radar-equipped vehicle entering an iron tunnel. 90

6.2 Snapshots for m = 150 (on a normal road, region A), m = 350 (in a

transitional region, region B), and m = 550 (in an iron tunnel, region

C). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

6.3 Instantaneous magnitude responses (Sm) for m = 150 (on a normal

road, region A), m = 350 (in a transitional region, region B), and

m = 550 (in an iron tunnel, region C). . . . . . . . . . . . . . . . . . 91

6.4 Relationship between the (m− 1)th and mth radar scans. . . . . . . . 94

6.5 Block diagram illustrating the whole signal processing chain in the

FMCW radar system. . . . . . . . . . . . . . . . . . . . . . . . . . . 96

6.6 Calculated delays over 100 radar scans. . . . . . . . . . . . . . . . . 96

6.7 Distance changes for a near steel frame (60 m) and a distant steel frame

(200 m). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

6.8 Original magnitude response (top), clutter-suppressed magnitude re-

sponse with α = 0.2 (middle), and clutter-suppressed magnitude re-

sponse with α = 0.5 (bottom) for the 600th radar scan. . . . . . . . . 98

6.9 Original magnitude response (upper) and clutter-suppressed magni-

tude response (lower) for the 601th radar scan. . . . . . . . . . . . . . 99

6.10 FFT results of original magnitude response (upper) and clutter-suppressed

magnitude response (lower) for the 601th radar scan. . . . . . . . . . 100

6.11 Proposed clutter-suppressed magnitude response (upper) and clutter-

suppressed magnitude response using the method of [59] (lower) for

the 601th radar scan. . . . . . . . . . . . . . . . . . . . . . . . . . . 101

xi

6.12 Original and clutter-suppressed magnitude responses for a radar-equipped

vehicle in an iron soundproof wall. . . . . . . . . . . . . . . . . . . . 101

7.1 Simple interference scenario with a desired target vehicle and an inter-

ferer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

7.2 Time-frequency slope trends of the interference signal: (a) same sign

as the transmitted signal and (b) different sign to the transmitted signal. 107

7.3 (a) Time-frequency slopes of the transmitted and interference signals

(different signs case). (b) Beat frequency between the transmitted and

interference signals. . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

7.4 Low-pass filter output consisting of the desired target signal and a

pulse-like interference signal: (a) in the time-domain and (b) in the

frequency-domain. . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

7.5 Two thresholding methods for wavelet coefficients: (a) soft threshold-

ing and (b) hard thresholding. . . . . . . . . . . . . . . . . . . . . . . 113

7.6 Reconstructed pulse-like interference signal in the time domain from

wavelet denoising. . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

7.7 Low-pass filter output with the proposed interference suppression in

the frequency-domain. . . . . . . . . . . . . . . . . . . . . . . . . . 115


the frequency-domain: (a) for entire FFT indices and (b) for FFT in-

dices near beat frequencies. . . . . . . . . . . . . . . . . . . . . . . . 116

7.9 MUSIC pseudospectrum for low-pass filter output with the proposed

interference suppression in the frequency-domain. . . . . . . . . . . . 118

7.10 (a) Time-frequency slopes of the transmitted and interference signals

(same signs + different signs case). (b) Beat frequency between the

transmitted and interference signals. . . . . . . . . . . . . . . . . . . 119

7.11 Low-pass filter output consisting of the desired target signal and a

pulse-like interference signal in the time-domain. . . . . . . . . . . . 119

xii



7.13 Low-pass filter output of the Mando radar with interference signals

from the Delphi radar. . . . . . . . . . . . . . . . . . . . . . . . . . . 121

7.14 Reconstructed pulse-like interference signal in the time domain. . . . 122



xiii

Chapter 1

FUNDAMENTALS OF AUTOMOTIVE FMCW RADAR

SYSTEMS

FMCW radars are widely used in automotive radar systems [1]. In this system, the

frequency of a transmitted signal varies linearly with time [2]. Therefore, the transmit-

ted signal T (t) is expressed as

T (t) = AT cos

(2π(fc −

∆B

2)t+ π

∆B

∆Tt2)

(0 ≤ t ≤ ∆T ), (1.1)

where AT is the amplitude of the transmitted signal, fc is the carrier frequency of

the modulated signal, ∆B is the operating bandwidth, and ∆T is the sweep time.

This transmitted signal is often referred to as an up-chirp signal because its frequency

increases rapidly. For ∆T ≤ t ≤ 2∆T , the radar system transmits a signal whose

frequency decreases rapidly, which is called a down-chirp signal. When the up-chirp

signal is reflected from L targets, the received signal R(t) is given as

R(t) =

L∑l=1

{ARl cos(2π(fc + fdl −∆B

2)(t− tdl) + π

∆B

∆T(t− tdl)

2)}+ n(t)

=L∑l=1

dl(t) + n(t) (minltdl ≤ t ≤ ∆T + max

ltdl), (1.2)

where ARl (l = 1, 2, · · · , L) is the amplitude of the signal reflected from the lth

target, fdl is the Doppler effect caused by the relative velocity between the lth target

1

and the radar, and tdl is the time delay caused by the distance between the lth target and

the radar. In addition, dl(t) is the desired signal, which includes the range information

of the lth target, and n(t) represents the noise added at the receiving antenna. Then,

the transmitted signal T (t) is multiplied with the received signalR(t) by passing them

through a frequency mixer; the output of the mixer M(t) is given as

M(t) = T (t)R(t)

= T (t)

(L∑l=1

dl(t) + n(t)

)

= T (t)

L∑l=1

dl(t) + T (t)n(t) (maxltdl ≤ t ≤ ∆T ). (1.3)

Thereafter, M(t) becomes the input signal of the low-pass filter, whose output can be

expressed as

LPF (M(t)) =1

2AT

L∑l=1

ARl cos(2π((∆B

∆Ttdl − fdl)t

+ (fc + fdl −∆B

2)tdl −

∆B

2∆Ttdl

2))

+LPF (T (t)n(t)) (maxltdl ≤ t ≤ ∆T ). (1.4)

Because LPF (M(t)) is the sum of cosine signals, the frequencies of each signal are

extracted by applying the Fourier transform (in actual automotive radar systems, the

fast Fourier transform (FFT) is used instead). Then, these extracted frequencies ful (l =

1, 2, · · · , L) are expressed as

ful =∆B

∆Ttdl − fdl

=∆B

∆T

2Rlc− 2vl

cfc, (1.5)

whereRl and vl are the relative distance and relative velocity between the lth target and

the radar, respectively, and c is the propagation velocity of the transmitted radar signal.

2

In addition, beat frequencies extracted from the down-chirp signal can be expressed as

fdl =∆B

∆Ttdl + fdl

=∆B

∆T

2Rlc

+2vlcfc. (1.6)

Thus, if I use beat frequencies extracted from both up-chirp and down-chirp signals

in the FMCW radar system, I can estimate Rl and vl by pairing ful and fdl [3]. The

estimated distance and velocity are calculated as

Rl =(ful + fdl

)× c∆T

4∆B,

vl =(fdl − ful

)× c

4fc, (1.7)

because ∆T , ∆B, c, and fc are already fixed in the radar system. To avoid the paring

process of beat frequencies, a fast-ramp FMCW radar was designed [4], [5].

3

Chapter 2

TWO-STAGE DIRECTION OF ARRIVAL ESTIMA-

TION METHOD FOR LOW SNR SIGNALS

2.1 Introduction

Many array signal processing concepts and techniques have been proposed to esti-

mate the direction-of-arrival (DOA) of incident signals with greater accuracy. Among

them, subspace-based DOA estimation algorithms such as multiple signal classifica-

tion (MUSIC) [6], [7], estimation of signal parameters via rotational invariance tech-

niques (ESPRIT) [8], [9], and Root-MUSIC [10] have high angular resolutions. As of

recent, these algorithms are equipped with automotive radar systems to find the angular

information of targets around a vehicle.

When a lot of clutter (i.e., unwanted echoes) exists in the radar systems, the noise

level on the received signals is increased [11]. In this case, the signal-to-noise ratio

(SNR) of a desired target signal decreases. Moreover, because the performance of the

subspace-based methods is highly dependent on the SNR of the received signal [7],

[9], [10], the desired target cannot be detected by those methods when received signals

have low SNR values. Therefore, in this chapter, I propose a concise two-stage DOA

estimation method for low SNR signals, which improves the angular resolution of the

4

conventional subspace-based methods. In the first stage, using received signals, DOAs

are roughly estimated using the conventional subspace-based method. Thereafter, in

the next stage, the fine DOA estimation is performed based on a priori information

(e.g., received signals, estimated DOA) obtained from the first stage. This stage in-

cludes a signal calibration, which is a method for focusing on signals coming from

the directions that are estimated in the previous stage. The proposed method yields a

better estimation result, without requiring additional received signals. In addition, the

desired signal information (e.g., desired signal strength, DOA information) is nearly

maintained, even after applying the signal calibration.

Some research studies have been conducted to overcome this undesirable circum-

stance [12], [13]. Because the methods in [12], [13] additionally use the signal sub-

space to create beamformers, they require new systems. In the proposed method, be-

cause I use the existing beamformers of the conventional subspace-based algorithms,

it eliminates the need to configure new beamformers. Moreover, the proposed method

is also efficient when the DOA estimation is conducted using a small number of array

antenna elements (e.g., automotive radar systems). The proposed method is similar

to beamspace high-resolution DOA estimation algorithms [14], [15], in the sense that

they are composed of coarse and fine estimations. However, these beamspace methods

do not result in an enhanced estimation performance for low SNR signals.

The remainder of this chapter is organized as follows. In Section 2.2, the signal

model for the array antenna and the subspace-based DOA estimation algorithms are

briefly introduced. Then, the proposed two-stage DOA estimation method is described

in Section 2.3. Next, in Section 2.4, simulation results are shown, and measurement re-

sults with an actual automotive radar are given in Section 2.5. Finally, the conclusions

are presented in Section 2.6.

5

2.2 DOA Estimation in Array Antenna

2.2.1 Signal Model for Array Antenna

I assume that signals, coming from L directions of θ1, θ2, · · · , θL, are incident on

N linearly placed antenna elements. The spacing between the adjacent elements is d,

and θl (l = 1, 2, · · · , L) is defined from the boresight direction of the array antenna.

Assuming far-field narrowband signal sources, the received signal vector of the array

at time t, x(t), can be expressed as

x(t) = A× s(t) + n(t)

= [x1(t), x2(t), · · · , xN (t)]T , (2.1)

where [·]T denotes the vector transpose operator, and A = [a(θ1), a(θ2), · · · , a(θL)]

is the steering matrix composed of the steering vectors a(θl), given by

a(θl) = [1, ej2πλd sin θl , · · · , ej

2πλ

(N−1)d sin θl ]T . (2.2)

Moreover, λ denotes the wavelength corresponding to the carrier frequency, and s(t) =

[s1(t), s2(t), · · · , sL(t)]T is the incident signal vector, where sl(t) (l = 1, 2, · · · , L)

is the complex amplitude of the incident signal from the lth signal source at time

t. These amplitudes are assumed to be zero-mean complex Gaussians, and they are

uncorrelated with each sample. In addition, the power of sl(t) is given as |sl(t)|2 =

Pl (l = 1, 2, · · · , L). The noise vector n(t) = [n1(t), n2(t), · · · , nN (t)]T is also

assumed to be the zero-mean complex Gaussian vector, and the correlation of each

element in the noise vector is given as

E[ni(t)nHj (t)] =

σn2 (i = j)

0 (i 6= j)

(i = 1, 2, · · · , N, j = 1, 2, · · · , N), (2.3)

where (·)H denotes the complex conjugate transpose operator, and E[·] denotes the

ensemble average of the random process. The samples from s(t) and n(t) are also

assumed to be uncorrelated with each other.

6

2.2.2 Subspace-Based DOA Estimation Algorithms

I utilize subspace-based DOA estimation algorithms such as the MUSIC and the

Root-MUSIC algorithms. The overall estimation process of the Root-MUSIC algo-

rithm is almost similar to that of the MUSIC algorithm. Therefore, I introduce the

MUSIC algorithm first, and then the Root-MUSIC algorithm.

MUSIC Algorithm

To make use of the MUSIC algorithm, a correlation matrix of x(t) has to be com-

puted. The correlation matrix is given as

Rxx = E[x(t)x(t)H ]

= AE[s(t)s(t)H ]AH + E[n(t)n(t)H ]

= ARssAH + σn

2IN, (2.4)

where IN denotes the N by N identity matrix. Moreover, the eigenvalues of Rxx can

be placed in descending order, as follows:

λ1 > λ2 > · · · > λL > λL+1 > · · · > λN . (2.5)

The first L eigenvalues are relevant to the signal subspace, and the remaining (N −L)

eigenvalues are related to the noise subspace. If the N × 1 orthonormal eigenvector

corresponding to λi is expressed as νi (i = 1, 2, · · · , N), then the MUSIC pseu-

dospectrum P (θ) is defined as

P (θ) =a(θ)Ha(θ)

a(θ)HENa(θ)(EN =

N∑i=L+1

νiνHi ), (2.6)

where EN constitutes the noise subspace that is orthogonal to the incident signal sub-

space. Estimated DOA values of incident signals are determined by the values of θ that

make the denominator of P (θ) nearly zero.

In practical situations, it is impossible to know the exact statistics for the signal

and the noise; therefore, the ensemble average in (2.4) is difficult to compute. In this

7

case, assuming that the process is ergodic, a time-averaged correlation matrix is calcu-

lated using K measurements (i.e., K time samples) in a noisy situation. The matrix is

defined as

Rxx =1

K

K∑k=1

xk(t)xk(t)H . (2.7)

Using this matrix, I perform the subspace-based DOA estimation algorithms.

Root-MUSIC Algorithm

The denominator of P (θ) in (2.6) can be expressed as

a(θ)HENa(θ) =N+1∑

m=−N+1

cmem×j 2π

λd sin θ, (2.8)

where cm is the sum of diagonal elements in EN along the mth diagonal. If I define

z = e−j2πλd sin θ, (2.8) can be simplified to the form of the polynomial D(z) whose

coefficients are cm, which can be expressed as

D(z) =N+1∑

m=−N+1

cmz−m. (2.9)

I then find a root z that makes D(z) to 0 (If z is one of the roots, 1z∗ is also a root of

D(z) = 0), and choose the root that lies closest to the unit circle. The phase angle of

the selected root includes the DOA information, and the DOA can be estimated as

θ = − sin−1

(λ

2πdarg(z)

), (2.10)

where arg(·) denotes the phase angle of z.

2.3 Proposed Two-Stage DOA Estimation

The proposed method consists of two stages. First, using the conventional subspace-

based DOA estimation algorithms, the DOAs are estimated approximately. Then, based

on a priori information, received signals at each antenna element are calibrated. Fi-

nally, the DOA estimation is conducted again. Details of the proposed method are

explained as follows.

8

2.3.1 Stage 1: Coarse DOA Estimation

In this stage, DOAs of incident signals are roughly estimated. Here, I assume that

L (L < N) dominant signal sources are located in the field of view (FOV) of the array

antenna. If L signals, sl(t) (l = 1, 2, · · · , L), are incident on the array in the directions

of θl (l = 1, 2, · · · , L), then the received signal from the qth antenna elements is given

as

xq(t) =L∑l=1

sl(t)ej 2πλ

(q−1)d sin θl + nq(t) (q = 1, 2, · · · , N). (2.11)

Based on these received signals, I apply the conventional subspace-based algorithm

and estimate DOA values. As mentioned in Section 2.2, to conduct the DOA esti-

mation, the time-averaged correlation matrix has to be constructed using K measure-

ments. The K time-sampled received signal vector from the qth antenna element can

be expressed as

Xq = [xq[1], xq[2], · · · , xq[K]]. (2.12)

With Xq, I create a correlation matrix RXX, which is expressed as

RXX =1

K

X1

X2

...

XN

×

X1

X2

...

XN

H

. (2.13)

Using RXX, the subspace-based DOA estimation is conducted, and DOAs are esti-

mated. For the case when antenna elements receive high SNR incident signals, and the

signal sources are quite far apart from each other, it is easy to find L different DOAs.

Otherwise, DOAs of the incident signals are overlapped, and there is a greater like-

lihood of estimating DOAs that are less than L [16]. Even though L different DOAs

are estimated in the latter case, they do not yield exact values. For those cases where

signals with low SNR values are received, more accurate DOAs can be estimated by

the fine estimation, which is introduced in the following section.

9

2.3.2 Stage 2: Fine DOA Estimation

The fine DOA estimation contains a signal calibration for improving the perfor-

mance of the subspace-based DOA estimation algorithms. For the signal calibration

method, I use the expanded form of the spatial interpolation proposed in [17]. When

estimated DOA values are θ1, θ2, · · · , θP (P ≤ L < N), where P is the number

of estimated DOA values in the previous stage, the received signal calibration is per-

formed based on these values. As mentioned, the number of estimated DOAs, P , can

be smaller than the actual number of targets, L. This is because incident signals from

adjacent sources are combined and it provides overlapped estimated values. Neverthe-

less, the calibration method can be applied whether P = L or P < L, and it offers

improved performance.

Calibration of Received Signals

The method of signal calibration is as follows. Using the estimated DOA θp (p =

1, 2, · · · , P ), the received signal of the qth antenna element is calibrated using sym-

metric 2M + 1 (M = 1, 2, · · · , N−12 , M ∈ N) antenna elements, such as

z(p)q,M (t) =

1

2M + 1

q+M∑r=q−M

xr(t)ej 2πλ

(q−r)d sin θp

(M + 1 ≤ q ≤ N −M, q ∈ N, M ∈ N). (2.14)

The conceptual diagram of the proposed calibration method is depicted in Fig. 2.1.

In addition, the calibrated signal can be rewritten as

z(p)q,M (t) = Ap × sp(t)× ej

2πλ

(q−1)d sin θp +

L∑l=1, l 6=p

Bl × sl(t)× ej2πλ

(q−1)d sin θl

+1

2M + 1

q+M∑r=q−M

nr(t)ej 2πλ

(q−r)d sin θp ,

(2.15)

10

Figure 2.1: A conceptual diagram for proposed signal calibration method.

where

Ap =1 + 2

∑Ms=1 cos

(2πλ sd

(sin θp − sin θp

))2M + 1

,

Bl =1 + 2

∑Ms=1 cos

(2πλ sd

(sin θp − sin θl

))2M + 1

. (2.16)

As given in (2.14), by compensating the phase delays of signals received at neighbor-

ing antenna elements based on the estimated DOA θp, and by averaging these signals,

I can focus on the signal coming from the direction of θp. In addition, when I use sig-

nals received from antenna elements that are symmetric to the qth antenna element, no

phase distortion occurs, since Ap ∈ R and Bl ∈ R. For the elements located at both

end parts of the array, I use only possible received signals from neighboring elements.

In other words, the calibrated received signal can be expressed as

z(p)q,M (t) =

1

min (q +M, N)−max (1, q −M) + 1

×min (q+M,N)∑r=max (1, q−M)

xr(t)ej 2πλ

(q−r)d sin θp

(q ≤M + 1 or q ≥ N −M, q ∈ N, M ∈ N). (2.17)

11

Moreover, the powers of the original received signal and the calibrated signal are

given as

E[|xq(t)|2

]= Pp +

L∑l=1, l 6=p

Pl + σ2q ,

E

[∣∣∣z(p)q,M (t)

∣∣∣2] = Ap2 × Pp +

L∑l=1, l 6=p

Bl2 × Pl

+1

(2M + 1)2

q+M∑r=q−M

σ2r . (2.18)

For the calibrated signal, the SNR of the incident signal from the pth signal source is

given as

γp =Ap

2 × Pp1

(2M+1)2

∑q+Mr=q−M σ2

r

. (2.19)

When θp is close to θp, γp becomes Pp/σ2q . Thus, even though I use the calibrated

received signal, the SNR value corresponding to the pth signal source is maintained al-

most equivalently. However, SNR values for other signal sources are greatly degraded,

because the difference between sin θp and sin θl (l = 1, 2, · · · , L and l 6= P ) always

makes B2l become smaller than A2

p. Therefore, when using the calibrated received sig-

nal, I can focus on the desired source direction θp, and mitigate the interference signals

from the undesired source directions. In addition, the noise variance is averaged over

all the antenna elements. For the stable performance of the subspace-based algorithms,

the time-average correlation matrix∑K

k=1 nk(t)nk(t)H has to converge to the ensem-

ble average E[n(t)n(t)H ]. However, in practical situations with the limited number

of measurements, the ergodicity is not always established. In this case, since noise

variances are not precisely estimated, the noise variance differences occur among an-

tenna elements. When the noise powers are somewhat different from each element, the

performance of the subspace-based algorithm is degraded [17]. However, if I use the

calibrated signals, the noise variances of each element are smoothed, and have almost

similar values.

12

For the case when the DOAs of incident signals are overlapped, which means that

P < L, the calibration method can be also applied. When two of the L signal sources

are adjacent and located at θp1 , θp2 , the DOA of these two signals can be estimated as

only one value θp. In this case, I can also use the proposed signal calibration method,

and then the calibrated received signal is expressed as

z(p)q,M (t) = Ap1 × sp1(t)× ej

2πλ

(q−1)d sin θp1 +Ap2 × sp2(t)× ej2πλ

(q−1)d sin θp2

+L∑

l=1, l 6=p1, l 6=p2

Bl × sl(t)× ej2πλ

(q−1)d sin θl

+1

2M + 1

q+M∑r=q−M

nr(t)ej 2πλ

(q−r)d sin θp , (2.20)

where

Ap1 =1 + 2

∑Ms=1 cos

(2πλ sd(sin θp − sin θp1)

)2M + 1

,

Ap2 =1 + 2

∑Ms=1 cos

(2πλ sd(sin θp − sin θp2)

)2M + 1

. (2.21)

When using this signal, I can also focus on the direction θp. In this case, since (sin θp−

sin θp1) and (sin θp− sin θp2) are close to 0, the SNR values corresponding to the p1th

and the p2th signal sources are high after the signal calibration. Then, except for these

adjacent signal sources, the SNR values for the other signal sources are decreased, and

the noise variances of each antenna element are smoothed. I can therefore distinguish

the signal sources located in the direction of θp, and achieve a better angular resolution.

Repetition of DOA Estimation

In summary, the original received signal xq(t) is replaced by the calibrated received

signal z(p)q,M (t), and I use z(p)

q,M (t) for the DOA estimation. In the same manner, the K

time-sampled calibrated received signal vector from the qth antenna element can be

expressed as

Z(p)q,M = [z

(p)q,M [1], z

(p)q,M [2], · · · , z(p)

q,M [K]]. (2.22)

13

From now on, I use Z(p)q,M instead of Xq. With Z

(p)q,M , I create a correlation matrix

RZZ(p)M , which is expressed as

RZZ(p)M =

1

K

Z

(p)1,M

Z(p)2,M...

Z(p)N,M

×

Z(p)1,M

Z(p)2,M...

Z(p)N,M

H

. (2.23)

Using RZZ(p)M , the same process of the subspace-based DOA estimation algorithm is

conducted again.

Computational Complexity

The total computational complexity of the subspace-based algorithms is mainly

dependent on the eigenvalue decomposition. It is well known that its complexity is

O(N3) [18]. In the fine estimation, the eigenvalue decomposition is conducted as the

number of DOAs estimated in the previous stage. In the first stage, with the subspace-

based DOA estimation algorithms, at most N − 1 targets can be estimated [6], [7],

[10]. If the number of estimated DOA values is P (P < N), the additional complexity

P × O(N3)

occurs. For systems using a small number of antenna elements, such as

the automotive radar systems (N = 4 or N = 8), the increase in computation time is

acceptable for real-time signal processing with commonly used radar hardware.

2.4 Simulation Results

In all the simulations, I assume that six receiving antenna elements (N = 6) ar-

ranged uniformly with half-wavelength spacings (d = λ/2), and that 500 time samples

(K = 500) of the received signals are used to build the correlation matrix. In the first

simulation, two signal sources are located at θ1 = 1 ◦ and θ2 = 6 ◦. Increasing the SNR

values of received signals from −5 dB to 5 dB, I calculate the root mean square er-

ror (RMSE) values for the conventional method and the proposed method. The RMSE

14

value derived from RZZ(p)M is given as

RMSE(p) =

√√√√√∑Nth=1

{(θp − θp, h

)2}

Nt(◦), (2.24)

where Nt denotes the number of experimental trials, and θp, h represents the estimated

θp in the hth (h = 1, 2, · · · , Nt) trial. I run this simulation 1000 times (Nt = 1000)

for each SNR value, in order to calculate the RMSE values. First, the DOA is estimated

with the conventional Root-MUSIC algorithm, and then the original received signals at

each antenna element are calibrated using the estimated value. For six array elements,

the possible values of M are 1 and 2, since 2M + 1 has to be smaller than N . Thus,

the performance of the signal calibration, using three received signals (i.e., M = 1,

2M + 1 = 3) and five received signals (i.e., M = 2, 2M + 1 = 5), are evaluated. The

calibrated received signals for each M can be expressed as

z(p)q, 1(t) =

1

3

min (q+1, 6)∑r=max (1, q−1)

xr(t)ej 2πλ

(q−r)d sin θp ,

z(p)q, 2(t) =

1

5

min (q+2, 6)∑r=max (1, q−2)

xr(t)ej 2πλ

(q−r)d sin θp

(q = 1, 2, · · · , N). (2.25)

Fig. 2.2 shows the RMSE values of the conventional Root-MUSIC method and

the Root-MUSIC with the proposed method using RZZ(p)1 and RZZ

(p)2 . As shown

in the figure, the RMSE values of the proposed method are lower than those of the

conventional method, in the low SNR region. When the SNR value becomes high,

both methods have almost the same RMSE values, and those values converge to a

specific value.

With respect to the method, two types of errors can be defined. One is the esti-

mation error caused by the low SNR signals, and the other is the approximation error

arising from the proposed calibration method. In the method, an unavoidable approxi-

mation error occurs when multiplying the estimated phase delays (i.e., (2π/λ)d sin θp)

15

-5 -4 -3 -2 -1 0 1 2 3 4 5

SNR (dB)

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

Root m

ean s

quare

err

or

(deg)

Root-MUSIC (M = 0)

Root-MUSIC (M = 1)

Root-MUSIC (M = 2)

-5 -4 -3 -2 -1 0 1 2 3 4 5

SNR (dB)

0

10

20

30

40

50

60

70

80

90

100

Resolu

tion p

robabili

ty (

%)

Root-MUSIC (M = 0)

Root-MUSIC (M = 1)

Root-MUSIC (M = 2)

Figure 2.2: RMSE values versus SNR values for Root-MUSIC and resolution proba-

bility versus SNR values for Root-MUSIC.

to the received signals. In the low SNR region, because the calibration effect of the

method is dominant, the former error is reduced significantly. On the other hand, in

the high SNR region, because the estimation accuracy of θp with the original received

signals is sufficient, the approximation error mainly affects the total estimation accu-

racy. In addition, as shown in the Fig. 2.2, the RMSE values with RZZ(p)2 are slightly

larger than those with RZZ(p)1 in the high SNR region. When I use a larger number

of received signals that are a distance 2d away from the qth element for the signal

calibration, doubled phase delays are compensated. In this case, z(p)q, 2(t) has a larger

approximation error than z(p)q, 1(t). Therefore, the performance is degraded when using

RZZ(p)2 rather than RZZ

(p)1 , in the high SNR region. Nevertheless, because the effect

of the approximation error is negligible in the high SNR region, I can use the proposed

method regardless of the SNR.

In addition, with the same simulation conditions, I compute the resolution proba-

bility Pr for the conventional method and the proposed method, with the change of the

SNR values, as depicted in Fig. 2.2. The probability can be defined as

Pr =Nr

Nt× 100 (%), (2.26)

where Nr denotes the number of times that two distinct DOAs are extracted from re-

16

ceived signals. As shown in the Fig. 2.2, the proposed methods can resolve the incident

signals that are hardly distinguishable in the low SNR region.

To verify the effect of the proposed method, I plot the estimated DOA and the

RMSE values for the first 200 trials (i.e., Nt = 1, 2, · · · , 200) when the SNR value is

given as −5 dB. For this SNR value, the conventional Root-MUSIC algorithm cannot

resolve the targets, and it estimates only one DOA value between θ1 = 1 ◦ and θ2 =

6 ◦, as depicted in blue in Fig. 2.3. However, when I apply the calibration method with

the estimated value, the targets are separated. As you can see in Fig. 2.3, when I use

z(p)q, 2(t), it shows estimated DOA values that are close to θ1 = 1 ◦, which is depicted

by the black horizontal line (for θ2 = 6 ◦, similar trends are observed). Moreover, the

variation of the RMSE values for the same number of trials is given in Fig. 2.3. When

applying the proposed signal calibration method, the variation of the RMSE values is

considerably reduced, and the RMSE values are also decreased.

I also carry out a simulation for the case when more than two targets are located

in the FOV of the array antenna. In this case, targets are located at [θ1, θ2, θ3, θ4] =

[−7 ◦, −2 ◦, 8 ◦, 14 ◦], and the SNR value is set to 0 dB. Fig. 2.4 shows the estimated

DOA values in the first and the second stages, for a single radar scan. In the first stage,

the number of estimated DOAs is two, and the values are [θ1, θ2] = [−6.4 ◦, 11.4 ◦]

0 20 40 60 80 100 120 140 160 180 200

Trial

-4

-2

0

2

4

6

8

Estim

ate

d D

OA

( °

)

Root-MUSIC (M = 0)

Root-MUSIC (M = 1)

Root-MUSIC (M = 2)

0 20 40 60 80 100 120 140 160 180 200

Trial

0

5

10

15

20

25

30

RM

SE

( °

)

Root-MUSIC (M = 0)

Root-MUSIC (M = 1)

Root-MUSIC (M = 2)

Figure 2.3: Estimated DOA values for 200 trials and calculated RMSE values for 200

trials.

17

1 2

Stage

-10

-5

0

5

10

15

Estim

ate

d D

OA

(d

eg

)

DOA of target 1

DOA of target 2

DOA of target 3

DOA of target 4

Figure 2.4: Estimated DOA values in the first and the second stages.

which are not close to the actual DOA values. Using these values, I conduct the fine es-

timation for θ1 and θ2, respectively. Thereafter, I am able to distinguish all the targets.

The final estimated values are [θ1, θ2, θ3, θ4] = [−7.7 ◦, −2.5 ◦, 7.3 ◦, 13.1 ◦], which

are close to the actual DOA values. Therefore, the proposed method can be applied

when the number of targets is more than two, and it offers an improved estimation

performance.

In addition, I apply the proposed method to other subspace-based DOA estimation

algorithms, such as the MUSIC and the total least squares (TLS) ESPRIT algorithms

[9]. All the simulation conditions are the same as suggested in the first simulation,

except for the location of the targets. In this case, the targets are located at θ1 = −2 ◦

and θ2 = 3 ◦. As depicted in Fig. 2.5, the MUSIC with the proposed method results in

lower RMSE values than the conventional MUSIC, in the low SNR region. In addition,

the proposed method is also used with the TLS ESPRIT. When I attempt to estimate

the DOAs based on the conventional TLS ESPRIT, it can barely estimate the DOAs,

and gives absurd numerical values. Although the SNR value is 5 dB, it is still a low

value for the conventional TLS ESPRIT to perform properly. As shown in Fig. 2.5, the

DOA estimation results with the conventional TLS ESPRIT are highly inaccurate for

the given SNR range. However, when I use RZZ(p)2 and apply the TLS ESPRIT with

it, the algorithm yields more accurate estimated values than those of the conventional

18

-5 -4 -3 -2 -1 0 1 2 3 4 5

SNR (dB)

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

RM

SE

( °

)

MUSIC (M = 0)MUSIC (M = 2)

-5 -4 -3 -2 -1 0 1 2 3 4 5

SNR (dB)

0

2

4

6

8

10

12

14

16

18

RM

SE

( °

)

TLS ESPRIT (M = 0)TLS ESPRIT (M = 2)

Figure 2.5: RMSE values versus SNR values for MUSIC and for TLS ESPRIT.

TLS ESPRIT. Therefore, I verify that the proposed method can be operated with other

subspace-based methods, as well as the root-MUSIC algorithm.

Finally, I compare the performance of the proposed method to beamspace high-

resolution DOA estimation algorithms. In this case, the targets are located at [θ1, θ2, θ3]

= [−3 ◦, 2 ◦, 10 ◦], and the SNR is set to 0 dB. Fig. 2.6 shows the estimated DOA

values for the conventional MUSIC, the MUSIC with the proposed signal calibra-

tion, and the beamspace MUSIC [14]. The conventional MUSIC algorithm finds two

DOAs, such as [θ1, θ2] = [−0.8 ◦, 8 ◦]. Then, based on these values, I apply the pro-

-6 -4 -2 0 2 4 6 8 10 12 14

Field of view (degree)

0

0.2

0.4

0.6

0.8

1

1.2

No

rma

lize

d M

US

IC p

se

ud

osp

ectr

um

MUSIC

MUSIC with calibration (θ1)

MUSIC with calibration (θ2)

Beamspace MUSIC

Figure 2.6: Normalized pseudospectrums for conventional MUSIC, MUSIC with pro-

posed signal calibration, and beamspace MUSIC.

19

posed signal calibration method for each direction. As can be seen in the Fig. 2.6, θ1

is separated into [−1.9 ◦, 1.1 ◦]. Moreover, θ2 is estimated as a more accurate value,

which is 8.6 ◦. To apply the beamspace MUSIC algorithm, I have to set a proper

range that includes the signal sources. When the range does not contain the sources, it

yields inaccurate estimation values. In this simulation, even though I focus the beam

on Θbf = {θbf | − 5 ≤ θbf ≤ 4}, which includes all signal sources in the direc-

tion of θ1, it cannot resolve the signal sources, and the estimated DOA values are

[θ1, θ2] = [−2.4 ◦, 6.6 ◦]. In conclusion, for low SNR received signals, the angular

resolution with the beamspace MUSIC is not improved. However, with the proposed

method, it is.

2.5 Measurement Results

To verify the proposed scheme, I conduct actual measurements on the testing

ground of Mando Corporation, using its LRR. The FOV of the LRR ranges from−10 ◦

to 10 ◦. In the measurement, a single-element transmit antenna and four-element re-

ceiving array antenna (N = 4) are used, and the spacing between adjacent elements is

1.8λ. Thus, the half-power beamwidth of the array antenna is 7 ◦. This antenna system

is equipped with the automotive radar, and a 76.5 GHz frequency modulated contin-

uous wave (FMCW) signal is transmitted. One period of the radar signal is 100 ms,

which is composed of 10 ms transmission time and 90 ms signal processing time. The

transmitted signal is reflected from the vehicles in the front, and the reflected signals

are received by the array antenna. In Fig. 2.7, the measurement environment is shown.

Two identical target vehicles are located at −2.5 ◦ and 2.5 ◦, and they are 70 m away

from a radar-equipped vehicle. In this measurement, I use the MUSIC as a DOA esti-

mation algorithm. In addition, I record 300 radar scans, using the same measurement

conditions, for statistical analysis.

First, the DOAs of each target vehicles are roughly estimated using the conven-

20

Figure 2.7: Actual measurement environment on the testing ground.

tional MUSIC algorithm. Because I place the two vehicles close enough and design

the received signals to have low SNR values, the two reflected signals are combined

and only one DOA is estimated (θp = 0.5◦), as depicted in Fig. 2.8. Then, with θp,

I apply the proposed signal calibration method to focus that direction. In this case, I

set M = 1; thus, three received signals are used for the calibration. As shown in the

Fig. 2.8, two vehicles are decomposed, and two different DOAs, −2.3 ◦ and 2.7 ◦, are

estimated. For 300 radar scans, the DOA estimation results show similar trends. Com-

pared with the real DOA values, the proposed method yields almost exact estimation

-6 -4 -2 0 2 4 6


0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

No

rim

aliz

ed

MU

SIC

pse

ud

osp

ectr

um

The 1st stage estimation

The 2nd stage estimation

Figure 2.8: Normalized MUSIC pseudospectrums of the first and the second stage

DOA estimations.

21

results and an improved resolution. In addition, because the proposed method can be

completed in the 90 ms signal processing time, I verify that it can be well applied to

actual automotive radar systems.

2.6 Conclusion

In this chapter, I proposed the two-stage DOA estimation method for low SNR sig-

nals. In the first stage, the DOAs of incident signals were estimated using the conven-

tional subspace-based methods. Then, in the second stage, using the estimated DOA

values, the received signals of each antenna element was focused on the specific di-

rections, which were roughly calculated in the previous stage. The proposed method

showed an enhanced angular resolution and estimation accuracy, particularly for the

case when the array antenna elements received the low SNR signals. The simulation re-

sults showed that the proposed method performed better than the conventional method

and the beamspace high-resolution method, in terms of the RMSE values and the res-

olution probability. In addition, it can be well applied to the multi-target cases. More-

over, from the measurement data, I verified that the proposed scheme can be expanded

to existing automotive radar systems. The advantage of the proposed method was that

it offered much better angular resolution for the low SNR signals, without demanding

additional received signal information and large computational complexity.

22

Chapter 3

LOGARITHMIC-DOMAIN ARRAY INTERPOLATION

FOR IMPROVED DIRECTION OF ARRIVAL ESTI-

MATION

3.1 Introduction

In general, to detect targets located in multiple directions, automotive radar systems

consist of several types of radars that cover relatively narrow ranges (e.g., front side,

rear side). To improve direction of arrival (DOA) estimation accuracy of targets in

the range of interest, an array interpolation method that moves array elements from an

original location to a desired location using a transformation matrix has been proposed

[19]-[21]. To this end, the linear least squares (LLS) method has been widely used to

identify the proper transformation matrix [19]-[25]. However, a transformation matrix

obtained by means of the LLS method is not the best solution for interpolating array

elements. When this transformation matrix is applied, interpolated array elements are

generated by linear combinations of original array elements. In this case, amplitudes

of interpolated array elements can be different from those of original array elements.

If amplitude differences exist among the array elements, the performance of DOA

estimation algorithms is degraded [17]. In addition, because the solution derived from

23

the LLS method is obtained in the process of simultaneously minimizing differences

in amplitudes and phases, the phase information of the interpolated array elements is

not accurately formulated, which is a critical factor for DOA estimation.

Few studies on enhanced array interpolation methods have been conducted [26],

[27]. In [26], the Taylor series approximation was used to generate interpolated array

elements in a uniform circular array, and achieved improved DOA estimation perfor-

mance; however, because the order of the series is limited to one less than the max-

imum number of array elements, the approximation performance is not guaranteed

for automotive radar systems that use only a few (e.g., four or eight) array elements.

In addition, the norm-constrained least squares method was used to find the interpo-

lated microphone array in [27] but the problem-solving process is heuristic because

the proper norm constraint parameter is determined empirically.

Thus, in this chapter, I propose a transformation matrix in a logarithmic domain

for the array interpolation. I focus on minimizing the phase differences between the

original and the interpolated array elements. First, I take logarithms for the array el-

ements, and extract the phase information from them. I then apply the LLS method

to the logarithmic-domain matrices to find an appropriate transformation matrix. Fi-

nally, the interpolated array elements are generated by the new matrix, and the DOA

estimation is conducted. Based on a comparison of interpolation errors of the pro-

posed and conventional transformation methods, the array transformation method suc-

cessfully interpolates newly produced array elements with more elaborate phases. In

addition, the proposed array transformation does not affect the amplitudes of the in-

terpolated array elements; they are conserved even after the transformation. Moreover,

since these transformation matrices are calculated and stored (offline) beforehand, cal-

culating them in real time is not necessary.

I also extend the proposed array interpolation scheme to received signal interpo-

lation. When I use the transformation matrices obtained by the LLS method and the

proposed method, the powers of the interpolated received signals are not uniform over

24

all array elements. In this case, the effect of the array interpolation and the perfor-

mance of the DOA estimation are not fully ensured. Thus, to mitigate this problem,

I also propose a calibration method for the interpolated received signal powers. Sim-

ulation results confirm that the proposed method performs better at DOA estimation

than does the conventional array interpolation method. In addition, based on actual

measurement data acquired using an automotive radar, the method shows improved

angular resolution and estimation performance.

The remainder of this chapter is organized as follows. In Section 3.2, I introduce

the conventional array interpolation technique using the LLS method. Next, the pro-

posed array interpolation method is described in Section 3.3. In this section, I also

propose a method of calibrating the interpolated received signals for more accurate

DOA estimation. Simulation and measurement results are provided in Section 3.4 and

Section 3.5, respectively. I conclude this chapter in Section 3.6.

3.2 Conventional Array Interpolation Method

In this section, I briefly introduce the conventional array interpolation technique

using the transformation matrix derived from the LLS method. For the field of view

(FOV) of an automotive radar, which is expressed as

Θ = {θp | θp = θL + (p− 1)× θR − θLP − 1

, p = 1, 2, · · · , P}, (3.1)

I find a suitable matrix that transforms original array elements to the interpolated array

elements (θL and θR are angles that indicate the left and the right boundaries of the

FOV). In this range, the steering matrix of the original array elements can be given as

A(Θ) = [a(θL), a(θL + ∆θ), · · · , a(θL + (P − 2)∆θ), a(θR)], (3.2)

where ∆θ = θR−θLP−1 is the angle step size. Then, if I want to interpolate array elements

in the location [g1, g2, · · · , gM ], the steering matrix of the interpolated array elements

25

is determined as

B(Θ) = [b(θL), b(θL + ∆θ), · · · , b(θL + (P − 2)∆θ), b(θR)], (3.3)

where b(θp) = [ej2πλg1 sin θp , ej

2πλg2 sin θp , · · · , ej

2πλgM sin θp ]T (p = 1, 2, · · · , P ).

Assuming that a matrix T transforms the original steering matrix to the interpolated

steering matrix, it can be expressed as

B(Θ) = T×A(Θ). (3.4)

To find the proper transformation matrix T, the least squares method is used as

T∗ = arg minT

(‖B(Θ)−T×A(Θ)‖F ), (3.5)

where ‖·‖F denotes the Frobenius matrix norm. Then, based on the method of LLS,

the transformation matrix can be determined as

T∗ = B(Θ)A(Θ)H(A(Θ)A(Θ)H)−1, (3.6)

where A(Θ)H indicates the Hermitian matrix of A(Θ). Finally, from (3.4) and (3.6),

the estimate of B(Θ) is given as

BT∗(Θ) = T∗ ×A(Θ)

= B(Θ)A(Θ)H(A(Θ)A(Θ)H)−1 ×A(Θ). (3.7)

In addition, the (m, p)th element of the matrix BT∗(Θ) can be expressed as

BT∗

(m, p)(Θ) =

N∑n=1

{T∗(m,n) ×A(n, p)(Θ)

}=

N∑n=1

{T∗(m,n) × ej

2πλdn sin θp

},

∀m ∈ {1, 2, · · · , M}, ∀p ∈ {1, 2, · · · , P}, (3.8)

where T∗(m,n) and A(n, p)(Θ) denote the (m, n)th and the (n, p)th elements of the

matrices T∗ and A(Θ), respectively.

26

Through this transformation matrix, received signals for the interpolated array el-

ements can also be generated, which are defined as

Y(t) = T∗ ×X(t)

= [y1(t), y2(t), · · · , yM (t)]. (3.9)

By utilizing these interpolated received signals, the authors of [19]-[25] conducted

improved DOA estimations.

3.3 Logarithmic-Domain Array Interpolation

3.3.1 Proposed Array Interpolation Method

When I use the conventional transformation matrix for array interpolation, a major

problem occurs. Based on the transformation matrix obtained from the LLS method,

interpolated array elements are generated by linear combinations of original array ele-

ments. In this case, amplitudes of the interpolated array elements may not be equivalent

to those of the original array elements. In other words,∣∣∣BT∗

(m, p)(Θ)∣∣∣ does not always

become unity. When the amplitudes of each array element are not uniform over the

entire array, DOA estimation performance is degraded [17]. In addition, based on the

solution derived from the LLS method, phases of the interpolated array elements are

not precisely generated. For DOA estimation, the phase information of the interpolated

array elements is critical. Therefore, in this section, I propose a more effective array

interpolation method that minimizes the phase differences between the original and the

interpolated array elements while maintaining the equivalent amplitudes of the array

elements.

For the elements of the steering matrices on both sides of (3.4), I take logarithms

27

such as

LOG(A(Θ)) =

log(A(1, 1)(Θ)) · · · log(A(1, P )(Θ))

log(A(2, 1)(Θ)) · · · log(A(2, P )(Θ))...

. . ....

log(A(N, 1)(Θ)) · · · log(A(N,P )(Θ))

,

LOG(B(Θ)) =

log(B(1, 1)(Θ)) · · · log(B(1, P )(Θ))

log(B(2, 1)(Θ)) · · · log(B(2, P )(Θ))...

. . ....

log(B(M, 1)(Θ)) · · · log(B(M,P )(Θ))

, (3.10)

where LOG(·) denotes the operator that takes logarithms for each element in the

matrix, and B(m, p)(Θ) indicates the (m, p)th element of the matrix B(Θ). All ele-

ments in matrices LOG(A(Θ)) and LOG(B(Θ)) have pure imaginary values. Then,

in the logarithmic domain, I find a proper transformation matrix V that transforms

LOG(A(Θ)) to LOG(B(Θ)), which is expressed as

LOG(B(Θ)) = V × LOG(A(Θ)). (3.11)

As in the original domain, the appropriate matrix V can be found using the LLS

method, and the solution is given as

V∗ = LOG(B(Θ))LOG(A(Θ))H

×{LOG(A(Θ))LOG(A(Θ))H

}−1. (3.12)

This matrix V∗ effectively transforms the phases of the original array elements into

those of the interpolated array elements. However, since the matrix is defined in the

logarithmic domain, it cannot be directly applied to the original array elements as in

(3.7). In other words, this transformation matrix cannot be expressed with a linear

operator. Instead, it can be written with the original array elements as

BV∗

(m, p)(Θ) =N∏n=1

{A(n, p)(Θ)

}V∗(m,n) ,

∀m {1, 2, · · · , M} , ∀p ∈ {1, 2, · · · , P} , (3.13)

28

where BV∗

(m, p)(Θ) is the (m, p)th element of the newly interpolated steering matrix

BV∗(Θ), and V∗(m,n) indicates the (m, n)th element of the matrix V∗.

The conventional transformation matrix in (3.6) formulates the interpolated array

elements with linear combinations of the original array elements. However, this new

transformation matrix generates only the phase information of the interpolated array

elements using combinations of the phases of the original array elements. In other

words, based on the transformation, it conserves the amplitudes of the original array

elements in the interpolated array elements because

∣∣∣BV∗

(m, p)(Θ)∣∣∣ =

∣∣∣∣∣N∏n=1

{A(n, p)(Θ)

}V∗(m,n)

∣∣∣∣∣=

∣∣∣e∑Nn=1{j 2π

λdn sin θpV∗(m,n)}

∣∣∣ = 1,

∀m ∈ {1, 2, · · · , M} , ∀p ∈ {1, 2, · · · , P} . (3.14)

Therefore, the proposed array transformation affects only the phases of the interpolated

array elements and generates more accurate phases for the interpolated array elements.

The transformation matrix T∗ does not preserve the amplitudes of the original array

elements because∣∣∣BT∗

(m, p)(Θ)∣∣∣ is not always unity. Thus, the interpolation accuracy

derived from the new transform matrix V∗ is higher than that from the conventional

matrix T∗.

3.3.2 Enhanced Received Signal Interpolation

Similar to the received signal interpolation in (3.9), received signals of the inter-

polated array elements with the transformation matrix V∗ are expressed as

zm(t) =N∏n=1

{xn(t)}V∗

(m,n) ∈ Z(t), ∀m ∈ {1, 2, · · · , M}. (3.15)

Using Z(t) = [z1(t), z2(t), · · · , zM (t)], I conduct the DOA estimation and can

achieve improved performance compared to the estimation using Y(t).

29

For a much better DOA estimation, I also consider the power of the received sig-

nals. When I use the interpolated received signal vectors, Y(t) and Z(t), power differ-

ences exist among the interpolated received signals. In other words,

|ym(t)|2 = |ym′(t)|2 and |zm(t)|2 = |zm′(t)|2

(for m 6= m′, m′ ∈ {1, 2, · · · , M}) (3.16)

does not always hold, because

N∑n=1

∣∣T∗(m,n)

∣∣2 6=N∑n=1

∣∣T∗(m′, n)

∣∣2 ,T∗(m,n)T∗(m,n′) 6= T∗(m′, n)T∗(m′, n′) and

N∑n=1

V∗(m,n) 6=N∑n=1

V∗(m′, n)

(for n 6= n′, n′ ∈ {1, 2, · · · , N},

for m 6= m′, m′ ∈ {1, 2, · · · , M}), (3.17)

where · denotes the complex conjugate of a complex number. This power imbal-

ance can cause performance degradation in the DOA estimation [17]. In the proposed

method, the amplitudes of BV∗

(m, p)(Θ) are equivalent for all array elements. However,

it is not directly related to the powers of the interpolated received signals, and power

differences exist among the interpolated received signals. Therefore, to mitigate this

problem, I propose an effective compensation method to formulate the received sig-

nals of each interpolated array element such that they have similar power levels while

maintaining the effect of the proposed phase interpolation method. In other words, the

compensated received signal is given as

wm(t) =

∏n∈N(m)

|xn(t)|

1

|N(m)|

× exp

j ∑n∈N(m)

{V∗(m,n)∠xn(t)

} ∈ W(t), (3.18)

30

where

N(m) = {n∗ | n∗ = argn(V∗(m,n) 6= 0

), n = 1, 2, · · · , N},

∀m ∈ {1, 2, · · · , M} , (3.19)

and∣∣N(m)

∣∣ denotes the cardinality of the set N(m). When comparing wm(t) with

zm(t), the interpolated phase of wm(t) is the same as that of zm(t). Therefore, the

phase interpolation effect from the transformation matrix V∗ is maintained. In addi-

tion, when I use this compensated interpolated received signal, the following equation

is always established as

|wm(t)|2 = |wm′(t)|2 (for m 6= m′, m′ ∈ {1, 2, · · · , M}), (3.20)

because

|wm(t)|2 =

∏n∈N(m)

|xn(t)|

2

|N(m)|

=

|x1(t)| × · · · × |xN (t)|︸︷︷︸|N(m)|

2

|N(m)|

=

|x1(t)|2 × · · · × |xN (t)|2︸︷︷︸|N(m)|

1

|N(m)|

∼= γ, ∀m ∈ {1, 2, · · · , M} . (3.21)

In other words, the powers of the interpolated received signals are nearly equivalent

among the array elements. Thus, if I use the received signal vector W(t) for the DOA

estimation, I can achieve more enhanced performance than when using Y(t) and Z(t).


Many studies have been conducted on the location in which to interpolate array

elements to improve the accuracy of DOA estimation algorithms. In [19] and [21],

31

the authors located the interpolated array elements that minimized interpolation errors

within given conditions. In addition, the array searching method proposed in [25] re-

vealed enhanced DOA estimation accuracy with the interpolated array. However, this

method was deemed too heuristic and time-consuming. In this section, to verify the

DOA estimation accuracy resulting from the proposed interpolation method, I trans-

form the original array elements to the minimum-redundancy linear arrays while main-

taining identical apertures. In general, minimum-redundancy linear arrays show the

maximum resolution for a given number of array elements by minimizing the number

of redundant spacings in the array [28], [29]. Moreover, previous studies have reported

that non-uniform linear arrays perform better at DOA estimation than do uniform lin-

ear arrays that have the same apertures [30], [31]. Therefore, in the simulation, by

transforming the original array to the non-uniform minimum-redundancy linear array,

I analyze the performance improvement in the DOA estimation.

In the simulation, I use four array elements (N = 4) that are widely used in an

automotive long-range radar (LRR). The location of the original array elements is

[d1, d2, d3, d4] = [0, 2λ, 4λ, 6λ]. It is well known that the minimum-redundancy lin-

ear array location of four array elements is [0, 1, 4, 6] [28], [29]. Thus, using the array

transformation matrices, I interpolate array elements in the location [g1, g2, g3, g4] =

[0, 1λ, 4λ, 6λ]. Here, I assume that two targets are located at [θ1, θ2] = [−3.5 ◦, 2.5 ◦]

and adopt the Bartlett method [32] as the DOA estimation algorithm. In addition, the

signal-to-noise ratio (SNR) at the array elements is set to 10 dB, and 1, 000 time sam-

ples are used to construct the correlation matrix used in the Bartlett algorithm. The

FOV is given as Θ = {θp | θp = −10 ◦+ (p− 1)× 0.1 ◦, p = 1, 2, · · · , 201}, which

is equivalent to the FOV of the LRR. Since T∗ and V∗ are calculated and stored only

once when the number of array elements and the FOV are given, the stored values can

be used repeatedly without having to identify another T∗ and V∗.

First, under these simulation conditions, I calculate two types of interpolation er-

32

rors, which are given as

EU =∥∥∥B(Θ)− BU(Θ)

∥∥∥2

F,

EUphase =

∥∥∥∠B(Θ)− ∠BU(Θ)∥∥∥2

F, ∀U ∈ {T∗, V∗}. (3.22)

The smaller the error values are calculated based on (3.22), the more accurate the array

interpolation is conducted. For both transformation matrices, T∗ and V∗, I calculate

the interpolation errors by changing the size of the FOV. The result is given in Fig.

3.1. As the figure shows, the interpolation errors calculated from V∗ are almost close

to 0. In addition, for the FOV of the LRR (i.e., the size of the FOV being 20 ◦), the

errors are given as [ET∗ , EV∗ ] = [1.240, 4.719 × 10−28] and [ET∗phase, E

V∗phase] =

[1.004, 4.700 × 10−28]. Therefore, judging from both types of interpolation errors,

the proposed array transformation matrix BV∗(Θ) is more approximate to B(Θ) than

is BT∗(Θ). In other words, the interpolated array elements are accurately generated

when the proposed interpolation method is employed. For larger FOV sizes, the in-

terpolation errors of the conventional method become larger because the interpolation

matrix is calculated more accurately when the DOA range of the targets is tightly

within the FOV.

Using these transformation matrices, I formulate the received signals and con-

duct the DOA estimation. As shown in Fig. 3.2, with the original received signals, the

10 12 14 16 18 20 22 24

Length of field of view (degree)

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Inte

rpo

latio

n E

rro

r

Interpolation error from T∗

Interpolation error from V∗

Phase interpolation error from T∗

Phase interpolation error from V∗

Figure 3.1: Two types of interpolation errors from T∗ and V∗.

33

-10 -8 -6 -4 -2 0 2 4 6 8 10


0.4

0.5

0.6

0.7

0.8

0.9

1

No

rma

lize

d B

art

lett

pse

ud

osp

ectr

um

Bartlett

Bartlett with T∗ and Y(t)

Bartlett with V∗ and Z(t)

Bartlett with V∗ and W(t)

Figure 3.2: Normalized Bartlett pseudospectrums for two adjacent targets located at

[−3.5 ◦, 2.5 ◦].

Bartlett method cannot resolve the two targets, and the estimated DOA is −0.1◦. In

general, when I use four array elements with 2λ spacing, the half-power beamwidth

becomes 6.5◦. Therefore, the difficulty to distinguish those given DOAs is reasonable.

Even with the interpolated received signals from T∗, two different DOAs are not es-

timated, and the estimated DOA is 1.2 ◦, which is not the exact value. However, with

the interpolated received signals from V∗, the Bartlett method shows enhanced angular

resolution, and I can find two different DOAs such as [−2.8 ◦, 2.0 ◦]. Moreover, when

using the interpolated received signal vector with the power calibration, W(t), the best

estimation result is achieved, and the estimated DOA values are [−3.1 ◦, 2.2 ◦], which

are close to the actual DOA values.

For the statistical performance evaluation, I calculate the resolution probability

Pr for the conventional Bartlett algorithm and the Bartlett with array interpolation

methods. This probability is defined as

Pr =Nr

Nt× 100 (%), (3.23)

where Nr indicates the number of times that two distinct DOAs are extracted from

the received signals, and Nt denotes the number of simulations. Since I conduct this

simulation 1, 000 times under the same conditions, Nt becomes 1, 000. In addition, I

34

calculate the root mean square error (RMSE) defined as

RMSE =

√√√√√∑Kk=1

∑Ntq=1

{(θk − θ

(q)k

)2}

Nt(◦), (3.24)

where θ(q)k is the estimated value of θk (k = 1, 2) in the qth (q = 1, 2 · · · , Nt) sim-

ulation. When the number of the estimated target is one, I use it as θ(q)k . The results

are shown in Table 3.1. Considering the resolution probability and the RMSE, the pro-

posed method performs better than the conventional Bartlett and the Bartlett with the

transformation matrix T∗. In addition, while maintaining the simulation conditions,

except the array SNR values, I calculate the resolution probability and the RMSE. As

Fig. 3.3 shows, the proposed method yields good estimation results despite the differ-

Table 3.1: Resolution probabilities and root mean square errors for two adjacent targets

located at [−3.5 ◦, 2.5 ◦]

DOA estimation method Pr (%) RMSE (◦)

Conventional Bartlett 0 4.28

Bartlett with T∗ and Y(t) 74.9 2.67

Bartlett with V∗ and Z(t) 99.4 0.64

Bartlett with V∗ and W(t) 99.9 0.45

0 1 2 3 4 5 6 7 8 9 10

SNR (dB)

0

10

20

30

40

50

60

70

80

90

100

Resolu

tion p

robabili

ty (

%)

Bartlett




0 1 2 3 4 5 6 7 8 9 10

SNR (dB)

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Root m

ean s

quare

err

or

(deg)

Bartlett




Figure 3.3: Resolution probabilities and root mean square errors versus SNR (N = 4).

35

ent array SNR values. Moreover, after changing the number of time samples used to

build the correlation matrix, a performance comparison among the interpolation meth-

ods is conducted, and the results of which are given in Fig. 3.4. Even though only a few

time samples are used, the proposed array transformation shows improved estimation

performance.

I also conduct a simulation for a case in which three targets exist in the FOV of

the radar. The simulation is conducted while maintaining the same simulation condi-

tions given in Fig. 3.1, except for the target information, and the result is shown in Fig.

3.5. Here, the targets are located at [θ1, θ2, θ3] = [−8 ◦, 1.5 ◦, 7.5 ◦]. The conven-

tional Bartlett and the Bartlett with the transformation matrix T∗ each estimate only

two DOAs: [−8.4 ◦, 3.2 ◦] and [−8.6 ◦, 2.7 ◦], respectively. Thus, these methods fail to

resolve the targets placed at [θ2, θ3] = [1.5 ◦, 7.5 ◦]. However, when applying the pro-

posed transformation matrix, I can identify the three different DOAs. Moreover, from

the power calibrated interpolated received signal vector W(t), the estimated DOAs are

calculated as [−8.6 ◦, 1.8 ◦, 8.8 ◦], which are the most exact estimated values. I also

compare the performance of the proposed method to that of the multiple signal classifi-

cation (MUSIC) algorithm, which is known as a high-resolution DOA estimation algo-

rithm [6]. To apply the MUSIC algorithm, the number of targets must be estimated in

200 300 400 500 600 700 800 900 1000

The number of time samples

0

10

20

30

40

50

60

70

80

90

100

Resolu

tion p

robabili

ty (

%)

Bartlett




200 300 400 500 600 700 800 900 1000

The number of time samples

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Root m

ean s

quare

err

or

(deg)

Bartlett




Figure 3.4: Resolution probabilities and root mean square errors versus the number of

time samples (SNR is 10 dB).

36

-10 -8 -6 -4 -2 0 2 4 6 8 10


0

0.5

1

1.5

No

rma

lize

d p

se

ud

osp

ectr

um

Bartlett




MUSIC (K = 1)

MUSIC (K = 2)

MUSIC (K = 3)

Figure 3.5: Normalized pseudospectrums for three targets located at

[−8 ◦, 1.5 ◦, 7.5 ◦].

advance using Akaike information criterion or minimum description length [33], [34].

If the number of targets is well estimated (K = 3), the most exact performance occurs.

However, if the number is not accurately estimated (e.g., K = 1 or K = 2), the es-

timation performance deteriorates considerably, and it cannot be used as shown in the

Fig. 3.5. In addition, since the MUSIC algorithm performs the eigenvalue decomposi-

tion and the multiplication of matrices spanned by the noise eigenvectors, additional

computational complexity O(N3 +N2 × (2N − 2L− 1)

)occurs compared to the

conventional beamforming algorithm (i.e., the Bartlett method) [18], [35]. Moreover,

the Bartlett method is more robust to noise variance than the MUSIC algorithm [32].

Thus, for automotive radars, the Bartlett algorithm may be more appropriate for stably

estimating the DOA of a target under noisy road environments.

Furthermore, simulations are conducted not only for the four array elements but

also for three and five array elements. When the number of array elements is three, the

original location of the array elements is given as [d1, d2, d3] = [0, 1.5λ, 3λ]. This ar-

ray is transformed to the minimum-redundancy array, and interpolated array elements

are located at [g1, g2, g3] = [0, 1λ, 3λ] [28], [29]. In addition, I assume that targets

are located at [θ1, θ2] = [−4 ◦, 6.5 ◦] and that the FOV ranges from −15 ◦ to 15 ◦.

Since the half-power beamwidth for the given array is 12 ◦, the array has a very low

37

angular resolution and the given DOAs are difficult to be distinguished from the con-

ventional Bartlett algorithm. In addition, for the five array elements, the location of the

original array elements is given as [d1, d2, d3, d4, d5] = [0, 2.25λ, 4.5λ, 6.75λ, 9λ],

and it is transformed to the location [g1, g2, g3, g4, g5] = [0, 1λ, 4λ, 7λ, 9λ] [28].

For this case, the FOV is equal to that of the LRR, and targets are placed at [θ1, θ2] =

[−1 ◦, 3 ◦]. These DOAs are hard to be separated out using the conventional Bartlett

because the half-power beamwidth for the given array is 4.5 ◦. For both cases of three

and five array elements, the resolution probability and the RMSE are given in Figs. 3.6

and 3.7 by increasing the array SNR from 0 dB to 10 dB. As shown in the figures, the

method also performs better for cases in which the number of array elements are three

0 1 2 3 4 5 6 7 8 9 10

SNR (dB)

0

10

20

30

40

50

60

70

80

90

100

Resolu

tion p

robabili

ty (

%)

Bartlett




0 1 2 3 4 5 6 7 8 9 10

SNR (dB)

0

0.5

1

1.5

2

2.5

3

Root m

ean s

quare

err

or

(deg)

Bartlett





0 1 2 3 4 5 6 7 8 9 10

SNR (dB)

0

10

20

30

40

50

60

70

80

90

100

Resolu

tion p

robabili

ty (

%)

Bartlett




0 1 2 3 4 5 6 7 8 9 10

SNR (dB)

3.5

4

4.5

5

5.5

6

6.5

7

7.5

8

Root m

ean s

quare

err

or

(deg)


38

and five.


To verify the performance of the proposed method, I also conduct actual measure-

ments on a testing ground of the Mando Corporation using its automotive LRR. In the

measurement, a single-element transmit antenna and four-element receiving uniform

linear array antenna (N = 4) are used, and the spacing between adjacent elements is

1.8λ. In addition, the half-power beamwidth of the array antenna is 7 ◦, and the FOV

of the LRR ranges from −10 ◦ to 10 ◦. This antenna system is equipped with an auto-

motive radar and transmits a 76.5 GHz frequency-modulated continuous wave signal.

The transmitted signal is reflected from the front targets, and then the reflected signals

are received by the array antenna.

Fig. 3.8 shows the measurement environment. Two identical target vehicles are lo-

cated at [θ1, θ2] = [−1.7 ◦, 4.6 ◦] and are 40 m away from a radar-equipped vehicle. In

this measurement, I also use the Bartlett algorithm for the DOA estimation method, and

calculate the resolution probability and the RMSE for the original received signals and

the interpolated received signals derived from the array interpolation methods. Under

the same measurement environment, I record 600 radar scans. Thus, Nt in (3.23) and

Figure 3.8: Measurement environment of two target vehicles located at [−1.7 ◦, 4.6 ◦].

39

(3.24) becomes 600 in this case. The results are listed in Table 3.2. Similar to the simu-

lation results, based on both measures, the DOA estimation with the proposed transfor-

mation matrix V∗ shows better angular resolution and estimation accuracy than that

of the conventional Bartlett and Bartlett method with the transformation matrix T∗.

Furthermore, the estimation with W(t) shows the most improved resolution and es-

timation performance; thus, the performance of the proposed interpolation method is

also verified through actual experimental data.

3.6 Conclusion

In this chapter, I proposed a logarithmic-domain transformation matrix used for

array interpolation to improve the accuracy of DOA estimation. The transformation

matrix was obtained by minimizing the differences between the phases of the original

array elements and the interpolated array elements. The proposed method identified a

more accurate transformation matrix with less phase distortion, and the amplitudes of

the array elements were maintained after the transformation. In addition, to improve

the accuracy of the DOA estimation algorithm, I proposed a method for adjusting

the powers of the interpolated received signals to a similar level. Finally, from the

simulation and the measurement results, I verified that the new method showed much

better angular resolution and estimation accuracy than did the DOA estimation using

Table 3.2: Resolution probabilities and root mean square errors for two target vehicles

located at [−1.7 ◦, 4.6 ◦]

DOA estimation method Pr (%) RMSE (◦)

Conventional Bartlett 0 5.72

Bartlett with T∗ and Y(t) 0.67 6.20

Bartlett with V∗ and Z(t) 46.7 4.65

Bartlett with V∗ and W(t) 68.0 3.90

40

the conventional transformation matrix derived from the LLS method.

41

Chapter 4

TARGET CLASSIFICATION USING FEATURE-BASED

SUPPORT VECTOR MACHINE

4.1 Introduction

To prevent and reduce accidents caused by automobiles, automotive sensors (e.g.,

sonar, vision, lidar, and radar systems) can be utilized. In particular, for the safety of

pedestrians, it becomes essential to detect pedestrians by using the automotive sen-

sors. These days, many studies on pedestrian recognition using vision sensors (e.g.,

cameras) have been conducted [36], [37]. The detection performance of the vision

sensors, however, rapidly degrades in low light conditions or bad weather. Thus, the

pedestrian recognition through radar sensors, which is more robust to environmen-

tal conditions, has proceeded together with other automotive sensors. If I can detect

pedestrians perfectly by using an automotive radar system, this is helpful for drivers

to prevent accidents. In this context, studies on classifying types of detected objects

through radar systems have to be conducted.

Above all, since commercialized automotive radars usually use frequency modu-

lated continuous waves (FMCW) operated in the 76-81 GHz band, target classification

using this type of radar is the most significant issue. However, studies of target classi-

42

fication with a 77-GHz FMCW radar system have not been intensively conducted. For

example, a study on the parameter estimation of the human gait using an FMCW radar

was conducted in [38]. In [39], using a 35-GHz FMCW radar system, measurement re-

sults for micro-Doppler features of human subjects were suggested. In addition, based

on measured micro-Doppler features, classification results for humans, dogs, and ve-

hicles in the 24-GHz frequency band using a support vector machine (SVM) and a

k-nearest neighbor classifier was given in [40]. However, because the classification in

[40] utilizes the total shape of the micro-Doppler, it has a high computational load, and

real-time target classification may not be available. Moreover, although magnitudes

and shapes of micro-Doppler returns depend on the types of the targets, they also have

considerable variations in a single species [41], and they do not appear prominently

in the 77-GHz frequency band. Recently, an FMCW radar that can detect human mo-

tions was proposed in [42]; however, it operates at 14.8 GHz which is not adequate for

the automotive radar systems. Thus, more fast and robust classification methods for

detected targets have to be suggested for 77-GHz FMCW radar systems.

Therefore, in this chapter, I suggest using a concept of radar cross section (RCS)

to classify human subjects and vehicles. Because the RCS is an unique feature that

reflects the inherent characteristics of targets, it can be used as a representative target

classification criterion. Some research using the RCS as the target classification crite-

rion was reported [43]. In [43], RCS-based target classification with a pulse-Doppler

ground surveillance radar system was conducted. To classify targets based on RCS

values with a 77-GHz FMCW radar, I first estimate those of the targets. Some research

has been conducted to measure the RCS values of pedestrians and vehicles in the 76-

81 GHz band [44]-[51]. However, the RCS measurements in [44]-[50] were conducted

without using FMCW radar signals. Although the RCS measurement for pedestrians

using a 76-GHz FMCW signal was given in [51], the measurement method for the

RCS was not directly addressed, and the RCS was simply replaced by the radio wave

reflection intensity. Since there are no exact references to the RCS measurement in the

43

FMCW radar system, to use the RCS as the classification standard, an RCS estimation

method with the FMCW radar has to be established. Thus, I propose a concise RCS

estimation method for a 77-GHz FMCW radar system in this chapter. Due to the high

operating frequency and the frequency modulation scheme, I cannot directly calculate

the conventional RCS in the time domain. For a 77-GHz signal sampling, a 154-GHz

sampler is required by the Nyquist sampling theorem. However, it cannot be realized

in practical automotive radar systems. Thus, it is effective to calculate the RCS indi-

rectly from the baseband signal in the frequency domain. Using the baseband signal,

I define a new parameter called root radar cross section (RRCS). It is based on the

conventional RCS, and reflects the reflection characteristics of targets. To define this

parameter, I adopt the properties of an frequency-domain FMCW radar signal. The

advantages of using the proposed parameter are that it includes the concept of RCS

and can be calculated immediately from the received FMCW radar signal.

Finally, using RRCS, a human-vehicle classification is conducted. In addition to

RRCS, some unique classification standards are established based on the proposed pa-

rameter. Then, as a classifier, I use an SVM which is a popular and simple machine

learning algorithm and is broadly used for target classification in radar signal process-

ing [40], [41], [52]. Based on the suggested standards, measured data is trained by

the SVM. For a more accurate and efficient validation of the data set, I use a fourfold

cross-validation method. In other words, 75 % of the total data sets are used to train

the data, and the remaining data set is used as the validation set. This is conducted

four times for four different validation sets, and an average classification accuracy is

calculated. From measurement scenarios in a test field, the classification accuracy is

higher than 90 %. The strong point of the proposed method is that real-time target

classification is available. After the target features are trained by the SVM, a clas-

sification function is determined. Then, when a new signal is received at the radar,

the features are extracted, and the received signal is classified by the predetermined

classification function in every scan (i.e., one transmission cycle of the FMCW radar

44

signal). Therefore, contrary to the classification methods that use entire signal shapes

in the time-frequency domain [40], [52], the proposed method is highly efficient and

has low computational complexity.

The remainder of this chapter is organized as follows. In Section 4.2, the defini-

tion of the RRCS is given in this section. Then, data measurement using the auto-

motive FMCW radar is introduced in Section 4.3. Next, based on the measured data,

some unique classification standards including the RRCS are introduced in Section 4.4.

Then, in Section 4.5, human-vehicle classification results using feature-based SVM is

provided. In addition, the proposed method is applied to a more practical situation,

and the classification results are given in Section 4.6. Finally, conclusion is presented

in Section 4.7.

4.2 Introduction of Root Radar Cross Section (RRCS)

The conventional RCS definition in [53] is given as

σ = 4πR2 × PsPi

[m2], (4.1)

wherePi [W/m2] is the time-average incident power density at the target, andPs [W/m2]

is the backscattered power density at the radar site. In addition, supposing an energy is

emitted by an isotropic radiator, (4.1) can be rewritten as

σ = 4πR2 × PrAe× (

PtGt4πR2

)−1

= KA ×R4 × PrPt

[m2], (4.2)

where Pt [W ] and Pr [W ] are the transmitted and the received powers, respectively,

Ae [m2] is the effective antenna aperture, and Gt is the antenna gain. In addition, KA

is the term that includes Ae and Gt. Based on this equation, to estimate the RCS, I

have to find out Pr. However, due to the properties of the high frequency band and the

frequency modulation technique that I use, it is difficult to directly calculate Pr in the

45

time domain. Therefore, I estimate Pr in the frequency domain using the properties of

the frequency-domain FMCW radar signal.

Desired Signal in Frequency Domain

The signal T (t)d(t) corresponds to the beat signal in the frequency domain. Its

low-pass filter output can be expressed as

Ld(t) = LPF (T (t)d(t))

∼=1

2ATAR cos(2π(fc −

∆B

2)td − πt2d

∆B

∆T

+ 2πtd∆B

∆Tt) (0.1∆T ≤ t ≤ 0.4∆T ), (4.3)

where LPF (·) denotes the output of the filter. Here, only the received signal in the

range of 0.1∆T ≤ t ≤ 0.4∆T is considered. Then, the continuous-time Fourier trans-

form (CTFT) of Ld(t) is calculated as

Fd(ω) =1

2ATARπe

−j(2π(fc−∆B2

)td−π∆B∆T

t2d)

× e−j(ω+2πtd∆B∆T

)( 0.5∆T2

) ×2 sin((ω + 2πtd

∆B∆T )(0.3∆T

2 ))

ω + 2πtd∆B∆T

+1

2ATARπe

j(2π(fc−∆B2

)td−π∆B∆T

t2d)

× e−j(ω−2πtd∆B∆T

)( 0.5∆T2

) ×2 sin((ω − 2πtd

∆B∆T )(0.3∆T

2 ))

ω − 2πtd∆B∆T

(−ωcut ≤ ω ≤ ωcut), (4.4)

where ωcut is the cut-off frequency of the low-pass filter. Although the magnitude

of the first term affects that of the second term, and vice versa, their influences are

sufficiently small and can be ignored. For example, if the target is only 5 m away from

the radar-equipped vehicle (i.e., R = 5), the two terms have little influence on each

other. Moreover, asR increases, the interference between them decreases considerably.

Therefore, the maximum value of |Fd(ω)| is almost the same as the maxima of each

term, and the value is 12 |AT | |AR|π(0.3∆T ) which appears at ω = ∓2πtd

∆B∆T = ωb.

46

This is known as the beat frequency. Thus, the peak value of the beat signal includes

the amplitude information of the received signal AR.

Noise Floor in Frequency Domain

In the frequency domain, T (t)n(t) constitutes the noise floor. Its low-pass filter

output is given as

Ln(t) = LPF (T (t)n(t))

= LPF (AT cos(2π(fc −∆B

2)t+ π

∆B

∆Tt2)n(t))

(0.1∆T ≤ t ≤ 0.4∆T ). (4.5)

Since n(t) is assumed to be the white Gaussian noise, Ln(t) has some low values in

the frequency range of −ωcut ≤ ω ≤ ωcut. In addition, since the CTFT of Ln(t) (i.e.,

Fn(ω)) is difficult to simplify in a closed-form expression, it is calculated by numerical

integration.

Definition of RRCS

Based on the conventional RCS definition, I define the RRCS with the ampli-

tudes of the transmitted and the received signals. Since, Pr/Pt is proportional to

|AR|2/|AT |2, the RCS in (4.2) can be rewritten as

σ = KA ×R4 × |AR|2

|AT |2[m2]. (4.6)

Therefore, the root of the RCS, γR, is defined as

γR =

√σ

KA

= R2 × |AR||AT |

= R2 × 2

|AT |2π(0.3∆T )× |Fd(ωb)| . (4.7)

Thus, since the RRCS is defined by using the frequency-domain received signal, I can

directly extract the reflection characteristics of targets (in (4.7),AT and ∆T are already

47

known and fixed in the FMCW radar system). Generally, the RCS is the parameter

that does not depend on the distance. Thus, also for the γR, I compensate the path loss

caused by the distance between the radar and the target by multiplying R2. In other

words, a reflected signal from a distant target has smaller AR than that of a reflected

signal from the same target located close to the radar. Therefore, to calibrate the effect

of the distance and compensate the signal power loss, a 20 dB/dec gain is applied

on the analog-digital converter (ADC). Through this process, the magnitudes of the

received signals for the same target are maintained regardless of the distance, and it

also gives almost equivalent RRCS values. With the radar hardware, applying R1.8

(18 dB/dec) gives more exact RRCS values based on the measurement in practical

roads. The main purpose of defining this parameter is to use it as a target classification

standard. Therefore, although it has the root form of the conventional RCS, it can be

utilized because it sufficiently indicates the reflection characteristics of targets.

From the received signal, however, it is impossible to extract the exact desired beat

signal. Instead, I have the received signal containing the noise floor, which is expressed

as

G(ω) = Fd(ω) + Fn(ω). (4.8)

Therefore, |G(ω)| is composed of a pair of sinc functions and the noise floor over

−ωcut ≤ ω ≤ ωcut. For this case, the RRCS is defined as

γR ∼= R2 × 2

|AT |2π(0.3∆T )× |G(ωb)|. (4.9)

Although the noise floor is included in |G(ωb)|, its magnitude is much lower than the

magnitude of the beat signal in the frequency domain (i.e., |Fd(ωb)| � |Fn(ωb)|).

Therefore, using |G(ωb)| instead of |Fd(ωb)| is acceptable when defining the RRCS

parameter.

In practical FMCW radar systems, the fast Fourier transform (FFT) is used instead

of the CTFT because of storage space and computational load. Thus, if the FFT output

48

is denoted as H[n], the RRCS is redefined in the FFT domain, which is given as

γR ∼= R2 ×KF × |H[nb]|, (4.10)

where KF is the scaling factor, and nb is the FFT index corresponding to the beat

signal. Therefore, using γR, I can immediately estimate the reflection characteristics of

targets from received signals in the practical automotive FMCW radar system without

demanding high computational complexity.

4.3 Data Measurement with FMCW Radar

In this section, actual measurement with an automotive FMCW radar is intro-

duced. In addition, with the measured received signal, I calculate the RRCS of targets.

Through the measurement, I verify that the proposed parameter can be used as a crucial

criterion for the target classification.

4.3.1 Measurement Campaign

The measurement is conducted on a testing ground of the Mando Corporation using

its automotive long-range radar (LRR). In the measurement, a single-element transmit

antenna and four-element receiving uniform linear array antenna are used, and the

spacing between adjacent elements in the receiving antenna is 1.8λ. In addition, the

half-power beamwidth of the array antenna is 7 ◦, and the field of view (FOV) of the

LRR ranges from −10 ◦ to 10 ◦. This antenna system is equipped with an automotive

radar, and transmits a frequency modulated continuous wave (FMCW) signal. The

transmitted signal is reflected from targets, and then reflected signals are received by

the array antenna. A block diagram for operation principle of the FMCW radar sensor

is given in Fig. 4.1. This radar sensor is mounted in the front bumper of the vehicle.

In the measurement, fc, ∆B, and ∆T are given as 76.5 GHz, 500 MHz, and 5 ms,

respectively. In addition, the sampling frequency fs is set to approximately 360 kHz,

and the number of the FFT point used is 2048. Moreover, one transmission period of

49

Figure 4.1: A block diagram for operation principle of an FMCW radar sensor.

the FMCW radar signal is 100 ms, which consists of a 10-ms transmission interval and

a 90-ms signal processing duration.

First, to understand the reflection characteristics of each target, the experiment is

conducted with the simplest scenario. I receive radar signals reflected from human

subjects and vehicles with the automotive FMCW radar system. In the measurement,

data for four human subjects (the body sizes of each subject are shown in Table 4.1)

and four different types of vehicles is collected. In addition, the radar signals reflected

from each target are recorded under line-of-sight (LOS) conditions. To obtain at least

1000 samples in each measurement, the data is measured during 100 s (i.e., 100 ms

(one transmission cycle) × 1000 = 100 s).

Table 4.1: Body sizes of four human subjects

Subject 1 Subject 2 Subject 3 Subject 4

Height (cm) 182 173 168 185

Weight (kg) 82 93 62 90

50

When a target is in the FOV of the radar, various aspects of the target can be

viewed from the radar. With the human subjects, I measure received signals with two

different postures for each person to check the angle dependency of the RRCS. At first,

the subject stands toward the radar, and then stands laterally to it (i.e., the left or the

right side of the subject is viewed from the radar). For the case when the subject faces

the radar, the RRCS value is large because the cross-sectional area viewed from the

radar is the widest. In the latter case, however, the RRCS is small due to the narrowest

cross-sectional area. Finally, similar to the case of the human subjects, measurements

are also performed for the four different types of vehicles. Using these measured data,

the characteristics of the reflected radar signals is analyzed.

Next, I measure the data for moving humans and vehicles. In this measurement,

I consider a variety of cases where the human subject and the vehicle exist together

and move in several directions in the FOV of the radar, as shown in Fig. 4.2. For this

measurement scenario, I collect two thousand samples of received signals, and, based

on these measured data, the proposed human-vehicle classification will be conducted

with the SVM, and its performance will be verified.

Figure 4.2: A measurement scenario used for a human-vehicle classification: a con-

ceptual illustration and an actual photograph.

51

4.3.2 Statistical Characteristics of RRCS

In this section, I examine whether the new parameter can be adequately used for

the target classification. Based on (4.10), I calculate the RRCS for the human subjects

and the vehicles, and identify their distributions. As an example, I find the RRCS

distributions for the targets located 15 m away from the radar-equipped vehicle (i.e.,

R = 15). For this case, distributions of the RRCS values from the human subjects

with the two different postures are depicted in Fig. 4.3. Regardless of the postures,

they have almost similar distributions, and there is little difference in the shape and the

scale. Within the measured data, the angle dependency of the RRCS is not noticeable.

In addition, I also find the RRCS distribution for the vehicles, which is also plotted

in Fig. 4.3. For the simplest measurement scenario (i.e., when the back sides of the

vehicles are viewed from the radar), the RRCS values of the two types of targets are

well separated, as depicted in the figure. In the case of the vehicles, since the rear sides

of the vehicles consist of metal components, the intensity of the reflected signal tends

to be stronger than the case of the human subjects. This results in differences between

the RRCS distributions of the targets. Therefore, I can use the RRCS as one of the

human-vehicle classification criteria.

0 2 4 6 8 10 12

Magnitude of RRCS ×108

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Pro

ba

bili

ty (

%)

×10-8

The 1st posture (human subjects)

The 2nd posture (human subjects)

The back side (vehicles)

Figure 4.3: RRCS distributions for human subjects and vehicles (R = 15).

52

4.4 Feature Extraction Based on RRCS

Now, from the measured data, I extract some distinctive target features including

the RRCS. When using the RRCS parameter only, is it difficult to classify the human

subjects and the vehicles perfectly in practical situations. In addition, the RCS values

of vehicles were measured to be smaller than those of human subjects in low-RCS ori-

entation angle cases [54]. Therefore, I also use other signal characteristics derived from

γR as the classification standards. Since the other classification criteria are established

based on RRCS, it is more effective to use RRCS, not the conventional RCS. The de-

tailed criteria used in the human-vehicle classification are introduced in the following

sections.

4.4.1 Magnitude of RRCS

First, I use the magnitude of γR. For example, the accumulated FFT results for a

moving human and a moving vehicle during 20 s is shown in Fig. 4.4. In this figure, the

X-axis, Y-axis, and Z-axis indicate the time, FFT index, and magnitude of FFT result,

respectively. Since the FFT index can be replaced with the distance in the FMCW radar

system, the Y-axis implies the relative distance from the radar-equipped vehicle. In the

figure, the human subject moves away from the radar-equipped vehicle from 0 s to 11

s, and then comes toward the radar from 12 s to 20 s. On the other hand, the vehicle

comes toward the radar from 4 s to 14 s, and moves far away from it from 17 s to 20 s.

In this measurement case, RRCS for each time sample is defined as

γ(i)R = KF ×

∣∣∣H(i)[n(i)b ]∣∣∣ , (4.11)

where i indicates the time sample number, and n(i)b denotes the beat frequency index

for the target in the ith time sample. The FFT result denoted as H(i)[n] is the distance-

calibrated FFT result, which means received signal power loss is compensated. As

shown in Fig. 4.4, the magnitudes of RRCS values of the human subject are smaller

than those of the vehicle. In other words, γR of the human subject usually has a lower

53

Figure 4.4: Accumulated FFT results for a human subject (upper) and a vehicle

(lower).

value than γR of the vehicle. From the measured data, γR of the vehicle is an average

15 times larger than that of the human subject. Therefore, it can be used as a major

criterion for the target classification.

4.4.2 Moving Pattern along RRCS

In addition to the magnitude of RRCS, another feature can be extracted from the

moving pattern along γR. The accumulated FFT results from a bird’s-eye view are

also given in Fig. 4.4. As shown in the figure, the moving curve of the vehicle along

γR has a smooth pattern; however, it has a rough pattern for the human subject. Due

to the nonuniform shape of the human body and the movement of its arms and legs,

slight micro-Doppler effect can occur for the human case. On the other hand, for the

54

vehicle, strong received signals reflected from the back of the vehicle exist. Therefore,

the moving curves have considerably different appearances from each other, and this

is also well exposed in instantaneous FFT results. In Fig. 4.5, the instantaneous FFT

results for the human subject and the vehicle are given. In the figure, values laid on

both sides of γR (γR is marked as a square) show different appearances for the two

cases. In other words, for the vehicle, the values around γR are considerably lower

than γR, but they are not in the case of the human. This means that deviations around

γR are different for the two cases. Therefore, based on this point, I define an additional

parameter for the classification criterion, which is expressed as

d(i) =1

Np

n(i)b +

Np−1

2∑n=n

(i)b −

NP−1

2

KF2∣∣∣H(i)[n]

∣∣∣2

−

1

Np

n(i)b +

Np−1

2∑n=n

(i)b −

NP−1

2

KF

∣∣∣H(i)[n]∣∣∣

2

, (4.12)

where Np is the number of points used to calculate the deviation. Here, I use three

points (i.e., Np = 3) to compute d(i). If more points are used, the target classification

performance can be degraded because the difference between the parameter values

of the human subjects and the vehicles is reduced. When calculating d(i) from the

measured data, d(i) of the vehicle has a value that is approximately 18 times higher

Figure 4.5: Instantaneous FFT results for a human subject and a vehicle.

55

than that of the human subject. Thus, this parameter also can be used as an important

criterion.

4.4.3 Slopes around RRCS

From the instantaneous FFT results, another classification criterion can be ex-

tracted. As a measure of the dispersion of the RRCS, I use slopes around γR. As

mentioned previously, the values on both sides of γR have extremely small values in

comparison with γR. Therefore, I use the multiplication of slopes around γR, which

can be defined as

s(i) =KF

∣∣∣H(i)[n(i)b ]∣∣∣−KF

∣∣∣H(i)[n(i)b − 1]

∣∣∣n

(i)b − (n

(i)b − 1)

×KF

∣∣∣H(i)[n(i)b ]∣∣∣−KF

∣∣∣H(i)[n(i)b + 1]

∣∣∣(n

(i)b + 1)− n(i)

b

. (4.13)

Although this measure also has similar properties to d(i), I use this parameter as the

classification standard for a more accurate target classification. Moreover, since d(i)

and s(i) are using the FFT results around γ(i)R , it can be calculated immediately after

identifying RRCS of the targets.

4.4.4 Extracted-Feature Space

With the data measured in various situations (i.e., the human subjects and the vehi-

cles are moving together in several directions in the FOV of the radar-equipped vehicle,

as depicted in Fig. 4.2), the suggested three features are extracted for each target from

the received radar signals. Using those three parameters, I calculate their mean values

within the measured data for the human subjects and the vehicles as given in Table 4.2.

Noticeable differences exist in the mean values; however, their distributions can have

overlapped regions. For example, from the measured data, three-dimensional spatial

distribution with the suggested features are plotted in Fig. 4.6. In the figure, each point

indicates (γ(i)R , d(i), s(i)) for the specific target. As depicted in the figure, an overlapped

56

Table 4.2: Mean values of three extracted featuresClass / Feature γ

(i)R d(i) s(i)

Human subject 8.38× 107 3.22× 107 3.51× 1015

Vehicle 1.24× 109 5.88× 108 7.13× 1017

0

0 2.5

2

1 2

4

Th

e 3

rd f

ea

ture

×1018

2 1.5

The 1st feature

×109

×109

The 2nd feature

6

3 1

8

4 0.5

5 0

Human

Vehicle

Figure 4.6: Three-dimensional spatial distribution of three features for human subjects

and vehicles.

area in the feature space appears. Therefore, a more advanced and effective classifica-

tion method is required. As an enhanced classification technique, I apply a support

vector classifier based on the extracted features, which is known as one of the simplest

machine learning algorithms.

4.5 Human-Vehicle Classification Using SVM

4.5.1 Training and Validation of Data

I apply the SVM to classify the human subjects and the vehicles based on the

suggested features derived from γR. The SVM is a bisection method that determines

the best classifier, which divides the given data into two different groups [55]. The

first suggested SVM used a linear classifier; however, an application of the SVM can

be expanded to solve nonlinear classification problems. For example, by using slack

57

variables or kernel functions, the SVM can be properly applied to those cases [55].

With the kernel technique, the data is transformed to high-dimensional space, and the

given data can be classified by a linear classifier in the transformed domain. In this

section, I utilize the SVM to train and validate the measured data, and I use a Gaussian

kernel function to construct a more effective classifier. With the SVM method, I can

establish an appropriate classification boundary with given features.

For the target classification using the SVM, I use a fourfold cross data validation.

Based on the measured data, I divide the data into four different partitions. First, three-

quarters of the four partitions are used to train the data (i.e., 75 % of the total data is

used to make a classification function), and the remaining partition is used to validate

the data. With the constructed classifier, the target classification is conducted four times

for four different test sets, and errors that occur in each classification are averaged.

4.5.2 Classification Results

Finally, a confusion matrix is derived from the SVM, and is shown in Table 4.3. In

the matrix, the horizontal axis indicates the actual type of the targets, and the vertical

axis indicates the estimated type of the targets. As given in the table, target classifica-

tion is conducted effectively with the suggested features, and the average classification

accuracy is found to be higher than 90 %. To improve the classification accuracy,

proper kernel functions rather than the Gaussian kernel need to be searched within the

computational complexity of the radar hardware can afford. In addition, to enhance the

classification performance, I can use several samples together. By tracking a target for

a specific time and using collected samples in that time, the classification performance

Table 4.3: Confusion matrix resulting from SVM

Estimated class / Actual class Human subject Vehicle

Human subject 94.7 % 6.4 %

Vehicle 5.3 % 93.6 %

58

can be stabilized. In other words, even though the target is mistakenly classified in one

sample, it can be corrected by using classification results from neighboring samples.

Moreover, misclassification which can be caused by the low-RCS orientation angles

in [54], [56] can be also mitigated by using multiple samples.

In addition, to determine the most crucial classification criterion among the three

parameters, I apply the SVM with each feature respectively. In other words, the target

classification is conducted based on only one of the features without using the rest of

the features. The accuracy of the classification is given in Table 4.4. As shown in the

table, γ(i)R is the most significant feature, and the average classification accuracy with

only γ(i)R is almost 89 %. In addition, while increasing the number of the features based

on the classification accuracy, I conduct the classification again, and the following clas-

sification accuracy is given in Table 4.5. With only two important parameters (i.e., γ(i)R

and d(i)), the accuracy is higher than 90 %. Thus, if a reduction in the computational

load is required, a classification using only two features can be acceptable. However,

for complex road situations, the classification performance using a small number of

features may be degraded.

Table 4.4: Classification accuracy for each feature

Accuracy / Feature γ(i)R d(i) s(i)

Accuracy (Human-Human) 89.7 % 88.7 % 88.1 %

Accuracy (Vehicle-Vehicle) 88.9 % 88.6 % 84.2 %

Average accuracy 89.3 % 88.65 % 86.15 %

Table 4.5: Average classification accuracy as increasing the number of features

Accuracy / Feature γ(i)R γ

(i)R , d(i) γ

(i)R , d(i), s(i)

Average accuracy 89.3 % 92.2 % 94.2 %

59

4.5.3 Real-Time Target Classification

For automobiles, the target classification must be conducted in real-time. Assum-

ing that the SVM with a linear classifier is used, the classification function can be

expressed as

f(~x) =1

s× ~x · ~β + b, (4.14)

where ~x is the feature vector, s is the scale parameter, ~β is the coefficient vector, and b

is the bias parameter. When I train the data with the SVM, s, ~β, and b are computed,

and then f(~x) is determined. For real-time signal processing, I must first determine the

suggested parameters using a significant amount of actual measurements.

Since I use the three classification features, ~x becomes [x1, x2, x3], and feature

spaces for the human subjects and the vehicles are divided by f(~x) = (1/s)×(β1x1 +

β2x2 + β3x3) + b = 0. If the feature vector extracted from the i-th measurement is

denoted as ~x(i), to know where this feature can be included, I must figure out the value

of the classification function (i.e., f(~x(i))). Due to the low probability of f(~x(i)) = 0,

the feature vector usually satisfies f(~x(i)) > 0 or f(~x(i)) < 0. In other words, if the

domain of f(~x(i)) > 0 is predetermined as the feature space of the human subjects

by the SVM, the target is classified as a human subject when satisfying f(~x(i)) > 0.

Otherwise, it can be estimated as a vehicle. Therefore, in the method, with the in-

stantly received radar signal, the automotive radar system can judge the types of the

targets. Although a simplest threshold (i.e., a linear function) is used, the classification

performance is guaranteed to some extent. With the linear classification function, I can

achieve 90 % classification accuracy which is 3-4 % lower than the classification using

the Gaussian kernel function. If I use more complicated classification functions rather

than the linear function in (4.14), the classification accuracy can be enhanced. The

computational complexity, however, may increase due to the complexity of the func-

tion. Therefore, for real-time classification, determining suitable classification function

may be an important issue.

60

4.6 Application to More Practical Situation

4.6.1 Other Types of Targets

In addition to human subjects and vehicles, I also extract proposed classification

features from signals reflected from cyclists in the FOV of the LRR. Also for the

cyclists, by changing the distance between the radar-equipped vehicle and the cyclists,

the features are extracted. In addition, the measurement is carried out while changing

the direction of the bicycle. The average values of the three classification standards,

which are calculated from this experiment, are given in Table 4.6. Compared with

Table 4.2, those values are distinct from those of the human subjects and the vehicles.

Therefore, I have determined that the proposed criteria also can be used to classify a

human, a vehicle, and a cyclist.

4.6.2 Target Classification in Real Road Environment

Based on the previous result, I also conduct an additional measurement to classify

the three types of targets in a practical road situation. The measurement environment

is described in Fig. 4.7. In this measurement, an automobile is stationary in front of the

radar-equipped vehicle. In addition, a pedestrian and a cyclist cross the crosswalk. In

this scenario, 2000 received radar signals are recorded and used for the SVM, and the

resulting confusion matrix is given in Table 4.7. As shown in the table, even though

I use a simple linear classification function, the proposed method well classify those

three types of targets and shows more than average 92 % classification accuracy. If I

use more complex kernel functions with the SVM method, it will give more precise

target classification performance.

Table 4.6: Mean values of three extracted featuresClass / Feature γ

(i)R d(i) s(i)

Cyclist 1.09× 108 4.66× 107 5.22× 1016

61

Figure 4.7: A measurement in a practical road environment (a conceptual illustration).

Table 4.7: Confusion matrix resulting from SVM

Estimated class / Actual class Pedestrian Vehicle Cyclist

Pedestrian 92.8 % 1.1 % 8.7 %

Vehicle 1.3 % 95.3 % 3.0 %

Cyclist 5.9 % 3.6 % 88.3 %

4.7 Conclusion

In this chapter, I proposed a human-vehicle classification method using a feature-

based SVM for an automotive FMCW radar system. First, for the 77-GHz FMCW

radar system, I defined a new parameter called RRCS which reflects the reflection

characteristics of targets. Based on this parameter, three significant target features were

extracted from the received radar signals, and were used as the classification criteria

for the SVM. Then, through a fourfold cross data validation, the classification accuracy

from the measured data was verified as higher than 90 %. In addition, the proposed

method can be operated in real-time with a simple classification function. The method

was also applied to classify a pedestrian, a vehicle, and a cyclist in a more practical

situation, and showed good classification performance.

To establish a more accurate classification function by the SVM, a significant

amount of measurements have to be conducted on actual road environments. In ad-

dition, if I subdivide the target types (e.g., vehicles to sedans and SUVs) and extract

62

features of each target, I will be able to classify the targets more elaborately. More-

over, additional radar signal features, such as phase characteristics of reflected signals

or higher order moments of received signals, can be used to improve the target classi-

fication performance.

63

Chapter 5

STATISTICAL CHARACTERISTIC-BASED ROAD STRUC-

TURE RECOGNITION AND CLASSIFICATION

5.1 Introduction

Recently, as automobile safety has been receiving considerable public attention,

sensors devised for automobiles, such as sonar, vision, lidar, and radar systems, have

become significant [57]. Among these sensors, the radar is robust to poor environ-

mental conditions, such as no-light conditions or bad weather [58]. The radar system,

mounted on automobiles, performs special functions such as adaptive cruise control

(ACC), autonomous emergency braking (AEB), and blind spot detection for driver

convenience. Above all, for driver safety, the radar must guarantee reliable detection

performance. If the radar does not accurately detect targets, it can pose a serious threat

to driver safety.

In general, a road comprises various structures, such as tunnels, guardrails, and

soundproof walls. Of these, certain structures made of iron generate undesired reflected

echoes, called radar clutter, owing to the presence of several metal reflectors. When

this clutter flows into the radar system, the target detection performance is not fully

guaranteed because beat frequency detection is not performed appropriately by the

64

constant false alarm rate (CFAR) algorithm [11], [59], [60]. In this case, the radar

can miss the target located in the front, which can pose a serious threat to the driver

in a radar-equipped vehicle using the ACC function. Moreover, if the missed target

is detected suddenly, the AEB will work autonomously, which can lead to a traffic

accident. To prevent such situations, an efficient method needs to be developed that

can, in advance, recognize structures that deteriorate the radar detection performance

by using an automotive radar sensor. Research on the recognition of road environments

using lidar systems or cameras has been actively conducted [61]-[65]; however, camera

systems do not perform well in low-light environments, and lidar systems have higher

production costs than radar sensors.

Research on road environment recognition with an automotive radar has not been

intensively conducted. In [66], a study was carried out to recognize several kinds of

road conditions using the backscattering properties in the 24 GHz automotive radar

system. In addition, research on road shape recognition, which can predict the road cur-

vature or control the driving direction, was conducted in [67], [68]. In [67], guardrails

were detected and their trajectory were modeled using radar measurement data, and

road boundaries were detected by combining camera measurement results [68]. More-

over, a few works on road structure recognition using an automotive radar have been

conducted so far [11], [60], [69]. The authors in [69] identified the bridge based on

the interference patten from the multipath propagation characteristics of the radar sig-

nal. In [11], a method for recognizing an iron tunnel using the 77 GHz automotive

frequency-modulated continuous wave (FMCW) radar system was developed based

on the concept of Shannon entropy [70]. In this method, the authors recognized the

iron tunnels using the degree of dispersion of frequency components in received sig-

nals. In [60], the iron road structures with periodic steel frames that degrade the radar

performance were recognized by measuring the fundamental frequency and its corre-

sponding harmonics using empirically determined parameters. In both methods, the

authors effectively recognized periodically installed road structures; however, a recog-

65

nition method that can be used regardless of the periodicity of road structures is re-

quired.

In this chapter, I propose an effective method for recognizing road structures using

an automotive FMCW radar. In this radar system, the output of the low-pass filter com-

prises frequency components, whose distribution depends on the road structures type.

For example, in structures with many metal reflectors, several frequency components

are detected by the 77-79 GHz radars [11], [59], [60], [71]; this is not the case for a

normal road environment. Thus, by identifying the shape, scale, and location parame-

ters of the distribution, I can determine what road structure the radar-equipped vehicle

is currently traveling on. However, to carry out this process in each radar scan in the

automotive radar system incurs considerable computational load. To address this issue,

I use a method of extracting parameters that represent statistical properties of each dis-

tribution, such as the mean, variance, coefficient of variance, skewness, and kurtosis.

These parameters can be easily calculated from the received signal, unlike the shape,

scale, and location parameters, and can be used as structure recognition standards.

Furthermore, for more effective recognition, I use a support vector machine (SVM)

method. The SVM method, which is a well-known and simple machine-learning algo-

rithm and is widely used for target classification in radar signal processing [40], [41],

[52], [72], divides the given data into two classes by determining a proper classifica-

tion function [55]. The measured data is trained by the SVM based on the suggested

parameters to derive an appropriate decision boundary. In addition, a fourfold cross-

validation method is used, which means 75 % of the total data is used to determine

the discriminant function, while the remaining data is used as a validation set to verify

the performance of the function. This process is repeated for the four different valida-

tion sets, and an average classification accuracy is derived. I verify the performance

of the proposed method using the measurement data obtained from the Yongin-Seoul

Expressway, which is 22.8 km long and composed of various road structures. Accord-

ing to the results, the proposed method successfully distinguishes the types of road

66

structures with high accuracy. Moreover, the proposed method effectively recognizes

the iron road structures that are known to degrade the radar detection performance. If

the road structures are efficiently recognized through an automotive radar, the safety

of the driver using the radar function can be ensured by applying additional signal

processing to suppress the clutter or sending a warning to the driver. The proposed

method reduces the real-time computational load because a classification function is

predetermined and stored offline. Thus, when the radar receives a new signal, the sta-

tistical parameters are extracted, and I can instantly determine the structure on which

the vehicle is traveling by using the predetermined classification function. In addition,

the proposed method can recognize the road structures without using other automotive

sensors. Moreover, unlike the methods proposed in [11] and [60], the method can be

applied regardless of the periodicity and even identify the types of road structures.

The remainder of this chapter is organized as follows. In Section 5.2, beat fre-

quency characteristics in periodic road structures are briefly explained. Then, the radar

signal measurement in actual road environments is introduced in Section 5.3, where I

show some examples of the difference in the distributions of signals received in differ-

ent road structures. Next, based on the measured data, the proposed iron road structure

recognition method is presented in Section 5.4, where parameters reflecting the char-

acteristics of the distribution and the SVM method using them are introduced. Addi-

tionally, the confusion matrices obtained from the SVM method are shown. Finally,

the conclusion is presented in Section 5.5.

5.2 Beat Frequencies in Periodic Road Structures

For iron road structures, steel frames are installed periodically at uniform inter-

vals. To calculate whether the beat frequencies corresponding to the periodic structure

appear regularly, I assume the environment, as shown in Fig. 5.1. Considering this fig-

ure, the distance between the pth steel frame and the radar-equipped vehicle can be

67

Figure 5.1: Distance difference between Rp and Rp+1.

expressed as

Rp =√l2x + l2y. (5.1)

In addition, if I define θp as tan−1 (lylx

), then the distance between the (p+ 1)th steel

frame and radar-equipped vehicle can be expressed as

Rp+1 =

√(Rp cos θp + I)2 + (Rp sin θp)

2

= Rp

√1 + 2 cos θp

I

Rp+ (

I

Rp)2, (5.2)

where I is the interval between the steel frames. Because I is significantly smaller than

Rp, the above equation can be approximated by using Taylor’s expansion:

Rp+1 ' Rp

√1 + 2 cos θp

I

Rp

' Rp + cos θpI. (5.3)

In addition, because the FOV of a long-range radar (LRR) generally ranges from−10 ◦

to 10 ◦, θp is always close to 1. Therefore, the difference between Rp+1 and Rp is

approximated to I . Thus, beat frequencies for the periodic frames can be expressed as

fp =∆B

∆Ttdp − fdp

=∆B

∆T

2(R1 + (p− 1)I)

c− 2vp

cfc

(p = 1, 2, · · · , P ). (5.4)

68

where p is the position of the steel frame and R1 is the distance between the first steel

frame and radar. In (5.4), the Doppler frequency can be regarded as a constant for all p

because the steel frames have no velocity; thus, this term depends only on the velocity

of the radar-equipped vehicle. In addition, the difference between the adjacent beat

frequencies, expressed as

fp+1 − fp =∆B

∆T

2I

c(p = 1, 2, · · · , P − 1), (5.5)

is kept constant because ∆B, ∆T , c, and I have fixed values. Therefore, the beat

frequencies corresponding to the steel frames appear at regular intervals. Moreover,

fp+1 − fp is maintained constant regardless of the velocity of the radar-equipped ve-

hicle because it does not depend on vp.

5.3 Measurement of Radar Signals in Actual Road Environ-

ments

In this section, I discuss the radar signal measurements and the signal analysis

method for the measured data. First, I describe the specifications of the automotive

radar used in the measurement, and then, analyze the characteristics of the signals

received in actual road structures.

5.3.1 Specifications of Automotive FMCW Radar Used in Measurements

I used a long-range radar (LRR) from Mando Corporation in the measurement.

To recognize distant road structures, it is effective to use detection results obtained

from the LRR [73]. For the antenna system, a single-element transmit antenna and

a four-element receiving uniform linear array antenna are used, with a spacing of

1.8λ between adjacent elements in the receiving antenna. In addition, the half-power

beamwidth of the array antenna is 7 ◦. The half-power beamwidth of a commercial

long-range radar usually ranges from 5 ◦ to 9 ◦ [74]. Also, the field of view (FOV) of

69

the LRR ranges from −10 ◦ to 10 ◦, which falls within the general range [75]. This

antenna system transmits the FMCW radar signal. The transmitted signal is reflected

from the targets in the FOV, and the reflected signals are received by the array antenna.

In the measurement, fc, ∆B, and ∆T are set as 76.5GHz, 500MHz, and 5ms,

respectively. In addition, one cycle of the FMCW radar signal is 60ms long, and com-

prises a 10ms signal transmission interval and a 50ms signal processing time. Here,

one such 60ms cycle is called a radar scan. During the 10ms of the signal trans-

mission interval, 5ms each is allocated to the transmission times of the up-chirp and

down-chirp signals. Fig. 5.2 shows a block diagram for the operation principle of the

FMCW radar sensor, which is mounted in the front bumper of the vehicle, as shown in

Fig. 5.3.

Figure 5.2: Block diagram for the FMCW radar sensor: signal processing in digital

signal processor.

70

Figure 5.3: Automotive FMCW radar sensor mounted in the front bumper.

5.3.2 Received Radar Signal Analysis Method for Measured Data

Using the automotive radar described in the previous section, I conducted mea-

surements on actual road environments. I gathered experimental data while driving a

radar-equipped vehicle on the Yongin-Seoul Expressway several times. In addition, to

understand the received radar signal characteristics in road structures, I have accumu-

lated a large amount of measurement data in particular environments, such as normal

roads, normal tunnels, iron tunnels, iron soundproof walls, and guardrails. The normal

road environment is defined as an environment without road structures. In addition,

an iron tunnel is a tunnel with periodic steel frames, and a normal tunnel is a tunnel

without such periodic frames. Further, an iron soundproof wall is a soundproof wall

made of iron, and a guardrail is an iron structure installed at the center of the road. For

each road structure type, at least 3000 received radar scans are stored to be analyzed.

When analyzing the received radar signal, it is effective to deal with the signal in the

frequency domain rather than the time domain because target detection is conducted

based on beat frequencies.

Received Signal Analysis

For a radar scan in the measurement, the time-sampled LPF (M(t)) in (1.4) can

be expressed as

xm = [xm(1), xm(2), · · · , xm(NS)], (5.6)

71

where m denotes the scan index and NS indicates the number of time samples. Then,

the FFT result of the time-sampled low-pass filter output of themth radar scan is given

as

Xm(k) =

NF∑n=1

xm(n)e−j 2π

NF(n−1)(k−1)

(k = 1, 2, · · · , NF ), (5.7)

whereNF is the number of FFT points, which is set to 211 = 2048 in the radar system.

In addition, the magnitude response of the FFT result is defined as

Sm =[|Xm(1)| , |Xm(2)| , · · · , |Xm(NF /2)|

]. (5.8)

Because |Xm(k)| (k = 1, 2, · · · , NF ) is symmetric about NF /2, only half of the

entire FFT result is processed.

Distributions of Frequency Components in Different Road Structures

When I apply FFT to the time-sampled low-pass filter output xm, the frequency

components corresponding to each cosine wave are extracted. Depending on the types

of road structures, the distribution of the frequency components in the FFT results

varies. For example, if a radar-equipped vehicle travels on a road structure that has

several metal reflectors, such as iron tunnels and iron soundproof walls, the transmit-

ted signal is reflected by these reflectors. Then, several reflected signals are received at

the receiving antenna, and the FFT result consists of many frequency components. In

contrast, when the vehicle travels on a road structure having a small number of reflec-

tors, only a few frequency components corresponding to the targets in the FOV appear

in the FFT result. Therefore, the distribution of the frequency components differs de-

pending on the characteristics of road structures.

The difference in frequency component distributions among different road struc-

tures can be confirmed from the measurement result. For example, Fig. 5.4 shows the

accumulated Sm in (5.8) over 600 radar scans for a radar-equipped vehicle entering an

iron tunnel. In the figure, the x− and y− axes indicate the scan index (m) and FFT

72

A B

100 200 300 400 500 600

Scan index, m

100

200

300

400

500

600

700

800

900

1000

FF

T in

de

x,

k

0

50

100

150

200

250

300

350

400

450

500

Figure 5.4: Accumulated Sm for a radar-equipped vehicle entering an iron tunnel.

index (k), respectively. In addition, the scan index m can be interpreted as the time

elapsed since the start of the measurement, because one radar scan is recorded every

60ms in the radar system. I divide the figure into two regions, region A, which rep-

resents the measurement data for a radar-equipped vehicle traveling on a normal road,

and region B, which represents the measurement data after the vehicle has completely

entered the iron tunnel. In the figure, as the vehicle approaches the tunnel, a unique

pattern appears. For a closer look, the representative snapshots and instantaneous mag-

nitude responses for the two regions are shown in Figs. 5.5 and 5.6, respectively. When

the radar-equipped vehicle travels on a normal road (e.g., S100), only frequency com-

ponents corresponding to the targets located in the FOV of the radar are dominant in the

instant magnitude response, because the number of reflectors that reflect the transmit-

ted signals is small; however, when the vehicle travels in the iron tunnel (e.g., S460),

several signals reflected from the steel frames of the iron tunnel are detected by the

radar. In other words, several frequency components corresponding to the steel frames

appear in the instantaneous magnitude response. These undesired reflected radar sig-

73

Figure 5.5: Snapshots for m = 100 (on a normal road, region A) and m = 460 (in an

iron tunnel, region B).

0 100 200 300 400 500 600 700 800 900 1000

FFT index, k

0

100

200

300

S1

00

0 100 200 300 400 500 600 700 800 900 1000

FFT index, k

0

100

200

300

S4

60

Figure 5.6: Instantaneous magnitude responses (Sm) for m = 100 (on a normal road,

region A) and m = 460 (in an iron tunnel, region B).

nals, called radar clutter, degrade the radar detection performance because the beat

frequency of the desired target gets buried in the clutter [11], [59], [60]. Therefore, by

judging the structures that degrade the radar detection performance, additional signal

processing methods need to be conducted to overcome the performance deterioration.

For this purpose, an effective method that recognizes the road structures needs to be

established first.

74

5.4 Proposed Road Structure Recognition Method

This section presents an effective way to recognize the road structures. Here, I will

attempt to recognize the structures using two methods. In the first method, I determine

what distributions the frequency components follow in each road structure. After de-

termining the distribution, I extract parameters that can represent the characteristics of

the distribution, such as shape, scale, and location. In contrast, in the second method,

I extract parameters that represent statistical properties of the distribution, such as the

mean, variance, correlation of variance, skewness, and kurtosis, without identifying

what the distribution the frequency components follow. Then, using these parameters,

the SVM method is used to set a proper classifier, and the following classification re-

sults are obtained. I introduce the two methods for the following reason. The former

recognition method incurs considerable computational load for use in practical radar

systems. Therefore, the latter recognition method, which uses relatively simple statis-

tical parameters, is considered to be more efficient in this section.

5.4.1 Distribution Fitting of Frequency Components

First, I introduce the road structure recognition method by identifying what distri-

butions the frequency components follow in some road structures. For a measurement

example in Fig. 5.6, I find the distributions of the frequency components in the normal

road and the iron tunnel. Fig. 5.7 shows the distributions of the frequency compo-

nents in S100 and S460. In this figure, the x−axis indicates the magnitude of frequency

components |Xm(k)| (k = 1, 2, · · · , NF /2) for the 100th and 460th radar scans,

and NF /2 = 1024 frequency components in each case are distributed in 128 magni-

tude bins. In addition, the y−axis indicates that the number of frequency components

belonging to each magnitude bin. As shown in the figure, the frequency component

distributions vary depending on the road structure types. To determine the most suit-

able distribution for each case, I conduct the Kolmogorov-Smirnov (K-S) test on the

75

Figure 5.7: Distributions of frequency components for a vehicle traveling on a normal

road and in an iron tunnel.

measurement results. In the K-S test, the most proper distribution is determined from

the smallest K-S statistic [76]. With 50 empirical distributions, I calculate the K-S

statistic; the result is given in Table 5.1. When the vehicle travels on a normal road,

the distribution follows the four-parameter Burr distribution, whose probability density

function is expressed as

fB(x; αB, βB, γB, δB) =αBδB

(x−γBβB

)αB−1

βB

(1 + (x−γBβB

)αB)δB+1

, (5.9)

where x indicates the magnitude of Xm(k) (k = 1, 2, · · · , NF /2). In addition, αB

and δB are the shape parameters, and βB and γB , respectively, denote the scale and

Table 5.1: K-S statistic for distributions in a normal road and an iron tunnelDistribution / Structure Normal road Iron tunnel

Burr - 0.01685 (3rd)

Burr (4 parameters) 0.03674 (1st) -

Log-Logistic (3 parameters) 0.03750 (2nd) 0.01652 (1st)

Dagum - 0.01673 (2nd)

Dagum (4 parameters) 0.04087 (3rd) -

76

location parameters. In addition, the frequency components in the iron tunnel follow

the three-parameter log-logistic distribution with the smallest K-S statistic, which is

formulated as

fL(x; αL, βL, γL) =αLβL

(x− γLβL

)αL−1

×(

1 + (x− γLβL

)αL)−2

, (5.10)

where αL, βL, and γL denote the shape, scale, and location parameters in the log-

logistic distribution, respectively, and are calculated as (αIL, βIL, γ

IL) = (4.233, 71.09,

12.12). The frequency components in the normal road follow the log-logistic distribu-

tion with the second-smallest K-S static. In this case, the three parameters are calcu-

lated as (αNL , βNL , γ

NL ) = (3.412, 16.92, 12.65), which differ from the value calcu-

lated in the iron tunnel. From the measurement results, I find that these three parameter

values are maintained when the radar-equipped vehicle is traveling in each road struc-

ture. Thus, if I identify the distribution from the frequency components in each radar

scan, I can determine the structure on which the radar-equipped vehicle is traveling.

However, determining the distribution and calculating its shape, scale, and location

parameter values instantaneously in each radar scan may not be practical in a radar

hardware. Therefore, a more concise yet effective recognition method is desired.

5.4.2 Parameters Representing Statistical Characteristics

As mentioned in the previous section, more efficient recognition standards need to

be established for automotive radar systems. Thus, I use a method to extract parame-

ters that represent statistical characteristics of the frequency components, rather than

identifying the entire distribution. In this method, I use parameters such as mean, vari-

ance, coefficient of variance, skewness, and kurtosis. It is expected that the values of

the suggested parameters vary depending on the road structure types. The coefficient

of variance, which is known as relative standard deviation, represents the dispersion of

the distribution about the mean value, and skewness is a measure of asymmetry of the

distribution about its mean [77]. In addition, kurtosis is a measure of the sharpness of

77

the distribution [77]. These parameters are extracted in each radar scan as

µm =1

NF /2

NF /2∑k=1

|Xm(k)|,

νm =1

NF /2− 1

NF /2∑k=1

{|Xm(k)| − µm}2,

cm =

√νmµm

,

wm =

1NF /2

∑NF /2k=1 {|Xm(k)| − µm}3[√

1NF /2

∑NF /2k=1 {|Xm(k)| − µm}2

]3 ,

km =

1NF /2

∑NF /2k=1 {|Xm(k)| − µm}4[

1NF /2

∑NF /2k=1 {|Xm(k)| − µm}2

]2 . (5.11)

Because these parameters are defined using simple operations such as addition, sub-

traction, multiplication, and division, they can be calculated in 50 ms signal process-

ing time. In addition, if I assume that the radar sends a warning message to a driver

every second, the processing time becomes about 16 times. Thus, the computational

complexity is affordable on the radar hardware.

Fig. 5.8 shows the trends of the five parameter values over 600 radar scans for the

example shown in Fig. 5.4. As shown in the figure, the parameters have different values

before and after entering the iron tunnel. In addition, Table 5.2 shows the average

values of these parameters for the five types of road structures, which are calculated

from 3000 radar scans received in each road structure. As shown in the table, the

Table 5.2: Average values of five parameters of five road structuresParameter / Structure Normal road Normal tunnel Iron tunnel Iron soundproof wall Guardrail

µm 1.414× 103 2.817× 103 6.299× 103 3.243× 103 2.140× 103

νm 1.843× 107 3.179× 107 5.952× 107 3.327× 107 1.297× 107

cm 2.353 1.900 1.186 1.618 1.611

wm 11.30 9.101 4.704 7.754 7.488

km 171.8 125.8 42.39 106.9 89.89

78

0 100 200 300 400 500 600

Scan index, m

0

2000

4000

6000

8000

10000

Para

mete

r valu

e

Mean, m

0 100 200 300 400 500 600

Scan index, m

0

2

4

6

8

10

12

14

16

18

Para

mete

r valu

e

108

Variance, m

0 100 200 300 400 500 600

Scan index, m

0

1

2

3

4

5

6

Para

mete

r valu

e

Coefficient of variance, cm

0 100 200 300 400 500 600

Scan index, m

0

5

10

15

20

25

30

Para

mete

r valu

e

Skewness, wm

0 100 200 300 400 500 600

Scan index, m

0

100

200

300

400

500

600

700

800

900

Para

mete

r valu

e

Kurtosis, km

Figure 5.8: Changes in values of the five parameters over 600 radar scans.

average values exhibit noticeable differences; however, the five parameter values can

have overlapping areas among road structures, as shown in Fig. 5.9. In this figure, the

parameter values calculated from 300 received radar scans in each road structure are

depicted, and overlapping areas between the two parameter values for the five types of

road structures are shown. Although areas of the parameter values are distinguishable

79

1000 2000 3000 4000 5000 6000 7000 8000

Mean, m

0

0.5

1

1.5

2

2.5

Variance,

m

108

Normal road

Normal tunnel

Iron tunnel

Iron soundproof wall

Guardrail

1000 2000 3000 4000 5000 6000 7000 8000

Mean, m

1

1.5

2

2.5

3

3.5

4

4.5

Coeffic

ient of variance, c

m

Normal road

Normal tunnel

Iron tunnel


Guardrail

1000 2000 3000 4000 5000 6000 7000 8000

Mean, m

5

10

15

20

25

Skew

ness, w

m

Normal road

Normal tunnel

Iron tunnel


Guardrail

1000 2000 3000 4000 5000 6000 7000 8000

Mean, m

0

100

200

300

400

500

600

700

800

Kurt

osis

, k

m

Normal road

Normal tunnel

Iron tunnel


Guardrail

0 0.5 1 1.5 2 2.5

Variance, m 108

1

1.5

2

2.5

3

3.5

4

4.5

Coeffic

ient of variance, c

m

Normal road

Normal tunnel

Iron tunnel


Guardrail

0 0.5 1 1.5 2 2.5

Variance, m 108

5

10

15

20

25

Skew

ness, w

m

Normal road

Normal tunnel

Iron tunnel


Guardrail

0 0.5 1 1.5 2 2.5

Variance, m 108

0

100

200

300

400

500

600

700

800

Kurt

osis

, k

m

Normal road

Normal tunnel

Iron tunnel


Guardrail

1 1.5 2 2.5 3 3.5 4 4.5


5

10

15

20

25

Skew

ness, w

m

Normal road

Normal tunnel

Iron tunnel


Guardrail

1 1.5 2 2.5 3 3.5 4 4.5


0

100

200

300

400

500

600

700

800

Kurt

osis

, k

m

Normal road

Normal tunnel

Iron tunnel


Guardrail

5 10 15 20 25

Skewness, wm

0

100

200

300

400

500

600

700

800

Kurt

osis

, k

m

Normal road

Normal tunnel

Iron tunnel


Guardrail

Figure 5.9: Overlapping areas between two parameters.

among road structures, it is ambiguous to determine where the points at the boundaries

belong to. Therefore, to determine which road structures the points in the overlapping

areas belong to, a more advanced and effective recognition method is required instead

of a simple determination based on the mean values. Thus, I use the SVM method

based on these statistical parameters, which is known as one of the simple but effective

machine learning algorithms.

80

5.4.3 Road Structure Recognition Using SVM Method

Principle of SVM Method

The SVM is a method originally designed to effectively divide the given data into

two groups by determining the appropriate classification function, and the first de-

signed SVM used a linear classifier. The use of SVM can also be expanded to con-

structing nonlinear classifiers by using slack variables or kernel functions [55]. Us-

ing the kernel method, the given data is sent to a higher-dimensional space, and can

be classified by a proper classifier in the new domain. In this section, to determine

the road structure on which the radar-equipped vehicle is traveling, I apply the SVM

method with the five proposed statistical parameters calculated from the radar scans.

Here, a fourfold cross-validation method is adopted. First, I divide the measured data

into four partitions, and three quarters of the four partitions (i.e., 75 % of the total mea-

sured data) are used to train the data to formulate a classification function. Next, the

remaining partition is used to validate the performance of the function. This process is

conducted four times for the four different partitions, as shown in Fig. 5.10.

In the case of the automotive radar system, because the target recognition must be

performed in a short time, the computational complexity needs to be considered; thus,

Figure 5.10: Conceptual diagram of the fourfold cross-validation method.

81

I first use a linear classification function in the SVM method to establish an appropriate

classification boundary within the given statistical parameters. The linear classification

function can be expressed as

h(fm; s, a, b) =1

s× fm · aT + b, (5.12)

where fm is the feature vector corresponding to the statistical parameters calculated

from the mth radar scan, s is the scale parameter, a is the coefficient vector, and b is

the bias parameter. In the method, because I use the five statistical parameters, elements

in the feature vector fm are expressed as

fm = [µm, νm, cm, wm, km]. (5.13)

When I train the measurement data using the SVM method to set a proper classification

function, values corresponding to s, a, and b are derived. Thus, the classification func-

tion h(fm; s, a, b) is predetermined from the measured data and acts as the decision

boundary. Based on this function, a given feature vector can be usually classified into

one of the following two different regions. One region satisfies h(fm; s, a, b) > 0

and the other satisfies h(fm; s, a, b) < 0. The case h(fm; s, a, b) = 0 has a low

probability. Thus, by evaluating the value of h(fm; s, a, b), I can determine the struc-

ture on which the radar-equipped vehicle is traveling. For instance, with respect to the

case in Fig. 5.4, if the domain of h(fm; s, a, b) > 0 is predetermined as a feature

space corresponding to the statistical parameters from the normal road, I can deter-

mine that the signal received at the mth scan is from the normal road when it satisfies

h(fm; s, a, b) > 0. Otherwise, the feature vector satisfying h(fm; s, a, b) < 0 can

be perceived as that measured in the iron tunnel. Therefore, after establishing the clas-

sification function using a significant amount of actual measurements, the automotive

radar can instantly determine the road structure type from the received radar signal.

The entire process of the proposed method is shown in Fig. 5.11.

In addition, even though another radar with different specifications is used in the

measurement, the proposed method can classify the road structures because the dif-

82

Figure 5.11: Block diagram for the proposed method.

ference between distributions of frequency components always exists according to

the road structure. When I use another LRR, only values of s, a, and b will change

while maintaining the recognition performance. In this study, because five types of

road structures have to be classified, a multi-class SVM method is required. Thus, I

use an error-correcting output code multi-class model for constructing SVM classi-

fiers, which shows high recognition accuracy for a small number of classes [78].

Recognition Results of SVM Method

First, a confusion matrix is derived from the SVM method using a linear classi-

fier trained by the five suggested features, as shown in Table 5.3. In the matrix, the

first row and first column indicate the actual and estimated classes of the road struc-

Table 5.3: Confusion matrix derived from SVM with a linear classifierEstimated class / Actual class Normal road Normal tunnel Iron tunnel Iron soundproof wall Guardrail

Normal road 100% 0% 0% 0% 0%

Normal tunnel 0% 80% 0% 10% 14%

Iron tunnel 0% 0% 100% 0% 0%

Iron soundproof wall 0% 15% 0% 89% 4%

Guardrail 0% 5% 0% 1% 82%

83

tures, respectively. In addition, because I use the fourfold cross-validation method,

the recognition accuracy is averaged over four trials. As shown in the table, the road

structure recognition is conducted effectively with the suggested statistical parameters.

Although overlapping regions exist among normal tunnels, iron soundproof walls, and

guardrails, average recognition accuracy is guaranteed to some extent.

I also use the Gaussian kernel to construct a more effective classifier rather than

using a simple linear classification function. This method can achieve 92.2 % recogni-

tion accuracy, which is higher than that obtained using the linear classifier, as shown

in Table 5.4. In addition, if I use more complicated nonlinear classification functions

rather than the linear classifier, the recognition accuracy can be further improved. The

computational complexity, however, may increase owing the complexity of the func-

tion. Therefore, to utilize the proposed method to a practical automotive radar system,

a suitable classification function needs to be determined by considering the trade-off

between the recognition accuracy and the computational complexity.

In addition, to determine the most crucial parameter in the recognition among the

proposed parameters, the SVM is applied using only one of the parameters. The recog-

nition accuracy is shown in Table 5.5, where µm is the most significant parameter and

km can be considered a negligible factor. Moreover, I conduct the SVM method by

increasing the number of suggested parameters based on the average accuracy in Ta-

ble 5.5, and the following result is given in Table 5.6. When only two parameters are

used, the recognition accuracy is over 85 %. Thus, to reduce the computational load,

the recognition using fewer parameters is acceptable. However, using more parameters

Table 5.4: Confusion matrix derived from SVM with a Gaussian kernelEstimated class / Actual class Normal road Normal tunnel Iron tunnel Iron soundproof wall Guardrail

Normal road 100% 0% 0% 0% 0%

Normal tunnel 0% 84% 0% 11% 10%

Iron tunnel 0% 0% 100% 0% 0%


Guardrail 0% 4% 0% 0% 88%

84

Table 5.5: Recognition accuracy when only one parameter is usedAccuracy (Actual class - Estimated class) / Parameter µm νm cm wm km

Accuracy (Normal road-Normal road) 88% 35% 68% 63% 59%

Accuracy (Normal tunnel-Normal tunnel) 82% 62% 21% 12% 6%

Accuracy (Iron tunnel-Iron tunnel) 99% 73% 82% 77% 79%

Accuracy (Iron soundproof wall-Iron soundproof wall) 47% 1% 38% 31% 5%

Accuracy (Guardrail-Guardrail) 64% 54% 43% 36% 46%

Average recognition accuracy 76% 45% 50.4% 43.8% 39%

Table 5.6: Recognition accuracy obtained by increasing the number of suggested pa-

rametersAccuracy (Actual class - Estimated class) / Parameter µm µm, cm µm, cm, νm µm, cm, νm, wm µm, cm, νm, wm, km

Accuracy (Normal road-Normal road) 88% 99% 100% 100% 100%

Accuracy (Normal tunnel-Normal tunnel) 82% 69% 73% 73% 80%

Accuracy (Iron tunnel-Iron tunnel) 99% 100% 100% 100% 100%

Accuracy (Iron soundproof wall-Iron soundproof wall) 47% 85% 84% 89% 89%

Accuracy (Guardrail-Guardrail) 64% 75% 75% 76% 82%

Average recognition accuracy 76% 85.6% 86.4% 87.6% 90.2%

can ensure more stable and accurate recognition performance.

I also compare the classification results from the SVM to those from decision tree

learning [79]. In this method, given feature vectors fm are successively divided into

binary sets at decision nodes. Thus, I have to determine the structure of the tree, which

is not required process in the proposed method. In addition, setting appropriate nodes

strongly affects the classification results. Here, I use a simple tree model with four

decision nodes and Gini’s diversity index as decision criterion, and the fourfold cross-

validation method is also used. As given in Table 5.7, the average classification accu-

racy from decision tree learning is 70 %, which is much less accurate than that from the

SVM. Moreover, iron soundproof walls cannot be recognized in decision tree learning

results.

Finally, I apply the proposed method to distinguish the normal road structures

from the iron road structures. In huge iron road structures, such as iron tunnels and

85

Table 5.7: Confusion matrix derived from decision tree learningEstimated class / Actual class Normal road Normal tunnel Iron tunnel Iron soundproof wall Guardrail

Normal road 85% 0% 0% 0% 2%

Normal tunnel 6% 98% 1% 98% 30%

Iron tunnel 0% 1% 98% 1% 0%


Guardrail 9% 1% 0% 0% 68%

soundproof walls, the radar detection performance is not fully guaranteed owing to the

periodic clutter generated from the steel frames. In addition, it causes the misdetection

of the targets located in front of the radar-equipped vehicle because the CFAR algo-

rithm does not operate appropriately [11], [59], [60]. The following confusion matrix

is given in Table 5.8. In this result, all five suggested parameters are used and the lin-

ear classifier without the Gaussian kernel is employed. When the structures are divided

into only two groups, the recognition accuracy shows more improvement. For practical

automotive radar systems, if I set the threshold values at which the radar detection per-

formance starts to degrade, the proposed method can be effectively utilized. In other

words, if the scale parameter, coefficient vector, and bias parameter in (5.12) are deter-

mined in advance through a vast amount of measurements, I can discriminate the road

environment where the radar detection performance is degraded. If the determination

of the road structures is performed stably, additional radar signal processing, such as

threshold adjustment in the CFAR algorithm [11] or periodic clutter suppression [59],

[60], can be applied to mitigate the radar detection performance degradation. In addi-

tion, by warning the driver when the ACC function is not operating reliably, accidents

Table 5.8: Confusion matrix derived from SVMEstimated class / Actual class Normal road structures Iron road structures

Normal road structures 92.7% 6.4%

Iron road structures 7.3% 93.6%

86

can be prevented. For these purposes, I think that the proposed method to recognize

the road structures is important.

5.5 Conclusion

This chapter proposed an efficient road structure recognition method for an auto-

motive FMCW radar system. Depending on the types of road structures, I confirmed

that the distributions of frequency components in the received signals were different.

I focused on this point and extracted representative parameters reflecting statistical

characteristics of each distribution. The average values of the extracted parameters

showed noticeable differences for different road structures, but also had overlapping

areas among them. Therefore, I used the SVM method to establish more effective clas-

sification criteria. By using the SVM with a linear classifier or a Gaussian kernel, the

recognition accuracy was derived. In addition, I determined which of the proposed pa-

rameters played the most important role in the road structure recognition. Moreover,

the proposed method successfully determined the iron road structures that degrade the

radar detection performance. I expect the proposed method will contribute to ensuring

the safety of radar-equipped vehicle drivers. To recognize more types of road structures

stably and to achieve more reliable recognition performance, various measurements

need to be conducted in actual road environments.

87

Chapter 6

PERIODIC CLUTTER SUPPRESSION IN IRON ROAD

STRUCTURES

6.1 Introduction

Some research has been conducted concerning clutter in road environments [80],

[81]. Above all, only a few studies have been conducted on radar clutter in road en-

vironments, where metallic structures with intense reflections are densely distributed

[68], [69]. When a radar-equipped vehicle travels through specific road structures made

of iron, such as tunnels, soundproof walls, and guardrails, the radar detection perfor-

mance can be degraded [11], [59], [60]. Since these road structures consist of periodic

steel frames, they periodically generate unwanted echo signals called radar clutter [59],

[60], [71]. When the radar clutter from iron road structures flows into an automotive

radar system, the desired targets located in the field of view (FOV) of the radar cannot

be detected by the radar sensor, or the clutter can be considered as a signal reflected

from the desired target [11], [59], [60]. Thus, this causes the misdetection of the de-

sired target, and the radar performance is not fully ensured for such structures.

Some studies have proposed methods to recognize iron road structures that de-

grade the radar detection performance [11], [60], [82]. In [11], iron tunnel recognition

88

was performed by adopting the concept of Shannon entropy [70]. Moreover, iron road

structures were recognized by measuring the periodicity of the clutter in [60], [82].

After the clutter recognition, efficient signal processing is required for mitigating the

adverse effect of the periodic clutter; however, most of studies on clutter suppression

have been conducted in general road environments [83], [84], and only a few studies

have been carried out to suppress the clutter in iron road structures with respect to an

automotive radar [59], [60]. For example, clutter suppression method in iron tunnels

was proposed in [59], in which the authors estimated the fundamental frequency and

its harmonics corresponding to steel frames and substituted zeros for them. In addition,

the authors found the fundamental frequency and its harmonics corresponding to iron

road structures using the fast Fourier transform (FFT), and substituted average values

[60].

This chapter proposes an efficient method to suppress the periodic clutter in iron

road structures. Since the steel frames are installed periodically and are stationary,

beat frequencies corresponding to the structures also appear at regular intervals. More-

over, this phenomenon is maintained over radar scans when a radar-equipped vehicle

travels through the iron structures. Thus, by using the relationship between the cur-

rent and previously received radar signals, I determine beat frequencies corresponding

to the periodic structures. First, I calculate the cross-correlation between the adjacent

radar scans and determine the delay between the two scans. Then, the previous radar

scan is moved by the extracted delay because the distance difference between the two

scans can be compensated using the estimated delay. Finally, magnitudes of common

frequency components of the distance-compensated and current radar scans are sup-

pressed. The proposed suppression method can be applied to various types of periodic

iron road structures, and it shows better performance than the methods in [59] and

[60].

The remainder of this chapter is organized as follows. In Section 6.2, the received

signal analysis in iron road structures is introduced. Next, the proposed periodic clutter

89

suppression method and its results are presented in Section 6.3. Finally, the conclusion

is provided in Section 6.4.

6.2 Received Signal Analysis in Iron Road Structures

Fig. 6.1 shows the accumulated Sm over 600 scans for a radar-equipped vehicle

entering an iron tunnel. In this measurement, the speed of vehicle is 100 km/h, and it

is maintained constant after entering the iron-tunnel. The x- and y- axes indicate the

scan number (m) and FFT index (k), respectively, and Sm for each m is indicated by

a color. In the figure, as the vehicle approaches the tunnel, a unique hatched pattern

appears. When the vehicle enters the tunnel, paths of the desired targets are masked by

the periodic clutter, as shown in Fig. 6.1. To show more details, snapshots and instanta-

neous magnitude responses of the FFT results are given for three regions (i.e., regions

A, B, and C) in Figs. 6.2 and 6.3, respectively. When the radar-equipped vehicle is

on a normal road (e.g., S150), a very low amount of periodic clutter appears, and only

Figure 6.1: Accumulated Sm for a radar-equipped vehicle entering an iron tunnel.

90

Figure 6.2: Snapshots for m = 150 (on a normal road, region A), m = 350 (in a

transitional region, region B), and m = 550 (in an iron tunnel, region C).

0 100 200 300 400 500 600 700 800 900 1000

FFT index, k

0

200

S1

50

0 100 200 300 400 500 600 700 800 900 1000

FFT index, k

0

200

S3

50

0 100 200 300 400 500 600 700 800 900 1000

FFT index, k

0

100

200

S5

50

Figure 6.3: Instantaneous magnitude responses (Sm) for m = 150 (on a normal road,

region A), m = 350 (in a transitional region, region B), and m = 550 (in an iron

tunnel, region C).

frequency components corresponding to targets located in front of the vehicle are de-

tected using the constant false-alarm rate (CFAR) algorithm [3]. In this section, I used

an order statistics CFAR algorithm as a peak detection algorithm, which can achieve a

reliable detection performance in multi-target environments [85]. In addition, no spe-

cific adjustments are enacted for the threshold value in the method depending on road

structures. However, when the vehicle is in the iron tunnel (e.g., S550), periodic signals

reflected from steel frames are detected. These unwanted echoes degrade the radar de-

tection performance because the desired target is buried in the periodic clutter at some

91

moments [11], [59], [60]. In addition, the target cannot be identified using the CFAR

algorithm in this case; thus, effective clutter suppression scheme should be established.

In region B, although the vehicle has not yet entered the iron tunnel, the distant tunnel

is detected by the automotive radar (e.g., S350). In this region, the characteristics of

the received signals are observed as a mixture of those of signals from regions A and

C. I call this region as a transitional region.

6.3 Periodic Clutter Suppression in Iron Road Structures

6.3.1 Proposed Periodic Clutter Suppression Method

To mitigate the adverse effect of the periodic clutter in the iron structures, efficient

clutter suppression must be conducted. Since the steel frames are installed periodically

and considered as stationary targets, the beat frequencies corresponding to them also

appear at uniform intervals. In addition, this phenomenon is maintained over adjacent

radar scans for a vehicle traveling in the iron road structure. Thus, based on this point,

I use the relationship between the mth and (m− 1)th radar scans to suppress the pe-

riodic clutter. In other words, I use the cross-correlation between two scans, which is

calculated as

R(m,m−1)(q) = E[SmSm−1]

=

∑qn=1 |Xm(n)| |Xm−1(n+NF /2− q)|

(q = 1, 2, · · · , NF /2)

∑NF−qn=1 |Xm(n+ q −NF /2)| |Xm−1(n)|

(q = NF /2 + 1, NF /2 + 2, · · · , NF − 1).

(6.1)

92

Then, I can find the maximum value of R(m,m−1)(q) expressed as

d(m,m−1) = arg maxqR(m,m−1)(q)

(q = 1, 2, · · · , NF − 1). (6.2)

Since the vehicle moves forward in stationary iron structures, d(m,m−1) will gen-

erally have a value greater than NF /2. After finding the index corresponding to the

highest peak in R(m,m−1)(q), I move elements in the magnitude response of the pre-

vious radar scan as d(m,m−1) −NF /2 FFT indices because d(m,m−1) −NF /2 can be

considered as the distance difference between the two radar scans. Then, the magnitude

response of distance-compensated (m− 1)th radar scan is expressed as

S∗m−1 =[ ∣∣Xm−1(1 + d(m,m−1) −NF /2)

∣∣ ,∣∣Xm−1(2 + d(m,m−1) −NF /2)∣∣ ,

· · · , |Xm−1(NF /2)| , 0, · · · , 0]

=[ ∣∣X∗m−1(1)

∣∣ , ∣∣X∗m−1(2)∣∣ , · · · , ∣∣X∗m−1(NF /2)

∣∣ ],(6.3)

where∣∣X∗m−1(k)

∣∣ (k = 1, 2 · · · , NF /2) is the element in the magnitude response

of the distance-compensated radar scan. If I move |Xm−1(k)| by d(m,m−1) − NF /2,

no signal exists in the last part of S∗m−1. Thus, I pad the part from which the value is

removed with d(m,m−1) −NF /2 zeros. Next, I find the FFT indices satisfying

k∗ = argk

(1− α < |Xm(k)|∣∣X∗m−1(k)

∣∣ < 1 + α

)(k = 1, 2 · · · , NF /2), (6.4)

where α is a small threshold value. Assuming that the intensities of the signals re-

flected from the steel frames are similar over the scans (compensation of the signal

intensity according to the distance has already been performed in the radar system),

the selected indices from the above equation denote the beat frequencies correspond-

ing to the periodic structures. Thus, the magnitudes of beat frequencies corresponding

93

to those indices should be suppressed. This process is briefly explained in Fig. 6.4.

By comparing the magnitude response of the distance-compensated (m − 1)th radar

scan to that of the mth radar scan, correlated frequency components can be found, as

indicated by the blue circles in the figure.

Finally, for the selected indices, I interpolate the magnitudes as

|Xm(k)| =

12NA

∑k∈K−{k∗} |Xm(k)|

(K = {k|k∗ −NA < k < k∗ +NA)}

(for k = k∗)

|Xm(k)| (for k 6= k∗),

(6.5)

where 2NA is the number of magnitudes used for the interpolation. Since |Xm(k∗)| is

the magnitude corresponding to the periodic clutter, it is excluded in the interpolation.

For those selected indices, the use of zero-padding for the interpolation can suppress

𝑑 𝑚,𝑚−1 − 𝑁𝐹/2

Figure 6.4: Relationship between the (m− 1)th and mth radar scans.

94

the clutter; however, in this case, the CFAR algorithm does not operate properly be-

cause the zero-padding lowers the threshold level, and thus all peaks are detected by

the CFAR. Therefore, I use the averaged magnitude except that of the clutter. In addi-

tion, the actual frequency peaks corresponding to the clutter can be shifted back and

forth by one index due to the limitation of the sampling, and the frequency components

corresponding to the clutter appear over three indices in the measured data. Thus, the

(k∗ − 1)th and (k∗ + 1)th magnitudes are also interpolated as

|Xm(k∗ − 1)| =1

2NA

k∗−1+NA∑k=k∗−1−NA, k 6=k∗−1

|Xm(k)| ,

|Xm(k∗ + 1)| =1

2NA

k∗+1+NA∑k=k∗+1−NA, k 6=k∗+1

|Xm(k)| .

(6.6)

In general, the relative distance and relative velocity between a moving target and a

radar-equipped vehicle cannot be kept constant [69]. Thus, the beat frequency cor-

responding to the front vehicle changes in each radar scan. Therefore, by using the

proposed cross-correlation method, only the magnitudes corresponding to stationary

periodic steel frames are suppressed except those of the desired targets. The entire

signal processing chain of the FMCW radar system, including the proposed clutter

suppression method, is shown in Fig. 6.5.

6.3.2 Clutter Suppression Results

In this section, I show some clutter suppression results of the proposed method.

First, for the 599th and the 600th radar scans in Fig. 6.1, I calculate the cross-correlation

between S599 and S600. Then, I determine the index corresponding to the maximum

of R(600,599)(q), which is calculated as 1030. Thus, the calculated distance difference

between the two radar scans is six points since 1030 − 2048/2 = 6, which implies

that S600 is considered as a six-point-delayed magnitude response of S599. Over 100

scans, the delays are calculated as 6 or 7 points, as shown in Fig. 6.6, because the ve-

95

Figure 6.5: Block diagram illustrating the whole signal processing chain in the FMCW

radar system.

520 530 540 550 560 570 580 590 600 610 620

Scan index, m

5

5.5

6

6.5

7

7.5

8

De

lay,

d(m

,m-1

)-NF/2

Figure 6.6: Calculated delays over 100 radar scans.

hicle maintains an almost uniform velocity. I also check if 6 or 7 points are reasonable

value. For the radar system, the frequency resolution is given as

∆f =1

NFfs ×

c∆T

2∆B, (6.7)

96

where fs is the sampling frequency. Following the above equation, the six points are

transformed into the distance as 6 ×∆f = 1.72m. In addition, since the one-signal-

processing cycle is fixed as 60ms, the vehicle moves 60ms × 100 km/h = 1.67m

in one scan. Therefore, by comparing the distance calculated from the delayed FFT

points to that calculated from the period of radar signal and velocity, 6 or 7 points are

a reasonable value. If the delay estimated in the current radar scan exhibits a larger

difference than that in the previous scan, then d(m,m−1) − NF /2 can be corrected by

comparing it with the delay calculated from the velocity of the radar-equipped vehicle.

Another factor to consider is whether the near and distant steel frames move the

same distance over two scans as the radar-equipped vehicle travels forward. If not, the

beat frequencies corresponding to the steel frames may not exhibit regular intervals

over the scans, and in this case the proposed method cannot be applied effectively. I

simulated the case in which two steel frames are located in the FOV, as shown in Fig.

6.7. One is 60m away from the radar, and the other is 200m away from the radar.

Both are within the detection range of the LRR. In addition, they are located at 10 ◦

and 3 ◦ from the y-axis in the figure, respectively. If the radar-equipped vehicle travels

with a velocity of 100 km/h, then the distances to the steel frames 1 and 2 are reduced

0 1 2 3 4 5 6 7 8 9 10 11

x-distance (m)

0

20

40

60

80

100

120

140

160

180

200

y-d

ista

nce

(m

)

Radar-euipped vehicle (1st scan)

Radar-euipped vehicle (2nd scan)

Steel frame 1 (60 m, 10 deg)

Steel frame 2 (200.27 m, 2.98 deg)

Distance from steel frame 1 (60 m, 1st scan)

Distance from steel frame 2 (200.27 m, 1st scan)

Distance from steel frame 1 (58.36 m, 2nd scan)

Distance from steel frame 2 (198.60 m, 2nd scan)

Figure 6.7: Distance changes for a near steel frame (60 m) and a distant steel frame

(200 m).

97

by 1.6406m and 1.6644m, respectively, in adjacent radar scans. Thus, both values

are almost the same, and the difference is sufficiently small to be neglected. This cal-

culation suggests that near and distant road structures move almost the same distance

in each radar scan, and the proposed suppression scheme can be suitably applied. In

addition, if the distance between two steel frames or the velocity of the radar-equipped

vehicle decreases, then the difference becomes considerably more negligible.

Then, I move elements in the magnitude response of the 599th six indices. After

that, I determine indices having almost equivalent magnitudes over the previous radar

scan from the current radar scan by using (6.4). In this equation, I use α = 0.2 for the

thresholding. Then, I interpolate the magnitudes of chosen indices following (6.5) and

(6.6). In the interpolation,NA is set to one, implying that only neighboring magnitudes

are used in the interpolation. Fig. 6.8 shows the corresponding suppression result. As

shown in this figure, before applying the clutter suppression, several frequency peaks

from the periodic iron structures exist in the magnitude response. From the beat fre-

quency peaks, the periodicity of the structure can be calculated as 7∆f . In this case,

the desired target is buried in the clutter and may not be detected. In addition, when the

0 50 100 150 200 250

FFT index, k

0

100

200

Ma

g.

resp

on

se Actual target

Detected by CFAR

0 50 100 150 200 250

FFT index, k

0

100

200

Ma

g.

resp

on

se

0 50 100 150 200 250

FFT index, k

0

100

200

Ma

g.

resp

on

se

Figure 6.8: Original magnitude response (top), clutter-suppressed magnitude response

with α = 0.2 (middle), and clutter-suppressed magnitude response with α = 0.5

(bottom) for the 600th radar scan.

98

peak detection is conducted using the CFAR algorithm, it is difficult to identify which

peak corresponds to the target. However, after applying the proposed clutter suppres-

sion scheme, the frequency peak corresponding to the actual target is well estimated,

and the clutter near the desired target is suppressed. In addition, the clutter suppression

result when α is set as 0.5 is also given in Fig. 6.8. In this case, because an FFT index

k exhibiting a large difference between the magnitudes of |Xm(k)| and |X∗m−1(k)| is

also selected and its corresponding magnitude is suppressed, this leads to the loss of

the target information. As shown in the figure, the beat frequency corresponding to the

desired target is also removed, and it cannot be detected using the CFAR algorithm.

I also conduct the same process for the 601th radar scan, and the result is given

in Fig. 6.9. In this radar scan, the periodic clutter is also well suppressed, and I can

identify the beat frequency corresponding to the actual target by using the CFAR al-

gorithm. To ensure that the periodic components are suppressed, I apply the FFT to

the magnitude responses in Fig. 6.9, and these are expressed in Fig. 6.10. In Fig. 6.10,

T601 and U601 denote the FFT results for the original magnitude response and the

clutter-suppressed magnitude response in Fig. 6.9, respectively. Before applying the

suppression method, the fundamental frequency and its harmonics corresponding to

0 50 100 150 200 250

FFT index, k

0

50

100

150

200

Ma

gn

itu

de

re

sp

on

se Actual target

Detected by CFAR

0 50 100 150 200 250

FFT index, k

0

50

100

150

200

Ma

gn

itu

de

re

sp

on

se

Figure 6.9: Original magnitude response (upper) and clutter-suppressed magnitude re-

sponse (lower) for the 601th radar scan.

99

550 600 650 700 750 800 850 900 950 1000

FFT index, j

0

5000

10000

T601

Fundamental frequency and its harmonics

550 600 650 700 750 800 850 900 950 1000

FFT index, j

0

5000

10000

U601

Fundamental frequency and its harmonics

Figure 6.10: FFT results of original magnitude response (upper) and clutter-suppressed

magnitude response (lower) for the 601th radar scan.

the periodic structures are dominant; however, after the suppression, these compo-

nents are decreased. In addition, I compare the suppression performance of the method

to that of [59], which uses the results obtained from Fig. 6.10. The process and per-

formance of the clutter suppression method proposed in [60] is almost equivalent to

those of [59]. This method substitutes zeros for the frequencies corresponding to the

fundamental frequency and its harmonics, and then applies the inverse FFT (IFFT)

to the zero-padded FFT result. As shown in Fig. 6.11, the use of zero-padding in the

method of [59] also suppresses the periodic clutter but the magnitude of the frequency

peak corresponding to the desired target is also reduced; this can make the CFAR al-

gorithm miss the target in some radar scans. Since the target information spreads in

all frequency components in T601, the substitution of zeros can eliminate the target

information

Moreover, the proposed method is also applied to other iron road structures, such

as iron soundproof walls. I also perform the same suppression process, and the corre-

sponding results are shown in Fig. 6.12. In this periodic structure, the proposed method

satisfactorily estimates the distance difference from the cross-correlation between ad-

jacent radar scans. The figure shows that the periodic clutter is suppressed, and the

100

0 50 100 150 200 250

FFT index, k

0

50

100

150

200

Magnitude r

esponse Actual target

Detected by CFAR

0 50 100 150 200 250

FFT index, k

0

50

100

150

200

Magnitude r

esponse Actual target

Detected by CFAR (Prop.)

Detected by CFAR [8]

Figure 6.11: Proposed clutter-suppressed magnitude response (upper) and clutter-

suppressed magnitude response using the method of [59] (lower) for the 601th radar

scan.

0 50 100 150 200 250

FFT index, k

0

50

100

150

200

250

Ma

gn

itu

de

re

sp

on

se

Orignal received signal

Clutter suppressed signal

Actual target

Figure 6.12: Original and clutter-suppressed magnitude responses for a radar-equipped

vehicle in an iron soundproof wall.

101

frequency peak corresponding to the desired target is well identified from the CFAR

algorithm. Thus, I expect that the method can well suppress the periodic clutter in other

types of iron road structures, including iron tunnels.

6.4 Conclusion

In this chapter, I proposed a method to suppress the periodic clutter generated

from iron road structures for automotive radar systems. Since such structures had

steel frames installed with equal spacings, beat frequencies corresponding to the steel

frames appeared at regular intervals. In addition, the regular intervals were also main-

tained in adjacent radar scans for a vehicle traveling in the iron structure. Using this

relationship, the cross-correlation between the current and previous received radar sig-

nals was calculated, and the distance difference between them was extracted. Then, by

comparing the magnitude response of the distance-compensated radar scan to that of

the currently received radar scan, I extracted beat frequencies corresponding to the

periodic structures, and suppressed them with averaged magnitudes. The proposed

method well suppressed the clutter in periodic iron road structures, including iron tun-

nels. Moreover, the misdetection of the forward target was mitigated by using the pro-

posed method. The proposed clutter suppression method may also suppress reflected

signals from stationary or slowly moving targets in a particular radar scan. However,

a case where the vehicle stops for a long time on the expressway does not occur fre-

quently.

102

Chapter 7

MUTUAL INTERFERENCE SUPPRESSION USING

WAVELET DENOISING

7.1 Introduction

In recent years, there has been growing interest in automotive sensors to provide

safety and convenience to drivers. Among these sensors, the importance of radar sen-

sors has been emphasized because they are robust under bad weather conditions and

have longer detection ranges than other sensors, such as sonar, vision, and lidar sen-

sors. For automotive radars, a frequency-modulated continuous wave (FMCW) radar

operating at 77 GHz is widely used due to its low production costs and power consump-

tion as well as small size [1]. This automotive FMCW radar can be used to estimate

the range and velocity of the target, recognize road structures [60], [82], and identify

the types of detected targets [72].

As the number of radar-equipped vehicles increases, signal interference between

automotive radar systems has become an important issue [86]. When an FMCW radar

signal from another vehicle flows into the radar system, the signal can act as an inter-

ference signal. When the frequency difference between the transmitted signal and the

interference signal is smaller than the cut-off frequency of the low-pass filter of the

103

radar system, a signal with undesired frequency components is detected. This unde-

sired signal appears as a pulse-like signal in the time domain and it then spreads over

all frequency components in the frequency domain. Thus, the beat frequency contain-

ing the desired target information is buried by the interference, and the desired target

cannot be detected [87]-[91]. Because misdetection of the target can be a great risk to

a driver using automotive radar functions such as adaptive cruise control, an efficient

method to mitigate the effect of mutual interference is required.

Some studies have been proposed to suppress the mutual interference between

automotive FMCW radar systems. In [92]-[98], methods to mitigate the interference

by modifying the FMCW radar waveforms were proposed. Moreover, a few studies

proposed to suppress the interference through signal processing techniques without

changing the existing radar systems [87], [99]-[102]. In [87], the author removed the

interference by substituting zeros for the period where the interference occurred in

the entire signal. If the period is short, the interference can be effectively suppressed

without loss of the desired target information; however, if the period is long, the infor-

mation of the target may be damaged by the zero-padding. To overcome the loss of the

target information caused by the zero-padding, the authors in [99]-[100] reconstructed

the interference signal by estimating its amplitude and phase and subtracted the re-

constructed signal from the original signal; however, because the phase of the FMCW

radar signal is often distorted by the phase noise in an actual environment [103], phase

noise mitigation has to be applied. In [102], the advanced weighted-envelope normal-

ization (AWEN) method effectively suppressed the mutual interference by sensing the

interference signal and reducing its amplitude. In this method, some parameters are

determined empirically, so they have to be adjusted according to each FMCW radar

system.

Therefore, I propose a simple but effective mutual interference suppression method

using wavelet denoising, which is widely used to remove a noise component from a

given signal [104]. In general, the time-domain low-pass filter output in the mutual

104

interference situation consists of cosine waves including the information of the de-

sired targets and the pulse-like signal caused by the interference. In this case, the in-

tensity of the interference signal is usually more than 30 dB larger than that of the

signal reflected from the desired target because the interference signal comes directly

from another vehicle [87]. Thus, from the perspective of wavelet denoising, the low-

intensity cosine waves are regarded as noise components to be removed and the high-

intensity pulse-like interference signal is regarded as a signal to be left in. By applying

a wavelet transform and thresholding the wavelet coefficients to the low-pass filter out-

put, I can reconstruct the pulse-like interference signal from which the cosine waves

are removed. After that, if I subtract the reconstructed pulse-like interference signal

from the original low-pass filter output, I can recover the filter output without the mu-

tual interference. The proposed suppression method is similar to those in [99]-[100]

in that the interference signal is reconstructed and subtracted from the original signal;

however, the proposed method is not greatly affected by the phase noise. In addition,

compared to the AWEN method in [102], large adjustments in the parameters depend-

ing on the radar systems are not required in the proposed method. Moreover, unlike the

methods proposed in [92]-[98], I do not need to create new FMCW radar waveforms

to mitigate the interference and can suppress the effect of the interference by simple

post signal processing without changing the existing radar hardware.

The remainder of this chapter is organized as follows. In Section 7.2, the effect

of mutual interference in the automotive FMCW radar system are explained. Then,

the proposed mutual interference suppression method using wavelet denoising is in-

troduced in Section 7.3. Next, the performance of the proposed method is verified

through simulations and actual measurements in Sections 7.4 and 7.5, respectively.

Finally, I conclude this chapter in Section 7.6.

105

7.2 Effect of Mutual Interference on Beat Frequency Esti-

mation

In this section, I analyze the effect of mutual interference between the FMCW radar

signals on beat frequency estimation. As shown in Fig. 7.1, suppose that an FMCW

radar-equipped vehicle (i.e., green car), which acts as an interferer, approaches the

FMCW radar-equipped vehicle (i.e., red car). The FMCW radar installed on the inter-

ferer may be the same as the radar, or it may not be. In this interference scenario, the

time-frequency slope of the interference signal received by the radar-equipped vehicle

can have two different trends, as shown in Fig. 7.2. On one hand, as shown in Fig. 7.2

(a), the time-frequency slope of the interference signal has the same sign as the slope of

the signal transmitted from the vehicle. On the other hand, two time-frequency slopes

have different signs, as shown in Fig. 7.2 (b).

Similar to R(t) in (1.2), the up-chirp interference signal in Fig. 7.2 (a) can be

Figure 7.1: Simple interference scenario with a desired target vehicle and an interferer.

106

Figure 7.2: Time-frequency slope trends of the interference signal: (a) same sign as the

transmitted signal and (b) different sign to the transmitted signal.

expressed as

ISS(t) =I∑i=1

{ARi exp

(j(2π(fci + fdi −

∆Bi2

)(t− tdi)

+π∆Bi∆Ti

(t− tdi)2)

)}+ n(t)

(minitdi ≤ t ≤ ∆T + max

itdi), (7.1)

where fci , ∆Bi, and ∆Ti denote the carrier frequency, operating bandwidth, and

sweep time of the interference signal transmitted from the ith (i = 1, 2, · · · , I) in-

terferer, respectively. In addition, fdi is the Doppler frequency caused by the relative

velocity between the ith interferer and the radar-equipped vehicle, and tdi is the time

delay caused by the distance between the ith interferer and the radar-equipped vehicle.

In other words, tdi indicates the difference between the starting points of two time-

frequency slopes, as indicated in Fig. 7.2 (a).

For the case where the time-frequency slopes of the transmitted and interference

107

signals have same signs, the output of the low-pass filter is expressed as

L(T (t)ISS(t)) = AT

I∑i=1

{ARi exp(j(2π((fc − fci)

− (∆B

2− ∆Bi

2) + (

∆Bi∆Ti

tdi − fdi))t

+π(∆B

∆T− ∆Bi

∆Ti)t2 + 2π(fci −

∆Bi2

+ fdi)tdi

−π∆Bi∆Ti

tdi2))}+ L(T (t)n(t))

(maxltdl ≤ t ≤ ∆T ). (7.2)

In the same manner, when the time-frequency slopes of the transmitted and interfer-

ence signals have different signs, the output of the low-pass filter can be also expressed

as

L(T (t)IDS(t)) = AT

I∑i=1

{ARi exp(j(2π((fc − fci)

− (∆B

2+

∆Bi2

)− (∆Bi∆Ti

tdi + fdi))t

+π(∆B

∆T+

∆Bi∆Ti

)t2 + 2π(fci +∆Bi

2+ fdi)tdi

+π∆Bi∆Ti

tdi2))}+ L(T (t)n(t))

(maxltdl ≤ t ≤ ∆T ). (7.3)

When these interference signals flow into the radar system, the beat frequency cor-

responding to the target cannot be accurately estimated in the frequency domain. For

example, consider the case where the slopes of the transmitted and interference signals

have different signs, as shown in Fig. 7.3 (a). In this case, a time interval where the

frequency difference between the two signals is smaller than the cut-off frequency of

the low-pass filter exists, which is indicated by Ti in Fig. 7.3 (b). Therefore, the low-

pass filter output contains an undesired frequency component in addition to the beat

frequency component corresponding to the target. This undesired frequency compo-

nent from the interference signal degrades the beat frequency estimation performance.

108

Figure 7.3: (a) Time-frequency slopes of the transmitted and interference signals (dif-

ferent signs case). (b) Beat frequency between the transmitted and interference signals.

Moreover, the intensity of the interference signal coming directly from the interferer

does not suffer much loss, but the intensity of the signal reflected from the desired

target is greatly attenuated [87]. Therefore, the influence of mutual interference on the

beat frequency estimation is further increased.

A simple example of the case mentioned above is as follows. In the case of Fig. 7.1,

I assume that the relative distances and velocities of the interferer and the target ve-

hicle are given by (RI , vI) = (20m, −15m/s) and (RT , vT ) = (100m, 10m/s),

respectively. For this case, the low-pass filter outputs including the interference sig-

nal (i.e, L(M(t)) + L(T (t)IDS(t))) in the time domain and the frequency domain

are shown in Fig. 7.4. In the time-domain, the low-pass filter output consists of a de-

sired target signal (i.e., a cosine wave) and a pulse-like interference signal. To extract

the beat frequency corresponding to the desired target, I apply the FFT to this time-

domain low-pass filter output. As shown in Fig. 7.4 (b), when the interference signal

does not exist, the beat frequency corresponding to the desired target is estimated well

109

2.5 2.55 2.6 2.65 2.7 2.75 2.8 2.85 2.9 2.95 3

Time (s) 10-3

-200

-100

0

100

200

300

No

rma

lize

d a

mp

litu

de

(V

)

Low-pass filter output (without interference)

Low-pass filter output (with interference)

(a)

0 100 200 300 400 500 600 700 800 900 1000

FFT index

0

5

10

15

20

25

30

35

Ma

gn

itu

de

(d

B)



Beat frequency corresponding to target

(b)

Figure 7.4: Low-pass filter output consisting of the desired target signal and a pulse-

like interference signal: (a) in the time-domain and (b) in the frequency-domain.

by a peak detection algorithm such as the constant false alarm rate (CFAR) algorithm

[3]. However, when the interference signal flows into the radar system, the interfer-

ence level over all frequency components increases. In this case, because no signif-

icant difference between the magnitudes of the beat frequency component and those

of nearby frequency components exists, the CFAR algorithm does not work properly,

which causes misdection of the desired target. Because this misdetection of the tar-

get can lead to a dangerous situation, an effective but simple interference suppression

method is required in automotive radar systems.

110

7.3 Proposed Mutual Interference Suppression Method Us-

ing Wavelet Denoising

In this section, I propose to suppress the mutual interference in the time domain

using wavelet denoising. As mentioned in Section 7.2, the low-pass filter output in-

cluding the interference signal can be expressed as

LI(t) = L(M(t)) + L(T (t)IDS(t)). (7.4)

As shown in Fig. 7.4 (a), LI(t) consists of a cosine wave and a pulse-like interference

signal in the time domain. In general, wavelet denoising is widely used to effectively

remove the noise component from a given signal [104]. Here, I consider the target

signal (i.e., a cosine wave) as the noise component and remove it from the low-pass

filter output using wavelet denoising. Then, by subtracting this denoised signal from

the original low-pass filter output, I only leave the cosine wave corresponding to the

target. In other words, I first reconstruct L(T (t)IDS(t)) using wavelet denoising and

then subtract it from LI(t) to recover only L(M(t)). The proposed interference sup-

pression method consists of the following steps.

7.3.1 Decomposition of Low-pass Filter Output Using Wavelet Trans-

form

First, I decompose the low-pass filter output using the wavelet transform. For ex-

ample, many wavelets such as the Haar, Daubechies, Coiflets, Symlets, Morlet, and

Mexican Hat wavelets can be used. Among these wavelets, I use the Haar wavelet be-

cause it is the simplest among the wavelets, yet still effective [104]. The Haar wavelet’s

mother wavelet function ψ(t) can be expressed as

ψ(t) =

1 (0 ≤ t < 1/2)

−1 (1/2 ≤ t < 1)

0 (t < 0, t ≥ 1)

. (7.5)

111

The Haar wavelet is discontinuous at the middle point (i.e., t = 12 ) and resembles a

step function. Then, I apply the Haar wavelet transform to LI(t) to find the wavelet

coefficients, which are expressed as

Wa, b =

∫ ∞−∞

LI(t)ψ∗a, b(t)dt, (7.6)

where

ψa, b(t) = 2a2ψ(2at− b) (a = 1, 2, · · · , aT ). (7.7)

Here, a and b are the scaling and time factors for the mother wavelet ψ(t), respectively.

Using these factors, ψ(t) can be expanded or contracted by a and can be shifted by b.

To decompose LI(t) with the wavelet, I have to choose aT , which is called a decom-

position level. The decomposition level is an index of how small the mother wavelet is

made. When a higher level wavelet is used, the signal can be decomposed more finely.

Thus, I have to choose the proper decomposition level considering the computational

complexity. After applying the wavelet transform, the coefficients corresponding to

each a-level Haar wavelet can be obtained.

7.3.2 Thresholding for Extracting Wavelet Coefficients of Interference

Signal

For each level from 1 to aT , I threshold the wavelet coefficients to extract only the

significant components of the interference signal. In general, two thresholding methods

are used: soft thresholding and hard thresholding. Each thresholding method can be

expressed as

fs(Wa, b) =

Wa, b − sgn(Wa, b)λ, if |Wa, b| ≥ λ

0, otherwise,

fh(Wa, b) =

Wa, b, if |Wa, b| ≥ λ

0, otherwise, (7.8)

112

where sgn(·) is the signum function and λ is the threshold value. The graphs for these

two thresholding methods are given in Fig. 7.5. Through this thresholding, the wavelet

coefficients whose magnitudes are smaller than λ are eliminated. In other words, the

components corresponding to the cosine wave L(M(t)) that are regarded as noise

components are removed, and the components corresponding to the interference sig-

nal L(T (t)IDS(t)) are maintained. There are many ways to determine the threshold

value λ. For instance, I can use the universal threshold [105] or Stein’s unbiased risk

estimate [106]. Here, I use the modified universal threshold in [107], considering the

computational complexity, which can be expressed in a fixed-form:

λ = σa√

2 log(NI), (7.9)

where σa is the rescaling factor for the threshold value that is derived from a level-

dependent estimation of the noise level and NI is the length of the data.

Figure 7.5: Two thresholding methods for wavelet coefficients: (a) soft thresholding

and (b) hard thresholding.

113

7.3.3 Reconstruction of Interference Signal

Using the modified wavelet coefficients of levels from 1 to aT , I reconstruct the

interference signal, L(T (t)IDS(t)). For the low-pass filter output given in Fig. 7.4 (a),

I reconstructed the interference signal using a three-level Haar wavelet with the hard

thresholding method, as shown in Fig. 7.6. In this case, because the interference signal

has a simple pulse-like shape, it is easily reconstructed with only three-level Haar

wavelet denoising process. Depending on the shape of the interference signal, I have

to determine which level of wavelet to use for the interference signal reconstruction.

7.3.4 Subtracting Reconstructed Interference Signal from Original Low-

pass Filter Output

Finally, I can extract only the desired target signal by subtracting the reconstructed

interference signal L(T (t)IDS(t)) from the original low-pass filter outputLI(t), which

can be expressed as

L(M(t)) = LI(t)− L(T (t)IDS(t)). (7.10)

2.5 2.55 2.6 2.65 2.7 2.75 2.8 2.85 2.9 2.95 3

Time (s) 10-3

-200

-100

0

100

200

300

No

rma

lize

d a

mp

litu

de

(V

)

Original interference signal

Reconstructed interference signal

Figure 7.6: Reconstructed pulse-like interference signal in the time domain from

wavelet denoising.

114

I can expect that L(M(t)) contains only cosine wave corresponding to the desired

target because the reconstructed interference signal is subtracted from the original

filter output. Therefore, if I use the interference-suppressed signal L(M(t)), an en-

hanced beat frequency estimation can be achieved. Fig. 7.7 shows the frequency-

domain low-pass filter output with the proposed interference suppression method ap-

plied. As shown in the figure, the interference level is reduced and the beat frequency

corresponding to the target is accurately estimated by the CFAR algorithm.


I also simulated the case when two targets and one interferer exist in the field

of view (FOV) of the radar system. The relative distances, relative velocities, and

angles of the two targets are given by (RT1 , vT1 , θT1) = (100m, 20m/s, 1◦) and

(RT2 vT2 , θT2) = (80m, 5m/s, 10◦), respectively. In addition, the relative distance,

relative velocity, and angle of an interferer are given by (RI , vI , θI) = (15m, −15m/s,

−3◦). Here, I assume that the time-frequency slopes of the transmitted and interference

signals have different signs, and I use the three-level Haar wavelet transform and hard

0 100 200 300 400 500 600 700 800 900 1000

FFT index

0

5

10

15

20

25

30

35

40

Ma

gn

itu

de

(d

B)



Low-pass filter output (with interference suppression)


Beat frequency estimated by CFAR (with interference suppression)

Figure 7.7: Low-pass filter output with the proposed interference suppression in the

frequency-domain.

115

thresholding to reconstruct the interference signal. The frequency-domain low-pass fil-

ter outputs with and without the proposed interference suppression are given in Fig.

7.8. Fig. 7.8 (b) is an enlargement of the part near the beat frequencies in Fig. 7.8 (a).

As shown in Fig. 7.8, when the interference suppression is not applied, the two beat

frequencies cannot be identified by the CFAR algorithm because their magnitudes are

little bigger than those of the nearby frequency components. In other words, the two

beat frequencies corresponding to the targets are buried by the interference. However,

0 100 200 300 400 500 600 700 800 900 1000

FFT index

0

5

10

15

20

25

30

35

40

45

50

55

Ma

gn

itu

de

(d

B)




Beat frequency corresponding to target 1


Beat frequency 1 estimated by CFAR (with interference suppression)


(a)

200 250 300 350

FFT index

26

27

28

29

30

31

32

33

34

35

Ma

gn

itu

de

(d

B)








(b)


frequency-domain: (a) for entire FFT indices and (b) for FFT indices near beat fre-

quencies.

116

when the interference signal is reconstructed and subtracted from the original low-pass

filter output in the time domain, two dominant beat frequencies are extracted by the

CFAR algorithm in the frequency domain, and it shows similar beat frequency estima-

tion result for the case when no mutual interference exists.

After applying the interference suppression method, the target angle estimation

result also shows a different pattern. In general, to estimate the direction of arrival

(DOA) of the signal reflected from the target, an array antenna system is usually used

in automotive radar systems [108]. When the reflected signal is received at each an-

tenna elements, the DOA information is included in the phase difference caused by

the antenna spacing [32]. Using this phase difference, the DOA can be estimated by

the Bartlett, estimation of signal parameters via rotational invariance techniques (ES-

PRIT), and multiple signal classification (MUSIC) algorithms [32]. These methods all

use the correlation matrix of the received signals, which is expressed as

R =1

P[LI, 1(t), LI, 2(t), · · · , LI, P (t)]T

× [LI, 1(t), LI, 2(t), · · · , LI, P (t)], (7.11)

where LI, p(t) (p = 1, 2 · · · , P ) is the low-pass filter output of the pth antenna ele-

ment. Without the mutual interference, the angle of the target can be estimated using

the correlation matrix. Otherwise, I expect that the angle of the target cannot be accu-

rately estimated and that of the interferer will be estimated instead. Fig. 7.9 shows the

target angle estimation results from the MUSIC algorithm when the interference exists

and when it is removed. In this simulation, I used the four-element receiving uniform

linear array antenna and set the spacing between adjacent elements as 0.5λ. As shown

in the MUSIC pseudospectrum, when the proposed interference suppression was not

applied, the angles of the interferer and one target were estimated, which were −3 ◦

and 9.5 ◦, respectivly. The angle of one target that is further from the radar-equipped

vehicle cannot be found in the estimation result. However, if I suppress the mutual

interference for all LI, p(t) with the proposed method, I can estimate the DOAs of the

117

-10 -5 0 5 10 15 20

Direction of arrival (degree)

-70

-60

-50

-40

-30

-20

-10

0

10

Ma

gn

itu

de

(d

B)

DOA of a target 1

DOA of a target 2

DOA of an interferer

MUSIC pseudospectrum (without interference suppression)

MUSIC pseudospectrum (with interference suppression)

Figure 7.9: MUSIC pseudospectrum for low-pass filter output with the proposed inter-

ference suppression in the frequency-domain.

two targets. When I used the interference-suppressed correlation matrix R with the

MUSIC algorithm, I could identify the two accurate DOAs corresponding to the two

desired targets, which were 0.6 ◦ and 10.4 ◦, respectively. Thus, the target angle esti-

mation result showed a different pattern when the proposed interference suppression

was applied.

Moreover, I also simulated the case where more than one chirp of the interference

signal interfered with the transmitted signal, as shown in Fig. 7.10. In other words, mu-

tual interference with the fast-ramp FMCW radar [4] is considered in this simulation.

In this case, the time-frequency slopes of the transmitted and interference signals can

have both same signs and different signs, as shown in Fig. 7.10 (a). Thus, the low-pass

filter output consists of L(T (t)ISS(t)) and L(T (t)IDS(t)) in (7.2) and (7.3). In addi-

tion, it can be expected that several pulse-like interference signals will appear where

the frequency difference between the transmitted and interference signals is smaller

than the cut-off frequency of the low-pass filter, as shown in Fig. 7.10 (b). Fig. 7.11

shows the low-pass filter output consisting of the desired target signal and the pulse-

like interference signals in the time domain. As predicted through Fig. 7.10 (b), the in-

terference signals appear in the time interval where the frequency difference is smaller

118

Figure 7.10: (a) Time-frequency slopes of the transmitted and interference signals

(same signs + different signs case). (b) Beat frequency between the transmitted and

interference signals.

0.5 1 1.5 2 2.5 3 3.5 4 4.5

Time (s) 10-3

-150

-100

-50

0

50

100

150

No

rma

lize

d a

mp

litu

de

(V

)



Figure 7.11: Low-pass filter output consisting of the desired target signal and a pulse-

like interference signal in the time-domain.

119

than the cut-off frequency. In addition, the frequency-domain low-pass filter output

for the same signal is shown in Fig. 7.12. As shown in the figure, the beat frequency

corresponding to target is buried by the interference. For this low-pass filter output, I

applied the proposed suppression method using the three-level Haar wavelet transform

and hard thresholding, and the result is also shown in Fig. 7.12. Even when the inter-

ference is caused by the fast-ramp FMCW radar, the beat frequency corresponding to

the target is accurately estimated by the CFAR algorithm after applying the proposed

suppression method.


I also conducted actual measurements using commercial automotive radar systems

to verify the performance of the proposed interference suppression method. To imple-

ment the mutual interference scenario, two different commercial automotive radars

were used; one is a radar produced by the Mando Corporation and the other is a

radar made by the Delphi Corporation. The Mando and Delphi radars act as the radar-

equipped vehicle and the interferer, respectively, as shown in Fig. 7.1, and the target

0 100 200 300 400 500 600 700 800 900 1000

FFT index

0

5

10

15

20

25

30

35

40

Ma

gn

itu

de

(d

B)







frequency-domain.

120

is located 145m from the Mando radar. For the antenna system of the Mando radar,

a single-element transmit antenna and a four-element receiving uniform linear array

antenna are used. In addition, the FOV of the Mando radar ranges from −10 ◦ to 10 ◦.

This antenna system transmits the FMCW radar signal in 10-ms signal transmission

interval. During the 10ms of the signal transmission interval, 5ms is allocated to the

transmission times of each up-chirp and down-chirp signal. This transmitted signal is

reflected by the target in the FOV and the reflected signals are received by the array

antenna. In the measurements, fc, ∆B, and ∆T are set to 76.5GHz, 500MHz, and

5ms, respectively. The exact specifications of the Delphi radar are unknown.

Fig. 7.13 shows the low-pass filter output LI(t) of the Mando radar. In the figure,

many pulse-like interference signals appear in the low-pass filter output. As mentioned

in Section 7.4, this phenomenon occurs because the sweep time of the Delphi radar is

much shorter than that of the Mando radar. Through this result, I can guess that the

Delphi radar uses fast-ramp FMCW radar signals. To extract the exact beat frequency

from this signal, I apply the proposed suppression method. Similar to the simulation,

I used a three-level Haar wavelet and hard thresholding method. Using the wavelet

denoising method, I reconstructed the interference signal L(T (t)IDS)(t), as shown

1 1.5 2 2.5 3 3.5 4

Time (s) 10-3

-1000

-800

-600

-400

-200

0

200

400

600

800

1000

Am

plit

ud

e

Figure 7.13: Low-pass filter output of the Mando radar with interference signals from

the Delphi radar.

121

in Fig. 7.14. Then, this reconstructed signal is subtracted from the original low-pass

filter output LI(t) that is given in Fig. 7.13 and the FFT is applied to the interference-

suppressed filter output to extract the beat frequency corresponding to the target.

As shown in Fig. 7.15, without the proposed interference suppression, the beat fre-

quency corresponding to target is buried by the interference, and thus the location of

the target cannot be estimated appropriately. However, the beat frequency correspond-

ing to the target is clearly revealed in the interference-suppressed filter output. In ad-

1 1.5 2 2.5 3 3.5 4

Time (s) 10-3

-1000

-800

-600

-400

-200

0

200

400

600

800

1000

Am

plit

ud

e

Figure 7.14: Reconstructed pulse-like interference signal in the time domain.

100 200 300 400 500 600 700 800 900 1000

FFT index

20

25

30

35

40

45

50

Ma

gn

itu

de

(d

B)

Low-pass filter output (without interference suppression)

Low-pass filter output (with AWEN algorithm)

Low-pass filter output (with proposed interference suppression)




frequency-domain.

122

dition, the estimated distance calculated from this beat frequency is 143.6m, which

is almost equal to the actual distance. I also compared the interference suppression

performance to the AWEN algorithm proposed in [102]. Compared to the proposed

method using wavelet denoising, the AWEN method shows similar interference sup-

pression result, as shown in Fig. 7.15. However, in the AWEN method, to find the in-

terval where the interference occurs, denoted by Ti in Fig. 7.3 (b), both forward-sliding

and backward-sliding windows are applied to the low-pass filter output. In other words,

the stored low-pass filter output must be processed twice. In addition, after identifying

Ti, I have to determine the envelope threshold empirically based on the measurement

data to suppress the amplitudes corresponding to the pulse-like interference signals.

When this threshold was set inappropriately, I confirmed that the interference was not

suppressed. On the other hand, the proposed method using wavelet denoising can be

applied more generally because only the level of the wavelet has to be set.

7.6 Conclusion

In this chapter, I proposed a method to suppress the mutual interference caused

by other radar-equipped vehicles in automotive radar systems. When the radar signal

transmitted from the other radar-equipped vehicle flows into the radar system, the beat

frequency cannot be estimated accurately because the frequency is buried by the in-

creased interference level in the frequency domain. To mitigate the effect of the mutual

interference, I proposed to use the wavelet denoising method. Through this proposed

method, the interference signal was reconstructed and the effect of the interference

was mitigated by subtracting the reconstructed signal from the original low-pass filter

output. The performance of the proposed method was verified through simulations and

actual measurements using heterogeneous automotive radars. In the simulation results,

the proposed method worked properly when multiple targets existed or the mutual in-

terference with a fast-ramp FMCW radar occurred. In addition, through the proposed

123

interference suppression, accurate angle information of the targets could be extracted.

Moreover, even though the exact specifications of the FMCW radar signal transmitted

from the other radar were not identified, the mutual interference was effectively sup-

pressed and the target’s range was estimated accurately in the measurement results.

124

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초록

최근에운전자와보행자의안전에대한관심이높아짐에따라,초음파,영상,라

이더, 그리고 레이더 센서와 같은 차량을 위한 센서들이 중요해지고 있다. 이러한

센서들 중에서, 특히 레이더는 빛이 없는 조건이나 악천후와 같은 악환경 조건에

강하다는 장점이 있다. 이러한 레이더는 차량의 전방이나 후방, 측방에 장착되어

적응형순항제어,자동긴급제동,사각지역탐색과같은특별한기능을수행하며

운전자에게안전과편의를제공한다.

본학위논문에서는차량용레이더시스템을위한향상된신호처리기법들을제

안한다. 일반적으로 차량용 레이더로는 주파수 변조 연속파 레이더가 널리 사용되

는데,이러한차량용레이더의주된목적은타깃까지의상대거리,상대속도,각도와

같은위치정보를추출하는것이다.이들중,차량용레이더시스템은한정된안테나

소자개수를이용하기때문에타깃의각도를추정하는것은쉽지않다.따라서이학

위논문에서는신호대잡음비보정방법이나배열보간법을통한향상된각도추정

기법을제안한다.단순한타깃추정이외에도,차량용레이더시스템은더욱향상된

기능을수행하는것을목표로한다.예를들어,차량용레이더는감지된타깃들을식

별할 수 있어야 한다. 따라서 보행자, 사이클리스트, 그리고 차량을 구분하기 위한

방법을 본 학위 논문에서 제안한다. 또한, 차량용 레이더의 타깃 추정 성능은 철제

터널이나 방음벽과 같은 특정 도로 환경에서 저하되기 때문에, 그러한 구조물들을

인식하고그영향을억제하기위한방법또한이학위논문에서제안한다.마지막으

로,앞으로차량용레이더를장착한차량이증가함에따라발생하는차량용레이더

간 상호 간섭은 타깃 감지 성능을 악화시키기 때문에 심각한 문제를 초래할 수 있

139

다. 따라서 그러한 상호 간섭을 완화하기 위한 방법 또한 본 학위 논문에서 제안할

것이다.

주요어:차량용레이더,타깃감지,타깃식별,클러터제거,상호간섭완화

학번: 2013-20849

140

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