Compressive Sampling based Radar Receiver

Giancarlo Prisco and Michele D’Urso

Innovative Sensors and Systems Analysis, Engineering Directorate, Selex Electronic Systems,

Via Circumvallazione Esterna di Napoli, zona ASI, Località Pontericci, Giugliano di Napoli, Napoli, Italy

E-mail: gianacrlo.prisco@selex-es.com; michele.durso@selex-es.com

Gianpiero Buzzo

SESM s.c.a.r.l.– Finmeccanica Company

c/o Selex Electronic System, Via Circumvallazione Esterna di Napoli, zona ASI,

Località Pontericci, Giugliano di Napoli, Napoli, Italy

E-mail: gianpiero.buzzo@gmail.com

Summary— A typical radar system transmits a wideband pulse (linear chirp, coded pulse, pseudonoise-PN

sequence, etc.) and then correlates the received signal with that same pulse in a matched filter (effecting pulse

compression). A traditional radar receiver consists of either an analog pulse compression system followed by a

high-rate analog-to-digital converter or a high-rate A/D converter followed by pulse compression in a digital

computer; both approaches are complicated and expensive. Achieving adequate A/D conversion of a wideband

PN/chirp radar signal (which is compressed into a short duration pulse by the matched filter) requires both a high

sampling frequency and a large dynamic range. Currently available A/D conversion technology is a limiting factor

in the design of ultra wideband (high resolution) radar systems, because in many cases the required performance

is either beyond what is technologically possible or too expensive. For these reasons, HW and SW solutions have

been adopted, in order to employ more effectively today's technology taking advantage of certain physical

characteristics of the signals, such as the sparsity. In this paper, we introduce a new kind of radar receiver based

on the Compressed Sampling theory - CS, through which is possible acquire and process signals, breaking the

constraint of sampling imposed by Nyquist/Shannon criterion. In CS, an incoherent linear projection is used to

acquire an efficient representation of a compressible signal directly using just a few measurements. The signal is

then reconstructed by solving an inverse problem either through a linear program or a greedy pursuit.

In that regard, the literature provides several alternatives, such as: Random Demodulation, Periodic Non-Uniform

Sampling-PNS; among the more recent and successful stands the so-called Modulated Wideband Converter, MWC.

The MWC extends conventional I/Q demodulation to multiband inputs with unknown carriers, and as such it also

provides a scalable solution that decouples undesired RF-ADC dependencies. The MWC combines the advantages

of RF demodulation and the blind recovery ideas, and allows sampling and reconstruction without requiring

knowledge of the band locations. To bypass analog bandwidth issues in the ADCs, an RF frontend mixes the input

with periodic waveforms. This operation imitates the effect of delayed undersampling, specifically folding the

spectrum to baseband with different weights for each frequency interval. In contrast to undersampling (or PNS),

aliasing is realized by RF components rather than by taking advantage of the ADC circuitry. In this way, bandwidth

requirements are shifted from ADC devices to RF mixing circuitries. The key idea is that periodic mixing serves

another goal—both the sampling and reconstruction stages do not require knowledge of the carrier positions.

In scenarios in which the carrier frequencies are known to the receiver, MWC could play a crucial role to simplify

the analog receiving chain of system radar, since it allows to eliminate the local oscillator STALO and the analog

mixer from the chain, ensuring the possibility of simultaneously acquiring multiband signals; current radar doesn’t

support this operation because it needs to re-tune STALO oscillation frequency for new acquisition. Tuning speed

measures the length of time required for the Local Oscillator to change from one center frequency to another

within a specified accuracy level. In typical systems, when tuning from one frequency to another, the LO usually

slightly overshoots the desired frequency and then settles to the desired frequency within a certain time period,

usually in the order of tens µs for a VCO-based LO; when using a YIG-based LO, it needs tens of ms. In case of

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spectrum blind acquisitions, this technique allows reconstruction of the received signal by sampling at a

minimum rate compared to the traditional rules of Nyquist/Shannon, without loss of accuracy; this means

reduction of the analog-digital converter cost and manage a smaller number of data, thanks to a more

sophisticated processing.

Aim of the paper. This article shows how it possible performs spectrum- blind acquisition of radar signals by using

MWC converter CS based. Results are numerically shown in MATLAB development environment, thanks to a

digital transposition of MWC converter. The software generates a typical signal, reconstructs it, finally calculates

in-phase and in-quadrature components, respectively I and Q. In order to validate the goodness of the information

extraction algorithm, a series of computer simulations have been carried out aimed to reproduce work conditions

as they are close to reality. For this reason, the software has been expressly adapted to generate, and then

acquire, signals whose spectral support is extended, but also scattered. The program generates a signal with

Nyquist frequency equal to 20 GHz. Nevertheless, this considerable spectral extension is occupied by only one

active band, whose thickness is less than 10 MHz. Therefore, in the case of real signals, they got of Hermitian

symmetry spectrum: the addition of the respective conjugated version provides a total calculation of two active

bands. Thus formulated, the signal is an excellent prototype for the RF communications study; being applications

in radar field, the tool generates a down-up chirp signal with carrier between [5-6] GHz, using the following

mathematical formula:

where:

fo = 5.5064 GHz carrier frequency, B = 10 MHz bandwidth, T = 50 μs pulse time

In practice, there is no acquisition entirely immune from noisy components, for this reason, the useful signal will

be overlaid on a white Gaussian noise. The figure below shows the frequency domain of the signals generated.

The spectral analysis shows how RF communications are characterized by a relatively small number of

transmission that deal with very narrow bands, scattered within a very large spectrum.

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

x 1010

0

0.005

0.01

0.015

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0.03Spectrum of original signal and noise

Frequency

Am

plit

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chirp

noise

5.5 5.502 5.504 5.506 5.508 5.51

x 109

0.012

0.014

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0.022

0.024

0.026

Spectrum of original signal and noise

Frequency

Am

plit

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Fig. 1- Right: the spectrum of the original signal and noise. Left: zoom of the chirp signal

Generated signals are processed by the following block diagram.

Fig. 2 - MWC software block diagram

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Following the generation of the useful signal and the noise, first a Radio Frequency band-pass filtering stage - IF

BPF has been provided, by using a digital filter with passband [5-6] GHz. This choice is caused by the MWC

operation, relatively to the fact of bringing in baseband both active bands of the useful signal and the entire

spectrum of the noise.

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x 1010

0

0.005

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Frequency

Am

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Fig. 3 – Signals spectrum after RF-filtering

So, after BPF filtering and mixing, the output of the converter’s LPF filter will only contain the information

content of two active bands of useful signal and the noise spectrum portion contained in [5-6] GHz. Since this is a

mono-band signal, N = 2, the theory ensures that the necessary and sufficient conditions for a good signal

reconstruction are: 1) �� ≥ �� ≥ �, 2) ≥ 2. Based these considerations, the mixing block on the block diagram

will be constituted by a n° of channels m = 4, and a frequency for mixing function of each mixer, fp =15 MHz.

Signals simultaneously enters in the m parallel input channels of mixer, in each of which is multiplied by the i-th

periodic mixing function pi(t), with period Tp. The figure below shows a section of the first channel mixing function,

p1(t):

2 4 6 8 10 12 14 16 18 20

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-0.8

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p1 (t)

Time [x 0.5 psec]

Fig. 4 – Mixing function p1(t)

In each channel, downstream of the mixing stage, both signal and noise are subjected to two further elaboration,

a low-pass filtering and a decimation, this means sampling in baseband. Then the signal and noise sampled

sequences are added up and sent to the CTF block, which implements the reconstruction algorithm, output

providing the reconstructed signal, in-phase and in-quadrature component. At this stage of the process that will

evidence the great advantage introduced by the CS technique, since it allows to acquire a signal at a sampling

frequency, fs = 15 MHz, for each channel, so the entire system is able to reconstruct the signal with overall

sampling frequency of 60 MHz, considerably lower than that required by conventional sampling techniques,

without information on the carrier signal; in this case it would be required sampling frequencies of the order of 10

GHz. The gain in computational time is impressive enough to consider that each channel receives a signal of

1066400 samples and acquires only 800, having defined a decimation factor equal to 1333 for each channel.

The software provides three output graphs:

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1. Overlap of the spectrums: generated signal and reconstructed signal;

2. Overlap of in-fase components: generated signal and reconstructed signal;

3. Overlap of in-quadrature components: generated signal and reconstructed signal;

Figures below shown the results respectively obtained in case of noiseless and signal to noise ratio equal to 20

dB. In all figures, the blue color trace regards the original signal, and magenta color trace regards the

reconstructed signal.

5.498 5.5 5.502 5.504 5.506 5.508 5.51 5.512 5.514

x 109

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Signals Spectrum

frequency

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

x 10-5

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0

1

I - Component

time

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

x 10-5

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0

1

Q - Component

time Fig. 5 – Output plots noiseless case

5.498 5.5 5.502 5.504 5.506 5.508 5.51 5.512 5.514 5.516

x 109

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Signals Spectrum

frequency

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

x 10-5

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1

I - Component

time

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

x 10-5

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Q - Component

time Fig. 6 – Output plots obtained with SNR = 20 dB

Next result shows the system’s ability to acquire multiband signals with unknown carriers. In this case, the useful

signal is composed by the sum of two chirp with carriers frequency f1= 5.2 GHz and f2= 5.5 GHz both with

bandwidth B = 10 MHz and SNR = 20 dB.

The figure below, fig. 7, shows the entire spectrum of filtered signals, chirp plus noise, in which are visible N=4

active bands of the useful signal; the amplitude difference is due to the ripple present in the filter passband which

attenuates frequency components around f1.

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-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

x 1010

0

0.005

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Frequency

Am

plit

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Fig. 7 – Entire spectrum of multiband transmission, N=4

In this case, for a good spectrum blind reconstruction it needs a mixing stage of m ≥ 2N= 8 channels and fp = fs

=15 MHz each one. Clearly, it would be beneficial to reduce the number of channels as low as possible. Theory

ensures that it possible reduces the number of channels at the expense of a higher sampling rate in each channel

and additional digital processing. For these reasons, it has been defined a reduction parameter q=3, so that m ≥

2N/q=2.66, it has been chosen the same m=4 and fs = q∙ fp =45 MHz each channel. In this way, the total sampling

rate of entire system is fTotal = m∙ fs =180 MHz.

Figure below shows output plot related to I-Q component of the generated and reconstructed signal at frequency

f1. The blue color trace regards the generated signal, and red color trace regards the reconstructed signal.

5.195 5.2 5.205 5.21 5.215 5.22

x 109

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Signals Spectrum at frequency f1

frequency

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

x 10-5

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1

2

I1 - Component

time

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

x 10-5

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2

Q1 - Component

time

Fig. 8 – Overlap I-Q component of generated and reconstructed signal at frequency f1

Figure below shows output plot related to I-Q component of the generated and reconstructed signal at frequency

f2. The blue color trace regards the generated signal, and magenta color trace regards the reconstructed signal.

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5.495 5.5 5.505 5.51 5.515

x 109

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Signals Spectrum at frequency f2

frequency

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

x 10-5

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1

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I2 - Component

time

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x 10-5

-2

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Q2 - Component

time

Fig. 9 – Overlap I-Q component of generated and reconstructed signal at frequency f2

Conclusions and future developments. The bottom line is that CS-based techniques are likely to be very useful in

selected but important situations, such as ones with a few relatively strong narrowband signals with unknown

carrier placed over a very large frequency band. The results shows how the use MWC converter based on CS

theory, could play a crucial role to simplify the analog receiving chain of a system radar, because it would allow to

reduce the cost of the analog-digital converter and manage a smaller number of data, by sampling at a minimum

rate compared to the traditional rules of Nyquist/Shannon, without loss of accuracy on the reconstruction of the

received signal, thanks to a more sophisticated processing. Next steps include the implementation of further

simulations aimed to validate the correctness of the signal acquisition software, with increasingly narrow spectral

widths signals on the order of 2-3 MHz, in order to make the system more robust and insensitive to noise and

evaluate a possible implementation FPGA.

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