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AbstractGSM is featured by significant inter-symbol interference. Equalization isthus an important function of the receiver system. Channel estimationand maximum likelihood sequence detection are performed by theequalizer.

In this thesis, the application of feedback for channel re-estimation andsequence detection is studied. Feedback data from the first equalizationand from the decoder output are considered for channel re-estimationwith extended data. In this case, taking two channel estimates per burstwas considered to cope with fast speeds. Decoder feedback, which is thehard bit decisions on coded bits, was also used in assisting sequencedetection during re-equalization. This was done for the speech service,TCH/FS, using its block diagonal interleaving feature. Channel re-esti-mation is also tested on one of the coding schemes of GPRS.

Using only equalizer feedback does not give any improvement. Feed-back from the decoder used for both channel estimation and sequencedetection results in a gain in SNR around 1 dB, considering the BER afterdecoding. This is allowing a delay of 20 ms in TCH/FS. To avoid delay,mixed decoder and equalizer feedback is used to give 0.5-0.6 dB gain.With co-channel interference, the gain reduces to 0.15-0.25 dB. ForGPRS, a gain of 0.8 dB is achieved for BLER.

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Acknowledgement

I am very much grateful to my supervisors Magnus Björklund and UlfHill at Ericsson Radio Systems for their valuable consultation and sup-port throughout this thesis work. I would also like to sincerely thank myexaminer at Chalmers, Prof. Arne Svensson.

Many thanks to all people in SRF/BT and SRF/BU from whom I hadhelp at different times.

I take this opportunity to record my indebtedness to the Swedish Insti-tute that sponsored my Master’s study in Sweden.

Finally, I humbly thank my family for blessing me with abundant loveand support all the time. My distance from home during this study andwhat I missed as a result, helped me realize how big and precious theirpart in my life is.

Girum Alebachew

Stockholm, SWEDEN

May 2001

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Table of Contents

1 Introduction 1

1.1 Background . . . . . . . . . . . . . . . . . 1

1.2 Theme of the Thesis . . . . . . . . . . . . . . 2

1.3 Outline . . . . . . . . . . . . . . . . . . . 2

1.4 Abbreviations . . . . . . . . . . . . . . . . 2

2 Basic Theory 4

2.1 Source coding . . . . . . . . . . . . . . . . 4

2.2 Channel coding . . . . . . . . . . . . . . . . 4

2.2.1 Block coding . . . . . . . . . . . . . . 52.2.2 Convolutional coding . . . . . . . . . . . 52.2.3 Decoding of convolutional codes . . . . . . . 72.2.4 The Viterbi Algorithm (VA) . . . . . . . . . 8

2.3 The radio channel . . . . . . . . . . . . . . . 9

2.3.1 Shadowing, fading and inter-symbol interference (ISI) 92.3.2 Models of multipath fading . . . . . . . . . 102.3.3 Noise and interference . . . . . . . . . . . 11

2.4 Interleaving . . . . . . . . . . . . . . . . . 12

2.5 Modulation, Demodulation and Equalization . . . . . 12

3 Overview of the GSM System 13

3.1 Basic architecture . . . . . . . . . . . . . . . 13

3.2 System features . . . . . . . . . . . . . . . . 14

3.2.1 Multiple access . . . . . . . . . . . . . 143.2.2 Physical and logical channels . . . . . . . . 14

3.3 Channel coding . . . . . . . . . . . . . . . . 15

3.3.1 TCH/FS . . . . . . . . . . . . . . . . 153.3.2 PDTCH/CS-1 . . . . . . . . . . . . . . 16

3.4 Modulation . . . . . . . . . . . . . . . . . 17

3.5 Propagation models . . . . . . . . . . . . . . 18

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4 Algorithms and Implementation 19

4.1 Simulation platform . . . . . . . . . . . . . . 19

4.2 The RBS receiver system . . . . . . . . . . . . . 19

4.2.1 Synchronization . . . . . . . . . . . . . 204.2.2 Channel estimation . . . . . . . . . . . . 204.2.3 Maximum Likelihood Sequence Estimation (MLSE) . 224.2.4 The Soft Output Viterbi Algorithm (SOVA) . . . . 224.2.5 Quality measures . . . . . . . . . . . . . 234.2.6 Deinterleaving and decoding . . . . . . . . 24

4.3 Implementations . . . . . . . . . . . . . . . 24

4.3.1 Schemes for channel re-estimation . . . . . . . 244.3.2 Channel estimator with extended training sequence 254.3.3 Variation of the channel . . . . . . . . . . 264.3.4 Delay adding and non-delay adding schemes . . . 264.3.5 Hard decision feedback for sequence detection . . 28

5 Test cases and results 30

5.1 Equalizer feedback for channel re-estimation . . . . . . 30

5.2 Decoder feedback with delay on TCH/FS . . . . . . . 30

5.2.1 Channel re-estimation . . . . . . . . . . . 305.2.2 Two channel estimates per burst . . . . . . . 345.2.3 Sequence detection using feedback . . . . . . 36

5.3 Decoder feedback without delay on TCH/FS. . . . . . 37

5.3.1 Channel re-estimation . . . . . . . . . . . 375.3.2 Sequence detection using feedback . . . . . . . 415.3.3 Diversity and interference tests . . . . . . . . 44

5.4 Channel re-estimation on GPRS-CS1. . . . . . . . . 47

6 Summary 48

Appendix 49

References 55

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1 Introduction

1.1 Background

GSM (Global System for Mobile communication) is a digital cellularradio communication system. There are several speech and data servicesthat the system supports. A reliable communication against noise, inter-ference and disturbances due to the radio channel is always of interest insuch a system. The GSM standard sets performance requirements leav-ing the receiver implementation open. Thus, new algorithms that boostreceiver performance could be implemented. That is what this study setsout to do.

The radio channel in GSM poses significant multipath fading leading tointer-symbol interference (ISI). Besides, the channel has stochasticnature and needs to be estimated. Such channel estimation is conven-tionally carried out using known training bits embedded in each trans-mitted burst. The part of the receiver that fights ISI is the equalizer. Itperforms channel estimation and optimal sequence detection on everyburst.

To achieve reliable communication, the system also uses channel coding.The type of coding used, differs from service to service but, in general,convolutional codes are involved for error correction. To render thecodes efficient, interleaving of coded blocks is also utilized, which is ser-vice specific. In full-rate speech (TCH/FS), for instance, two blocks areinterleaved together into each burst.

In a conventional receiver system, a cascade of independent equaliza-tion and decoding is used. Joint equalization and decoding, called turboequalization is aimed at combining the two processes with a feedbackbetween them. Due to better coupling between the equalizer anddecoder, turbo equalization leads to improved performance [16-18].Using the nature of interleaving, it is also possible to apply hard bit deci-sion feedback from the decoder and help the equalizer to select a bettersequence in a manner simpler than the turbo approach [19]. This kind ofscheme is used in this study.

Another focus of improved detection is in channel estimation. The aimhere is to improve the initial channel estimate derived from the trainingbits. Since the training sequence is relatively short, the accuracy of thechannel estimate may be low. Using decision feedback to extend the dataused for channel estimation, a better estimate could be achieved. Thisleads to improved performance of the equalizer [20,21]. Such a feedbackcould come from the first equalization or from the decoder.

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1.2 Theme of the Thesis

The task of this thesis is to explore methods of using feedback toimprove the performance of the GSM equalizer, with the focus on thechannel estimation and sequence detection operations.

Relevant schemes are to be formulated and implemented in the systemsimulator, SYSSIM. Comparison is to be made between equalizer anddecoder feedback, delay-adding and non delay-adding schemes etc. Theexisting receiver system is used as a baseline and modifications will bemade in the affected functional blocks.

Performance and complexity analysis on the implementations is also tobe carried out. Different channel models under interference and diver-sity will be considered.

1.3 Outline

Chapter 2 opens the thesis with some basic theory on digital communi-cation, relevant to this study. An overview of the GSM system is given inchapter 3. Chapter 4 deals with algorithms and implementation. Herethe receiver system used as a baseline in the study is described. Besides,the implemented schemes are outlined. The specific test cases and theresults obtained from simulation are presented in chapter 5. Summariz-ing notes are finally given in chapter 6. Plots of simulation results arealso documented as an appendix.

1.4 Abbreviations

AFC Automatic Frequency CorrectionAWGN Additive White Gaussian NoiseBER Bit Error RateBTS Base Transceiver StationCRC Cyclic Redundancy CheckCS Coding SchemeFIR Finite Impulse ResponseFS Full-rate SpeechGMSK Gaussian Minimum Shift KeyingGSM Global System for Mobile communicationIRC Impulse Response CombiningISI Inter-Symbol InterferenceLLR Log Likelihood RatioLS Least SquareML Maximum LikelihoodMLSE Maximum Likelihood Sequence EstimationMS Mobile StationPCM Pulse Code ModulationPDTCH Packet Data Traffic Channel

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SFQ Soft Frame QualitySOVA Soft Output Viterbi AlgorithmTCH Traffic ChannelTDMA Time Division Multiple AccessTSC Training SequenceVA Viterbi Algorithm

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2 Basic TheoryFig. 1 shows basic functional blocks of transmission and reception indigital radio communication. It is used as a starting point to discusssome basic principles pertaining to this work.

2.1 Source coding

The purpose of source coding is to transform the information from thesource into digital format (if not already so) and remove redundancies(compress the data) to achieve low data rate. The reverse task of regener-ating the original signal is done by the source decoder in the receiver.The compression process could be lossy or lossless. The former intro-duces some distortion that the decoder can not compensate even witherror free communication. A typical example of source coding is speechcoding. In GSM, the speech coder has a bit rate of 13 kbps that gives acompression ratio of 4.92 compared to the 64 kbps in PCM telephony.More on source coding can be found in [1].

2.2 Channel coding

Channel coding is a process whereby redundancy is cleverly added tothe desired information prior to transmission. The aim here is to enablethe receiver to detect the presence of errors and/or correct them andrecover the information. The major cost is increased data rate and band-width. The two major types of channel coding schemes, namely, blockand convolutional codes, are briefly discussed next.

Figure 1. System model for digital radio.

{Source SourceCoding

ChannelCoding

Interleaving Modulation

RadioChannel

SourceDecoding

ChannelDecoding Deinterleaving

DemodulationSink &

Equalization

Transmitter

Receiver

{

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2.2.1 Block coding

A binary (n,k) block code maps a block of k information bits into an n-bitcode word by adding (n-k) redundant bits (parity check bits) computedfrom the information bits. The code rate

(1)

shows the amount of overhead due to the code.

If the information bits appear unaltered in the code word, the code iscalled a systematic code. The code word v will then have a structure as

(2)

Block codes can be used to detect or correct errors or simultaneously doboth. An important feature of merit in this regard is the minimum Ham-ming distance of the code, dmin, which is defined as the minimum numberof bit positions on which any possible pair of code words could ever dif-fer. This relates to the error detecting capacity of the code, defined as themaximum number of errors that could be detected in a given receivedword as

(3)

With a similar definition, error correcting capacity of a block code is givenby

(4)

and simultaneous error correction and detection are related by

(5)

where Ncorrect < Ndetect < dmin.

Among block codes, a subset called cyclic codes have simple encodingand decoding schemes that makes them popular. More on block codescould be found in [2].

2.2.2 Convolutional coding

A convolutional code (n,k,m) has n outputs, at any given time, thatdepend on the k inputs at that time and the previous m input blocks. The

Rkn---=

v u0 u1 … uk 1–, , , p0 p1 … pn k– 1–, , ,,( )=

Information bits Parity bits

Ndetect dmin 1–=

Ncorrectdmin 1–

2-------------------=

Ndetect dmin Ncorrect– 1–=

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code rate is defined as in block codes. In the more common case where k= 1, the encoding can be done with a sequential circuit using a shift reg-ister of length m+1. A convolutional code is used together with a likeli-hood decoding scheme that makes it efficient in correcting errors. Such adecoding algorithm is discussed later in this section.

The convolutional code used in GSM (TCH/FS) (see section 3.3.1) istaken here as an example. It is a (2,1,4) code defined by the generatorpolynomials

G0 = D4 + D3 + 1 (6)

G1 = D4 + D3 + D + 1 (7)

These polynomials represent the discrete impulse response that theinput sequence is convolved with to generate the convolutional code.Fig. 2 depicts the encoder.

Unlike block coding, the convolutional coding scheme can work with acontinuous stream of input data. However, blocks are used in practice.Thus, in this example, for a block input sequence u = (u0, u1,...., uN-1),the output sequence will be v = (v0, v1,..., v2N-1) having double thelength of the input (the code rate is 1/2).

For each new block to be decoded, the encoder memory is reset to zeroat first. The output of the encoder at time n depends on the input bit unand the encoder state, defined by the 4 preceding bits that have beenshifted into the registers, (un-1, un-2, un-3, un-4). Thus, there are 42 = 16possible states. The total number of bits that the output depends on, at agiven time, is referred to as the constraint length1 of the code, which inthis case is five. At the end of the information bits, the encoder memoryis cleared by shifting in m=4 zeros, called tail bits.

Figure 2. Convolutional encoder for GSM TCH/FS.

1. Constraint length may also be defined as just the memory, m, of the code.

D0 D1 D2 D3 D4

G0

G1

Encoder State (memory)InputSequence

Coded sequence

u=(u0, u1, ...)

(v1,v3,...)

(v0,v2,...)

v=(v0,v1,v2,...)

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2.2.3 Decoding of convolutional codes

The state and input define the output of a convolutional encoder at agiven time. The state diagram of a sample (2,1,2) convolutional code ispresented in Fig. 3a. It gives a complete information regarding the code.A convolutional code could be visualized as a series of transitions fromone state to another, dictated by the input. It could be noticed that thereare two possible branches originating from, and leading to, a given state,which is true for any (n,1,m) binary code.

An insightful representation of the encoding/decoding process is thetrellis diagram which depicts the evolution of state transitions in time(Fig. 3b).

The task of the maximum-likelihood(ML) decoding is, given a receivedsequence, r, to find the code vector, , that maximizes the log likelihoodfunction

Figure 3. State and trellis diagrams for a convolutional code.

00

01

10

11

...

...

...

...

state t=0 t=1 t=2 t=3 t=4 t=N-2 t=N-2 t=N-1

00

1001

11

0/00

1/110/

11

1/00

0/01

1/10

1/01

0/10

old stateinputoutput

new state

(a) state diagram of a (2,1,2) convolutional code

(b) trellis diagram

1/11

1/10 0/10

1/00

0/10

0/11

Example: input (1,1,0,1,...,0,0)output (11, 10, 10, 00, ..., 10, 11)

statepossibletransitionactualtransition

v

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(8)

where

(9)

and vi and ri correspond to time instant i. In the case of a binary sym-metric channel, the ML criterion is equivalent to minimizing the Ham-ming distance metric [2] given by

(10)

There are 2N possible code words corresponding to an N-bit input. Anysuch code word corresponds to a path that could be traced on the trellisdiagram following some of the possible transitions. The search for thesequence that minimizes Eq(10) is efficiently done using the Viterbi algo-rithm which is based on the notion of such state transitions.

2.2.4 The Viterbi Algorithm (VA)

Consider the trellis of an (n,1,m) code. Suppose that at time step k, theminimum partial metrics and the corresponding path (input sequence)u(sk) = {u0(sk), u1(sk),...,uk(sk)} leading to all states, sk, are known andstored. The metrics could be as in Eq(10) for hard symbol decisions, or asin Eq(9) if the probabilities of the received symbols (soft decisions) areavailable. It was mentioned earlier that there are two branches that leadto a given state. At the next step, k+1, the metrics of these two branchesare compared. The path with the smaller metric will be kept as the survi-vor and the other is discarded. The new metric and path will then bestored for that state. This will be done for each state, at all time steps.The procedure is initialized with zero metric for the initial state (zerostate) and infinite for all the rest. For a code concluded by known tailbits, the trellis converges to a single state (Fig. 3b). The path history ofthe state at the last step is then the result of the decoding according toEq(10).

To realize the above outlined procedure, for an (n,1,m) code with blocksize N, a storage of the metric as well as an N-bit path history, is requiredfor the 2m states. As this becomes impractically big for large N, the algo-

v P r v( )log{ }v

maxarg=

P r v( )log P ri vi( )logi 0=

N 1–

∑=

d r v,( ) d ri vi,( )i 0=

N 1–

∑=

v d r v,( ){ }v

minarg=

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rithm is modified to work with a storage of a δ−bit path history. Thisdemands making the first bit decision at time step δ and continuing todo so for subsequent bits thereafter. For δ > 5m, all survivors stem fromthe same input, δ steps back, with “high” probability and such decisionsare likely to be identical to the ML decision [2].

2.3 The radio channel

2.3.1 Shadowing, fading and inter-symbol interference (ISI)

Shadowing vs. fading

The intensity of radio waves in free space decays with the square ofpropagation distance. In the practical indoor or outdoor radio channel,the average signal power decays exponentially with distance, with somepathloss exponent, n, greater than two. Besides, the random variation ofthe signal power over the same propagation distance, in dB, is modelledto have normal distribution, which is known as log-normal shadowing.Therefore, the received power at a distance d is given by

(11)

where do is a reference distance, and Xσ is a zero-mean, Gaussian ran-dom variable of variance σ2.

In mobile radio communication like GSM, a line of sight between BTSand MS is not in general available due to natural and man-made barri-ers. Thus, the signal envelope at the antenna output is the composite ofseveral waves reaching the receiver after reflection, scattering and dif-fraction along different paths and transmission conditions. Unlike log-normal shadowing, this process, known as multipath fading, causes largesignal variation over distances in the order of a wavelength. Mobility ofthe MS or the barriers in the transmission path will also result in fasttime variation of the signal, in the order of seconds [3].

Flat fading vs. frequency selective fading

The effect of multipath fading on the received signal depends on thebandwidth of the signal. This is because, the different frequency compo-nents in a signal will be affected differently by the multipath fadingchannel. An important parameter in this regard is the coherence band-width, that reflects the frequency range for “strong” amplitude correla-tion after fading [3].

P d( ) Pav do( ) 10nddo----- log– Xσ+= dB[ ]

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For a narrow-band transmission where the signal bandwidth is muchgreater than the coherence bandwidth, fading introduces very little orno frequency distortion. This is called flat fading. Flat fading could alsobe viewed in the time domain to be the result of multipath signals whosetime shift is so small, compared to the symbol duration, that they add upto one undistorted signal.

On the other hand, if the signal bandwidth is larger than the coherencebandwidth of the channel, different frequency components of the signalwill be affected differently by the channel. This is referred to as fre-quency-selective fading. In time domain, the multipath components of thesignal will have significant time dispersion compared to the symbolperiod. The result is inter-symbol interference (ISI). In GSM, the trans-mission bandwidth is large enough to result in frequency selective fad-ing with significant ISI. Notice that the term “symbol” in the abovediscussion refers to what is modulated and appears on the channel; inCDMA for instance, this would be the “chip”.

2.3.2 Models of multipath fading

Rayleigh fading

The envelope of a flat fading signal is commonly modelled by a Ray-leigh distribution which is given as

(12)

Such a model is more accurate when there is no line of sight pathbetween transmitter and receiver. In the case when such a non-fadingcomponent is present, the multipath scenario is modelled by Ricean dis-tribution.

An important parameter for the spectrum of a flat fading signal, and totime variation of the envelope, is the doppler frequency shift, whicharises from the relative motion between receiver and transmitter. It isrelated to the speed, v, as

(13)

With a higher doppler shift (higher speed), the envelope variation will

p x( )x σ2⁄( ) x2

2σ2---------–

exp 0 x ∞<≤

0 x < 0

=

where x is amplitude of the signal envelope.

f dvλ---= where λ c

f--- is the wavelength=

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also be faster. This, in turn, will have an effect on the choice of channelcoding and interleaving.

Tapped delay line channel model

One possible model for a frequency selective radio channel is a transver-sal filter with tap spacing τi and random complex gains αi(t) as in Fig. 4[4]. This is an approximation of the actual multipath components thatare continuous in time into discrete pathes at different delays. Each ray,αi(t), will then be modelled as a flat fading channel, with Rayleigh orRicean spectrum.

2.3.3 Noise and interference

Noise and interference are common transmission nuisances in radiocommunication. Noise is an inevitable problem, that is usually modelledas additive, white and gaussian (AWGN). The Gaussian distributionmodel is due to the central limit theorem and the fact that noise is thecumulative result of contributions from a number of independentsources.

Cellular mobile radio communication systems like GSM rely on fre-quency reuse, where the same radio frequency serves users in geograph-ically separated cells. This introduces co-channel interference coming fromthe cells using the same carrier frequency as the one of interest. There isalso adjacent channel interference due to partial spectral overlap betweenneighboring radio frequency channels in the case when there are suchchannels.

Figure 4. Tapped delay line model.

τ1 τ2 τ3 τN...

α1(t) α2(t) αN(t)

y t( ) αn t( )s t τn–( )n 1=

N

∑=

s(t)

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2.4 Interleaving

A salient feature of the radio channel, as surveyed in the previous sec-tion, is fading. Under fading, the received signal becomes particularly“bad”, when the channel is in deep fade, at some times. This results in anumber of bits being in error at the receiver output, in bursts. Suchbursty errors are intractable to most channel codes, which howeverwork quite well with random errors. Interleaving is a mechanism usedto counteract this problem. It is the reshuffling of the coded bits beforethey are sent over the fading radio channel. The reverse operation, de-interleaving, then randomizes the burst errors at the receiver output,before channel decoding. The cost of interleaving is delay and need forbuffering at both transmitter and receiver.

2.5 Modulation, Demodulation and Equalization

Referring to Fig. 1, modulation is performed in the transmitter using thedigital signal to vary the frequency, phase or amplitude of the high fre-quency carrier. This creates a signal suitable for transmission over theradio channel. The selection of modulation involves trade-offs betweenefficient use of the radio spectrum, power efficiency, resistance to chan-nel impairments, system complexity, etc. Further discussion of modula-tion is not relevant to this thesis and will not be pursued.

The demodulator in the receiver is responsible to extract the basebandsignal from the modulated carrier. If the radio channel is frequencyselective fading, the demodulated signal will suffer from ISI. Thisrequires further processing called equalization. Equalization is discussedfurther with respect to the GSM receiver in section 4.2.

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3 Overview of the GSM System

3.1 Basic architecture

GSM is a digital cellular mobile communication standard aimed at giv-ing voice and data services. The basic functional entities and intercon-nections of the system are shown in Fig. 5.

The Mobile Station (MS) is the subscriber equipment used to access ser-vices from the system. It is typically hand held or vehicle mounted. Italso has a unique identity. The base station system (BSS) comprises ofthe base transceiver station (BTS) and the base station controller (BSC).The BTS gives radio coverage to a given geographical area called a cell.All MS’s in a given cell will thus communicate via a radio interface to aBTS. The control functions of the BSS are carried out by the BSC, whichserves several BTSs. Its tasks include power control, connection moni-toring and intra-BSC handover.

The mobile-services switching center (MSC) handles the switching func-tions needed for mobiles in an area consisting of a number of BSCs.Together with registry subsystems, the MSC manages the set-up, rout-ing, control and termination of calls. It also takes care of handoverbetween BSCs under its control or involving other MSCs. Interworkingfunctions with fixed networks is also the task of the MSC [7].

Figure 5. Fundamental architecture of GSM.

MSC&

registrysub-systems

Fixed

Networks

MS BTS

other MSC

MS - Mobile StationBTS - Base Transceiver StationBSC - Base Station ControllerMSC - Mobile services Switching

Center

BTSMS

MS

BSC

other BSC

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In this thesis, only the radio link between the MS and the BTS, specifi-cally, the receiver system within the BTS, is of interest. Thus, all furthersystem descriptions will focus on relevant items.

3.2 System features

3.2.1 Multiple access

GSM is an FDD/TDMA system. Frequency bands are allocated in the900, 1800 and 1900 MHz bands for the system. Distinct up and downlinkfrequency channels constitute the full duplex communication, which iscalled frequency division duple (FDD). The multiple access scheme isTDMA with 8 time slots per carrier. The available radio spectrum is par-titioned into 200 kHz radio frequency channels. The time and frequencydomain layout of the system looks as in Fig. 6.

3.2.2 Physical and logical channels

A physical channel of GSM consists of one of the eight time slots in thesequence of TDMA frames of a given carrier. Broadly, there are twotypes of logical channels called traffic and control channels. Traffic chan-nels carry user speech or data, while control channels convey signallingor synchronization data.

In this thesis, the full rate speech (TCH/FS) traffic channel for speechservices at a gross rate of 22.8 kbps and one of the packet data traffic

Figure 6. Time and frequency layout of GSM [5].

Time

Fre

qu

ency

ch 1

ch 2

....

.

ch 3

0 1 2 3 4 5 6 7 8

8 time slots200 kHz

TDMA Frame

= physicalchannel

time slot

4.615 ms

Radio frequency channels0.577 ms

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channels (PDTCH - CS1) were considered. The channel specific featuresin the upcoming sections will thus focus on these two logical channels.A number of other traffic and control channels are also available in GSMthat will not be mentioned here.

During a given time slot of a physical channel, a modulated data streamcalled burst is transmitted/received. The type of burst pertinent to thisstudy is the normal burst which has the format of Fig. 7.

The training sequence in the middle of the burst takes one of the 8 possi-ble sequences and will be known to the receiver. 114 user bits are carriedon the left and right half of the burst (57 bits each) and could beencrypted. The tail bits are also specified as zeros. The guard periodallows for the necessary ramp up and down to attenuate transmission atthe beginning and end of bursts. In TCH/FS, the steal-flag bits indicateif the traffic channel was “stolen” and control data was sent instead onthat specific burst [8].

3.3 Channel coding

The channel coding in GSM is in general an outer block coding followedby inner convolutional coding. The coded blocks are then interleavedover a number of bursts. The block size and interleaving depth are chan-nel dependent. The exact schemes are next discussed for the TCH/FSand PDTCH/CS1 logical channels.

3.3.1 TCH/FS

In the full-rate speech channel, data blocks of 260 bits (20 ms of speech)come from the speech encoder. These bits are classified according totheir importance and protected differently as shown in table 1. Thechannel coding looks as in Fig. 8.

Figure 7. Structure of a Normal Burst.

Duration

(bits) 3 57 1 26 1 57 3 8.25

1 time slot = 577us (15/26) ms

content:bitstail encrypted

bitsencryptedbits bits

tail guardperiod

trainingsequencebits

steal flag bits(0,0,0) (0,0,0)

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The CRC code is a systematic cyclic code used for single error detection,while the convolutional code was cited as an example in section 2.2.2.Details on the codes and reordering can be found in [9]. The interleavinghas however an impact on this study and deserves more discussion.

The 456 bits consisting of 378 coded bits (82.7%) and 78 uncoded bits(17.3%) are input to the interleaver. These bits could be accommodatedon 4 normal bursts (4 x 114 = 456). However for better performance, theyare further spread out into 8 bursts. The so called block diagonal inter-leaving is applied in which a given block is interleaved with two neigh-boring blocks. This is depicted in Fig. 9.

3.3.2 PDTCH/CS-1

There are thirteen coding schemes specified for the packet data trafficchannel (PDTCH) of which CS-1 is one. Fig. 10 illustrates this codingscheme.

The FIRE code is a systematic binary block code used for error correctionand detection. This code is particularly suited for burst errors as exhib-ited by the output of convolutional decoding when the code fails to cor-rect all errors. The inner convolutional code is identical to the one usedin TCH/FS. The interleaving however is block rectangular. This meansthat a new data block starts every fourth burst and it is reordered and

Category Number of bits Protection

Class 1a 50 CRC code for single error detection;1/2 rate convolutional code

Class 1b 132 1/2 rate convolutional code

Class 2 78 unprotected

Table 1 Class of bits and coding in TCH/FS.

Figure 8. Channel coding for TCH/FS [20].

CRCcode

Reo

rder

ing

Convolutional

Reo

rder

ing

coding, R=1/2

4 tail bits

456 bits

class 1a - 50

class 1b - 132

class 2 - 78

53

185 378

to interleaver

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distributed over four bursts, without mixing with other blocks.

3.4 Modulation

GSM uses Gaussian Minimum Shift Keying (GMSK) which is a modula-tion scheme in which the phase of the carrier is instantaneously variedby the modulating signal (i.e. the information to transmit). It is featuredby constant envelope, good spectral efficiency and robustness againstsignal fading and interference [12].

Fig. 11 is a schematic representation of the modulation process. The pre-modulation Gaussian filter with 3 dB bandwidth bit-interval product,BT=0.3, is used to smooth out the phase response of ordinary MSK. Thisresults in a desirable, compact output spectrum. However, it alsospreads the effect of an input bit over several bit periods thereby intro-ducing intersymbol interference. The receiver should thus use an equal-izer to remove this controlled interference. Equalization is described insection 4.2.

Details about modulation can be obtained in [10].

Figure 9. Block-diagonal interleaving in TCH/FS.

Figure 10. Channel coding of PDTCH/CS-1.

......

......

ReorderedBlocks

Bursts

FIRE codeConvolutional

code

4 tail bits

InputBlock

184 224 456 Block-rectangu-lar Interleaving

4 bursts

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3.5 Propagation models

In the GSM system, the mobile radio environment between the base sta-tion and MS is featured by highly dispersive multipath resulting in fre-quency selective fading. The tapped delay line model that uses discretemultipath rays was discussed in section 2.3, for these kind of channels.In line with this model, the GSM standard presents typical real-life prop-agation parameters for rural area (RA), hilly terrain (HT), typical urbanarea (TU) and very small cells (TI) as well as a model for equalizationtest (EQ) [11]. The parameters are the time delay, average power andtype of fading (Rayleigh or Ricean) of the taps in 12 and 6 tap settings.This is used together with the speed of the MS for simulating the radiochannel. The notation used to refer to a propagation condition is thetwo-letter name and speed in km/h; TU50, for instance, denotes an MStravelling at 50 km/h in urban area. As an example, Fig. 12 depicts themultipath profile of the TU model in the 6-tap setting.

Figure 11. Schematic representation of GMSK modulation [12].

Figure 12. Multipath profile of the TU model, 6-tap setting.

Gaussianfilter

α t( )

ϕ t α i,( )

td∫

cos

sin

2πf 0t( )cos

2πf 0t( )sin–

differentiallyencoded,

bipolar NRZmodulating

signal

2πf ot ϕ t α i,( )+( )cos

phase pulse shaping

BT = 0.3

Modulated carrier

0 1 2 3 4 50

0.2

0.4

0.6

0.8

1

1.2

Delay in us

Rel

. Pow

er

Multipath Profile of the TU Model

All taps Rayleigh fading

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4 Algorithms and Implementation

4.1 Simulation platform

The simulation platform called SYSSIM is used to analyze the perfor-mance of the algorithms in this study. In this simulator, the actual signalprocessing modules are coded in C and stored in a library called CESIL.The functional blocks like ‘Equalizer’, ‘Encoder’, etc. are realized by aC++ program at a higher level using objects which are the modules inCESIL. A model building tool is used to configure the functional blocksforming the desired communication chain to be simulated. The blocksare also controlled by a set of parameters passed as an argument beforeexecution.

4.2 The RBS1 receiver system

The discrete-signal part of the GSM receiver system used in this studylooks as in Fig. 13.

The GMSK demodulator provides I and Q samples, represented by thecomplex signal rk, at a rate of one sample per symbol. If diversity isused, there will be two branches of such samples.

The big block called equalizer is the main focus of this study. In the equal-izer, synchronization, channel estimation and maximum likelihoodsequence estimation are performed on every burst. The outputs are bitdecision and reliability values (soft values) as well as parameters indi-cating quality of the detected burst. The detected bursts are then deinter-

1. RBS (Radio Base Station) is the Ericsson terminology for BTS

Figure 13. Digital part of the RBS receiver system.

MLSE

Synchronization&

Channel Estimation

Deinterleaver

Decoder&

From GMSKdemodulator

rk

trainingsequence

h

bits &soft

transmitted bits, bk

bk BERAnalysis

Equalizer

quality

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leaved and decoded. In the simulator, the output of the decoder isanalyzed for error rates.

In the sequel, the operations within the receiver system are described.

4.2.1 Synchronization

To find the position of the burst in the sample buffer, synchronization isperformed. All eight possible training sequences used in normal burstsare cyclic white. If T = {t0, t1,..., t25}, ti ε {-1, 1}, is the training sequence thenormalized autocorrelation computed over the central 16 bits, RT(k) isthe delta function over lags between -5 and 5, given as

(14)

Utilizing this property, synchronization is performed by correlating thereceived samples and the central sixteen bits of the training sequenceover a correlation window of size eleven, around the nominal burst cen-ter. The actual burst position is then estimated using an algorithm thatconsiders the energy center of the computed correlation sequence.

4.2.2 Channel estimation

The transmission of bits between source and demodulator output ismodelled as in Fig. 14. The complex FIR filter represents the multipathnature of the radio channel as well as the controlled ISI due to GMSK, inbase band. A five-tap filter is used in the specific implementation that isstudied. The noise process within the receiver could be modelled ascomplex AWGN. However, in practice there will also be interferenceand n represents all disturbances in general. The task here is to find opti-mum filter coefficients, h, from the received sample sequence, r, and theknown training sequence for a given burst. This approach implicitlyassumes that the radio channel does not vary significantly in the dura-tion of one burst. More investigation on this issue is presented in section4.3.3.

Consider only the part of the burst corresponding to the trainingsequence (TSC), assuming the TSC bits are b0,...,bN-1, for simpler nota-tion. The first 4 samples of the received signal are interfered by data out-side the TSC; the rest, that depend only on the TSC bits, could be writtenin matrix form as

RT k( ) 116------ ti k+ ti⋅

i 5=

20

∑ δ k( )= = for k = -5,...,5

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(15)

In vector notation, Eq(15) can be written as

(16)

Using the method of least squares, the optimum channel impulseresponse, called LS estimate, is given by

(17)

The solution to Eq(17) is [6]

(18)

The elements of the matrix BHB are actually correlations along the col-umns of matrix B, which are parts of the same sequence with relativeshift. Thus, the off diagonal elements are small compared to the maindiagonal. The approximation

(19)

and a sub-optimal channel estimate

(20)

follow from this observation.

Figure 14. Transmission model.

FIR filterh

noise + interference

rreceived samples

nchannel model

inputsequence

b

r4

r5

˙

˙

rN 1–

r

b4 b3 … b0

b5 b4 … b1

˙ ˙ ˙

˙ ˙ ˙

bN 1– bN 2– … bN 5–

B

h0

h1

h2

h3

h4

h

•

n4

n5

˙

˙

nN 1–

n

+=

r B h n+⋅=

hLS

h r Bh–2{ }

hminarg=

h BT B( ) 1–BT r=

BT B( ) N 4–( )I5 5×≈

h1

N 4–-------------BT r=

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Eq(20) is simply a set of correlations between the received sequence andthe training sequence and can be called correlation estimate.

The LS estimate is used in the system under study. Since the training bitsare known before hand, matrix inversion is avoided by using table look-up where the term (BTB)-1 is pre-computed and stored.

The estimated taps of the channel inevitably contain noise. To reducethis, the LS estimate is modified by an algorithm called impulseresponse combining (IRC) which scales up the largest tap of the channelestimate, relative to the rest. A single-tap channel estimate is used hereto set the scaling factor. This process is considered to give better perfor-mance even though it introduces some distortion in the LS estimate [13].

4.2.3 Maximum Likelihood Sequence Estimation (MLSE)

Once the channel estimates are obtained, the task is to demodulate theburst bits. MLSE is a popular approach and is employed by the studiedsystem. The ML criterion leads to finding the sequence with minimumEuclidean distance from the received sequence, as

(21)

Apart from the bit decisions, it is also advantageous to the decoding pro-cess, if the reliability of bits, called soft value, could be available. Anappropriate measure for the soft value is the log-likelihood ratio (LLR)

(22)

where U is a random variable that may assume values {-1, +1} withprobability PU(u). Besides, the hard decision value of u is simply thesign of its soft value,

(23)

To solve for the ML sequence as in Eq(21) and provide with soft values,the Soft Output Viterbi Algorithm (SOVA) is used.

4.2.4 The Soft Output Viterbi Algorithm (SOVA)

The Viterbi algorithm is used in the decoding of convolutional codes asdiscussed in section 2.2.4. The 5-tap FIR filter channel model resembles a(1,1,4) convolutional code. And the minimum path problems posed byEq(21) and (10) are comparable. The difference in applying the VA in the

b r b∗ h–2{ }

bminarg rn hibn i–

i 0=

4

∑–2

n∑

bminarg= =

LU u( )PU u = +1( )PU u 1–=( )-----------------------------ln=

u LU u( )( )sgn=

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equalizer will thus only be in the metrics involved.

The modification of the VA for soft outputs, SOVA, is discussed in [15],where a simplification of the algorithm to give less accurate soft valuesis also presented. This simplified algorithm described next is used in thereceiver system.

Consider state sk at time k. (sk-1, sk) represents the two possible transi-tions via which sk could be reached and Γ(sk) is the accumulated metricvalue. The SOVA involves the following steps for each state sk:

a) For both transitions (sk-1, sk), compute the metrics,

b) Store metric, and path, bk(sk), of the sur-vivor;

c) Store the soft value of the survivor approximated by,;

The soft value of step (c) could be interpreted intuitively; if the metricsof the two contesting paths are very close, the bit decision is definitelynot as reliable as the case when there is a wide range between them.

A decision window is also used to start making decisions without wait-ing until the end of the sequence. Furthermore, due to the structure ofthe normal burst, the left and right half parts of the burst are equalizedindependently from the center and outwards.

Another auxiliary operation accomplished together with sequencedetection is automatic frequency correction (AFC). It attempts to removethe phase drift in the samples coming from the demodulator due to dop-pler shift and frequency error. The algorithm tracks this phase error andadjusts the phase of the samples before they are used in metric computa-tion. The AFC algorithm, however, will not be discussed further.

4.2.5 Quality measures

The equalizer also computes parameters that indicate the quality of thedetected burst. These include access delay, signal quality, signal leveland frequency error.

Γ sk 1– sk,( ) Γ sk 1–( ) rk hibk i–i 0=

4

∑– 2

;+=

Γ sk( ) Γ sk 1– sk,( )min=

Lk sk( ) Γ sk 1– sk,( )max Γ sk 1– sk,( )min–=

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4.2.6 Deinterleaving and decoding

Deinterleaving and decoding operations differ among logical channelsas does the channel coding used. However, a few points of general inter-est will be highlighted here.

The VA used in the convolutional decoder exploits the soft values fromthe equalizer. This is achieved by scaling the Hamming distance metricsdiscussed in section 2.2.2 with the soft value of the bits as

(24)

where dsoft is the metric for the burst sequence v and L(ri) is the softvalue of received bit ri. The criterion is then maximization of Eq(24) incontrast to the minimization of Eq(10).

As an indicator on the quality of the decoded block, a parameter calledthe soft frame quality (SFQ) is computed from those bits on which convo-lutional coding is used. It carries the number of bits changed by the con-volutional decoding process. The higher the SFQ, the more unreliablethe block is deemed.

In TCH/FS, a block is not used if it contains ‘bad’ data. A decision onerasure is made using the CRC check on class 1a bits and the SFQ. Afterconvolutional decoding of the whole class 1 bits, the block code is usedto detect errors on the class 1a bits and shows that by setting a CRC flag.However, passing the CRC check does not guarantee an error free blocksince the code can detect only single errors for sure. Thus, blocks withCRC set or an SFQ exceeding a certain threshold are erased.

4.3 Implementations

In this thesis, channel re-estimation and re-equalization using equalizerand decoder feedback were studied. Different schemes that have beenconsidered are presented in the coming sections.

4.3.1 Schemes for channel re-estimation

As presented in section 4.2, channel estimation is conventionally doneusing the training sequence bits in each burst. The idea with re-estima-tion is to use feedback data to extend the training sequence. Two possi-ble scenarios, equalizer feedback and decoder feedback, are shown in Fig. 15.

In the case of equalizer feedback, data is ready immediately after eachburst is equalized. This can then be used to re-equalize the same burstwith updated channel estimates. The process can also be iterated several

dsoft r v,( ) L ri( )vii∑=

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times before the final decision is passed to the decoder. However, itera-tion was not implemented in the studied test cases because of the com-plexity it would incur. Besides, in related works like [19,21], it is shownthat significant gain is achieved only in the first feedback processing.

The decoder feedback, on the other hand, will be available after a com-plete block is equalized, deinterleaved and decoded. Encoding andinterleaving will then get feedback data ready back in the burst format.Thus, in this case, re-equalization could not be performed burst-by-burst. Rather, bursts should be buffered before they are re-equalized ingroups. Since some error correction is achieved at the decoder, the qual-ity of feedback is higher than equalizer feedback. However, for logicalchannels where block diagonal interleaving is used, this scheme forcessome delay. To avoid this, mixed decoder and equalizer feedback wasalso implemented. More on the specific test cases is presented in the nextchapter.

4.3.2 Channel estimator with extended training sequence

In section 4.2 the LS channel estimator was derived. Consider Eq(15)once again. When using feedback data, the bits, bk, outside the trainingsequence can be taken as a random variable. The corresponding LSchannel estimate will then be in terms of the expected values of the bitdecisions fed back, as [20]

(25)

where expectation is taken over the bits bk and

(26)

Figure 15. Feedback schemes for channel re-estimation.

MLSE

Channel Estimation

Deinterleaver

Decoder&

From GMSKdemodulator

rk

trainingsequence

h

bits &soft

bk

Encoding

Interleaving&

Equalizerfeedback

Decoderfeedback

h E r Bh–2{ }minarg=

h BT B( )1–BT r=

B E B r{ }=

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If the feedback bits have the LLR available, the expectation in Eq(26) canbe computed as

(27)

The benefit of soft decision feedback is that the low soft value of unreli-able decisions scales down the effect of wrong decisions on the channelestimate. However, in the case when only hard decisions are available,all decisions are taken as correct, including erroneous ones without anyscaling.

The soft output of the SOVA is a scaled version of the LLR with anunknown scaling factor. Thus, when using Eq(27), a factor was selectedempirically by running several simulations for different factors.

4.3.3 Variation of the channel

We have seen in section 2.3.2 that the speed of the MS dictates the dop-pler frequency and the variation of the channel. If the channel changesso fast that there is significant variation over the duration of one burst,then a single channel estimate from the midamble would not be ade-quately accurate for the whole burst duration. In this case, an adaptivechannel tracking would be needed. However such a scheme is notadopted in the receiver system for complexity reasons.

When using channel re-estimation, there is a chance to perform severalchannel estimates over different segments of the burst. To evaluate theneed for this kind of channel estimation, the BER profile after the equal-izer of the unmodified receiver was observed as a function of position ofbit in burst. This is shown for TU50 and TU250 in Fig. 16 for Eb/No = 10dB and without interference. The bit positions are numbered from left toright skipping over the training bits.

The result shows that the channel estimate works well at the lowerspeed, 50 km/hr, with the BER distribution almost flat. However, at 250km/hr the channel variation gives rise to high error rates for peripheralbits. Thus, the multiple channel estimates per burst were considered, aspresented in the next chapter.

4.3.4 Delay adding and non-delay adding schemes

The block-diagonal interleaving of TCH/FS is such that groups of 4bursts contain bits from the same two blocks that are interleavedtogether. These groups are marked by the decoding positions that occur

bk

L bk r( )2

------------------ tanh=

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at an interval of 4 bursts. Besides, each block is contained in two burstgroups. The simplified diagram in Fig. 17 illustrates this point.

Block A, which has been decoded at time instant t1, could only be pro-cessed with complete decoder feedback at a later time, t2, when the nextblock, B, is decoded. This involves a delay of one burst group (~20 ms).

Figure 16. Channel variation consideration.

Figure 17. Delaying effect of block-diagonal interleaving.

0 20 40 60 80 100 1200.055

0.06

0.065

0.07

0.075

0.08

0.085

0.09

Bit position in burst

BE

R

BER distribution by bit position

tu50 tu250

Block A

Block B

Burst group (4 bursts each)

- Block A decoded

- Block B decoded

time

t1

t1

t2

t2- Decoder feedback

ready for block A

decoded bits

not yet available

available at t=t2decoded bits

Block C

decoding position

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To avoid delay, a combination of decoder and equalizer feedback couldbe used. Consider Fig. 17, and the processing of block B. At time instantt2, decoder feedback is available for all bits in the first burst group ofblock B, and for only half of the bits in the other burst group that is inter-leaved with block C. Instead of waiting until block C is decoded, equal-izer feedback could be used for these bits. This would enable a nondelay-adding scheme.

4.3.5 Hard decision feedback for sequence detection

The VA used in the sequence detection could also benefit from decoderfeedback. In the conventional system, the equalizer does not take thenature of the convolutional code into account when it finds the MLsequence. The equalizer and decoder blocks are thus loosely combined.However, if feedback is available from the decoder, it would help theequalizer select sequences that best fit the convolutional code, therebyleading to better performance.

In a more refined manner, the above concept is used in turbo codes. Inthese codes, a cleverly chosen parallel concatenation of convolutionalcodes is used. The decoding will then be done iteratively using twodecoders in a cascade arrangement, coupled with a feedback of soft val-ues [14].

The cascade of a sequence detector and a convolutional decoder, whichis a common receiver structure could also be adapted to use the turbo-principle. In this turbo equalization approach, a soft output decoderwould be needed for the feedback to the sequence detector. Thesequence detector should also be capable of soft outputs as well asaccepting a priori information. Such a soft output decoder would how-ever increase the complexity of the decoder by 2 to 4 times [21].

The use of hard decision decoder feedback in the VA for sequence detec-tion was considered in [19]. This scheme adds very little extra computa-tion on top of channel re-estimation. Besides, it does not demandmodification of the decoder. This was implemented in this work for thetraffic channel TCH/FS.

A burst in TCH/FS consists of class 1 and class 2 bits coming from twoblocks. The idea is to take the hard decisions from the decoder for theclass 1 bits of one of the blocks as correct a priori information and usethem to lock the corresponding state transitions in the trellis used by theVA. If some of the a priori bits are changed by the decoder from whathas been detected by the first equalization, then the re-equalization willbe forced to take a new path than before. This affects neighboring bits

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which are the class 2 bits of the block used as source of feedback, and allbits of the other block. The specific schemes are more thoroughly dis-cussed in the next chapter. Fig. 18 is an illustration of the discussionabove on a simple 4-state trellis.

Figure 18. Hard decision feedback in sequence detection.

00

01

10

11

state 1 0 0

A priori bits

Impossible transitions left blank

Original detection(dotted line): (0,1,0,0,1,1,0) ;

A priori bits from decoder: (1,x,x,0,x,0,x) ; “x” means no feedback

New detection(solid line): (1,0,0,0,1,0,1) ; changed decisions in bold

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5 Test cases and resultsThe test cases studied in this thesis are presented and discussed next. Toevaluate the potential of different schemes, simulations were made inAWGN without diversity combining (single channel) and interference.Frequency hopping was not used either. This is called sensitivity test.The most successful scheme was afterwards tested with two-branchdiversity and under interference.

5.1 Equalizer feedback for channel re-estimation

The simplest test case was to use equalizer feedback for channel estima-tion. Hard and soft decision feedback were tested. Besides, the LS andcorrelation channel estimations were compared.

Algorithm

Each burst is re-equalized using the bit decisions of the first equalizationas feedback for channel re-estimation. This doubles the number ofequalizations but does not add extra delay.

Simulation results

Both the LS and correlation estimates were tested. The LS estimationperformed better than the correlation estimate. However, only a mar-ginal gain around 0.1 dB was achieved on TU50 and slightly worse per-formance than the conventional system on HT100. This suggests that thequality of the feedback data at the equalizer output is rather poor.

In [20], a gain of about 0.7-0.8 dB is quoted using equalizer feedbacksame as the test case under consideration. However, the implementationof the equalizer used as a reference is not clearly stated in that paper,which makes direct comparison inappropriate. A possible reason is thatthe receiver system used in this study is superior. The synchronization,AFC and IRC algorithms are some of the features that could be thestrengths of the system.

5.2 Decoder feedback with delay on TCH/FS

5.2.1 Channel re-estimation

Algorithm

Here, hard decision decoder feedback was used for channel re-estima-tion. As pointed out in section 4.3.4, complete decoder feedback onTCH/FS forces a delay of 4 bursts (~20 ms). The flow chart of Fig. 19

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depicts the operations involved in this processing. As an indicator of the

potential of channel estimation, the ideal feedback case, which meanserror free decisions by the decoder, was also simulated.

Complexity

To estimate complexity of the different schemes, relative comparison ismade with the conventional receiver in terms of additional functionaloperations and memory. A detailed complexity analysis in terms of basicnumerical operations was not done in this work as the focus was moreon the formulation and performance analysis of relevant algorithms.

a) A delay of one block (4 bursts);

b) Buffer space for 8 burst samples;

Figure 19. Flow chart of the delay adding processing.

Decoding position?

Encode & interleave

Buffer burst sample

decoded block

use decoder feedback for

Pop buffered samples & re-equalize 4 bursts

Next burst

N

Y

For each burst

Deinterleave and decodeDecoded

channel re-estimation

block

Out:

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c) One more channel estimation and sequence detection (SOVA)per burst;

d) One encoding and interleaving per block with associated bufferspace;

e) One more decoding and deinterleaving per block with associatedbuffer space;

Simulation results

The results using a single channel estimate per burst are shown in Fig.20 for the channel model TU50. The bit error rate (BER) for class 1 bits isafter decoding. The BER of class 2 actually indicates the performance ofthe equalizer, as those bits are not coded. The gains are indicated at BERof 0.1% and 5% for class 1 and class 2 bits, respectively.

A gain of 0.6-0.7 dB was obtained in this case on the TU50 channelmodel. Similar results were obtained for TU3 and TU250 (Appendix-A1). The gain on class 1 bits is slightly higher than the class 2 because ofthe second decoding. Besides, the performance gets better for higherspeeds; TU250 performs better than TU3 for instance. Comparing BER ofclass 1 bits of the conventional receiver for different speeds of the same

Figure 20.

4 5 6 7 8 9 1010

−5

10−4

10−3

10−2

10−1

Eb/No [dB]

BE

R o

f Cla

ss 1

Decoder feedback, delay−adding on TU50

Conventional Correlation estimateLS estimate Known burst

0.7dB 0.7dB

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channel model (say, TU3 and TU250), we find that it is lower for higherspeeds, at a given SNR. This is because the interleaver is more effectiveat higher speeds resulting in more coding gain. Therefore, the feedbackdata is of better quality and so is the gain of feedback processing.

Due to errors in the feedback data, the gain obtained is almost half of theideal case if the burst was known to the channel estimator. The correla-tion and LS channel estimates also gave close performance, with the LSmarginally better. Thus, the correlation estimate is preferable since it haslower computational complexity.

To investigate the effect of avoiding “bad” frames for feedback, theframe erasure criterion was considered to decide whether or not to usefeedback. The idea was to perform channel re-estimation only for thosebursts whose data comes from unerased blocks. However, indiscrimi-nate use of feedback happens to work better than the selective case. Thereason for this could be as follows.

A block of data is interleaved into 8 bursts. If the block is erased, thefeedback data is ignored for all 8 bursts and the block would not behelped. In fact, this precludes improvement in frame erasure. However,by processing all bursts without any feedback criterion, some improve-ment would be obtained from those bursts with good data and the BER

Figure 21.

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Conventional Correlation estimateLS estimate Known burst

0.6dB 0.4dB

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could be improved, as the simulation results show.

5.2.2 Two channel estimates per burst

As shown in section 4.3.1, the channel estimate from the training bits isnot adequate at high speeds when the channel varies fast. This is mani-fested in the higher error rates for bits away from the burst center. In theprevious section, the feedback was used to compute a single averagechannel estimate for each burst, using all bits therein. In order to accountfor channel variation, taking two distinct channel estimates for the leftand right half of a burst was considered. As Fig. 22 shows, the trainingbits are included in both estimates to benefit from the fact that they areknown for sure unlike the feedback bits that could be erroneous.

This scheme is particularly suitable since the sequence detection is per-formed independently for the left and right burst halves. Thus, apartfrom computing one additional channel estimate per burst, other pro-cesses are not affected.

Simulation results

Figs. 23 and 24 show the result on TU250. At this fast speed, an improve-ment of 0.3 dB and 0.4 dB, on class 1 and 2 respectively, is achieved rela-tive to the single channel estimation. The gain even gets higher at higherSNR when the feedback data becomes more reliable. On lower speeds,like TU3 and TU50 however, a reduction in gain around 0.1 dB isencountered. This is not unexpected since in the low speed case a singlechannel estimate performs well. Thus, splitting the burst into two willunnecessarily reduce the data used in the channel estimation. Results onTU3 and TU50 are placed in Appendix A2.

The position profile of the BER after re-equalization also looks as in Fig.25 for TU250. An improvement could be noticed in the variance of thebit error distribution compared to the conventional and the single esti-mate cases. Yet, it is also apparent that satisfactory channel trackingcould not be achieved with this simple scheme.

Figure 22. Two channel estimates per burst.

}} TSC

data used for theleft half

data used for theright half

data (left) data (right)

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Another likely benefit of this scheme is to cope with an unsynchronizedinterferer that affects part of a burst. Having two channel estimates perburst gives better opportunity to salvage part of the burst that is notaffected much by the interferer. However, this kind of interference which

Figure 23.

Figure 24.

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Single and Two−part channel estimates − Delay−adding, TU250

Conventional Single estimateTwo parts

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is difficult to model, is not supported in SYSSIM and hence not tested.

5.2.3 Sequence detection using feedback

Algorithm

Sequence detection using decoded class 1 bits as a priori informationwas utilized in conjunction with the channel re-estimation. Besides, the

feedback sequence detection alone was also studied by disabling thechannel re-estimation operation. The algorithm is described with thehelp of Fig. 26.

Figure 25. Comparison of BER profiles.

Figure 26. Re-equalization algorithm with delay.

0 20 40 60 80 100 1200.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

Bit position in burst

BE

R

BER profile by bit position


Block A

Block B

Burst groups

timet1

a bdecoded bits

not yet available

available

decoded bits

Block C

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Consider t = t1 when block B is decoded and burst group a is processed.The following operations would then be performed.

a) Encode and interleave block B to reform burst group a;

b) Re-equalize the 4 bursts of burst group a using new channel esti-mates from decoder feedback and taking the class 1 bits of block Bas a priori information in the SOVA. The a priori information isused only if block B has not been erased. This process helps allbits in the re-equalized bursts coming from block A.

c) De-interleave, decode and output block A. Notice the delay of 1block.

d) Re-equalize the same burst group using the channel estimates ofstep (b) and the newly decoded class 1 bits of block A as a prioriinformation in the SOVA. This time all bits belonging to block Bare helped.

e) Block B bits will wait in the pipeline of the deinterleaver bufferuntil the next block, C, is decoded, as has been the case with blockA before step (a).

The complexity of the combined scheme differs from the channel re-esti-mation case with one more sequence detection (SOVA) per burst in step(d). Generating a priori bits and using them to lock states in the VA addsnegligible overhead.

Simulation results

An additional gain of 0.35-0.4 dB was achieved by employing thesequence detection on top of the two-part channel estimation on TU50.The overall gain is close to 1 dB. Figs. 27 and 28 show the results.

5.3 Decoder feedback without delay on TCH/FS

The delay adding scheme is not favorable for the speech service. How-ever, its investigation could indicate the potential of the method if usedon other data channels not very much sensitive to delay. The next imple-mentations are non delay-adding with mixed decoder and equalizerfeedback.

5.3.1 Channel re-estimation

The flow chart for the channel re-estimation algorithm is presented inFig. 29. It is to be noted that all 8 bursts that constitute a block are re-equalized at each decoding position. Since two blocks are interleaved ineach burst, it means that every burst is equalized 3 times including orig-inally in the conventional manner.

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Figure 27.

Figure 28.

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Channel Re−estimation and Seq. Detection − Delay, TU50

Conventional Two−part chan. est. Combined with seq. det.

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Channel Re−estimation and Seq. Detection − Delay, TU50

Conventional Two−part chan. est. Combined with seq. det.

0.35dB

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Figure 29. Flow chart of non-delay adding channel re-estimation.

Decoding position?

Encode & interleave

Buffer burst sample

decoded block

Use decoder feedback

Pop buffered samples & re-equalize 8 bursts

Next burst

N

Y

For each burst

Deinterleave and decodeDecoded block

Out:

Buffer equalized bits

for 1st burst group

Use mixed decoder and

for 2nd burst groupequalizer feedback

Encode and updateInterleaver buffer

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Complexity

a) Buffer space for 8 burst samples and 8 burst bits from first equal-ization;

b) Two more channel estimations and sequence detection (SOVA)per burst; when two-part channel estimates are used, therewould be 3 channel estimates per burst;

c) Two encodings and interleavings per block and one interleavingbuffer space;

d) One more decoding and deinterleaving per block with associatedbuffer space;

Simulation results

a) Single channel estimate per burst

Figs. 30 and 31 compare the delay-adding and non delay-adding cases.The gain is reduced by almost half relative to the delay adding case. This

is a result of degraded feedback quality when using equalized bitsinstead of decoded bits.

Figure 30.

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Single channel estimates on TU250 − with and without delay

ConventionalNon−Delay Delay adding

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0.45dB

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b) Two channel estimates per burst

In the case when two channel estimates per-burst were used, this wasdone only for those bursts that have complete decoder feedback, as itwas noticed to give better results. An improvement of about 0.2 dB isachieved on TU250 (Figs. 32 and 33). The performance on TU50remained almost identical to the single channel estimation case (Appen-dix A3).

5.3.2 Sequence detection using feedback

In this scheme, at each decoding instance, both burst groups that consti-tute the decoded block are processed. For the first group, completedecoder feedback is available while only half of the class 1 bits comefrom the decoder for the second group. The other bits are fed back justover the equalizer.

The steps involved are summarized using Fig. 26 at the time when blockB is decoded (t = t1):

a) Encode and interleave block B;

Figure 31.

4 5 6 7 8 9 10

10−1

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Single channel estimates on TU250 − with and without delay

Unmodified Non−Delay Delay adding

0.35dB

0.4dB

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Figure 32.

Figure 33.

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Single and Two−part channel estimates − Non−delay, TU250


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0.2dB

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b) If block A has not been erased, use its class 1 bits as a priori infor-mation and re-equalize the first burst group of block B (‘a’ in Fig.26). Channel re-estimation is also done for this group that enjoyscomplete decoder feedback;

c) Re-equalize the second group, b, with only channel re-estimationusing mixed equalizer and decoder feedback;

d) De-interleave, decode and output block B;

e) Encode block B and update the interleaver buffer for the process-ing of the next block.

The sequence detection scheme outlined above adds nothing more thanthe modification needed by the VA to use a priori bits. This adds little tothe complexity when used in conjunction with channel re-estimation.

Simulation results

The combination of two-part channel estimation and sequence detectiongives the results shown in Figs. 34 and 35 on TU250, with a gain of 0.7-0.8 dB. On TU50, the gain is around 0.5 dB (Appendix A4). The sequencedetection contributes 0.1-0.2 dB.

Figure 34.

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Channel Re−estimation and Sequence det. − Non−delay, TU250

Conventional Two−part chan. est. with sequence det.

0.8dB

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5.3.3 Diversity and interference tests

For the speech service, the non-delay adding processing is appropriate.From the sensitivity tests in the non delay-adding mode, the combina-tion of two-part channel estimation and feedback sequence detectiongave better result. This scheme was further tested on the channel modelsTU50, HT100 and RA250, with two-branch diversity. Co-channel inter-ference test was also carried out. The simulation results are documentedin Figs. 36-39.

In the sensitivity test with diversity, a gain of 0.5-0.6 dB is obtained. Thedifferent channel types appeared to benefit in a similar manner. Further-more, the result is similar to the case without diversity. However, chan-nel re-estimation turned out to be less effective in the case of co-channelinterference. Only an improvement of 0.15-0.25 dB was achieved. A pos-sible reason for this could be that MLSE is an optimum solution only inthe AWGN case and not for interference. Thus, the potential of improv-ing performance by better channel estimates is low in the interferencecase.

Figure 35.

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Conventional Two−part chan. est. with sequence det.

0.7dB

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Figure 36.

Figure 37.

0 0.5 1 1.5 2 2.5 3 3.5 410

−6

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BE

R o

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Channel Re−estimation and Sequence Det. with diversity

Conventional With processingTU50 HT100 RA250

0 0.5 1 1.5 2 2.5 3 3.5 410

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BE

R o

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Channel Re−estimation and Sequence Det. with diversity

Conventional With processingTU50 HT100 RA250

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Figure 38.

Figure 39.

2.5 3 3.5 4 4.5 5 5.5 610

−5

10−4

10−3

10−2

C/I [dB]

BE

R o

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Co−channel interference test

Conventional With processingTU50 RA250

2.5 3 3.5 4 4.5 5 5.5 610

−2

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BE

R o

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ss 2

Co−channel interference test

Conventional With processingTU50 RA250

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5.4 Channel re-estimation on GPRS-CS1

The GPRS-CS1 is featured by block-rectangular interleaving and chan-nel coding with equal protection for all bits. The interleaving structureallows operation with no delay as each block could be processed with-out waiting for others. Thus, the algorithm is straight forward with fourburst samples buffered before the block they constitute is decoded andthen re-equalization is performed with new channel estimates usingdecoder feedback on these four bursts. However, the same interleavingstructure makes sequence detection using hard decision decoder feed-back inapplicable, as we can’t take decoded bits of one block as a prioriinformation on another. The equal protection coding is a strength to geta better quality decoder feedback.

The block error rate (BLER) and the BER after decoding are used as mea-sures of performance. The results show an improvement of 0.8 dB onBLER and 0.5 dB on BER. (Fig. 40)

Figure 40.

1 2 3 4 5 6 710

−5

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100

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Err

or ra

te

Channel re−estimation on GPRS−CS1, TU250

Conventional With processingBLER BER

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6 SummaryThe focus of this thesis has been investigation, implementation and eval-uation of feedback schemes to improve the performance of the equalizerin the GSM receiver system. Channel re-estimation and sequence detec-tion were central to the study. The feedback data was used to obtainmore data and hence a better channel estimate. Besides, for TCH/FS,feedback from decoded bits could be used as a priori information assist-ing in sequence detection. This was carried out by using the decodedbits as correct and locking corresponding state transitions in the VA.This forces the detected sequence to one that fits to the a priori bits. If thea priori bits are correct, then the sequence detected this way tends to beenhanced.

Different feedback schemes were considered. The first scheme, equalizerfeedback for channel re-estimation, gave no performance gain. In fact,some degradation resulted for the HT100 channel model. This is becausethe equalizer output is very noisy. Using decoder feedback was investi-gated further. Since errors are corrected at the decoding stage, the qual-ity of such feedback is better. However, to obtain complete decoderfeedback, delay should be accepted in the processing due to block diago-nal interleaving of TCH/FS. By combining equalizer and decoder feed-back, the delay obstacle could be overcome, with some sacrifice in thequality of feedback. Since simulations indicate that the channel variessignificantly at higher speeds, like 250 km/hr, taking two channel esti-mates per burst was considered in the channel re-estimation process.

A gain close to 1 dB was achieved on TU50 with the delay-adding pro-cessing. In this and other cases, the gain increases with increasing SNRdue to the better feedback quality with lower BER. The computationallysimpler correlation channel estimate gave performance close to theactual least square estimate. Even though the 20 ms processing delay isnot tolerable for the speech service, the investigation is indicative of thepotential of using such a scheme for other data services where delay isnot so critical. However, this study did not look into such services.

With a non delay-adding scheme, the gain reduces to 0.5-0.6 dB, testedon TU50, HT100 and RA250 with 2-branch diversity combining. In theco-channel interference case, the gain is only 0.15-0.25 dB showing thatthe method is not as robust in this case.

The sensitivity test on one of the coding schemes of GPRS, PDTCH-CS1,turned out with a gain of 0.8 dB and 0.5 dB for BLER and BER respec-tively.

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AppendixA1. Delay-adding scheme, TU3 & TU250.

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10−1

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BER

of C

lass

1


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4 5 6 7 8 9 1010

−5

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10−3

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10−1

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BE

R o

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ss 1



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A2. Two-part channel estimation with delay, TU3 & TU50.

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BER

of C

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2



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4 5 6 7 8 9 1010

−5

10−4

10−3

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10−1

Eb/No [dB]

BE

R o

f Cla

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A3. Two-part channel estimation without delay, TU50.

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A4. Two-part channel estimation and sequence detection withoutdelay, TU50.

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References[1] J. G. Proakis, Digital Communications, McGraw-Hill, Inc., 1989.

[2] S. Lin, D. J. Costello, Jr., Error Control Coding Fundamentals andApplications, Prentice-Hall, Englewood Cliffs, N.J., 1983.

[3] T. S. Rappaport, Wireless Communication: Principles & Practice,Prentice-Hall, Inc., 1996.

[4] G. L. Stuber, Principles of Mobile Communication, Kluwer Aca-demic Publishers Group, Norwell, Massachusetts, 1996.

[5] Mehrotra, Asha, GSM System Engineering, Norwood, MA: ArtechHouse, 1997 p. 68

[6] Haykin, S., Adaptive Filter Theory, 2nd ed., Prentice-Hall, Engle-wood Cliffs, N.J., 1991.

[7] “GSM System Survey - Student Text”, Ericsson Radio SystemsAB, 1998.

[8] GSM 05.02, "Digital cellular telecommunications system (phase2+); Multiplexing and multiple access on the radio path".

[9] GSM 05.03, “Digital cellular telecommunications system (Phase2+); Channel coding”.

[10]GSM 05.04, “Digital cellular telecommunications system (phase2+); Modulation”.

[11]GSM 05.05, “Digital cellular telecommunications system (phase2+); Radio transmission and reception.

[12]L. Hanzo, R. Steele, “The Pan-European Mobile Radio SystemPart II,” European Trans. on Telecom. & Related Tech., vol. 5, no.2, March-April 1994, p. 261-76.

[13]Johan Sköld, et. al., “Method and Apparatus for Channel Estima-tion”, World Intellectual Property Organization, Int. PublicationNo. WO 96/13910.

[14]C. Berrou, A. Glavieux and P. Thitimajshima, “Near ShannonLimit Error-correcting Coding and Decoding: Turbo Codes,”IEEE Int. Conf. on Communication, Geneva, May 1993, p. 1064-1070.

[15]J. Hagenauer and P. Hoeher, “A Viterbi Algorithm with Soft-Decision Outputs and its Applications,“ Proc., IEEE GlobecomConf., Dallas, TX, Nov. 1989, p. 1680-1686.

[16]F. Jordan, K.-D. Kammeyer, “A study on Iterative Decoding Tech-

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niques Applied to GSM Full-Rate Channels,” PIMRC, 1998.

[17]F. Jordan, K.-D. Kammeyer, “On the Application of Turbo Equal-izers in GSM Compatible Receivers,” PIMRC, 1998.

[18]G. Bauch, V. Franz, “Iterative Equalization and Decoding for theGSM-System,” VTC’98, May 1998, pp.2262-2266.

[19]S. Jäverbring, “Detection and Equalization in GSM Assisted byForward Error Control,” Master of Science Thesis Project, KTHand Ericsson Radio Systems AB, Feb. 1997.

[20]M. Sandell, C. Luschi, P. Strauch, R. Yan, “Iterative Channel Esti-mation Using Soft Decision Feedback,” IEEE, 1998.

[21]N. Nefedov, M. Pukkila, “Iterative Channel Estimation forGPRS,” PIMRC’2000, London, Sept. 2000.

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