WIRELESS COMMUNICATIONS AND MOBILE COMPUTINGWirel. Commun. Mob. Comput. 2002; 2:719–733 (DOI: 10.1002/wcm.89)

Space—time receivers for GSM radio interfaces in subwaytunnel environments

Miguel Gonzalez-Lopez, Adriana Dapena andLuis Castedo*,†

Departamento de Electronica y Sistemas,Universidad de A Coruna,Facultad de Informatica,Campus de Elvina, A Coruna,Spain

Martine Lienard and Pierre DegauqueUniversite de Lille,Dept. Electronique,Bat. P3,59655 Villeneuve d’Ascq cedexFrance

Marıa J. Asarta and Pedro CrespoCentro de Estudios e InvestigacionesTecnicas de Guipuzcoa (CEIT)Paseo de Manuel Lardizabal, 15,20018 San Sebastian,Spain

Summary

In this paper, we investigate how to increase thecapacity of GSM (Global System for Mobilecommunications) radio interfaces in subway tunnelenvironments by means of antenna arrays andSpace–Time (ST) receivers. We address themodeling, both theoretically and experimentally, ofthe multiple-antenna wireless channels encounteredin subway tunnels. We demonstrate that propagationis conveniently modeled by a flat-fading channel, butthere exist strong spatial correlations among channelcomponents that decrease capacity and affectreceivers’ performance. Different space–time GSMreceiving strategies have also been investigated. Wefirst consider ST equalization techniques that onlyaccount for the noise and the controlled IntersymbolInterference (ISI) introduced by the modulationformat employed in GSM. Then, we analyze theperformance of receivers that incorporate ST codingcapabilities and show the superior performance ofiterative MAP (Maximum a Posteriori) receivers thatinterchange soft information among the equalizerand the ST decoder. All receivers are evaluated withexperimental channels measured in the subway ofParis. Copyright 2002 John Wiley & Sons, Ltd.

KEY WORDSspace–time receiversGSM radio interfacesMultiple-Input Multiple-Output (MIMO)

channelsiterative Maximum a Posteriori (MAP)

decoding

ŁCorrespondence to: Luis Castedo, Departamento de Electronica y Sistemas, Universidad de A Coruna, Facultad deInformatica, Campus de Elvina, A Coruna, Spain.†E-mail: luis@udc.esContract/grant sponsor: European Commission; contract/grant number: IST-1999-20006 (ESCORT project).

Copyright 2002 John Wiley & Sons, Ltd.

720 M. GONZALEZ-LOPEZ ET AL.

1. Introduction

GSM is undoubtedly the most successful second-generation digital mobile radio system. Since it hasbeen sponsored by the European telecommunicationindustry, a large number of European companiesdominate the technologies related with GSM radiotransmission. As a consequence, the GSM radiointerface (GSM-R) has been also adopted in 1993by the standardized digital radio system availablefor the European railway networks and a specificfrequency band, called the R band (876–880 MHz921–925 MHz), has been reserved for them. Becauseof the conservative nature of its market, it isexpected that railway radio communication systemswill employ GSM-R for the long-term future.

It is very likely that urban transport operators (typ-ically metro operators) adopt a digital radio systemsimilar to that used in conventional railway trans-portation. In urban transportation systems, however,requirements for radio communications are morestringent, and it is highly desirable to offer phone andvideo services for either security or entertainment.These increasing needs for communication imply theavailability of a high data rate and a high-qualitywireless access over fading channels at almost wire-line quality. In this paper, we investigate the use ofmultiple antennas at the transmit and receive sides incombination with signal processing and coding as apromising means to meet all these requirements.

Recent information theory investigations have de-monstrated that the capacity of wireless channels canbe considerably increased, at no extra bandwidth orpower consumption, if the multipath is sufficientlyrich and properly exploited by means of multielementantennas at both transmission and reception [1,2,3].The basic idea is to approach the transmission throughmultipath channels from a new perspective in whichmultipath signal propagation is no longer viewed asan impairment but as a phenomenon that providesspatial diversity that can be successfully exploited toimprove reception. Multipath propagation enables theexistence of multiple spatial parallel data pipes thatallow the spatial multiplexing of several data streamsand, thus, the possibility of increasing channel capac-ity with the number of antennas.

Spatial diversity can be successfully exploited bymeans of specific signal processing techniques suit-able for multiple transmitting and receiving anten-nas. An overview of the most relevant existing STsignal processing schemes can be found in Refer-ence [4]. The performance of these techniques can

be substantially improved by including codes specif-ically designed to take into account both the spatialand temporal dimensions [5]. These techniques arecollectively known as Space–Time Coding (STC)and for a tutorial review of them the reader isreferred to Reference [6] and references therein. Inthis paper we will investigate how to use STC toincrease the capacity of GSM radio interfaces insubway tunnel environments. To our knowledge nowork has been done on this specific topic. Exist-ing works on STC have been mainly devoted tooutdoors and Small Office/HOme (SOHO) environ-ments, and advanced third-generation mobile com-munication technologies [7].

GSM radio interfaces impose the specific constraintthat the modulation format to be used should beGaussian Minimum Shift Keying (GMSK) and thus,certain controlled ISI is deliberately introduced attransmission. This means that the coder/modulatorstages can be interpreted as a concatenated code thatcan be very efficiently decoded using iterative (turbo)ST decoding strategies. The design of ST turbo codeshave been investigated by several authors [8,9,10,11].In this work, however, we will not address the prob-lem of coding design. Instead, we will assume thatthe outer encoder is a conventional ST convolutionalencoder, and we will investigate the advantages ofusing an iterative approach to combine the equaliza-tion and decoding stages.

Channel modeling is an important issue whendesigning ST communication systems. In subwayscenarios, radio propagation is severely affected bynumerous reflections on the walls and ceilings oftunnels and stations. In this paper we demonstrate,both theoretically and experimentally, that the relativedelays between these reflections are negligible whencompared to the symbol rate used in GSM systems.As a consequence, wireless channels are appropri-ately modeled as flat-fading channels. In addition, itis common practice to assume that spatial correlationamong multipath components is low and model chan-nels as spatially uncorrelated fading channels. Experi-mental measurements reveal, however, that this is notthe case in subway environments in which, due to thegeometrical characteristics of the tunnels, there existstrong spatial correlations that severely affect channelcapacity [12]. These strong spatial correlations willalso have an enormous impact on the performance ofST receivers.

The remainder of this paper is organized as follows:We describe the signal model of a GSM wireless com-munication system with spatial diversity in Section 2.

Copyright 2002 John Wiley & Sons, Ltd. Wirel. Commun. Mob. Comput. 2002; 2:719–733

SPACE–TIME RECEIVERS FOR GSM RADIO INTERFACES 721

Section 3 is devoted to channel modeling, whereasSection 4 is dedicated to ST equalizers that do nottake into account the redundancy induced by the STencoder in transmission. These receivers only com-bat the noise and the controlled ISI introduced by themodulation format used in GSM. Receivers that con-sider the ST encoder at transmission are examinedin Section 5 in which both iterative and nonitera-tive MAP decoding strategies are considered. Finally,Section 6 ends the paper with the conclusions.

2. Signal Model

Let us consider the block diagram of a GSM wirelesscommunication system with ST coding depicted inFigure 1. The original bit sequence u�n� is encodedwith a ST encoder to produce a vector of sym-bols c�n� D [c1�n�, . . . , cN�n�]T (N is the number oftransmitting antennas) with a certain spatiotemporalcorrelation structure. These symbols are subsequentlyinterleaved, resulting in the sequence b�n� and mod-ulated using the GMSK modulation format. Thetransmitted symbols s�n� D s1�n�, . . . , sN�n� are thenup-converted to produce the analog signal radiatedthrough the antennas. Multipath propagation occursbetween each transmitting and receiving elementresulting in a Multiple Input Multiple Output (MIMO)channel. A bank of L ð 1 matched filters is employedat the receiver to obtain a set of sufficient statis-tics x�n� D [x1�n�, x2�n�, . . . , xL�n�]T. The goal inST decoding is to detect the original sequence u�n�from the observations x�n�. Toward this aim we pro-pose a two-stage decoding scheme. The first stage isan ST equalizer that compensates the effect of both

the noise and the controlled ISI induced by the GMSKmodulation format. Perfect Channel State Information(CSI) is assumed in this equalizing stage althoughin practical implementations this information wouldbe supplied by a channel estimation step. The sec-ond stage is a ST decoder that undoes the channelencoding introduced at transmission.

Let us further elaborate the signal model. GMSKis a partial response Continuous Phase Modulation(CPM) with fixed modulation index h D 0.5. Theperformance analysis of GMSK systems is difficultbecause GMSK is a nonlinear modulation format.Nevertheless, it can be approximated by a partialresponse PAM signal that can be analyzed moreeasily. Indeed, CPM signals can be expressed by aLaurent expansion [13] that consists of the sum of2m�1 PAM signals where m is the memory of themodulation (m D 3 in GSM). It can be demonstratedthat the first PAM component contains 99.63% of thetotal GMSK signal energy. As a consequence, theGMSK signal radiated by the ith transmitting antennafor a GSM frame of K bits, si�t; bi�0: K � 1��, can beaccurately approximated by the following expression

si�t; bi�0: K � 1�� ³√

2Eb

T

K�1∑nD0

ai�n�p�t � nT�

�1�where bi�0: K � 1� D [bi�0�bi�1� Ð Ð Ð bi�K � 1�]T isthe binary information bearing sequence, Eb is thebit energy, T is the symbol period, ai�n� D j ai�n �1�bi�n� are the transmitted symbols and p�t� is apartial response pulse waveform that expands alongthe interval [0, mT]. It is important to note thatthe transmitted symbols belong to a QuadraturePhase Shift Keying (QPSK) constellation (i.e. ai�n� 2

u(n)

c1(n) b1(n)

s1(t;b1(n)) x1(t)

x1(n) b1(n) c1(n)

u(n)

N

cN(n)

xL(n)bN(n)cN(n)

xL(t)sN(t;bN(n))bN(n)

STCoder

Inter-leaver

GMSK

MF&

WF

Deinter-leaver

STDecoder

Deinterleaver

MF&

WF

Multipathchannel

GMSK

Inter-leaver

Space-Time

EqualizerN

Fig. 1. Block diagram of a GSM wireless communication system.

Copyright 2002 John Wiley & Sons, Ltd. Wirel. Commun. Mob. Comput. 2002; 2:719–733

722 M. GONZALEZ-LOPEZ ET AL.

f1, j, �1, �jg), are uncorrelated and have unit vari-ance [13]. We assume that differential precoding isemployed before the modulator, so ai�n� D jnbi�n�.

The transmitted signals arrive at an array of Lreceiving antennas and thus we can model the prop-agation channel as a N ð L MIMO system. As it isexplained in the following section, multipath propaga-tion introduces a negligible amount of time dispersionin subway tunnel environments and, thus, the wirelesschannel can be modeled as flat-fading. In this case,the received signal in the jth receiving antenna canbe expressed as follows:

xj�t� DN∑

iD1

hjisi�t; bi�0: K � 1�� C nj�t�,

j D 1, . . . , L �2�

where hji is the channel impulse response that modelsthe fading corresponding to the subchannel betweenthe ith transmitting antenna and the jth receivingantenna. The noise component nj�t� is modeled asa continuous-time white Gaussian random process.

In order to detect the transmitted symbols, thesignals xj�t�, j D 1, . . . , L are passed through a bankof filters matched to the impulse response of themodulation pulse, p�t�, and sampled at the symbolrate to produce a set of sufficient statistics [14]. Itis important to note that the noise at the output ofthe matched filters is colored because p�t� does notsatisfy the zero-ISI condition. In order to simplifythe mathematical derivations, it is highly desirable tohandle observations contaminated with white noiseand thus a discrete-time Whitening Filter (WF) isplaced after each Matched Filter (MF) [15]. In orderto eliminate the rotation introduced by the GMSKmodulation, we multiply the available observationsby j�n, resulting in a set of observations of the form

xj�n� DN∑

iD1

hji

m�1∑lD0

f�l�bi�n � l� C gj�n�

DN∑

iD1

hjisi�n� C gj�n� �3�

where gj�n� is a discrete-time white Gaussian noise,m is the memory of the modulation (m D 3 in GSM)and f�l� D [0.8053, 0.5853, 0.0704] is the equiva-lent discrete-time impulse response that takes intoaccount the transmitting, receiving and whitening fil-ters. Finally, vector notation can be used to write theobservations in a more compact way as follows:

x�n� D Hs�n� C g�n� �4�

This is the vector that will be processed to detect theoriginal sequence u�n�.

3. Channel Modeling

This section deals with the theoretical and experi-mental modeling of the propagation in tunnels whenmultiple antennas are used at both transmission andreception. We will start by applying the image theoryto determine the delay spread and coherence band-width of a straight tunnel with a rectangular crosssection when a single antenna is used at both trans-mission and reception. Next, we will explain theexperimental measurements that have been carriedout in the subway of Paris with four transmittingand four receiving antennas. These experiments cor-roborate that the channel delay spread is negligiblewhen compared to the GSM symbol period. In addi-tion, statistical analysis carried out on the obtainedmeasurements reveal the existence of strong spatialcorrelations that diminish the channel capacity withrespect to an uncorrelated Rayleigh-fading channel.

3.1. Single-Antenna Theoretical Modeling

Image theory is the most widely used method tomodel the propagation of high-frequency waves incomplex environments. Although its principle is quitesimple, it nevertheless assumes that all possible pathslinking the transmitting and the receiving antennascan be determined. These paths can be easily obtainedif the tunnel is straight and has a rectangular section.This assumption will be made in order to obtaina first approximation of the single-antenna channelcharacteristics in subway environments. If the tunnelis arched and/or curved, more accurate models have tobe considered that make use of diverse ray-launchingtechniques such as those proposed in References [16]and [17]. These methods, however, are difficult toimplement, and the computational time may becomeprohibitive for a wide-band analysis in long tunnels.

The application of the image-theory principle tomodel the propagation in tunnels was originallydescribed by Mahmoud and Wait [18]. This work hasbeen subsequently extended to consider many differ-ent applications such as mines, roads and railways inReferences [19] and [20]. In the sequel, we empha-size the main theoretical results that may have animpact on the measurement procedure.

Let us consider a rectangular tunnel 7 m highwhere one transmitting and one receiving half-wave

Copyright 2002 John Wiley & Sons, Ltd. Wirel. Commun. Mob. Comput. 2002; 2:719–733

SPACE–TIME RECEIVERS FOR GSM RADIO INTERFACES 723

antennas are put at a height of 2 m and located at adistance of 1 m and 6 m from the tunnel wall, respec-tively. Figure 2 plots the variation of the coherencebandwidth, Bc, versus the tunnel width at a distancefrom the transmitter of 300 m obtained with con-ventional image theory techniques. The equivalentconductivity of the walls is � D 10�2 S m�1 and therelative permittivity εr has been chosen to be equalto 5. Nevertheless, it must be noted that parametricstudies show that neither the position of the antennasinside the tunnel nor the electrical characteristics ofthe walls are critical.

Figure 2 also plots the regression line that approx-imates the obtained results. It is apparent that Bc is adecreasing function of the tunnel width. For instance,in a large tunnel 15 m wide, a coherence bandwidthof 20 MHz is obtained. In order to provide a sim-ple explanation of this result, let us analyze the timedomain impulse response of the tunnel. The decreaseof the power delay profile can be partly due to theincreasing distance between each image of the trans-mitter and the receiver. However, the power decreasesmainly because of the large number of reflections onthe walls of images located far away from the tunnelaxis. This is because most of the energy is guidedinside the tunnel whose walls are imperfect conduc-tors (i.e the reflection coefficient is less than one)and part of the energy is dissipated at each reflection.Therefore, as the distance between the transmitterand the receiver increases, so does the number ofreflections and the amount of energy dissipated in thewalls of the tunnels. Furthermore, a detailed analy-sis shows that the contribution of the rays reflecting

6 8 10 12 14 16 18 20107

108

cohe

renc

e ba

ndw

idth

(H

z)

tunnel width (m)

20 MHz/15 m

Fig. 2. Variation of the coherence bandwidth versus thetunnel width.

many times on the horizontal walls are strongly atten-uated because of the poor reflection coefficient asso-ciated with a vertical polarization. As a consequence,the shape of the channel impulse response is mainlydetermined by the images of the transmitter locatedin horizontal planes, either containing the transmittingantenna, or placed nearby.

In order to simplify the calculation of the slope ofthe power delay profile, let us consider the contribu-tion of the images situated in the plane containingthe transmitting antenna centered in the tunnel. Thetwo-dimensional geometry is represented in Figure 3.The transmitting and receiving points (Tx and Rx) aresituated in a tunnel of width L at the points O and A,respectively. For large values of the distance x, wecan assume that x × mL, where mL is the transversedistance between the mth image and the transmitter.The reflection coefficient RTE associated with the TEpolarization on the vertical walls is given by

RTE D sin ˛ �√

n2 � cos2 ˛

sin ˛ C√

n2 � cos2 ˛�5�

where n is the relative refractive index of the walls.Since, at high frequencies, the inequality � × ωεr

holds, and assuming that the distance between thetransmitter and the receiver is large enough so thatonly rays impinging the walls with a grazing angleof incidence (˛ − 1) play a leading part in the prop-agation, Equation (5) can be rewritten as

RTE D ˛ � k

˛ C k�6�

where k D pεr � 1. As ˛ is much smaller than k,

an approximate expression of RTE can be obtained asfollows:

RTE ³ ��1 � 2˛/k� �7�

The mth ray reflects m times on the vertical walls. Itsattenuation a�m�, expressed in dB and referred to the

∆x

A

x

α

α

mL

B

Tx

O

Rx

Fig. 3. Geometrical configuration in a horizontal plane.

Copyright 2002 John Wiley & Sons, Ltd. Wirel. Commun. Mob. Comput. 2002; 2:719–733

724 M. GONZALEZ-LOPEZ ET AL.

direct ray, is deduced from Equation (7) and from thefollowing trigonometric relations in Figure 3

tan ˛ ³ ˛ ³ mL

x³ x

mL�8�

This leads to

a�m� ³ 40 m2L

kx³ 40x

kL�9�

Considering the relationship between the additionaldelay t of the mth ray and its additional path x,the decay of the power delay profile, expressed in dBper 100 ns, is given by

a�m� ³ 1200

L√

εr � 1dB/100 ns �10�

From Equation (10), it is apparent that the decayin dB is inversely proportional to the tunnel width,which will thus be a crucial parameter. A simplenumerical particularization shows that, even for atunnel 15 m wide, this slope reaches the value of40 dB/100 ns. Taking into account that the durationof a GSM-R symbol is 3.7 µs, we deduce that thechannel can be modeled as a single-tap flat-fadingchannel. Consequently, for this ideal geometrical con-figuration, only rays having a grazing angle of inci-dence on the tunnel walls play a leading part in thepropagation and most of the energy propagates alongthe tunnel axis.

In real tunnel environments, distributed obstaclesand variations in the tunnel shape give rise to alarger angular spread. In any case, however, it wouldbe necessary to find a compromise between usingdirective antennas that increase the mean signal-to-noise ratio (SNR) and using omnidirectional anten-nas that allow a good exploitation of reflections onrandom obstacles. Indeed, one can imagine that thegain, which can be obtained with a multiple-antennatransmission and omnidirectional antennas, may alsobe obtained by only increasing the antenna gain ofa single-antenna transmission. For the experimen-tal measurements whose results are described in thenext subsection, horn and patch antennas having atotal beam width of about 90° have thus been cho-sen a priori. Nevertheless, additional measurementsmade with half-wave vertical dipoles have shown thatthe statistical properties of the MIMO channel werenearly identical.

3.2. Measurement Experiments and DataProcessing

Experimental measurements of subway tunnel chan-nels with multiple antennas have been carried out

in the subway of Paris, at the station ‘Porte desLilas’ in a tunnel presenting successively straightand slightly curved parts (one way) and in a tun-nel exhibiting a large bend (two way). The exper-imental measurements setup consists of four fixedhorn antennas placed on the station platform at aheight of 2 m and four patch antennas placed behindthe windscreen of the train. The complex impulseresponses were measured with a channel sounder hav-ing a bandwidth of 35 MHz by switching the antennassuccessively. The measurements were taken stoppingthe train approximately each 2 m and taking about1 second to measure and to store the 4 ð 4 compleximpulse responses. Since there is nobody on the plat-form or on the track, the channel remains stationaryduring each set of measurements.

Typical impulse responses in a one-way tunnel ofthe Paris subway are shown in Figure 4 for distancesbetween the transmitting and the receiving antennasequal to 75 m and 350 m, respectively. For the small-est distance, the train is in the line of sight of theplatform while, at 350 m, the train is situated aftera bend that masks the transmitting antenna. The ver-tical axis of Figure 4 is on an arbitrary linear scale,while the horizontal scale is 200 ns div�1. For GSM-R applications, it clearly appears that a single-tapmodel is sufficient to characterize the channel. This isin accordance with theoretical propagation modelingdescribed before. Nevertheless, it must be emphasizedthat this result could be questionable in other situa-tions in which the approximate translation symmetryis no longer valid, such as a two way tunnel in thepresence of other trains.

Since the channel is flat-fading, each impulseresponse hji�t�, corresponding to the time domainchannel characteristics between ith transmittingantenna and the jth receiving antenna, reduces toa complex number corresponding to the maximumvalue of the impulse response. One of the mainproblems to be solved before interpreting the data isto subtract the effect of the longitudinal attenuation.Indeed, in an indoor environment, for example, themovement of the mobile occurs in a small area, andwe can assume that the mean value of the electricfield remains a constant. In a tunnel, however, thelongitudinal attenuation is very important, on theorder of or greater than 10 dB/100 m. Since we areinterested in the improvement brought by spatialdiversity techniques for a given mean value of theSNR, the path loss must be subtracted. For straighttunnels, both theoretical results and experimentalmeasurements in the frequency domain have shown

Copyright 2002 John Wiley & Sons, Ltd. Wirel. Commun. Mob. Comput. 2002; 2:719–733

SPACE–TIME RECEIVERS FOR GSM RADIO INTERFACES 725

2.5 3 3.5 4 4.5 5 5.5 6

× 10−6

0

10

20

30

40

50

60

70

time s

2.52 3 3.5 4 4.5 5 5.5

× 10−6time s

linea

r am

plitu

de

0

10

20

30

40

50

60

linea

r am

plitu

de

Fig. 4. Typical impulse responses in a one-way tunnel fortwo distances between the fixed and mobile antennas:

(a) 75 m and (b) 350 m.

that the tunnel length can be divided into variousintervals or ‘zones’ so that the mean value of thefield exhibits an exponential decrease (therefore linearin dB) versus distance inside each zone. To removethe mean path loss, the statistical analysis is thususually made on the basis of field fluctuations aroundthe regression lines in the various zones of thetunnel [20].

In the Paris subway, where the measurements areperformed, there is a succession of curves, straightparts and various changes of the tunnel cross section.In spite of this, however, a one-slope model conve-niently fits the mean decrease of the field amplitudefor each set of measurements that correspond to alength of about 200 m. The preliminary data pro-cessing is thus the following: store the H matrix forsuccessive positions every 2 m; compute the averagepower of each matrix and then the regression line ofthe variation of the average power versus distance and

finally, normalize the amplitude of each element hji

around the square root of the value that the regressionline takes at that position.

3.3. Capacity Analysis

Many trials have been performed to find out the opti-mum position of the antennas inside each array, look-ing for minimizing the spatial correlation betweenthe various paths and always taking into account theoperational constraints. It is apparent that the patchantennas at reception must be placed as far as possibleand this is accomplished when locating the patches ateach corner of the windscreen of the train. Again, ata first glance it seems that the transmit horn anten-nas should be positioned perpendicular to the tracksince this configuration yields to larger spatial diver-sity. Because of the platform width, the maximumspace between the horn antennas is 1 m, that is, 3�.In order to validate this statement about the positionof the transmit horn antennas, we will also show theobtained results for a different configuration in whichthe horn antennas are placed parallel to the track.

From the sets of measured H matrices, the capacityof a given MIMO channel, C, can be calculated as [1]

C D log2 det

(ILðL C SNR

NHHH

)bps/Hz �11�

where SNR is the average signal-to-noise ratio perreceiving antenna, ILðL is the L ð L identity matrix,N is the number of transmitting antennas and theupper scriptH means transpose conjugate (Hermitian).

5 6 7 8 9 10 11 12 13 14

Capacity (b/s/Hz)

One way – perpendicularOne way – parallel Two way – perpendicularTwo way – parallel Rayleigh

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Pro

babi

lity

Fig. 5. Complementary cumulative distribution function ofthe channel capacity calculated for various shapes of the

tunnel (4 ð 4 antennas). Comparison with the case of i.i.d.Rayleigh channels.

Copyright 2002 John Wiley & Sons, Ltd. Wirel. Commun. Mob. Comput. 2002; 2:719–733

726 M. GONZALEZ-LOPEZ ET AL.

The complementary cumulative distribution functionof the capacity is given in Figure 5 for the pre-vious configurations, by assuming a mean SNR of10 dB. For comparison purposes, Figures 6 and 7show, respectively, the capacity for a 2 ð 2 anten-nas system (obtained by picking up the coefficientsof the channel matrix corresponding to the most sep-arated antennas) and for an 1 ð 1 antennas system.It is apparent that channel capacity increases withthe number of antennas. For instance, considering anoutage probability of 0.5 and the one-way-parallelconfiguration, the channel capacities for the 4 ð 4,2 ð 2 and 1 ð 1 antennas cases are, respectively, 6.7,4.6 and 3 (b s�1 Hz�1). Note also that for the otherconfigurations the capacity gains obtained by increas-ing the number of antennas are greater.

It is interesting to note that the one-way-parallelconfiguration has the maximum capacity in the 1 ð 1case, while it has the poorest capacity in the 2 ð 2 and4 ð 4 antennas cases. This is due to the presence ofhigh correlations between the coefficients of the chan-nel matrix. Figure 8 shows the observed correlationbetween the first coefficient, h11, and the other coeffi-cients of the channel matrix for the one-way configu-rations. It is clear that the one-way-parallel configura-tion exhibits a higher spatial correlation than the one-way-perpendicular configuration. Similar conclusionswere obtained when making comparisons betweenother configurations.

From the above explanations, we conclude thatwhen considering tunnels that present large bends(two way), the position of the transmit antennas is not

4 4.5 5 5.5 6 6.5 7

Capacity (b/s/Hz)

One way – perpendicularOne way – parallel Two way – perpendicularTwo way – parallelRayleigh

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Pro

babi

lity

Fig. 6. Complementary cumulative distribution function ofthe channel capacity calculated for various shapes of the

tunnel (2 ð 2 antennas). Comparison with the case of i.i.d.Rayleigh channels.

0 1 2 3 4 5 6 7 8 90

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Capacity (b/s/Hz)

Pro

babi

lity

One way – perpendicular One way – parallel Two way – perpendicular Two way – parallel Rayleigh

Fig. 7. Complementary cumulative distribution function ofthe channel capacity calculated for various shapes of the

tunnel (1 ð 1 antennas). Comparison with the case of i.i.d.Rayleigh channels.

h11 h12 h13 h140

0.5

1one way, parallel

one way, perpendicular

h21 h22 h23 h240

0.5

1

h31 h32 h33 h340

0.5

1

h41 h42 h43 h440

0.5

1

Fig. 8. Spatial correlations between coefficients of thechannel matrix.

important since spatial diversity is introduced by thechannel bend. On the other hand, the position of thetransmit antennas is crucial for straight tunnels (oneway). In this case, measurements reveal that placingthe antennas perpendicular to the track is the bestchoice.

4. Space—time Equalization

In this section we address the problem of compen-sating the effect of both the noise and the controlledISI induced by the GMSK modulation format. Math-ematically speaking, this problem is equivalent to

Copyright 2002 John Wiley & Sons, Ltd. Wirel. Commun. Mob. Comput. 2002; 2:719–733

SPACE–TIME RECEIVERS FOR GSM RADIO INTERFACES 727

detecting uncoded data that are mutually independentin both temporal and spatial dimensions. The firstconsidered approach is the Space–Time Maximum-Likelihood (STML) equalizer [21]. If all input mes-sage sequences are equally likely, it is well knownfrom information theory that the equalizing strategythat achieves the minimum probability of error is theone that chooses the transmitted message that max-imizes the conditional probabilities known as likeli-hood functions.

In order to formulate the STML equalizer, let usrewrite the observations vector given by Equation (4)in a different way

x�n� D H b�n� C g�n� �12�

where

H D [H f�m � 1� H f�m � 2� Ð Ð Ð H f�0�]�13�

is the channel matrix, with dimensions Nm ð L.Recall that m is the memory of the modulation(m D 3 in GSM) and f�l� is the equivalentdiscrete-time impulse response. The term b�n� inEquation (12) is the set of transmitted symbolsthat take part in the n-th vector of observationsand is given by b�n� D [bT�n � m C 1� bT�n � m C2� Ð Ð Ð bT�n�]T and g�n� D [g1�n�, . . . , gL�n�]T is avector of white Gaussian random processes thatrepresents the noise.

It is well known that for a Gaussian channeland equiprobable transmitted symbols, the ML cri-terion is equivalent to minimizing the Euclideandistance between the transmitted and the receivedsymbols. Having in mind the definition of x�n�given by Equation (12), the ML criterion consistsof choosing the transmitted sequence b�0: K � 1� D[bT�0� Ð Ð Ð bT�K � 1�]T that minimizes the followingEuclidean distance

Ob�0: K � 1� D arg minb�0:K�1�

ð{

�ML�b�0: K � 1�� DK�1∑nD0

jjx�n� � H b�n�jj2}

�14�

This optimization problem can be efficiently solvedby means of a multistream Viterbi algorithm whosemetric associated to each step is

�ML D jjx�n� � H b�n�jj2 �15�

Formulating the Viterbi algorithm requires a trellisrepresentation of the ST modulator. The number of

states at each trellis step is 2N�m�1�, and the numberof branches that outputs from each state is 2N. At thesame time, the number of branches that arrive at eachstate is also 2N. The Viterbi algorithm calculates the2N metrics associated with each of the 2N�m�1� stepsand retains the smallest values (survivors). Neverthe-less, when using the Viterbi algorithm, complexity isproportional to 2N�m�1�, and thus, exponential in boththe number of transmitting antennas and the memoryof the modulation (m D 3 in GSM). When the numberof antennas increases, the solution of Equation (14)becomes impractical.

Further complexity reduction can only be achievedat the expense of formulating suboptimum ST equal-ization algorithms. We have considered a Space–TimeLinear Separation (STLS) equalizer that utilizes thereceiver structure plotted in Figure 9. The objectiveof the linear filters is to spatially separate the trans-mitted signals in a way that each output extracts asingle signal, that is,

y�n� D WHx�n� D WHHs�n� C r�n� �16�

where r�n� D WHg�n� is the Gaussian noise at theoutput of the linear filters. The source signals areseparated when each output corresponds to a singleand different signal, that is, when WHH ³ INðN.In this case, yi�n� ³ si�n� C ri�n�, i D 1, . . . , N andthe Maximum-Likelihood estimation of the GMSKsymbols bi�0: K � 1� can be carried out by solvingthe following optimization problem

Obi,ML�0: K � 1�

D arg minbi�0:K�1�

{i,ML�bi�0: K � 1��

DK�1∑nD0

jjyi�n� � si�n�jj2}

MF&

WF

MF&

WF

b(n)

y1(n)

yN(n)

b1(n)

P/S

Linear filterw1

Linear filterwN

xL(n)

xL(t)

x1(n)

x1(t)

bN(n)Single-stream

Viterbi decoder

Single-streamViterbi decoder

Fig. 9. Space–Time Linear Separation (STLS) equalizerstructure.

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728 M. GONZALEZ-LOPEZ ET AL.

D arg minbi�0:K�1�

{i,ML�bi�0: K � 1��

DK�1∑nD0

jjyi�n� �m�1∑lD0

f�l�bi�n � l�jj2}

�17�

that can be efficiently solved using a single-streamViterbi algorithm. Note that the complexity of theSTLS structure, although exponential with the mod-ulation memory, grows linearly with the number oftransmitting antennas.

Different criteria can be used to select the coef-ficients of the linear separating system [21, 4]. TheMinimum Mean Square Error (MMSE) criterion isthe most reasonable choice since it leads to a com-promise between signal separation and noise amplifi-cation. It is well known that the weight vectors thatminimize the MSE between y�n� D WHx�n� and s�n�are given by the Wiener solution

WMMSE D Rx�1P D ��2

s 0HHH C �2gILðL��1H

�18�where Rx D E[x�n�xH�n�] D �2

s HHH C �2g ILðL is

the autocorrelation matrix of the observations andP D E[x�n�sH�n�] D H. The signal power and noisepower are represented by �2

s and �2g , respectively.

In the above solution, we have assumed that boththe channel matrix and the signal and noise powerare known. In practice, the Wiener solution canbe estimated using the training sequence included

in the GSM frames using conventional adaptivealgorithms [22].

The performance of the previous ST equalizer canbe considerably improved at the expense of little com-plexity increase, if the equalizer structure with linearcancellers shown in Figure 10 is employed [21]. Wewill use the term Space–Time Successive Cancella-tion (STSC) to denote this equalizer. The basic ideais to use a linear filter followed by a single- streamViterbi equalizer to initially demodulate one of thetransmitted data streams. The detected symbols arethen used to reconstruct the transmitted signal toeliminate it from the received vector and to obtaina new input with fewer components. This new inputis now used to demodulate a second data stream thatis again remodulated and subtracted from the input.This deflation process is repeated consecutively untilall the transmitted streams have been detected. Asbefore, note that the complexity of this ST equal-izer grows linearly with the number of transmittingantennas

Again, we have chosen the MMSE criterion toselect the coefficients of the linear filters, that is,

wi D N∑

jDi

�2s hjhH

j C �2gILðL

�1

hi, i D 1, . . . , N

�19�where wi are the coefficients of the i-th linear filterand hi represents the ith column of the channel

b1(n)

P/Sb(n)

x1(t)

+

+−

−

y1(n)Linear filterw1

Linear filterw2

y2(n) b2(n)

x2(n)

x2(t)

MF&

WF

MF&

WF

Signalreconstruction

Single-streamViterbi decoder

Single streamViterbi decoder

First stage

x1(n)

Fig. 10. Space–Time Successive Cancellation (STSC) equalizer structure.

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SPACE–TIME RECEIVERS FOR GSM RADIO INTERFACES 729

matrix H. The next step is to estimate the transmittedsequence bi�0: K � 1� from the output of each linearfilter

yi�n� D wHi xi�n� ³ si�n� C ri�n�, i D 1, . . . , N

�20�using a Viterbi equalizer. As mentioned above, theadvantages of the STSC equalizer rely on the remod-ulation of the detected bits at each stage and thesubtraction of the resulting signal, that is, the suc-cessive inputs are iteratively obtained as

xiC1�n� D xi�n� �(

m�1∑lD0

f�l�Obi�n � l�

)hi �21�

4.1. Computer Simulations

Computer simulations were carried out to illustratethe performance of the previously described STequalizers for a 4 ð 4 antennas system. We only focuson this number of antennas because significant gainsin capacity are obtained with respect to a systemwith fewer transmitting and/or receiving antennas,as shown in Section 3. Figures 11, 12 and 13 plotthe Bit-Error-Rate (BER) versus the Signal-to-Noise-Ratio (SNR) achieved with the STML, STSC andSTLS space–time equalizers. The strong differencesthat exist between the equalizing methods are clearlyseen: STLS is the worst method, STSC provides again with respect to STLS and STML is the best. Notethat for an uncorrelated Rayleigh channel the differ-ence in performance of the methods is much smaller.Also, it is interesting to observe that the configura-tion with worst performance is the one-way-parallel,which also exhibited the smaller channel capacity(see Section 3). The obtained results are in accor-dance with the fact that linear equalizers and decisionfeedback equalizers in single sensor systems severelydegrade their performance when channels have badspectral characteristics [15].

5. Space—time Decoding Receivers

This section deals with receivers that take intoaccount the existence of a convolutional space–timeencoder at transmission (see Figure 1). We can inter-pret the transmitter as the serial concatenation of theST convolutional encoder and the GMSK modula-tor. The optimum receiving strategy is to perform theMaximum-Likelihood (ML) detection of the originalinformation bearing sequence, u�n�, from the obser-vations, x�n�. This can be accomplished by means

5 10 15 20 25 30

SNR (dB)

One way – perpendicular One way – parallel Two way – perpendicular Two way – parallel Rayleigh

10−4

10−3

10−2

10−1

100

Bit–

Err

or–R

ate

Fig. 11. Performance results for the STML equalizer.

15 20 25 30 35 40 45 50

SNR (dB)

One way – perpendicular One way – parallel Two way – perpendicular Two way – parallel Rayleigh

10−4

10−3

10−2

10−1

100

Bit–

Err

or–R

ate

Fig. 12. Performance results for the STLS equalizer.

10 15 20 25 30 35 40

SNR (dB)

One way – perpendicularOne way – parallel Two way – perpendicularTwo way – parallel Rayleigh

10−3

10−4

10−2

10−1

100

Bit–

Err

or–R

ate

Fig. 13. Performance results for the STSC equalizer.

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730 M. GONZALEZ-LOPEZ ET AL.

of a Viterbi algorithm that considers the supertrel-lis resulting from the combination of the trellisesof the convolutional encoder and the GMSK mod-ulator. The states of this supertrellis take the form�sc, sm� where sc is a state belonging to the convo-lutional encoder trellis, and sm is a state belongingto the GMSK modulator trellis. The supertrellis hasSc ð Sm states, where Sc is the number of states ofthe convolutional encoder trellis, and Sm D 4N is thenumber of states of the GMSK modulator trellis,as explained in Section 4. To give an idea of howlarge this number can be, for an ST convolutionalencoder of Sc D 64 states and N D 4 transmittingantennas, the number of states of the supertrellis isSc ð Sm D 16384.

In order to avoid the above limitations, we willinsert an interleaver between the ST encoder andthe GMSK modulators to decouple both stages, andwe will consider two suboptimal detection strate-gies. The first one simply consists of the concate-nation of the STML equalizer described in the pre-vious section with a Viterbi ML decoder. Hard deci-sions are passed from the equalizer to the decoderand there is no feedback from the decoder to theequalizer.

The second approach, shown in Figure 14, will betermed the iterative Maximum A Posteriori (MAP)decoding scheme. The equalizer and the decoderstages are more properly coupled in the sense thatsoft decisions are interchanged between the equalizerand the decoder in an iterative fashion. The key aspectin this strategy is that all the information about thesymbols b�n� that the equalizer extracts from theobservations x�n� is passed to the decoder. Note thatin the previous scheme hard decisions are made (witha significant loss of information) before passing theinformation to the decoder.

From a statistical point of view, the best informa-tion about the coded bits b�n� that the equalizer can

produce after observing x�n� are their a posterioriprobabilities, that is, the probabilities of b�n� condi-tioned to the observed data x�n�. These probabilitiescan be obtained by means of the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm. A more general form ofthis algorithm that considers, among other things, notonly the computation of the a posteriori probabili-ties of the source bits but also the computation ofthe a posteriori probabilities of the coded bits is pre-sented in References [23,24] and this is the versionthat we have used in this work. The work in Ref-erences [23,24] refers to scalar valued sources andscalar coded symbols, but it can be easily extendedto the vector case since no assumption is made aboutthe symbol alphabet.

Let us start by denoting P[b�n�; I] to the a prioriprobability of b�n�, P[s�n�; I] to the a priori probabil-ity of s�n�, P[b�n�; O] to the a posteriori probabilityof b�n� and P[s�n�; O] to the a posteriori probabilityof s�n�. The a priori probabilities and the a posterioriprobabilities are the inputs and the outputs, respec-tively, of the algorithm. Taking the logarithm on allthe probabilities

[b�n�; I] � log P[b�n�; I]

[s�n�; I] � log P[s�n�; I]

[b�n�; O] � log P[b�n�; O]

[s�n�; O] � log P[s�n�; O] �22�

the algorithm adopts a desirable additive form.The iterative MAP decoding algorithm works as

follows: Let e be an edge of the trellis with the fol-lowing quantities associated: the starting state sS�e�,the ending state sE�e�, the input symbol b�n, e� andthe output symbol s�n, e�. The trellis is assumed tohave a unique initial state S0 and is assumed to finishin a unique ending state SKCm�1 where m is thememory corresponding to channel ISI. In order to

P[b(n);I]

P[b(n);O] P[c(n);I]

P[u(n);I]

x(n)

P[u(n);O]

Decision

P[c(n);O]

Space-TimeEqualizer

Interleaver

Deinterleaver

Space-TimeDecoder

Fig. 14. Block Diagram of an iterative space–time decoder.

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SPACE–TIME RECEIVERS FOR GSM RADIO INTERFACES 731

compute [b�n�; O] the algorithm performs the fol-lowing recursions:

(1) Forward recursion

˛n�s� D log

∑

e:sE�e�Ds

expf˛n�1[sS�e�]

C [b�n, e�; I] C [s�n, e�; I]g

n D 1, . . . , K C m �23�

(2) Backward recursion

ˇn�s� D log

∑

e:sS�e�Ds

expfˇnC1[sE�e�]

C [b�n C 1, e�; I] C [s�n C 1, e�; I]g

n D K C m � 1, . . . , 0 �24�

[b�n�; O] D log

∑

e:b�n,e�Db�n�

expf˛n�1[sS�e�]

C [b�n, e�; I] C ˇn[sE�e�]g C hb �25�

where

˛0�s� D{ 0 s D S0

�1 otherwise�26�

ˇKCm�s� D{

0 s D SkCm

�1 otherwise�27�

are the initial values for the recursions and hb is theconstant that makes P[b�n�; O] a probability densityfunction, that is, ∑

b�n�

P[b�n�; O] D 1 �28�

In the first iteration of the decoding process, it isassumed that the a priori probabilities of the infor-mation symbols, P[b�n�; I] are uniform densities. Theother input to the algorithm, P[s�n�; I] is equal to theconditioned density of s�n� to the observations x�n�,that is, P[s�n�jx�n�].

Once computed in this way, the a posteriori prob-abilities are passed to the decoder. A deinterleaver isused in order to feed this set of a posteriori probabil-ities into the decoder in the same order that the coded

symbols were emitted. Then the decoder uses theseprobabilities as a priori probabilities of the codedsymbols, P[c�n�; I], to compute the a posteriori prob-abilities of the original symbols assuming that thecorresponding a priori probabilities, P[u�n�; I], areuniformly valued. Note that the algorithm for thedecoding stage is the same as that for the equaliz-ing stage described below, taking into account onlythe trellis of the convolutional code instead of thetrellis of the GMSK modulator. Finally, a decisionis made just choosing the original symbol with thehigher a posteriori probability of having been trans-mitted

Ou�n� D arg maxu

P[u�n�; O] �29�

Up to this moment the only (although important)difference between this scheme and the ML approachdescribed as our first suboptimal scheme is the usageof soft-valued decisions (i.e. the a posteriori proba-bilities) between the equalizer and the decoder. How-ever, more refined decisions can be obtained if thedecoder also computes the a posteriori probabilitiesof the coded symbols, P[c�n�; O], and feeds themback into the equalizer as the a priori probabilities ofthe modulator input symbols, P[b�n�; O]. The com-putation of the a posteriori probabilities of the codedsymbols can be made at the same point in the algo-rithm in which the a posteriori probabilities of theoriginal symbols are computed, and through a similarexpression given by

[c�n�; O] D log

∑

e:c�n��e�Db�n�

expf˛n�1[sS�e�]

C [u�n, e�; I] C ˇn[sE�e�]g C hb

�30�

where u�n, e� is the input symbol associated with thetrellis edge e. Note that these a posteriori probabil-ities must be interleaved to be properly fed back tothe equalizer. The overall process is then repeateduntil no more improvement in symbol-error-rate isachieved.

Computer simulations were carried out to illus-trate the performance of the previously describedreceiving strategies. We considered the same com-munication system as in the previous section butwith the ST full diversity binary code given by thegenerator matrix G D [52, 56, 66, 76] (in octal repre-sentation) [25]. Figure 15 shows the BER versus the

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732 M. GONZALEZ-LOPEZ ET AL.

−5 0 5 10 15 20 25

SNR (dB)

MAP 1st iteration

10−4

10−5

10−6

10−3

10−2

10−1

Bit–

Err

or–R

ate

Space–Time ML

Space–Time MLcoded data

MAP 2nd, 3rditerations

MAP Idealfeedback

Fig. 15. Performance results for space–time decodingreceivers.

SNR at the reception for the decoding schemes pre-sented before, as well as for the STML uncoded sys-tem presented in Section 4, for comparison. Resultswere obtained for the one-way-perpendicular config-uration. It can be seen that simply adding an STencoder and performing ML decoding improves theperformance of the system (e.g. the required SNRto reach a BER of 10�4 diminishes in 12 dB). Alsonote that this improvement with respect to the STML,is higher when MAP decoding is performed. Forinstance, it can be seen that in the first iteration an18-dB gain in SNR is obtained for a BER of 10�4.Nevertheless, no significant improvement has beenobtained when performing more iterations. Some rea-sons explaining why the GMSK modulation formatdoes not present improvement through iterations aregiven in Reference [26]. This phenomenon, however,does not mean that the iterative scheme does notwork: we have also included in Figure 15 the BERobtained by an ideal MAP decoder, that is, the onethat permits to feed into the equalizer the true a pri-ori probabilities of the modulator input symbols. Notethat there exists no significant difference between thecurve corresponding to the ideal MAP decoder andthe curves obtained after the second and third itera-tions. This means that, even when we have perfectknowledge of the symbols that were fed into theGMSK modulator, the performance of the equaliz-ing stage is not significantly better than the perfor-mance when the knowledge, in the form of a prioriprobabilities, is fed back from the decoder to theequalizer.

6. Conclusion

The improvement of GSM radio interfaces in subwaytunnels by means of antenna arrays and ST receivershas been investigated. We have demonstrated, boththeoretically and experimentally, how the wirelesspropagation in subway tunnels can be convenientlymodeled as a flat-fading channel. Nevertheless, exper-iments revealed that there exist strong spatial corre-lations among channel components that reduce chan-nel capacity and severely affect receivers’ perfor-mance. Receivers comprising of an ST equalizer andan ST decoder have been considered. Three differ-ent ST equalization strategies have been described.STML equalization is the technique that exhibits thelowest BER and the largest robustness but presentsthe largest complexity. On the other hand, STLSand STSC are much less complex but their perfor-mance is considerably worse. Thus, the selection ofone method or the other will depend on the trade-off between complexity and performance that thereceiver designer wishes to reach. We have also ana-lyzed the performance of receivers with ST cod-ing capabilities. We have demonstrated that MAPreceivers that interchange soft information among theequalization and the ST coding stages exhibit a muchbetter performance than those ML receivers that dealwith hard decisions. Because of the poor character-istics of the GMSK modulation employed in GSMsystems, the most important improvement in perfor-mance is achieved after the first iteration of the MAPreceiver. However, no more significant improvementis observed after the following iterations.

Acknowledgments

This work has been supported by the EuropeanCommission under contract number IST-1999-20006(ESCORT project).

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