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In this paper, we investigate how to increase the capacity of GSM (Global System for Mobile communications) radio interfaces in subway tunnel environments by means of antenna arrays and Space–Time (ST) receivers. We address the modeling, both

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WIRELESS COMMUNICATIONS AND MOBILE COMPUTING
Wirel. Commun. Mob. Comput.
2002;
2
:719–733 (DOI: 10.1002/wcm.89)
Space—time receivers for GSM radio interfaces in subwaytunnel environments
Miguel Gonz´alez-L´opez, Adriana Dapena andLuis Castedo*
,
†
Departamento de Electr´onica y Sistemas,Universidad de A Coru˜na,Facultad de Inform´atica,Campus de Elvi˜na, A Coru˜na,Spain
Martine Lienard and Pierre Degauque
Universit´e de Lille,Dept. Electronique,Bat. P3,59655 Villeneuve d’Ascq cedexFrance
Mar´ıa J. Asarta and Pedro Crespo
Centro de Estudios e InvestigacionesT´ecnicas de Guipuzcoa (CEIT)Paseo de Manuel Lardiz´abal, 15,20018 San Sebasti´an,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, of the 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 of iterative MAP (
Maximum a Posteriori
) receivers thatinterchange soft information among the equalizerand the ST decoder. All receivers are evaluated withexperimental channels measured in the subway of Paris. Copyright
©
2002 John Wiley & Sons, Ltd.
KEY WORDS
space–time receiversGSM radio interfacesMultiple-Input Multiple-Output (MIMO)channelsiterative
Maximum a Posteriori
(MAP)decoding
Ł
Correspondence to: Luis Castedo, Departamento de Electr´onica y Sistemas, Universidad de A Coru˜na, Facultad deInform´atica, Campus de Elvi˜na, A Coru˜na, 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. GONZ´ALEZ-L ´OPEZ
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 of multiple 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 canbe 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 of using 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 of tunnels 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 of ST 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 srcinal bit sequence
un
is encodedwith a ST encoder to produce a vector of sym-bols
c
n
D
[
c
1
n,...,c
N
n
]
T
(
N
is the number of transmitting 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
s
1
n,...,s
N
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
[
x
1
n,x
2
n,...,x
L
n
]
T
. The goal inST decoding is to detect the srcinal sequence
un
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 boththe 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 of 2
m
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
i
th transmitting antennafor a GSM frame of
K
bits,
s
i
t
;
b
i
0:
K
1
, can beaccurately approximated by the following expression
s
i
t
;
b
i
0:
K
1
³
2
E
b
T
K
1
n
D
0
a
i
npt
nT
1
where
b
i
0:
K
1
D
[
b
i
0
b
i
1
ÐÐÐ
b
i
K
1
]
T
isthe binary information bearing sequence,
E
b
is thebit energy,
T
is the symbol period,
a
i
n
D
j a
i
n
1
b
i
n
are the transmitted symbols and
pt
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.
a
i
n
2
u(n)c
1
(n) b
1
(n)s
1
(t;b
1
(n)) x
1
(t) x
1
(n) b
^
1
(n) c
^
1
(n)u
^
(n)
N
c
^
N
(n) x
L
(n)b
N
(n)c
N
(n) x
L
(t)s
N
(t;b
N
(n))b
^
N
(n)
STCoderInter-leaverGMSKMF&WFDeinter-leaverSTDecoderDeinterleaverMF&WFMultipathchannelGMSKInter-leaverSpace-TimeEqualizerN
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. GONZ´ALEZ-L ´OPEZ
ET AL
.
f
1
,j,
1
,
j
g
), are uncorrelated and have unit vari-ance [13]. We assume that differential precoding isemployed before the modulator, so
a
i
n
D
j
n
b
i
n
.The transmitted signals arrive at an array of
L
receiving 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
j
th receiving antenna canbe expressed as follows:
x
j
t
D
N
i
D
1
h
ji
s
i
t
;
b
i
0:
K
1
C
n
j
t,j
D
1
,...,L
2
where
h
ji
is the channel impulse response that modelsthe fading corresponding to the subchannel betweenthe
i
th transmitting antenna and the
j
th receivingantenna. The noise component
n
j
t
is modeled asa continuous-time white Gaussian random process.In order to detect the transmitted symbols, thesignals
x
j
t,j
D
1
,...,L
are passed through a bank of ﬁlters matched to the impulse response of themodulation pulse,
pt
, and sampled at the symbolrate to produce a set of sufﬁcient statistics [14]. Itis important to note that the noise at the output of the matched ﬁlters is colored because
pt
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
x
j
n
D
N
i
D
1
h
jim
1
l
D
0
flb
i
n
l
C
g
j
n
D
N
i
D
1
h
ji
s
i
n
C
g
j
n
3
where
g
j
n
is a discrete-time white Gaussian noise,
m
is the memory of the modulation (
m
D
3 in GSM)and
fl
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 thesrcinal sequence
un
.
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,
B
c
,
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
ε
r
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 of the walls are critical.Figure 2 also plots the regression line that approx-imates the obtained results. It is apparent that
B
c
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 of reﬂections 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 2010
7
10
8
c o h e r e n c e b a n d w i d t h ( 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 of the 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
m
th image and the transmitter.The reﬂection coefﬁcient
R
TE
associated with the TEpolarization on the vertical walls is given by
R
TE
D
sin
˛
n
2
cos
2
˛
sin
˛
C
n
2
cos
2
˛
5
where
n
is the relative refractive index of the walls.Since, at high frequencies, the inequality
×
ωε
r
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
R
TE
D
˛
k ˛
C
k
6
where
k
Dp
ε
r
1. As
˛
is much smaller than
k
,an approximate expression of
R
TE
can be obtained asfollows:
R
TE
³
1
2
˛/k
7
The
m
th ray reﬂects
m
times on the vertical walls. Itsattenuation
a
m
, expressed in dB and referred to the
∆
xAx
αα
mLBTxORx
Fig. 3. Geometrical conﬁguration in a horizontal plane.
Copyright
©
2002 John Wiley & Sons, Ltd.
Wirel. Commun. Mob. Comput.
2002;
2
:719–733

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