Neural network-based techniques for efficient detection of variable-bit-rate signals in MC-CDMA...

ARTICLE IN PRESS

0165-1684/$ - se

doi:10.1016/j.sig

$This work h

SHINES projec�Correspondi

control; FFT,

likelihood; ML

interference; M

multiplexing; O

network.

E-mail addre

Signal Processing 85 (2005) 505–522

www.elsevier.com/locate/sigpro

Neural network-based techniques for efficient detection ofvariable-bit-rate signals in MC-CDMA systems

working over LEO satellite networks$

Claudio Sacchia, Gianluca Gerab, Carlo S. Regazzonib,�

aDepartment of Information and Communication Technology (DIT), University of Trento,

Multimedia Communications and Networking Labs, Via Sommarive 14, I-38050 Trento, ItalybDepartment of Biophysical and Electronic Engineering (DIBE), CNIT-DIBE, University of Genoa,

Signal Processing and Telecommunications Group (SP&T), Via Opera Pia 11/A, I-16145 Genoa, Italy

Received 22 November 2001; received in revised form 8 October 2004

Abstract

For a few years, multicarrier modulations have been proposed as valuable alternatives with respect to state-of-the-art

single carrier ones due to their resilience against interference and channel distortion effects. In particular, many studies

are arising about multicarrier-CDMA (MC-CDMA) techniques that provide improved robustness and flexibility with

respect to single-carrier spread-spectrum techniques. Satellite communications considered the employment of MC-

CDMA for multimedia transmission very recently, especially for what concerns the delivery of variable-bit-rate services

over low-earth-orbit (LEO) satellite networks. To this aim, the problems to be faced are mainly related to the

development of efficient methodologies for satellite channel estimation, equalization and multi-user detection, in order

to exploit in an optimal way the natural diversity inherent to MC-CDMA. In this paper we compare two different

neural-network-based approaches for efficient reception of MC-CDMA signals in the case of asynchronous, multi-user,

and variable-bit-rate transmission over LEO satellite channels. The first approach introduces neural networks for

supporting receiver decision. The second more sophisticated approach exploits neural networks for joint channel

estimation and symbol detection. Simulation results will be presented that demonstrate the improved effectiveness of

e front matter r 2004 Elsevier B.V. All rights reserved.

pro.2004.10.018

as been partially supported by the Italian Ministry of University and Scientific Research within the framework of the

t.

ng author. Tel.: +39 10 3532792; fax: +39 10 3532134. Abbreviations: EGC, equal gain combining; FEC, forward error

fast Fourier transform; GEO, geo-stationary; LEO, low-earth-orbit; LSR, linear shift register; ML, maximum-

P, multi-layer perceptron; MSE, mean square error; MMSE, minimum mean square error; MUI, multi-user

C-CDMA, multicarrier code division multiple access; NN, neural network; OFDM, orthogonal frequency division

VSF, orthogonal variable spreading factor; PN, pseudo-noise; VBR, variable bit rate; WLAN, wireless local area

sses: [email protected] (C. Sacchi), [email protected] (G. Gera), [email protected] (C.S. Regazzoni).

www.elsevier.com/locate/sigpro

ARTICLE IN PRESS

C. Sacchi et al. / Signal Processing 85 (2005) 505–522506

the proposed methodologies, with respect to state-of-the-art MC-CDMA detection techniques, both in terms of reduced

BER and in terms of low computational complexity.

r 2004 Elsevier B.V. All rights reserved.

Keywords: Multi-carrier demodulators; Multi-user detection; Channel equalization; Neural Networks; Digital communications

1. Introduction

The use of low-earth-orbit (LEO) satelliteconstellations for multimedia service provisionpresents some advantages with respect to the useof geostationary (GEO) constellations for thesame purposes. The costs required for launchingand maintaining in orbit a LEO satellite are muchlower than GEO ones [18]. Moreover, the latencytime is reduced in a consistent way, thus ensuringreal-time response in interactive multimedia appli-cations mostly supported by satellite networks(e.g. videoconference, distance learning, remotemonitoring, etc.). For a few years, data transmis-sion over LEO satellite networks has beenperformed only by using the lowest portions ofsatellite spectrum, i.e.: L-band (0.8–2GHz), S-band (2–3GHz) and C-band (3–7GHz). Advan-tages in terms of low costs of home terminals andearth-station devices are obvious in such bands.Indeed most of commercial applications supportedby LEO networks, e.g. radio localization (GPS,GNSS), vehicular communications, etc., currentlyemploy L-band and S-band for data trans-mission [10]. The main drawback of low-frequencybands in satellite communications is relatedto the presence of relevant signal propagationimpairments quite similar to the ones affectingterrestrial networks, i.e. frequency selective multi-path fading [10,18] that induces time-varyingpower fluctuations of the received signal. Theuse of Ka-band (18–30GHz) should be almostadvisable in such a perspective, mainly dueto the consolidate technology refined by about 40years of use in geostationary applications.Indeed some satellite systems, devoted to INTER-NET provision to residential users [12], currentlyexploit LEO satellites for reducing latency timeand Ka-band for improving system capacity.Nevertheless, Ka-band transmission presents awell-known problem, i.e. the heavy power attenua-

tion due to rain fading. Rain fading attenuationcan even be equal to 20 or 30 dB [22], pra-ctically causing the interruption of the providedservices if appropriate countermeasures are notapplied [25].This work is inserted in the above mentioned

state-of-the art framework, however considering adifferent approach. Instead of looking for highertransmission frequencies, we tried to test uncon-ventional modulation and multiple access techni-ques for high-bit-rate transmission over LEOsatellite networks working in low-frequency bands.In such a context, critical aspects to be envisagedare related to the reduced bandwidth availabilityand the channel distortions involved by multi-path fading that should be taken into account byusing appropriate modulation and coding techni-ques. Recently, the use of innovative multi-

carrier CDMA techniques (MC-CDMA) for datatransmission over LEO satellite networks hasbeen considered in literature (see e.g. [19,23]).MC-CDMA techniques are strictly derived byorthogonal frequency division multiplexing(OFDM) ones [6]. MC-CDMA are classified asSpread Spectrum techniques, as a single databit is modulated over orthogonally-spaced multi-ple carriers [11], with a consequential spectralspreading of the transmitted signal. MC-CDMAexhibits an improved resilience against multi-userinterference (MUI), even when the channel isaffected by severe time and frequency varyingdistortions, like indoor channels [11]. This im-provement is due to the double orthogonality atfrequency level and at code level inherent to MC-CDMA techniques, which is retained also inmultipath fading channels [27]. This fact couldnot be verified for DS/CDMA systems, becausemultipath fading might destroy the orthogo-nality of user codes in the time domain, andthe resulting MUI may render symbol re-covery quite problematic [11,27] if proper

ARTICLE IN PRESS

C. Sacchi et al. / Signal Processing 85 (2005) 505–522 507

multi-user detection (MUD) algorithms are notadopted. Moreover, as shown in [23], MC-CDMAexhibits a natural inclination to variable-bit-rate(VBR) transmission. Indeed, VBR services can beeasily managed by assigning to each user avariable-cardinality set of subcarriers dependingon each bit-rate request. In [11], some basicmethods for detection of MC-CDMA signals overradio channels are presented. Conventional MC-CDMA detection schemes are based on thecanonical diversity-combining methodologies, i.e.equal-gain-combining (EGC), maximal-ratio-combining (MRC), orthogonality-restoring-combining (ORC), and minimum-mean-squared-error (MMSE) combining [11]. Such criteriaare best suited for the single user case and de-crease their performances as the number oftransmitting users increase. On the other hand,theoretically optimal MUD in MC-CDMA sys-tems could be obtained by applying the maximumlikelihood (ML) criterion [11]. The main drawbackof this solution consists in the unsustainablecomputational load exponentially growing withthe user number [11]. For this reason, sub-optimalmulti-user receivers are intensively studied inrecent literature in order to improve MC-CDMAsystem performances with affordable computa-tional expense.

In this paper, the use of backpropagationmulti-layer perceptron neural networks is investi-gated in order to implement computationallysustainable VBR MC-CDMA receivers. Neuralnetworks (NNs) have been proposed since begin-ning of 1990s as efficient solutions to a widerange of signal processing and communicationproblems [4,13,16]. Neural networks are notprogrammed in a conventional fashion. Rather,they are trained by example. Neural networkslearn how to produce a desired output whenshown a particular set of inputs (training phase

[16]). The learning process internally forces thesystem to identify relationships between inputsand learn about the history of inputs. Bysynthesizing relationships, the neural network isable to generalize from situations that it hasencountered before (test phase [16]). In practice,most of computational load is required by theNNs in the training phase, which is generally

performed off-line. Due to such suitable features,the use of neural networks in digital commu-nications and signal processing has becomequite common. In [13,14] some related applica-tions are presented, ranging from non-linearchannel modelling and equalization, to FECdecoding, up to DS/CDMA MUD in terrestrialand satellite (S-UMTS [14]) environments. Fromthis point of view, the application of neuralnetworks to variable-bit-rate MC-CDMA recep-tion in LEO satellite environment is surely aninnovative research topic. Some very recentworks have dealt with the application of neuralnetworks to MC-CDMA signal reception. MC-CDMA techniques allow obtaining frequencydiversity by spreading the same symbol overmultiple orthogonal carriers. The multi-branchMC-CDMA receiver has actually to combinemultiple signal paths (corresponding to eachdifferent subcarrier), each one characterized bydifferent attenuation and phase shift. Thismeans that a frequency-selective channel is splitinto a set of N flat-fading channels, where N

is the number of subcarriers. In such a frame-work, NNs can be employed for supportingdecision at the output of the conventionalreceiver (following an approach similar to oneshown in [1] for DS/CDMA systems) as wellas for combining multiple paths in an optimalway. The later is the approach shown in [15],where a radial-basis-function (RBF)-basedmulti-user detector has been employed for optimalcombination of the MC-CDMA receiver di-versity branches. In [24], a Hopfield neural net-work (HNN) has been employed for MUD ofasynchronous MC-CDMA signals in multi-path fading channels. The HNN requires channelstate information (CSI) in order to improve itsperformances for time-varying multipath fadingchannels (without CSI the performances of theHNN degrades similarly to matched filter [15]). Ofcourse, the availability of CSI is conditioned onthe insertion of training bits involving redundancyin the transmitted message.This paper considers the interesting application

case of neural-network based receivers to variable-bit-rate MC-CDMA systems, working over LEOsatellite channels, usually characterized by fast

ARTICLE IN PRESS


time-varying impulse response. The VBR trans-mission involves additional problems with respectto the fixed-bit-rate one considered in [15,24],because user classes with few subcarriers aresubjected to heavy interference effects producedby user classes with a larger number of subcarriers.Moreover, we considered in our work the use ofMLP neural-networks with backpropagationlearning rule, which is the simplest NN schemewidely used in most of signal processing andcommunication tasks [16]. In particular, two NN-based schemes have been tested:

�
a supporting-decision scheme, using a neuralnetwork as decision-maker working on thesingle output of the conventional receiver;
�

Fig. 1. Single user’s VBR MC-SS transmitter.

a joint channel equalization and symbol estima-tion scheme, aimed at equalizing the frequency-selective channel impulse response and jointlyestimating the transmitted symbol.

No channel information is provided to the NN-based scheme during the test phase, so as to avoidthe insertion of training bits in the message. Forthis reason, the proposed algorithms can beinserted in the framework of the blind detectionmethodologies [9]. The performances of theproposed NN-based reception schemes are thencompared with ones provided by the conventionalEGC receiver and by a modified orthogonality-restoring (ORC) scheme, employing a low-com-plexity adaptive channel estimation algorithm(quite similar to one described in [23]).

The paper is structured as follows: Section 2contains the description of the VBR MC-CDMAtransmission system, Section 3 summarizes thearchitecture of a generic MC-CDMA receiver,reporting also some brief notes about conventionalMC-CDMA reception techniques (EGC, ORC;MMSE, ML). Section 4 describes a realisticexample of a VBR MC-CDMA conventionalreceiver based on an improved ORC algorithmemploying a computationally tractable channelestimation algorithm. Section 5 focuses the in-novative aspects related to the utilization of neuralnetworks for the efficient reception of VBR MC-CDMA signals in the considered test case relatedto a L-band transmission over LEO satellite

networks. Section 6 will present some selectedsimulation results, and finally Section 7 drawsconclusions.

2. Transmission system description and satellite

channel modelling

2.1. VBR MC-CDMA transmission system

The block diagram of the mth user’s ðm ¼

1; . . . ;MÞ variable-bit-rate MC-SS transmitterconsidered for simulation is depicted in Fig. 1.The transmitted symbol data stream of the mthuser amðtÞ is copied into Nm parallel streams. Eachcopied stream is multiplied by a binary pseudo-random coefficient cm½i� 2 f1; 1g; i ¼ 1; . . . ;Nm:The pseudo-random vector cm is the signature

code of the mth transmitter, distinguishing it fromthe other transmitters of the system. Then, thesigned data streams are sent to an OFDM block,that can be implemented by using a baseband I-FFT-based scheme, followed by an IF stage, asshown in [6]. The number of subcarriers attributedto the mth user for multiplexing the informationstream in the frequency domain is equal to Nm:This value can be regarded as the actual processinggain of the MC-SS transceiver. As a fixed amountof bandwidth is employed for transmission, eachuser’s MC-SS modulator is provided with adifferent number of orthogonal sub-carriers Nm;depending on the user’s bit-rate. The userstransmitting at the highest bit-rate will use thesmallest number of carriers, whereas the userstransmitting at the lowest bit-rate will use thehighest number of carriers, thus complying withthe usual trade-off between transmission speed

ARTICLE IN PRESS


and protection against channel effects [8]. Thus,the signal transmitted over the satellite channel bythe mth user can be expressed as follows:

smðtÞ

¼ ReXþ1

k¼1

XNm1

i¼0

cm½i�am½k�e2pjðf cþf m;iÞt

(

pTmðt kTmÞ

); ð1Þ

where f c is the L-band transmission frequencyselected by the RF stage, Tm is the time ofduration of a single symbol transmitted by the mthuser, and pTm

ðtÞ is the pulse-shape waveform,assumed for simplicity as a rectangular pulse ofamplitude

ffiffiffiffiffiffi2P

p(P is the transmission power

assumed equal for all users) and duration Tm: Ina MC-CDMA VBR transmission system, theorthogonal subcarrier set allocated to each user(and hence the term f m;i of Eq. (1)) must be chosenso that the correct orthogonal spacing amongsubcarriers is ensured for the different user classes.Following a common approach (see e.g. [8]), J

classes of variable-bit-rate users are assigned asfollows:

rj ¼ 2Jjr; j ¼ 1; . . . ; J; (2)

where r is the symbol-rate of the slowest users (i.e.class J) given as

r ¼1

T log2 B; (3)

where B is the number of modulation levelsand T is the bit duration of slowest users. Inthe present dealing, we consider a BPSK modula-tion for all users and hence B is fixed to 2. Theformula providing the correct orthogonal spacingof the subcarriers for the mth user of class jm

Fig. 2. Tree structure of the variable

is given by

f m;i ¼F

2ð2jm1 1Þr þ iFrjm

i ¼ 0; . . . ;Nm 1:

(4)

F is the subcarrier spacing factor ðFX1Þ [11]. Inthis paper, it has been hypothesized that the‘‘slowest’’ user have to transmit data at 512Kb/sover 64 orthogonal carriers, other users at 1Mb/sover 32 orthogonal carriers and the ‘‘fastest’’ usersat 2Mb/s over 16 orthogonal carriers (i.e. threedifferent classes of VBR users).Let us suppose that class 1, class 2 and class 3

identify 2Mb/s ðN ¼ 16Þ; 1Mb/s ðN ¼ 32Þ; 512kb/sðN ¼ 64Þ users respectively. In such a case,rm¼1=Tm ¼ rjm

2 f2Mbps; 1Mbps; 512 kbpsg8m ¼

1; . . . ;M: By assuming a subcarrier spacing factorF ¼ 2; all users utilize a bandwidth portion of64MHz for transmitting their VBR messages. Thesignature codes cm½i� have been chosen in therecursive, tree-structured, mutually orthogonal andvariable-length set described in [8] (orthogonal vari-able spreading factor—OVSF codes). The first fourlevels of the binary sequence tree are depicted inFig. 2. Each code is characterized by a ‘‘father’’staying at the upper level of the tree. The set ofcodes at each level is a mutually orthogonal Walshset. Couples of codes belonging to different levelsof the tree are also mutually orthogonal, except inthe case when one of the codes belonging to ahigher level is the father of one or more codesbelonging to a lower level. It is worth noting thatOVSF codes, employed also as short codes for theUMTS uplink [8], are orthogonal only in the caseof synchronous transmission. In case of asynchro-nous transmission, OVSF codes present correla-tion properties almost similar to the quite poorones characterizing the Hadamard–Walsh set.Nevertheless, the correlation properties of other

length OVSF signature codes.

ARTICLE IN PRESS


LSR codes, like Gold and Kasami sequences [21],are very bad when spreading codes of differentqlength must be adopted in DS/CDMA multi-ratetransmission [3]. This happens because the fairciclostationarity properties of the aforesaid LSRcodes are completely lost in case of variable spreadingfactor applications [3]. As MUI in MC-CDMAsystems mainly depends by the correlationproperties of the signature codes, as shown in [20],we considered the use of OVSF codes also forVBR MC-CDMA transmission, as an acceptablesolution.

The asynchronous MC-CDMA VBR upstreamtransmission is performed upon the modalityshown in Fig. 3. M earth terminals send theirmultirate data-streams over the same bandwidthto a LEO satellite with random delays tmðm ¼

1; . . . ;MÞ; assumed as uniformly distributed withinthe bit duration time interval Tm: For sake ofsimplicity, we assume here that the LEO satellite isnon-regenerative: this means that the overall tasksof demodulation are performed at the base-station.

Considering the system shown in Fig. 3, theMC-CDMA VBR signal transmitted in upstreamhas the following formulation:

xðtÞ¼XM

m¼1

smðt tmÞ

¼ ReXM

m¼1

Xþ1

k¼1

XNm1

i¼0

cm½i� am½k�e2pjðf cþ f m;iÞt

(

e2pjðf cþf m;iÞtm pTmðt tm kTmÞ

): ð5aÞ

Fig. 3. VBR multi-user MC-CDMA transmission over LEO

satellite networks.

Note that the asynchronous delays tm appear in Eq.(5a) as random phase delay terms. This fact shouldinvolve the presence of MUI also in case oftransmission over AWGN channel as clearly shownin [20]. In the following of the paper, we shall showthat another source of orthogonality loss is thetransmission over multipath fading channels, likelow-frequency LEO satellite channels.

2.2. Channel modelling

The LEO satellite channel has been modelled asa wideband andfrequency selective multipath-fad-ing channel. In particular, we considered a tapped-

delay-line channel model [21], with a direct LOSpath and Rayleigh distributed channel coefficientsfor the secondary paths. The number of multipathsis defined as L ¼ bWDsc þ 1 where W is the signalbandwidth, assumed equal to 64MHz for overallusers, whereas the delay spread DS has been setequal to 100 ns according to the experimentalmeasurements shown in [5]. This means that wecan resolve up to seven separated paths [21].The computation of the Doppler spread, which

is the measure of the time variability of channelimpulse response [21], has been performed byfollowing the approach shown in [2]. Assuming theparameterization shown in [2], the computedDoppler spread of a L-band LEO satellite channelis equal to 40KHz (coherence time 25ms). Assum-ing the aforesaid channel model, the signalreceived by the generic MC-CDMA receiver,whose block diagram is shown in Fig. 4, can begiven as follows:

yðtÞ ¼XL

l¼1

BlðtÞxðt DlÞ þ nðtÞ (5b)

being BlðtÞ the complex tap gains related to eachchannel path, Dl the associated path delays, andnðtÞ the white Gaussian noise, whose one-sidedpower spectral density is equal to N0 W=Hz:

3. MC-CDMA receiver structure

The basic structure of a MC-CDMA receiver(see Fig. 4) relies on a matched filter bank [11,20];

ARTICLE IN PRESS

Fig. 4. Generic scheme of a MC-CDMA receiver.


one for each intended user. Ideal carrier andclock recovery is assumed as hypothesis foreach user’s receiver. When asynchronous transmis-sion delays, and/or frequency-selective multipathfading occur in the transmission, MUI is ge-nerated at the output of the matched filter bank[11,20]. After a coherent OFDM demux (per-formed by means of a FFT block), the receivedsignal yðtÞ is passed through a low-pass filter(typically an integrator with integration periodequal to the symbol duration [20]), and thenweighted by complex receiver gains qm;i [11]. So,the expression of the decision variable sampled int ¼ kTm at the output of the mth user’s MC-CDMA generic receiver of Fig. 4 has the followingexpression:

Y mðkÞ ¼ SmðkÞ þ NmðkÞ þ ImðkÞ ¼ffiffiffiffiffiffi2P

pTm

XNm1

i¼0

qm;igm;icm;iejym;i amðkÞ þ

XNm1

i¼0

qm;iZm;iðkÞ

þXM

u¼1uam

XNu1

i¼0

qm;igu;icu;iejyu;i

Z ðk1ÞTmþtu

ðk1ÞTmþtm

�

auðk 1ÞpTuðt ðk 1ÞTu tuÞdt

þ

Z kTmþtm

ðk1ÞTmþtu

auðkÞpTuðt kTu tuÞdt

�;

m ¼ 1; 2; . . . ;M; k ¼ 1; 2; . . . : ð6Þ

Three terms are added in the equation above: afirst contribution SmðkÞ containing the desiredsymbol, a second contribution NmðkÞ related toGaussian noise, and a third contribution ImðkÞ

taking into account MUI produced by asynchro-nous transmission and multipath channel distor-tions. In order to explain in a clearer way what thedifferent quantities of Eq. (6) represent, it must besaid that:

�
gm;i ¼ am;i expðjfm;iÞ is the complex channel coef-
ficient related to the ith subcarrier of the mthuser. Such a coefficient takes into account thefrequency-selective channel distortion due tomultipath fading. In general, it is regarded as atime-varying coefficient;

�
ym;i ¼ 2pf m;itm is the delay phase associated tothe ith receiver branch of the mth user. Withoutlosing generality, we can assume that thechannel phase fm;i and the delay phase areindependent r.v. uniformly distributed in ½p;p�[11,20];
�
Zm;iðkÞ is the filtered Gaussian noise affecting theith subchannel of the mth user. According toliterature, Zm;iðkÞ is assumed as independent andidentically distributed 8m; i:k [11]. Zm;iðkÞ arezero-mean noise samples with variance equal toN0Tm=4;
�
qm;i is the complex receiver gain related to the ithsubcarrier of the mth user. Such a gain is

ARTICLE IN PRESS


assigned on the basis of specific diversitycombination methodologies and depends onthe corresponding channel coefficient gm;i:

The implementation of most of state-of-the-artMC-CDMA receivers relies on different assign-ments of the receiver gains qm;i: Theoretically, MC-CDMA detection methodologies require perfectknowledge of the channel coefficients [11]. Such anassumption is not realistic in many applications oftechnical interest; therefore some kind of channelestimation technique is needed in order to achieveinformation about the channel status. Imperfec-tions in the channel estimation may severelydegrade performances of MC-CDMA receivers.On the other hand, channel estimation methodsproviding better performances in terms of preci-sion are often computationally expensive [9]. InSection 4 a computationally tractable method foradaptive channel estimation in MC-CDMA recep-tion applications will be exploited in order tosimulate a realistic MC-CDMA receiver based ona conventional technique. In every case, assumingthe ideal knowledge of gm;i; and the ideal timesynchronization for each user, (so that the delayphases are perfectly known too) we can list thefollowing MC-CDMA signal reception algorithms[11]:

�
Equal-gain-combining (EGC) receiver: the re-ceiver gains are assigned as: qm;i ¼ cm;i
expðjðym;i fm;iÞÞ: As previously mentioned,this is the coherent multi-branch matched filterreceiver, which is optimal in the AWGN case[20]. Indeed, the receiver branches are onlyphased and not weighted in amplitude [11].Such a receiver scheme is sub-optimal overmultipath fading channels, but it allows ex-ploiting the natural diversity provided by MC-CDMA techniques without additional algo-rithms needed for channel estimation. For thisreason, it is preferred in many practicalapplications.

�
Orthogonality restoring combining (ORC) re-
ceiver: the receiver gains are assigned in thefollowing way: qm;i ¼ cm;i expðjðym;i fm;iÞÞ=am;i: The strategy employed here is similarin some way to the zero-forcing equalization[9]. In fact,the received signal over the ith

subcarrier is multiplied by the inverse of therelated complex channel coefficient. The well-known problem of Gaussian noise amplifica-tion [9,11] occurring when am;i51 dramaticallydegrades the performances of such a receptionmethod. For this reason,some mechanism ofcontrolled equalization [11] is strongly required(e.g.,if the complex magnitude of the channelcoefficient gm;i is much lower than 1,it isadvisable to set qm;i ¼ cm;i expðjðym;i fm;iÞÞ;asin the EGC criterion). In Section 4,an improvedORC receiver scheme will be proposed with aunique averaged receiver gain in order toachieve acceptable performances in terms ofbit-error-rates.

�
Maximal ratio combining (MRC) receiver: thereceiver gains are assigned equal to thesignature code chip multiplied by the complexconjugate of the channel coefficients, i.e. qm;i ¼
cm;iam;i expðjðym;i fm;iÞÞ: This criterion isoptimal in the single-user case, as the totalsignal-to-noise ratio at the output of thereceiver equals the sum of the signal-to-noiseratios at the output of the single branches (allbranches cooperate to the signal detection), butits performances dramatically decrease as thenumber of asynchronous users increases [11].

�
Minimum mean squared error (MMSE) recei-
ver: the receiver gains are assigned in order tominimize the minimum mean squared errorbetween the transmitted symbol by the mth userand its estimate produced by the receiver [11].Solving the MMSE equation in the synchro-nous case, we can obtain the following coeffi-cient assignment [11]:

qm;i ¼cm;ig

�m;i

ðMjgm;ij2 þ N0Þ

i ¼ 0; . . . ;Nm 1;

m ¼ 1; . . . ;M : ð7Þ

For small values of jgm;ij2; the receiver gain is

small to avoid excessive noise amplification,whereas for large values of jgm;ij

2; it becomesproportional to the inverse of the channelcoefficient in order to recover orthogonalityamong users. The resolution of the MMSEequation in the VBR asynchronous case is notso trivial and requires in any case the perfect

ARTICLE IN PRESS


knowledge of the channel coefficients. InSection 5, a NN-based receiver scheme will beproposed that can face in an efficient way sucha non-trivial mathematical task without anyknowledge of channel coefficients during thetest phase.

�

Table 1

VBR user classes, assigned bit-rates, and length of the bit

blocks assembled for the adaptive channel estimation (im-

proved ORC-based receiver scheme)

User class Number of

subcarriers

Bit-rate Block length

1 16 2Mbps 56 bit

2 32 1Mbps 28 bit

3 64 512Kbps 14 bit

Minimum likelihood (ML) receiver: from atheoretical point of view, the optimal multi-user MC-CDMA receiver is based on themaximum-likelihood criterion. As shown in[11], the ML receiver decides that the trans-mitted symbol by the mth user during the lthsignalling interval amðkÞ is the one minimizingthe squared Euclidean distance between thereceived noise-corrupted signal Y mðkÞ (given inEq. (6) and the noise-free transmission patternX mðkÞ; i.e.

LðkÞ ¼XMm¼1

jY mðkÞ X mðkÞj2 k ¼ 1; 2; . . . ;

(8a)

where

X mðkÞ ¼ffiffiffiffiffiffi2P

pTm

XNm1

i¼0

gm;icm;iejym;i amðkÞ

þXM

u¼1uam

XNu1

i¼0

gu;icu;iejyu;i

Z ðk1ÞTmþtu

ðk1ÞTmþtm

auðk 1Þ

�

pTuðt ðk 1ÞTu tuÞdt þ

Z kTmþtm

ðk1ÞTmþtu

auðkÞpTuðt kTu tuÞdt

�;

m ¼ 1; 2; . . . ;M; k ¼ 1; 2; . . . : ð8bÞ

The minimization of (8a) is a NP-completeproblem, as shown in [17]. This fact implies thatno algorithm can solve the minimizationproblem in polynomial time in M. Thiscomputational load is unsustainable in manyapplications. Despite such implementation pro-blems, the ML receiver could completelyneutralize the effect of the interfering signals,as proven in the DS/CDMA case [17]. Also inthe ML case, the perfect knowledge of complexchannel coefficients fgm;ig is supposed. Neuralnetworks will be employed in the following (see

Section 5) in order to approximate the solutionof the ML problem, without requiring anyknowledge of the channel coefficients.

4. Improved ORC receiver with adaptive channel

estimation

In order to provide some kind of touchstone forevaluating the performances of the proposedneural-network-based receivers, we considered, asan alternative to the basic EGC receiver, a sub-optimal ORC MC-CDMA receiver using a state-of-the-art channel estimation algorithm. In thispaper, we considered channel estimation per-formed by means of the adaptive least-square

(LS) strategy shown in [26]. Such a method has areasonable computational load (the complexityorder is polynomial with respect to the number ofusers) and provides a satisfactory, however notideal, precision. In particular, the LS channelestimation is performed by means of the followingalgorithm [26]:

~gm;i ¼1

BE

XBE

k¼1

ym;iðkÞ

vm;iðkÞ; (9)

where BE is the length of the training sequence, vm;i

is the known training symbol, and ym;i is thereceived signal component of the mth user relatedto the ith subcarrier.A training sequence of 5-bit length has been

selected in order to improve the robustness of theabove-mentioned method. The training sequence isperiodically inserted in the transmitted datastream, thus assembling blocks of bits each ofone composed by the training sequence and by the

ARTICLE IN PRESS


information bits. The length of each block iscomputed on the basis of the coherence time of thechannel and of the transmission bit-rate, as shownin Table 1.

The equalization strategy considered is anaveraged orthogonality restoring [23]. Actually aunique channel coefficient, obtained by averagingthe overall estimated coefficients is employed forrestoring orthogonality of all the different sub-carriers (see Eq. (10)).

~gAm ¼

1

Nm

XNm1

i¼0

~gm;i: (10)

Some ad hoc experimental trials have evidencedthe substantial advantages in terms of reducedBER achieved by the choice of the averagedorthogonality restoring, instead of the canonicalORC combining in the application context con-sidered.

5. Use of neural networks in MC-CDMA VBR

receivers

5.1. Preliminary considerations

It is widely known that state-of-the-art max-imum likelihood algorithms for channel estimationand MVD provide best performances in timeinvariant channels [9], but this is not true in timevarying channels. In this environment the perfor-mances of these algorithms are greatly reduced,and a solution to overcome this problem can beaddressed using neural networks. The key feature

Fig. 5. MC-CDMA receiver with a neural networ

of this approach consists in the non-linearboundary created by the neural network after thetraining phase in order to recognize the classesthat, in our case, are related to the polarity of thetransmitted BPSK symbol (class 1 corresponds toa ‘‘+1’’ symbol, class 2 corresponds to a ‘‘1’’symbol). Indeed, Cybenko [7] has shown that asingle-layer neural network can approximate everycontinuous function with an error provided onlyby the number of neurons in the hidden layer. Thisapproach can theoretically allow one to recoverthe signal polarity without any channel estimation.In this paper, we use a multi-layer perceptron

(MLP) network [16] that consists in a layerednetwork, where each layer can be divided in aninput layer, output layer and some hidden layers.Input neurons just propagate input features to

the next layer. The output layer is composed oftwo neurons. Each output neuron computes asimple weighted summation over the responses ofthe hidden neurons for a given input pattern. Thesigmoid function has been chosen as activationfunction and, furthermore the conventional back-propagation learning rule [16] has been employedfor training.The input–output relation that is learned by the

neural network is based on a set of examples ofpossible system outputs in different parametricsettings of the unknown channel response trappedonto transmitted data. The solution can be found,provided that a significant set of training patternsis fed as input in the training phase. The trainingof neural networks illustrated in Figs. 5 and 6 hasbeen performed ‘‘by pattern’’ [16]. The back-

k employed for supporting symbol decision.

ARTICLE IN PRESS

Fig. 6. MC-CDMA receiver with a neural network employed for joint channel equalization and symbol decision.


propagation algorithm is an iterative gradientdescent algorithm that minimizes an empiricalerror function [16]. The error function is defined asthe sum of errors due to each exemplary pattern.At any step of the iteration, changes in the weightare in the direction of the negative gradient of theerror. In the following text of the section, the useof MLP neural networks will be detailed in thespecific application cases of VBR MC-CDMAsignal reception.

5.2. Supporting-decision neural network

In Fig. 5 the first application is illustrated of theneural networks to the detection of VBR MC-CDMA signals transmitted over the LEO satellitechannel modelled in Section 2.2.

Substantially we have an EGC MC-CDMAcoherent receiver with a neural network-baseddecision block replacing the conventional hard-limiter. In our specific case, the MLP has twoneurons in the input layer (one for the real partand one for the imaginary part of the signal,because we considered the equivalent basebandmodel for simulation), one hidden layer with 10neurons and two neurons in the output layer. Theweight initialization is random. The features used

as input to the mth user’s neural network receiverare the samples provided as output by the EGCcoherent matched filter after the remultiplicationfor the signature code and the sum of overallreceiver branches, i.e.

~Y mðkÞ ¼XNm1

i¼0

½ffiffiffiffiffiffi2P

pTmam;i ~amðkÞ þ Zm;iðkÞ�

þXM

u¼1uam

XNu1

i¼0

gu;icm;icu;iejðyu;iym;iþfm;iÞ

Z ðk1ÞTmþtu

ðk1ÞTmþtm

~auðk 1Þ

� pTu

ðt ðk 1ÞTu tuÞdt

þ

Z kTmþtm

ðk1ÞTmþtu

~auðkÞpTuðt kTu tuÞdt

�;

m ¼ 1; 2; . . . ;M ; k ¼ 1; 2; . . . : ð11Þ

As alternative to the costly likelihood computationof Eq. (8a), we have considered here an approachsimilar to [1] in order to train the layered neuralnetwork for the demodulation of the mth user’ssymbol. In particular, the MLP is trained to classifythe wanted information symbol ~amðkÞ in thepresence of M 1 interfering signals and fre-

ARTICLE IN PRESS


quency-selective channel distortions, as shown inEq. (11). During the test phase, the neural networkprocesses the received signal without requiring anyfeedback information coming from the channel.

5.3. Neural network for joint channel equalization

and symbol detection

In Fig. 6, the architecture of the other neural-network based MC-CDMA receiver proposed inthis paper is shown.

The neural network is placed in cascade with thematched filter bank, working as channel equaliza-tion and symbol decision block. The MLP NN-based receiver consists into an input layer, a singlehidden layer and an output layer.

One can realize that, differently from the schemeof Fig. 5, we have no explicit remultiplication ofthe baseband-recovered signal with the PN signa-ture code vector. Actually, we shall introduce thesignature codes in the weight initialization phase.

In the proposed approach the cardinality of theinput and hidden layer neuron set is the same, andit is equal to the number of sub-carriers used bythe user m. One can notice that the complexity ofthe network depends on the sub-carrier used byeach user; therefore the time and the computa-tional effort to learn the pattern vary from user touser. The weights connecting the input and thehidden layer of the neural network works byapproximating the solution of the MMSE MC-CDMA receiver, providing the optimal assignmentof the receiver gains shown in Eq. (7). On the otherhand, weights connecting hidden and output layerrecombine the Nm equalized contributions comingfrom the hidden layer, and decide about thetransmitted symbol in a fashion similar to theNN-based receiver scheme previously described inSection 5.2.

The weight initialization process is done usingthe information about signature codes. Formallythe weight vector for the connection between theinput-hidden layer and hidden-output layer can beexpressed respectively as follows:

wijðmÞ ¼cm;j expðjym;jÞ i ¼ j;

e iaj;

((12)

where wijðmÞ is the weight between the ith inputand the jth hidden neuron, m is the user index, cm;j

is the jth element of the mth user signature code,and e is a random variable, whose value is close to0. The basic idea of such an initialization approachcan be summarized in this way: if the channel isflat, only a short training time is required becausethe weights are just set at near optimal values.When a frequency-selective channel realizationoccurs, the above-mentioned procedure allows torecognize the presence of MUI due to multipathchannel distortions, and therefore to reach a fasterconvergence of the weight updating. Starting fromthis initialization, the back-propagation algorithmallows minimizing a cost functional that convergesto the optimal weight configuration. This config-uration is represented by equalization coefficientscharacterized by minimum mean squared errorwith respect to several channel configurationspresented in the training set.In such a receiver model, the most critical

point to be addressed is the choice of the trainingset. This latter should be selected in order to trainthe NN to recognize during the test phase thelargest set of channel coefficients. In terms ofconvergence time, such a kind of weight initializa-tion provides better results as compared withrandom weight initialization, done after theremultiplication of the baseband-recovered signalwith the PN signature code. This improvement isshown in Fig. 7.As well as for the supporting-decision scheme,

also for this improved NN-based receiver nofeedback information about the channel is re-quired in the test phase. The frequency-selectivedistortion characteristics of the LEO satellitechannel are completely learned off-line by theneural receiver.

6. Simulation results

The system simulation has been performedby using a baseband equivalent model of theVBR MC-CDMA system working over the LEOsatellite channel described in Section 2. Thesimulator was implemented in MATLAB SIMU-LINK 6.1 environment. The configuration of the

ARTICLE IN PRESS

Fig. 7. Error (MSE) dynamic curves for the neural network-based receiver of Fig. 6 provided by the different initialization strategies.

Table 2

Multi-user VBR transmission configurations chosen for simula-

tions

Total

number

of users

Class 3 users

ðRb ¼ 512Kb=sÞClass 2 users

ðRb ¼ 1Mb=sÞClass 1 users

ðRb ¼ 2Mb=sÞ

5 1 3 1

6 1 4 1

7 3 3 1

8 4 3 1

9 4 4 1

10 4 4 2


VBR user classes chosen for simulations isreported in Table 2.

The training set has been created to cover alarge set of different channels configurations (i.e.1000). Only one constrained hypothesis is as-sumed: the maximum number of paths has beenfixed (see Section 2.2). Every channel duration is25ms and the number of training bits transmittedis equal to 12 000, 25 000 and 50 000 for userstransmitting over 64, 32 and 16 carriers respec-tively. The weights are updated every time avariation of the channel impulse response occurs

(training by epochs), and the two NN are trainedby showing the overall channel configuration 50times.Simulation results achieved in terms of channel

bit-error-rate (BER) are shown in Figs. 8–11. BERresults have been achieved by simulating thetransmission during the test-phase of more than100,000 bits over the LEO satellite channel, whosestatistic realizations, both in terms of distortionsand in terms of AWGN noise, were completelydifferent from the training phase ones. Figs. 8–10depict BER performances provided by usersbelonging to the three different classes (i.e.: class1: 16-subcarrier users, class 2: 32-subcarrier users,class 3: 64-subcarrier users) vs. different values ofEb=N0; considering a fixed number of asynchro-nous VBR users (i.e. M ¼ 10). On the other hand,results provided by a 32-subcarrier user trans-mitting at a fixed EbN0 ¼ 7 dB vs. differentvalues of asynchronous user M are plotted inFig. 11. As a fixed transmission power P has beenconsidered for all user classes, we shall havedifferent values of the transmission signal-to-noiseratios for different userclasses, i.e. Eb=N0 ¼

ðEb=N0Þjm¼ PTjm

=N0;8m ¼ 1; . . . ;M: This im-plies that if the signal-to-noise ratio for the user

ARTICLE IN PRESS

Fig. 8. BER performance comparison among neural network-based receivers, conventional EGC receiver and improved ORC receiver

with adaptive channel estimation: user class ¼ 1; M ¼ 10 asynchronous transmitting users.

Fig. 9. BER performances vs. Eb=N0 for neural network-based receivers, conventional EGC receiver and improved ORC receiver with

adaptive channel estimation: user class ¼ 2; M ¼ 10 asynchronous transmitting users.


ARTICLE IN PRESS

Fig. 10. BER performances vs. Eb=N0 for neural network-based receivers, conventional EGC receiver and improved ORC receiver

with adaptive channel estimation: user class ¼ 3; M ¼ 10 asynchronous transmitting users.

Fig. 11. BER performances vs. number of asynchronous transmitting users M for neural network-based receivers, conventional EGC

receiver and improved ORC receiver with adaptive channel estimation: user class ¼ 2; Eb=N0 ¼ 7 dB:


ARTICLE IN PRESS


belonging to the class 2 ðEb=EbN0Þ2 equals to7 dB, the user belonging to the class 1 transmits atðEb=N0Þ1 ¼ 4 dB and the user belonging to theclass 3 transmits at Eb=N0Þ3 ¼ 13 dB:

The performances provided by the two pro-posed NN-based receiver schemes describeded inSections 5.2 and 5.3 are compared with theconventional EGC receiver (described in Section3) and the improved ORC receiver with adaptivechannel estimation (described in Section 4).

It is clear from the figures above that bothneural-network-based receivers provide better per-formances than EGC and ORC MC-CDMAreceivers. Nevertheless the most relevant improve-ment is provided by the receiver scheme where theneural network is employed both for channelequalization and for symbol decision. This fact ismore evident when the number of asynchronoususers increases. This is not surprising, because thejoint equalization and supporting decision NNproposed is firstly devoted at restoring the lostorthogonality among different users’ subcarriersby approximating the optimal MMSE criterion,and then to take a decision about the symbol byexploiting the orthogonality among users partiallyrecovered at the previous stage. The trade-off isrelated to the increased complexity of the neuralreceiver, which depends on the number of sub-carrier attributed to each user (see Appendix A forsome notes about the computational load requiredby the proposed NN receivers).

The neural network used only for supportingsymbol decision provides, in all cases, BERperformances always better than ones yielded byEGC receiver and quite close to the ORC receiverones (but slightly better in any case). However, itmust be said that the effective data rate of thecompared receivers is not the same. Indeed, theneural network-based receivers do not need anykind of redundancy added to the transmitted bitdue to the introduction of training sequences, as inthe case of blind equalization.

7. Conclusion

This paper presented a performance analysis ofa variable-bit-rate asynchronous multi-user MC-

CDMA transmission over a LEO satellite channelwith two possible architectures of neural network-based receiver. The first architecture employs theneural network for supporting the decision aboutthe transmitted symbol. The second architectureutilizes the neural network for joint channelequalization and symbol decision. The achievedresults show that the neural-network-based MC-CDMA receivers can obtain better performancesin terms of BER with respect to the ones yielded byother receivers using both EGC combining andadaptive channel estimation, and ORC combining.The most significant improvements yielded byproposed neural-network-based approaches canbe summarized as follows:

�
The lower computational cost in the test phase(most of the computational cost is moved to theoff-line training phase).
�
A higher data-rate compared with the onesupported by MC-CDMA receivers based onadaptive equalization methods. In fact, duringthe test phase, neural-network-based receiversrequire no training bit. Thus the transmitted bitsare only information bits. This is the samesituation encountered when blind equalizationalgorithms are employed, however with areduced computational cost.
As far as the performance comparison between thetwo proposed NN-based receivers is concerned,better results in terms of BER are provided by thereceiver architecture using the neural network forjoint channel equalization and symbol decision,with respect to the more conventional decisionsupporting neural network. The cost to be paid isan increased computational load required both inthe training and in the test phase. An openproblem is the cardinality of the training set thatwould theoretically be infinite in order to keep intoaccount all of the possible situations of a timevarying channels. The solution to such a pro-blem—i.e. to determine a suitable finite dimensionof the training set in order to achieve optimalchannel equalization—could be the topic forfuture works. The proposed analysis about theemployment of NNs in VBR MC-CDMA signalreception can be straightforwardly extended toother application contexts of technical interest,

ARTICLE IN PRESS

Table 3

Computational complexity of the different NN-based receivers

Network Computational

configuration cost

Supporting-decision NN 2-10-2 79 � TOP

Joint Chan. Eq. and Supp. Dec. NN (16 users) 16-16-2 361 � TOP




like e.g., WLAN, terrestrial mobile networks, etc.,not only limited to the satellite transmissionenvironment dealt in this paper.

Appendix A

The computational cost C of a neural net-work depends on the number of connectionsbetween the different layers, and it is given asfollows:

CðQi;Qh;QoÞ ¼ ðQi þ Qo þ 1ÞðQh þ 1ÞTOP

þ 2ðQh þ QoÞTOP; ð13Þ

where

�
Qi;Qh;Qo represent the number of neurons inthe input layer, hidden layer and output layerrespectively;
�
TOP is the time required by an elementaryoperation.
The first term of the sum of (13) represents thenumber of weights of the network as well as thenumber of multiplications done; the second termcontains the number of additions and activationoperations implied by the use of the sigmoidfunction. Eq. (13) exactly depicts the computa-tional load required by the test phase, but it is agood approximation also for what concerns thetraining phase, because the weight update is madeonce every thousand bits. By this, the computa-tional cost required by the training phase can beregarded as slightly similar to the one required bythe test phase.

In particular, Table 3 shows the computationalcost of each NN-based receiver configurationproposed in this paper.

From the table above, one can notice that thecomputational cost of each NN-based receiverincreases with the square of the total number ofneurons.

References

[1] B. Aazhang, B. Paris, G.C. Orsak, Neural networks for

multiuser detection in code-division multiple-access com-

munications, IEEE Trans. Comm. 40 (7) (July 1992)

1212–1222.

[2] F. Babich, G. Lombardi, E. Valentinuzzi, Variable order

Markov modelling for LEO mobile satellite channels,

Electron. Lett. 35 (8) (April 1998) 621–623.

[3] X.H. Chen, T. Lang, J. Oksman, Multiple chip-rate DS/

CDMA system and its spreading code dependent perfor-

mance analysis, IEE Proc.–Comm. 145 (5) (October 1998)

371–377.

[4] K.G. Coleman, Neural networks: a high impact technol-

ogy with applications in telecommunications, Proceedings

of IEEE GLOBECOM ’91 Conference, 5–12 December

1991, pp. 30B.1.1–30B.1.5.

[5] G.E. Corazza, F. Vatalaro, A statistical model for land

mobile satellite channels and its applications to non-

geostationary orbits systems, IEEE Trans. Veh. Technol.

43 (3) (August 1994) 738–742.

[6] T. De Couasnoun, R. Monnier, J.B. Rault, OFDM for

digital TV broadcasting, Signal Processing 39 (9) (Septem-

ber 1994) 1–32.

[7] G. Cybenko, Approximations by superposition of a

sigmoid function, Math. Control Signals Systems 2 (4)

(1989) 303–314.

[8] E.H. Dinan, B. Jabbari, Spreading codes for direct

sequence CDMA and wideband CDMA cellular networks,

IEEE Comm. Mag. (September 1998), 48–54.

[9] Z. Ding, Y. Li, Blind Equalization a Identification, Marcel

Dekker Inc., NY, 2001.

[10] J.V. Evans, Satellite systems for personal communications,

Proc. IEEE 86 (7) (July 1998) 1325–1341.

[11] S. Hara, R. Prasad, Overview of multicarrier CDMA,

IEEE Comm. Mag. (December 1997), 126–133.

[12] Y. Hu, V.O.K. Li, Satellite-based internet: a tutorial, IEEE

Comm. Mag. (March 2001), 154–162.

ARTICLE IN PRESS


[13] M. Ibnkahla, Applications of neural networks to digital

communications—a survey, Signal Processing 80 (2000)

1185–1215.

[14] M. Ibnkahla, F. Castanie, D. Roviras, Newtest project and

the impact of neural networks on S-UMTS communica-

tions, IEE Colloquium on EU’s initiatives in Satellite

Communications, May 8, 1997, pp. 6/1–6/16.

[15] K.B. Ko, S. Choi, C. Kang, D. Hong, RBF multiuser

detector with channel estimation capability in a synchro-

nous MC-CDMA system, IEEE Trans. Neural Networks

12 (6) (November 2001) 1536–1539.

[16] F.L. Luo, R. Ubenhauen, Applied Neural Networks for

Signal Processing, Cambridge University Press, UK, 1997.

[17] R. Lupas, S. Verdu, Linear multiuser detectors for

synchronous code-division multiple access channels, IEEE

Trans. Inform. Theory 34 (1) (January 1989) 123–126.

[18] G. Maral, M. Bousquet, Satellite communications systems,

Third ed., Wiley, UK, 1998.

[19] F. Petre, M. Engels, M. Moonen, B. Gyselinckx, H. De

Man, Adaptive MMSE/pcPIC-MMSE multiuser detector

for MC-CDMA satellite system, Proceedings of 2001 IEEE

International Conference on Communications (ICC’01),

Helsinki (SF), 11–14 June 2001, pp. 2640–2644.

[20] B.M. Popovic, Spreading sequences for multicarrier CDMA

systems, IEEE Trans. Comm. 47 (6) (June 1999) 918–926.

[21] J.G. Proakis, Digital Communications, Third ed.,

McGraw-Hill, NY, 1995.

[22] D. Rogers, L.J. Ippolito, F. Davarian, System require-

ments for Ka-band earth-satellite propagation data, Proc.

IEEE 85 (5) (June 1997) 810–820.

[23] C. Sacchi, G. Gera, C. Regazzoni, Performance eva-

luation of MC-CDMA techniques for variable bit-rate

transmission in LEO satellite networks, Proceedings of

2001 IEEE International Conference on Communi-

cations (ICC’01), Helsinki (SF), 11–14 June, 2001,

pp. 2650–2654.

[24] E. Soujeri, H. Bilgekul, Hopfield multiuser detection of

asynchronous MC-CDMA signals in multipath fading

channels, IEEE Comm. Lett. 6 (4) (April 2002)

147–149.

[25] P. Takats, Rain fade mitigation scheme for a regional

GEO multimedia satellite architecture, Proceedings of

seventh Ka-band Utilization Conference, S.Margherita

Ligure (I), 26–28 September 2001, pp. 279–286.

[26] L. Tomba, W.A. Krzymien, Downlink detection schemes

for MC-CDMA systems in indoor environments, IEICE

Trans. Comm. 79 (9) (September 1996) 1351–1360.

[27] Z. Wang, G.B. Giannakis, Wireless multicarrier commu-

nications, where Fourier meets Shannon, IEEE Signal

Process. Mag. (May 2000) 29–48.

Neural network-based techniques for efficient detection of variable-bit-rate signals in MC-CDMA...

Documents

Transcript of Neural network-based techniques for efficient detection of variable-bit-rate signals in MC-CDMA...