1

On Receiver Design for Uplink Low DensitySignature OFDM (LDS-OFDM)

Razieh Razavi,Student Member, IEEE,Mohammed AL-Imari,Student Member, IEEE,Muhammad Ali Imran,Member, IEEE,Reza Hoshyar,Member, IEEE,and Dageng Chen,Member, IEEE

Abstract—Low density signature orthogonal frequency divisionmultiplexing (LDS-OFDM) is an uplink multi-carrier multiple ac-cess scheme that uses low density signatures (LDS) for spreadingthe symbols in the frequency domain. In this paper, we introducean effective receiver for the LDS-OFDM scheme. We propose aframework to analyze and design this iterative receiver usingextrinsic information transfer (EXIT) charts. Furthermore, aturbo multi-user detector/decoder (MUDD) is proposed for theLDS-OFDM receiver. We show how the turbo MUDD is tunedusing EXIT charts analysis. By tuning the turbo-style processing,the turbo MUDD can approach the performance of optimumMUDD with a smaller number of inner iterations. Using the sug-gested design guidelines in this paper, we show that the proposedstructure brings about 2.3 dB performance improvement at a biterror rate (BER) equal to 10−5 over conventional LDS-OFDMwhile keeping the complexity affordable. Simulations for differentscenarios also show that the LDS-OFDM outperforms similarwell-known multiple access techniques such as multi-carrier codedivision multiple access (MC-CDMA) and group-orthogonal MC-CDMA.

Index Terms—Multi access communication, Iterative methods,Code division multi access, Multi-user channels.

I. I NTRODUCTION

M ULTI-carrier code division multiple access (MC-CDMA) is considered to be a suitable approach to

cope with challenging service demands due to its abilityof exploiting both time and frequency resources [1]–[4]. Inthe uplink channel using MC-CDMA, non-orthogonality ofreceived effective signatures causes multi-user interference(MUI). Multi-user detection (MUD) can be used to moderatethe detrimental effects of MUI. However, implementation ofoptimum MUDs is not practical due to their prohibitively highcomputational complexity. Even for a moderate number ofinterfering users, the complexity grows exponentially with thenumber of users [5]. In order to reduce the complexity ofMUD for MC-CDMA systems, group-orthogonal MC-CDMA(GO-MC-CDMA) [6] has been proposed. It has been shownthat by dividing users into subgroups, GO-MC-CDMA is ableto achieve a performance very close to the single-user bound[6] while keeping the complexity affordable.

In order to achieve a further reduction in the complexity ofMUD for uplink MC-CDMA, we have recently proposed lowdensity signature (LDS) structures for MC-CDMA systems

R. Razavi, M. AL-Imari and M. A. Imran are with the Centre forCommunications Systems Research, University of Surrey, Guildford, Surrey,GU2 7XH, UK, (e-mail: R.Razavi, M.Al-imari, M.Imran @surrey.ac.uk).

R. Hoshyar is with Texas Instruments, California, USA.D. Chen is with Huawei Technologies Co. Ltd, No.2222, Xin JinQiao Road,

Pudong, Shanghai, 201206, P.R.China.

known as LDS-OFDM [7]. In LDS-OFDM systems, becauseof their low density signature structures, each data symbol isonly spread over a limited number of chips (effective process-ing gain). Then, each user’s generated chip is transmitted overan orthogonal sub-carrier. Furthermore, each sub-carrier isonly used by a limited number of data symbols that may possi-bly belong to different users. Therefore each user, transmittingon a given sub-carrier, will experience interference from onlya small number of other data symbols. In other words, LDS-OFDM is a special case of the MC-CDMA system where itsspreading sequences have low density. In theory, low densitysignatures were introduced in [8] for downlink multi-carriersystems. Since the LDS-OFDM system is proposed for uplinkmulti-carrier systems, the design of the receiver is differentfrom the one proposed in [8], because in uplink we havea single centralised receiver. Designing this receiver to haveminimal or affordable complexity while being able to achievethe single user performance bound is a challenge. This paperaims to address this challenge by proposing a suitable designand analysis tool to obtain an efficient detection/decodingalgorithm. The contributions of this paper are as follows:

1) An efficient implementation of the message-passingalgorithm (MPA) [9] to approximate the maximumaposteriori (MAP) detection for the LDS structure is pre-sented. This algorithm is able to reduce the complexityof the receiver compared to the existing state-of-the-art multiple access systems. This technique calculatesthe extrinsic information for each sub-carrier by usingthe MAP-based detections: Log-MAP with brute-forcesearching among possible combinations of symbols.

2) The iterative detector is analysed using extrinsic in-formation transfer (EXIT) charts. Furthermore, designguidelines are provided for improving the LDS structure.

3) A tuned turbo multi-user detector/decoder (MUDD) forLDS-OFDM is proposed. The proposed turbo receivercomprises two basic components: an LDS multi-usersymbol detector and a collection of users’ decoders.Using the EXIT chart analysis we show how to tune thereceiver in a way that the turbo MUDD can approachits final performance using a smaller number of inneriterations. In [10], we have already shown a primarystudy on LDS-OFDM with turbo iterations to demon-strate the effect of various loads, and here we extendthis work further by showing how the turbo receiver istuned using a novel technique.

4) Finally, using design guidelines extracted from the EXIT

2

y1

yNc

d1

dK

OFDM De-

Modulator

LDS Detector

AWGN

xK Symbol Mapper

FEC Encoder

LDS Spreader

OFDM Modulator

Radio Channel

Symbol Demapper

Symbol Demapper

FEC decoder

FEC decoder

x1 Symbol Mapper

FEC Encoder

LDS Spreader

OFDM Modulator

Radio Channel

d1 ^

dK ^

Fig. 1. LDS-OFDM block diagram.

chart analysis of the receiver, we provide the BER resultsto show why LDS-OFDM is a promising technique incomparison with well-known multiple access techniqueswith similar principles.

The rest of this paper is organized as follows. SectionII presents the structure of LDS-OFDM and its iterativereceiver. In section III, the design guidelines for an LDS-OFDM receiver is extracted using EXIT chart analysis. Theanalysis of turbo MUDD for LDS-OFDM is presented insection IV, and then the simulation results and comparisonwith similar techniques are both given in section V. In sectionVI, different aspects of the LDS-OFDM system are comparedwith those of other multiple access techniques. Finally, sectionVII is devoted to concluding remarks.

II. LDS-OFDM SYSTEM MODEL

Consider a multiple access channel (MAC), correspondingto the uplink communications from multiple users to a singlebase station in a practical system. The block diagram of LDS-OFDM for an uplink system is shown in Fig. 1. It can be notedthat the main blocks are similar to an MC-CDMA system.Similar to an MC-CDMA spreading process, we multiplythe modulated symbol with a spreading signature (a randomsequence of chips). However, in the LDS-OFDM case, themain difference is that the spreading signature has a lowdensity (a large number of chips in the sequence are equatedto zero). In this section, we first explain the system model ofLDS-OFDM, which is similar to the one published in [10].Then the iterative receiver for this system is described. It isassumed that the LDS-OFDM system hasK users with userindicesk = 1, . . . ,K. Let Xk be the constellation alphabet,from which the transmitted symbol for userk will take itsvalue. Thus, the modulated symbol for userk is formed bymapping a sequence of independent information bitsbk ∈ F

qk2

to Xk, and can be represented by the functionφk : Fqk2 → Xk,

where qk is the number of information bits per symbol foruser k. Without loss of generality, all users are assumed totake their symbols from the same constellation alphabet, i.e.,X = Xk, ∀k = 1, . . . ,K. In addition, we assume that thedifferent users have identical number of data symbols,M .

IntroducingNc as the number of total chips, the spreadingmatrix for userk will be Sk = [sk,1, . . . , sk,M ] ∈ CNc×M ,

where matrixSk has onlydv (effective spreading factor) non-zero values on each column. Let us defineS= [S1, . . . ,SK ] ∈CNc×MK as the low density signature matrix of the multi-user system. The norm of each signature vector is unity.Furthermore, let variabledc be the number of symbols thatinterfere with each other at each chip. We defineA =diag(A1, . . . , AK) as the transmit power gain of users andGk = diag(gk,1, . . . , gk,Nc) as the corresponding channel gainfor the kth user.

In LDS-OFDM, each user’s generated chip will be trans-mitted over an orthogonal sub-carrier. Therefore, the receivedspreading sequence for data symbolm ∈ {1, . . . ,M} ofuser k can be represented byhk,m = AkGksk,m. To bemore specific, the received signature gain at chipn of datasymbol m of user k will be hnk,m = Akgk,ns

nk,m. Let

Jn = {(k,m) : snk,m 6= 0} be the set of data symbols (whichmay belong to different users) that interfere on chipn. Also,let Ek,m = {n : snk,m 6= 0} be the set of different sub-carriersthat themth symbol of userk is spread on.

For an uplink MC-CDMA system, the received signal atsub-carrier indexn is written as

yn =

K∑

k=1

M∑

m=1

hnk,mxk,m + vn, (1)

where vn is the AWGN for sub-carriern and xk,m is themth data symbol of userk. Thus, considering that in LDS-OFDM system, the signature has a limited number of non-zeropositions, we can express the received signal at thenth chip(sub-carrier) as follows:

yn =∑

(k,m)∈Jn

hnk,mxk,m + vn. (2)

At the receiver side, after OFDM demodulation, the signal issent to a near-optimum MUD based on MPA. An LDS system,with K users andNc sub-carriers, is represented by the factorgraphG(U , C) whereC andU are the sets of function nodesand variable nodes, respectively. Each chip is represented bya function nodec ∈ C and each user-symbol is representedby a variable nodeu ∈ U . The connections between thereceived sub-carrier and its related users are shown by edges.Let en(xk,m) be the edge that connects function noden tovariable nodem of userk. Because this receiver is iterative andoperates at the chip-level, the resultant technique is termed thechip-level iterated (CLi) MUD. Because of small number ofinterferers in each sub-carrier, applying maximuma posterioribased chip-level iterated (MAP-CLi) MUD is feasible forLDS-OFDM. The design of this receiver is based on MPA,which requires iterative exchange of messages between thefunction and the variable nodes.

The CLi MUD technique can be explained as follows. LetLjn,→(xk,m) be the message sent along the edgeen(xk,m),at jth iteration, from variable nodeuk,m to function nodecn. Similarly, the message sent from the function node to thevariable node is given byLjn,←(xk,m). Assuming there are noa priori probabilities available, the initial messages (j = 0)are set to zeros:L0n,→(xk,m) = 0, ∀k,m, ∀n. The messages

3

are updated using the following rules

Ljn,→(xk,m) =∑

l∈Ek,m\n

Lj−1l,← (xk,m), (3)

Ljn,←(xk,m) ∝

f(xk,m|yn, L

jn,→(xk′,m′), ∀(k

′,m′) ∈ Jn \ (k,m)). (4)

It can easily be seen from (3) and (4), that all messages areupdated by the extrinsic information. In order to approximatethe optimum MAP detector, the right hand side of (4) repre-sents marginalization function, which is based on (2), and canbe written as

f(xk,m|yn, L

jn,→(xk′,m′), ∀(k

′,m′)∈ Jn \ (k,m))=

log

∑

x[n]∈Xdcxk,m

pj(yn|x[n])P jn(x[n] \ xk,m)

=

log

∑

x[n]∈Xdcxk,m

pj(yn|x[n])∏

(k′,m′)∈Jn\(k,m)

P jn(xk′,m′)

.

(5)

Where the conditional probability density function (PDF)pj(yn|x[n]) anda priori probabilityP jn(xk′,m′) are given as

pj(yn|x[n]) ∝ exp(

−1

(2σ2)‖yn − hT[n]x

[n]‖2)

, (6)

P jn(xk′,m′) = exp(Ljn,→(xk′,m′)

), (7)

wherex[n] andh[n] denote the vector containing the symbolstransmitted by every user that spread its data on chipnand their corresponding effective received signature values,respectively. As can be seen in (5) based on received chipynand a priori input informationP jn(xk′,m′), extrinsic valuesare calculated for all the constituent bits involved in (2).Combining (6) and (7) into (5), the message update will be

Ljn,←(xk,m) = κn,k,m?max

x[n]∈Xdcxk,m(

∑

(k′,m′)∈Jn\(k,m)

Ljn,→(xk′,m′)−1

(2σ2)‖yn− hT[n]x

[n]‖2)

, (8)

whereκn,k,m denotes the normalization coefficient and

?max (a, b) , log

(ea + eb

). (9)

This technique is termed log-MAP CLi detection. After themessage-passing has converged or has reached the maximumnumber of iterationsJ , a posteriori probability of the trans-mitted symbolxk,m is estimated as

Lk,m(xk,m) =∑

l∈Ek,m

LJl,←(xk,m). (10)

By using the hard decision, the estimated value ofxk,m is

x̂k,m = arg maxxk,m∈X

Lk,m(xk,m). (11)

-1Variable

Node Detector

+

Edge Interleaving

-

-

From Channel

To FEC Decoder

+Function

Node Detector

Fig. 2. Iterative MUD for LDS-OFDM.

For a system with forward error correction (FEC), afteran appropriate number of iterations the soft output calculatedusing (10) for each variable node can be sent to the channeldecoder to have the final hard decision at the decoder. Oneof the main advantages of the iterative receiver for LDS-OFDM is its ability to support high loads while maintainingthe affordable complexity and acceptable performance. In thenext section we will show how using EXIT chart analysis helpsus improve the performance of the receiver.

III. EXIT C HART ANALYSIS OF MULTI -USERDETECTOR

OF LDS SCHEME

EXIT chart is a useful tool for analysing the flow ofinformation between the constituents of an iterative decoder.This section assesses the extrinsic information transfer char-acteristics to analyse the transfer of information between thesoft-input soft-output (SISO) constituents of the multi-usersymbol detector of LDS-OFDM. This would help us finddesign guidelines to improve the performance of LDS-OFDM.

Although LDS-OFDM by nature is designed for channelsthat vary over frequency, the design guidelines are related tothe performance of the algorithm used for symbol detection.Therefore, the evaluation is carried out for the AWGN channeland then it is extended to the multi-path fading channel. It isimportant to note that the results presented at this stage arerelated to a system without FEC.

A. Application of EXIT Charts to the MUD of LDS Scheme

In order to be able to apply EXIT charts to the MUD ofLDS-OFDM we must first explain its structure. The factorgraph of LDS receiver contains variable and function nodes,which are connected via appropriate edges. Using MPA inan iterative manner, variable nodes calculate the extrinsicmessages related to function nodes according toa priori infor-mation they receive from other connected function nodes, andthe same rule applies to the extrinsic messages that functionnodes send to variable nodes. Note that the message that isexchanged on each edge on either direction only containsinformation about the corresponding variable node. To beable to evaluate the transformation of extrinsic informationfor the detector, the sets of variable and function nodes arereferred to as variable node detector (VND) and function nodedetector (FND), respectively. The edge interleaver connects thefunction nodes and variable nodes, each of which representsa spreading matrix. Fig. 2 shows the structure of the iterativeLDS multi-user detector. As it is shown the extrinsic L-valuesthat have been passed on are considered asa priori information

4

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

IE,VND

I A,V

ND

dv = 6

dv = 3

dv = 2

dv = 4

Fig. 3. VND EXIT curves for differentdv .

by the other detector. In this section, EXIT charts are used tocharacterize the operation of these two iterative detectors.EXIT charts are applied to the MUD of LDS using the

property of the factor graph of LDS receiver that both vari-able and function nodes exchange the same information. Theinformation exchanged is the soft value that represents thereliability of the symbol related to each edge. In other words,the information on each edge is about the adjusted variablenode, whether it is sent from the variable node itself or theconnected function node. Therefore, knowing the transmittedsignal we could find the mutual information between the actualvalue for the variable nodes and thea priori or extrinsicvalues on the edges. In this paper,IA refers to the averagemutual information between the bits on the detector graphedges and thea priori L-values. Also, IE is the averagemutual information between the bits on the graph edges andthe extrinsic L-values. Therefore, in order to find the EXITcurve for each detector constituent we must representIE as afunction of IA for VND and FND separately.

1) EXIT Curve for the Variable Node Detector:In a regularLDS each variable node hasdv incoming messages from theedge interleaver, which is equal to the variable node degree inthe factor graph. The variable node produces its messages bycalculating (3) fordv connected function nodes. In order tocompute an EXIT curve for variable nodes,Lj−1l,← (xk,m) in (3)is modelled as the soft output of an AWGN channel when theinput is thelth interleaver bit transmitted using BPSK (binaryphase shift keying). Then the mutual information betweenthe variable node’s extrinsic messages and actual values ofsymbols on the edges is calculated. Thus,a priori L-valuecan be calculated by

A = μAx+ nA, (12)

wherenA is an independent Gaussian random variable withvarianceσ2A and mean zero andx ∈ ±1 are original bits onthe detector graph edges. Then we will have

μA =σ2A2. (13)

The mutual informationIA = I(X;A) can be calculatedby [11]

IA =1

2

∑

x=−1,1

∫ +∞

−∞pA(ξ|X = x)

log22pA(ξ|X = x)

pA(ξ|X = −1) + pA(ξ|X = 1)dξ.

(14)

Knowing that the conditional probability density functionpA(ξ|X = x) depends on L-valueA, with Gaussian distribu-tion and with properties mentioned in (14), we can write

IA(σA) = 1−∫ +∞

−∞

e−((ξ − σ2A/2)

2/2σ2A)

√2πσA

log2(1 + e−ξ)dξ.

(15)

For abbreviation we define

J(σ) := IA(σA = σ), (16)

with

limσ→0J(σ) = 0, lim

σ→∞J(σ) = 1, σ ≥ 0. (17)

Considering (3) together with the fact that the sum oftwo normally distributed random variables is also normallydistributed with the mean and variance equal to the sum oftheirs, the EXIT function of a degreedv variable node is

IE,V ND(IA, dv) = J

(√(dv − 1) (J−1(IA))

2

)

. (18)

Fig. 3 plots variable node EXIT curves for differentdvs using(18).

2) EXIT Curve for the Function Node Detector:A functionnode of degreedc hasdc+1 incoming messages,dc from theedge interleaver and one message from the channel. The outputL-values are calculated in (8) in details. We modela priori L-values,Ljn,→(xk′,m′), as the output of an AWGN channel thatits input is the corresponding transmitted bit using BPSK andthen calculate the mutual information of output with regardsto the actual value on the edges. Due to the complexity ofthe calculation in function nodes, the EXIT curve for themis computed by simulations over AWGN channel. Therefore,first the distributionpE for extrinsic information is determinedby Monte Carlo simulation (histogram measurements). Thenusing (14) the mutual information between the extrinsic infor-mation and the bits on the detector graph edges, is calculated.

Fig. 4 illustrates the EXIT charts for the MUD with 252chips and different number of users (overloading conditions)which lead to differentdcs for a fixeddv = 2. Fig.4 showsthat for a load of 400% the performance degrades noticeablycompared to a load of 200% and 300%. As we can see inthis figure, the iterative process starts withIA,FND = 0since no prior information is given to the function nodesin the beginning. In the next steps, the output L-values areexchanged between VND and FND curves. Fig. 4 also showsthat the FND curves for different loading conditions intersectat IA = 1, which is because for completea priori information,the function nodes are able to eliminate the multiple access

5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

IA,FND

& IE,VND

I E,F

ND &

IA

,VN

D

VN-detector

FN-detector

Load 100%

Load 200%

Load 300%

Load 400%

Fig. 4. EXIT charts for MUD atEb/N0 = 8 dB for differentdcs.

interference (MAI) fully and the effect of overloading will becancelled. Fig. 5 reveals the EXIT charts and the trajectories ofthe system forEb/N0 equal to 5 dB and 8 dB. It shows that anincrease in signal to noise ratio (SNR) would shift the FNDcurve vertically towards higher extrinsic output. This figurealso shows the trajectories of the iterative process obtained bysimulation. Except for a slight difference in the early iterations,which occurs because of the finite size of edge interleaver inthe LDS structure, the system trajectories closely follow thetransfer curves of the MUD components, which indicates thatthe EXIT charts analysis is valid for LDS-OFDM’s MUD.

B. EXIT Chart Analysis Aided Signature Design for LDS

There are different parameters in the design of the LDS ma-trix that affect the performance of the system. Two importantparameters are the number of chips that each symbol is spreadon, dv, and the number of symbols that share the same chip,dc. The relation between these two parameters for overloadingequal toβ is as follows:

dc = βdv. (19)

To design a robust LDS, the EXIT charts are drawn fordifferent dvs to evaluate the effect of processing gain on theconvergence behavior of MUD. Fig. 6 shows the EXIT chartsfor a load of 200% andEb/N0 = 8 for an LDS design withdifferent processing gains. As it can be noted, usingdv = 3improves the intersection point compared todv = 2. Thisis due to the larger frequency diversity offered atdv = 3.Also the performance atdv = 4 is close todv = 3, thereforeconsidering that complexity increases exponentially withdv(for fixed overloading conditions),dv = 3 can be regarded asa suitable value in the design of LDS systems with a load of200%. Thus, as an example, we have found thatdv = 3 is aproper value for a load of 200%, this can be extended to otherscenarios to find suitable parameters for them.

IV. EXIT C HART ANALYSIS OF TURBO MULTI -USER

DETECTOR/DECODER

In this section we propose a new receiver for LDS-OFDMbased on iterative exchange of extrinsic information between

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

IA,FND

& IE,VND

I E,F

ND &

IA

,VN

D

FND Eb/N

0= 8dB

VND dv=2

FND Eb/N

0= 5dB

Trajectory for Eb/N

0= 5dB

Trajectory for Eb/N

0= 8dB

Fig. 5. EXIT chart for MUD atEb/N0 = 8&5 dB for load 200%.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

IA,FND

& IE,VND

I E,F

ND &

IA

,VN

D

FND dc=4

FND dc=6

FND dc=8

VND dv=2

VND dv=3

VND dv=4

Fig. 6. EXIT chart for MUD atEb/N0 = 8 dB for differentdc&dv .

LDS multi-user detector and FEC decoders of different users.There exist two iterative processes in the turbo MUDD: innerprocessing for MUD and outer processing for turbo MUDD.Having two iterative processes involved, the message updatealgorithm must be modified accordingly. Definingt as theturbo iteration index for outer iteration, the message updatesin (3) and (4) can be adapted

Lj,tn,→(xk,m) =∑

l∈Ek,m\n

Lj−1,tl,← (xk,m) + Lt−1dec,out(xk,m), (20)

Ljn,←(xk,m) ∝

f(xk,m|yn, L

j,tn,→(xk′,m′), ∀(k

′,m′) ∈ Jn \ (k,m)). (21)

Where Lt−1dec,out is the extrinsic information that an FECdecoder sent to its corresponding variable node in the priorturbo iteration. Therefore, considering the message-passingalgorithm the messages sent by variable nodes to the decoderare as follows:

Lj,tdec,in =∑

l∈Ek,m

Lj−1,tl,← (xk,m). (22)

6

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

IA,MUD

& IE,FEC

I E,M

UD &

IA

,FE

C

BER=0.3

BER=0.2BER=0.1 BER=0.05

BER=0.01

BER=0.001

MUD with 1 iterationMUD with 3 iterationsMUD with 6 iterationsTrajectoryConv. Code G=(133,171)

Switch from MUDwith 6 iterations toMUD with 1 iteration

Fig. 7. EXIT charts for turbo MUDD atEb/N0 = 0.5 dB for load 200%.

Applying the message-passing rule to the new graph, themessage sent by the variable node to a function node must bebased on all the messages it has received from the remainderof the connected function nodes in addition to the message thathas been received from the corresponding FEC decoder. Forfunction nodes the message update follows the same procedureas for the conventional LDS-OFDM MUD.

In this section, EXIT charts are used to investigate andreduce the complexity of the turbo MUDD. To calculate theEXIT charts, both the MUD and FEC decoder are assumedto be a device that produce a new sequence of extrinsicinformation using a sequence of observations and the inputapriori information. Therefore, in order to calculate the mutualinformation using (15), it is necessary to estimate the PDFfrom the histogram of the soft output of a constituent decoder.Furthermore, EXIT chart is a useful tool for predicting theBER performance [12]. The BER can be predicted by esti-mating the soft output of the coded bits by summing up theextrinsic information and thea priori information

Λ = LMUD + LDEC , (23)

σ2Λ = σ2LMUD

+ σ2LDEC , (24)

where (24) assumesa priori information and the extrinsicinformation are independent. Both variances can be calculatedfrom their related mutual information using (17). Thus, theBER can be calculated as follows:

pb ≈1

2erfc

(√μ2Λσ2Λ

)

=1

2erfc

(σΛ2

). (25)

Fig. 7 illustrates the EXIT chart for turbo MUDD withdifferent number of inner iterations for a system load of200% over AWGN channel. Here we implemented the sys-tem with 60 chips and a convolutional code with generatorG = (133, 171) in octal notation (FEC decoder). Additionally,the BER scaling according to (25) is given as a contour plot.

Fig. 7 shows that the curves for different numbers ofinner iterations intersect at the same point at input mutualinformation equal to one. This is due to full interference

1 1.5 2 2.5 3 3.5 4 4.5 510

-6

10-5

10-4

10-3

10-2

10-1

Eb/N

0 (dB)

BE

R

LDS-OFDM with Normal MUDLDS-OFDM with Turbo MUDD (6,6,6)LDS-OFDM with Turbo MUDD (6,1,1)

Inneriterations(6,1,1)

Inneriterations(6,6,6)

Fig. 8. BER comparison for LDS-OFDM with different MUD techniques.

cancellation at FNDs when perfecta priori information isprovided to them. In this case just one inner iteration willsuffice to detect the data symbols. However, as it is observedfrom Fig. 7 larger number of turbo iterations will be requiredif only one inner iteration is used. In contrast, the cases with3 and 6 inner iterations exhibits a marginally open tunnelbetween the EXIT curves for the FEC decoders and the MUD,hence for these cases turbo MUDD can approach its finalperformance by less number of turbo iterations.

To efficiently utilize both inner and outer iterations wesuggest using 6 inner iterations at first turbo iteration andthen reducing the inner iterations to 1 from the second turboiteration and onward. This will considerably reduce the overallcomplexity while maintaining the same performance. As thesimulated trajectory in Fig. 7 shows, the simulated resultsfollow the suggested iteration schedule very closely and theturbo MUDD converges by only 4 turbo iterations.

Monte Carlo based simulation results for LDS-OFDM’sBER with a load of 200% ,Nc = 60 over AWGN channelis shown in Fig. 8. This result proves the prediction con-cluded using EXIT charts. As it is observed, the receiverbrings about a significant performance improvement overconventional LDS-OFDM receivers. 2.3 dB gain at BER=10−5

is achieved by turbo MUDD with 3 turbo iterations overconventional LDS-OFDM receiver. As expected from EXITchart analysis, the performance of the turbo MUDD with(6,1,1) inner iterations is close to the one with (6,6,6) inneriterations. Consequently, the complexity was reduced whilekeeping the performance of the two systems close to eachother. This result is important because in a real system, turboiteration requires a huge processing overhead.

Finally, to show the validity of using previous analysis ona fading channel, the EXIT chart is calculated for the turboLDS-OFDM under multi-path fading channel (ITU PedestrianChannel B). Fig.9 shows the convergence behavior of LDS-OFDM with effective spreading size of 3 and 60 chips and120 data symbols which belong to 10 users. The graphs fordifferent SNRs show that an increase in the SNR only resultin a vertical shift of MUD curve, which is a complete match

7

TABLE ISIMULATION PARAMETERS

Number ofUsers 10

Number of datasub-channels 60

FFT size 64

Sub-channelbandwidth 15KHz

Multipath channelmodel ITU Pedestrian ChannelB

LDS-OFDM MUD technique Max-Log-MAP

Channelcoding Half-rate convolutionalcode

Modulation BPSK

Data streams peruser100%Loading 6

200%Loading 12

Effective spreading factor(LDS) dv = 3

Symbols persub-carrier(LDS)

100%Loading dc = 3

200%Loading dc = 6

to the behaviour of the system for AWGN channel shown inFig. 5. It is also shown that the simulated decoding trajectorytravel within the open tunnel between the EXIT curves for theMUD and the FEC decoder. Therefore, the validity of EXITchart analysis for multi-path fading channels can be verified.It is necessary to mention that EXIT chart analysis assumesthat the PDF of the exchanged messages approaches Gaussian-like distributions with increasing number of iterations, thus, itcan be applied under multi-path fading channel as long as thetrajectory follows the curves of the receiver components.

The receiver that its parameters are selected according toour proposed design guidelines can be called tailor-designedLDS receiver. In next section, the performance of a tailor-designed LDS-OFDM system is shown and compared withwell-known multiple access techniques with similar principles.

V. PERFORMANCECOMPARISON WITH MC-CDMA AND

GO-MC-CDMA

In this section, the performance of tailor-designed LDS-OFDM is evaluated and compared with MC-CDMA and GO-MC-CDMA in terms of BER performance and computationalcomplexity. Considering the prohibitive complexity of theoptimum MUD, LDS-OFDM is compared with a MC-CDMAsystem that has linear minimum mean-square error (MMSE)detector. The linear MMSE detector is the optimal lineardetector that maximizes the output signal-to-interference andnoise ratio (SINR) [13]. On the other hand, it has been shownthat the performance of GO-MC-CDMA is very close to thesingle-user bound [6], thus it is necessary to show that theproposed receiver design for LDS-OFDM is able to keep theperformance the same while reducing the complexity.

The performances are evaluated using Monte Carlo basedsimulations over multi-path fading channel. The single-userBER bound with the same channel profile is also consideredin the comparison. Throughout the simulations, the overallnumber of information bits transmitted by all the systems iskept equal to ensure a fair comparison between the systems.The simulation parameters are listed in Table I. The number ofsub-carriers used is the same as in [6] to keep the complexity

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

IA,MUD

& IE,FEC

I E,M

UD &

IA

,FE

C

Conv. Code G=(133,171)Eb/N0=2 dBEb/N0=0.3 dBTrajectory for Eb/N0=2 dB

Fig. 9. EXIT chart for turbo MUDD for 200% load under multi-path fadingchannel.

0 2 4 6 8 10 12 14 16 18 20

10-4

10-3

10-2

10-1

100

Eb/N

0 (dB)

BE

R

MC-CDMA 100%GO-MC-CDMA 100%LDS-OFDM 100%MC-CDMA 200%GO-MC-CDMA 200%LDS-OFDM 200%Single-User Bound

Fig. 10. Performance results for LDS-OFDM, MC-CDMA and GO-MC-CDMA.

of the optimum MUD feasible. For GO-MC-CDMA, thenumber of sub-carriers per group is set to 4 and maximumlikelihood (ML) detection is employed per group. For MC-CDMA the processing gain is equal to the number of datasub-channels. For MC-CDMA and GO-MC-CDMA systemsorthogonal codes for a load of 100% and Welch bound equality(WBE) for a load of 200% are used. The spreading codesare constructed using the algorithm developed in [14]. Aregular graph structure is maintained for LDS-OFDM while itssignatures are generated randomly. Using the design guidelinesachieved in section III, the effective spreading factor for LDS-OFDM is equal to 3. To keep the complexity of LDS-OFDM’sreceiver at a similar level with the receiver for MC-CDMAand GO-MC-CDMA, its receiver is not turbo MUDD (theperformance of turbo MUDD is shown in section IV).

Fig. 10 shows the BER results for systems with loads of100% and 200%. As it can be observed from the figure, LDS-OFDM system achieves performance close to the GO-MC-CDMA system, which employs optimum MUD. However, thecomplexity of the LDS detector is less than the complexity ofGO-MC-CDMA. As in LDS-OFDM the complexity increases

8

exponentially by the number of symbols per sub-carrier (dc),a complexity order ofO(|X|3)and O(|X|6) is required fora load of 100% and 200%, respectively. However, in GO-MC-CDMA the complexity increases exponentially by thenumber of transmitted symbols in each group, which results incomplexity order ofO(|X|4) andO(|X|8) for loads of 100%and 200%, respectively. Furthermore, the results show that,LDS-OFDM outperforms the performance of MC-CDMA withMMSE detector. This is because the LDS detector is moreefficient than the MMSE detector in eliminating the MUI.For a load of 100%, LDS-OFDM outperforms MC-CDMAby 8.7 dB at BER= 10−3. The MMSE detector fails to attaina satisfactory BER performance under the overloaded condi-tions. Considering all the results, it can be concluded that thetailor-designed LDS-OFDM system can achieve performanceclose to the GO-MC-CDMA system with less complexity.Moreover, the LDS-OFDM system outperforms the systemthat employs MC-CDMA with linear MMSE detector. At theend, to highlight the importance of LDS-OFDM receiver wewill compare this newly proposed technique with the existingmultiple access techniques in next section.

VI. LDS-OFDM IN COMPARISON WITH EXISTING

MULTIPLE ACCESSTECHNIQUES

In this section, the properties of LDS-OFDM are discussedand the scheme is compared with different MAC techniques.

A. Frequency Diversity

For OFDMA systems, it is not possible to exploit the fre-quency domain diversity at modulation symbol level becausethe symbols of users are assigned directly to sub-channelsin such systems. Therefore, in order to exploit the frequencydiversity for OFDMA system at a later stage, it is crucial toincorporate properly the designed error correction coding andinterleaving schemes [15].

For LDS-OFDM, the performance of the system was im-proved by introducing a larger degree of frequency diversityproportional todv, the effective spreading factor. Furthermore,considering that the detection of user symbols in LDS structureis done completely in the sub-carrier level, frequency diversitycan be achieved by assigning distributed and spaced-sufficientsub-carriers for spreading of a given data symbol. Also, thecreated LDS structure will produce diversity on the interfer-ence experienced by each data symbol. Although LDS-OFDMbetter exploits frequency diversity, as compared to OFDMA,its diversity gain is less than the one for MC-CDMA and GO-MC-CDMA, as they offer full frequency diversity [6], [16].

B. Computational Complexity of MUD

Applying the close-to-optimum MUD based on MPA be-came feasible for LDS structure by reducing the numberof interferers in each chip. As mentioned earlier,dc is thenumber of symbols that interfere with each other on each chip.Therefore, at each received chip a user’s symbol will have onlydc − 1 interferers, wheredc � K.

The complexity of the proposed receiver for LDS-OFDMwill be in order ofO(|X|dc) which is a considerable reduction

compared toO(|X|K) for optimal MUD. The complexity ofLDS MUD will be

Complexity= |X|dc × (No. of MUD iterations)×Nc. (26)

Consequently, although the complexity is increased com-pared to OFDMA, its growth is much less than the optimumMUD used in MC-CDMA. Comparing the factor graph ofGO-MC-CDMA and LDS-OFDM we can see that in contrastto the LDS structure for GO-MC-CDMA in each group thereis full connection between the function nodes and variablenodes and there is no connection between the groups. There-fore, applying message-passing algorithm is inefficient dueto the full connectivity of the graph for GO-MC-CDMA.For GO-MC-CDMA the complexity of the system dependson the size of orthogonal groups because the complexity formaximum likelihood detection in GO-MC-CDMA increasesexponentially with the number of active users per group [6].As mentioned earlier the complexity of LDS-OFDM is lessthan the complexity of GO-MC-CDMA.

C. Overloaded Conditions

In wireless systems the number of users naturally exceedsthe available dimensions as the demand for the spectrum isincreasing while the bandwidth is limited. Conventional sig-nature design for multiple access systems such as MC-CDMAand GO-MC-CDMA is based on orthogonality between thesequences to avoid interference. Therefore, these systems canperform reliably when the number of users is equal to thenumber of chips [17]. However, overloaded conditions can besupported by LDS-OFDM as the design of this system is notbased on orthogonality. The LDS system is able to approachnear single-user performance for a CDMA system with up to200% loading [18].

D. Near-Far Effect

The near-far problem (i.e., the effect of unequal receivedenergies) is the principal shortcoming of direct sequenceCDMA systems. On the other hand, by jointly detectingall users’ symbols, optimum multi-user detection for CDMAsystems is near-far resistant [19]. Considering that in the MUDof LDS-OFDM an iterative joint process has been employedfor detecting different users’ symbols and the fact that theperformance of LDS MUD is close to optimum MUD, we canconclude that LDS-OFDM is robust against unequal receivedpowers. Fig. 11 shows the performance of near-far resistancefor LDS-OFDM MUD with different numbers of chips. Thesimulation is done for the case whereEb/N0 is equal to 15dB for the first user, andEb/N0 of other users is different.The BER performance of the first user is shown accordingto ΔEb/N0, which represents the difference inEb/N0 ofuser of interest from theEb/N0 of other users (all otherusers have equalEb/N0). The results are shown for an LDS-OFDM system with different numbers of chips and loads. Itcan be seen that unequal received power has a minor effecton the performance of user of interest for all the scenarios.Furthermore, the performance of the LDS-CDMA systemagainst the near-far effect problem has been analysed in [18].

9

-2 -1 0 1 2 3 4 5 6

10-4

10-3

10-2

10-1

Δ Eb/N

0

BE

R

Load 200% LDS-OFDM with 48 chips, dv=2

Load 200% LDS-OFDM with 60 chips, dv=3

Load 250% LDS-OFDM with 60 chips, dv=3

Fig. 11. Near-far resistance performance of LDS-OFDM.

These results match the results shown for LDS-OFDM, sinceboth techniques are based on low density signatures. In orderto achieve an even better near-far resistance, the system canresort to power control mechanisms. Several algorithms areintroduced in the literature for the optimum power control ofMC-CDMA systems [20]–[22], which can be applied to LDS-OFDM if necessary.

VII. C ONCLUSIONS

In this paper, a close-to-optimum MUD for LDS-OFDMsystems was introduced and analysed. The LDS-OFDM re-ceiver was evaluated using EXIT charts. By analyzing theinner iterations for MUD under AWGN channel, it was shownthat the signature design with effective processing gain equalto 3 was a suitable value for a load of 200%, considering thecomplexity and performance. This could be extended to otherscenarios in order to find suitable values for other conditions.In addition, we showed how the performance is affected byloading as the curves intersected in lower mutual informationpoints for higher loading values. Furthermore, the proposedturbo MUDD was investigated and by deriving and analysingits EXIT charts we could reduce the complexity by properlytuning the number of inner iterations along the outer turboiterations. It was shown that 2.3 dB performance improvementat BER equal to10−5 could be obtained when turbo MUDDwas employed over an AWGN channel.

Applying the achieved guidelines, the performance of LDS-OFDM was evaluated over a typical multi-path fading channelunder different spectral efficiency conditions. The simulationresults showed a noticeable performance improvement com-pared to MC-CDMA systems with MMSE MUD. This largeperformance gain could be achieved at the cost of slightlyincreased computational complexity. This improvement ismainly due to capability of LDS-OFDM to exploit frequencydomain diversity in addition to avoiding a strong interferenceto corrupt all the sub-carriers. In terms of complexity it wasshown that the performance of LDS-OFDM was close toGO-MC-CDMA while reducing the computational complexity

of the MUD. Interference handling property of LDS-OFDMmakes it a suitable candidate for use in heterogeneous wirelessnetworks. However, their use in these specific scenarios needsfurther detailed analysis.

ACKNOWLEDGMENT

This work was supported by Huawei Technologies Co., Ltd,China. The authors would also like to thank Colin O’Reillyfor his editorial comments.

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[8] J. Choi, “Low density spreading for multicarrier systems,” inProc. IEEEEighth Int Spread Spectrum Techniques and Applications Symp, 2004,pp. 575–578.

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[14] S. Ulukus and R. D. Yates, “Iterative construction of optimum signaturesequence sets in synchronous CDMA systems,”IEEE Trans. Inf. Theory,vol. 47, no. 5, pp. 1989–1998, 2001.

[15] D. Tse and P. Viswanath,Fundamentals of Wireless Communication.Cambridge, 2005.

[16] S. Zhou, G. B. Giannakis, and A. Swami, “Frequency-hopped general-ized MC-CDMA for multipath and interference suppression,” inProc.21st Century Military Communications MILCOM 2000, vol. 2, 2000,pp. 937–941.

[17] M. M. B. J. Choi T. Keller L. Hanzo,OFDM and MC-CDMA forBroadband Multi-User Communications, WLANs and Broadcasting.John Wiley & Sons Ltd, 2003.

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[21] J. G. Andrews and T. H. Y. Meng, “Performance of multicarrier CDMAwith successive interference cancellation in a multipath fading channel,”IEEE Trans. Commun., vol. 52, no. 5, pp. 811–822, 2004.

[22] A. Hamid, R. Hoshyar, and R. Tafazolli, “Band based power control(BBPC) for MC-CDMA radio interface,” inProc. VTC2004-Fall Vehic-ular Technology Conf. 2004 IEEE 60th, vol. 1, 2004, pp. 404–408.

Razieh Razavi (S’10) received her B.Sc. degreein electrical engineering from University of Tehran,Tehran, Iran, and her M.Sc. degree (with distinction)in Wireless Communication Systems from BrunelUniversity, London, United Kingdom, in 2006 and2008, respectively. She is currently working to-ward the Ph.D. degree in mobile communicationsin the Centre for Communication Systems Research(CCSR), University of Surrey, Surrey, U.K.

Her research interests include information theory,advanced multi-user detection and decoding tech-

niques, advanced multiple access techniques, and stochastic processes.

Mohammed Al-Imari (S’10) received the B.Sc.degree in electronic and communications engineer-ing from University of Technology, Baghdad, Iraq,in 2005, and the M.Sc. degree (with distinction)in wireless communication systems from BrunelUniversity, London, UK, in 2008. He secured firstrank in his B.Sc. and M.Sc. degrees along with theIEEE Communications Prize for the best projectfrom the department of Electronic and ComputerEngineering, Brunel University, for the 2008/2009academic year. He is currently pursuing the Ph.D.

degree in mobile communications at the University of Surrey, U.K. Hisresearch interests include information theory, multiple access techniques, andradio resource management in multicarrier communications.

Dr. Muhammad Ali Imran (M’03) received hisM.Sc. (Distinction) and Ph.D. degrees from Im-perial College London, UK, in 2002 and 2007,respectively. He secured first rank in his B.Sc. anda distinction in his M.Sc. degree along with anaward of excellence conferred by the President ofPakistan, in recognition of his academic achieve-ments. He is currently a lecturer in the Centre forCommunication Systems Research (CCSR) at theUniversity of Surrey, UK. He has been activelyinvolved in European Commission funded research

projects ROCKET and EARTH, Mobile VCE funded project on fundamentalcapacity limits and EPSRC-UK funded project India-UK ATC. For EARTHproject he coordinated CCSR research theme. For IU-ATC project he lead theresearch theme on self organising networks. He is the principal investigatorof EPSRC-UK funded multidisciplinary REDUCE project aiming at usingICT to reduce energy consumption of users. He is also involved in severalindustry funded projects on the design of spectrum and energy efficient linkand system level solutions for wireless communications. His main researchinterests include the analysis and modelling of the physical layer, optimisationfor the energy efficient wireless communication networks and the evaluationof the fundamental capacity limits of wireless networks.

Reza Hoshyarreceived his B.S. degree in commu-nications engineering and his M.S. and Ph.D. de-grees, both in mobile communications, from TehranUniversity, Tehran, Iran, in 1991, 1996, and 2001,respectively. He received the top and second rankawards for his B.S. and M.S. degrees from TehranUniversity. From 2002 to September 2010, he hasbeen a Research Fellow and then Senior ResearchFellow in the Mobile Communications ResearchGroup, Centre for Communication Systems Re-search (CCSR), University of Surrey, Surrey, United

Kingdom. During this period, he was actively involved in several Europeanprojects focusing on advanced digital signal processing, coding and modula-tion, and scheduling techniques for relaying, and cooperative communicationsin OFDM/OFDMA systems. Currently he is a principal system engineer atSilicon Valley Labs, Texas Instruments, California, USA. His current focus ison advanced mixed analog/digital signal processing and compressive sensing.

Dageng Chen (S’04, M’06) was born in Hubei,China in 1982. He received the B.E. degree in 2004and the M.S. degree in 2006, both from the WuhanUniversity at Wuhan.

He is currently one of the team leaders in Com-munication Technologies Lab, Huawei, Shanghai.His primary research focus is on advanced wire-less communications, next generation communica-tion system, large scale cooperation system, link andsystem level evaluation.