Performance of Cooperative CDMA withSuccessive Interference Cancellation

Indu Shakya, Falah H.Ali, Elias StipidisCommunications Research Group

Department of Engineering and DesignUniversity of Sussex

Brighton,UKEmail:i.l.shakya, f.h.ali, e.stipidis@sussex.ac.uk

Abstract— We investigate the BER and achievable rate of usercooperation schemes in practical uplink CDMA channels withmultiple access interference (MAI). It is shown that when thesystem loading increases, cooperation alone becomes less effectiveif simple matched filters (MF) followed by combining from eachpartners’ signals are employed for obtaining decision variables.By performing successive interference cancellation (SIC) for eachreceived signals from the partners and then using the maximumratio combining technique, the diversity gain and hence theuplink capacity is enhanced. We further analyse the outputdecision variable signals and also provide a simplified boundon achievable rate based on Gaussian Approximation of MAIsignals. Illustrative simulation results are given, which confirmthat the proposed scheme using SIC achieves much improveddiversity and error performance under high system loading andnearfar conditions.

I. INTRODUCTION

It is well known that the use of antenna diversity providessignificant capacity improvement of wireless communications[1]. While employing multiple antenna at the base-station iseasier to perform than that in mobile handsets to achievethe diversity, in many situations, alternative solutions to thescheme may be desirable. To address this problem, recentlycooperative diversity has emerged as an interesting approach toimprove the link performance of wireless networks by sharingthe antennas and other resources among the users [2], [3],[4], [5], [6], [7], [8]. It becomes more useful particularly forthe mobile users, which can not due to their size and powerlimitations, employ more than one antenna to communicatewith other users or base-station.

Cooperative diversity is also very beneficial for uplink ofCDMA and has been the subject of study in many recentwork e. g. [2], [6], [7], [8], [9], [10], [11]. The paper bySendonaris et. al. [2] has considered user cooperation forCDMA system. However, the main practical problem of mul-tiple access interference (MAI) is not considered. In practiceMAI may have profound effects the performance in coopera-tive CDMA systems. The performance of a single user withrelay assisted diversity for uplink of CDMA under differentpropagation environments is investigated in [11]. It is shownthat the conventional matched filter detector fails to attain fulldiversity gain. And hence an improved receiver is proposedthat suppresses MAI from relays. However, the cooperation

and reception techniques for CDMA under realistic multiuserenvironment has not been considered. To address the MAI,more complex multiuser detection (MUD) techniques such asdecorrelation or MMSE combined with user cooperation arealso investigated in [6], [9], [10]. It is well known that SIC is avery effective detection technique for CDMA with complexitycomparable to that of simple MF receivers. Hence, a newscheme combining user cooperation and SIC is described in[8]. Where it is shown that the cooperation provides muchimproved performance compared with the SIC only. In thispaper, we further investigate it’s achievable rates and compareit’s BER with a cooperative scheme using conventional MFreceiver under various user loading and nearfar conditions.Our results show that the proposed Cooperative SIC can pro-vide much improved BER under practical power imbalancedconditions when system loading is less than half.

The paper is organized as follows. In section II, the systemmodel is presented. The proposed cooperative transmissionscheme is described in section III and the operation of thenew SIC receiver is described in section IV. The achievablerate of the new scheme and comparisons are then presented insection V. Section VI shows the BER simulation results andcomparison analysis. Finally the paper is concluded in VII.

II. SYSTEM MODEL

A typical multiuser communication scenario of an uplinksynchronous CDMA with a pair of cooperating users e.g.1, 2, ..k, i, .., K − 1,K and base-station receiver dsystem employing the proposed cooperative scheme is shownin Figure 1. A common multiple access channel (MAC) withequal power BPSK modulated user signals with fading andAWGN is assumed. It is easy to understand that the samecooperation scenario applies to all pairs of cooperating users.

To gain clear insight into the impact of cooperation onmultiuser SIC reception under MAI conditions, we make noteson few assumptions made in this paper as follows:

1) The cooperating pair of users are chip synchronizedbefore they start to cooperate and transmit each others’ data.Extension to asynchronous case should be possible with somemodification to the scheme.

2) The amount of interference from non paired user nodesto the cooperating pair of users is small and can be treated as

background noise. This may be easily justified due to uniformdistribution of users within the coverage of a typical cellularsystem; the cooperating user nodes see much less interferencefrom other users compared with the base-station receiver (which is usually placed in the center of a cell to be able totransmit and receive to/from all users more efficiently).

3) The pairing users are assumed to know the phases of theirtransmit channels such that while transmission their signalsare multiplied with appropriate phase offsets for coherentcombining at the base-station receiver [2].

Fig. 1. Cooperation scenario between pairs of users

In the proposed cooperative uplink CDMA system, duringthe first symbol period, the users transmit their own datawith their originally assigned spreading sequences. At thesame time, the users that are pairing with transmitting usersreceive and decode the transmitted signals. During the secondperiod, the pairing users forward the decoded data using thespreading sequences of their partners. The signals received atthe cooperating pairs k, i at the first period can be writtenas:

ri(t)=√

Pkgki(t)bk(t)ck(t) + vi(t),

rk(t)=√

Pigik(t)bi(t)ci(t) + vk(t),(1)

where, P is the signal power, g(t) = α(t)ejπφ(t) isthe complex fading channel of the users with amplitudeα(t) and phase φ(t) components with variance σ2, bk(t) =∑∞

m=−∞ bk(m)p(t−mTb) is the data signal, where bk(m) isa binary sequence taking values [−1,+1] with equal probabil-ities, p(t) is rectangular pulse with period Tb. The spreadingsequence is denoted as ck(t) =

∑∞n=−∞ ck(n)p(t−nTc) with

antipodal chips ck(n) of rectangular pulse shaping functionp(t) with period Tc and with normalized power over a symbolperiod equal to unity

∫ Tb

0ck(t)2dt = 1. The spreading factor

is N = Tb/Tc and v(t) is the AWGN with two sided powerspectral density N0/2.

The received composite signal at the base-station receiver dfrom all users’ transmissions during the first period rd(t) andfrom that of the partnering users’ in the second period r′d(t)can be written as:

rd(t)=K∑

k=1

gkd(t)sk(t) + v(t),

r′d(t)=K∑

i=1,i 6=k

gid(t)si(t) + v(t),

(2)

where sk(t) =√

Pkbk(t)ck(t) is the transmitted signal ofkth user. The model of signal si(t) transmitted during thesecond period is exactly the same as above but they areoriginated from the i, i 6= k user with kth user’s estimateddata b′k(t) with their own channels gid(t) = αi(t)e−jπφid(t).The signal model described above applies to all pairs ofcooperating users with appropriate modifications.

For a cooperative scheme to perform satisfactorily, the inter-user channel gains are desired to be higher or at least equalto that of the respective transmit channels of the users to thedestination (base-station in this work) [12]. Assuming averagenoise variances of all users and the base-station receivers areequal, the relative signal to noise ratio (SNR) gain in dB ofinter-user channels βk, βi compared to the respective transmitchannels of the users to the base-station can be expressed as

βk=σ2

ki

σ2kd

, βi=σ2

ik

σ2id

(3)

where, σ2ki, σ2

ik and σ2kd, σ2

id are the variances of inter-userchannels gki, gik and the users’ channels to the base-stationreceiver gkd, gid, respectively. Symmetry of inter-user channelsi.e. gki = gik,∀k assumed here is reasonable as in [1].In the near far condition, σ2

kd 6= σ2id and hence βk 6= βi

with nearfar ratio being defined as Ω = maxσ2jd/σ2

kd, j ∈1, 2, ., i, ., K, j 6= k.

III. PROPOSED MULTIUSER COOPERATIVE TRANSMISSIONSCHEME

Based on the system model, a signalling structure of theproposed scheme with two users spanned over two consecutivesymbol periods is shown in (4). The same signalling structureapplies to all other consecutive periods. When appropriate,the signals are presented in vector form and indices denotingtime dependance are dropped. A single cycle of cooperativetransmission scheme can also be written as

sk =√

Pkgkbkck︸ ︷︷ ︸,√Pkgkb′ici︸ ︷︷ ︸first period second period

si =√

Pigibici︸ ︷︷ ︸,√Pigib′kck)︸ ︷︷ ︸

first period second period

(4)

In the first period, the users transmit their signals as shownin equation (4). Due to the broadcast nature of the channels,the signals are simultaneously received both at the cooperating

users and at the base-station receiver. At the same time, thereceived signals are independently processed at the users’receivers. For handling these operations, it is assumed thatfull duplex capabilities or echo cancellation technique [12] isavailable. Alternatively, the use of relay nodes as in [7] canalso be used without effecting our cooperative protocol fora more practical half duplex operations. The received signalsat the cooperating pairs at this period are given in (1). Thedetection of signals at each other user node is performed byfirst obtaining the soft estimates of the signals by despreadingthe received signal with the known spreading sequence, forexample the kth user this is given by

zk =1Tb

∫ Tb

0

rkck,∀k (5)

Then, by performing channel phase correction and takingthe sign of the real part of the signal zk , the estimate of thekth user’s transmitted signal b′k is obtained

b′k = sgn[<

zkg∗ik

](6)

where, sgn., <. and ∗ denote sign and real and complexconjugation operation, respectively.

During the second period, the cooperating users simplyforward the detected data the partners b′k to the base-stationreceiver using the their partners spreading sequences ck. Itshould be noted that the estimated data may not be identicalto the transmitted data of the by originating users due to thedetection errors in (5) and (6). The accuracy of detection andthus error performance improvement of the system due to thecooperation depends on the relative SNR gains of the inter-user channels gki and gik to their respective transmit channelsto the base-station receiver gkd and gid. The processes (5) and(6) are performed at all the mobile nodes each acting both asa user and a partner for transmitting their data.

IV. DESIGN OF COOPERATIVE SIC

During both the first and second period of the proposedcooperative scheme, the base-station receiver processes thereceived signals to perform detection of users’ data. TheCooperative SIC receiver performs the detection of user signalsbased on order of their estimated strength using the principleof a SIC, e.g. [13], [14], [15], [16]. In the first period thesignal estimation of the strongest among the users is carriedout, followed by the cancellation of its MAI contributionfrom the remaining composite received signal. The relativepower estimates of the users are generated at the output ofthe corresponding users’ matched filters and the one withmaximum is selected at a time given by

zmax = max

1Tb

∫ Tb

0

rdck

,∀k (7)

In the second period the estimate for the strongest userdenoted by index max from the first period is carried outfrom the out of bank of MF as follows:

z′max =1Tb

∫ Tb

0

r′dcmax, (8)

The estimated signals of the user from the two periods ismaximum ratio (MRC) combined to form a final decisionstatistic Zmax. Note that other combining methods such asEGC, MMSEC [17] are equally applicable for the diversitycombining. For MRC with coherent detection , the combinedsignal can be shown as follows:

Zmax = zmaxαmax + z′maxα′max (9)

where, αmax and α′max are amplitudes of estimatedstrongest user in first period. Finally, the hard decision of dataof the user with index k = max is performed from the SICstage as follows:

bk = sgn[<

Zmax

](10)

The cancellation process now has to be applied to boththe received signals from the first and second periods forimproving the estimation of weaker users signal that followsthe same processes (7) - (10). The estimates of the user’s signalin the first and second period zmax and z′max are separatelyspread using the spreading sequence of the detected user withindex k = max and subtracted from the respective receivedsignals rd(t), r′d(t) to obtained less interfered received signalsas follows

rd = rd − zmaxck

r′d = r′d − z′maxck

(11)

The processes (7) - (11) are then carried out until all users’data signals are detected.

V. ACHIEVABLE RATE OF THE COOPERATIVE SIC

The achievable rate analysis presented here for the proposedsystem is developed based on some well-known theories ofcapacity of single user channel [18], that of relay channels[12] and also the Gaussian Approximation method [19] usedextensively in CDMA systems. The cooperation between twousers is considered for simplicity, however the method appliesto more than two users with appropriate modifications. Theachievable rates for the cooperating users Rk and Ri can beshown as [2]:

Rk = Rkd + Rki

Ri = Rid + Rik

(12)

where, Rkd and Rid are the rates using the kth and ith users’own channels to the transmitter. Rki and Rik are the additionalrates that come from employing the cooperation scheme usingthe inter-user channels. Since, the CDMA systems often oper-ate in an interference limited environment ( i.e. assuming highSNR region with Pk/TbN0 >> 1), the capacity calculationhas to be done not on the given SNR basis but on the signalto noise plus interference ratio (SINR) at the decision point ofeach user. The SINR expression Γkd for the kth user’s decisionvariable conditioned on it’s data bk can be shown as follows:

Γkd =E2zk|bkvarzk|bk

=α2

kd∑Kj 6=k ρ2

jkα2jd + N0

(13)

where, E. and var. denote the expectation and varianceof a random variable zk and ρ2

jk is the power of cross correla-tion or MAI between users’ sequences. We make a simplifiedassumption that the SIC perfectly cancels the interferenceat each stage to obtain the expected SINR EΓkd at thedetection point for kth user. The SINR at the output of kth

stage (equi-correlated spreading sequences are assumed forsimplicity with ρ2

jk = ρ2,∀j, ∀k ) can be given by

Γkd = E

[N0

α2kd

+K∑

j=k+1

ρ2α2jd

]−1

Γid = E

[N0

α2id

+K∑

j=i+1

ρ2α2jd

]−1(14)

where, Γ0 = Eα2kd

N0 is the SNR for a given transmit power

under single user condition and assumed equal for all usersunless otherwise stated. Here, the Gaussian approximation canbe used for MAI signal distributions [19] and when randomspreading sequences are used, this allows us to approximatethe variance of a user’s MAI contribution to be ρ2 = 1/Nfor each user. To further simplify the analysis and to obtainthe average SINR for kth under the SIC, it is assumed thatk = K/2 i.e., in average kth user is detected after (K − 1)/2users are canceled from the order statistic used [15] and thisleads to the SINR of kth user using random sequence withSIC as

Γkd =α2

kd

Kα2jd/2N + N0

> 2 for K −→ N (15)

Although the SINR calculation given above may not wellcharacterize the true SIC performance, this approach may beuseful to gain an insight into the upper and lower boundson rates a practical SIC can give. A very useful study onachievable rate analysis of a non cooperative SIC with randomsequences under different conditions such as different powerordering as well as power control, the effect of channel fadingdistributions are carried out in [20]. It was also noted that thewell known Rayleigh distributed fading of channels have nearoptimum distribution for SIC with power ordering. The valueof Γkd is maximized when distribution of interfering users’channel gains αjd is such that

Γkd =⇒ Γ0

ifK∑

j=k+1

ρ2jkα2

jd << α2kd

(16)

Also, it can be clearly seen from (16) that the value of Γkd

is also effected by the type of sequences used i.e. cross cor-relation values ρjk. Thorough analysis of such system is verymuch involved and hence is not carried out here. Assuminginterference free inter-user channel, the upper bound on the

achievable rate of kth user with the proposed cooperationscheme can be given by

Rk < E

[C

Γkd + min

Γki,Γid

](17)

where, C(X) = log2(1 + X) is the well-known expressionfrom the AWGN channel capacity theorem [18]. From therate Rk achieved for kth user as in (12), it can be justifiedthat under the most practical cooperation conditions whereΓki ≥ Γid each user’s achievable rate under the proposedCooperative SIC scheme Rc−sic, is strictly higher than therate that can be achieved from cooperation using MF (withoutinterference cancellation) Rc−mf or SIC detection withoutcooperation Rsic. The expression for achievable rates for theseschemes dependent on system loading, cross correlation andperfect MAI cancellation in the case of using SIC can also beshown as:

Rc−sic > Rc−mf =⇒

E

[C

[E

N0

α2kd

+K∑

j=k+1

ρ2α2jd

−1]]+

min

[C

[E

α2ki

N0

, E

N0

α2id

+K∑

j=i+1

ρ2α2jd

−1]]

> E

[C

[E

N0

α2kd

+K∑

j=1,j 6=k

ρ2α2jd

−1]]+

min

[C

[E

α2ki

N0

, E

N0

α2id

+K∑

j=1,j 6=i

ρ2α2jd

−1]](18)

Rc−sic > Rsic =⇒

E

[C

[E

N0

α2kd

+K∑

j=k+1

ρ2α2jd

−1]]+

min

[C

[E

α2ki

N0

, E

N0

α2id

+K∑

j=i+1

ρ2α2jd

−1]]

> E

[C

[E

N0

α2kd

+K∑

j=k+1

ρ2α2jd

−1]](19)

From above, it becomes clear that the rate increase dueto cooperation can be maximized if technique of interferencecancellation is designed as such that maximizes the SINR foreach user. In reality, the SIC always generates residual errordue to imperfect cancellation therefore reducing the achievablerates of the user cooperation scheme. The numerical results onachievable rates of the scheme employing different sequenceswill be presented in future work. Next, the BER simulationresults obtained for the proposed scheme are presented tosupport our performance analysis.

VI. SIMULATION RESULTS AND COMPARISONS

A baseband model of K user synchronous uplink DS-CDMA system employing BPSK and short binary Gold se-quences of length N = 31 is used. The channel used is Rayleigh

Fig. 2. Performance of Cooperative SIC in flat Rayleigh fading channel withK=10, Gold sequence, N=31

flat fading channel with Doppler shift of 185Hz with carrierfrequency of 2GHz corresponding to a normalized Dopplerrate of fdTb = 0.003.

The BER performance of Cooperative SIC (C-SIC) receiverunder system load of K = 10 users is shown in Figure 2.The BER of cooperative scheme employing conventional MF(C-MF) is shown for comparison. The perfect collaborationdenotes the case of no error in detection of user’s data at it’scooperating pair which can be achieved as βk −→ ∞. Theperformance of C-SIC is significantly better compared with theC-MF as expected. The effect of improved inter-user channelSNR βk on improvement in BER for both schemes is seenfrom the figure. The performance gap between the C-MF andC-SIC under higher values of βk is large, as it can be notedthat the interference estimation and cancellation for a SIC isquite accurate. The C-SIC shows near single user performancewhereas with C-MF, the remaining MAI signals are so highthat inevitable error floor is seen under high SNR region.

The BER under different system loading condition underthe average uplink channel SNR per bit of 20 dB is shown inFigure 3. The results for the C-SIC system shows that the BERperformance under different user loading conditions does notdegrade significantly to unacceptable level as the number ofusers increases. The C-MF as shown in the Figure performsmuch worse than the C-SIC. Also, it is noted that the BERperformance of C-MF does not improve much with higherSNR gains of inter-user channels βk under higher user loadingconditions. Although the performance results are shown interms BER vs. SNR, it is expected that the C-SIC will alsoprovide similar improvement in outage probabilities for givendesired user rates.

Figure 4 shows the performance of the C-SIC in Rayleigh

Fig. 3. Performance of Cooperative SIC in flat Rayleigh fading channel withaverage Eb/N0 = 20dB (No near far), Gold sequence, N=31

fading channels and nearfar condition of Ω = max |gjd|2|gkd|2 = 10

dB. The desired kth user (weakest user) has unity powercorresponding to the expected SNR at the receiver of 15 dB,while all other users j ∈ 1, 2, ..,K, j 6= k are assumed tobe transmitting with power uniformly distributed between 0and 10dB higher than the weakest user; see Figure 1. It canbe clearly seen from the figure that the BER performance ofthe desired user with the C-SIC is much improved comparedto that of MF receiver with cooperation as βk increases. Asthe number of users increases, the system BER performanceis degraded. Due to the cooperation, it is expected that thedesired weak user benefits from the strong channel of it’spartner. From Figure 4, it can be noted that the performanceof the desired user is indeed improved compared to the case ofequal power users case as in Figure 3. Also, it is observed thatuse of C-MF does not improve BER with nearfar conditions asit did with C-SIC. The performance of C-MF is shown to bemuch worse than in equal power case as in Figure 3. The mainreason behind this is that, in nearfar conditions the estimatesof users’ data becomes highly unreliable and hence diversitycombining does not assist much to improve the performanceof final decision.

VII. CONCLUSION

The performance of a low complexity cooperative SIC tech-nique for an uplink CDMA that attempts to improve the usercooperation diversity by removing MAI before the detection isanalysed. Using Gaussian approximation, the achievable rateof the technique is obtained and compared to that with existingscheme without interference cancellation or cooperation. Also,it is demonstrated by simulations that the proposed schemeprovides much improved BER under high system loading

Fig. 4. Performance of Cooperative SIC in in flat Rayleigh fading channelwith nearfar condition of Ω = 10 dB, Eb/N0 of the weakest user=15dB,Gold sequence, N=31

and nearfar conditions. It is noted that as the system loadingincreases, due to the imperfect MAI estimation the achievablediversity gain of the cooperative SIC is reduced, but at a muchslower rate than that with cooperative MF receiver.

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