Effect of Cooperative CSI in Adaptive SubcarrierAllocation for OFCDM based Decode-and-Forward

Relay SystemsS. Senthuran, A. Anpalagan and O. Das

Dept. of ELCE, Ryerson UniversityToronto, Canada

Sehrish KhanECE Discipline, Khulna University

Khulna, Bangladesh

Abstract—In this paper, we first propose a modified adap-tive subcarrier allocation algorithm for a two-hop decode-and-forward OFCDM relay system and then its BER performanceanalysis is formulated and numerically evaluated via Monte-Carlo simulation. The effect of considering the CSI of source-base station and source-relay links are evaluated in a cooperativediversity system. Results show that the allocation of subcarriersbased on source-relay link CSI provides better BER performanceat higher Eb/No and at lower Eb/No, both the source-relay andsource-base station links need to be considered. We also introducea parameter called cooperative channel state information, C-CSI-(0 ≤ ν ≤ 1), that weighs in end-to-end SINR and hence impactsthe subcarrier allocation in OFCDM systems. From our numeri-cal simulation, we notice that the cross-over Eb/No point (aroundwhich frequency spreading gives better performance than timespreading) moves towards the lower Eb/No when ν approaches 1;that is, when the subcarrier allocation is done giving more weightto source-base station link rather than the source-relay link. Wealso observe a relationship between the cross-over point (Eb/No

in dB) and the C-CSI, which provides additional flexibility inoperating environment for OFCDM systems.

Index Terms: two-hop relay system, decode-and-forwardsystems, OFCDM, subcarrier allocation, cooperative CSI

I. INTRODUCTION

Emerging applications in wire-free communication createfurther need for higher data rate services with reliable perfor-mance. For such wideband applications, code division multipleaccess (CDMA) based systems were widely considered inthe literature to provide effective multiple access capabilities.First was the multicarrier direct-sequence CDMA (MC-DS-CDMA) [1] system where multicarrier modulation was usedwith time spreading. The other system was the multicarrierCDMA [2] where multicarrier modulation and frequency do-main spreading were used. Even though MC-CDMA providesfrequency diversity, it is vulnerable to multiple access inter-ference (MAI) in a frequency selective subchannels since thefrequency selectivity destroys the orthogonality property ofthe codes of the users that are using the same subcarrier setwith their own spreading codes. In this case, each subcarriershould have frequency non selective fading in order to keepthe orthogonality and, for wideband transmission, a largenumber of such subcarriers is needed. In order to realize the

This work was supported in part by a grant from National Science andEngineering Research Council of Canada.

benefits from both systems, a multicarrier CDMA system wasproposed in [3] where both frequency and time spreadingcodes were used according to the channel conditions. Thisproposed system was shown to provide frequency diversitywhile reducing the MAI.

Multicarriers can be selected orthogonally and orthogonalfrequency and code division multiplexing (OFCDM) systemwas proposed in [4]. OFCDM uses data spreading in both timeand frequency domain, where each data stream is segmentedinto multiple substreams and spread over multiple subcarriersand several OFCDM symbols, exploiting additional frequencyand time diversity. In [5], OFDM based two dimensionalspreading was proposed and, field tests were successfullycarried out by NTT DoCoMo to support the use of OFCDMtechnology in future wideband communications [6]. Recently,there has been some research work on subcarrier groupingand allocation to further improve the performance in OFCDMsystems. For example, subcarriers are grouped and adaptivelyallocated in [7] to users by improving the signal to interferenceand noise ratio (SINR) while minimizing the MAI.

On the other hand, cooperative relay systems can im-prove the throughput and the reliability in wideband wirelesscommunications [8]. CDMA technique is also introduced inrelay systems in [9] to take advantage of spread spectrumtechniques. In [10], MC-CDMA decode-and-forward relaysystem performance was analyzed. However, there has beenno study for an OFCDM relay system or subcarrier allocationfor that system in the literature. In this paper, we modifythe adaptive subcarrier allocation algorithm proposed in [7]for two-hop decode-and-forward wireless relay system andanalyze its BER performance due to the effect of differentcooperative channel state information (C-CSI).

The rest of the paper is organized as follows: In sectionII, the system model, relevant literature for direct link (one-hop) OFCDM system and the proposed OFCDM decode-and-forward two-hop relay system analysis are presented. Insection III, the adaptive subcarrier allocation algorithm for theproposed system is described. Section IV presents the per-formance comparison for different time-frequency spreadingcodes and subcarrier allocation based on different link channelstate information. Finally, this paper concludes in section Vwith future work that could possibly be done in this area.

978-1-4244-2515-0/09/$25.00 ©2009 Crown

II. TWO-HOP COOPERATIVE RELAY SYSTEM MODEL

We consider an uncoded two-hop wireless system whereOFCDM is employed as multiple access technology. Usersare denoted by Uk and total number of users is K (assumedto be even number). Odd numbered users (U1, U3, . . . , UK−1)are classified into one group and even numbered users(U2, U4, . . . , UK) into another group as done in [11]. Further,it is assumed that there is a one-to-one mapping betweentwo groups of users and they are paired (as partners) forcooperative relaying.

Source nodes and relaying nodes are allocated separatechannels (time slots) during the transmission. Each nodetransmits its own data as well as the estimated data of itspartner which was received in the previous time slot. Allthe relay nodes operate in a decode-and-forward mode andthe transmitted information is spread by its own pre-assignedspreading codes [11]. Fig. 1 shows a couple of transmissioncycles (t = j, j+1) to understand the pair-wise communicationand Table I shows 4 consecutive transmission time instances.The user 1 is considered as source and the user 2 as relay.Further, the binary data stream of user k is denoted bybk

j = ±1 and its estimate at the relay node by b̂kj where

jεℵ indicates the time instance.

Source(User 1)

Relay (User 2)

Base Station

Source

Relay

Base Station

(a) (b)

t = j t = j+1

Fig. 1. System model (a) at time t = j, (b) at time t = j + 1.

Time instanceTransmitting node t=j t=j+1 t=j+2 t=j+3

User 1 b1j - b̂2j+1, b1j+2 -

User 2 - b̂1j , b2j+1 - b̂1j+2, b2j+3

TABLE ITWO USER’S COOPERATIVE COMMUNICATION DURING 4 TIME SLOTS.

In the analysis, the channel is assumed to be slowly varyingwith respect to the OFCDM symbol duration. It is also as-sumed that the subcarrier spacing is larger than the coherencebandwidth of the channel in a group and hence, frequencynon-selective fading occurs on each subcarrier within a sub-carrier group. This allows the frequency domain channel to bemodeled as:

Hk,lj,m = αk,l

j,meiφk,lj,m ,

where i =√−1. The term αk,l

j,m is the Rayleigh fading gain for

the mth subcarrier of the kth user during the time instance jon the link l. The link l can be either source to relay (s→r) orsource to base station (s→bs) or relay to base station (r→bs).The phase is a uniformly distributed random variable over theinterval (0, 2π], which is assumed to be independent for eachbit, user, and subcarrier.

A. Single Link (One-Hop) Transmission

For the direct one-hop transmission, the adaptive subcarrierallocation for an OFCDM system was proposed in [7]. In orderto recover the data from user 1 at the receiver, the receivedsignal is copied to the subcarrier branches that are assignedto user 1. Then it is restored to the baseband considering thephase shift of the channel. Each branch is multiplied by thesynchronized time domain spreading sequence and the fre-quency domain pseudo-random (PN) chip. The despread signalis then multiplied by the fading gain, α1,s→bs

j,m , according to themaximal ratio combining algorithm. Finally, the subcarriersare summed, integrated over the bit period, and sampled toyield the decision variable for user 1 as:

Z1j = D1

j + I1j + η1

j , (1)

where D1j is the desired signal, I1

j is the interference fromthe other users on group y, y = {1, 2, . . . , Y }, where Yis total number of subcarrier groups and η1

j is the noiseterm which is considered as the AWGN noise signal with adouble-sided power spectral density of No/2. Further, Gy , My

and Ky denote the set of subcarriers, number of subcarriersand the number of users respectively occupying a group ysimultaneously.

The desired signal can be written as [7] for a single linkdirect transmission,

D1j = N

√εcb

1j

∑mεGy

(α1,s→bsj,m )2 (2)

where εc is the chip energy, N is the length of the PNsequence and mεGy is the set of subcarriers in group y.

The power of the desired signal for user 1 is determined bycomputing the variance D1

j . Since the bit stream, b1j has zero

mean, the power of the desired signal can be written as:

PD1j

= Var[D1

j

]= N2εc

[ ∑mεGy

(α1,s→bsj,m )2

]2

(3)

The interference term is calculated by considering thecorrelation between the received signals from all Ky usersoccupying subcarrier group y simultaneously, with the timeand frequency domain spreading sequences for user 1.

The interference power can be approximated as a Gaussianrandom variable when the number of users is moderate tolarge, and the input data stream is random [3] [12]. Theresulting interference power is,

PI1j

= Nεc(Ky − 1)E[(αk,s→bs

j,y )2] ∑

mεGy

(α1,s→bsj,m )2, (4)

where E[(αk,s→bs

j,y )2]

is the average fading gain for the Ky

users and My subcarriers in group y at time instance j in thelink s → bs. It can be calculated as follows:

E[(αk,s→bsj,y )2] =

1KyMy

∑k∈Gy

∑m∈Gy

(αk,s→bsj,m )2

The noise power at output of the correlator can be writtenas:

Pη1j

= Var[η1

j

]= NNo

∑mεGy

(α1,s→bsj,m )2 (5)

Based on the equations (3)-(5), the SINR at the base stationfor the bit that was transmitted during the time instance j byuser 1 on the subcarrier group y on the link s → bs, γ1,s→bs

j,y ,can be written as:

γ1,s→bsj,y =

Nεc

∑mεGy

(α1,s→bsj,m )2

(Ky − 1)εcE[(αk,s→bs

j,y )2]+ No

(6)

Further, the corresponding probability of bit error can bedetermined as follows assuming BPSK modulation,

BER1,s→bsj,y = Q

(√2γ1,s→bs

j,y

)(7)

B. Two-hop Cooperative Transmission

Based on the results in the previous section for one-hopsystem, the BER performance of the two-hop relay system isderived in this section. As shown in Fig. 1, the same sourceinformation is received at the base station (bs) during twoconsecutive time slots. In the jth time slot, the information isreceived from the source (s) and, during the (j + 1)th time slotthe information is decoded and forwarded by the correspond-ing relaying (r) node. Considering these two consecutive timeslots (j, j +1), user 1’s desired signal of the decision variableat base station can be written as in (8) from (2).

D1j+1 = D1,s→bs

j + D1,r→bsj+1

= N√

εc

(b1j

∑m∈Gy

(α1,s→bsj,m )2

+ b̂1j+1

∑m∈Gy′

(α2,r→bsj+1,m )2

), (8)

where mεGy is the set of subcarriers in group y while sourcetransmitting and mεGy′ is the set of subcarriers in group y′

while relay node transmitting. The α1,s→bsj,m and α2,r→bs

j+1,m are

the Rayleigh fading gain for the mth subcarrier of the 1st

user during the jth time instance in the link s→bs and, of the

2nd user during the (j + 1)th time instance in the link r→bsrespectively.

We can rewrite the desired decision variable at the basestation on the condition of correct (D1,c

j+1)/ incorrect (D1,fj+1)

decoding at the relay node as:

D1,cj+1 = [D1

j+1|b1j = 1, b̂1

j+1 = 1]

= N√

εc

⎛⎝ ∑

m∈Gy

(α1,s→bsj,m )2 +

∑m∈Gy′

(α2,r→bsj+1,m )2

⎞⎠

D1,fj+1 = [D1

j+1|b1j = 1, b̂1

j+1 = −1]

= N√

εc

⎛⎝ ∑

m∈Gy

(α1,s→bsj,m )2 −

∑m∈Gy′

(α2,r→bsj+1,m )2

⎞⎠

and the interference and noise power terms can be writtenfrom (4), (5) as in equation (9). Where Ky′ is the number ofusers occupying a group y′ while relay node is transmitting.

Based on the above result, the probability of bit error at thebase station can be determined for the bit that was transmittedduring the jth time instance by the user 1 (after 2 slots) as:

BER1j+1,y =

(1 − BER1,s→r

j,y

)Q

⎛⎝√

2(D1,cj+1)√

Ω1j+1

⎞⎠

+(BER1,s→r

j,y

)Q

⎛⎝√

2(D1,fj+1)√

Ω1j+1

⎞⎠ , (10)

where, Ω1j+1 is defined in (9) and BER1,s→r

j,y is defined asthe probability of bit error of user 1 at the relay node whiledecoding before retransmitting to the base station. It can becalculated using (7) with

γ1,s→rj,y =

Nεc

∑mεGy

(α1,s→rj,m )2

(Ky − 1)εcE[(αk,s→r

j,y )2]+ No

(11)

III. ADAPTIVE SUBCARRIER ALLOCATION

In [7], an adaptive subcarrier allocation algorithm wasproposed for a single link transmission to improve the overallBER performance of an OFCDM system. The subcarriers areassigned to users that are having higher SINR at the sametime reducing the interference caused by this assignment toother users in the same subcarrier group. In this section,the subcarrier allocation algorithm is first modified for adecode-and-forward OFCDM two-hop relay system and thenits performance is evaluated based on the numerical analysisin section II-B.

In a two-hop relay system, there are 3 links, (namelys→r, s→bs and r→bs) that contribute to the overall BERperformance of the system. As described earlier, the twoconsecutive time slot transmission from the source and therelay are assumed to fade independently; hence, the subcarrierallocation is also done separately.

During the jth time slot, the source will transmit and, thebase station and the cooperating relay node will receive on asame set of subcarrier group (Gy). Therefore, the subcarrierallocation algorithm is carried out based on the channel stateinformation (CSI) of the links s→r, and s→bs.

Ω1j+1 = N

∑m∈Gy

(α1,s→bs

j,m

)2((Ky − 1)εcE[(αk,s→bsj,y )2] + No

)+ N

∑m∈Gy′

(α2,r→bs

j+1,m

)2((Ky′ − 1)εcE[(αk,r→bsj+1,y′ )2] + No

). (9)

We introduce a parameter ν (0 ≤ ν ≤ 1), called cooperativeCSI (C-CSI) which weighs in end-to-end SINR for a two-hop transmission and hence provides different impact on sub-carrier allocation. ν=0.5 means that the subcarrier allocationalgorithm tries to optimize both the links (s→bs and s→r)simultaneously giving equal weight. In this case, maximizingthe SINR while minimizing the MAI would be performed onboth the links together with equal weight. When ν=1, thesubcarrier allocation is done solely based on the CSI of thelink s→bs whereas when ν=0, it is solely on the CSI of thelink s→r. ν is therefore called cooperative CSI that adjuststhe weight of different cooperative links.

Hereafter, the time instance j is dropped in the notations forsimplicity. Decision variable (SINR) in subcarrier allocationfor a two-hop relay system for user k is defined giving differentweights to cooperative links as:

γky = νγk,s→bs

y + (1 − ν)γk,s→ry , (12)

where γk,s→bsy and γk,s→r

y are defined as SINR of user kbelonging to subcarrier group y at the base station (links → bs) and the relay node (link s → r) respectively andthey are calculated using (6) and (11).

The subcarrier allocation algorithm is described briefly asfollows:

(a) Subcarrier group that has the largest SINR γky as defined

in (12) for all k users is found as follows:

γkmax = max{γk

1 , γk2 , . . . , γk

Y }The index denoted yk

max is recorded.

(b) From the result in (a), the subcarrier group with thesmallest SINR is found as follows:

γmin = min{γ1max, γ2

max, . . . , γKmax}

The index of the user with the lowest SINR value, denotedkmin is recorded.

(c) User kmin is assigned to the subcarrier group ykminmax and

the SINR is re-calculated for that assigned group using (6) and(11). The algorithm is repeated until all the data streams areassigned.

IV. NUMERICAL SIMULATION AND DISCUSSION

In this section, the BER performance results are numeri-cally evaluated using Monte-Carlo simulation. The subcarrier

allocation is done based on the the CSI between the linkss→r and s→bs. Subcarriers are grouped so that within agroup, all the subcarriers undergo independent fading. Further,the uplink bandwidth is assumed to be 20MHz with 128subcarriers. There are 64 users grouped into two and paired.In one time slot 32 users assigned to the channel by thesubcarrier allocation algorithm. Each of the users is assumedto be traveling at a velocity of 5km/h, which correspondsto a Doppler frequency of 23.14Hz. This corresponds to acoherence time of approximately 18μs. It is assumed that delayspread is 6.4μs which is common in urban areas [12].

The numerical simulation is carried out for the proposeddecode-and-forward multicarrier CDMA two-hop relay systemwith different time and frequency spreading. When a timedomain spreading factor of 4 is utilized with a frequencydomain processing gain of 8, it is denoted by 4×8. Further,the impact of CSI knowledge between source to base station(s→bs) and source to relay node (s→r) are investigated.

Fig. 2(a) shows the different BER performance of a 4×8(time x frequency) spread two-hop decode-and-forward relaysystem for different C-CSI (ν) values. From this figure, wecan notice that the subcarrier allocation of a decode-and-forward two-hop relay critically depends on the channel stateinformation of the link s→r as further explained next.

In a typical relay system, the CSI of the link s→bs isusually available. When the CSI of both links s→bs and s→rare available and equal weight is given (i.e., ν=0.5) in thesubcarrier allocation, it gives 4 dB gain over the subcarrierallocation with ν=0.75, where subcarrier allocation is donemainly based on the link s→bs at BER of 10−2. Interestingly,when the subcarrier allocation is done mainly based on thelink s→r (ν=0.25), it outperforms the allocation which isdone mainly based on the link s→bs (ν=0.75) by 5 dB atBER of 10−2. The decision variable at the receiver (bs) isconsidered during the decoding process giving equal weighton both the received signal from the source and the forwardedsignal from its partner. Therefore, the incorrectly decoded bitsat the relay node will cause higher error probability at thebase station. At higher Eb/No, it is better to do the subcarrierallocation considering mainly the inter-partner (source-relay)CSI, provided it is accurate.

Similar characteristic is observed in Fig. 2(b) for a systemwith spreading factor of 8×4. We can notice that the error floorimproves when the value of ν decreases, i.e., the subcarrierallocation is done giving higher weight to the link s→r. Theerror floor is 0.0169 when ν=0.75 whereas it is 0.0125 whenν=0.25. The performance is highly interference-limited athigher Eb/No for higher time spreading schemes as shown in

−10 −5 0 5 10 15 20 25

10−2

10−1

100

Eb/N

o, [dB]

(a)

BE

R

ν=0.75ν=0.5ν=0.25

−10 −5 0 5 10 15 20 25

10−2

10−1

100

Eb/N

o, [dB]

(b)

BE

R

ν=0.75ν=0.5ν=0.25

Fig. 2. BER performance comparison for different spreading systems with different C-CSI (ν): (a) 4×8 (b) 8×4.

Fig. 2. Further, the error floors for the schemes 16×2 and2×16are shown in Table II.

In the case of a specific spreading factor (for example8×4), different Eb/No values influence in selecting the indexν when both link CSIs are perfectly available. For example,even though ν=0.25 is performing better at higher Eb/No, forEb/No < 0 dB, ν=0.5 is preferred over ν=0.25 for an 8×4system as shown in Fig. 2. We also observed the significance ofthis selection in higher time spreading systems such as 16×2and 32×1 (for which results are not included in this paper).

In Fig. 3, BER performance is shown for different spread-ing factors, from higher(lower) time(frequency) spreading tolower(higher), by varying the parameter C-CSI (ν). The cross-over point is defined as an Eb/No value around whichthe performance of the frequency spreading becomes betterthan the time spreading. It is noticed that in selecting thespreading factor to operate in different environment, the cross-over point is important. At lower Eb/No, it is better to usehigher spreading in time, and lower spreading in frequencyas also reported in [7]. At lower Eb/No, the performanceis limited by thermal noise. Higher number of groups withfew subcarriers lead to allocate subcarriers with best channelconditions. Therefore, lower frequency spreading with highertime spreading offers better performance. Also the multipleaccess interference (MAI) is minimal since a relatively lowernumber of users is sharing each group of subcarriers. Onthe other hand, at higher Eb/No, the system performance islimited by MAI. Therefore, selecting a better channel doesnot necessarily offer better performance. Further, larger groupsize offers better frequency diversity and at higher Eb/No itis better to have higher frequency spreading with lower timespreading.

Further it is also noticed in Fig. 3 that when ν increases from0.25 to 0.75, the cross-over point (Eb/No) value moves from 4dB to 1 dB. It is also tabulated for different values of ν in TableIII and it shows a relationship between the cross-over point(Eb/No) and the C-CSI (ν) which provide additional flexibilityin operating environment for OFCDM systems between timeand frequency spreading.

BERC-CSI (ν) 16×2 2×16

0.25 0.0208 0.00570.5 0.0253 0.00580.75 0.0294 0.0059

TABLE IIERROR FLOOR FOR DIFFERENT

SPREADING AND ν .

C-CSI (ν) Eb/No (dB)

0 50.25 40.5 30.75 1

1 -1

TABLE IIICROSS-OVER POINT FROM

FREQUENCY TO TIME SPREADING.

V. CONCLUSIONS

We proposed a cooperative CSI-based subcarrier allocationalgorithm for an OFCDM-based two-hop decode-and-forwardrelay system. Its BER performance was evaluated via MonteCarlo simulation. In the case of equal weight given at thebase station receiver for the source and its partner’s forwardeddata in a decode-and-forward OFCDM two-hop relay diversitysystem, CSI of the source-relay link with lower cooperativeCSI significantly impacts the subcarrier allocation at moderateto high Eb/No values. It is feasible to get better performanceby knowing CSI of the source-relay link (inter-partner’s CSI)than having the CSI of the source-base station link in a decodeand forward relay diversity system where source-relay link has

−10 −5 0 5 10 15 20 25

10−2

10−1

100

Eb/N

0, [dB]

(c)

BE

R

16x2 8x4 4x8 2x16

−10 −5 0 5 10 15 20 25

10−2

10−1

100

Eb/N

o, [dB]

(b)

BE

R

16x2 8x4 4x8 2x16

−10 −5 0 5 10 15 20 25

10−2

10−1

100

Eb/N

o, [dB]

(a)

BE

R

16x2 8x4 4x8 2x16

Fig. 3. BER performance comparison with various spreading factor: (a) ν=0.25 (b) ν=0.5 (c) ν=0.75.

similar fading gains as the other links. Even though lower νvalues provides better performance at moderate to high Eb/No

values, for higher time spreading systems the higher ν valuesperforms better at lower Eb/No values. That is, subcarrierallocation considering both links s→bs and s→r providesbetter performance at lower Eb/No. Further, when subcarrierallocation is done giving higher weight on the CSI of the links→bs (as ν is increased) the time-frequency spreading cross-over point moves towards lower SINR.

This work can be further extended to investigate the per-formance when different level of confidence is applied oncooperative links in combining the received diversity signaland the appropriate adaptive power allocation system betweenthe cooperative nodes. Also it can be further investigated onthe effect of using partial or unreliable CSI.

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