This paper proposes a high capacity carrier interfer-ometry/multicarrier code division multiple access (CI/MC-CDMA) system through the simultaneous support of highand low data rate transmission. High data rate users trans-mit data through all sub-carriers while alternate odd andeven subcarriers are shared by the low data rate users.The usage of alternate sub-carriers suggests to split CIcodes in odd and even parts leading to an increase incapacity. The cross-correlations among the code patternsare reduced through the phase shift of even (odd) CI codeusing odd (even) sub-carriers by an amount of π/2 andodd (even) CI code using odd (even) sub-carriers by -π/2,all measured with respect to orthogonal codes assigned tosupport high data rate transmission. Performance in termof BER (bit error rate) is then analyzed by carrying outsimulation on frequency selective Rayleigh fading channel.The MAI (multiple access interference) effect is subtractedat the subcarrier projection domain leading to the reductionin high computation cost inherent in parallel interferencecancelation. Performance improvement for different combi-nations of low and high data rate users are shown comparedto the conventional CI/MC-CDMA system as well as blockPIC scheme.
1. Introduction
Multicarrier code division multiple access (MC-CDMA)nowadays becomes a preferable choice for high capacity andhigh data rate transmission in mobile wireless communica-tion. The usage of novel carrier interferometry (CI) complexspreading codes in MC-CDMA system offers enhancedperformance and flexibility relative to other conventionalspreading codes [1]. The CI codes of length N have a uniquefeature that allows CI/MC-CDMA systems to support Nnumber of users orthogonally, and then as system demandincreases, codes can be selected to accommodate up to anadditional (N − 1) users pseudo-orthogonally. Additionally,there is no restriction on the length N of the CI code
(i.e., N − 1) making it more suitable for diverse wirelessenvironments. We further like to increase the capacity to3N users where additional low data rate users are supportedthrough the split of spreading sequences as well as odd-evenseparation of available sub-carriers.
CDMA suffers from an intrinsic problem of multipleaccess interference (MAI) and multiuser detection (MUD) isa powerful technique to combats MAI effect by subtractingthe estimated interferences from the received signal [2].The optimum multiuser detector proposed in [3] achievessignificant performance improvement relative to single userreceivers but the computational complexity increases ex-ponentially with the number of users. This has motivatedthe use of low complexity linear [4] and decision drivensuboptimal multiuser detection techniques. To overcomethe disadvantage intrinsic to the total PIC, some modifiedversions like partial parallel interference canceling [5] andlinear parallel interference cancelation technique [6] havebeen proposed. Parallel interference weighted canceler hasbeen proposed in [7] to mitigate the degrading effects of un-reliable interference estimation. Two variants of PIC knownas threshold PIC and block PIC have been proposed in[8] for synchronous CI/MCCDMA uplink and block PIC isshown to provide performance gain relative to conventionalPIC. Maity et al [9] further improves BER performance ofdiversity assisted block PIC using genetic algorithms.
The above PIC schemes in MC-CDMA either suffer fromthe large computation complexity to achieve desired lowBER or BER performance achieved is not of acceptable levelfor the high payload system with affordable computationcost. This paper attempts to make a good compromiseamong BER, capacity and computation cost through thedevelopment of a new CI/MC-CDMA system where userstransmit their data at different rates. This is achieved byallocating all sub-carriers to the users who transmit highdata rate. The users of low data rate share alternate oddand even subcarriers. The effect of MAI (multiple accessinterference), arising out from the cross-correlation amongthe code patterns, is reduced through the phase shift ofeven (odd) CI code using even (odd) sub-carriers by an
Figure 1. Block diagram of the proposed CI/MC-CDMAtransmitter
amount π/2 and odd (even) CI code using even (odd) sub-carriers by -π/2, all measured with respect to the orthogonalCI codes assigned to support high data rate transmission.The estimated MAI (multiple access interference) effectfor the high data rate users, calculated on the subcarrierprojection domain, is then subtracted from the receivedsignal. Performance improvement for different combinationsof low and high data rate users are shown compared to theconventional as well as block PIC CI/MC-CDMA system.
The rest of the paper is organized as follows: Section2 describes model for the proposed CI/MC-CDMA system.Section 3 describes proposed subcarrier PIC scheme. Section4 presents performance evaluation while conclusions andscope of future work are stated in section 5.
2. Proposed CI/MC-CDMA System Model
The CI/MC-CDMA is an MC-CDMA scheme employingcomplex carrier interferometry spreading codes. Assumingthat there are K users and N subcarriers in the MC-CDMAsystem, the CI code for the k-th user (1 ≤ k ≤ K) is givenby [1]: [1, ejΔθk ,...ej(N−1)Δθk] where Δθk = 2π.k/N . Inthis paper, we have developed a new variation of the CI/MC-CDMA model used in [1]. Therefore, we present a briefreview of the model in [1] followed by our new model.
2.1. Transmitter Model
In CI/MC-CDMA transmitter [8],[9], the incoming dataak[n] for the k-th user is transmitted over N narrow-bandsub-carriers each multiplied with an element of the k-thuser’s spreading code. The BPSK modulation is assumed,i.e. ak[n] = ±1 where ak[n] represents the n-th bit of thek-th user. The transmitted signal corresponding to the n-thbit of the incoming data is given by
S(t) =K∑
k=1
N−1∑
i=0
ak[n]expj(2π.fit+iΔθk)p(t) (1)
where fi = fc + i.Δf is the i-th subcarrier, and p(t) isa rectangular pulse of duration Tb. As with the traditionalMC-CDMA, the Δf ’s are selected such that the carrier fre-quencies are orthogonal to each other, typically Δf = 1/Tb,where Tb is the bit duration.
Future multimedia data communication service demandsvariable data rate transmission as diverse classes of traffichave different requirement of quality of services (QoS).This may require transmitter optimization in order to meetdesired QoS with high data rate in a power and bandwidthlimited channel [10]. To accommodate variable data rateswith high capacity, we modify the transmitter model of [1]by allocating all sub-carriers to the users of high data ratetransmission and at the same time odd and even sub-carriersare shared alternately among the users of low data rate. Itis logical to assign all subcarriers to support high data ratetransmission in order to overcome ISI (inter symbol interfer-ence) problem leading to the reduction in BER. On the otherhand, it is also seen from the simulation results that MAIeffect for a given number of subcarriers is comparativelylower when alternate subcarriers rather than consecutivesubcarriers are allocated for the users. This in turn allowssplitting of the sub-carriers in even and odd parts as well asthe ‘N’ length PO-CI (pseudo-orthogonal) in N/2 odd andN/2 even parts. Fig. 1 shows block diagram representationof the proposed transmitter model. The mathematical formfor the transmitted signal S1(t) becomes
S1(t) = [N−1∑
k=0
N−1∑
i=0
ak[n]expj(2π.fit+2π.i.k/N)
+3N/2−1∑
k=N
N−1∑
∀i=odd
ak[n]expj(2π.fit+2π.i.k/N+iΔφ1)
+2N−1∑
k=3N/2
N−1∑
∀i=odd
ak[n]expj(2π.fit+2π.(i+1).k/N+iΔφ2)
+5N/2−1∑
k=2N
N−1∑
∀i=even
ak[n]expj(2π.fit+2π.i.k/N+iΔφ3)
+3N−1∑
k=5N/2
N−1∑
∀i=even
ak[n]expj(2π.fit+2π.(i+1).k/N+iΔφ4)
]p(t − n.Tb) (2)
where Δφ1 = +π/2,Δφ2 = −π/2,Δφ3 = −π/N − π andΔφ4 = −π/N indicate respective phase shift angles withrespect to the orthogonal CI codes. The phase shift angles areshown in Fig. 2 to have a better understanding of the systemmodel. The phase shifts are given in order to reduce the
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cross-correlation among the spreading code patterns whichin turn reduces MAI.
Figure 2. Phasor diagram of phase shift for different CIcodes
2.2. Channel Model
An uplink model has been considered where all theusers’ transmissions are assumed to be synchronized forsimplification of analysis, although, this condition is difficultto be valid practically. It is also assumed that every userexperiences an independent propagation environment that ismodeled as a slowly varying multipath channel. Multipathpropagation in time translates into frequency selectivity inthe frequency domain [11]. Frequency selectivity refers tothe selectivity over the entire bandwidth of transmissionand not over each subcarrier transmission. This is because1Tb
� (Δfc) � BW , where Δfc is the coherence band-width and BW is the total bandwidth.
2.3. Receiver model
In this subsection, we describe the multiuser receiveroperation for S(t) in Eq. (1). The received signal r(t) forthis S(t) corresponds to
r(t) =K∑
k=1
N−1∑
i=0
αikak[n]cos(2π.fit+i.Δθk+βik).p(t)+η(t)
(3)where αik is the rayleigh fading gain and βik is uniformlydistributed phase offset of the k-th user in the i-th carrierand η(t) represents additive white gaussian noise (AWGN).The received signal is projected onto N-orthogonal carriersand is despread using j-th users CI code resulting in rj =(rj
0, rj1, ....r
jN−1), where rj
i corresponds to
rji = αij .aj [n] +
K∑
k=1,k �=j
αikak[n]cos(i(Δθk − Δθj)
+βik − βij) + ηi (4)
where ηi is a gaussian random variable with mean 0 andvariance N0/2. Exact phase and frequency synchronizationfor the desired user is assumed i.e.,βij = βij . Now, asuitable combining strategy is used to create a decisionvariable Dj , which then enters a decision device that outputsaj . Minimum mean square error combining (MMSEC) isemployed as it is shown to provide the best performance ina frequency selective fading channel [12].
The decision variable Dj for the n-th bit is [8]
Dj =N∑
i=1
rji wij (5)
wherewij =
αij
(var(ak)Aij + N0/2)(6)
where Aij =∑K
k=1 α2ikcos(iΔθk − iΔθj + βik − βij)2
and var(ak) = 1. Thus, the outputs as the single userdetector for all the users generate a decision vector D =[D1, D2, ...DK ] which is used to obtain the initial estimatesof the data a = (a1, a2, ...ak). These initial estimates arethen used to evaluate the MAI experienced by each user inthe interference cancelation technique.
3. Proposed subcarrier PIC scheme
The multicarrier (MC) signal can be modeled as a vectorin N -dimensions where N -mutually orthogonal subcarriersform the basis signals. Accordingly, MC-CDMA signalswith high and low data rates can be modeled as vectorsof different dimensions in subcarrier signal space. In MUD,CDMA signal is treated as a vector and is projected ontoindividual orthogonal spreading function to estimate theinterference of other users for the respective user. In PIC,for a given user, CDMA composite signal is projectedsimultaneously to all spreading codes except the desiredone and the process demands high computation cost. Themultiple access interference (MAI) estimation and its sub-sequent cancelation in MC-CDMA with variable data ratescan be implemented in the respective subcarrier componentrather than projecting it onto spreading functions followedby calculation of vector magnitude (Eq. 5 and Eq. 6), as isdone in case of conventional PIC method. This very simpleconcept is used to develop a low computation cost PICscheme when MAI is subtracted at the sub-carriers level. Fig.3 shows the block diagram representation of the proposedPIC method. The users are divided in two different blocks,block 1(B-1) with high data rate transmission and block-2(B-2) with low data rate transmission.
The received multiuser signal r(t) is first passed througha lowpass filter followed by single user detection throughMMSEC. The decision vector D = [D1, D2, ...DK ] thengenerates the initial estimates of the data a = (a1, a2, ...ak)which are used to determine the polarity of the interference.
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Figure 3. Block diagram representation of proposedPIC scheme
To estimate the interference experienced by j-th user at i-thsubcarrier, the received signal r(t) and the signal of all otherusers, except the j-th user, are projected onto i-th subcarrier.The interference of other users are subtracted collectivelyfrom the former.
We now analyze mathematically the interference freeestimation for the n-th bit of j-th user for conventionalPIC, two block PIC and the proposed subcarrier PIC. Theexpression of the same for the conventional PIC system is
ajn = rn −
K∑
k=1,k �=j
akn (7)
The similar expression for an arbitrary j-th user belonging tostrong group and when belong to weak group, respectively(of a two block PIC system) can be written as follows:
ajn = rn −
∑
∀k1∈S1,k1 �=j
ak1n (8)
ajn = rn −
∑
∀k1∈S1
ak1n −
∑
∀k2∈S2,k2 �=j
ak2n (9)
where the symbols of ajn, rn,S1 and S2 represent n-th
estimated bit of j-th user, resultant received signal for n-thbit, set of strong and weak user groups, respectively.
The interference free estimation of the i-th subcarrier forthe j-th user of block B1,
rji = ri −
∑
∀k1∈B1,k1 �=j
rk1i (10)
while the expression for the same belonging to block B2,
rji = ri −
∑
∀k1∈B1
rk1i −
∑
∀k2∈S2,k2 �=j
rk2i (11)
where rji and ri indicate the i-th subcarrier component of
the j-th user and the i-th subcarrier component of resultantreceived signal, respectively.
Now, the decision variable Djn for the n-th bit of an
arbitrary j-th user of block B1 can be written accordingly to
Eq. (5). The equation is rewritten in Eq. (12) for convenienceof further analysis. The similar expression for the j-th userof the block B2 is written in Eq.(13)
Djn =
N∑
i=1
rji wij (12)
Djn =
N∑
∀i=oddoreven
rji wij (13)
The values of rji for Eq. (12) and Eq. (13) can be put from
Eq. (10) and Eq. (11), respectively.Mathematical analysis of Eq. (5)-Eq.(13) show that stable
decision variable Djn can be achieved for subcarrier PIC
method compared to conventional PIC and block PIC. Thisis because interference due to other users are subtractedbefore forming Dj
n in the case of former unlike the lattermethods where Dj
n is formed first and then interference issubtracted. This stable decision variable Dj
n gives rise tobetter estimation of aj leading to an improvement in BERthrough interference cancelation. Moreover, the computationcost and time requirement is less compared to the con-ventional PIC and other block PIC [8]. This can be wellunderstood considering the fact that the users of block-1,transmit data at ‘q’ times higher rate (say) compared to theusers of block-2. So, for ‘q’ consecutive bits detection ofhigh data rate users, estimated interferences for the singlebit due to low data rate users can be made use. In otherwords, interferences estimated for low users’ single bitcan be applied to improve subsequent BER of high userdata. It is to be mentioned here that the projection of thereceived signal on the mutually orthogonal subcarriers isessentially the same for both the conventional PIC and theproposed PIC. However, the interference in the former issubtracted after combining them as decision vector while inthe later, interference is subtracted in subcarrier level itself.The computation complexity, for CI codes of length N , isO(2N −1) for conventional PIC, 2 O(N) for block PIC [8]and O(N) for the proposed subcarrier PIC.
4. Performance Evaluation
In this section, we present the performance of theproposed PIC scheme in synchronous CI/MC-CDMAuplink system. The expression of cross correlation (CC)between the k- and j-th users’ signature waveforms can bewritten as follows [1]:
Rk,j(τ) =1
2Δf
sin(1/2N.2π.Δf.τ)sin(1/2.2π.Δf.τ)
cos((N − 1)
22πΔf)
(14)where τ = Δtk − Δtj = (Δθk − Δθj)/2π.Δf . Table Ishows the cross-correlation values for some arbitrary pairof spreading codes under various phase shifts shown in
138
Fig. 2. Numerical values show that Rj,k values are reducedsignificantly due to the low values of Sinc function of Eq.(14) for the proposed phase shifts of the sub-carriers.
Table 1. Cross correlation values for arbitrary code pair
The BER values are calculated from the average proba-bility of error (PE) for the incorrectly received binary dataof all users when transmitting a large number of data. ThePE is calculated as follows:
PE =1
(k × n)
k∑
j=1
n∑
x=1
(aj,x − aj,x) (15)
where ‘k’ and ‘n’ indicate the number of users and thenumber of bits for each user, aj,x is the transmitted bitvectors and aj,x is the received bit vector.
Fig. 4 shows BER performance of the proposed schemeat 14 dB SNR and with N=16 subcarriers for 3N userssystem where N number of users transmit high data rate and2N number of users transmit low data rate. The graphicalresult shows that when capacity is low (less than 20 users),MMSEC receiver of conventional CI/MC-CDMA system(shown as Con. MMSEC in the figure) performs significantlybetter compared to MMSEC receiver of the proposed system(shown as MMSEC in the figure). This is due to the factthat all users in the former transmit data using all sub-carriers while some of the users in the latter transmits datausing either odd or even sub-carriers. However, significantimprovement in BER performance is achieved in the lattercase compared to the former when the number of users aregradually increasing over 20. Further significant improve-ment in BER performance can be achieved after differentstages of the proposed subcarrier PIC scheme. Simulationresults show that the proposed subcarrier PIC scheme afterthird stage iteration, can support the number of users threetimes the number of sub-carriers with BER of the order of0.0428 (0.11071 for [1]), and it can support users upto fourtimes the number of sub-carriers with BER of the order of0.1350 (0.2193 for [1]).
We also test BER performance of the proposed schemethrough the increase of number of users transmitting highdata rate. Fig. 5 shows BER performance of the proposedscheme at SNR 14 dB with N=16 sub-carriers under 2.5Nusers system where 1.5 N number of users transmit highdata rate and N number of users transmit low data rate.Simulation results show that the system supports the number
of users two-and-half and three times the number of sub-carriers with BER values of 0.0591 and 0.104, respectivelyafter three stage iterations. The relative degradation in BERperformance for 2.5 N system, over 3N system, based onthe proposed subcarrier PIC is due to the increase in overalldata transmission rate for the former compared to the latter.The over all data transmission rate is 0.7742 times for 3Nuser and 0.9032 times for 2.5 N system with respect tothe conventional CI/MC-CDMA system [1]. The numericalvalues specified here for data transmission rate is obtainedwhen transmission rate between high and low data rate userdiffers by a factor of 4.
Figure 4. Performance of subcarrier PIC scheme for 3Nuser system
Figure 5. Performance of subcarrier PIC scheme for2.5N users system
We also compare BER performance of the proposedsubcarrier PIC scheme (SCPIC) and block PIC (BPIC)scheme [8]. The results are reported with the performance of[1]through interference cancelation (IC). Fig. 6 shows thatBER performance of the proposed subcarrier PIC scheme issignificantly better compared to that of block PIC schemeand needless to mention its superior BER performance
139
compared to MMSE scheme of [1]. The performance im-provement for the proposed subcarrier PIC is due to thetwofold advantages in interference cancelation. Since thehigh data rate transmission uses all sub-carriers, the datacan be decoded with greater reliability and interference dueto these users can be estimated with greater accuracy. Thisinterference when subtracted from the resultant receivedsignal improves detection performance of the low data rateusers. On the other hand, low data rate transmission usesalternate sub-carriers, so sub-carriers of high data rate usersexperience less interference that leads to an improvementin BER performance of the latter. This cumulative effecton BER performance in multistage interference cancelationsignificantly improves overall BER performance of the pro-posed system unlike to that of the block PIC scheme in [8].In block PIC, in any stage of interference cancelation, weakusers data noway benefits BER performance of strong usersdata unlike the proposed subcarrier PIC scheme.
Figure 6. Performance comparison of subcarrier PIC &block PIC schemes for 3N users system
5. Conclusions and scope of future works
A new model of high capacity CI/MC-CDMA systemalong with simple, fast and efficient PIC scheme is proposedin this paper. The effect of MAI reduction is achievedthrough phase shift of pseudo-orthogonal codes with respectto the orthogonal spreading codes assigned for low andhigh data rate transmission respectively. BER performanceof the proposed method not only shows improved resultcompared to the conventional PIC and block PIC system butalso requires low computation complexity. Future work maybe carried out for joint transmitter-receiver optimization toachieve low PAPR and BER value at high capacity throughthe estimation of channel parameters.
Acknowledgment
This work is the outcome of the project on “Developmentof high power and spectral efficiency multiuser system forbroadband wireless communication” funded by Ministryof Communication and Information Technology, Govt. ofIndia vide administrative approval no. 13(2)/2008-CC & BTdated 31.03.2008 and the authors gratefully acknowledgethis financial support.
References
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[9] S. P. Maity, S. Hati, S. Maity, Diversity Assisted BlockPIC for Synchronous CI/MC-CDMA Uplink Systems UsingGenetic Algorithm, Proceedings of the third IEEE InternationalConf. on Industrial and Information System, Indian Institute ofTechnology, Kharagpur, India, December 2008.
[10] S. P. Maity, S. Hati, S. Maity, M. K. Mandal, Trans-mitter Optimization in Diversity Assisted Synchronous CI/MC-CDMA Uplink Systems Using Genetic Algorithm, 24th IEEEQueen’s Biennial Symposium on Communications (QBSC-2008), Canada, pp. 62-67, 2008.
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