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A New Iterative Soft Decision Subcarrier PIC Scheme for CI/MC-CDMA System

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  • 1. A New Iterative Soft Decision Subcarrier PIC Scheme for CI/MC-CDMA System Mithun Mukherjee Department of Electrical Engineering Indian Institute of Technology Patna Patna - 800013, India Email: mithun@iitp.ac.in Preetam Kumar Department of Electrical Engineering Indian Institute of Technology Patna Patna - 800013, India Email: pkumar@iitp.ac.in Abstract—This paper introduces an improved iterative soft decision subcarrier parallel interference cancellation (SDSub- PIC) technique for the carrier interferometry/multicarrier code division multiple access (CI/MC-CDMA) system that significantly reduces the multiple access interference (MAI) for the desired user. Carrier interferometry (CI) codes are used to minimize the cross-correlation between different users. In this paper, the interference cancellation is done by taking the soft decision estimates of transmitted data bit at the subcarrier level. MAI estimates become more reliable with multistage iterative structure of the receiver, which ensures improved bit error rate (BER) performance. Simulation results show that SDSub-PIC provides average BER of 1e-04 at 10 dB SNR which is about 1.5 dB off from single user bound in an AWGN channel at 50% overloading. In slow frequency selective Rayleigh fading channel, SDSub-PIC ensures BER of 4e-05 at 25 dB SNR with four-fold diversity at 100% overloading. We have observed that the new scheme performs considerably better than Block-PIC [14] and Sub-PIC [15] proposed earlier for CI/MC-CDMA system. Complexity of SDSub-PIC is O(N) while for conventional PIC and Block-PIC, it is O(2N-1) and 2O(N) respectively. I. INTRODUCTION Multicarrier code division multiple access (MC-CDMA) system, based on the advantage of robustness against intersym- bol interference (ISI) of orthogonal frequency-division multi- plexing (OFDM) and high spectral efficiency, large system capacity and high flexibility of CDMA, has been a promising technique for future wireless communication. As in CDMA, MC-CDMA also suffers from multiple access interference (MAI) that limits the number of simultaneous transmitting active users using the same channel bandwidth for communi- cation. To alleviate MAI, several multiuser detection schemes have been proposed in the literature [1]. Although notable performance gains are obtained with maximum likelihood multiuser detector, the complexity of the detector grows expo- nentially with the number of users. Considerable performance improvement can be achieved by the use of interference can- cellation (IC) technique. Different IC like successive interfer- ence cancellation (SIC) [2], parallel interference cancellation (PIC), improved PIC [3] have been analyzed earlier. In a typical IC, for detection of desired user the interference from other users’ is estimated and cancelled from the desired user signal. The data estimated from first stage is then fed into next stage of cancellation to get better estimates of the transmitted data. However, if some of users’ information is wrongly detected then the estimated MAI increases the interference power resulting in degraded bit error rate (BER) performance of the desired user. Significant performance improvement is obtained with iterative interference cancellation receiver for underloaded CDMA [4]–[7] and overloaded CDMA systems [8], [9]. Recently, iterative multiuser detection with soft IC for multirate MC-CDMA has been proposed in [10]. The effect of MAI, that arises from the cross-correlation among different users can be minimized by using Carrier Interferometry (CI) code [11]. CI code having good spectral sharing characteristics provides flexible system capacity [12]. CI code of length N can support N simultaneous users orthogonally and user capacity can be increased up to 2N by adding additional N pseudo-orthogonal users to the existing system [13]. For synchronous CI/MC-CDMA uplink, in [14] threshold PIC (TPIC) and Block-PIC have been designed to provide better performance than conventional PIC scheme. In [15], subcarrier PIC (Sub-PIC) has been developed for high capacity CI/MC-CDMA with variable data rate. Although the system capacity has been increased up to three times (i.e. system capacity 3N), but higher BER restricts real-time data communication. In Sub-PIC, estimated MAI is removed based on hard decision interference cancellation technique. In this paper, we have shown that BER performance of CI/MC- CDMA improves considerably by using soft estimates of the interfering users. Comparison with other schemes are also presented in this work. The paper is organized as follows. Brief description of CI/MC-CDMA with hard decision subcarrier parallel inter- ference cancellation technique is discussed in section II. In section III, soft decision Sub-PIC (SDSub-PIC) is explained. Simulation results are presented in Section IV. Finally, in section V conclusions are drawn. II. HARD DECISION SUBCARRIER PARALLEL INTERFERENCE CANCELLATION TECHNIQUE (HDSUB-PIC) In CI/MC-CDMA system, assuming that there are K users, each user employs N subcarriers to transmit data si- multaneously using the same available channel bandwidth. The CI code for kth user (1 ≤ k ≤ K) is given by 2010 IEEE 21st International Symposium on Personal Indoor and Mobile Radio Communications 978-1-4244-8016-6/10/$26.00 ©2010 IEEE 768
  • 2. 1, ejΔθk , ...ej(N−1)Δθk [11], [13], where Δθk may be ex- pressed as Δθk = 2πk N k = 1, 2, . . . N 2πk N + π N k = N + 1, N + 2, . . . 2N (1) In the receiver, while making the decision of kth user, in parallel interference cancellation, we have to subtract the esti- mated value of (K-1) users’ information that creates multiple access interference (MAI). The received signal r(t) can be written as, r(t) = K k=1 N−1 i=0 αi,kak[n].exp j(2πfit + iΔθk + βi,k) .p(t − nTb) + η(t)(2) where, αi,k is the complex-valued channel gain and βi,k is the uniformly distributed phase offset for the kth user in ith subcarrier. For BPSK modulation, ak[n] = ±1 represents nth bit of kth user. {fi = fc + iΔf, (i = 0, 1, . . . N − 1)} is the frequency of ith narrow band subcarrier with center frequency fc and Δf is selected such that orthogonality between carrier frequencies can be maintained. Typically Δf = 1/Tb, where Tb is bit duration of Nyquist pulse shape p(t). η(t) represents AWGN at the multiuser receiver. The received signal r(t) is projected onto N orthogonal subcarriers and is despread using kth user’s CI code. The ith subcarrier component of received signal r(t) can be written as yi = 2 N0Tb Tb 0 r(t)exp − j(2πfit) dt (3) The decision variables for kth user at different subcarriers may be expressed as rk = rk 0 , rk 1 , . . . rk N−1 (4) rk i,iter = α∗ i,k.exp − j(iΔθk) yi + K m=1,m=k 2Eb N0 ˆa(iter−1) m α∗ i,kαi,mexp j(i(Δθm − Δθk) + ˆβi,m − βi,k + ηiexp − j(iΔθk) (5) where, rk i,iter is decision variable for kth user at ith subcarrier in iterth iteration stage. Here, ∗ denote the complex conjugate and yi is the projected N-orthogonal subcarriers component of the received signal r(t). ηi is a Gaussian random variable with zero mean and variance of N0/2. For simplification of analysis, the transmission is assumed to be synchronous i.e., ˆβi,m = βi,k. Further, we assumed that the received power of every user is same, so that |αi,k| = 1. Eb is the transmitted bit energy and ˆa (iter) k is the estimated data of kth user at iterth iteration stage. When yi is multiplied by kth user’s spreading code, the expression becomes: N−1 i=0 exp − j(iΔθk) yi = 2Eb N0 ak[n] + N−1 i=0 K m=1,m=k 2Eb N0 amexp j(i(Δθm − Δθk)) + N−1 i=0 ηiexp − j(iΔθk) (6) Taking the real part, Yk = 2Eb N0 ak[n] + Ik + Nk (7) Yk ∼= 2Eb N0 ak[n] + ˆIk + Wk where, Yk = N−1 i=0 exp − j(iΔθk) yi (8) Nk = N−1 i=0 ηiexp − j(iΔθk) (9) Nk is zero mean Gaussian random variable with variance of N0/2 for kth user. Ik is the MAI experienced by kth user due to (K-1) users and ˆIk is denoted as estimation of Ik based on other users’ information. Wk = Ik − ˆIk + Nk (10) In conventional PIC scheme, the estimated interference is directly subtracted from r(t). But in case of Sub-PIC, the received signal is projected onto N orthogonal subcarrier and the interference due to other users is subtracted at subcarrier level. Wk arises due to imperfect cancellation which reduces with iterative receiver structure. Now, (7) can be written as Yk = 2Eb N0 ak[n] + ˆIiter k + Witer k (11) and ˆIiter k is the estimated MAI experienced by kth user due to (K-1) users at iterth iteration. ˆIiter k = N−1 i=0 K m=1,m=k 2Eb N0 ˆaiter−1 m exp j(i(Δθm − Δθk)) (12) For synchronous transmission between transmitter and re- ceiver and assuming spreading code availability at the receiver, only uncertainty lies in ˆIk. The term (Ik − ˆIk) represents the residual or uncancelled interference power. For initial 769
  • 3. estimation, after forming the decision variables rk , minimum mean square error combiner (MMSEC) is employed to get decision in an AWGN channel [16]. So, for ˆa0 k[n], Yk = rk ω, where ω is the weight vector of the combiner [16]. The decision of kth user information at iterth iteration: ˆaiter k [n] ∼= sgn Yk − ˆIiter k (13) ˆa0 k[n] = sgn Yk The scheme represented by (13) referred is as hard deci- sion subcarrier parallel interference cancellation technique (HDSub-PIC) [15]. III. SOFT DECISION SUBCARRIER PIC (SDSUB-PIC) In SDSub-PIC the received signal is first projected onto N orthogonal subcarrier, and the interference is cancelled in the subcarrier level as discussed earlier. The estimation of the transmitted data is performed by taking soft decisions using nonlinear function [8]. The soft decision of ak[n] is given by ˜ak[n] = φ{(Yk − ˆIiter k ); iter}, where the nonlinear function φ{(x); iter} may depend on the iteration number ‘iter’. Different types of nonlinearities like dead-zone non- linearities, hyperbolic tangent, Piecewise linear approximation of hyperbolic tangent can be used for φ{(x); iter}. i. Dead-Zone Nonlinearity: φ(x) = sgn(x) |x| ≥ λ 0 |x| < λ (14) If λ = 0 then it becomes similar to hard decision based estimation in (13). ii. Hyperbolic Tangent: φ(x) = sgn(x) |x| ≥ λ tanh(x/λ) |x| < λ (15) iii. Piecewise linear approximation of Hyperbolic Tangent: In piecewise linear approximation, for all iteration the function φ{(x); iter} can be written as φ(x) = sgn(x) |x| ≥ λ x/λ |x| < λ (16) The nonlinear parameter λ is selected such that minimum BER can be obtained for iterated IC process. Here in SDSub-PIC technique, we have considered piecewise linear approximation of Hyperbolic Tangent [3] as a nonlinear function of soft decision IC process. In the last stage of iteration, the final decision is made by hard detector, ˆak[n] = sgn{Yk − ˆIiter k }. IV. SIMULATION RESULTS In this section we present the BER performance results of the SDSub-PIC scheme for CI/MC-CDMA system under different conditions (λ, N, number of iterations, and loading conditions) using Monte Carlo simulation. The simulations have been carried out in MATLAB. We have assumed syn- chronous uplink transmission with BPSK modulation. 1 2 3 4 5 6 7 8 9 10 10 −5 10 −4 10 −3 10 −2 10 −1 SNR (in dB) BER Single User Bound 2.0N λ=0.9 2.0N λ=0.7 1.5N λ=0.4 1.5N λ=0.7 Fig. 1. Performance of the SDSub-PIC with different λ value after 8th iteration with subcarrier (N) = 64 1 2 3 4 5 6 7 8 9 10 10 −4 10 −3 10 −2 10 −1 SNR (in dB) BER Single User Bound 2.0N (N=64) after 3 rd iteration 2.0N (N=64) after 8 th iteration 2.0N (N=64) after 10 th iteration Fig. 2. Performance of the SDSub-PIC with different iteration for 2N system; subcarrier (N) = 64, and λ = 0.7 A. Simulation for getting optimum value of λ and number of iterations Fig. 1 shows the performance of SDSub-PIC with different λ values (soft decision parameter (16) after 8th iteration. 2N and 1.5N overloaded systems are being analyzed with subcarrier N = 64. In the simulation, we have kept same value of λ in all iteration. From the figure it can be said that if we take λ = 0.7 then it gives better performance compared to other λ values. So, we have taken λ = 0.7 for the soft decision parameter. Fig. 2 and 3 represent BER performance after different iteration for 2N and 1.5N system. This performance shows that if we increase the number of iteration, BER performance improves. As iteration increases the estimated MAI becomes more closer to actual MAI so the residual part of MAI (Ik − ˆIiter k ) becomes less and the subtraction of estimated MAI provides improvement in BER. After a certain number of iteration, we see that performance 770
  • 4. 1 2 3 4 5 6 7 8 9 10 10 −5 10 −4 10 −3 10 −2 10 −1 SNR (in dB) BER Single User Bound 1.5N (N=64) after 4 th iteration 1.5N (N=64) after 8 th iteration 1.5N (N=64) after 10 th iteration Fig. 3. Performance of the SDSub-PIC with different iteration for 1.5N system; subcarrier (N) = 64, and λ = 0.7 does not improve by increasing the number of iteration. The residual part can not be removed further by using this type of iterative interference cancellation process. From the figure we observe that there is a BER improvement when number of iteration is increased from 3 to 8 (Fig. 2) and 4 to 8 (Fig. 3) in case of 2N and 1.5N respectively. So, we have taken number of iteration as 8 so that lowest BER performance is achieved. The system is tested at 100% overloading, so it is quite obvious that it can ensure acceptable BER at lower loading conditions. B. Comparison of Block-PIC and Sub-PIC with SDSub-PIC 1 2 3 4 5 6 7 8 9 10 10 −4 10 −3 10 −2 10 −1 SNR (in dB) BER Single User Bound Block PIC [14] Sub−PIC [15] SDSub−PIC Fig. 4. Comparison of SDSub-PIC with Sub-PIC and BlockPIC with subcarrier = 64 for 2N system Other PIC techniques like Block PIC [14], Sub-PIC [15] have been compared with the proposed SDSub-PIC scheme in Fig. 4 and 5. Those figures illustrate the comparison of other two schemes with SDSub-PIC. We have considered λ = 0.7 and 8 iteration. In Sub-PIC the MAI is cancelled out at 1 2 3 4 5 6 7 8 9 10 10 −5 10 −4 10 −3 10 −2 10 −1 SNR (in dB) BER Single User Bound Block PIC [14] Sub−PIC [15] SDSub−PIC Fig. 5. Comparison of SDSub-PIC with Sub-PIC and BlockPIC with subcarrier = 64 for 1.5N system subcarrier level before taking the final decision. This scheme offers improvement over Block-PIC [14]. We have shown that SDSub-PIC offers better BER performance than hard decision based Sub-PIC. In SDSub-PIC, soft decision is involved for the interference cancellation process. This technique ensures BER of the order 5e-04 at 10 dB SNR with N = 64 subcarrier for 128 users (i.e., 100% overloaded system). In Sub-PIC, we observed that BER is 3e-03 at 10 dB SNR. Fig. 5 shows that if we reduce the overloading to 1.5N, BER performance improves considerably compared to other two schemes. Here we obtained a BER of 1e-04 at 10 dB SNR with SDSub- PIC. So, this technique can be utilized for high data rate communication with some penalty in SNR (∼1.5 dB). For Block-PIC BER is about 5.5e-03 for 2N system and 4.5e- 03 for 1.5N system. In case of SDSub-PIC the BER goes down from 5e-04 (2N) to 1e-04 (1.5N) at 10 dB SNR with subcarrier (N) = 64. It is also observed that Sub-PIC and Block-PIC result a bit error floor. C. Different loading condition In real time communication, it is desirable to make cellular system overloaded. The system is said to be more bandwidth efficient when it can handle extra active simultaneous users with a desirable BER performance. When the active user gets reduced (i.e., 1.2N, 1.4N system), it is interesting to observe that (Fig. 6), system performance is closer to single user bound. D. Performance in frequency selective channel We have also considered slow frequency selective Rayleigh fading chananel with four-fold diversity [14] for subcarrier (N) = 64 and 128 users (K). In the Fig. 7, we have shown the performance comparision among Block PIC [14], Sub-PIC [15], and proposed SDSub-PIC technique. In Block PIC [14] BER is 6e-04 at 25 dB SNR after 10th iteration. We can get BER of 3e-04 using Sub-PIC [15] after 10th iteration. It is 771
  • 5. 1 2 3 4 5 6 7 8 9 10 10 −5 10 −4 10 −3 10 −2 10 −1 SNR (in dB) BER Single User Bound 2.0N 1.5N 1.4N 1.2N Fig. 6. Different loading condition with subcarrier = 64, λ = 0.7, after 8th iteration 5 10 15 20 25 10 −5 10 −4 10 −3 10 −2 10 −1 SNR (in dB) BER Single User Bound Block PIC [14] Sub−PIC [15] SDSub−PIC Fig. 7. Comparison of SDSub-PIC (After 8th iteration) with Sub-PIC (After 10th iteration) and BlockPIC (After 10th iteration) with subcarrier = 64 for 2N system with four-fold diversity in slow frequency selective Rayleigh fading chananel interesting to observe that (Fig. 7), the SDSub-PIC performs considerably better than other two interference techniques. In case of SDSub-PIC, BER of 4e-05 is obtained after 8th iterations only at 25 dB of SNR. So, it is clear that, SDSub- PIC scheme performs better than other two schemes even on slow frequency selective channel. E. Multirate Transmission and Peak-to-average power ratio (PAPR) Modern digital communication needs multimedia transmis- sion. For this type of transmission, users have to transmit data simultaneously at different data rates depending upon voice, video or multimedia data. So, multiple access schemes like CDMA should be able to support multimedia communication. CI/MC-CDMA system can be designed to support ‘N’ high data rate users with ‘N’ subcarriers each and lesser number 1 2 3 4 5 6 7 8 9 10 10 −5 10 −4 10 −3 10 −2 10 −1 SNR (in dB) BER Single User Bound 2.0N (64 HDR + 32x2 LoDR) 1.4N (64 HDR + 13x2 LoDR) 1.2N (64 HDR + 6x2 LoDR) Fig. 8. Performance of SDSub-PIC in multirate transmission after 8th iteration, subcarrier (N) = 64, λ = 0.7 in AWGN channel 10 15 20 25 30 35 10 −15 10 −10 10 −5 10 0 PAPR (in dB) ProbabilityofPAPR conventional Partition(all PO−CI Shift π/N) Partition(osc π/N, esc π/2N) Partition(osc π/2N, esc π/N ) Proposed phase shift Fig. 9. Complementary cumulative distribution of PAPR for 2N system with N = 64 of subcarriers to low data rate users. In this paper, the implementation is done by allocating all sub-carriers to the users who transmit high-data-rate (HDR) and alternate odd and even subcarriers are assigned to the other set of users who need to transmit at low data-rate (LoDR). The usage of alternate sub-carriers suggests to split CI codes in odd and even parts leading to increase in capacity. Fig. 8 illustrates the BER performance of three multirate systems where N users transmit at high data rate with N = 64 available subcarrier. For 1.2N multirate system, the BER is 3.7e-05 after 8th iteration at 10 dB SNR which is 1 dB away from single user permance in an AWGN channel. Multicarrier systems, like OFDM and MC-CDMA, support high data rate transmission with an increased peak-to-average power ratio (PAPR). In multicarrier transmission, when the subcarriers are superimposed in same phase, then probability of getting high PAPR becomes more. PAPR not only affects 772
  • 6. the power amplifier at transmitter section, it also deteriorates BER performance. The transmitted signals get distorted due to high PAPR. Further, the information signal is lost due to the non-linear operation of power amplifier. Here, reduction in PAPR value is achieved through the phase shift of even CI code using odd sub-carriers by an amount of π/2 and odd CI code using even sub-carriers by −π/2, all measured with respect to the orthogonal codes supporting high data rate transmission. From the Fig. 9 it is observed that the proposed system also ensures low probabilty of PAPR, which reduces the effect of power amplifier. So, in our proposed CI/MC- CDMA system it is clear that the probability of high PAPR becomes less compared to other schemes [14]. F. Complexity Conventional PIC has the complexity of O(2N-1) for ‘N’ length of CI code. In case of Block-PIC [14], the complexity reduces to 2O(N). Our proposed SDSub-PIC provides consid- erably better BER performance at complexity of O(N) which is much lower than other two previous schemes. V. CONCLUSION In this paper, a new soft decision based subcarrier PIC scheme has been introduced for CI/MC-CDMA system. We have observed that the SNR penalty is about 1.6 dB at a BER of 1e-04 with proposed SDSub-PIC scheme for N = 64 and 96 users in an AWGN channel. In slow frequency selective Rayleigh fading channel, SDSub-PIC ensures a BER of 4e-05 at 25 dB SNR with four-fold diversity at 100% overloading. Block PIC [14] and Sub-PIC [15] result in a BER of 6e- 04 and 3e-04 respectively after 10th iteration at 25 dB of SNR. Hence, the proposed receiver scheme provides improved BER performance with less complexity. It will be interesting to evaluate the performance of this scheme under non ideal channel conditions. The SNR penalty can be reduced further by using suitable error correcting codes. REFERENCES [1] S. Verdu, Multiuser Detection. 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