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

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

3. 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