2.9 Chapter Summary
3.2.5 Performance Results and Comparisons
where expectation is taken over the fading power distribution of desired kthuser, η = SN Rk/SN R0
is the asymptotic multiuser efficiency as defined in [28] to assess the multiuser receiver techniques. The SE of system employing CMA-SIC can be obtained as follows
CCM A−SIC ≤ K N log2 " 1 + E 2{z k} var{zk} # , (3.25)
where the expectation is taken over the fading power distribution of the desired kthuser, var{zk}
is the variance of decision variable of kth user by employing the CMA-SIC. The reduced vari- ance of decision variable for CMA-SIC is due to the improved interference estimation used for cancellation at each stage. Therefore, it is expected that, among the receivers analysed, CMA-SIC provides highest spectral efficiency.
3.2.5 Performance Results and Comparisons
A model of K user synchronous uplink DS-CDMA system employing BPSK and short binary Gold sequences [89] of length N = 31 is used. The initial code acquisition for such sequences are investigated in [90] and can be used here without much difficulties. The channel is Rayleigh flat fading channel with Doppler shift of 185Hz. A fixed step size of µk= 0.0001, for all k is assumed
in the CMA algorithm. The selection of step size in CDMA is generally based on the spreading factor used, the dynamic range of the received signal and effects the convergence of the algorithm [91], [59].
The BER performance of the proposed receiver (CMA-SIC) is shown in Figure 3.3 and com- pared with conventional receiver (Matched Filter), CMA receiver without interference cancel- lation (CMA only) [59], conventional SIC (SIC), and SIC with sorting each cancellation (SIC- Sorting)[53]. The proposed CMA-SIC showed a superior BER performance reaching the single user bound with 10 users. This also explains the accuracy of the proposed CMA-SIC algorithm in detection and MAI cancellation of the desired user signals.
The significant result of CMA-SIC compared to other receivers, can be explained as follows. As the signal-to-noise ratio increases, MAI becomes dominant source affecting the error perfor- mance. The error is introduced whenever the magnitude of the decision variable zkbecomes such
that the polarity of transmitted user signals is reverted. Conventional SIC can not correct the magnitude of the signal zk and, hence, suffers from error propagation. The CMA-SIC considers the decision variable of previous symbol period to adapt weights to make the variable closer to +1, −1. It is intuitive that with high probability the magnitude of the adapted output signal will be closer to the correct polarity of the transmitted data than that without adapting, as done in con- ventional despreading. The CMA only receiver has this capability, but it suffers from the problem of locking interferer than to the desired user signal due to dissimilar power profiles of the users.
Figure 3.3: Performance of CMA-SIC in flat Rayleigh fading channel with K=10 and Gold sequences of N=31
The conventional SIC showed better performance than the Matched Filters and the CMA only receivers. The SIC-Sorting slightly outperformed SIC. It can also be seen that the CMA only receiver provides much improvement performance compared to Matched Filters. This clearly indicates the robustness of the CMA in suppressing the MAI even in fading channel.
The BER of CMA-SIC and conventional SIC are compared under higher loading of K = 20 users in Figure 3.4. The CMA-SIC retains near single user performance even with increase in number of users. The conventional SIC however is shown to perform far worse in this case and only slightly better than MF receivers. The reason for improved performance of CMA-SIC is due to both reliable interference estimation/cancellation and use of adaptive despreading. Figure 3.5 shows the performance of the proposed CMA-SIC in different system loading. The CMA-SIC does not exhibit error propagation when the number of users increase. It shows near single user performance even under heavily loaded system, while the error performances of SIC and SIC-
Figure 3.4: Performance of CMA-SIC in flat Rayleigh fading channel with K=20 and Gold sequences of N=31
Sorting and CMA only receivers start to degrade as the number of users increase above 15 users. SIC and SIC-Sorting showed good performance when system is lightly loaded, however, at high load their performance degraded approaching that of conventional Matched Filters. The CMA based receivers showed to offer comparatively better performance under such conditions.
In Figure 3.6, the output signal waveform of CMA-SIC and conventional SIC receiver are shown for K = 20 and under a) for Eb/N0= 20 and b) for 40 dB, respectively. For reference, the
output of users’ true fading channel output is also shown. It can be clearly seen from the figure that the CMA-SIC provides much accurate estimation of users’ channel magnitude and hence leading to improved BER and spectral efficiency. The magnitude of channel estimation error is evaluated in terms of mean square error (MSE), ε2 = En|α − z ˜α|o2. The CMA-SIC shows much improved MSE performance compared with conventional SIC as the Eb/N0 increases as can be seen in
Figure 3.7.
Figure 3.8 shows the performance of CMA-SIC in fading channels and nearfar ratio of 10 dB. Here, the step size µk= 0.00001, ∀k is assumed in the CMA algorithm. The desired user (weak-
est user) has unity power, while all other users have been assigned powers uniformly distributed between 0 and 10dB. It can be clearly seen from the figure that CMA-SIC is more robust compared to all other receivers. Performance of SIC and SIC-Sorting receivers degraded dramatically as the system load increased above 15 users. CMA only receiver performed worse than in equal power.
Figure 3.5: BER vs. number of users of CMA-SIC in flat Rayleigh fading channel with Eb/N0 = 20dB
and Gold sequences of N=31
Figure 3.6: Amplitudes estimates at the output of CMA-SIC in flat Rayleigh fading channel with K=20 and Gold sequences of N=31
Figure 3.7: MSE performance of amplitude estimation of CMA-SIC in flat Rayleigh fading channel with K=20 and Gold sequences of N=31
Figure 3.8: Performance of CMA-SIC in flat Rayleigh fading channel with nearfar ratio of 10 dB; Eb/N0
Figure 3.9: Performance of CMA-SIC in flat Rayleigh fading channel with near far ratio of 0-20 dB; K = 20, Eb/N0of the weakest user=20dB, and Gold sequences of N=31
users. The power of desired weak kthuser to unity is fixed and other users are let to transmit at higher power. The power of other users are uniformly distributed between 0 − λdB as shown in Figure 3.9. The step size chosen for the algorithm is made variable according to considered nearfar ratio of λ, which is given by µk = 0.0001/λ. It can be seen in Figure 3.9 that BER performance
of CMA-SIC does gracefully degrade with increase in nearfar conditions. However, its near single user performance is retained at the nearfar ratio of as high as 15dB.
In Figure 3.10 the BER performance of CMA-SIC is compared in an AWGN environment with nearfar conditions. The desired user (weakest user) has unity power, while all other users have been assigned powers uniformly distributed between 0 and 10dB. It clearly shows that CMA-SIC is more robust compared to all receivers in this condition.
The Figure 3.11 shows the normalized spectral efficiency performance of CMA-SIC in Rayleigh fading channels with K = 20 users using the expression in (3.25). The variances of noise and in- terference components are obtained using Monte Carlo Integration of output signals from different receivers (MF, SIC and CMA-SIC) using simulations. The capacity of a single user transmission under Rayleigh fading channel with AWGN is also shown for comparison. As expected, the CMA- SIC shows considerable improvement in the achieved spectral efficiency compared with MF and conventional SIC. The conventional SIC that obtains the amplitude estimates from the output of matched filters are shown to achieve only slightly higher spectral efficiency than MF due to esti- mation error and imperfect cancellation contributing to noise term within the expression in (3.24).
Figure 3.10: Performance of CMA-SIC in AWGN with a nearfar ratio of 10 dB; Eb/N0 of the weakest
user=6dB and Gold sequences of N=31
Figure 3.11: Spectral Efficiency of CMA-SIC in Rayleigh flat fading channel, K=20 and Gold sequences of N=31
The effect of different step-size µ = 0.00001 − 0.001 on the BER in Rayleigh flat fading channels is investigated in Figure 3.12. The system loading of K = 20 equal power Pk = 1, ∀k
users are used and operating of Eb/N0 = 20 and 30 dB are selected. It can be seen that the
performance of CMA-SIC is effected by the step-sizes used. Also noted that the µ = 0.0001 used in previous simulations is not the optimum step-size and there is still room for further performance improvement.
Figure 3.12: The effect of step-size on the performance of CMA-SIC in flat Rayleigh fading channel under different Eb/N0; K=20 and Gold sequences of N=31
As can be seen from the results, the blind adaptive approach for a SIC has shown to address the imperfect MAI estimation and cancellation very well. In the next Section, the idea is further refined and carefully applied to address the unreliable MAI estimation and nearfar problems that limit the performance of PIC receivers.