The general simulation parameters are summarized in Table 3-2 and Table 3-3 according to 3GPP standard if they are not explicitly specified in the text. βc is chosen for the optimal
BER according to the simulation results. The average SNR denotes the average of energy per bit of each user divided by noise variance. The chip resolution in AWGN is chosen to be 1 chip since chip synchronous is assumed, while the general chip resolution in multipath fading environment is 0.25 chips where chip asynchronous is assumed.
3.6.1 Channel Estimation
Fig. 3-10 shows the analytical and simulated results of mean square error (MSE) with W=64 and W=128 over flat Rayleigh fading channels where Doppler shift fd =222Hz, corresponding to a vehicle speed of 120 km/hr. We can see that the analytical MSE provides good approximation to the simulated MSE. Besides, large βc results in better channel estimates since λ in (3-9) is alleviated in proportion to the reciprocal of βc.
3.6.2 Data Detection
AWGN Channel
In Fig. 3-11, we examine the influence of various grouping intervals and power distribution ratios in AWGN channel. The analytical results of G=1 and G=2400 are shown in dotted line where SIC I with G=2400 is used to approximate SIC II and SIC III with G=2400, and it shows good approximation to the simulated results. The BER difference of the three SICs is explicit when G is small and PDR is close to unity, and SIC II outperforms the other two SICs in this situation. As G or PDR increases, all SICs have almost the same performance. This is because that the difference in the cancellation order of the three SICs is less and less as PDR or G increases.
Fig. 3-12 (a) shows the individual BER of the u-th detected user with eight active users in the system. When G=1, we find that the late-detected users of SIC I outperform those of SIC II and SIC III. Nevertheless, the early-detected users of SIC II and SIC III perform much
better than those of SIC I, thus, SIC II and SIC III still outperform SIC I after averaging as shown in Fig. 3-12(b). Fig. 3-12(b) shows the average BER versus user number for the three SICs when G=1 and 2400. Only SIC I with G=2400 is presented since it is shown in Fig. 3-11 that the three SICs have almost the same BER. All users in SIC II in Fig. 3-12(a), except the last one, outperform those in SIC III, and thus the average BER of SIC II in Fig. 3-12(b) is lower than that of SIC III.
In Fig. 3-13, the BER with different PDRs and SNRs are examined when G=1 and G=2400. βc is chosen for optimal BER of the corresponding SNR. In this chapter, SIC without PCSR denotes that the pilot-channel signals are not removed first from the received signal, but they are removed accompanying with the data-channel signal of the corresponding user. Thus, SIC with PCSR outperforms SIC without PCSR only at the cost of demanding slightly more latency. As SNR increases, the benefit of SIC with PCSR becomes obvious, and all SICs with G=2400 outperform SIC II with G=1. For G=2400 as shown in Fig. 3-13(d), increasing SNR also results in the increasing in PDR for the optimum BER. The reason is that MAI dominates the BER at high SNR, and increasing PDR can alleviate MAI from early detected users.
In Fig. 3-14, we examine the influence of pilot-to-traffic amplitude ratio (βc).For the last two lines in Fig. 3-14 (a) and Fig. 3-14 (b), the PDRs are chosen for the minimum BER for the SIC with PCSR when G=2400, i.e. PDR=1.3 (K=8) and PDR=1.1 (K=16) for all SICs. In Fig. 3-10, it is shown that large βc brings better channel estimates. However, large βc also leads to poor data detection since the percentage of transmitted power for data signal decreases, and MAI from pilot signal increases. It is shown that SIC with PCSR can dramatically alleviate MAI from pilot signal, especially when βc increases. Also, SIC with PCSR is less sensitive to the variation of βc in both moderately loaded case in Fig. 3-14(a) and heavily loaded case in Fig. 3-14(b).
Multipath Fading Channels
Four cases of propagation conditions for multipath fading environments used in the following are presented in Table 3-3. It is assumed that all paths are tracked and combined in the RAKE, i.e., F=P.
In Fig. 3-15, we can find that three SICs in all considered channels perform much better than the RAKE receiver. The best BER occurs at PDR=1.3 for SIC I in all cases, while it occurs at PDR=1.0 for SIC II and SIC III in channel Case 1 and channel Case 2, and at PDR≠1.0 in channel Case 3 and channel Case 4. SIC II performs slightly better than SIC III when PDR is close to unity and G is small, and they both achieve better BER than SIC I. This is because SIC II and SIC III have the ability to track channel variation but SIC I does not.
In Fig. 3-16, the BER is investigated with channel estimation where W=128. The timing estimation errors are modeled as Gaussian distributed random variables with zero mean and variance 0.0625 (2 samples) at 1/32 chips resolution where 95% of the probability mass is concentrated within ±4 samples [59]. The simulated results are similar to those in Fig. 3-15 except that the best BER occurs at PDR=1.0 for SIC II and SIC III in all channel cases.
Fig. 3-17 indicates the BER of individual user in different cancellation order with the PDR for the optimum BER in each SIC in channel Case 3. For SIC I in Fig. 3-17(a), influences of G are obvious only when G is small. For SIC II in Fig. 3-17(b) and SIC III in Fig. 3-17(c), the early canceled users have smaller BER than that of the late canceled users for small G. As G>1000, their BER becomes worse than SIC I where the early canceled users have larger BER than that of the late canceled users. Also, SIC II slightly outperforms SIC III when G is small.
The BER versusβcover all channel cases are given in Fig. 3-18 where G and PDR are selected for the best BER, i.e., G=2400 in channel Case 1 and channel Case 2, G=32 in channel Case 3, and G=16 in channel Case 4 for all SICs. Similar to the results shown in Fig.
3-14 for AWGN channel, the PCSR helps to improve BER and increase βc for the optimum BER. Better timing synchronization can be achieved since pilot-channel signal power is increased. SIC II and SIC III still perform much better than SIC I. Moreover, SIC II and SIC III have similar performance.
In Fig. 3-19, the BER for various channel cases are examined. According to the results in Fig. 3-15, the PDRs for the minimum BER of each SIC are chosen. In channel Case 1 and channel Case 2, the one-frame long grouping interval, i.e., G=2400, results in the best BER for all SICs. However, in channel Case 3 and channel Case 4, the optimum BER for SIC II and SIC III occur at about G=100 and G=50, respectively. Among all channel cases, SIC II and SIC III outperform SIC I, and except in channel Case 3 and channel Case 4 when G is small than about 20 with channel estimation, these two SICs almost have the same BER. It is worthy to note that SIC II and SIC III with properly chosen G as PDR=1 are suitable for fast fading channels such as channel Case 4.
3.6.3 Discussion
From the above simulations and analyses, we find that:
The SIC with PCSR can achieve better BER than that without PCSR when βc is large in both AWGN and selective fading channels. The optimal βc for SIC with PCSR is larger than that without PCSR. Larger βc implies less timing estimation error which is critical in most communication systems.
The benefit of detecting and canceling a group of G-bit in AWGN channel becomes obvious when noise and MAI decrease. The reason has been mentioned in 3.4. The relationship between fd and the optimal G of SIC III-like SIC in multirate systems in multipath fading channels is examined in the later section [70] where the optimal G is shown inversely proportional to fd in fading environment. In addition, larger G results in better BER
in SIC I in all fading channel casessince the detection order is not affected by G.
There is also tradeoff between decreasing MAI and propagation error to later detected users (increasing PDR) and increasing SNR of the later detected users (decreasing PDR).
When the noise (including estimation errors) and MAI increase, the PDR for the optimum BER in AWGN channel becomes closer to one, and the reason has been explained in Fig.
3-13. For SIC I over fading channels, it is shown that the optimum BER always occurs at PDR≠1. And as for SIC II and SIC III, whether the PDR of optimum BER is equal to unity depends on the channel condition.
The BER of SIC I is inferior to the other two SICs when G is small. For SIC II and SIC III, they perform almost the same in both AWGN channel and fading channel when G or PDR is larger than one. Since in these cases, SIC II and SIC III has similar detection. In the view of BER, SIC II would be a good choice when it is applied to a heavily loaded system over AWGN channel with G=1 or when G for the optimum BER is smaller than 16over multipath fading channels. (With the simulation parameters used in chapter, G=16 when the vehicle speed is at about 250km/hr.)