14 *3.5.2. Synchronous DS-CDMA wireless communication system*

15 To demonstrate a usefulness of the optimal PCF range given by (108), we performed a 16 number of simulations for asynchronous DS-CDMA wireless communication system with 17 perfect power control. In simulations, the random spreading codes with length *N* 64 18 were used for each user and the number of users was *K* 40 [61]. Figure 6 shows the BER 19 performance of single-stage hard-decision GR based on PPIC for different magnitudes of 20 SNR and various values of PCF where the optimal PCF for the first stage lies between 0.3169 21 (lower boundary) and 0.7998 (upper boundary). It can be seen that, for all the SNR cases, the 22 GR based on PPIC using the average of the lower and upper boundary values, i.e., 0.5584, as 23 the PCF, has the close BER performance to that using the optimal PCF. Additionally, 34 BookTitle

3

1 comparison of GR implementation in DS-CDMA systems with the conventional detector 2 discussed in [43] is presented.

4 **Figure 5.** Comparison of the average BER of coherent BPSK and 8-PAM for GR with quadrature 5 subbranch HS/MRC and HS/MRC schemes versus the average SNR per symbol per diversity for various 6 values of 2*L* with *N* 8 .

7 These results demonstrate us a great superiority of the GR employment over the 8 conventional detector in [43].

9 Figure 7 shows the BER performance at each stage for the three-stage GR based on the PPIC 10 using different PCFs at the first stage, i.e., the average value and an arbitrary value. PCFs for 11 these two three-stage cases are

$$(a\_1, a\_2, a\_3) = (0.\\$584, 0.8, 0.9) \quad \text{and} \quad (0.7, 0.8, 0.9) \tag{137}$$

13 respectively. The results demonstrate that the BER performances of GR employed by DS-14 CDMA systems for the cases using the proposed PCF at the first stage outperform ones of 15 GR implemented in DS-CDMA system using arbitrary PCF at the first stage. Furthermore, 16 the GR BER performance at the second stage for the case using the proposed PCF at the first 17 stage achieves the GR BER performance of the GR comparable to that of the three-stage GR 18 based on PPIC using an arbitrary PCF at the first stage. Comparison between the AWCN 19 and multipath channels is also presented in Fig.7. We see that in the case of multipath 20 channel, the BER performance is deteriorated. This fact can be explained by the additional 21 correlation terms in (133)–(136).

Signal Processing by Generalized Receiver in DS-CDMA Wireless Communications Systems 35 Signal Processing by Generalized Receiver in DS-CDMA Wireless Communications Systems http://dx.doi.org/10.5772/58990 113

34 BookTitle

3

6 values of 2*L* with *N* 8 .

8 conventional detector in [43].

11 these two three-stage cases are

21 correlation terms in (133)–(136).

2 discussed in [43] is presented.

112 Contemporary Issues in Wireless Communications

1 comparison of GR implementation in DS-CDMA systems with the conventional detector

4 **Figure 5.** Comparison of the average BER of coherent BPSK and 8-PAM for GR with quadrature 5 subbranch HS/MRC and HS/MRC schemes versus the average SNR per symbol per diversity for various

7 These results demonstrate us a great superiority of the GR employment over the

9 Figure 7 shows the BER performance at each stage for the three-stage GR based on the PPIC 10 using different PCFs at the first stage, i.e., the average value and an arbitrary value. PCFs for

( , , ) (0.5584,0.8,0.9) and (0.7,0.8,0.9) 12 *a*<sup>1</sup> *a*<sup>2</sup> *a*<sup>3</sup> (137)

13 respectively. The results demonstrate that the BER performances of GR employed by DS-14 CDMA systems for the cases using the proposed PCF at the first stage outperform ones of 15 GR implemented in DS-CDMA system using arbitrary PCF at the first stage. Furthermore, 16 the GR BER performance at the second stage for the case using the proposed PCF at the first 17 stage achieves the GR BER performance of the GR comparable to that of the three-stage GR 18 based on PPIC using an arbitrary PCF at the first stage. Comparison between the AWCN 19 and multipath channels is also presented in Fig.7. We see that in the case of multipath 20 channel, the BER performance is deteriorated. This fact can be explained by the additional

2 **Figure 6.** The BER performance of the single-state GR based on PPIC with hard decisions for different 3 SNRs and PCFs.

1

4

5 **Figure 7.** The BER performance at each stage for three-stage GR based on the PPIC with hard decisions 6 for different PCFs at the first stage, i.e., the average value and an arbitrary value: AWGN and multipath 7 channels.

36 BookTitle

1 Figure 8 demonstrates the optimal PCF versus the number of users both for the synchronous 2 AWGN and for the multipath channels. We carry out simulation for the AWGN channel 3 under the following conditions: the Gold codes, *SNR*=12 dB, the spreading codes are the 4 periodic and perfect power control. The multipath channel assumed is a two-ray channel 5 with the transfer function

$$W\_k(Z) = 0.762 + 0.648Z^{-2} \tag{138}$$

7 for all users. In the case of multipath channel, we employ aperiodic codes, *SNR* =12 dB, and 8 perfect power control.

10 **Figure 8.** Optimal PCF versus the number of users: the AWGN and multipath channels.

#### 11 **3.6. Conclusions**

9

12 The GR performance with quadrature subbranch HS/MRC and HS/MRC schemes for a 1-D 13 signal modulation in Rayleigh fading was investigated. The SER of *M*-ary PAM, including 14 coherent BPSK modulation, was derived. Results show the GR with quadrature subbranch 15 HS/MRC and HS/MRC schemes performs substantially better the GR with traditional 16 HS/MRC scheme, particularly, when *L* is smaller than one half *N*, and much better the 17 traditional HS/MRC receiver. We have also derived the optimal PCF range for GR first stage 18 based on the PPIC, which is employed by DS-CDMA system, with hard decisions in 19 multipath fading channel. Computer simulation shows that the BER performance of the GR 20 employed by DS-CDMA wireless communication system with multipath fading channel in 21 the case of periodic code scenario and using the average of the lower and upper boundary 22 values is close to that of the GR of the case using the real optimal PCF, whether the SNR is 23 high or low. It has also been shown that GR employment in DS-CDMA system with 24 multipath fading channel in the case of periodic code scenario allows us to observe a great

1 superiority over the conventional receiver discussed in [43]. The procedure discussed in [43] 2 is also acceptable for GR employment by DS-CDMA systems. It has also been demonstrated 3 that the two-stage GR based on PPIC using the proposed PCF at the first stage achieves such 4 BER performance comparable to that of the three-stage GR based on PPIC using an arbitrary 5 PCF at the first stage. This means that at the same BER performance, the number of stages 6 (or complexity) required for the multistage GR based on PPIC could be reduced when the 7 proposed PCF is used at the first stage. It can be shown that the proposed PCF selection 8 approach is applicable to multipath fading cases at GR employment in DS-CDMA systems 9 even if no perfect power control is assumed but this is a subject of future work. We have 10 also compared the BER performance at the optimal PCF in the case of AWGN and multipath 11 channels and presented a sensitivity of the BER performance to the values of PCF for both 12 cases.
