2 **5.1. Brief review**

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130 Contemporary Issues in Wireless Communications

1

4 **4.7. Conclusions**

3 b) receiver spatially correlated MIMO channel.

21 in the case of spatially independent MIMO channel.

2 **Figure 10.** *BER* performance of different detectors under a) spatially independent MIMO channel and

5 In the present section, we have considered the FIR beamforming at the GR with perfect 6 channel state information for single carrier transmission over frequency-selective fading 7 channels with zero-forcing linear equalization and GR MMSE linear equalization. We 8 employed a gradient algorithm for efficient recursive calculation of the FIR beamforming 9 filters at the GR. Our results show that for typical GSM/EDGE channel profiles short FIR 10 beamforming filters at the GR suffice to closely approach the performance of optimum 11 infinite impulse response beamforming at the GR discussed in [52]. This is a significant 12 result, since in practice, the quantized beamforming filter coefficients have to be fed back 13 from the receiver to the transmitter, which makes short beamforming filters preferable.

14 The proposed MMSE GR outperforms all the existing schemes with considerable gain 15 especially for receiver correlation MIMO channel scenario. The underlying reason of this 16 improvement is that the MMSE GR, by taking channel estimation error, decision error 17 propagation, and channel correlation into account, can output more reliable LLR to channel 18 decoder. As channel estimation error is the dominant factor influencing the system 19 performance under the lower *SNR* region, it can observed that the *BER* of the conventional 20 soft-output MMSE GR [87] is slightly better than that of the modified soft-output MMSE GR

3 It is well known that the DS-CDMA transmission technique allows multiple users to share 4 the same spectrum range simultaneously. Using DS-CDMA transmission technique in 5 wireless communication systems, we can reach spectrum efficiency, high system capacity, 6 robustness against interference, high quality of service (QoS) and so on [88,89]. In DS-7 CDMA wireless communication systems, the concatenating orthogonal Walsh-Hadamard 8 (WH) channelization sequences and pseudonoise (PN) random scrambling sequences are 9 used to generate the orthogonal spreading codes employed by multiple users for 10 simultaneous signal transmission. There are multipaths in DS-CDMA wireless 11 communication systems that destroy orthogonality between codes by introducing non-zero 12 time delays and lead to interference among the transmitted signals in the downlink. One 13 way to solve this problem is to use the scrambling sequences with the purpose to randomize 14 signals transmitted by users and inhomogeneous behavior at nonzero time delays. One 15 technique demonstrating how this problem can be solved is discussed in [90].

16 At the present time, the wideband DS-CDMA technique employed by wireless 17 communication systems attracts a great attention of researchers, in particular, in mobile 18 communication systems. An important feature of wideband DS-CDMA is an 19 implementation of complex spreading sequences. The term "complex spreading" was 20 generated from terminology used in constant to dual-channel spreading [91]. It is shown in 21 [92-94] that the complex spreading can be realized either by a complex-valued sequence or 22 by two binary sequences. As was shown in [92], the complex sequences can be 3 dB better 23 than the binary Gold sequences [95] in the maximum periodic correlation parameters. 24 Moreover, larger sets are available in complex sequences. Unfortunately, all these sequences 25 are nonorthogonal and can be characterized as the complex-valued PN spreading 26 sequences. Lam and Ozluturk investigated in [95] an application area of nonorthogonal 27 complex sequences in DS-CDMA downlink wireless communication systems. As was 28 defined in [95], the performance bounds were derived for the DS-CDMA wireless 29 communication systems with complex signature sequences over the AWGN channels.

30 In this section, we investigate a generalized receiver (GR) constructed on the basis of GASP 31 [1-3,6-8]. Using the GR in the DS-CDMA downlink wireless communication system, we 32 would like to get answers on the following questions:


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1 What are benefits under GR implementation in DS-CDMA downlink wireless 2 communication system in comparison with other conventional receivers, for example, 3 the Rake receiver?

4 To give answers on these questions we carry out our analysis using, for instance, the 5 orthogonal 4-phase complex sequences in the DS-CDMA downlink wireless communication 6 system. These sequences are generated by the unified complex Hadamard transform matrix 7 discussed in [96], the correlation properties of which are studied in [97], where it is shown 8 that the unified complex Hadamard transform sequences possess the better autocorrelation 9 properties in comparison with the WH sequences, which are characterrized by very poor 10 autocorrelation properties.

11 The use of orthogonal unified complex Hadamard transform sequences by the transmitter as 12 channelization spreading codes scrambled by long PN sequences and further processing 13 these sequences by the GR allows us to maintain the orthogonality between the users, and at 14 the same time, to reduce the effect of multipath fading and interference from other users. A 15 coherent GR [6], for example, can be used to combat the adverse effects of short-term 16 multipath fading in mobile radio propagation environments. Owing to computational 17 simplicity of the signal-to-interference-plus-noise ratio (SINR) in comparison with the 18 probability of error, SINR is mostly used for evaluating and selecting code sequences among 19 several candidates. Therefore, in this section, we investigate the SINR at the GR output 20 when the unified complex Hadamard transform spreading sequences are generated by 21 transmitter in the DS-CDMA downlink wireless communication system and compare this 22 with the SINR at the GR output under transmission of WH real sequences. It is shown that 23 the SINR at the GR output is independent of the phase offsets between different paths when 24 the unified complex Hadamard transform spreading sequences are generated by the 25 transmitter in the DS-CDMA downlink wireless communication system. The SINR at the GR 26 output of the same system is a function of the squared cosine of path phase offsets under 27 generation of WH real sequences by the transmitter. Because of this, as a direct result, the bit 28 error rate (BER) performance of GR employing by the DS-CDMA downlink wireless 29 communication system when the unified complex Hadamard transform spreading 30 sequences are generated by the transmitter is better that that of the system with the WH 31 sequences under Gaussian approximation. Also, we carry out a BER performance 32 comparison of the DS-CDMA system employing the GR with the same system using then 33 conventional receiver, for example, the Rake receiver [95]. Comparative analysis shows us a 34 great superiority in the BER performance under GR employment in the DS-CDMA 35 downlink wireless communication system over the use of the Rake receiver.

36 This section is organized as follows. At first, we present some basic definitions of the unified 37 complex Hadamard transform sequences. Additionally, we study the DS-CDMA downlink 38 wireless communication system model under the GR employment when the unified 39 complex Hadamard transform spreading sequences are generated and propagated in a 40 multipath fading channel. Further, we investigate the SINR performance at the GR output 1 when the unified complex Hadamard transform spreading sequences are generated and 2 compare this with the SINR of the same system using the WH sequences. Computer 3 simulation and comparison with the Rake receiver are also presented. Some concluding 4 remarks are given.
