18 *4.1.1. Linear equalization and FIR beamforming filters*

19 The use of multiple antennas in wireless communication system attracts significant interest 20 and attention of researchers. Transmit beamforming has received considerable attention 21 because of its simplicity and ability to exploit the benefits of multiple transmit antenna [62]. 22 Information about channel state at the transmitter is generally required for beamforming. At 23 the present time, an impact of noisy and/or quantized information about channel state is a 24 pivot of recent research owing to the fact that the perfect channel state information may not 25 be available at the transmitter [63–65]. In [66], beamforming techniques for DS-CDMA 26 wireless communication systems used a multicarrier approach to cope with frequency-27 selective fading were also proposed. We should note, however, that the multicarrier 28 techniques are not used in single carrier systems. In this section, we investigate the transmit 29 beamforming for single carrier transmission over frequency-selective fading channels with 30 the perfect channel state information at the GR. A necessity of equalization at the GR is 31 generated by the intersymbol interference (ISI) caused by the channel frequency selectivity. 32 It must be emphasized that the optimum beamforming depends on the equalizer used. As it 33 is well-known, the linear equalization possesses a low complexity. By this reason, we adopt 34 the linear equalization. In comparison and in contrast to [67], we consider the more realistic 35 case of FIR beamforming filters at the GR. Unlike the infinite impulse response case, a 36 closed-form solution for the FIR beamforming filters at the GR does not seem to exist. 37 Because of this, we need to calculate the optimum FIR beamforming filters. Numerical

38 BookTitle

1 results show that for typical Global System for Mobile Communications/Enhanced Data 2 Rates for GSM Evolution (GSM/EDGE) channels the performance of short GR FIR 3 beamforming filters can be closely approached with infinite impulse response beamforming 4 at the GR and significant gains over single antenna transmission can be achieved.
