4 **4.7. Conclusions**

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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 21 in the case of spatially independent MIMO channel.
