Multiple-input multiple-output (MIMO) wireless systems can achieve significant diversity and array gain by using transmit beamforming and receive combining. In the absence of full channel knowledge at the transmitter, a quantized beamforming vector can be made available to the transmitter using a low-rate feedback channel, called limited feedback. A codebook based quantization approach is considered. Based on metrics such as signal-to-noise ratio and outage probability, maximization of the minimum distance between any pair of codewords has already been proposed as a codebook design criterion. An upper bound on the average SNR achieved by an optimal codebook designed using such criterion is derived as a function of the feedback rate. A lower bound on outage probability is also obtained. This analysis quantifies the impact of the feedback rate and the number of transmit and receive antennas on the performance of the system.
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