An upper bound on SNR for limited feedback MIMO beamforming systems

Muitiple-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 a criterion is derived as a function of the feedback rate. This analysis quantifies the impact of the feedback rate and the number of transmit and receive antennas on the performance of the system.