Beamforming codebook design for temporally correlated fading channels

In this paper, we consider the problem of transmit beamforming codebook design for temporally correlated fading channels based on limited feedback from the receiver to the transmitter. We propose a low-complexity algorithm to design the beamforming codebook of time n + 1 by rotating a root codebook by a unitary matrix that is determined by the selected beamforming codeword at time n. We investigate the design of root codebook according to different optimization criteria, aiming to either maximize the average received signal-to-noise ratio (SNR), maximize the capacity, or to minimize the bit-error-rate (BER). Performance evaluations for uncoded systems reveal that the SNR based design does not perform as well as the codebook designed for the identical and independently distributed (i.i.d.) channel (i.e. a high SNR problem). We show that the BER based design alleviates the high SNR problem effectively and leads to good performance in both coded and uncoded systems. Compared to systems that do not take channel temporal correlation into account, the proposed design achieves about 2 dB performance gain at a low feedback rate of only 3 bits per channel use.