Limited feedback precoding for orthogonal space-time block codes

Orthogonal space-time block codes (OSTBCs) are an efficient solution for obtaining full diversity order in Rayleigh fading channels. Unfortunately, OSTBCs exist for only certain numbers of transmit antennas and do not provide array gain as diversity techniques that exploit transmit channel information do. When channel state information is available at the transmitter, linearly precoded space-time codes can he used to support different numbers of transmit antennas and to improve array gain. Precoding generally requires complete channel knowledge, thus motivating limited feedback methods such as channel quantization or antenna subset selection. The paper investigates limited feedback precoding that uses a codebook of matrices known a priori to both the transmitter and receiver. Using the codebook, the receiver chooses a matrix based on current channel conditions and conveys the optimal codebook matrix to the transmitter over an error-free, zero-delay feedback channel A precoder matrix selection criterion is proposed that relates directly to minimizing the probability of symbol error of the precoded system. Low average distortion codebooks based on Grassmannian subspace packing are derived for the optimal codeword selection criterion. It is shown that codebooks designed by this method provide full diversity order in Rayleigh fading channels.