Achievable rates for MIMO fading channels with limited feedback

Channel information at the transmitter can simplify the coding scheme and increase the achievable data rate over a multiple-input multiple-output (MIMO) fading channel. Feedback from the receiver can be used to specify a precoding matrix, which selectively activates the strongest channel modes. We evaluate the sum data rate per receive antenna when the precoding matrix is quantized with a random vector quantization (RVQ) scheme, assuming a matched filter, or linear minimum mean squared error (MMSE) receiver. Our results are asymptotic as the number of transmit and receive antennas increases with fixed ratio, for a fixed number of feedback bits per dimension. Numerical results show that given a target spectral efficiency, the amount of feedback required by the linear MMSE receiver is only slightly more than that required by the optimal receiver, whereas the matched filter can require significantly more feedback. We also compare these results with a simpler reduced-rank scheme for quantizing the precoding matrix.