Cut-off Rate and Signal Design for the Rayleigh Fading Space-time Channel

We consider the single-user computational cut-off rate for the complex Rayleigh flat fading spatio-temporal channel under a peak power constraint. Determination of the cutoff rate requires maximization of an average error exponent over all possible space-time codeword probability distributions. This error exponent is monotone decreasing in a measure of dissimilarity between pairs of codeword matrices. For low SNR the dissimilarity function reduces to a trace norm of differences between outerproducts of pairs of codewords. We characterize the cut-offrate and the rate achieving constellation under different operating regimes depending on the number of transmit and receive antennas, the number of codewords in the constellation, and the received SNR.