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 cut-off 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 matices. For low SNR the dissimilarity function reduces to a trace norm of differences between outerproducts of pairs of codewords. We characterize the cut-off rate 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.