Cutoff rate and signal design for the quasi-static Rayleigh-fading space-time channel

We consider the computational cutoff rate and its implications on signal de sign for the complex quasi-static Rayleigh flat-fading spatio-temporal chan nel under a peak-power constraint where neither transmitter nor receiver kn ow the channel matrix. The cutoff rate has an integral representation which is an increasing function of the distance between pairs of complex signal matrices. When the analysis is restricted to finite-dimensional. sets of si gnals, interesting characterizations of the optimal rate-achieving signal c onstellation can be obtained. For an arbitrary finite dimension, the rate-o ptimal constellation must admit an equalizer distribution, i.e., a positive set of signal probabilities which equalizes the average distance between s ignal matrices in the constellation. When the number N of receive antennas is large, the distance-optimal constellation is nearly rate-optimal. When t he number of matrices in the constellation is less than the ratio of the nu mber of time samples to the number of transmit antennas, the rate-optimal c utoff rate attaining constellation is a set of equiprobable mutually orthog onal unitary matrices. When the signal-to-noise ratio (SNR) is below a spec ified threshold, the matrices in the constellation are rank one and the cut off rate is achieved by applying all transmit power to a single antenna and using orthogonal signaling. Finally, we derive recursive necessary conditi ons and sufficient conditions for a constellation to lie in the feasible se t.