Space-time autocoding

Prior treatments of space-time communications in Rayleigh flat fading gener ally assume that channel coding covers either one fading interval-in which case there is a nonzero "outage capacity" -or multiple fading intervals in which case there is a nonzero Shannon capacity. However, we establish condi tions under which channel codes span only one fading interval and yet are a rbitrarily reliable. In short, space-time signals are their own channel cod es. We call this phenomenon space-time autocoding, and the accompanying cap acity the space-time autocapacity. Let an M-transmitter-antenna, N-receiver-antenna Rayleigh fiat-fading chann el be characterized by an M x N matrix of independent propagation coefficie nts, distributed as zero-mean, unit-variance complex Gaussian random variab les. This propagation matrix is unknown to the transmitter, it remains cons tant during a T-symbol coherence interval, and there is a fixed total trans mit power. Let the coherence interval and number of transmitter antennas be related as T = betaM for some constant beta .A T x M matrix-valued signal, associated with R (.) T bits of information for some rate R is transmitted during the T-symbol coherence interval. Then there is a positive space-tim e autocapacity Ca such that for all R < C-a, the block probability of error goes to zero as the pair (T, M) --> infinity such that T/M = beta. The aut ocoding effect occurs whether or not the propagation matrix is known to the receiver, and C-a = N log(1 + rho) in either case, independently of beta, where p is the expected signal-to-noise ratio (SNR) at each receiver antenn a. Lower bounds on the cutoff rate derived from random unitary space-time s ignals suggest that the autocoding effect manifests itself for relatively s mall values of T and M. For example, within a single coherence interval of duration T = 16, for M = 7 transmitter antennas and N = 4 receiver antennas , and an 18-dB expected SNR, a total of 80 bits (corresponding to rate R = 5) can theoretically be transmitted with a block probability of error less than 10(-9), all without any training or knowledge of the propagation matri x.