Space-Time autocoding

Prior treatments of space–time communications in Rayleigh flat fading generally 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 conditions under which channel codes span only one fading interval and yet are arbitrarily reliable. In short, space–time signals are their own channel codes. We call this phenomenon space–time autocoding, and the accompanying capacity the space–time autocapacity. Let an -transmitter-antenna, -receiver-antenna Rayleigh flat-fading channel be characterized by an matrix of independent propagation coefficients, distributed as zero-mean, unitvariance complex Gaussian random variables. This propagation matrix is unknown to the transmitter, it remains constant during a -symbol coherence interval, and there is a fixed total transmit power. Let the coherence interval and number of transmitter antennas be related as = for some constant . A matrix-valued signal, associated with bits of information for some rate is transmitted during the -symbol coherence interval. Then there is a positive space–time autocapacity such that for all , the block probability of error goes to zero as the pair ( ) such that = . The autocoding effect occurs whether or not the propagation matrix is known to the receiver, and = log(1 + ) in either case, independently of , where is the expected signal-to-noise ratio (SNR) at each receiver antenna. Lower bounds on the cutoff rate derived from random unitary space–time signals suggest that the autocoding effect manifests itself for relatively small values of and . For example, within a single coherence interval of duration = 16, for = 7 transmitter antennas and = 4 receiver antennas, and an 18-dB expected SNR, a total of 80 bits (corresponding to rate = 5) can theoretically be transmitted with a block probability of error less than 10 , all without any training or knowledge of the propagation matrix.