Space-time autocoding

Abstract

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 M-transmitter antenna, N-receiver antenna Rayleigh flat fading channel be characterized by an M/spl times/N matrix of independent propagation coefficients, distributed as zero-mean, unit-variance complex Gaussian random variables. This propagation matrix is unknown to the transmitter, it remains constant during a T-symbol coherence interval, and there is a fixed total transmit power. Let the coherence interval and number of transmitter antennas be related as T=/spl beta/M for some constant /spl beta/. A T/spl times/M matrix-valued signal, associated with R/spl middot/T bits of information for some rate R is transmitted during the T-symbol coherence interval. Then there is a positive space-time autocapacity C/sub a/ such that for all R<C/sub a/, the block probability of error goes to zero as the pair (T, M)/spl rarr//spl infin/ such that T/M=/spl beta/. The autocoding effect occurs whether or not the propagation matrix is known to the receiver, and C/sub a/=Nlog(1+/spl rho/) in either case, independently of /spl beta/, where /spl rho/ 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 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/sup -9/, all without any training or knowledge of the propagation matrix.