Space - Time Autocoding : Arbitrarily Reliable Communication in a Single Fading Interval

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 autocapacLet an M-transmitter-antenna, N-receiver-antenna Rayleigh flat fading channel be characterized by an M x N matrix of independent propagation coefficients, distributed as zero-mean, unit-variance complex Gaussian random variables. This propagation matrix is unknown to the transmitter, remains constant during a T-symbol coherence interval, and there is a Axed total transmit power. Let the coherence interval and number of transmitter antennas be related as T = PM for some p. 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-time autocapacity C, such that for all R < C,, the block proba6ility of error goes to zero as the pair ( T , M ) -+ 00 such that TIM = p. The autocoding effect occurs whether or not the propagation matrix is known to the receiver, and C, = Nlog(1 + p ) in either case independently of p, where p is the expected 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 lo-’, all without any training or knowledge of the propagation matrix. A complete copy of this paper is available on the web at http://mars.bell-labs.com. ity.