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Random coding exponents for unitary space-time modulation

We consider a single-user block-fading multiple antenna link with M transmit and N receive antennas described by a propagation matrix that is constant during coherence intervals of length T symbols, after which it jumps to a new independent value for T more symbols, and so on. We assume throughout the paper that the random propagation matrix is unknown to both the transmitter and the receiver. Computing the capacity of the above channel is still an open problem. Hassibi and Marzetta (see IEEE Trans. Info. Theory) took an important step towards this by obtaining in close-form the probability density of the received signal when transmitting isotropically-random unitary matrices. The technique used for doing this which involves taking expectations with respect to the isotropically random unitary matrix - has other interesting ramifications. In this paper we make use of this technique to obtain a variety of new bounds on the random coding exponent, which provide improved estimates, compared with the simple union bound, of the autocoding performance of codebooks of isotropically random unitary signals.