Space-time autocoding constellations with pairwise-independent signals

Abstract

The space-time autocoding effect implies that arbitrarily reliable communication is possible within a single coherence interval in Rayleigh flat fading as the symbol-duration of the coherence interval and the number of transmit antennas grow simultaneously. For relatively short (e.g., 16-symbol) coherence intervals, a codebook of isotropically random unitary space-time signals theoretically supports transmission rates that are a significant fraction of autocapacity with an extremely low probability of error. However a constellation of the required size (typically L = 280) is impossible to generate and store, and due to lack of structure there is little hope of finding a fast decoding scheme. We propose a random, but highly structured, constellation that is completely specified by log, L independent isotropically distributed unitary matrices. The distinguishing property of this construction is that any two signals in the constellation are pairwise statistically independent and isotropically distributed. Thus, the pairwise probability of error, and hence the union bound on the block probability of error, of the structured constellation is identical to that of a fully random constellation of independent signals.

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