Abstract:
We recently showed 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. This effect, where
the space-time signals act as their own channel codes, is called
autocoding. 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=2^80) is
impossible to generate and store, and due to lack of structure there
is little hope of finding a fast decoding scheme. In this paper we propose a
random, but highly structured, constellation that is completely specified by
\log_2 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. As part of this work we have established a
subsidiary result that is interesting in its own right: the square
(or for that matter, any integer power greater than one) of an
isotropically random unitary matrix is not isotropically
random, with two exceptions: 1) a one-by-one complex unitary matrix, and
2) a two-by-two real orthogonal matrix.
Status:
Submitted to IEEE Trans. Info. Theory
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