Cutoff rate and signal design for the quasi-static Rayleigh-fadingspace-time channel
Hero, A.O., III.; Marzetta, T.L.
Information Theory, IEEE Transactions on
Volume 47, Issue 6, Sep 2001 Page(s):2400 - 2416
Digital Object Identifier 10.1109/18.945254
Summary:We consider the computational cutoff rate and its implications on
signal design for the complex quasi-static Rayleigh flat-fading
spatio-temporal channel under a peak-power constraint where neither
transmitter nor receiver know the channel matrix. The cutoff rate has an
integral representation which is an increasing function of the distance
between pairs of complex signal matrices. When the analysis is
restricted to finite-dimensional sets of signals, interesting
characterizations of the optimal rate-achieving signal constellation can
be obtained. For an arbitrary finite dimension, the rate-optimal
constellation must admit an equalizer distribution, i.e., a positive set
of signal probabilities which equalizes the average distance between
signal matrices in the constellation. When the number N of receive
antennas is large, the distance-optimal constellation is nearly
rate-optimal. When the number of matrices in the constellation is less
than the ratio of the number of time samples to the number of transmit
antennas, the rate-optimal cutoff rate attaining constellation is a set
of equiprobable mutually orthogonal unitary matrices. When the
signal-to-noise ratio (SNR) is below a specified threshold, the matrices
in the constellation are rank one and the cutoff rate is achieved by
applying all transmit power to a single antenna and using orthogonal
signaling. Finally, we derive recursive necessary conditions and
sufficient conditions for a constellation to lie in the feasible set
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