Conference Paper

Cut-off rate and signal design for the Rayleigh fading space-timechannel

Dept. of Electr. Eng. & Comput. Sci., Michigan Univ., Ann Arbor, MI;
DOI: 10.1109/SAM.2000.877991 Conference: Sensor Array and Multichannel Signal Processing Workshop. 2000. Proceedings of the 2000 IEEE
Source: IEEE Xplore

ABSTRACT We consider the single-user computational cut-off-rate for the complex Rayleigh flat fading spatio-temporal channel under a peak power constraint. Determination of the cut-off rate requires maximization of an average error exponent over all possible space-time codeword probability distributions. This error exponent is monotone decreasing in a measure of dissimilarity between pairs of codeword matrices. For low SNR the dissimilarity function reduces to a trace norm of differences between outer products of pairs of codewords. We characterize the cut-off rate and the rate achieving constellation under different operating regimes depending on the number of transmit and receive antennas, the number of codewords in the constellation, and the received SNR

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    ABSTRACT: Constellation design for the noncoherent multiple-input-multiple-output (MIMO) block Rayleigh-fading channel is considered. For general signal-to-noise ratios (SNRs), starting from a given base unitary constellation of finite cardinality, and using the cutoff rate expression as the design criterion, input probabilities and per-antenna amplitudes for the constellation points are obtained via a difference of convex programming formulation. Using the mutual information as a performance metric, it is shown that the optimized constellations significantly outperform the base unitary designs from which they are obtained in the low-medium SNR regime, and indeed they also similarly outperform the mutual information achieved by isotropically distributed unitary inputs for the continuous input channel [i.e., the so-called unitary space-time capacity (USTC)]. At sufficiently high SNRs, the resulting mutual information coincides with that of the base unitary designs. Thus the optimum constellation design technique works over the entire range of SNRs. The bit energy/spectral efficiency tradeoff of the optimized constellations are also obtained, and these provide valuable insights on modulation and coding, which are especially useful for wideband channels where the SNR per degree of freedom is low
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