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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• "For the noncoherent MIMO channel at low SNR, the cutoff rate expression is easily shown to be (c.f. [21]) "
##### Article: Optimal Constellations for the Low-SNR Noncoherent MIMO Block Rayleigh-Fading Channel
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ABSTRACT: Reliable communication over the discrete-input/continuous-output noncoherent multiple-input multiple-output (MIMO) Rayleigh block-fading channel is considered when the signal-to-noise ratio (SNR) per degree of freedom is low. Two key problems are posed and solved to obtain the optimum discrete input. In both problems, the average and peak power per space-time slot of the input constellation are constrained. In the first one, the peak power to average power ratio (PPAPR) of the input constellation is held fixed, while in the second problem, the peak power is fixed independently of the average power. In the first PPAPR-constrained problem, the mutual information, which grows as O (SNR<sup>2</sup>), is maximized up to second order in SNR. In the second peak-constrained problem, where the mutual information behaves as O (SNR), the structure of constellations that are optimal up to first order, or equivalently, that minimize energy per bit, are explicitly characterized. Furthermore, among constellations that are first-order optimal, those that maximize the mutual information up to second order, or equivalently, the wideband slope, are characterized. In both PPAPR-constrained and peak-constrained problems, the optimal constellations are obtained in closed form as solutions to nonconvex optimizations, and interestingly, they are found to be identical. Due to its special structure, the common solution is referred to as space-time orthogonal rank one modulation, or STORM. In both problems, it is seen that STORM provides a sharp characterization of the behavior of noncoherent MIMO capacity.
IEEE Transactions on Information Theory 03/2009; 55(2-55):776 - 796. DOI:10.1109/TIT.2008.2009602 · 2.33 Impact Factor
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• "The next proposition is an extension of a result for the i.i.d. channel by Hero and Marzetta in [15] to the correlated channel. "
##### Article: Optimal Spatial Correlations for the Noncoherent MIMO Rayleigh Fading Channel
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ABSTRACT: The behavior in terms of information theoretic metrics of the discrete-input, continuous-output noncoherent MIMO Rayleigh fading channel is studied as a function of spatial correlations. In the low SNR regime, the mutual information metric is considered, while at higher SNR regimes the cutoff rate expression is employed. For any fixed input constellation and at sufficiently low SNR, a fully correlated channel matrix is shown to maximize the mutual information. In contrast, at high SNR, a fully uncorrelated channel matrix (with independent identically distributed elements) is shown to be optimal, under a condition on the constellation which ensures full diversity. In the special case of the separable correlation model, it is shown that as a function of the receive correlation eigenvalues, the cutoff rate expression is a Schur-convex function at low SNR and a Schur-concave function at high SNR, and as a function of transmit correlation eigenvalues, the cutoff rate expression is Schur-concave at high SNR for full diversity constellations. Moreover, at sufficiently low SNR, the fully correlated transmit correlation matrix is optimal. Finally, for the general model, it is shown that the optimal correlation matrices at a general SNR can be obtained using a difference of convex programming formulation.
IEEE Transactions on Wireless Communications 11/2007; 6(10-6):3760 - 3769. DOI:10.1109/TWC.2007.060125 · 2.50 Impact Factor
• ##### Conference Paper: Capacity of flat-fading channels associated with a subspace-invariant detector
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