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

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**ABSTRACT:**Space-time codes for multiple-input, multiple-output (MIMO) channels have received considerable attention due to the extraordinary spectral efficiencies offered by some space-time channels. In particular, the flat-fading channel, with identical, independently distributed gains between all transmitter and receiver pairs has been one of the space-time channels studied extensively. Most of these studies have focused on the capacity of the additive white Gaussian noise MIMO channel. When the noise-background has an unknown spatial covariance due, for example, interference, receivers that adapt to the noise background can be more robust. One way of achieving robustness involves building invariances into the receiver and channel coding. We consider receivers that are invariant both to the background covariance and to the MIMO channel transfer function. For the particular case of the flat-fading, additive white Gaussian noise channel, the MIMO capacity of the invariant receiver is calculated and compared with the capacity of the MIMO channel with an optimal receiver and known channel. The results indicate the cost of unsupervised (i.e., no training sequences) training for the combination of an unknown channel and unknown background.Signals, Systems and Computers, 2000. Conference Record of the Thirty-Fourth Asilomar Conference on; 02/2000 - [Show abstract] [Hide abstract]

**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; · 2.42 Impact Factor - [Show abstract] [Hide abstract]

**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 lowIEEE Transactions on Information Theory 05/2007; · 2.62 Impact Factor

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