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:**Constellation design for the noncoherent multi-input, multi-output (MIMO) block Rayleigh fading channel is considered. For general SNRs, starting from a given base unitary constellation of finite cardinality, and using the cutoff rate expression as the design criterion, we obtain input probabilities and per-antenna amplitudes for the constellation points via a global optimization formulation. Using the mutual information as a performance metric we obtain numerical results that show 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 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 we have an optimum constellation design technique that 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 01/2007; 53:1572-1584. · 2.62 Impact Factor - [Show abstract] [Hide abstract]

**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:**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; · 2.62 Impact Factor

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