DocumentCode :
1136178
Title :
Capacity of the Class of MIMO Channels With Incomplete CDI—Properties of Mutual Information for a Class of Channels
Author :
Charalambous, Charalambos D. ; Denic, Stojan Z. ; Constantinou, Costas
Author_Institution :
Dept. of Electr. & Comput. Eng., Univ. of Cyprus, Nicosia, Cyprus
Volume :
55
Issue :
8
fYear :
2009
Firstpage :
3725
Lastpage :
3734
Abstract :
This paper is concerned with multiple-input multiple-output (MIMO) wireless channel capacity, when the probability distribution of the channel matrix p(H) is not completely known to the transmitter and the receiver. The partial knowledge of a true probability distribution of the channel matrix p(H) is modelled by a relative entropy D(middot||middot) such that D(p||pnom) les d, d ges 0, where d is the distance from the so-called nominal channel matrix distribution pnom(H). The capacity of this compound channel is equal to the maximin of the mutual information, where the minimum is with respect to the channel matrix distribution, and the maximum is with respect to the covariance matrix of a transmitted signal. The existence of a minimizing probability distribution is proved, and the explicit formula for the minimizing distribution is derived in terms of the nominal distribution pnom(H) and parameter d. A number of properties of the mutual information, minimized over the set of channel distributions, are derived. Specifically, upper and lower bounds are derived for the minimized mutual information, while its convexity with respect to d is shown. In the case of the Rayleigh fading, an explicit formula for the capacity and the optimal transmit covariance matrix are derived.
Keywords :
MIMO communication; Rayleigh channels; antenna arrays; channel capacity; convex programming; covariance matrices; minimax techniques; statistical distributions; MIMO communication channel; Rayleigh fading channel; convex programming; covariance matrix; incomplete CDI-property; maximin optimization problem; multiple-input multiple-output wireless channel capacity; nominal channel matrix distribution; probability distribution; receiver antenna array; relative entropy; Channel capacity; Covariance matrix; Entropy; Gaussian channels; MIMO; Mutual information; Probability distribution; Rayleigh channels; Transmitters; Uncertainty; Compound channel; multiple-input multiple- output (MIMO) Gaussian channel; power allocation; relative entropy constraint; robustness;
fLanguage :
English
Journal_Title :
Information Theory, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9448
Type :
jour
DOI :
10.1109/TIT.2009.2023716
Filename :
5165166
Link To Document :
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