Capacity of the class of MIMO channels with incomplete CDI  Properties of mutual information for a class of channels
Date
2009Source
IEEE Transactions on Information TheoryVolume
55Issue
8Pages
37253734Google Scholar check
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This paper is concerned with multipleinput multipleoutput (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(·∥·) such that D(p∥p nom)≤d, d≥0, where d is the distance from the socalled nominal channel matrix distribution p nom(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 p nom(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. © 2009 IEEE.
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