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 entropyD(middot||middot) such thatD(p||pnom) lesd,dges 0, wheredis 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 parameterd. 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 todis shown. In the case of the Rayleigh fading, an explicit formula for the capacity and the optimal transmit covariance matrix are derived.

This paper addresses the issue of 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 is modelled by using a relative entropy D(pparq). All possible channel matrix distributions p(H) satisfy D(pparpnom) les d, d ges 0, i.e., they lie within d distance from the so-called nominal channel matrix distribution pnom(H). The information channel capacity is defined as a maximin optimization problem, where the mutual information is a pay-off function. The minimum is with respect to the channel matrix distribution, and the maximum is with respect to the covariance matrix of a transmitted signal. Based on the derived characteristics of the pay-off function, the formula for the channel matrix distribution, which minimizes the mutual information, is derived. In the case of the Rayleigh fading, the formula for the information capacity and the optimal transmit covariance matrix are obtained. In addition, the existence of the saddle point of the maximin optimization problem is established for this particular case