Information theoretic bounds for compound MIMO Gaussian channels
IEEE Transactions on Information Theory
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Information capacity is considered for a communication channel in which the noise is the sum of a known Gaussian component and an independent component with unknown statistical distributions. A lower bound on capacity is sought; the unknown noise component is thus assumed to be under the control of an adversary---a jammer. The problem is modeled as a zero-sum two-person game with mutual information as the payoff function. Appropriate constraints are determined on the transmitted signal and the unknown noise component. Although the usual conditions sufficient for application of the general form of the von Neumann minimax theorem are shown not to hold, a solution is obtained for the game: a saddle value, saddle point, and minimax strategy for the jammer are obtained. The essential effect of jamming is to convert the infinite-dimensional channel into a finite-dimensional channel having the same constraints, with the dimensionality depending upon the problem parameters: the covariance of the known Gaussian noise component and the constraints on the transmitted signal and the unknown noise component.