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We undertake an information-theoretic approach to characterize the optimal design of a broadband multi-antenna system in the presence of mutual coupling. It was shown recently that mutual coupling effectively decomposes otherwise spectrally-identical spatial modes of an antenna array into spectrally non-identical eigen-modes. We shall use Shannon's information theory and Fano's broadband matching theory to develop optimal transceiver designs for a compact broadband MIMO system. It will be shown that in the presence of channel state information, optimal transmit power allocation and matching characteristic follow a mutual space-frequency water-pouring solution.