On the Compound MIMO Broadcast Channel

We consider the Gaussian multi-antenna compound broadcast channel where one transmitter transmits several mes- sages, each intended for a different user whose channel realization is arbitrarily chosen from a finite set. Our investigation focuses on the behavior of this channel at high SNRs and we obtain the multiplexing gain of the sum capacity for a number of cases, and point out some implications of the total achievable multiplexing gain region. 1

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