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In this paper, the authors characterize the capacity boundary of the two-user Multiple-Input Multiple-Output (MIMO) Broadcast Channel (BC) when the multi-antenna terminals use analog beam-forming at both sides of the link. Basically, the problem reduces to finding the optimal transmit direction and the optimal power allocation between users to operate at any point on the boundary. They show that both optimization problems can be solved in closed form. First, exploiting the fact that any Pareto optimal pair of rates must also be Pareto optimal of a convex region defined by the channel energies, the optimal transmit direction is shown to be the principal eigenvector of a matrix. Second, the optimal power allocation is obtained by exploiting again the Pareto optimality of the sought pair of rates.
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