Block diagonalization (BD) is a practical linear precoding technique thateliminates the inter-user interference in downlink multiuser multiple-inputmultiple-output (MIMO) systems. In this paper, we apply BD to the downlinktransmission in a cooperative multi-cell MIMO system, where the signals fromdifferent base stations (BSs) to all the mobile stations (MSs) are jointlydesigned with the perfect knowledge of the downlink channels and transmitmessages. Specifically, we study the optimal BD precoder design to maximize theweighted sum-rate of all the MSs subject to a set of per-BS power constraints.This design problem is formulated in an auxiliary MIMO broadcast channel (BC)with a set of transmit power constraints corresponding to those for individualBSs in the multi-cell system. By applying convex optimization techniques, thispaper develops an efficient algorithm to solve this problem, and derives theclosed-form expression for the optimal BD precoding matrix. It is revealed thatthe optimal BD precoding vectors for each MS in the per-BS power constraintcase are in general non-orthogonal, which differs from the conventionalorthogonal BD precoder design for the MIMO-BC under one single sum-powerconstraint. Moreover, for the special case of single-antenna BSs and MSs, theproposed solution reduces to the optimal zero-forcing beamforming (ZF-BF)precoder design for the weighted sum-rate maximization in the multiple-inputsingle-output (MISO) BC with per-antenna power constraints. Suboptimal andlow-complexity BD/ZF-BF precoding schemes are also presented, and theirachievable rates are compared against those with the optimal schemes.
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