Block diagonalization (BD) is a practically favorable precoding technique that eliminates the interuser interference in downlink multiuser multiple-input multiple-output (MIMO) systems. In this paper, we apply BD to the downlink transmission in a cooperative multi-cell system, where the signals from different base stations (BSs) to all the mobile stations (MSs) are jointly designed with the perfect knowledge of the downlink channels and transmit messages. Specifically, this paper studies the BD precoder design to maximize the weighted sum-rate achievable for all the MSs. The associated optimization problem can be formulated in an auxiliary MIMO broadcast channel (BC) with a set of transmit power constraints equivalent to those for different BSs in the multi-cell system. Based on convex optimization techniques, this paper designs an efficient algorithm to solve this problem, and derives the structure of the corresponding optimal BD precoding matrix. Moreover, for the special case of single-antenna BSs and MSs, it is shown that the proposed solution leads to the optimal zero-forcing beamforming (ZF-BF) precoder design for the multiple-input single-output (MISO) BC with the per-antenna power constraints.
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