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This paper considers weighted sum rate maximization constrained with a perbase station (BS) antenna power problem for multiuser multiple-inputmultiple-output (MIMO) systems. For this problem, we propose newdownlink-uplink duality based solution. We solve the problem as follows. First,by introducing additional optimization variables, we reformulate our probleminto an equivalent problem that incorporates a weighted sum mean-square-error(MSE) term. Second, we establish novel weighted sum MSE duality. The duality isestablished by modifying the input covariance matrix of the dual uplinkproblem, and formulating the noise covariance matrix of the uplink channel as afixed point function. Third, we optimize the introduced variables and powers inthe downlink channel by a Geometric Program (GP) method. Fourth, using theduality result and the solution of GP, we apply alternating optimizationtechnique to solve the original downlink problem. In our simulation results, wehave observed that the proposed duality based solution utilizes less power thanthat of existing algorithms.

Weighted Sum Rate Optimization for Downlink Multiuser MIMO Systems with per Antenna Power Constraint: Downlink-Uplink Duality Approach