Sum MSE optimization for downlink multiuser MIMO systems with per antenna power constraint: Downlink-uplink duality approach

This paper considers transceiver design problem for downlink multiuser multiple-input multiple-output (MIMO) systems. We examine minimization of sum mean-square-error (MSE) constrained with each base station (BS) antenna power problem. The problem is examined for the practically relevant scenario where the noise vector of each mobile station (MS) is a zero-mean circularly symmetric complex Gaussian random variable with arbitrary covariance matrix. We propose a novel downlink-uplink duality based iterative solution to solve the problem. The problem is solved as follows. First, we establish novel sum MSE downlink-uplink duality. Our duality is established by formulating the noise covariance matrix of the uplink channel as a fixed point function. Second, we formulate the power allocation part of each problem in the downlink channel as a Geometric Program (GP). Third, using the duality result and the solution of GP, we utilize alternating optimization technique to solve the original downlink problem. In our simulation results, we have observed that the proposed duality based solution utilizes less power than that of existing algorithm.