MSE uplink-downlink duality of MIMO systems with arbitrary noise covariance matrices

This paper establishes three kinds of mean-square-error (MSE) uplink-downlink duality for multiple-input multiple-output (MIMO) systems. Our duality is established for the practically relevant scenario where the noise vector of each mobile station (MS) is a zero-mean circularly symmetric complex Gaussian (ZMCSCG) random variable with arbitrary covariance matrix. As an application example of our duality, we examine the linear transceiver design for the weighted sum MSE minimization constrained with a total base station (BS) power problem for the downlink multiuser MIMO systems. To solve this problem, first we establish the MSE uplink-downlink duality. Then, we formulate the power allocation part of the equivalent problem in the uplink channel as a Geometric Programming (GP). Finally, using the duality result and the solution of GP, we utilize alternating optimization technique to solve the original downlink problem. The proposed duality maintains the easier-to-handle mathematical structure of MSE-based problems in the uplink channel and generalizes the existing MSE uplink-downlink duality. Furthermore, by utilizing our duality, we exploit the hidden convexity of the sum MSE minimization constrained with a total BS power problem in the downlink channel.