MSE uplink-downlink duality of MIMO systems under imperfect CSI

This paper addresses the mean square error (MSE) uplink/downlink duality for the multiple input multiple output (MIMO) systems where imperfect channel state information (CSI) is available at the base station (BS) and mobile stations (MSs). The channel is modeled by incorporating antenna correlation at the BS. In contrast to the perfect CSI case where instantaneous MSE duality is considered, the average mean square error (AMSE) duality is exploited. To show the application of our AMSE duality we consider the minimum mean square error (MMSE) transceiver design for the downlink multiuser MIMO systems. Our objective is to minimize the sum MSE constrained with a total BS power and provide robustness against channel uncertainties. In the uplink channel, the power allocation part of this problem is formulated as a geometric program (GP). Based on the solution of GP and the AMSE duality analysis, we propose an iterative algorithm that performs optimization alternatively between the uplink and the downlink channels. The convergence behavior of the proposed algorithm is studied. Computer simulations verify the robustness of the proposed design when compared to the non-robust/naive design.