Robust Sum MSE Optimization for Downlink Multiuser MIMO Systems with Arbitrary Power Constraint: Generalized Duality Approach

This paper considers linear minimum meansquare- error (MMSE) transceiver design problems for downlink multiuser multiple-input multiple-output (MIMO) systems where imperfect channel state information is available at the base station (BS) and mobile stations (MSs). We examine robust sum mean-square-error (MSE) minimization problems. The problems are examined for the generalized scenario where the power constraint is per BS, per BS antenna, per user or per symbol, and the noise vector of each MS is a zero-mean circularly symmetric complex Gaussian random variable with arbitrary covariance matrix. For each of these problems, we propose a novel duality based iterative solution. Each of these problems is solved as follows. First, we establish a novel sum average meansquare- error (AMSE) duality. Second, we formulate the power allocation part of the 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. To solve robust sum MSE minimization constrained with per BS antenna and per BS power problems, we have established novel downlink-uplink duality. On the other hand, to solve robust sum MSE minimization constrained with per user and per symbol power problems, we have established novel downlink-interference duality. For the total BS power constrained robust sum MSE minimization problem, the current duality is established by modifying the constraint function of the dual uplink channel problem. And, for the robust sum MSE minimization with per BS antenna and per user (symbol) power constraint problems, our duality are established by formulating the noise covariance matrices of the uplink and interference channels as fixed point functions, respectively.Comment: IEEE TSP Journa

Maximizing the Sum Rate in Cellular Networks Using Multi-Convex Optimization

In this paper, we propose a novel algorithm to maximize the sum rate in interference-limited scenarios where each user decodes its own message with the presence of unknown interferences and noise considering the signal-to-interference-plus-noise-ratio. It is known that the problem of adapting the transmit and receive filters of the users to maximize the sum rate with a sum transmit power constraint is non-convex. Our novel approach is to formulate the sum rate maximization problem as an equivalent multi-convex optimization problem by adding two sets of auxiliary variables. An iterative algorithm which alternatingly adjusts the system variables and the auxiliary variables is proposed to solve the multi-convex optimization problem. The proposed algorithm is applied to a downlink cellular scenario consisting of several cells each of which contains a base station serving several mobile stations. We examine the two cases, with or without several half-duplex amplify-and-forward relays assisting the transmission. A sum power constraint at the base stations and a sum power constraint at the relays are assumed. Finally, we show that the proposed multi-convex formulation of the sum rate maximization problem is applicable to many other wireless systems in which the estimated data symbols are multi-affine functions of the system variables.Comment: 24 pages, 5 figure