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

Abstract

Abstract-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. We also show that our sum AMSE duality are able to solve other sum MSE-based robust design problems. Computer simulations verify the robustness of the proposed robust designs compared to the non-robust/naive designs.

Coordinated Multi-Point Transmission Strategies for TDD Systems with Non-Ideal Channel Reciprocity

“…With the uplink channel and the statistics of the calibration errors, the MMSE estimate of |h H u,D w j | 2 is w H j R u w j , which is given in (9). Therefore, we can obtain an estimate of h H u,D w u as w H u R u w u e jθu with an arbitrary phase θ u .…”

“…Consequently, the well-explored transmission strategies cannot be extended to CoMP in a straightforward manner. First of all, per-BS power constraints (PBPC) should be considered instead of sum power constraints, which yield more complicated optimization [9][10][11]. Second, CoMP channel is a concatenation of multiple single-cell channels.…”

Robust beamforming designs for multiuser MISO downlink with per-antenna power constraints

“…Under such more realistic power constraints, the transmitter optimization was addressed in [20], where the elegant uplink-downlink duality under a sum-power constraint was extended to downlink problems with per-antenna power constraints. The robust sum-MSE minimizations with per BS antenna and per BS power constraints were investigated in [21] through the downlink-uplink duality. By establishing the MSE downlink-interference duality, the authors in [22] extended the work of [21] to solve the weighted sum-MSE minimization and min-max MSE problems under general power constraints for multiuser MIMO systems.…”

“…The robust sum-MSE minimizations with per BS antenna and per BS power constraints were investigated in [21] through the downlink-uplink duality. By establishing the MSE downlink-interference duality, the authors in [22] extended the work of [21] to solve the weighted sum-MSE minimization and min-max MSE problems under general power constraints for multiuser MIMO systems. Downlink beamforming designs under per-antenna power constraints were also addressed in some other works.…”

Robust Hybrid Precoding for Multiuser MIMO Wireless Communication Systems

“…The objective function is not convex in this case which means that the globally optimum solution may not always be achieved. Some of the more recent work on robust linear transceiver design for the MU-MIMO downlink can be found in [30], [31], [32].…”