Linear precoding via conic optimization for fixed MIMO receivers

TLDR

The study examines the relationship between fixed‑MIMO precoder design and the established uplink‑downlink duality in joint transmit beamforming and power control. The authors aim to develop a general linear precoder for fixed MIMO receivers, encompassing the rank‑one beamforming case, and to derive optimality conditions and fixed‑point algorithms. They formulate two conic optimization problems—power minimization under SINR constraints and worst‑case SINR maximization under a power limit—and solve them with standard conic solvers, providing optimality conditions and simple fixed‑point iterations. The resulting precoders are solvable via conic optimization and, in multi‑user simulations, outperform existing linear precoding schemes.

Abstract

In this paper, the problem of designing linear precoders for fixed multiple-input-multiple-output (MIMO) receivers is considered. Two different design criteria are considered. In the first, the transmitted power is minimized subject to signal-to-interference-plus-noise-ratio (SINR) constraints. In the second, the worst case SINR is maximized subject to a power constraint. It is shown that both problems can be solved using standard conic optimization packages. In addition, conditions are developed for the optimal precoder for both of these problems, and two simple fixed-point iterations are proposed to find the solutions that satisfy these conditions. The relation to the well-known uplink-downlink duality in the context of joint transmit beamforming and power control is also explored. The proposed precoder design is general, and as a special case, it solves the transmit rank-one beamforming problem. Simulation results in a multiuser system show that the resulting precoders can significantly outperform existing linear precoders.