Low-Complexity Robust MISO Downlink Precoder Design With Per-Antenna Power Constraints

This paper considers the design of beamformers for a multiple-input single-output downlink system with per-antenna power constraints (PAPCs) that seek to mitigate the impact of the imperfections in the channel state information that is available at the base station. The goal of the design is to minimize the outage probability of specified signal-to-interference-and-noise ratio targets, and to do so at a low computational cost. The proposed design strategy provides an efficient way to handle PAPCs, in addition to a total power constraint, for a variety of precoding techniques, including the offset maximization approach to robust beamforming, and the nominal zero-forcing and maximum ratio transmission approaches. Through observations regarding the structure of the optimality conditions for each of the design formulations, low-complexity iterative algorithms that involve the evaluation of closed-form expressions are developed. In systems with a large number of antennas, the computational cost of some of these algorithms can be reduced to being linear in the number of antennas, without a significant degradation in performance. Simulation results show that the proposed robust designs can provide substantial reductions in the outage probability while satisfying the PAPCs.