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

## TL;DR

This paper introduces low-complexity robust beamforming algorithms for MISO downlink systems that minimize outage probability under per-antenna power constraints, improving performance with reduced computational effort.

## Contribution

It develops novel iterative algorithms based on offset maximization for robust beamforming with per-antenna power constraints, including variants for zero-forcing and maximum ratio transmission.

## Key findings

- Significant outage probability reduction demonstrated in simulations
- Algorithms achieve low computational complexity
- Effective for systems with many antennas

## Abstract

This paper considers the design of the beamformers for a multiple-input single-output (MISO) downlink system that seeks to mitigate the impact of the imperfections in the channel state information (CSI) that is available at the base station (BS). The goal of the design is to minimize the outage probability of specified signal-to-interference-and-noise ratio (SINR) targets, while satisfying per-antenna power constraints (PAPCs), and to do so at a low computational cost. Based on insights from the offset maximization technique for robust beamforming, and observations regarding the structure of the optimality conditions, low-complexity iterative algorithms that involve the evaluation of closed-form expressions are developed. To further reduce the computational cost, algorithms are developed for per-antenna power-constrained variants of the zero-forcing (ZF) and maximum ratio transmission (MRT) beamforming directions. In the MRT case, our low-complexity version for systems with a large number of antennas may be of independent interest. The proposed algorithms are extended to systems with both PAPCs and a total power constraint. Simulation results show that the proposed robust designs can provide substantial gains in the outage probability while satisfying the PAPCs.