# Robust Low-Complexity WMMSE Precoding Under Imperfect CSI with Per-Antenna Power Constraints

## TL;DR

This paper introduces a new low-complexity WMMSE precoding method for massive MU-MIMO systems that handles imperfect CSI and per-antenna power constraints efficiently.

## Contribution

The novel RLC-WMMSE framework reduces computational complexity while maintaining performance under imperfect CSI and PAPCs.

## Key findings

- The RLC-WMMSE algorithm achieves WSR performance close to standard WMMSE-PAPCs designs.
- The proposed method significantly reduces runtime and strictly satisfies per-antenna power constraints.
- Simulations show effectiveness over i.i.d. and spatially correlated channels.

## Abstract

Weighted sum-rate (WSR) maximization in downlink massive multi-user multiple-input (MU-MIMO) with per-antenna power constraints (PAPCs) and imperfect channel state information (CSI) is computationally challenging. Classical weighted minimum mean-square error (WMMSE) algorithms, in particular, have per-iteration costs that scale cubically with the number of base-station antennas. This article proposes a robust low-complexity WMMSE-based precoding framework (RLC-WMMSE) tailored for massive MU-MIMO downlink under PAPCs and stochastic CSI mismatch. The algorithm retains the standard WMMSE structure but incorporates three key enhancements: a diagonal dual-regularization scheme that enforces PAPCs via a lightweight projected dual ascent with row-wise safety projection; a Woodbury-based transmit update that replaces the dominant M×M inversion with an (NK)×(NK) symmetric positive-definite solve, greatly reducing the per-iteration complexity; and a hybrid switching mechanism with adaptive damping that blends classical and low-complexity updates to improve robustness and convergence under channel estimation errors. We also analyze computational complexity and signaling overhead for both TDD and FDD deployments. Simulation results over i.i.d. and spatially correlated channels show that the proposed RLC-WMMSE scheme achieves WSR performance close to benchmark WMMSE-PAPCs designs while providing substantial runtime savings and strictly satisfying the per-antenna power limits. These properties make RLC-WMMSE a practical and scalable precoding solution for large-scale MU-MIMO systems in future wireless sensor and communication networks.