# Joint Precoder and Combiner Design for MMSE Distributed Beamforming with Per-Antenna Power Constraints

## TL;DR

This paper proposes an iterative Gauss-Seidel algorithm for joint MMSE precoder and combiner design in distributed beamforming systems with per-antenna power constraints, improving SNR performance.

## Contribution

It introduces a novel iterative optimization method for MMSE beamforming with per-antenna constraints, applicable to single and multi-carrier systems, with demonstrated performance gains.

## Key findings

- Achieved 0.7 dB SNR improvement over existing methods.
- Developed a dual gradient algorithm for multicarrier transmit coefficient optimization.
- Validated the approach through numerical simulations in Rayleigh-faded channels.

## Abstract

We consider minimum mean square error (MMSE) joint precoder and combiner design for single and multi carrier distributed beamforming systems with nonuniform per-antenna transmit power constraints. We show that, similar to the maximum-gain problem, an iterative Gauss-Seidel algorithm can be used for minimizing MSE which alternately optimizes the transmitter and receiver coefficients. In a single carrier system the optimum transmit coefficients are obtained by a simple projection of the effective MISO channel. In the multicarrier case with a sum-MSE objective, the Gauss-Seidel approach is once again applicable, but the transmit coefficients must be found by solving a quadratically constrained quadratic problem for which we apply a dual gradient algorithm. A numerical example is presented which shows improvement of 0.7 dB in carrier signal-to-noise ratio (SNR) relative to a projected eigenvector method for a multicarrier DBF system with Rayleigh-faded multipath channels.