Power-Efficient Over-the-Air Aggregation with Receive Beamforming for Federated Learning

TL;DR

This paper proposes a power-efficient over-the-air aggregation method with receive beamforming for federated learning, optimizing device transmit power and server beamforming to ensure convergence and reduce power consumption.

Contribution

It introduces a joint transmit and receive beamforming optimization framework with a novel alternating optimization algorithm for power minimization in federated learning.

Findings

Significant power reduction compared to benchmarks.

Effective convergence guarantees under optimized beamforming.

Robustness to channel estimation errors with proposed algorithms.

Abstract

This paper studies power-efficient uplink transmission design for federated learning (FL) that employs over-the-air analog aggregation and multi-antenna beamforming at the server. We jointly optimize device transmit weights and receive beamforming at each FL communication round to minimize the total device transmit power while ensuring convergence in FL training. Through our convergence analysis, we establish sufficient conditions on the aggregation error to guarantee FL training convergence. Utilizing these conditions, we reformulate the power minimization problem into a unique bi-convex structure that contains a transmit beamforming optimization subproblem and a receive beamforming feasibility subproblem. Despite this unconventional structure, we propose a novel alternating optimization approach that guarantees monotonic decrease of the objective value, to allow convergence to a partial optimum. We further consider imperfect channel state information (CSI), which requires accounting for the channel estimation errors in the power minimization problem and FL convergence analysis. We propose a CSI-error-aware joint beamforming algorithm, which can substantially outperform one that does not account for channel estimation errors. Simulation with canonical classification datasets demonstrates that our proposed methods achieve significant power reduction compared to existing benchmarks across a wide range of parameter settings, while attaining the same target accuracy under the same convergence rate.