Over-the-Air FEEL with Integrated Sensing: Joint Scheduling and Beamforming Design

TL;DR

This work studies over-the-air federated edge learning with integrated sensing, addressing target-echo interference that degrades analog model aggregation. It derives a Cramér-Rao bound-based sensing metric and an aggregation MSE metric, and jointly optimizes device scheduling and beamforming under sensing and communication constraints. A low-complexity hierarchical matching pursuit algorithm is proposed to solve the resulting MINLP by decoupling marginal precoding and post-processing problems and iteratively pruning devices. The approach demonstrates improved scheduling efficiency and robust learning performance on MNIST and CIFAR-10, highlighting the ability to suppress echoes via accurate sensing and maintain high-quality model aggregation in challenging interference environments.

Abstract

Employing wireless systems with dual sensing and communications functionalities is becoming critical in next generation of wireless networks. In this paper, we propose a robust design for over-the-air federated edge learning (OTA-FEEL) that leverages sensing capabilities at the parameter server (PS) to mitigate the impact of target echoes on the analog model aggregation. We first derive novel expressions for the Cramer-Rao bound of the target response and mean squared error (MSE) of the estimated global model to measure radar sensing and model aggregation quality, respectively. Then, we develop a joint scheduling and beamforming framework that optimizes the OTA-FEEL performance while keeping the sensing and communication quality, determined respectively in terms of Cramer-Rao bound and achievable downlink rate, in a desired range. The resulting scheduling problem reduces to a combinatorial mixed-integer nonlinear programming problem (MINLP). We develop a low-complexity hierarchical method based on the matching pursuit algorithm used widely for sparse recovery in the literature of compressed sensing. The proposed algorithm uses a step-wise strategy to omit the least effective devices in each iteration based on a metric that captures both the aggregation and sensing quality of the system. It further invokes alternating optimization scheme to iteratively update the downlink beamforming and uplink post-processing by marginally optimizing them in each iteration. Convergence and complexity analysis of the proposed algorithm is presented. Numerical evaluations on MNIST and CIFAR-10 datasets demonstrate the effectiveness of our proposed algorithm. The results show that by leveraging accurate sensing, the target echoes on the uplink signal can be effectively suppressed, ensuring the quality of model aggregation to remain intact despite the interference.

Figures (10)

• Figure 1: Illustration of the integrated OTA-FEEL and sensing setting.
• Figure 2: Schematic representation of communication in time domain.
• Figure 3: Average of selected devices versus aggregation error threshold.
• Figure 4: Average number of selected devices versus sensing estimation error threshold.
• Figure 5: Average of selected devices versus aggregation error threshold.

Theorems & Definitions (12)

• Lemma 1: Distribution of $\tilde{{\mathbf{z}}} \left[ \ell \right]$
• proof
• Proposition 1: Cramér-Rao bound
• proof
• Lemma 2
• proof
• Lemma 3
• proof
• Lemma 4
• proof