Jie Xu

Yilong Chen, Huijun Xing, Jie Xu et al.

This paper studies the over-the-air computation (AirComp) in an orthogonal frequency division multiplexing (OFDM) system with imperfect channel state information (CSI), in which multiple single-antenna wireless devices (WDs) simultaneously send uncoded signals to a multi-antenna access point (AP) for distributed functional computation over multiple subcarriers. In particular, we consider two scenarios with best-effort and error-constrained computation tasks, with the objectives of minimizing the average computation mean squared error (MSE) and the computation outage probability over the multiple subcarriers, respectively. Towards this end, we jointly optimize the transmit coefficients at the WDs and the receive beamforming vectors at the AP over subcarriers, subject to the maximum transmit power constraints at individual WDs. First, for the special case with a single receive antenna at the AP, we propose the semi-closed-form globally optimal solutions to the two problems using the Lagrange-duality method. It is shown that at each subcarrier, the WDs' optimized power control policy for average MSE minimization follows a regularized channel inversion structure, while that for computation outage probability minimization follows an on-off regularized channel inversion, with the regularization dependent on the transmit power budget and channel estimation error. Next, for the general case with multiple receive antennas at the AP, we present efficient algorithms based on alternating optimization and convex optimization to find converged solutions to both problems.

Heqiang Wang, Jie Xu

The increasing demand for wireless communication underscores the need to optimize radio frequency spectrum utilization. An effective strategy for leveraging underutilized licensed frequency bands is cooperative spectrum sensing (CSS), which enable multiple secondary users (SUs) to collaboratively detect the spectrum usage of primary users (PUs) prior to accessing the licensed spectrum. The increasing popularity of machine learning has led to a shift from traditional CSS methods to those based on deep learning. However, deep learning-based CSS methods often rely on centralized learning, posing challenges like communication overhead and data privacy risks. Recent research suggests vertical federated learning (VFL) as a potential solution, with its core concept centered on partitioning the deep neural network into distinct segments, with each segment is trained separately. However, existing VFL-based CSS works do not fully address the practical challenges arising from streaming data and the objective shift. In this work, we introduce online vertical federated learning (OVFL), a robust framework designed to address the challenges of ongoing data stream and shifting learning goals. Our theoretical analysis reveals that OVFL achieves a sublinear regret bound, thereby evidencing its efficiency. Empirical results from our experiments show that OVFL outperforms benchmarks in CSS tasks. We also explore the impact of various parameters on the learning performance.