Optimal Structure of Receive Beamforming for Over-the-Air Computation

We investigate fast data aggregation via over-the-air computation (AirComp) over wireless networks. In this scenario, an access point (AP) with multiple antennas aims to recover the arithmetic mean of sensory data from multiple wireless devices. To minimize estimation distortion, we formulate a mean-squared-error (MSE) minimization problem that considers joint optimization of transmit scalars at wireless devices, denoising factor, and receive beamforming vector at the AP. We derive closed-form expressions for the transmit scalars and denoising factor, resulting in a non-convex quadratic constrained quadratic programming (QCQP) problem concerning the receive beamforming vector. To tackle the computational complexity of the beamforming design, particularly relevant in massive multiple-input multiple-output (MIMO) AirComp systems, we explore the optimal structure of receive beamforming using successive convex approximation (SCA) and Lagrange duality. By leveraging the proposed optimal beamforming structure, we develop two efficient algorithms based on SCA and semi-definite relaxation (SDR). These algorithms enable fast wireless aggregation with low computational complexity and yield almost identical mean square error (MSE) performance compared to baseline algorithms. Simulation results validate the effectiveness of our proposed methods.

Optimal Receive Beamforming for Over-the-Air Computation

In this paper, we consider fast wireless data aggregation via over-the-air computation (AirComp) in Internet of Things (IoT) networks, where an access point (AP) with multiple antennas aim to recover the arithmetic mean of sensory data from multiple IoT devices. To minimize the estimation distortion, we formulate a mean-squared-error (MSE) minimization problem that involves the joint optimization of the transmit scalars at the IoT devices as well as the denoising factor and the receive beamforming vector at the AP. To this end, we derive the transmit scalars and the denoising factor in closed-form, resulting in a non-convex quadratic constrained quadratic programming (QCQP) problem concerning the receive beamforming vector.Different from the existing studies that only obtain sub-optimal beamformers, we propose a branch and bound (BnB) algorithm to design the globally optimal receive beamformer.Extensive simulations demonstrate the superior performance of the proposed algorithm in terms of MSE. Moreover, the proposed BnB algorithm can serve as a benchmark to evaluate the performance of the existing sub-optimal algorithms.

Peer Offloading with Delayed Feedback in Fog Networks

Comparing to cloud computing, fog computing performs computation and services at the edge of networks, thus relieving the computation burden of the data center and reducing the task latency of end devices. Computation latency is a crucial performance metric in fog computing, especially for real-time applications. In this paper, we study a peer computation offloading problem for a fog network with unknown dynamics. In this scenario, each fog node (FN) can offload their computation tasks to neighboring FNs in a time slot manner. The offloading latency, however, could not be fed back to the task dispatcher instantaneously due to the uncertainty of the processing time in peer FNs. Besides, peer competition occurs when different FNs offload tasks to one FN at the same time. To tackle the above difficulties, we model the computation offloading problem as a sequential FN selection problem with delayed information feedback. Using adversarial multi-arm bandit framework, we construct an online learning policy to deal with delayed information feedback. Different contention resolution approaches are considered to resolve peer competition. Performance analysis shows that the regret of the proposed algorithm, or the performance loss with suboptimal FN selections, achieves a sub-linear order, suggesting an optimal FN selection policy. In addition, we prove that the proposed strategy can result in a Nash equilibrium (NE) with all FNs playing the same policy. Simulation results validate the effectiveness of the proposed policy.

Federated learning with class imbalance reduction

Federated learning (FL) is a promising technique that enables a large amount of edge computing devices to collaboratively train a global learning model. Due to privacy concerns, the raw data on devices could not be available for centralized server. Constrained by the spectrum limitation and computation capacity, only a subset of devices can be engaged to train and transmit the trained model to centralized server for aggregation. Since the local data distribution varies among all devices, class imbalance problem arises along with the unfavorable client selection, resulting in a slow converge rate of the global model. In this paper, an estimation scheme is designed to reveal the class distribution without the awareness of raw data. Based on the scheme, a device selection algorithm towards minimal class imbalance is proposed, thus can improve the convergence performance of the global model. Simulation results demonstrate the effectiveness of the proposed algorithm.