The stringent requirements for low-latency and privacy of the emerging high-stake applications with intelligent devices such as drones and smart vehicles make the cloud computing inapplicable in these scenarios. Instead, edge machine learning becomes increasingly attractive for performing training and inference directly at network edges without sending data to a centralized data center. This stimulates a nascent field termed as federated learning for training a machine learning model on computation, storage, energy and bandwidth limited mobile devices in a distributed manner. To preserve data privacy and address the issues of unbalanced and non-IID data points across different devices, the federated averaging algorithm has been proposed for global model aggregation by computing the weighted average of locally updated model at each selected device. However, the limited communication bandwidth becomes the main bottleneck for aggregating the locally computed updates. We thus propose a novel over-the-air computation based approach for fast global model aggregation via exploring the superposition property of a wireless multiple-access channel. This is achieved by joint device selection and beamforming design, which is modeled as a sparse and low-rank optimization problem to support efficient algorithms design. To achieve this goal, we provide a difference-of-convex-functions (DC) representation for the sparse and low-rank function to enhance sparsity and accurately detect the fixed-rank constraint in the procedure of device selection. A DC algorithm is further developed to solve the resulting DC program with global convergence guarantees. The algorithmic advantages and admirable performance of the proposed methodologies are demonstrated through extensive numerical results.

Federated Learning via Over-the-Air Computation

Over-the-air computation (AirComp) becomes a promising approach for fast wireless data aggregation via exploiting the superposition property in a multiple access channel. To further overcome the unfavorable signal propagation conditions for AirComp, in this paper, we propose an intelligent reflecting surface (IRS) aided AirComp system to build controllable wireless environments, thereby boosting the received signal power significantly. This is achieved by smartly tuning the phase shifts for the incoming electromagnetic waves at IRS, resulting in reconfigurable signal propagations. Unfortunately, it turns out that the joint design problem for AirComp transceivers and IRS phase shifts becomes a highly intractable nonconvex bi- quadratic programming problem, for which a novel alternating difference-of-convex (DC) programming algorithm is developed. This is achieved by providing a novel DC function representation for the rank-one constraint in the low-rank matrix optimization problem via matrix lifting. Simulation results demonstrate the algorithmic advantages and admirable performance of the proposed approaches compared with the state-of-art solutions.

Over-the-Air Computation via Intelligent Reflecting Surfaces

Power-domain non-orthogonal multiple access (NOMA) has become a promising technology to exploit the new dimension of the power domain to enhance the spectral efficiency of wireless networks. However, most existing NOMA schemes rely on the strong assumption that users’ channel gains are quite different, which may be invalid in practice. To unleash the potential of power-domain NOMA, we propose a reconfigurable intelligent surface (RIS)-empowered NOMA scheme to introduce desirable channel gain differences among the users by adjusting the phase shifts at the RIS. Our goal is to minimize the total transmit power by jointly optimizing the beamforming vectors at the base station, the phase-shift matrix at the RIS, and user ordering. To address challenge due to the highly coupled optimization variables, we present an alternating optimization framework to decompose the non-convex bi-quadratically constrained quadratic problem under a specific user ordering into two rank-one constrained matrices optimization problems via matrix lifting. To accurately detect the feasibility of the non-convex rank-one constraints and improve performance by avoiding early stopping in the alternating optimization procedure, we equivalently represent the rank-one constraint as the difference between nuclear norm and spectral norm. A difference-of-convex (DC) algorithm is further developed to solve the resulting DC programs via successive convex relaxation, followed by establishing the convergence of the proposed DC-based alternating optimization method. We further propose an efficient user ordering scheme with closed-form expressions, considering both the channel conditions and users’ target data rates. Simulation results validate the ability of an RIS in enlarging the channel-gain difference when the users’ original channel conditions are similar and the superiority of the proposed DC-based alternating optimization method in reducing the total transmit power.

Reconfigurable Intelligent Surface Empowered Downlink Non-Orthogonal Multiple Access

Fast wireless data aggregation and efficient battery recharging are two critical design challenges of Internet-of-Things (IoT) networks. Over-the-air computation (AirComp) and energy beamforming (EB) turn out to be two promising techniques that can address these two challenges, necessitating the design of wireless-powered AirComp. However, due to severe channel propagation, the energy harvested by IoT devices may not be sufficient to support AirComp. In this article, we propose to leverage the intelligent reflecting surface (IRS) that is capable of dynamically reconfiguring the propagation environment to drastically enhance the efficiency of both downlink EB and uplink AirComp in IoT networks. Due to the coupled problems of downlink EB and uplink AirComp, we further propose the joint design of energy and aggregation beamformers at the access point, downlink/uplink phase-shift matrices at the IRS, and transmit power at the IoT devices, to minimize the mean-squared error (MSE), which quantifies the AirComp distortion. However, the formulated problem is a highly intractable nonconvex quadratic programming problem. To solve this problem, we first obtain the closed-form expressions of the energy beamformer and the device transmit power, and then develop an alternating optimization framework based on difference-of-convex programming to design the aggregation beamformers and IRS phase-shift matrices. Simulation results demonstrate the performance gains of the proposed algorithm over the baseline methods and show that deploying an IRS can significantly reduce the MSE of AirComp.

Wireless-Powered Over-the-Air Computation in Intelligent Reflecting Surface-Aided IoT Networks

The future Internet-of-Things network is expected to connect billions of sensors, which incurs high latency for data aggregation. To overcome this challenge, a new technique called over-the-air function computation was recently developed to enable fusion center to receive a desired function directly. It utilizes the superposition property of wireless channel to realize the uniform summation of the desired function. In order to compensate the non-uniform fading of different sensors, we propose a novel uniform-forcing transceiver design for over-the-air function computation. A corresponding min-max optimization problem is formulated to minimize the distortion of the computation which is measured by mean squared error. Due to the non-convexity of the problem, it is relaxed to semidefinite programming first. Then, the performance of the initial solution is improved through successive convex approximation. Simulation results show that the proposed design is able to achieve significant performance gain with low complexity.

A Uniform-Forcing Transceiver Design for Over-the-Air Function Computation

The next generation wireless network is expected to connect billions of nodes, which brings up the bottleneck on the communication speed for distributed data fusion. To overcome this challenge, computation over multiple access channel (CoMAC) was recently developed to compute the desired functions with a summation structure (e.g., mean, norm, etc.) by using the superposition property of wireless channels. This work aims to maximize the achievable function rate of reliable CoMAC in wireless networks. More specifically, considering channel fading and transceiver design, we derive the achievable function rate adopting the quantization and the nested lattice coding, which is determined by the number of nodes, the maximum value of messages and the quantization error threshold. Based on the derived result, the transceiver design is optimized to maximize the achievable function rate of the network. We first study a single cluster network without inter-cluster interference (ICI). Then, a multi-cluster network is further analyzed in which the clusters work in the same channel with ICI. In order to avoid the global channel state information (CSI) aggregation during the optimization, a low-complexity signaling procedure irrelevant with the number of nodes is proposed utilizing the channel reciprocity and the defined effective CSI.

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Xiaowei Qin

Papers

A Uniform-Forcing Transceiver Design for Over-the-Air Function Computation

Computation Over MAC: Achievable Function Rate Maximization in Wireless Networks