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 differenceof-convex-functions (DC) representation for the sparse and lowrank 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.

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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 biquadratic 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.

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Massive device connectivity is a crucial communication challenge for Internet of Things (IoT) networks, which consist of a large number of devices with sporadic traffic. In each coherence block, the serving base station needs to identify the active devices and estimate their channel state information for effective communication. By exploiting the sparsity pattern of data transmission, we develop a structured group sparsity estimation method to simultaneously detect the active devices and estimate the corresponding channels. This method significantly reduces the signature sequence length while supporting massive IoT access. To determine the optimal signature sequence length, we study the phase transition behavior of the group sparsity estimation problem. Specifically, user activity can be successfully estimated with a high probability when the signature sequence length exceeds a threshold; otherwise, it fails with a high probability. The location and width of the phase transition region are characterized via the theory of conic integral geometry. We further develop a smoothing method to solve the highdimensional structured estimation problem with a given limited time budget. This is achieved by sharply characterizing the convergence rate in terms of the smoothing parameter, signature sequence length and estimation accuracy, yielding a tradeoff between the estimation accuracy and computational cost. Numerical results are provided to illustrate the accuracy of our theoretical results and the benefits of smoothing techniques.