Proximal Gradient-Based Unfolding for Massive Random Access in IoT Networks

Grant-free random access is an effective technology for enabling low-overhead and low-latency massive access, where joint activity detection and channel estimation (JADCE) is a critical issue. Although existing compressive sensing algorithms can be applied for JADCE, they usually fail to simultaneously harvest the following properties: effective sparsity inducing, fast convergence, robust to different pilot sequences, and adaptive to time-varying networks. To this end, we propose an unfolding framework for JADCE based on the proximal gradient method. Specifically, we formulate the JADCE problem as a group-row-sparse matrix recovery problem and leverage a minimax concave penalty rather than the widely-used $\ell_1$-norm to induce sparsity. We then develop a proximal gradient-based unfolding neural network that parameterizes the algorithmic iterations. To improve convergence rate, we incorporate momentum into the unfolding neural network, and prove the accelerated convergence theoretically. Based on the convergence analysis, we further develop an adaptive-tuning algorithm, which adjusts its parameters to different signal-to-noise ratio settings. Simulations show that the proposed unfolding neural network achieves better recovery performance, convergence rate, and adaptivity than current baselines.

Gan-Based Joint Activity Detection and Channel Estimation For Grant-free Random Access

Joint activity detection and channel estimation (JADCE) for grant-free random access is a critical issue that needs to be addressed to support massive connectivity in IoT networks. However, the existing model-free learning method can only achieve either activity detection or channel estimation, but not both. In this paper, we propose a novel model-free learning method based on generative adversarial network (GAN) to tackle the JADCE problem. We adopt the U-net architecture to build the generator rather than the standard GAN architecture, where a pre-estimated value that contains the activity information is adopted as input to the generator. By leveraging the properties of the pseudoinverse, the generator is refined by using an affine projection and a skip connection to ensure the output of the generator is consistent with the measurement. Moreover, we build a two-layer fully-connected neural network to design pilot matrix for reducing the impact of receiver noise. Simulation results show that the proposed method outperforms the existing methods in high SNR regimes, as both data consistency projection and pilot matrix optimization improve the learning ability.

Knowledge-Guided Learning for Transceiver Design in Over-the-Air Federated Learning

In this paper, we consider communication-efficient over-the-air federated learning (FL), where multiple edge devices with non-independent and identically distributed datasets perform multiple local iterations in each communication round and then concurrently transmit their updated gradients to an edge server over the same radio channel for global model aggregation using over-the-air computation (AirComp). We derive the upper bound of the time-average norm of the gradients to characterize the convergence of AirComp-assisted FL, which reveals the impact of the model aggregation errors accumulated over all communication rounds on convergence. Based on the convergence analysis, we formulate an optimization problem to minimize the upper bound to enhance the learning performance, followed by proposing an alternating optimization algorithm to facilitate the optimal transceiver design for AirComp-assisted FL. As the alternating optimization algorithm suffers from high computation complexity, we further develop a knowledge-guided learning algorithm that exploits the structure of the analytic expression of the optimal transmit power to achieve computation-efficient transceiver design. Simulation results demonstrate that the proposed knowledge-guided learning algorithm achieves a comparable performance as the alternating optimization algorithm, but with a much lower computation complexity. Moreover, both proposed algorithms outperform the baseline methods in terms of convergence speed and test accuracy.

Learning Proximal Operator Methods for Massive Connectivity in IoT Networks

Grant-free random access has the potential to support massive connectivity in Internet of Things (IoT) networks, where joint activity detection and channel estimation (JADCE) is a key issue that needs to be tackled. The existing methods for JADCE usually suffer from one of the following limitations: high computational complexity, ineffective in inducing sparsity, and incapable of handling complex matrix estimation. To mitigate all the aforementioned limitations, we in this paper develop an effective unfolding neural network framework built upon the proximal operator method to tackle the JADCE problem in IoT networks, where the base station is equipped with multiple antennas. Specifically, the JADCE problem is formulated as a group-sparse-matrix estimation problem, which is regularized by non-convex minimax concave penalty (MCP). This problem can be iteratively solved by using the proximal operator method, based on which we develop a unfolding neural network structure by parameterizing the algorithmic iterations. By further exploiting the coupling structure among the training parameters as well as the analytical computation, we develop two additional unfolding structures to reduce the training complexity. We prove that the proposed algorithm achieves a linear convergence rate. Results show that our proposed three unfolding structures not only achieve a faster convergence rate but also obtain a higher estimation accuracy than the baseline 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.