Joint Activity Detection and Channel Estimation for IoT Networks: Phase Transition and Computation-Estimation Tradeoff

TL;DR

This paper addresses the challenge of massive device connectivity in IoT networks by developing a structured group sparsity estimation method for joint activity detection and channel estimation, analyzing phase transition behavior and computational tradeoffs.

Contribution

It introduces a novel structured estimation approach that reduces signature sequence length and characterizes phase transition thresholds using conic integral geometry.

Findings

Successful activity detection when sequence length exceeds threshold

Phase transition region characterized by conic integral geometry

Smoothing method improves computational efficiency with quantifiable tradeoffs

Abstract

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 \emph{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 high-dimensional 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 trade-off 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.