Phase Transitions of Massive Device Connectivity via Convex Geometry

Massive device connectivity is a crucial communication requirement for Internet of Things (IoT) networks consisting of a large number of devices with sporadic traffic communications. In each coherence time interval, base station (BS) needs to identify the active devices and estimate the channel state information, thereby supporting communication services for the active IoT devices. By exploiting the sparsity pattern in device activity, we develop a group-structured sparsity estimation approach to simultaneously detect the active devices and estimate the wireless channels. This significantly reduces the signature sequence length while supporting massive connectivity with sporadic traffic communications. Specifically, we adopt the convex geometry approach to characterize the phase transition behaviors of the group-structured sparsity estimation problem in complex field. The developed results provide guidelines for choosing appropriate signature sequence length in practice. Numerical results are provided to illustrate the accuracy of our theoretical results.