Activity Detection for Massive Connectivity under Frequency Offsets via First-Order Algorithms

Abstract

Activity detection in machine-type communication (MTC) has been recognized as an effective way to support massive connectivity of the Internet-of-Things (IoT) devices. However, due to the sporadic traffic pattern of the MTC, only a small portion of the massive potential devices are active, making the activity detection a challenging large-scale sparsity-constrained problem. On the other hand, since the low-cost IoT devices are commonly equipped with cheap crystal oscillators, the resulting frequency offsets would intensify the multi-user interference during the activity detection and invalidate existing detection methods that are designed under ideal frequency synchronization. To fill this gap, this paper proposes two methods for activity detection under unknown frequency offsets: a Lasso-based method and a sparsity-constrained method. Both the methods are first-order algorithms, making them suitable for large-scale IoT systems. Furthermore, the sparsity-constrained method can be executed in parallel and is proved to converge to a set of critical points. The simulation results show that both the proposed methods achieve much better detection performance than a two-stage approach that separately performs frequency synchronization and activity detection. Moreover, the proposed sparsity-constrained method is shown to perform better than two competing algorithms exploiting hierarchical sparsity.