Asynchronous Massive Connectivity with Deep-Learned Approximate Message Passing

This paper considers massive connectivity in asynchronous systems, where a large number of devices sporadically send data to the base station (BS) with imperfect synchronization. Grant-free random access is considered and each device is assigned with a unique but not necessarily orthogonal pilot sequence for identification and channel estimation. The goal is to design algorithms for joint user activity detection, delay detection, and channel estimation. We first adopt a transmission model where a guard interval is inserted between pilot and data in order to eliminate the potential cross pilot-data interference between asynchronous devices. By exploiting the feature of the asynchronous massive connectivity, we formulate a sparse signal recovery problem with hierarchical sparsity on the user activity and the time delays. We propose the Learned approximate message passing (LAMP) network that combines deep learning in the AMP framework to solve the problem. This neural network benefits from parameter learning ability of deep learning and low computation complexity of the AMP algorithm. Simulation results demonstrate that the LAMP network can perform much better than the AMP algorithm with no prior knowledge of the system statistics. Its performance is also insensitive to the maximal delay spread of the asynchronous users.