Block sparse bayesian learning based joint user activity detection and channel estimation for grant-free NOMA systems

This paper concerns uplink grant-free nonorthogonal multiple access, where the handshaking procedure is not required to reduce control signaling overhead and transmission latency. In especially the dynamic scenarios, e.g., Internet of vehicles, the active users have to be identified and their channel state information needs to be estimated before performing multiuser detection. We investigate the joint user activity detection (UAD) and channel estimation (CE), which provides necessary information for data detection. In this paper, the joint UAD and CE is formulated as a block sparse signal recovery problem. First, the block orthogonal matching pursuit (BOMP) algorithm is studied for this problem, but its complexity grows with the fourth power of active user number, which hinders its application. Then, block sparse Bayesian learning (BSBL) is investigated to solve this problem, and in particular a low complexity message passing based implementation of BSBL with belief propagation and mean field is developed. The proposed message passing based BSBL (MP-BSBL) algorithm has a complexity independent of active user number, which can be significantly lower than that of the BOMP algorithm. In addition, MP-BSBL provides an estimate of the noise power, which can be readily used for data detection. Simulation results show that the MP-BSBL algorithm delivers almost the same performance as BOMP with the exact knowledge of active user number and can reach the performance bound for channel estimation.