Sparse Activity, Timing Detection And Channel Estimation For Grant-Free Uplink Communications

This paper considers a grant-free uplink scenario in which the user activity (UA), the timing offsets (TOs), and the channel state information (CSI) of user equipments (UEs) are unknown to the serving base station (BS). In this scenario, the number of potential UEs is large while only a few UEs are active. Due to the sparse nature of the UA, a detection algorithm using approximate message passing (AMP), a compressed sensing (CS) algorithm, is proposed to recover the UA, TOs, and CSI. The proposed algorithm maps the asynchronous system to a virtual system and applies AMP to it. After AMP converges, to minimize the detection error probability, a Bayes test is derived and utilized. Besides, state evolution (SE) analysis is conducted on the virtual system to predict the performance of the proposed algorithm. Simulation results show that when the number of pilot symbols is large enough, the proposed algorithm can achieve the same detection error probability and channel estimation error as those of an ideal system in which the UEs are synchronized. Analytical results show that SE is able to predict the minimum number of pilot symbols needed to achieve a required detection error probability, and predict the performance when the number of pilot symbols is large.