Pilot Design Based on the Distribution of Inter-User Interference for Grant-Free Access

Massive random access (MRA) involves massive devices sporadically and randomly sending short-packet messages through a shared wireless channel. It is a crucial scenario in 6G communications to support the Internet-of-Things. Grant-free access, where devices complete transmission without grants, is a promising scheme for MRA. In grant-free access, the design of pilot sequences has a significant effect on joint activity detection and channel estimation (JADCE) and, consequently, system performance. Inter-user interference (IUI), caused by non-orthogonal pilots, is random owing to the random set of active users, and existing studies on pilot design for grant-free access often attempt to reduce the mean IUI. However, the performance of JADCE is affected not only by the mean IUI but also by the tail behavior of the IUI distribution. In this paper, we propose a metric for pilot design, exploiting the distribution of IUI to reflect the impact of pilots on JADCE more precisely. We further develop a pilot design algorithm based on the proposed metric, with modified approximate message passing (AMP) adopted as the JADCE algorithm. Simulation results demonstrate that the proposed pilot design reduces the probability of missed detection of active users and channel estimation error, compared with existing pilot designs.