MAP-Based Pilot State Detection in Grant-Free Random Access for mMTC

Device activity detection and joint device activity and data detection (or equivalently, detection of pilots being transmitted) are main challenges in grant-free random access, which is recently proposed to support massive machine-type communications (mMTC). In this paper, we adopt a general and tractable model for distributions of pilot states (being transmitted or not), namely the multivariate Bernoulli (MVB) model, which can explicitly specify general correlation among device activities and relation among the states of pilots assigned to one device. Then, based on the MVB model, we formulate the estimation of pilot states as a maximum a posterior probability (MAP) estimation problem, which is a challenging non-convex problem. We propose a low-complexity coordinate descent algorithm to obtain a stationary point. The proposed MAP estimation enhances the existing maximum likelihood (ML) estimation and MAP estimation, by effectively exploiting the general prior distribution of pilot states and tackling the estimation problem in a rigorous way. Numerical results show the substantial gains of the proposed MAP-based design over well-known existing designs, and reveal the value of the proposed solution framework in pilot state detection.