Joint Activity Detection and Channel Estimation for Massive Connectivity: An Information Geometry Approach

In this paper, we propose an information geometry (IG) approach for joint activity detection and channel estimation (JADCE) in a massive connectivity scenario, where a large number of devices access a base station (BS) in a sporadic fashion. We formulate the JADCE problem as a classic sparse signal recovery problem, known as the multiple measurement vector (MMV) problem, and we convert it to several single measurement vector (SMV) problems to resolve it in an iterative way. To compute the marginal mean from a high-dimensional joint probability density function (PDF), we construct auxiliary manifolds (AMs) and the objective manifold for each SMV stage. While the Bernoulli-Gaussian priors cause the manifolds to be not e-flat, we can calculate the approximations of auxiliary manifolds since the sparse user transmission patterns. Simulation results demonstrate that this approximation holds an accurate performance and the proposed IG-JADCE has a better convergence rate than the approximate message passing (AMP) algorithm.