Distributed estimation of sparse user activity for multi-base station on-off random access

We consider user activity estimation for on-off random access in multi-base station systems. With on-off random access, each user, at a fixed slot, transmits its unique codeword (and is hence active) with probability p, and is heard by all base stations in its vicinity; the goal for each base station is then to determine which of the users in its coverage region are active. This problem models various relevant control (signalling) tasks like initial access and scheduling requests in multi-base station cellular wireless systems. In this paper, we develop a fully distributed estimator, where neighboring base stations exchange messages through backhaul links to determine the active users set. Our estimator assumes no prior knowledge on the user-base station channel gains and, as a byproduct, estimates the channel gains from base stations to their active neighboring users. Our estimator is based on a convex loss function which enhances group-sparsity of the channel gains from each user to all its neighboring base stations. Simulation examples demonstrate that our distributed estimator achieves a low error probability (in determining the active users set) over a wide range of system loads (expected number of active users per base station, per slot).