Device activity detection is one main challenge in grant-free massive access, which is recently proposed to support massive machine-type communications (mMTC). Existing solutions for device activity detection fail to consider inter-cell interference generated by massive IoT devices or important prior information on device activities and inter-cell interference. In this paper, given different numbers of observations and network parameters, we consider both non-cooperative device activity detection and cooperative device activity detection in a multi-cell network, consisting of many access points (APs) and IoT devices. Under each activity detection mechanism, we consider the joint maximum likelihood (ML) estimation and joint maximum a posterior probability (MAP) estimation of both device activities and interference powers, utilizing tools from probability, stochastic geometry, and optimization. Each estimation problem is a challenging non-convex problem, and a coordinate descent algorithm is proposed to obtain a stationary point. Each proposed joint ML estimation extends the existing one for a single-cell network by considering the estimation of interference powers, together with the estimation of device activities. Each proposed joint MAP estimation further enhances the corresponding joint ML estimation by exploiting prior distributions of device activities and interference powers. The proposed joint ML estimation and joint MAP estimation under cooperative detection outperform the respective ones under non-cooperative detection at the costs of increasing backhaul burden, knowledge of network parameters, and computational complexities.
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