  Device activity detection is one main challenge in grant-free random access,
which is recently proposed to support massive access for massive machine-type
communications (mMTC). Existing solutions fail to consider interference
generated by massive Internet of Things (IoT) devices, or important prior
information on device activities and interference. In this paper, we consider
device activity detection at an access point (AP) in the presence of
interference generated by massive devices from other cells. We consider the
joint maximum likelihood (ML) estimation and the joint maximum a posterior
probability (MAP) estimation of both the device activities and interference
powers, jointly utilizing tools from probability, stochastic geometry and
optimization. Each estimation problem is a difference of convex (DC)
programming problem, and a coordinate descent algorithm is proposed to obtain a
stationary point. The proposed ML estimation extends the existing ML estimation
by considering the estimation of interference powers together with the
estimation of device activities. The proposed MAP estimation further enhances
the proposed ML estimation by exploiting prior distributions of device
activities and interference powers. Numerical results show the substantial
gains of the proposed joint estimation designs, and reveal the importance of
explicit consideration of interference and the value of prior information in
device activity detection.
