  This paper investigates the issue of cooperative activity detection for
grant-free random access in the sixth-generation (6G) cell-free wireless
networks with sourced and unsourced paradigms. First, we propose a cooperative
framework for solving the problem of device activity detection in sourced
random access. In particular, multiple access points (APs) cooperatively detect
the device activity via exchanging low-dimensional intermediate information
with their neighbors. This is enabled by the proposed covariance-based
algorithm via exploiting both the sparsity-promoting and similarity-promoting
terms of the device state vectors among neighboring APs. A decentralized
approximate separating approach is introduced based on the forward-backward
splitting strategy for addressing the formulated problem. Then, the proposed
activity detection algorithm is adopted as a decoder of cooperative unsourced
random access, where the multiple APs cooperatively detect the list of
transmitted messages regardless of the identity of the transmitting devices.
Finally, we provide sufficient conditions on the step sizes that ensure the
convergence of the proposed algorithm in the sense of Bregman divergence.
Simulation results show that the proposed algorithm is efficient for addressing
both sourced and unsourced massive random access problems, while requires a
shorter signature sequence and accommodates a significantly larger number of
active devices with a reasonable antenna array size, compared with the
state-of-art algorithms.
