  We develop a new algorithm for activity detection for grant-free multiple
access in distributed multiple-input multiple-output (MIMO). The algorithm is a
distributed version of the approximate message passing (AMP) based on a soft
combination of likelihood ratios computed independently at multiple access
points. The underpinning theoretical basis of our algorithm is a new
observation that we made about the state evolution in the AMP. Specifically,
with a minimum mean-square error denoiser, the state maintains a block-diagonal
structure whenever the covariance matrices of the signals have such a
structure. We show by numerical examples that the algorithm outperforms
competing schemes from the literature.
