Unsourced massive random access manages simultaneously a massive number of uncoordinated and bursty transmitters with a single receiver. Many traditional nonlinear least squares decoders at the receiver are inadequate and perform poorly for low signal-to-noise ratio cases, especially for impulsive (non-Gaussian) noise. In this paper, to deal with these heavy-tailed impulsive noise, we first propose a novel \(\ell _1\) -norm based tensor optimization model for decoding active users’ symbols at the receiver. Then, we introduce a practical alternating direction method of multipliers (ADMM) equipped with a novel inexact strategy for dealing with a class of nonconvex and nonsmooth composite optimization problems. It is noteworthy that our new algorithm can efficiently alleviate the computational burden caused by the composite objective with a nonsmooth outer function and a nonlinear inner part. Theoretically, under some standard conditions, we analyze the global convergence of the proposed practical ADMM. Numerical experiments on unsourced massive random access with up to 1000 active users illustrate that the proposed \(\ell _1\) -norm based optimization model and the newly introduced ADMM work well in practice.
