Cross Validation Aided Approximated Message Passing Algorithm for User Identification in mMTC

Recently, the approximate message passing (AMP) algorithm is advocated for overcoming the active user identification challenge in grant free (GF) massive random access (RA). However, requiring the perfect knowledge of user sparsity is a quite strong assumption of AMP algorithm in practical applications. Accordingly, we incorporate the cross validation (CV) method into the minimum mean square error (MMSE) denoiser based AMP algorithm, resulting a basic CV aided AMP algorithm (BCV-AMP) that can adaptively estimate the user sparsity. In order to further reduce its complexity, an improved CV aided MMSE denoiser based AMP algorithm (ICV-AMP) is proposed. Simulation results show that both the BCV-AMP and the ICV-AMP algorithms achieve almost the same user identification performance as the well-known MMSE denoiser based AMP algorithm, while the ICV-AMP algorithm has essentially the same complexity as that of the latter.