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Compressed sensing multi-user detection (CS-MUD) algorithms play a key role in optimizing grant-free (GF) non-orthogonal multiple access (NOMA) for massive machine-type communications (mMTC). However, current CS-MUD algorithms cannot be efficiently parallelized, leading to computationally expensive implementations of joint activity detection and channel estimation (JADCE) as the number of deployed machine-type devices (MTDs) increases. To address this, the present work proposes novel JADCE algorithms that can be applied in parallel for different clusters of MTDs by exploiting the structure of the pilot sequences. These are the approximation error method (AEM)-alternating direction method of multipliers (ADMM), and AEM-sparse Bayesian learning (SBL). Results presented in terms of the normalized mean square error and the probability of miss detection show comparable performance to the conventional algorithms. However, both AEM-ADMM and AEM-SBL algorithms have significantly reduced computational complexity and run times, thus, facilitating network scalability.

Joint Activity Detection and Channel Estimation for Clustered Massive Machine Type Communications