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In this letter, we propose a joint active device detection and channelestimation framework based on factor graphs for asynchronous uplink grant-freemassive multiple-antenna systems. We then develop the message-scheduling GAMP(MSGAMP) algorithm to perform joint active device detection and channelestimation. In MSGAMP we apply scheduling techniques based on the residualbelief propagation (RBP) and the activity user detection (AUD) in whichmessages are generated using the latest available information. MSGAMP-typeschemes show a good performance in terms of activity error rate and normalizedmean squared error, requiring a smaller number of iterations for convergenceand lower complexity than state-of-the-art techniques.

Dynamic Message Scheduling With Activity-Aware Residual Belief Propagation for Asynchronous mMTC Systems