Joint User Activity Detection, Channel Estimation, and Data Detection with Delay-Calibration for Asynchronous mMTC

This work considers uplink asynchronous massive machine-type communications (mMTC), where a large number of low-power and low-cost devices with sporadic activity patterns asynchronously transmit short packets to an access point (AP) equipped with multiple receive antennas. The asynchronous transmission reduces the required coordination between the activated devices and the AP, simplifying the transmitter design but making the receiver design more challenging. In this work, we propose a joint user activity detection, channel estimation, and data detection with delay-calibration (JUCED-DC) algorithm, and investigate the benefits of oversampling in estimating continuous-valued time delays at the receiver. The proposed JUCED-DC algorithm is based on the expectation-maximization (EM) method. In the expectation step of EM, a message passing based joint user activity detection, channel estimation, and data detection (JUCED) algorithm is proposed to obtain the posterior probabilities of channel and data; in the maximization step of EM, a greedy search based delay-calibration algorithm is utilized to update the time delays. We analyze the efficacy of the proposed JUCED algorithm through the Bayesian Cramér-Rao bound. Moreover, we propose to incorporate soft input and soft output decoding into the message passing of the JUCED algorithm to further improve the system's performance. Numerical results demonstrate the effectiveness of the proposed algorithms in terms of the normalized mean-squared errors of channel and data symbols, the bit error rate of data bits, and the probability of misdetection. Compared to the baseline methods, the proposed algorithms can achieve performance improvements of over 80%.