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The introduction of 5G and beyond systems brings new challenges for efficiently supporting the random access of a massive number of users with ultra-reliable low-latency requirements. To address these challenges, we propose a novel compressed sensing (CS)-based nonorthogonal multiple access (NOMA) multiple-input multiple-output (MIMO) scheme, called the CS-NOMA MIMO scheme, for the downlink of massive mission-critical machine-type communication (mmcMTC). By taking advantage of tensor CS techniques, a novel tensor CS-based packet (frame) structure, called TCS packet (frame), is proposed for the CS-NOMA MIMO scheme to further reduce the transmit time intervals (TTIs), resulting in smaller latency than that using the conventional packet (frame) structure. In the TCS packet (frame) structure, the CS signatures are assigned not only to different users but also to different time slots and different symbols of a time slot, thus achieving a user, time slot, and symbol overload system. We present a sufficient condition for the construction of the CS signatures that ensure effective deployment of tensor CS-based multiuser detection (CS-MUD) in user receivers. Furthermore, we consider the case of imperfect channel state information (CSI) and present an upper bound for the performance of the proposed scheme. Finally, the simulation results show that the proposed scheme can achieve high user overload (up to 5) and time slot overload (up to 3) when the activity ratio of users is 1%. When the time slot overload is 3, the proposed scheme with the TCS packet (frame) shortens time slots by at least 2/3 times that of the typical grant-based NOMA schemes. In addition, the block error rate (BLER) of the proposed scheme with the TCS packet (frame) is much lower than that with the conventional packet (frame), even less than 10−9 by repeat transmission when the time slot overload is 3.

A Novel Tensor CS-Based NOMA MIMO System for the Downlink of Massive Mission-Critical MTC in 5G and Beyond