This paper focuses on random uplink transmissions of a subset of nodes disseminated in a cell. Under the constraints of massive Machine Type Communication (mMTC) in cellular Low Power Wide Area Networks (LPWAN) and Ultra Reliable Low Latency Communications (URLLC), improving the capability of a receiver to detect simultaneously several transmissions with a high probability is important. Considering a very limited coordination between the receiver and the distributed transmitters, the usage of coded Non Orthogonal Multiple Access (NOMA) strategies is seducing. In this framework, we target synchronous direct data transmissions and propose an optimal detector of the active users with channel state information at the receiver limited to statistical knowledge. This algorithm is based on a Maximum Likelihood (ML) detector, under statistical channel knowledge only. We give the formulation of the optimal detector and we evaluate its performance, with different codelengths, code types (random Gaussian and Grassmannian codes) and for various number of antennas at the base station.

We focus on the random uplink transmissions of an unknown subset of nodes, disseminated in a cell. Under the constraints of massive Machine Type Communication (MTC) in cellular Low Power Wide Area Networks (LPWAN) and Ultra Reliable Low Latency Communications (URLLC), we assume a low coordination with the receiver and the usage of Gaussian coded Non Orthogonal Multiple Access (NOMA). We then target direct data transmission and thus propose a low complexity optimal-based detection of the active users: the It-MAP. This algorithm relies on the Maximum A Posteriori (MAP) detector and, similarly to Orthogonal Matching Pursuit (OMP)like algorithms, proceeds by iteration to decrease its intrinsic complexity. We also show the gain of employing It-MAP rather than an OMP-based detection and the advantage of exploiting the possibility to tune the algorithm, in order to avoid either Missed Detection or False Alarm, depending on the wished trade-off between the reliability, the latency and the resource usage of the full transmission.