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.