The Internet of Things (IoT) framework requires a massive number of connection thus demanding spectral efficient solutions such as Non-Orthogonal Multiple Access (NOMA). However, the main drawback of NOMA with successive interference canceler (SIC)-based detectors is the error floor in the uplink. In this letter, a reliable multi-user detection in uplink IoT NOMA is guaranteed by a Joint Maximum-Likelihood (JML) detector (i.e., optimum detection algorithm). We derive a closed-form upper bound of bit error rate (BER) of JML over Rayleigh fading channels for arbitrary number of IoT devices and an adaptive M-ary phase shift keying (M-PSK). Based on the extensive simulations, the derived expressions are validated and it is revealed that the JML improves the error performance in uplink NOMA and removes the error floor. Furthermore, regardless of the number of the IoT devices and modulation order, a full diversity order (i.e., number of receiving antennas) is guaranteed for each device.