I. Introduction
Since non-orthogonal multiple access (NOMA) has a higher spectral efficiency than orthogonal multiple access (OMA), it has been extensively studied [1], [2], although there are a number of challenges (e.g., optimal user clustering [3] and beamforming [4], [5]). In [6], [7], the notion of NOMA can be employed in uncoordinated transmissions such as random access for uplink transmissions in order to improve the throughput, which is important for massive machine-type communication (MTC) that provides the connectivity for various Internet-of-Things (IoT) applications [8].