Uplink Non-Orthogonal Multiple Access With Finite-Alphabet Inputs

This paper focuses on the non-orthogonal multiple access (NOMA) design for a classical two-user multiple access channel (MAC) with finite-alphabet inputs. In contrast to most of the existing NOMA designs using continuous Gaussian input distributions, we consider practical quadrature amplitude modulation (QAM) constellations at both transmitters, the sizes of which are assumed to be not necessarily identical. We propose maximizing the minimum Euclidean distance of the received sum constellation with a maximum likelihood (ML) detector by adjusting the scaling factors (i.e., instantaneous transmitted powers and phases) of both users. The formulated problem is a mixed continuous-discrete optimization problem, which is nontrivial to resolve in general. By carefully observing the structure of the objective function, we define a new type of Farey sequence, termed punched Farey sequence to tackle the formulated problem. Based on this, we manage to achieve a closed-form optimal solution to the original problem by first dividing the entire feasible region into a finite number of Farey intervals and then taking the maximum over all possible intervals. The resulting sum constellation is proved to be a regular QAM constellation of a larger size, and hence, a simple quantization receiver can be implemented as the ML detector for the demodulation. Moreover, the superiority of NOMA over time-division multiple access in terms of minimum Euclidean distance is rigorously proved. We subsequently address how to extend our design framework intended for the two-user MAC to systems with multiple users and multiple antennas. Finally, simulation results are provided to verify our theoretical analysis and demonstrate the merits of the proposed NOMA over existing orthogonal and non-orthogonal designs.