Optimal Minimum Euclidean Distance-Based Precoder for NOMA With Finite-Alphabet Inputs

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Non-orthogonal multiple access (NOMA) scheme with Gaussian input signals, which have no constellation constraint on the input alphabets, has been investigated intensively, whereas the research on finite input constellations is relatively few. This paper focuses on the power allocation in practical NOMA application with finite-alphabet inputs. We propose a practical power allocation scheme for downlink NOMA scenario based on the merit of maximizing the minimum Euclidean distance (MMED) by adopting the constellation-constrained (CC) capacity. Applying the nearest neighbor approximation and Jensen's inequality, we prove that optimal CC capacity can be achieved under the MMED criterion at high signal-to-noise ratio (SNR). Instead of updating power allocation coefficient instantaneously, a preset fixed power factor α MMED derived from the MMED criterion is preferred and thus reduces the complexity of overall system implementation. We take two cases into consideration, namely, Gaussian broadcast channel (GBC) and fading broadcast channel (FBC). We model close channel conditions, which are challenging for conventional NOMA as the GBC scenario, and model near-far effect as well Rayleigh fading as the FBC scenario. In these two cases, we show that the optimal performance can be guaranteed at high SNR without the knowledge of channel state information (CSI). We study the power coefficient pairs for the most commonly used Mary quadrature amplitude modulation (M-QAM) constellations based on the MMED criterion. We explore the relationship between the power allocation coefficients and the sizes of constellations. The numerical simulations on CC sum capacity and capacity regions are provided to validate our analysis.