Joint-Multiuser Gray-Labeling for Non-Orthogonal Multiple Access Techniques

Non-orthogonal multiple access (NOMA) is a promising technology to improve the spectral efficiency of future wireless communication systems. Nonetheless, the imposed intentional non-orthogonality among users degrades the bit error rate (BER) performance. Therefore, this work presents joint-multiuser Gray-labeling (J-Gray) to improve the BER performance of downlink (DL) NOMA systems. Unlike the conventional disjoint-multiuser Gray-labeling (D-Gray), J-Gray ensures that the NOMA constellation is Gray-labeled per user. Hence, the successive interference cancellation (SIC) error propagation problem can be mitigated. Closed-form BER expressions are presented for the two-user scenario with arbitrary M-ary quadrature amplitude modulation (M-QAM), considering both J-Gray and D-Gray in additive white Gaussian noise (AWGN) and various fading channels including Rayleigh fading, Nakagami-n fading, and Nakagami-m fading. In addition, an approximation for the BER is presented at high signal to noise ratios (SNRs). The numerical results show that the performance gain of J-Gray is maximized for power coefficients approaching the bounds, giving J-Gray the highest flexibility in selecting an appropriate power coefficient.