Design and Analysis of Probabilistic Shaping Scheme for Uplink Nonorthogonal Multiple Access Systems

Probabilistic shaping (PS) combined with bipolar amplitude shift keying modulation is a promising transmission scheme to increase spectral efficiency. Different from the existing design of the point to point communications, we propose a PS-based uplink nonorthogonal multiple access (NOMA) scheme for fading channels to support multiple connections simultaneously, where successive interference cancellation (SIC)-based maximum a posterior (MAP) detection is implemented at the receiver. To exploit the shaping gain for each user, we first theoretically analyze the ergodic channel capacity and the constellation constrained (CC) capacity with discrete-constellation inputs, respectively. And then, a multi-step optimization scheme for maximizing the ergodic CC capacity is proposed to obtain the optimal probability mass function (PMF) of these input signals. The order of optimization is inverse to the SIC decoding order so that for each specific user, the remaining multiuser interference is calculated based on the optimal PMF of the later decoded users. Furthermore, based on this non-equiprobable transmission scheme, the closed-form pairwise error probability expressions for each user are obtained for the first time. Finally, compared with the uniform scheme, the simulations show that the proposed PS NOMA strategies achieve more than 1 dB gain in terms of the error performance.