  In future B5G/6G broadband communication systems, non-linear signal
distortion caused by the impairment of transmit power amplifier (PA) can
severely degrade the communication performance, especially when uplink users
share the wireless medium using non-orthogonal multiple access (NOMA) schemes.
This is because the successive interference cancellation (SIC) decoding
technique, used in NOMA, is incapable of eliminating the interference caused by
PA distortion. Consequently, each user's decoding process suffers from the
cumulative distortion noise of all uplink users. In this paper, we establish a
new and tractable PA distortion signal model based on real-world measurements,
where the distortion noise power is a polynomial function of PA transmit power
diverging from the oversimplified linear function commonly employed in existing
studies. Applying the proposed signal model, we characterize the capacity rate
region of multi-user uplink NOMA by optimizing the user transmit power. Our
findings reveal a significant contraction in the capacity region of NOMA,
attributable to polynomial distortion noise power. For practical engineering
applications, we formulate a general weighted sum rate maximization (WSRMax)
problem under individual user rate constraints. We further propose an efficient
power control algorithm to attain the optimal performance. Numerical results
show that the optimal power control policy under the proposed non-linear PA
model achieves on average 13\% higher throughput compared to the policies
assuming an ideal linear PA model. Overall, our findings demonstrate the
importance of accurate PA distortion modeling to the performance of NOMA and
provide efficient optimal power control method accordingly.
