Achievable Rates of Asynchronous Uplink Non-orthogonal Multiple Access with GMSK

Non-orthogonal multiple access (NOMA) is proposed to address the challenges of future wireless network. Recently, asynchronous NOMA (ANOMA) has gained attention due to its higher achievable rates. However, the known NOMA/ANOMA usually focus on linear modulations, which ignores the linearity of the power amplifier (PA) of the transmitter that can lead to a power backoff. Gaussian minimum shift keying (GMSK) is an attractive nonlinear waveform with constant envelope, which allows the PA to be operated at a high efficiency. In this paper, an uplink ANOMA scheme with GMSK is proposed for the first time. Then, the achievable sum rates with different detectors are derived to evaluate the performance of the proposed scheme. Further, the ANOMA with linear waveforms is provided to highlight the significance of our work. Numerical results show the advantages of nonlinear systems in nonlinear performance are more significant than that of linear systems in the achievable sum rate. For any detectors, the achievable sum rate has a negligible loss for the approximate GMSK signal based on Laurent decomposition, and a larger achievable sum rate can be obtained by setting the time offset between users.