Transceiver design for an uplink asynchronous NOMA using MSK-type signals

•Asynchronous NOMA with time offsets further enhances the performance of NOMA.•Asynchronous NOMA with nonlinear waveforms brings power efficiency benefits.•Two transceivers based on the maximum likelihood criterion are developed.•The properties of Hermitian- and banded-Toeplitz matrices are fully exploited.•The performance in various perspectives is investigated by numerical simulation.