Power-domain non-orthogonal multiple access (NOMA) is a promising radio access technique with non-orthogonal resource allocation that provides a greater spectrum efficiency than the conventional orthogonal multiple access (OMA). In this paper, an iterative receiver is derived for NOMA. It is based on soft-information successive interference cancellation (SIC) combined with a minimum mean square error parallel interference cancellation (MMSE-PIC) detector. Orthogonal frequency division multiplexing (OFDM) is usually the typical waveform employed. However, with the proposed receiver design, any linear modulation can be used. In addition to OFDM, single-carrier (SC) and the recently proposed sparse Walsh-Hadamard (SWH) are investigated. The NOMA scheme is analysed in a multi-path fading channel, where two users have different power ratios and waveforms. Simulation results show that mixing OFDM and SWH for a two-user NOMA gives the best performance with low receiver complexity.