This paper presents the design and bit error rate (BER) analysis of a phase-independent non-orthogonal

multiple access (NOMA) system. The proposed NOMA system can utilize amplitude-coherent detection

(ACD) which requires only the channel amplitude for equalization purposes. In what follows, three

different designs for realizing the detection of the proposed NOMA are investigated. One is based on the

maximum likelihood (ML) principle, while the other two are based on successive interference cancellation

(SIC). Closed-form expressions for the BER of all detectors are derived and compared with the BER of

the coherent ML detector. The obtained results, which are corroborated by simulations, demonstrate that,

in most scenarios, the BER is dominated by multiuser interference rather than the absence of the channel

phase information. Consequently, the BER using ML and ACD are comparable for various cases of

interest. The paper also shows that the SIC detector is just an alternative approach to realize the ML

detector, and hence, both detectors provide the same BER performance.