In this paper, a bit error rate (BER) performance is evaluated for power domain non-orthogonal multiple access (PD-NOMA) system. The performance test is examined considering; additive white gaussian noise (AWGN), flat and long-term evolution (LTE)-multipath selective channels such as; pedestrian channel model (EPA), vehicular channel model (EVA), and typical urban model (ETU). The proposed system considering two user equipment's (UE1 and UE2) with a single base station (BS) for downlink channel. Two different powers were allocated to each user according to their positions from the BS. The superposition coding process is performed with successive-interference-cancelation (SIC) at both transmitter/receiver sides respectively to distinguish the desired received signal. The performance evaluations proves that the degree of power allocated to each user plays a significant rule in frequency selection environments. UE1 has a better BER performance than UE 2 by about 9 dB in EPA, 6 dB in EVA, and 7 dB in ETU environments respectively at a BER of 10 -3 . However, in flat fading environment, the distance for each user represents a significant factor affecting the BER performance, where, UE 2 has a better BER performance than UE 1 by about 10 dB at a BER of 10 -3 .