In this paper, the performance of a promising technology for the next generation wireless communications, non-orthogonal multiple access (NOMA), is investigated. In particular, the bit error rate (BER) performance of downlink NOMA systems over Nakagami-m flat fading channels, is presented. Under various conditions and scenarios, the exact BER of downlink NOMA systems considering successive interference cancellation (SIC) is derived. The transmitted signals are randomly generated from quadrature phase shift keying (QPSK) and two NOMA systems are considered; two users' and three users' systems. The obtained BER expressions are then used to evaluate the optimal power allocation for two different objectives, achieving fairness and minimizing average BER. The two objectives can be used in a variety of applications such as satellite applications with constrained transmitted power. Numerical results and Monte Carlo simulations perfectly match with the derived BER analytical results and provide valuable insight into the advantages of optimal power allocation which show the full potential of downlink NOMA systems.

17 pages, 12 figures