Closed-form BER Expressions of QPSK Modulation over NOMA-PNC Parallel Relay Channels

With the advancement of the wireless communication technologies, parallel relay channels have been very popular. Both non-orthogonal multiple access and physical layer network coding have proven to be a very efficient techniques to provide superior spectral efficiencies in parallel relay systems. Though there are many previous attempts to derive theoretical bit error rate performance of either physical layer network coded or non-orthogonal multiple access based systems, the theoretical bit error rate performance has not been evaluated for physical layer network coded relay channels with non-orthogonal multiple access. We proposed a mechanism to analyse the theoretical bit error rate of a hybrid aforementioned system using quadrature phase shift keying modulation. The approach can be conveniently extended to more generic modulation schemes such as M-array phase shift keying. The derived theoretical bit error rate expressions for different nodes are verified using the Monte-Carlo simulations.