Phase Shift Optimization for RIS Enabled PNC System With Multiple Antennas

Reconfigurable intelligent surfaces (RIS) have been developed to exploit the stochastic characteristics of the propagation environment for next generation wireless systems. On the other hand, the integration of wireless physical network coding (PNC) and multiple antennas yields notable enhancements in system performance. This paper presents a multiuser system, employing RIS enabled PNC alongside multiple antennas to minimize both delay and error probability. Our aim is to establish reliable communication between the user pairs, which communicate through a base station (BS) via RIS. Therefore, the reflecting coefficients including both phases and amplitudes of the RIS are optimized by using the alternating direction method of multipliers (ADMM) algorithm for both single and multiple RIS cases. Extensive results are presented to compare the proposed algorithm with random phase shift, network coding (NC) and the search algorithm to illustrate its superiority.