RIS-Assisted Wireless System in the Presence of Direct Channel: Channel Statistics and Performance Analysis

A reconfigurable intelligent surface (RIS)-aided wireless communication system is considered in this paper, where the transmitter sends data to the receiver via a direct link and the RIS. The phases of the reflecting elements of the RIS are selected considering the phases of all the fading channels to maximize the performance of the system. Series-form expressions for the probability density function (p.d.f.) and cumulative distribution function (c.d.f.) are derived for the composite channel of the communication system by considering the RIS channels to follow independent Nakagami-m distributions and the envelope of the direct channel to follow a Rayleigh distribution. Furthermore, the expressions for the statistics of the composite channel in terms of its p.d.f. and c.d.f. are also derived by considering the approximation of the central limit theorem (CLT) and the square of the channel envelope without the direct channel to approximately follow a Gamma distribution. Utilizing the derived statistics, the performance of the RIS-assisted system is studied by deriving series-form expressions for the symbol error probability (SEP) and outage probability. Numerical results are presented to corroborate the analytical framework. It is observed that a decreasing number of reflecting elements of the RIS and an increasing shape parameter of the fading channels increase the randomness of the overall channel of the RIS-assisted wireless system. Moreover, the inefficacy of both the approximate statistics is demonstrated via simulation studies of the p.d.f., c.d.f., SEP, and outage probability.