Link Performance of Multiple Reconfigurable Intelligent Surfaces and Direct Path in General Fading

We analyze the performance of a single-input single-output wireless link that is aided by multiple reconfigurable intelligent surfaces (RISs) – in terms of outage probability, average symbol error probability and ergodic capacity, for which we derive analytical expressions in closed form. In particular, we consider a realistic system model, where the direct path may not be blocked and for which channels corresponding to different RISs are assumed to be independent but not identical and follow the generic $\kappa-\mu$ fading distribution, which can be reduced to a number of fading scenarios (namely Rayleigh, Rice, Nakagami-m, and one-sided Gaussian). This enables the evaluation of the system performance when adopting any combination of these special cases or the generic $\kappa-\mu$ distribution for both hops of the multiple distributed RISs. The direct path is modeled by Rayleigh fading assuming no line-of-sight between the source and the destination. We verify the accuracy of the adopted approach by means of Monte Carlo simulations and conduct a performance analysis that demonstrates the significant improvement in the system performance due to the usage of the RISs. Especially, we show that increasing the number of reflecting elements equipped on the RISs and placing the RISs closer to either communication endpoints improve the performance considerably.