Symbolic representation of RIS-assisted FSO channels

The concept of reconfigurable intelligent surfaces (RIS) has gained significant interest over the past couple of years as a promising technology for beyond fifth generation (B5G) and sixth generation (6G) mobile networks. This observation is valid for radio-frequency, visible light, and free-space optical (FSO) communication systems. In order to better understand RIS-aided FSO systems, the symbolic approach can be employed. A symbolic approach involves analyzing the statistics and performance of a complex system using symbolic functions, resulting in a comprehensive picture of the system. To this end, the RIS-assisted FSO channel is regarded in this paper as a black box containing a single mathematical function with symbolic parameters. Through this symbolic representation, it is possible to easily obtain closed-form expressions for different metrics required to analyze a communication link. Given that the symbolic approach can be applied to all RIS-based systems, this paper discusses a case where the sub-channels, obtained with the introduction of the RIS infrastructure, are modeled by the generalized-K distribution, taken as an example. Using the Meijer G-function, closed-form expressions of the probability density function, cumulative distribution function, and moment generating function are derived. These are used to find closed-form expressions of the outage probability, average bit error rate, and ergodic channel capacity. Results are provided for selected values of the fading parameters, and they show that the higher the product of sub-channels shadowing and severity parameters, the better the system performances, specifically the outage probability, average bit error rate, and ergodic channel capacity.