Error Performance Analysis of Access Point-Based Reconfigurable Intelligent Surfaces in the Presence of Gaussian-Plus-Laplacian Additive Noise

In this paper, we investigate the error performance of access point-based reconfigurable intelligent surfaces (AP-RISs) under a Rayleigh frequency-flat slow fading channel with path loss in the presence of Gaussian-plus-Laplacian additive noise. Since the additive noise includes an impulsive Laplacian component, it describes a scenario that is more realistic in practice. A closed-form expression of the average bit error probability (ABEP) is derived and validated by simulation results. The ABEP formulation employs an approximation of the sum of Rayleigh random variables and agrees well with simulation results for arbitrary surface sizes. However, the ABEP expression takes relatively long to evaluate due to the required multiple computations of the confluent hypergeometric function. On this note, a simplified expression of the ABEP is formulated by employing an asymptotic cumulative distribution function representation of the Gaussian-plus-Laplacian noise. The simplified ABEP agrees well with simulation results. An asymptotic analysis of the ABEP shows that the asymptotic diversity order is not affected by the Laplacian component. Finally, the ABEP formulations are used in the validations of error performance for an AP-RIS-assisted two-way relaying network under the same channel conditions. Overall, the investigations in this paper demonstrates the vulnerability of RISs to this type of noise and highlights the need for the design of suitable mitigation techniques.