Intelligent Connectivity Through RIS-Assisted Wireless Communication: Exact Performance Analysis With Phase Errors and Mobility

Abstract

The current research offers only approximations for evaluating the performance of wireless systems that use reconfigurable intelligent surfaces (RIS) over generalized fading channels with phase error caused by imperfect phase compensation at the RIS. This paper presents an exact analysis of RIS-assisted vehicular communication considering uniformly distributed phase error and generalized fading channels with a coherent combining of received signals reflected by RIS elements and direct transmissions from the source terminal. We use a generalized- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$K$</tex-math></inline-formula> shadowed distribution for the direct link and asymmetrical channels for the RIS-assisted transmission with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\kappa$</tex-math></inline-formula> - <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mu$</tex-math></inline-formula> distribution for the first link and double generalized Gamma (dGG) distribution for the second link, combined with a statistical random waypoint (RWP) model for the moving vehicle. We employ a novel approach to represent the probability density function (PDF) and cumulative distribution function (CDF) of the resultant channel in terms of a single univariate Fox-H function and use the multivariate Fox-H approach to develop an exact statistical analysis of the end-to-end signal-to-noise ratio (SNR) for the RIS-assisted system. We also use the inequality between the arithmetic and geometric means to simplify the statistical results of the considered system in terms of the univariate Fox-H function. Our analysis also provides exact, upper bound, and asymptotic expressions of the outage probability and average bit-error-rate (BER) performance using the derived density and distribution functions. We conduct computer simulations in various practically relevant scenarios to assert that mitigating phase errors is achievable by augmenting the number of elements in the RIS module and employing a higher quantization level.