  Recent research provides an approximation on the performance for
reconfigurable intelligent surface (RIS) assisted systems over generalized
fading channels with phase noise resulting from imperfect phase compensation at
the RIS. In this paper, we developed exact analysis and upper bounds on the
performance of RIS-assisted vehicular communication system considering phase
noise with mobility over asymmetric fading channels by coherently combining
received signals reflected by RIS elements and direct transmissions from the
source terminal. We employ a novel approach to represent the PDF and CDF of the
product of four channel coefficients in terms of a single univariate Fox-H
function. We use the derived PDF to develop an exact statistical analysis of
the end-to-end SNR for the RIS-assisted system using multi-variate Fox-H
function.
