Approximate Composite Channel Statistics and Performance Analysis of IRS-Aided Wireless System Under Nakagami-<i>m</i> Fading
Arathi P. Ajayan, Soumya P. Dash, Barathram Ramkumar
Abstract
An intelligent reflecting surface (IRS) enhances the performance of a wireless channel by controlling the phase of signals reflected by them. This paper investigates an IRS-aided single input single output wireless communication system. Owing to the closely spaced placement of the IRS elements, the channels between the IRS and the transmitter, as well as the channels between the IRS and the receiver, are considered to be spatially correlated. Assuming optimal phase configuration at the IRS, correlated Nakagami- <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> random vectors are used to model the magnitude of the channel coefficient vectors between the IRS and the transmitter as well as between the IRS and the receiver. A statistical approximation of the distribution of composite channel is obtained as a Gamma distribution. The parameters of the approximated Gamma distribution are derived in terms of the scale parameter and spread parameter of Nakagami- <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> random vectors. The approximated Gamma distribution is validated using Monte-Carlo simulations and found to be closely following the actual distribution of the composite channel coefficient. Using the approximation, closed form expressions of the performance metrics such as symbol error probability (SEP), outage probability and average channel capacity are derived and validated.