Performance Analysis of IRS-Assisted Networks with Product-Distance

In intelligent reflecting surface (IRS) assisted networks, most works select collaborative IRS only based on the nearest distance without considering the joint influence of double path loss. This paper proposes a tractable model of product-distance association in IRS-assisted networks, where the Cassini oval is leveraged to characterize the IRS association mechanism theoretically, and the system coverage probability is analyzed by stochastic geometry. Specifically, modeling the product-distance of IRS by the mathematical model of the Cassini curve and considering the physical limitations of the half-space reflection in IRS, the probability density function of the minimum product-distance of IRS that can successfully reflect the signal is derived by approximating the area of Cassini oval. Furthermore, a semi-closed expression of the coverage probability is obtained under Rician fading through the Gamma approximation of expected signal power and the Laplace transform of interference power. In addition, the analysis results indicate a trade-off between the number of IRS elements deployed in the network and the density of base stations, and the tendency of this trade-off changes with IRS density. The numerical results reveal the optimal coverage performance based on product-distance association is 28.8% higher than that of nearest-distance-based association.