Spatially Correlated Dual Hop RIS Aided Next Generation Wireless Systems: An Outage Perspective

Abstract

Authors 1 & 2 contributed equally. We thank the management of Thiagarajar College of Engineering, Madurai for their constant support.

BER analysis of tightly packed planar RIS system using the level of spatial correlation and discrete phase shifter

“…The statistical distribution fits and their corresponding range of diversity factors are tabulated in Table 3. If an ideal continuous phase shifter is employed, mean of the spatially correlated summation term 18,22 and is defined as…”

“…$$ Due to tightly packed RIS array geometry of RIS, spatial correlation is introduced. Hence, for a large $$$ L $$$, , where $$$ \mathbf{R} $$$ is $$$ N\times N $$$ covariance matrix of $$$ \mathbf{h} $$$, defined as, 18 $$$$ \mathbf{R}=\left(\begin{array}{ccccc}1& {\rho}_{1,2}& {\rho}_{1,3}& \cdots & {\rho}_{1,N}\\ {}{\rho}_{2,1}& 1& {\rho}_{2,3}& \cdots & {\rho}_{2,N}\\ {}\vdots & & & & \\ {}{\rho}_{N,1}& {\rho}_{N,2}& {\rho}_{N,3}& \cdots & 1\end{array}\right), $$$$ where $$$$ {\rho}_{n,m}=\operatorname{sinc}\left(2\left\Vert {\mathbf{u}}_n-{\mathbf{u}}_m\right\Vert \right). $$$$ …”

“…The statistical distribution fits and their corresponding range of diversity factors are tabulated in Table 3. If an ideal continuous phase shifter is employed, mean of the spatially correlated summation term $$$ \left|{\sum}_{i=1}^N{\alpha}_i{e}^{j\left({\phi}_i-{\vartheta}_i\right)}\right| $$$ remains unaffected 18,22 and is defined as $$$$ \boldsymbol{\mu} =N\sqrt{d_H{d}_V\pi /4}. $$$$ On the other hand, the variance of $$$ \left|{\sum}_{i=1}^N{\alpha}_i{e}^{j\left({\phi}_i-{\vartheta}_i\right)}\right| $$$ is significantly impacted due to spatial correlation.…”

“…17 Our previous work extensively dealt with algorithms in simulating correlated fading channels and the impact of spatial correlation in outage performance metric. 18 In this work, according to majorization theory, 19 the level of spatial correlation is quantified as the diversity factor of multiple antenna wireless system. The significant contributions of this article are as follows:…”

“…In a recent paper, distribution of channel gain is modeled as inverse Gaussian model and outage probability of RIS assisted non orthogonal power domain systems are derived 17 . Our previous work extensively dealt with algorithms in simulating correlated fading channels and the impact of spatial correlation in outage performance metric 18 …”