Dimensionality Reduction of Sparse Wireless Channel Based on Spatial Geometrical Structure of RIS Assisted Communication System

Reconfigurable Intelligent Surfaces (RIS) makes the channel more controllable by manipulating the propagation environment, so that wireless medium becomes smart when compared to conventional wireless communication system. In this study dataset from SPCUP 2021 is considered for a communication system involving two dimensional RIS consisting of
$N_{V}$
reflecting elements vertically and
$N_{H}$
elements horizontally each operating in binary state. When operating with fewer number of configurations the system becomes underdetermined which makes it difficult to estimate channel based on received signals. Hence it is required to reduce the dimension in the channel by finding the spatial geometry of RIS depending upon the similarities in the channel coefficients. Based on the simulations carried out in MATLAB it is concluded that square geometry (
$N_{V}=N_{H}$
)) is more preferable compared to rectangular geometry (
$N_{V}\neq N_{H}$
) since it exhibits periodicity in the channel coefficient.