Beyond Diagonal RIS Enhanced Cognitive Radio Enabled Multilayer Non-Terrestrial Networks
Wali Ullah Khan, Chandan Kumar Sheemar, Eva Lagunas, Symeon Chatzinotas
TL;DR
The paper studies BD-RIS-enabled cognitive radio in a multilayer NTN setting with a primary LEO link and a secondary HAPS link, formulating a non-convex joint optimization to maximize the secondary rate under PU interference constraints, with $R_s = \log_2(1+\gamma_s)$ and $\gamma_s = \frac{|\mathbf{h}\boldsymbol{\Phi}|^2 P_s}{\sigma^2+|f|^2 Q_p}$ under $|\mathbf{g}\boldsymbol{\Phi}|^2 P_s \le I_{\text{th}}$ and $\boldsymbol{\Phi}\boldsymbol{\Phi}^H = \mathbf{I}_M$. It decomposes the problem via alternating optimization into power allocation, solved by a water-filling expression $P_s^* = \min \left( \left[\frac{1}{\lambda} - \frac{\sigma^2+|f|^2 Q_p}{|\mathbf{h}\boldsymbol{\Phi}|^2}\right]^+, P_{\max} \right)$ with $\lambda = |\mathbf{g}\boldsymbol{\Phi}|^2 / I_{\text{th}}$, and BD-RIS design via Riemannian optimization on the Stiefel manifold with an SVD-based projection. Results indicate BD-RIS yields higher spectral efficiency than diagonal RIS across scenarios, with gains increasing as the BD-RIS size $M$ grows and under higher $I_{\text{th}}$, demonstrating enhanced beamforming and interference management. The work demonstrates BD-RIS's practical potential for coordinated terrestrial and non-terrestrial networks, enabling more reliable and efficient spectrum sharing in 6G-era NTN deployments.
Abstract
Beyond diagonal reconfigurable intelligent surfaces (BD-RIS) have emerged as a transformative technology for enhancing wireless communication by intelligently manipulating the propagation environment. Its interconnected elements offer enhanced control over signal redirection, making it a promising solution for integrated terrestrial and non-terrestrial networks (NTNs). This paper explores the potential of BD-RIS in improving cognitive radio enabled multilayer non-terrestrial networks. We formulate a joint optimization problem that maximizes the achievable spectral efficiency by optimizing BD-RIS phase shifts and secondary transmitter power allocation while controlling the interference temperature from the secondary network to the primary network. To solve this problem efficiently, we decouple the original problem and propose a novel solution based on an alternating optimization approach. Simulation results demonstrate the effectiveness of BD-RIS in cognitive radio enabled multilayer NTNs.