Energy Efficiency Optimization for CR-Enabled Integrated Terrestrial and NTNs with BD-RIS

This paper presents a novel framework for cognitive radio (CR)-enabled integrated terrestrial and non- terrestrial networks (ITNTNs), comprising a primary low-Earth-orbit (LEO) satellite network and a secondary terres- trial network. In particular, a beyond-diagonal reconfigurable intelligent surface (BD-RIS) mounted secondary base station (BS) reuses the same spectrum to communicate with the secondary user. The proposed framework improves the energy efficiency of the secondary network while ensuring that the interference temperature threshold of the primary LEO network is not violated. The joint optimization of BS power allocation and BD-RIS phase shifts is considered, which results in a highly nonconvex problem. To address this challenge, the Dinkelbach method is first employed to transform the fractional objective function, followed by the development of an alternating optimization strategy. Specifically, the BS power allocation is optimized using the Lagrangian method with Karush-Kuhn-Tucker (KKT) conditions, while the BD- RIS phase shifts are updated through manifold optimization techniques. Numerical results demonstrate that the proposed BD-RIS framework performs better than conventional diagonal RIS (D-RIS) configurations in terms of energy and spectral efficiency, highlighting its potential to enable green, adaptive, and high-capacity 6G ITNTN deployments.