Individual Channel Estimation for Beyond Diagonal Reconfigurable Intelligent Surfaces

Beyond Diagonal Reconfigurable Intelligent Surfaces (BD-RIS) has emerged as a promising evolution of RIS technology. By enabling interconnections between RIS elements, BD-RIS architectures offer greater flexibility in wave manipulation compared to traditional diagonal RIS designs. However, these interconnections introduce new research challenges for channel estimation, making existing approaches developed for conventional diagonal RISs ineffective and significantly increasing pilot overhead. To address these challenges, we propose a novel individual channel estimation framework that separately estimates the BS-RIS channel, which typically remains static over time, and the RIS-user channels, which vary rapidly due to user mobility. Specifically, we develop a full-duplex (FD) approach to estimate the BS-RIS channel by leveraging its inherent sparsity. Following this, the RIS-user channels are estimated using a least squares (LS) approach. Numerical results demonstrate that the proposed framework achieves significantly higher channel estimation accuracy, particularly when the number of RIS elements is large, while substantially reducing pilot overhead compared to conventional cascaded channel estimation methods.