Low-Overhead Channel Estimation for Beyond Diagonal Reconfigurable Intelligent Surface Aided Single-User Communication

We explore channel estimation for a beyond diagonal reconfigurable intelligent surface (BD-RIS) aided single-user communication system. We first reveal a pivotal property within the cascaded channel that can be leveraged to dramatically reduce the channel estimation overhead, which, to the best of our knowledge, has not been exploited in existing literature. Owing to the interconnections among the BD-RIS elements, the cascaded channels associated to different elements share a common RIS-BS channel component. Consequently, the coefficients in these cascaded channels exhibit a high degree of correlation, enabling a substantial reduction in the number of independent channel coefficients to be estimated. Building upon this finding, we propose a novel two-phase channel estimation strategy in the uplink communication. Specifically, in Phase I, the cascaded channel associated to the reference BD-RIS element is estimated; while in Phase II, the correlation coefficients of the other BD-RIS elements are estimated. Under this strategy, it is theoretically demonstrated that the number of time instants required for perfect channel estimation is merely twice the number of BD-RIS elements in the ideal case without BS noise. Furthermore, in the case with BS noise, we show by simulation that the channel estimation error under our proposed scheme is markedly lower than that of the least square (LS) estimation scheme proposed in [1], attributed to the exploitation of the channel's inherent property.