Orthogonal Complement-Driven Channel Estimation for Multi-RIS Wireless Systems

Recent breakthroughs in reconfigurable intelligent surface (RIS) technology are reshaping next-generation wireless networks. In multi-RIS deployments, however, the received signal is a superposition of numerous single- and double-reflection paths, some arrive from different angles while others overlap at the same angle, which makes channel estimation challenging. Conventional approaches attempt to separate these paths by sequentially turning each RIS on and off, but the required switching overhead grows rapidly with the number of channels and becomes impractical. To overcome this limitation, we propose a two-stage channel estimation method for multi-RIS systems. In the first stage, the received signal is projected onto angle subspaces to separate components from different directions. In the second stage, the remaining components that share the same angle are resolved by exploiting the reflection coefficient design of the RISs. Both stages operate on the same superposed received signal, enabling path separation without exhaustive switching. The method further extends beyond the two-RIS case to an arbitrary number of RISs. Simulation results demonstrate that the proposed scheme maintains estimation accuracy while reducing switching overhead, thereby providing a practical solution for large-scale multi-RIS deployments in future wireless networks.