We study channel estimation for a beyond diagonal reconfigurable intelligent surface (BD-RIS) aided multiple input single output system. We first describe the channel estimation strategy based on the least square (LS) method, derive the mean square error (MSE) of the LS estimator, and formulate the BD-RIS design problem that minimizes the estimation MSE with unique constraints induced by group-connected architectures of BD-RIS. Then, we propose an efficient BD-RIS design which theoretically guarantees to achieve the MSE lower bound. Finally, we provide simulation results to verify the effectiveness of the proposed channel estimation scheme.

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