Beyond Diagonal RIS Design for Parameter Estimation With and Without Eavesdropping

In this letter, we study the transmission of a complex-valued parameter vector from a transmitter to an intended receiver in the presence or absence of an eavesdropper. Direct links are blocked, and communication is enabled via a beyond-diagonal reconfigurable intelligent surface (BD-RIS). Extending prior work on diagonal RIS, we incorporate BD-RIS and quantify its impact on estimation performance at the intended receiver, measured by the trace of the Fisher information matrix (FIM), equivalently, the average Fisher information, while constraining the eavesdropper’s estimation capability. We propose optimization algorithms for the BD-RIS response and demonstrate their effectiveness. Numerical results show that BD-RIS offers significant gains over conventional RIS. To the best of our knowledge, this is the first study to address secure parameter estimation under BD-RIS architectures with both closed-form and efficient algorithmic solutions.