Beyond Diagonal RIS for ISAC Network: Statistical Analysis and Network Parameter Estimation

This paper investigates the use of beyond diagonal reconfigurable intelligent surface (BD-RIS) with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$N$</tex> elements to advance integrated sensing and communication (ISAC). We address a key gap in the statistical characterizations of the radar signal-to-noise ratio (SNR) and the communication signal-to-interference-plus-noise ratio (SINR) by deriving tractable closedform cumulative distribution functions (CDFs) for these metrics. Our approach maximizes the radar SNR by jointly configuring radar beamforming and BD-RIS phase shifts. Subsequently, zeroforcing is adopted to mitigate user interference, enhancing the communication SINR. To meet ISAC outage requirements, we propose an analytically-driven successive non-inversion sampling (SNIS) algorithm for estimating network parameters satisfying network outage constraints. Numerical results illustrate the accuracy of the derived CDFs and demonstrate the effectiveness of the proposed SNIS algorithm.