Physics-Informed Expectation-Maximization for Enhanced Gaussian Signal Detection in Dynamic ISAC Environments

الملخص

Integrated Sensing and Communication (ISAC) sys- tems  are  pivotal  for  6G  networks,  demanding  robust  signal detection and highly accurate parameter estimation in complex, dynamic   environments.   Traditional   Expectation-Maximization (EM) algorithms, while effective for Gaussian signal parameter estimation, often exhibit slow convergence and suboptimal per- formance in low Signal-to-Noise Ratio (SNR) regimes, especially when  parameters  are  unknown  and  rapidly  changing.  This paper introduces a novel Adaptive Physics-Informed Expectation- Maximization (API-EM) algorithm specifically designed for dy- namic ISAC scenarios. Our key innovation lies in dynamically ad- justing the physical regularization weight within the EM M-step, based on real-time channel state information (CSI) or estimated environmental  uncertainty.  This  adaptive  approach  allows  the algorithm to optimally balance data-driven estimation with physi- cal priors, significantly enhancing the robustness and convergence speed  of parameter  estimation  for  unknown  signal  amplitudes and noise variances. We integrate this API-EM estimator with a Generalized Likelihood Ratio Test (GLRT) to form an API-EM- GLRT detector. Comprehensive simulations demonstrate that the proposed API-EM-GLRT significantly outperforms static PI-EM and traditional EM-GLRT methods, achieving superior detection probability and substantially lower Mean Squared Error (MSE) in parameter estimation across a wider range of dynamic SNR and environmental conditions.