  In this paper, we present an advanced model for Channel State Information
(CSI) tracking, leveraging a dynamical system approach to adapt CSI dynamically
based on exogenous contextual information. This methodology allows for
continuous updates to the Channel Knowledge Map (CKM), enhancing communication
reliability and responsiveness in dynamic environments. To generate realistic
and comprehensive datasets for training and evaluation, we developed a new
MATLAB simulator that models radio wave propagation in urban environments. We
address the challenge of real-time CKM adaptation using online learning of the
Koopman operator, a technique that forecasts channel behaviour by exploiting
dynamical system properties. Our approach supports real-time updates with high
accuracy and efficiency, as demonstrated by experiments with varying window
sizes for the Koopman Autoencoder model. A window size of 100 was found to
offer the best balance between prediction accuracy (RMSE: 1.8323 +- 1.1071,
MAE: 0.3780 +- 0.2221) and computational efficiency (training time: 231.1 +-
82.5 ms, prediction time: 109.0 +- 55.7 ms). Additionally, we introduce a
moving window mechanism to address privacy and security concerns by updating
the Koopman operator within the window and purging input data thereafter,
minimising data retention and storage risks. This ensures the CKM remains
accurate and relevant while maintaining stringent data privacy standards. Our
findings suggest that this approach can significantly improve the resilience
and security of communication systems, making them highly adaptable to
environmental changes without compromising user privacy.
