Delay-Doppler Domain Feature Extraction for Explainable Wi-Fi Activity Recognition via SVM

Joint Communication and Sensing (JCAS) activity recognition applications often operate directly on the Channel State Information (CSI) time series through Neural Networks. This work proposes the use of the Symplectic Fourier Transform coupled with a linear Support Vector Machine classifier, yielding a computationally light and explainable methodology. CSI samples are mapped onto the Delay-Doppler (DD) domain, where the variations in the propagation environment due to human motion manifest as changes in multipath components and Doppler shifts with direct physical interpretation. From short DD-domain CSI blocks, we extract 11 features describing energy distribution, delay and Doppler statistics, entropy, and dominant scattering components. The resulting low-dimensional feature vectors are classified by a linear SVM. The methodology is validated on two independent IEEE 802.11ax Wi-Fi datasets collected during normal indoor activities under different Line of Sight conditions. Results show that DD-based feature extraction combined with a linear SVM achieves consistently high activity recognition accuracy in real life scenarios, even when relying solely on CSI extracted from standard Wi-Fi beacon frames. The approach proves robust across frame rates and propagation conditions while maintaining low computational complexity and full physical interpretability. Moreover, it yields better results than state of the art AI-based classification over the same experiments. The results support the feasibility of lightweight, explainable JCAS applications using commercial Wi-Fi hardware without dedicated sensing transmissions, posing DD feature extraction as a competitor for Deep Learning-based CSI processing.