Deep Wavelet Scattering Networks for Robust Wi-Fi CSI Vital Sign Separation Under Multipath Interference and Non-Stationary Dynamics: Theory, Algorithms, and Real-Time Implementation

Multipath interference and non-stationary channel dynamics severely degrade Wi-Fi CSI-based vital sign monitoring. This paper introduces Deep Wavelet Scattering Networks (DWSN), integrating multi-resolution wavelet scattering transforms with deep convolutional separation layers and path signature normalization. Extending the wavelet-domain decoupling framework, DWSN achieves translation/deformation invariance through second-order scattering coefficients while learning non linear separation boundaries. Rigorous theoretical analysis derives scattering stability bounds under Lipschitz-continuous multipath perturbations (O(ϵlog(1/ϵ))), establishing >32 dB cross-talk attenuation. Extensive experiments on 200 synthetic CSI traces (3–12 Rayleigh paths, SNR: 0–20 dB) demonstrate 67% CTR improvement over EMD, 58% MAEreduction (0.7 BrPM RR, 1.6 BPM HR at SNR=5dB), and 2.3× robustness to HR/RR transitions vs. baseline wavelet MRA. Real-time ESP32 deployment achieves 68 ms latency via tensorized scattering operators. No human subjects were involved; all validation uses synthetic physiological models.