Nonlinear-Feature K-R Receiver for LiFi: Physics-Driven Residual Correction with Closed-Form Per-Slot Training

We propose the Nonlinear-Feature Learned K-R (NL-feat K-R) receiver , a physics-driven architecture for Light Fidelity (LiFi) systems based on IEEE 802.11bb. The receiver decomposes equalization into a physics-based K step (MMSE optical equalization) and a data-driven R step that trains a two-layer MLP per 0.5 ms slot from available pilot symbols using closed-form least squares — requiring no backpropagation and no offline dataset. The R step employs a 9-dimensional nonlinear feature expansion including the Saleh polynomial terms y² and y3 that directly capture the quadratic and cubic LED nonlinearity structure, enabling correction of both quantisation floor noise (γₚ) and implicit channel-error residuals (γᴄᴇ, the dominant gain). The proposed method is validated across 12 simulation scenarios (8,000 Monte Carlo trials per scenario): ADC bit-width sweep (1–8 bit), full optical SNR curve (−5 to 40 dB), four channel models (LoS, reflection, NLOS, Rician), imperfect CSI with pointing errors, feature ablation, mobility (0–5 km/h), train/test SNR generalization, pilot overhead sensitivity (Np = 8 to 256), LED nonlinearity strength sweep, and end-to-end BLER with LDPC [18] (CR = 2/3). Against MMSE, the proposed receiver achieves SE gains of +0.79 bps/Hz at 4-bit ADC and +4.82 bps/Hz at 1-bit ADC (all p < 0.001). Unlike OAMP-Net, which degrades outside its training SNR due to the LED Saleh polynomial violating the Gaussian Onsager assumption, K-R adapts per slot with no training SNR dependence, maintaining stable performance from −5 to 40 dB. Pilot sensitivity confirms deployment viability with as few as Np = 8 pilots, and SE gain increases monotonically with LED distortion strength, confirming the receiver exploits structured Saleh nonlinearity rather than noise.