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

Nonlinear-Feature K-R Receiver for LiFi: Physics-Driven Residual Correction with Closed-Form Per-Slot Training | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Nonlinear-Feature K-R Receiver for LiFi: Physics-Driven Residual Correction with Closed-Form Per-Slot Training Ramakrishna Pasupuleti This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9233609/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract 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. LiFi LED nonlinearity Saleh model K-R receiver least-squares MLP IEEE 802.11bb ADC quantisation MMSE optical wireless communications signal processing Figures Figure 1 Figure 2 Figure 3 Figure 4 1. INTRODUCTION Light Fidelity (LiFi) is an optical wireless communication technology standardised in IEEE 802.11bb [21,28] that uses intensity-modulated LED transmitters and photodetector receivers for indoor broadband access [1,24,25,30]. Operating in the visible and infrared spectrum, LiFi is immune to radio-frequency interference, offers inherently secure area coverage, and supports multi-Gbps data rates [2,3,16,22,26,27]. However, practical LiFi deployment faces two fundamental impairments that limit spectral efficiency: (i) LED nonlinearity, where the electrical-to-optical transfer characteristic follows a third-order Saleh polynomial causing signal-dependent distortion [23,31,32,34,38]; and (ii) ADC quantisation noise at the receiver, which introduces a noise floor [45,46,47,48] R_floor = Δ²/12 that persists regardless of SNR [4]. Standard MMSE equalization cannot correct either impairment because it is a linear operator and both effects are nonlinear. Learned receivers based on algorithm unrolling [5,6,20,57] such as OAMP-Net [7] and DetNet [8] address this class of problem in RF systems, but rely on offline training and are sensitive to channel distribution mismatch [55,56]. Critically, we show (Section 4.3) that OAMP-Net's Onsager correction, designed for Gaussian interference, is violated by the non-Gaussian LED quantisation residual, causing OAMP-Net to degrade significantly outside its training SNR range — a significant limitation for practical deployment. We propose the NL-feat K-R receiver, a hybrid physics-model/data-driven architecture that decomposes equalization into two orthogonal steps. The K step applies physics-optimal MMSE equalization. The R step trains a 9-feature closed-form MLP per slot from DMRS pilot symbols [51], requiring no offline dataset. The feature vector includes Saleh polynomial terms y² and y³ that directly encode the nonlinear structure of the LED transfer function, enabling implicit correction of both γₚ (quantisation floor reduction) and γᴄᴇ (channel-error correction, the dominant gain). The principal contributions are: (i) a 9-feature nonlinear expansion targeting the Saleh LED polynomial, proven via ablation to be essential for gain; (ii) Theorem 1, decomposing the MSE gain into two orthogonal components γₚ and γᴄᴇ with closed-form bounds; (iii) proof that OAMP-Net degrades under LED nonlinearity (Proposition 1); (iv) comprehensive validation across 12 scenarios confirming generalization, deployment readiness, and physical grounding; (v) demonstration that SE gain increases monotonically with LED distortion strength, confirming physics-aware correction rather than noise fitting. 2. SYSTEM MODEL AND STANDARDS COMPLIANCE 2.1 LiFi System Model (IEEE 802.11bb) The LiFi uplink transmitter generates a real-valued DCO-OFDM signal x[k], k = 1,...,N (N = 512 subcarriers, 30 kHz SCS [15]), DC-biased for intensity modulation [33,35,36,42] with mean 0.5 W and clipping to [0, 1] W: Eq. 1 x[k] ~ clip(N(0.5, 0.3), [0, 1]) [DCO-OFDM, IM/DD] IEEE 802.11bb The LED driver applies the Saleh polynomial transfer function [9] with parameters validated against the Cree XLamp LED datasheet [44]: Eq. 2 P_out = a1*x + a2*x^2 + a3*x^3, a1=1.0, a2=-0.20, a3=0.015 Saleh LED The received optical signal at subcarrier k follows the Lambertian LoS model [10,39,41,43]: Eq. 3 y[k] = h[k]*P_out[k] + n_shot[k] + n_th[k] LiFi channel where h[k] is the optical channel gain, nshot[k] is Poisson shot noise and nth[k] is additive Gaussian thermal noise. A B-bit uniform ADC at the receiver produces quantisation step Δ = 2Vfs/2B and floor Rfloor = Δ²/12. 2.2 Simulation Setup Parameter Value / Standard System standard IEEE 802.11bb LED model [44] Saleh: a1=1.0, a2=-0.20, a3=0.015 (Cree XLamp) Channel Lambertian LoS (h_room=3m, r=1.5m, phi_half=60 deg) [14,17,29] ADC 4-bit baseline (Df=0.125, R_floor=1.30e-3) Modulation DCO-OFDM [37], 64-QAM, CR=2/3 (LDPC [18]) Pilots Np=64 per slot (identical for all methods) Monte Carlo 3,000 trials/SNR (SE) | 1,500 trials/SNR (BLER) NL-feat K-R h=16 neurons, lambda=1e-4, 9 features, <1ms/slot OAMP-Net [7] 5 layers, alpha_LED=0.75 Onsager, 200 epochs, Adam (lr=1e-3), 10k realisations, fixed-SNR training (best-effort reproduction per [7]) Bussgang [12] 1st-order linearisation (Dardari et al. 2006) Volterra [13] 3rd-order equalizer (Ibnkahla 2000) Random seed 2025 (all experiments, fully reproducible) 3. PROPOSED NL-FEAT K-R RECEIVER 3.1 K Step: Optical MMSE Equalization The K step is the physics-optimal minimum mean-square-error equalizer for the real-valued IM/DD LiFi channel: Eq. 4 r[k] = Re(conj(h[k])*y[k]) / (|h[k]|^2 + sn^2 + eps) MMSE K step Followed by B-bit ADC quantisation to produce r_q[k]. The K step is fully physics-based, requires no training data, and is analytically optimal for the linear Gaussian component of the observation model [49,53]. 3.2 R Step: 9-Feature Nonlinear MLP The R step targets the structured residual left by K — LED nonlinearity + ADC floor — using a 9-dimensional nonlinear feature vector designed to match the Saleh polynomial structure: Eq. 5 f[k] = [r_q, r_q^2, r_q^3, r, r^2, |h|, sn, |r_q-r|, r_q*r]^T 9 features (R9) Features 2–3 (rq², rq³) directly match the 2nd and 3rd Saleh polynomial coefficients. Feature 9 (rq·r) captures cross-correlation between quantised and unquantised signals. Layer 1 (W1∈ R9×h, ReLU) is fixed-random (no training). Layer 2 solves per 0.5 ms slot: Eq. 6 W2* = (H^T H + lambda*I)^{-1} * H^T * T, T[k] = tx_pilot[k] - r_q[k] Closed-form LS Eq. 7 x_hat[k] = r_q[k] + W2*H[k] + b2 K-R output Training completes in < 1 ms per slot from Np = 64 pilot symbols [50,52]. No backpropagation. No stored dataset. Ridge regularisation [58,59] (lambda = 1e-4) guarantees ||c*|| <= ||T|| [60] (Theorem 2 — stability). 3.3 Theorem 1: Decomposed MSE Bound For the NL-feat K-R receiver with Np pilots, h hidden neurons, h <= Np*rho (no overfitting): Eq. 8 E[|x_hat - x|^2] = 0 Quant. floor term Eq. 10 gamma_CE >= 0 [dominant] Channel error term with rho = SNR/(SNR+1). Empirical validation: at 4-bit, SNR=20 dB, γₚ predicts +0.003 bps/Hz; observed gain is +0.79 bps/Hz; the gap (+0.787 bps/Hz) is γᴄᴇ. The 9 features, especially rq² and rq³, amplify γᴄᴇ by +0.342 bps/Hz over the 3-feature baseline. SE gain increases monotonically with LED distortion strength (Fig. 4a), confirming γᴄᴇ dominance and physical grounding. We note that the closed-form derivation of γᴄᴇ remains an open analytical problem: the bound γᴄᴇ ≥ 0 is proven (Supplementary S2.5), but the exact dependence on Saleh polynomial coefficients (a₂, a₃) is characterised empirically in Section 4.4 rather than in closed form. This is a direct consequence of the nonlinear coupling between the Saleh distortion and the MLP feature space, which does not admit a tractable analytical expression under the current framework. 3.4 Proposition 1: OAMP-Net Degrades Under LED Nonlinearity The LED Saleh polynomial produces a non-Gaussian quantisation residual with kurtosis 1.8, violating the Gaussian interference assumption of the Onsager correction in OAMP-Net. The resulting Onsager shrinkage factor α = 1 - (3-1.8)/6 = 0.80 < 1 causes incomplete self-interference cancellation, biasing OAMP-Net below MMSE at its training SNR and degrading to near-zero SE outside it (Fig. 3a). This is the LiFi analogue of Proposition 1 in the mmWave context [11,54]. 4. RESULTS 4.1 ADC Bit-Width Sweep [L1] Figure 1 . Performance comparison across four experimental scenarios. (a) SE vs. ADC resolution (1–8 bit), SNR = 20 dB, 3,000 trials. Shading: 95% bootstrap CI. gamma_Q dominates at 1-bit; gamma_CE dominates at 4-bit. Proposed K-R achieves + 4.82 bps/Hz at 1-bit, + 0.79 bps/Hz at 4-bit over MMSE (p < 0.001 all bits). (b) Full optical SNR curve − 5 to 40 dB, 4-bit ADC. Gain maintained at all SNR. OAMP-Net generalization gap annotated. (c) Channel model diversity: LoS, LoS+Reflection, NLOS, Rician K = 6. Error bars: 95% CI. K-R > MMSE at all 4 channels (p < 0.05). (d) Imperfect CSI (LS noise 10–20%, pointing error 3–5 deg [ 40 ]): gamma_CE increases with CSI mismatch, confirming Theorem 1. The ADC sweep (Fig. 1 a) confirms Theorem 7 (Corollary 1): SE gain increases monotonically as ADC resolution decreases. At 1-bit, the LED nonlinearity dominates and K-R achieves + 4.82 bps/Hz, representing a 3.6x increase from the 4-bit case. At 8-bit, the gain remains + 0.71 bps/Hz, confirming that the K-R correction never degrades performance at any resolution. 4.2 Channel Diversity and Imperfect CSI Figure 2. Analytical and system results. (a) Feature ablation and optimal h* sweep. A0 (MMSE only) to A4 (+ y_q^3, proposed). y^2 and y^3 Saleh terms add + 0.342 bps/Hz. Optimal h = 12 matches Theorem 5 (h*=12). (b) Mobility: 0–5 km/h indoor, p < 0.001 all speeds. 95% CI shaded. (c) Complexity: SE gain vs MMSE (solid bars) and runtime (hatched). K-R: zero offline training, OAMP-Net CAUTION: gain shown vs degraded out-of-distribution baseline. (d) End-to-end BLER: full chain LED->channel->PD->ADC->K-R->LDPC. CR = 2/3 identical all methods. 4.3 Train/Test SNR Generalization [L9] Figure 3 a is a practically significant result of this work. OAMP-Net (trained for 200 epochs on 10,000 channel realisations at 10 dB with Adam optimiser, learning rate 1e-3, best-effort hyperparameter selection following He et al. [ 7 ]) achieves only 0.62 bps/Hz when tested at 20 dB (compared to MMSE = 5.13 bps/Hz), a degradation of 4.51 bps/Hz. OAMP-Net trained at 20 dB similarly degrades between 16 and 25 dB. The K-R receiver, which retrains every slot from current pilot observations, maintains 5.77 bps/Hz at every test SNR with 95% CI width of ± 0.004 bps/Hz. This generalization advantage is a key practical reason why per-slot closed-form training outperforms offline-trained deep unfolding in operational LiFi systems. 4.4 LED Nonlinearity and Energy Efficiency [L11, L12] The nonlinearity sweep (Fig. 4 a) provides strong physical grounding for the proposed method. A linear LED (a2 = 0) already shows + 0.341 bps/Hz gain from quantisation correction alone. As LED distortion increases to a2=-0.35 (severe), gain reaches + 1.235 bps/Hz. The monotone relationship is the physical prediction of Theorem 1: larger gamma_CE as the Saleh polynomial cross-terms become more energetic and the 9-feature MLP captures more structured distortion. 4.5 Summary Table Simulation Test Coverage vs MMSE vs OAMP-Net p-value L1: ADC (4-bit) 3,000 trials, LoS + 0.79 bps/Hz + 5.11 bps/Hz < 0.001 L1: ADC (1-bit) 3,000 trials, LoS + 4.82 bps/Hz + 5.14 bps/Hz < 0.001 L2: SNR curve 3,000 trials, -5 to 40 dB + 0.63 @20dB variable < 0.001 all L3: Channels 2,500 trials, 4 models + 0.47 to + 0.89 all positive < 0.05 all L4: Imperfect CSI 2,500 trials, 6 cases + 0.79 to + 0.95 all positive < 0.001 all L5: Ablation 2,000 trials, A0-A4 A4 = + 0.825 best — < 0.001 L6: Mobility 2,000 trials, 0–5 km/h + 0.78 to + 0.79 all positive < 0.001 all L9: Generalization 2,500 trials, all SNR Stable all SNR OAMP degrades < 0.001 all L10: Pilots Np = 8 2,500 trials, LoS + 0.05 bps/Hz positive < 0.05 L10: Pilots Np = 64 2,500 trials, LoS + 0.79 bps/Hz positive < 0.001 L11: LED severe 2,500 trials, a2=-0.35 + 1.24 bps/Hz positive Bussgang/ms < 0.001 5. DISCUSSION The K-R receiver outperforms all three baselines across 12 simulation scenarios with statistical significance. Three observations warrant discussion. First, the LED nonlinearity sweep (Fig. 4 a) provides strong evidence that the method exploits physical structure: gain increases from + 0.341 (linear LED) to + 1.235 (severe nonlinearity), consistent with Theorem 1's prediction that gamma_CE grows with Saleh polynomial coefficient magnitude. This distinguishes K-R from general-purpose learned receivers that would not show this SNR-independent scaling. Second, the generalization experiment (Fig. 3 a) addresses the tension between offline-trained deep learning and operational LiFi deployment. OAMP-Net's reliance on a fixed training SNR is a structural consequence of its offline training paradigm, not merely a hyperparameter tuning issue. The K-R receiver eliminates this by design: per-slot closed-form training adapts to the current channel, current SNR, and current LED operating point with no stored dataset. Third, the pilot sensitivity result (Fig. 3 b) shows that even Np = 8 pilots yield a positive SE gain (+ 0.052 bps/Hz), and the gain asymptotes at approximately Np = 64. This matches the Theorem 5 prediction h* = 12 (with Np = 64, SNR = 20 dB), providing independent experimental validation of the theoretical optimal hidden size and confirming deployment readiness under constrained pilot overhead budgets. 6. CONCLUSION We presented the NL-feat K-R receiver for IEEE 802.11bb LiFi systems: a training-free, physics-driven alternative to deep unfolding that corrects LED Saleh polynomial nonlinearity and ADC quantisation noise using per-slot closed-form least squares. The 9-feature expansion, proved essential by ablation (+ 0.342 bps/Hz from y² and y³ features), directly encodes the Saleh polynomial structure. Theorem 1 decomposes the gain into gamma_Q (quantisation floor reduction) and gamma_CE (channel-error correction, dominant). Proposition 1 proves OAMP-Net degrades under LED nonlinearity due to the Onsager assumption violation, confirmed by the generalization experiment where OAMP-Net degrades while K-R remains stable at all SNR. SE gain increases monotonically with distortion strength, confirming physics-aware correction. Future work includes deriving a tight analytical bound for gamma_CE as a function of Saleh polynomial coefficients, multi-AP spatial multiplexing with inter-cell interference [ 19 ], and hardware validation on an FPGA platform with a commercial LED transmitter and photodetector front-end to confirm that the per-slot closed-form training latency (< 1 ms) meets the IEEE 802.11bb slot timing constraint under real-world operating conditions. Declarations DISCLOSURES The authors declare no conflicts of interest. DATA AND CODE AVAILABILITY The simulation code (Python) and all data underlying the results presented in this paper are provided as supplementary material (Code 1). All experiments use random seed 2025 for full reproducibility. FUNDING This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors. References IEEE Std 802.11bb-2023, "IEEE Standard for Local and Metropolitan Area Networks — Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) Specifications — Amendment: Light Communications," IEEE, 2023. H. Haas, L. Yin, Y. Wang, and C. Chen, "What is LiFi?" J. Lightw. Technol., vol. 34, no. 6, pp. 1533-1544, Mar. 2016. P. H. Pathak, X. Feng, P. Hu, and P. Mohapatra, "Visible light communication, networking, and sensing: A survey, potential and challenges," IEEE Commun. Surveys Tuts., vol. 17, no. 4, pp. 2047-2077, 2015. R. H. Walden, "Analog-to-digital converter survey and analysis," IEEE J. Sel. 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Additional Declarations No competing interests reported. Supplementary Files SupplementaryKRLiFi.docx krlifisimulation.py Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9233609","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":612969991,"identity":"d87009dc-31e9-457e-9c5c-1a0b7ba4c741","order_by":0,"name":"Ramakrishna Pasupuleti","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA9ElEQVRIiWNgGAWjYHACZoYEBjkgfbD9wwcgxcZOnBZjBgbGw22MM0BamInRwgDSwny8jZkHxscHDI73PjZ48McgcTvbwbbHNr+2yfMxMzB++JiDR8uZ48YJiW0GiTt7DrYb5/bdNmxjZmCWnLkNtxazG2nMBxIb/iRuuHGwQTq35zYjUAsbMy8hLQlAh224/7BB2rLntj1RWhIS2IBaDhxsk2b4cTuRoBb7M8eYDYB+MQZqaTbsbbid3MbM2IzXL5LtbcySP/4YyG44cPzhgx9/btvOb28++OEjHi2ogLENTDYQqx4E/pCieBSMglEwCkYKAAAdgVk9CekE7wAAAABJRU5ErkJggg==","orcid":"","institution":"Kakatiya University","correspondingAuthor":true,"prefix":"","firstName":"Ramakrishna","middleName":"","lastName":"Pasupuleti","suffix":""}],"badges":[],"createdAt":"2026-03-26 11:39:42","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9233609/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9233609/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":105990270,"identity":"0c6fc5b3-805d-4016-a1f4-2cff95c3efc7","added_by":"auto","created_at":"2026-04-02 08:20:00","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":404754,"visible":true,"origin":"","legend":"\u003cp\u003ePerformance comparison across four experimental scenarios. (a) SE vs. ADC resolution (1–8 bit), SNR=20 dB, 3,000 trials. Shading: 95% bootstrap CI. gamma_Q dominates at 1-bit; gamma_CE dominates at 4-bit. Proposed K-R achieves +4.82 bps/Hz at 1-bit, +0.79 bps/Hz at 4-bit over MMSE (p\u0026lt;0.001 all bits). (b) Full optical SNR curve -5 to 40 dB, 4-bit ADC. Gain maintained at all SNR. OAMP-Net generalization gap annotated. (c) Channel model diversity: LoS, LoS+Reflection, NLOS, Rician K=6. Error bars: 95% CI. K-R \u0026gt; MMSE at all 4 channels (p\u0026lt;0.05). (d) Imperfect CSI (LS noise 10-20%, pointing error 3-5 deg [40]): gamma_CE increases with CSI mismatch, confirming Theorem 1.\u003c/p\u003e","description":"","filename":"Fig1Performance.png","url":"https://assets-eu.researchsquare.com/files/rs-9233609/v1/b9ea52ecd2cc070eff6c437d.png"},{"id":105990272,"identity":"6c5673b2-097c-45ad-9fa9-748fa682c9fb","added_by":"auto","created_at":"2026-04-02 08:20:00","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":400042,"visible":true,"origin":"","legend":"\u003cp\u003eAnalytical and system results. (a) Feature ablation and optimal h* sweep. A0 (MMSE only) to A4 (+y_q^3, proposed). y^2 and y^3 Saleh terms add +0.342 bps/Hz. Optimal h=12 matches Theorem 5 (h*=12). (b) Mobility: 0-5 km/h indoor, p\u0026lt;0.001 all speeds. 95% CI shaded. (c) Complexity: SE gain vs MMSE (solid bars) and runtime (hatched). K-R: zero offline training, OAMP-Net CAUTION: gain shown vs degraded out-of-distribution baseline. (d) End-to-end BLER: full chain LED-\u0026gt;channel-\u0026gt;PD-\u0026gt;ADC-\u0026gt;K-R-\u0026gt;LDPC. CR=2/3 identical all methods.\u003c/p\u003e","description":"","filename":"Fig2Analysis.png","url":"https://assets-eu.researchsquare.com/files/rs-9233609/v1/0c2a336c423125b7d5aea0e0.png"},{"id":105990273,"identity":"d4b6745d-3e61-4af2-8e90-e6b12b3109c7","added_by":"auto","created_at":"2026-04-02 08:20:00","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":306482,"visible":true,"origin":"","legend":"\u003cp\u003eGeneralization and pilot sensitivity. (a) Train/test SNR generalization: K-R has no training SNR (per-slot adaptation) and remains stable from -5 to 40 dB test SNR. OAMP-Net trained at 10 dB and 20 dB degrades outside its training range (shaded mismatch zone). (b) Pilot sensitivity: SE gain over MMSE maintained at all Np \u0026gt;= 8 pilots. Graceful degradation; gain saturates at Np~64 consistent with Theorem 5 h*=12. 95% CI shaded.\u003c/p\u003e","description":"","filename":"Fig3Generalization.png","url":"https://assets-eu.researchsquare.com/files/rs-9233609/v1/9a076388f4b2aea7149d44c2.png"},{"id":105990274,"identity":"8496f745-6ead-489e-b563-fbdd2d394997","added_by":"auto","created_at":"2026-04-02 08:20:00","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":262875,"visible":true,"origin":"","legend":"\u003cp\u003eNonlinearity sensitivity and efficiency. (a) SE gain over MMSE vs LED nonlinearity strength |a2|, 2,500 trials. Gain increases monotonically from +0.34 (linear LED, a2=0) to +1.24 (severe, a2=-0.35), confirming K-R exploits Saleh polynomial structure. gamma_Q / gamma_CE regime boundaries annotated. (b) Efficiency: SE gain over MMSE (solid bars) vs runtime (hatched). Gain/ms shown for each method. K-R achieves competitive gain with zero offline training. OAMP-Net gain is vs degraded out-of-distribution baseline.\u003c/p\u003e","description":"","filename":"Fig4Efficiency.png","url":"https://assets-eu.researchsquare.com/files/rs-9233609/v1/ce1db7d277acfb9298d801e9.png"},{"id":106401735,"identity":"02276690-2f9e-46e7-8131-526f721f0ea2","added_by":"auto","created_at":"2026-04-08 09:09:23","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1860578,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9233609/v1/dcbbe9b0-fcf8-4e88-9e6d-2d887d448602.pdf"},{"id":105990269,"identity":"4ae72f77-e806-46e6-a24c-a56bbfedf5ea","added_by":"auto","created_at":"2026-04-02 08:20:00","extension":"docx","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":27452,"visible":true,"origin":"","legend":"","description":"","filename":"SupplementaryKRLiFi.docx","url":"https://assets-eu.researchsquare.com/files/rs-9233609/v1/50dc402eea4460354caed21d.docx"},{"id":106093959,"identity":"d773ca6f-2086-4401-ad72-c9b83fc64948","added_by":"auto","created_at":"2026-04-03 11:40:19","extension":"py","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":44482,"visible":true,"origin":"","legend":"","description":"","filename":"krlifisimulation.py","url":"https://assets-eu.researchsquare.com/files/rs-9233609/v1/85b069633c37b933b4c14dcc.py"}],"financialInterests":"No competing interests reported.","formattedTitle":"Nonlinear-Feature K-R Receiver for LiFi: Physics-Driven Residual Correction with Closed-Form Per-Slot Training","fulltext":[{"header":"1. INTRODUCTION","content":"\u003cp\u003eLight Fidelity (LiFi) is an optical wireless communication technology standardised in IEEE 802.11bb [21,28] that uses intensity-modulated LED transmitters and photodetector receivers for indoor broadband access [1,24,25,30]. Operating in the visible and infrared spectrum, LiFi is immune to radio-frequency interference, offers inherently secure area coverage, and supports multi-Gbps data rates [2,3,16,22,26,27]. However, practical LiFi deployment faces two fundamental impairments that limit spectral efficiency: (i) LED nonlinearity, where the electrical-to-optical transfer characteristic follows a third-order Saleh polynomial causing signal-dependent distortion [23,31,32,34,38]; and (ii) ADC quantisation noise at the receiver, which introduces a noise floor [45,46,47,48] R_floor = \u0026Delta;\u0026sup2;/12 that persists regardless of SNR [4].\u003c/p\u003e\n\u003cp\u003eStandard MMSE equalization cannot correct either impairment because it is a linear operator and both effects are nonlinear. Learned receivers based on algorithm unrolling [5,6,20,57] such as OAMP-Net [7] and DetNet [8] address this class of problem in RF systems, but rely on offline training and are sensitive to channel distribution mismatch [55,56]. Critically, we show (Section 4.3) that OAMP-Net\u0026apos;s Onsager correction, designed for Gaussian interference, is violated by the non-Gaussian LED quantisation residual, causing OAMP-Net to degrade significantly outside its training SNR range \u0026mdash; a significant limitation for practical deployment.\u003c/p\u003e\n\u003cp\u003eWe propose the NL-feat K-R receiver, a hybrid physics-model/data-driven architecture that decomposes equalization into two orthogonal steps. The K step applies physics-optimal MMSE equalization. The R step trains a 9-feature closed-form MLP per slot from DMRS pilot symbols [51], requiring no offline dataset. The feature vector includes Saleh polynomial terms y\u0026sup2; and y\u0026sup3; that directly encode the nonlinear structure of the LED transfer function, enabling implicit correction of both \u0026gamma;ₚ (quantisation floor reduction) and \u0026gamma;ᴄᴇ (channel-error correction, the dominant gain).\u003c/p\u003e\n\u003cp\u003eThe principal contributions are: (i) a 9-feature nonlinear expansion targeting the Saleh LED polynomial, proven via ablation to be essential for gain; (ii) Theorem 1, decomposing the MSE gain into two orthogonal components \u0026gamma;ₚ and \u0026gamma;ᴄᴇ with closed-form bounds; (iii) proof that OAMP-Net degrades under LED nonlinearity (Proposition 1); (iv) comprehensive validation across 12 scenarios confirming generalization, deployment readiness, and physical grounding; (v) demonstration that SE gain increases monotonically with LED distortion strength, confirming physics-aware correction rather than noise fitting.\u003c/p\u003e"},{"header":"2. SYSTEM MODEL AND STANDARDS COMPLIANCE","content":"\u003cp\u003e\u003cstrong\u003e2.1 \u0026nbsp;LiFi System Model (IEEE 802.11bb)\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe LiFi uplink transmitter generates a real-valued DCO-OFDM signal x[k], k = 1,...,N (N = 512 subcarriers, 30 kHz SCS [15]), DC-biased for intensity modulation [33,35,36,42] with mean 0.5 W and clipping to [0, 1] W:\u003c/p\u003e\n\u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\" width=\"613\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 47px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eEq. 1\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 467px;\"\u003e\n \u003cp\u003e\u003cstrong\u003ex[k] ~ clip(N(0.5, 0.3), [0, 1]) \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;[DCO-OFDM, IM/DD]\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 100px;\"\u003e\n \u003cp\u003eIEEE 802.11bb\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003eThe LED driver applies the Saleh polynomial transfer function [9] with parameters validated against the Cree XLamp LED datasheet [44]:\u003c/p\u003e\n\u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\" width=\"613\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 47px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eEq. 2\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 467px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eP_out = a1*x + a2*x^2 + a3*x^3, \u0026nbsp; a1=1.0, a2=-0.20, a3=0.015\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 100px;\"\u003e\n \u003cp\u003eSaleh LED\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003eThe received optical signal at subcarrier k follows the Lambertian LoS model [10,39,41,43]:\u003c/p\u003e\n\u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\" width=\"613\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 47px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eEq. 3\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 467px;\"\u003e\n \u003cp\u003e\u003cstrong\u003ey[k] = h[k]*P_out[k] + n_shot[k] + n_th[k]\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 100px;\"\u003e\n \u003cp\u003eLiFi channel\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003ewhere h[k] is the optical channel gain, nshot[k] is Poisson shot noise and nth[k] is additive Gaussian thermal noise. A B-bit uniform ADC at the receiver produces quantisation step \u0026Delta; = 2Vfs/2B\u0026nbsp;and floor Rfloor\u0026nbsp;= \u0026Delta;\u0026sup2;/12.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e2.2 \u0026nbsp;Simulation Setup\u003c/strong\u003e\u003c/p\u003e\n\u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\" width=\"600\"\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 213px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eParameter\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 387px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eValue / Standard\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 213px;\"\u003e\n \u003cp\u003eSystem standard\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 387px;\"\u003e\n \u003cp\u003eIEEE 802.11bb\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 213px;\"\u003e\n \u003cp\u003eLED model [44]\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 387px;\"\u003e\n \u003cp\u003eSaleh: a1=1.0, a2=-0.20, a3=0.015 (Cree XLamp)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 213px;\"\u003e\n \u003cp\u003eChannel\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 387px;\"\u003e\n \u003cp\u003eLambertian LoS (h_room=3m, r=1.5m, phi_half=60 deg) [14,17,29]\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 213px;\"\u003e\n \u003cp\u003eADC\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 387px;\"\u003e\n \u003cp\u003e4-bit baseline (Df=0.125, R_floor=1.30e-3)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 213px;\"\u003e\n \u003cp\u003eModulation\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 387px;\"\u003e\n \u003cp\u003eDCO-OFDM [37], 64-QAM, CR=2/3 (LDPC [18])\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 213px;\"\u003e\n \u003cp\u003ePilots\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 387px;\"\u003e\n \u003cp\u003eNp=64 per slot (identical for all methods)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 213px;\"\u003e\n \u003cp\u003eMonte Carlo\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 387px;\"\u003e\n \u003cp\u003e3,000 trials/SNR (SE) | 1,500 trials/SNR (BLER)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 213px;\"\u003e\n \u003cp\u003eNL-feat K-R\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 387px;\"\u003e\n \u003cp\u003eh=16 neurons, lambda=1e-4, 9 features, \u0026lt;1ms/slot\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 213px;\"\u003e\n \u003cp\u003eOAMP-Net [7]\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 387px;\"\u003e\n \u003cp\u003e5 layers, alpha_LED=0.75 Onsager, 200 epochs, Adam (lr=1e-3), 10k realisations, fixed-SNR training (best-effort reproduction per [7])\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 213px;\"\u003e\n \u003cp\u003eBussgang [12]\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 387px;\"\u003e\n \u003cp\u003e1st-order linearisation (Dardari et al. 2006)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 213px;\"\u003e\n \u003cp\u003eVolterra [13]\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 387px;\"\u003e\n \u003cp\u003e3rd-order equalizer (Ibnkahla 2000)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 213px;\"\u003e\n \u003cp\u003eRandom seed\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 387px;\"\u003e\n \u003cp\u003e2025 (all experiments, fully reproducible)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e"},{"header":"3. PROPOSED NL-FEAT K-R RECEIVER","content":"\u003cp\u003e\u003cstrong\u003e3.1 \u0026nbsp;K Step: Optical MMSE Equalization\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe K step is the physics-optimal minimum mean-square-error equalizer for the real-valued IM/DD LiFi channel:\u003c/p\u003e\n\u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\" width=\"613\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 47px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eEq. 4\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 467px;\"\u003e\n \u003cp\u003e\u003cstrong\u003er[k] = Re(conj(h[k])*y[k]) / (|h[k]|^2 + sn^2 + eps)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 100px;\"\u003e\n \u003cp\u003eMMSE K step\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003eFollowed by B-bit ADC quantisation to produce r_q[k]. The K step is fully physics-based, requires no training data, and is analytically optimal for the linear Gaussian component of the observation model [49,53].\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e3.2 \u0026nbsp;R Step: 9-Feature Nonlinear MLP\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe R step targets the structured residual left by K \u0026mdash; LED nonlinearity + ADC floor \u0026mdash; using a 9-dimensional nonlinear feature vector designed to match the Saleh polynomial structure:\u003c/p\u003e\n\u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\" width=\"613\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 47px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eEq. 5\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 467px;\"\u003e\n \u003cp\u003e\u003cstrong\u003ef[k] = [r_q, r_q^2, r_q^3, r, r^2, |h|, sn, |r_q-r|, r_q*r]^T\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 100px;\"\u003e\n \u003cp\u003e9 features (R9)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003eFeatures 2\u0026ndash;3 (rq\u0026sup2;, rq\u0026sup3;) directly match the 2nd and 3rd Saleh polynomial coefficients. Feature 9 (rq\u0026middot;r) captures cross-correlation between quantised and unquantised signals. Layer 1 (W1\u0026isin; R9\u0026times;h, ReLU) is fixed-random (no training). Layer 2 solves per 0.5 ms slot:\u003c/p\u003e\n\u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\" width=\"613\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 47px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eEq. 6\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 467px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eW2* = (H^T H + lambda*I)^{-1} * H^T * T, \u0026nbsp; \u0026nbsp; \u0026nbsp;T[k] = tx_pilot[k] - r_q[k]\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 100px;\"\u003e\n \u003cp\u003eClosed-form LS\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 47px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eEq. 7\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 467px;\"\u003e\n \u003cp\u003e\u003cstrong\u003ex_hat[k] = r_q[k] + W2*H[k] + b2\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 100px;\"\u003e\n \u003cp\u003eK-R output\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003eTraining completes in \u0026lt; 1 ms per slot from Np = 64 pilot symbols [50,52]. No backpropagation. No stored dataset. Ridge regularisation [58,59] (lambda = 1e-4) guarantees ||c*|| \u0026lt;= ||T|| [60] (Theorem 2 \u0026mdash; stability).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e3.3 \u0026nbsp;Theorem 1: Decomposed MSE Bound\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eFor the NL-feat K-R receiver with Np pilots, h hidden neurons, h \u0026lt;= Np*rho (no overfitting):\u003c/p\u003e\n\u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\" width=\"613\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 47px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eEq. 8\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 467px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eE[|x_hat - x|^2] \u0026lt;= MSE_MMSE - gamma_Q - gamma_CE\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 100px;\"\u003e\n \u003cp\u003eDecomposed bound\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 47px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eEq. 9\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 467px;\"\u003e\n \u003cp\u003e\u003cstrong\u003egamma_Q = R_floor*rho*(1 - h/(Np*rho+h)) \u0026gt;= 0\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 100px;\"\u003e\n \u003cp\u003eQuant. floor term\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 47px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eEq. 10\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 467px;\"\u003e\n \u003cp\u003e\u003cstrong\u003egamma_CE \u0026gt;= 0 \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; [dominant]\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 100px;\"\u003e\n \u003cp\u003eChannel error term\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003ewith rho = SNR/(SNR+1). Empirical validation: at 4-bit, SNR=20 dB, \u0026gamma;ₚ predicts +0.003 bps/Hz; observed gain is +0.79 bps/Hz; the gap (+0.787 bps/Hz) is \u0026gamma;ᴄᴇ. The 9 features, especially rq\u0026sup2; and rq\u0026sup3;, amplify \u0026gamma;ᴄᴇ by +0.342 bps/Hz over the 3-feature baseline. SE gain increases monotonically with LED distortion strength (Fig. 4a), confirming \u0026gamma;ᴄᴇ dominance and physical grounding. We note that the closed-form derivation of \u0026gamma;ᴄᴇ remains an open analytical problem: the bound \u0026gamma;ᴄᴇ \u0026ge; 0 is proven (Supplementary S2.5), but the exact dependence on Saleh polynomial coefficients (a₂, a₃) is characterised empirically in Section 4.4 rather than in closed form. This is a direct consequence of the nonlinear coupling between the Saleh distortion and the MLP feature space, which does not admit a tractable analytical expression under the current framework.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e3.4 \u0026nbsp;Proposition 1: OAMP-Net Degrades Under LED Nonlinearity\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe LED Saleh polynomial produces a non-Gaussian quantisation residual with kurtosis 1.8, violating the Gaussian interference assumption of the Onsager correction in OAMP-Net. The resulting Onsager shrinkage factor \u0026alpha; = 1 - (3-1.8)/6 = 0.80 \u0026lt; 1 causes incomplete self-interference cancellation, biasing OAMP-Net below MMSE at its training SNR and degrading to near-zero SE outside it (Fig. 3a). This is the LiFi analogue of Proposition 1 in the mmWave context [11,54].\u003c/p\u003e"},{"header":"4. RESULTS","content":"\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003e4.1 ADC Bit-Width Sweep [L1]\u003c/h2\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. Performance comparison across four experimental scenarios. (a) SE vs. ADC resolution (1\u0026ndash;8 bit), SNR\u0026thinsp;=\u0026thinsp;20 dB, 3,000 trials. Shading: 95% bootstrap CI. gamma_Q dominates at 1-bit; gamma_CE dominates at 4-bit. Proposed K-R achieves\u0026thinsp;+\u0026thinsp;4.82 bps/Hz at 1-bit, +\u0026thinsp;0.79 bps/Hz at 4-bit over MMSE (p\u0026thinsp;\u0026lt;\u0026thinsp;0.001 all bits). (b) Full optical SNR curve\u0026thinsp;\u0026minus;\u0026thinsp;5 to 40 dB, 4-bit ADC. Gain maintained at all SNR. OAMP-Net generalization gap annotated. (c) Channel model diversity: LoS, LoS+Reflection, NLOS, Rician K\u0026thinsp;=\u0026thinsp;6. Error bars: 95% CI. K-R\u0026thinsp;\u0026gt;\u0026thinsp;MMSE at all 4 channels (p\u0026thinsp;\u0026lt;\u0026thinsp;0.05). (d) Imperfect CSI (LS noise 10\u0026ndash;20%, pointing error 3\u0026ndash;5 deg [\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e]): gamma_CE increases with CSI mismatch, confirming Theorem 1.\u003c/p\u003e \u003cp\u003eThe ADC sweep (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea) confirms Theorem 7 (Corollary 1): SE gain increases monotonically as ADC resolution decreases. At 1-bit, the LED nonlinearity dominates and K-R achieves\u0026thinsp;+\u0026thinsp;4.82 bps/Hz, representing a 3.6x increase from the 4-bit case. At 8-bit, the gain remains\u0026thinsp;+\u0026thinsp;0.71 bps/Hz, confirming that the K-R correction never degrades performance at any resolution.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003e4.2 Channel Diversity and Imperfect CSI\u003c/h2\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003eFigure\u0026nbsp;2.\u003c/b\u003e Analytical and system results. (a) Feature ablation and optimal h* sweep. A0 (MMSE only) to A4 (+\u0026thinsp;y_q^3, proposed). y^2 and y^3 Saleh terms add\u0026thinsp;+\u0026thinsp;0.342 bps/Hz. Optimal h\u0026thinsp;=\u0026thinsp;12 matches Theorem 5 (h*=12). (b) Mobility: 0\u0026ndash;5 km/h indoor, p\u0026thinsp;\u0026lt;\u0026thinsp;0.001 all speeds. 95% CI shaded. (c) Complexity: SE gain vs MMSE (solid bars) and runtime (hatched). K-R: zero offline training, OAMP-Net CAUTION: gain shown vs degraded out-of-distribution baseline. (d) End-to-end BLER: full chain LED-\u0026gt;channel-\u0026gt;PD-\u0026gt;ADC-\u0026gt;K-R-\u0026gt;LDPC. CR\u0026thinsp;=\u0026thinsp;2/3 identical all methods.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003e4.3 Train/Test SNR Generalization [L9]\u003c/h2\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e3\u003c/span\u003ea is a practically significant result of this work. OAMP-Net (trained for 200 epochs on 10,000 channel realisations at 10 dB with Adam optimiser, learning rate 1e-3, best-effort hyperparameter selection following He et al. [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]) achieves only 0.62 bps/Hz when tested at 20 dB (compared to MMSE\u0026thinsp;=\u0026thinsp;5.13 bps/Hz), a degradation of 4.51 bps/Hz. OAMP-Net trained at 20 dB similarly degrades between 16 and 25 dB. The K-R receiver, which retrains every slot from current pilot observations, maintains 5.77 bps/Hz at every test SNR with 95% CI width of \u0026plusmn;\u0026thinsp;0.004 bps/Hz. This generalization advantage is a key practical reason why per-slot closed-form training outperforms offline-trained deep unfolding in operational LiFi systems.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003e4.4 LED Nonlinearity and Energy Efficiency [L11, L12]\u003c/h2\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe nonlinearity sweep (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e4\u003c/span\u003ea) provides strong physical grounding for the proposed method. A linear LED (a2\u0026thinsp;=\u0026thinsp;0) already shows\u0026thinsp;+\u0026thinsp;0.341 bps/Hz gain from quantisation correction alone. As LED distortion increases to a2=-0.35 (severe), gain reaches\u0026thinsp;+\u0026thinsp;1.235 bps/Hz. The monotone relationship is the physical prediction of Theorem 1: larger gamma_CE as the Saleh polynomial cross-terms become more energetic and the 9-feature MLP captures more structured distortion.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec15\" class=\"Section2\"\u003e \u003ch2\u003e4.5 Summary Table\u003c/h2\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabi\" border=\"1\"\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSimulation\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTest Coverage\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003evs MMSE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003evs OAMP-Net\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003ep-value\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eL1: ADC (4-bit)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3,000 trials, LoS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e+\u0026thinsp;0.79 bps/Hz\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e+\u0026thinsp;5.11 bps/Hz\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eL1: ADC (1-bit)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3,000 trials, LoS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e+\u0026thinsp;4.82 bps/Hz\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e+\u0026thinsp;5.14 bps/Hz\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eL2: SNR curve\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3,000 trials, -5 to 40 dB\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e+\u0026thinsp;0.63 @20dB\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003evariable\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001 all\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eL3: Channels\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2,500 trials, 4 models\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e+\u0026thinsp;0.47 to +\u0026thinsp;0.89\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eall positive\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.05 all\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eL4: Imperfect CSI\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2,500 trials, 6 cases\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e+\u0026thinsp;0.79 to +\u0026thinsp;0.95\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eall positive\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001 all\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eL5: Ablation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2,000 trials, A0-A4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eA4\u0026thinsp;=\u0026thinsp;+\u0026thinsp;0.825 best\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026mdash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eL6: Mobility\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2,000 trials, 0\u0026ndash;5 km/h\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e+\u0026thinsp;0.78 to +\u0026thinsp;0.79\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eall positive\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001 all\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eL9: Generalization\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2,500 trials, all SNR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eStable all SNR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eOAMP degrades\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001 all\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eL10: Pilots Np\u0026thinsp;=\u0026thinsp;8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2,500 trials, LoS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e+\u0026thinsp;0.05 bps/Hz\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003epositive\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.05\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eL10: Pilots Np\u0026thinsp;=\u0026thinsp;64\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2,500 trials, LoS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e+\u0026thinsp;0.79 bps/Hz\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003epositive\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eL11: LED severe\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2,500 trials, a2=-0.35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e+\u0026thinsp;1.24 bps/Hz\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003epositive\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eL12: Efficiency\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1,500 trials, timing\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.79/0.26ms\u0026thinsp;=\u0026thinsp;3.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026gt;Bussgang/ms\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"5. DISCUSSION","content":"\u003cp\u003eThe K-R receiver outperforms all three baselines across 12 simulation scenarios with statistical significance. Three observations warrant discussion. First, the LED nonlinearity sweep (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e4\u003c/span\u003ea) provides strong evidence that the method exploits physical structure: gain increases from +\u0026thinsp;0.341 (linear LED) to +\u0026thinsp;1.235 (severe nonlinearity), consistent with Theorem 1's prediction that gamma_CE grows with Saleh polynomial coefficient magnitude. This distinguishes K-R from general-purpose learned receivers that would not show this SNR-independent scaling.\u003c/p\u003e \u003cp\u003eSecond, the generalization experiment (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e3\u003c/span\u003ea) addresses the tension between offline-trained deep learning and operational LiFi deployment. OAMP-Net's reliance on a fixed training SNR is a structural consequence of its offline training paradigm, not merely a hyperparameter tuning issue. The K-R receiver eliminates this by design: per-slot closed-form training adapts to the current channel, current SNR, and current LED operating point with no stored dataset.\u003c/p\u003e \u003cp\u003eThird, the pilot sensitivity result (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e3\u003c/span\u003eb) shows that even Np\u0026thinsp;=\u0026thinsp;8 pilots yield a positive SE gain (+\u0026thinsp;0.052 bps/Hz), and the gain asymptotes at approximately Np\u0026thinsp;=\u0026thinsp;64. This matches the Theorem 5 prediction h* = 12 (with Np\u0026thinsp;=\u0026thinsp;64, SNR\u0026thinsp;=\u0026thinsp;20 dB), providing independent experimental validation of the theoretical optimal hidden size and confirming deployment readiness under constrained pilot overhead budgets.\u003c/p\u003e"},{"header":"6. CONCLUSION","content":"\u003cp\u003eWe presented the NL-feat K-R receiver for IEEE 802.11bb LiFi systems: a training-free, physics-driven alternative to deep unfolding that corrects LED Saleh polynomial nonlinearity and ADC quantisation noise using per-slot closed-form least squares. The 9-feature expansion, proved essential by ablation (+\u0026thinsp;0.342 bps/Hz from y\u0026sup2; and y\u0026sup3; features), directly encodes the Saleh polynomial structure. Theorem 1 decomposes the gain into gamma_Q (quantisation floor reduction) and gamma_CE (channel-error correction, dominant). Proposition 1 proves OAMP-Net degrades under LED nonlinearity due to the Onsager assumption violation, confirmed by the generalization experiment where OAMP-Net degrades while K-R remains stable at all SNR. SE gain increases monotonically with distortion strength, confirming physics-aware correction. Future work includes deriving a tight analytical bound for gamma_CE as a function of Saleh polynomial coefficients, multi-AP spatial multiplexing with inter-cell interference [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e], and hardware validation on an FPGA platform with a commercial LED transmitter and photodetector front-end to confirm that the per-slot closed-form training latency (\u0026lt;\u0026thinsp;1 ms) meets the IEEE 802.11bb slot timing constraint under real-world operating conditions.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eDISCLOSURES\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare no conflicts of interest.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eDATA AND CODE AVAILABILITY\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe simulation code (Python) and all data underlying the results presented in this paper are provided as supplementary material (Code 1). All experiments use random seed 2025 for full reproducibility.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFUNDING\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eIEEE Std 802.11bb-2023, \u0026quot;IEEE Standard for Local and Metropolitan Area Networks \u0026mdash; Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) Specifications \u0026mdash; Amendment: Light Communications,\u0026quot; IEEE, 2023.\u003c/li\u003e\n\u003cli\u003eH. Haas, L. Yin, Y. Wang, and C. Chen, \u0026quot;What is LiFi?\u0026quot; J. Lightw. Technol., vol. 34, no. 6, pp. 1533-1544, Mar. 2016.\u003c/li\u003e\n\u003cli\u003eP. H. Pathak, X. Feng, P. Hu, and P. Mohapatra, \u0026quot;Visible light communication, networking, and sensing: A survey, potential and challenges,\u0026quot; IEEE Commun. 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Sayed, \u0026quot;Adaptive Filters,\u0026quot; John Wiley and Sons, Hoboken, NJ, USA, 2008.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"LiFi, LED nonlinearity, Saleh model, K-R receiver, least-squares MLP, IEEE 802.11bb, ADC quantisation, MMSE, optical wireless communications, signal processing","lastPublishedDoi":"10.21203/rs.3.rs-9233609/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9233609/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWe propose the \u003cstrong\u003eNonlinear-Feature Learned K-R (NL-feat K-R) receiver\u003c/strong\u003e, 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 \u0026lt; 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.\u003c/p\u003e","manuscriptTitle":"Nonlinear-Feature K-R Receiver for LiFi: Physics-Driven Residual Correction with Closed-Form Per-Slot Training","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-04-02 08:19:56","doi":"10.21203/rs.3.rs-9233609/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"dafb1023-9678-48dc-92fe-bcfd0983ee2d","owner":[],"postedDate":"April 2nd, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-04-02T08:19:56+00:00","versionOfRecord":[],"versionCreatedAt":"2026-04-02 08:19:56","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9233609","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9233609","identity":"rs-9233609","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}