[Paper Review] Statistical Modelling of the Clipping Noise in OFDM-based Visible Light Communication System

Nima Taherkhani, Kamran Kıasaleh|arXiv (Cornell University)|Sep 9, 2019

Optical Wireless Communication Technologies9 references4 citations

TL;DR

This paper proposes a closed-form probability density function (PDF) for clipping noise in OFDM-based visible light communication (VLC) systems, challenging the common assumption that clipped and original signals share identical statistics under tight power constraints. The derived PDF enables statistical hypothesis testing in an optimum receiver, significantly improving performance in high dynamic range scenarios where traditional linear equalization fails.

ABSTRACT

This paper analyses the statistics of the clipping noise in orthogonal frequency-division-multiplex (OFDM) based visible light Communication systems. The clipped signal is generally modelled as the summation of the scaled original signal and clipping noise, which is treated by the linear equalizer in the receiver. Generally, it is assumed that the clipped and original signal share the same statistics. Although valid in some cases, we show that such assumption is invalid when the transmitter is tightly constrained. We derive closed-form probability distribution function (pdf) for the clipping noise and use the pdf for statistical hypothesis testing in an optimum receiver

Motivation & Objective

• To address the statistical mismatch in clipping noise modeling when transmitter power is tightly constrained.
• To derive an accurate probability distribution function (PDF) for clipping noise in OFDM-based visible light communication systems.
• To enable statistical hypothesis testing in an optimum receiver by leveraging the derived PDF.
• To improve system performance beyond linear equalization in high peak-to-average power ratio (PAPR) scenarios.

Proposed method

• Derives the exact closed-form probability density function (PDF) of the clipping noise in OFDM-based VLC systems under peak power constraints.
• Models the clipped signal as the sum of the original signal and a non-Gaussian clipping noise component.
• Analyzes the statistical dependence between the original signal and the clipping noise, showing they are not identically distributed under tight constraints.
• Applies the derived PDF to design a statistical hypothesis testing-based receiver for optimal decision-making.
• Uses the PDF to compute likelihood ratios for maximum-likelihood detection in the presence of clipping distortion.
• Validates the model through theoretical analysis and demonstrates its superiority over conventional linear equalization.

Experimental results

Research questions

• RQ1 How does the statistical distribution of clipping noise deviate from the original signal under tight power constraints in OFDM-based VLC systems?
• RQ2 Can a closed-form PDF be derived for the clipping noise in OFDM-based visible light communication systems?
• RQ3 Does the assumption of identical statistics between original and clipped signals hold in practical high-PAPR scenarios?
• RQ4 How does the proposed statistical model improve detection performance compared to linear equalization?
• RQ5 What is the impact of the derived PDF on the design of an optimum receiver in clipping-impacted VLC systems?

Key findings

• The clipping noise does not follow the same statistical distribution as the original signal when the transmitter is under tight power constraints, invalidating a common assumption in prior work.
• A closed-form expression for the probability density function (PDF) of the clipping noise is derived, enabling precise statistical modeling.
• The derived PDF enables the design of a statistically optimal receiver based on likelihood ratio testing, outperforming linear equalization.
• Simulation results show that the optimum receiver using the derived PDF achieves significant SNR gain over conventional linear equalization in high-PAPR regimes.
• The model reveals that clipping noise is non-Gaussian and exhibits a non-stationary statistical structure dependent on the signal's envelope and clipping threshold.
• The proposed approach enables reliable detection even when the clipping ratio is high, where linear equalization fails due to residual inter-carrier interference.