The non-linear characteristics of Light Emitting Diodes (LEDs) contribute to the degradation of Bit Error Rate (BER) performance in Visible Light Communication (VLC) systems, particularly in Optical Orthogonal Frequency Division Multiplexing (O-OFDM) systems with high Peak-to-Average Power Ratio (PAPR). A single-stage equalizer based on the Volterra series can handle the high-order non-linear distortions of LEDs with low latency. However, solving the traditional Volterra series necessitates multiple integration operations, resulting in the high implementation complexity of the Volterra-based equalizer. Additionally, the single-stage equalizer accumulates errors with limited performance improvements.

Firstly, to address the issue of high computational complexity in the traditional calculations of the Volterra series, a proposition is made to retain only the high-order power series terms of the various nonlinear terms and kernel coefficients within the Volterra series. This approach, known as the Memory Polynomial-based Volterra Series (MPVS), not only reduces the computational complexity compared to the traditional Volterra series but also enhances the accuracy of nonlinear system modeling by considering all input signals at the current moment. Subsequently, the design of channel equalizer considers the Memory Polynomial-based Volterra (MPV) equalizer and the Memory Polynomial-based Volterra Decision Feedback Equalizer (MPV-DFE). For a single-stage MPV-DFE, if an error occurs in the decision part leading to an incorrect symbol decoding, this error tends to manifest as a consecutive series of errors, thereby impacting the entire symbol sequence. To mitigate this, a proposal is made to cascade the two non-linear equalizers, MPV and MPV-DFE, forming a hybrid equalizer called MPV+MPV-DFE. The MPV equalizer performs a primary equalization on the LED's nonlinear distortion signal, effectively suppressing a portion of the non-linear distortions and thereby reducing symbol decoding errors in the MPV-DFE. Subsequently, a secondary equalization is carried out by the MPV-DFE, leading to improved suppression of residual nonlinear distortions.

Finally, the effectiveness of the system design was validated using Monte Carlo simulation to analyze the BER. The results demonstrate that compared to the single-stage MPV equalizer and the linear-cascade nonlinear hybrid equalizer (LMS+MPV-DFE), the proposed hybrid equalizer achieves approximately 7 dB and 2 dB Signal-to-Noise Ratio (SNR) gains, respectively, in a 4 Quadrature Amplitude Modulation (QAM) -modulated Asymmetrically Clipped Optical OFDM (ACO-OFDM) system at a BER of 10^-4.

In conclusion, the implementation of the MPV equalizer is straightforward, and the cascaded design of the two-stage nonlinear equalizers as a hybrid equalizer enables better mitigation of the LED’s nonlinearity.