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The limited bandwidth and nonlinearity of light-emitting diodes (LEDs) causes inter-symbol interference (ISI) and nonlinear distortions, which restrict capacity and/or spectral efficiency of LED-based visible light communication (VLC) systems. In this paper, a light-weight polynomial activation neural network (PANN)-based equalizer is investigated for mitigation of the ISI and nonlinear distortion effects. As a variant of classic deep neural networks (DNNs), PANN has polynomial activation functions instead of classical activation functions such as sigmoid and rectified linear unit (ReLU). Therefore, small parameter volume and good interpretability are key features of PANN. The relation between mathematical expressions of the PANN and the traditional DNN using continuous derivable non-polynomial activation functions (such as sigmoid) can be obtained by the Taylor series expansion. The polynomial function can thereby be regarded as a partial summation of the expanded Taylor series. To evaluate the effectiveness of the PANN solution, we experimentally investigate the transmission performance of the PANN-based equalizers compared with traditional linear/nonlinear equalizers, and DNN-based equalizers. Experimental results show that a well-designed PANN equalizer with relatively small parameter volume improves the transmission performance, compared with the Volterra and Chebyshev equalizers. 500Mb/s CAP256-based VLC transmission over 1m is demonstrated with phosphorescent white LEDs and a light-weight PANN equalizer with only 94 parameters. The number of parameters is 6.9% and 48% less than the DNN equalizer using sigmoid and parametric rectified linear unit (PReLU) activation functions, respectively. The error vector magnitude (EVM) performance with the PANN equalizer is 0.6dB better than the third-order Chebyshev equalizer.
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