LED Nonlinearity Post-compensator with Legendre polynomials in Visible Light Communications

The nonlinear effect of Light-Emitting Diodes (LEDs) is one of the important factors that hamper the bit rate of Visible Light Communications (VLC). To mitigate the nonlinearity, we propose a Legendre-polynomials-based post-compensator derived from a post-distorter deduced by a physical-based nonlinear LED model. We represent the formulation of the post-distorter with Legendre series expansion to ease the computation burden for training coefficients. Since only feed-forward structure is embodied in the series representation, the coefficients of the proposed compensator are easy to access with adaptive algorithms of low complexity. To validate the effectiveness of our proposed model, we adopt Recursive Least Square (RLS) and Least Mean Square (LMS) algorithms to train the coefficients of our proposed compensator with the same iteration steps. In particular, RLS achieves lower Mean square Errors (MSEs) with faster convergence speed. Due to the relatively low complexity of these nonlinear algorithms, our proposed compensator is more actual for implementation on VLC hardware platforms like Field-Programmable Gate Array (FPGA).