Sparsity-Aware Nonlinear Equalization With Greedy Algorithms for LED-Based Visible Light Communication Systems

The nonlinearity of light emitting diode (LED) in visible light communication (VLC) systems is considered as one major limiting factor that deteriorates the systems' performance. In this paper, the nonlinear equalization in VLC systems is deemed to be a sparse recovery problem. Three different greedy sparse recovery algorithms, namely matching pursuit (MP), orthogonal MP (OMP), and regularized OMP (ROMP) are employed in constructing the sparsity-aware nonlinear equalizer for LED-based VLC systems. By adopting these greedy algorithms, the number of kernels in the nonlinear equalizer can be significantly reduced with minor performance loss, which enables low-complexity and high-performance nonlinear equalization. The performance of the proposed sparsity-aware nonlinear equalizers is investigated experimentally in orthogonal frequency division multiplexing (OFDM) based VLC systems with commercially available red-green-blue LEDs. The results show that, with the help of greedy sparse recovery algorithms, the number of kernels in nonlinear equalization can be reduced by 32.5%~62.5% for only 0.5-dB signal-to-noise ratio loss. The compatibility of the proposed sparsity-aware nonlinear equalizer in a ~1 Gbit/s adaptive bit-power loading OFDM VLC system is also experimentally demonstrated. The ROMP-based nonlinear equalizer is found to be the best choice that offers the optimal balance between performance and complexity, which achieves almost the same performance as the conventional Volterra time domain nonlinear equalizer in OFDM VLC systems with approximately halved number of kernels.