Low complexity post-distorter based on extended kernel recursive least squares for visible light communications

•The post distortion can obtain more energy efficiency than predistortion.•Nonlinear post distortion can improve the performance in visible light communication systems.•The reproducing kernel Hilbert space post-distortion scheme at the receiver.•EX-KRLS can outperform the conventional polynomial, KLMS and KRLS methods.•The approximate linear dependency criterion can be combined with coherence criterion. In visible light communication (VLC) systems, the data transmission quality could be deteriorated by the nonlinear distortion, which stems from the inherent characteristic of light-emitting diode. In order to eliminate the influence of nonlinearity, reproducing kernel Hilbert space based post distortion technology is an effective solution. As a kind of kernel methods, extended kernel recursive least squares (EX-KRLS) has played a role in providing linear approximation ability and adapting to environment with fast speed. Due to the fact that the implementation of EX-KRLS algorithm relies on constantly growing dictionaries, it leads to high computational complexity. To solve this problem, the approximate linear dependency (ALD) and coherence sparsification criteria (CALD) are introduced in this paper, forming the EX-KRLS-ALD/CALD post-distortions. Simulation results show that compared with the original EX-KRLS, the dictionary size of EX-KRLS-ALD is reduced by 52.6 %, while the size of EX-KRLS-CALD can be reduced by about 77 %, with the same bit error rate performance. The numerical results prove that the proposed strategy meets the expectations in suppressing the dictionary size and reducing the computational costs.