Adaptive Nonlinear Equalization Combining Sparse Bayesian Learning and Kalman Filtering for Visible Light Communications

Nonlinear post equalization (NPE) based on Volterra series (VS) is considered as an effective way to mitigate the severe light emitting diode (LED) nonlinearity and multipath effect in a visible light communication (VLC) system. However, it is restricted by kernel complexity in practical applications. In this paper, we formulate the kernel extraction of VS-based NPE to be a sparse recovery problem, and propose an efficient sparsity-aware approach, using combined sparse Bayesian learning (SBL) and Kalman filtering (KF) to extract the active VS kernels and thus to reduce the redundancy of NPE. First, from the view of probability, a Bayesian strategy is applied to select the dominant regressors from the original measurement matrices by exploiting the learning of hyperparameters, which encourages the sparseness of VS kernels with an imposed prior. Then, based on the specified regression matrix, the improved KF iteration is used in the estimation of the kernel coefficients to overcome the system instability in a dynamic noise environment. With this methodology, the active VS kernels can be effectively extracted and the corresponding kernel quantity is significantly reduced at least by 65%. Moreover, the system can still work effectively in the case of a lower size of training samples. The simulation results show that the proposed scheme is beneficial to both the nonlinearity compensation and multipath interference mitigation, and exhibits better overall performance than some existing methods, which demonstrates the potential and validity of kernel extraction in VS-based NPE.