Mixture-Kernel Based Post-Distortion in RKHS for Time-Varying VLC Channels

Visible light communication (VLC) based systems are a viable green supplement to existing radio frequency based communication systems. However, it has been found that the performance of VLC based systems is impaired in conditions when the users are mobile with respect to the transmit luminaire. The relative motion of the mobile users with respect to the luminaire renders the overall VLC channel to be time-varying. Recently, the impact of user mobility on the overall channel impulse response has been modeled by a generalized time-varying VLC channel model, which necessitates for an efficient mechanism at the receiver to tackle this phenomenon. In addition to user mobility, the inter-symbol interference, and the nonlinear characteristics of the light emitting diode are major factors that limit throughput of a VLC-based communication system. To mitigate these impairments, existing techniques such as Volterra/Hammerstein based receivers suffer from modeling error due to truncation of the polynomial kernel till second order terms. Recently, sparse reproducing kernel Hilbert space (RKHS) based methods have been suggested that guarantee universal approximation with the reasonable computational simplicity. However, the choice of a single hyper-parameter restricts its ability to model time-varying channels/systems. Therefore, this paper proposes a novel RKHS based post-distorter that adaptively learns a sparse dictionary based on the incoming observations, and monitors validity of the dictionary based on a proposed metric in RKHS. In order to mitigate the time-varying VLC channel based on this metric, a criterion for clearing the contents of the existing dictionary is proposed, and the requirement to learn a new dictionary is detected. Furthermore, the concept of mixture-adaptive kernel learning is introduced in this work for the minimum symbol error rate (MSER) criterion. From the convergence analysis presented in this paper, faster mean squared error (MSE) convergence is proved for the mixture-kernel based post-distorter. Additionally, it is also proven that for a given step-size, the proposed mixture-kernel MSER post-distorter always converges to a lower MSE as compared to the classical single-kernel MSER.