Kalman Filter-Aided Bayesian Learning for Sparse Multipath Channel Estimation in ACO/DCO-OFDM Visible Light Communication Systems

This paper proposes a novel Kalman Filter-Aided Bayesian Learning (Kalman-BL) channel estimator for sparse multipath channel impulse response (CIR) estimation in intensity-modulation and direct-detection (IM/DD)-based optical orthogonal frequency division multiplexing (O-OFDM) visible light communication (VLC) systems. The proposed estimator models the VLC channel as a Gauss–Markov random process with temporal correlation coefficient α and integrates a Kalman predictor-updater stage with a warm-started Bayesian Learning (BL) sparse refiner. The Kalman filter draws on the correlation between successive frames to lower the effective observation noise; the BL stage that follows then exploits the delay-domain sparsity that is inherent to the VLC channel impulse response. Together, this two-stage scheme outperforms five competing estimators—least squares (LS), linear minimum mean square error (LMMSE), orthogonal matching pursuit (OMP), FOCUSS, and single-snapshot BL—across NMSE, BER, outage probability (OP), and pilot overhead, with the improvement holding for both ACO-OFDM and DCO-OFDM. Benchmarking against the Bayesian Cramér–Rao Lower Bound (BCRLB) and the Oracle-MMSE bound confirms that performance sits close to optimal. While ensuring filter consistency, the prediction process is validated with a dedicated NMSE-versus-α study performed on real trajectories of the Gauss–Markov channels of indoor VLC scenarios to demonstrate an average gain of around 1–1.5 dB compared to standalone BL, for α∈[0.90,0.99] typical for quasi-static indoor VLC channels. Most of the advantages are the reduction of pilot overhead 30–40% and about half the number of EM iterations required for convergence versus standalone BL.