Sparse Channel Estimation for Visible Light Optical OFDM Systems Relying on Bayesian Learning

Sparse multipath channel impulse response (CIR) estimation schemes are conceived for optical orthogonal frequency division multiplexing (O-OFDM) visible light communication (VLC) systems. We commence by deriving the input-output models for both asymmetrically clipped optical OFDM (ACO-OFDM) and direct current-biased optical OFDM (DCO-OFDM) systems. A multipath CIR model is derived that captures both the diffusive as well as specular reflections of the VLC channel. Next, we introduce both the sparsity-agnostic conventional least square (LS) and the linear minimum mean square error (LMMSE) channel estimation (CE) techniques. This is followed by the orthogonal matching pursuit (OMP)-based sparse recovery technique, which exploits the delay-domain sparsity of the CIR. Furthermore, a novel sparse multipath CIR estimation scheme is proposed using the Bayesian learning (BL) framework, which requires only a limited number of pilot subcarriers, hence resulting in a reduced pilot overhead as compared to other state-of-the-art (SoA) CE techniques. The Bayesian Cramer Rao lower bound (BCRLB) as well as the Oracle-minimum mean squared error (O-MMSE) estimator are also derived for benchmarking the estimation performance of the proposed BL-based framework. Our simulation results demonstrate that the proposed BL method outperforms other existing sparse and conventional CE methods in terms of various metrics, such as the normalized mean-square-error (NMSE), the outage probability (OP), and the bit error-rate (BER) despite its reduced pilot overhead.