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.INDEX TERMS Bayesian learning (BL), BCRLB, channel estimation (CE), expectation maximization, visible light communication.
I. INTRODUCTIONT HE current radio-frequency (RF) spectral bands have limited time-frequency resources to fulfil the evergrowing mobile data traffic demands, resulting in an impending spectral bottleneck in next-generation wireless communication systems. To overcome this barrier, visible light communication (VLC), which operates in the currently underutilized 400 THz to 800 THz frequency band, has evolved as a viable substitute to conventional RF-based wireless communication systems, particularly for indoor scenarios [1]-[3]. To achieve the dual objectives of communication and illumination, VLC employs light-emitting diodes (LEDs) wherein the intensity modulation occurs at a rate that is imperceivable by the human eyes. Compared to traditional RF systems, VLC offers various benefits, including improved security, reduced biological effects due to radiation, energy efficiency, and a superior signal-to-noise ratio (SNR) [1], [4]. Hence, the energy efficiency and low cost of LEDs render VLC a promising green technology for next generation communication systems [5].The channel in VLC is comprised of line-of-sight (LoS) and non-line-of-sight (NLoS) paths. The LoS path is the direct path from the LED source to the photodetector (PD) receiver, whereas the NLoS paths are created when the