Sherman-Morrison Formula Aided Adaptive Channel Estimation for Underwater Visible Light Communication With Fractionally-Sampled OFDM

In this paper, we investigate the channel estimation (CE) problem in an underwater visible light communication (UVLC) system invoking fractionally-sampled optical orthogonal frequency division multiplexing (FS-OOFDM). In practical UVLC scenarios, the communication links inevitably suffer from many stochastic channel effects including multi-path dispersion, scattering, turbulence, etc., and/or from the mobility of the transceiver, therefore resulting in a time-varying, location-dependent non-stationary propagation environment. Naturally, compared with the indoor visible light communication (VLC) scenario with a typical assumption being the time-flat channel models, it becomes a notable challenge for designing a low-complexity adaptive CE in the much more complicated UVLC scenarios. To solve this problem, we derive a class of Bayesian CE algorithms referred to as the Sherman-Morrison formula (SMF) based CE (SMF-CE), by exploiting the property of rank-one structure of the second-order channel statistics in the delay domain. Furthermore, an adaptive version of SMF-CE (ASMF-CE) can be obtained through updating the imperfect a priori knowledge of the channel and the noise's statistics. Simulation results demonstrate the superior performances of the proposed algorithms in comparison to existing methods, while maintaining a reduced computational complexity in comparison to the conventional linear minimum mean square error (LMMSE) scheme.