Hierarchically Sparse Channel Estimation for Underwater Visible Light Communication

Materializing effective underwater visible light communication (UVLC) channel estimation is intractable due to the complex underwater propagation environment. Fortunately, the sparsity of UVLC channels can be judiciously utilized for improved channel estimation performance. However, the practical use of sparsity is precluded due to the unsatisfactory mutual incoherence property (MIP) of the sensing matrix. In this paper, we propose to achieve exceptional sparse channel estimation for UVLC. Specially, the intrinsic problem is modeled as a hierarchically sparse recovery formulation exploiting the near continuity of the channel’s distance ingredients. A brand-new algorithm, called hierarchically block orthogonal least squares (HiBOLS), is elaborated to provide assured performance with the stunning ability of addressing the impaired MIP issue. Furthermore, in-depth theoretical guarantees are developed to provide sufficient interpretability of HiBOLS. Simulation results demonstrate that the proposed HiBOLS outperforms off-the-shelf algorithms from various perspectives including number of pilot sub-carriers, number of paths and signal-to-noise ratio.