Optical Wireless Scattering Channel Estimation for Photon-Counting and Photomultiplier Tube Receivers

Channel estimation is conceived for optical wireless scattering channels associated with laser diode transmitters and photon-counting/photomultiplier tube receivers. The proposed channel estimation approach consists of two stages, namely, of the estimation of the channel tap second-order moments followed by the estimation of the channel taps based on the estimate of second-order moments. In the first stage, we provide the general framework of the moment estimation complemented by the conception of an estimation approach based on a sparse pilot structure, as well as by the analysis of the estimation error. We also propose a novel sparse pilot design as well as the associated low-complexity channel estimation, and prove the optimality of the proposed channel estimation. In the second stage, we conceive the associated channel tap estimation based on the eigenvalue decomposition of the matrix of estimated second-order moments, and analyze the associated performance. It is shown that as the length of the pilot sequence tends to infinity, the probability of having an estimation distortion above a certain threshold can be reduced arbitrarily small. Simulation results show that the proposed sparse pilot sequence can lead to a smaller estimation error than the pilot design using random 0-1 bits.