The Interplay Between Block Design Theory and Channel Estimation in Visible Light System

The problem of channel gain estimation in visible light communications and positioning is considered in this article. Pilot sequences are designed for simultaneously estimating the channel gains of multiple transmitters in a light system and satisfying the average and maximum transmit power constraint due to illumination purpose. This article illustrates how to design the optimal pilot sequences that minimise the noise variance experienced by a receiver although the optimisation problem is non-convex. Lower bounds on the noise variance are derived for systems with ambient light and systems without ambient light. These bounds reveal the relationship between noise variance, the average transmit power, the maximum transmit power, the number of light sources and pilot length. The necessary and sufficient conditions for the bounds to hold with equality are derived. These conditions establish a bridge between block design theory and channel estimation in visible light systems. Optimal pilot designs which achieve the lower bounds on noise variance can be obtained from balanced block designs and pairwise balanced designs. This article also shows how to optimise the average transmit power of a pilot design for minimising noise variance.