The Interplay Between Block Design and Channel Estimation in VLC Systems

Abstract

The accuracy of channel gain estimation affects the performance of systems for visible light communications (VLC) and visible light positioning (VLP). Pilot sequences were designed for simultaneously estimating the channel gains of multiple transmitters and minimising the total noise variance experienced by receivers. Due to illumination purpose, the sequences also satisfy the constraints on the average and maximum transmitted power. The existing pilot designs in the literature can only be applied to some special cases of average transmitted power. The pilot length is sometimes unnecessarily long. For pilot designs satisfying the power constraints, this paper shows a lower bound on the total noise variance. This bound reveals the relationship between the average and maximum power constraints, the number of LED and pilot length. The necessary and sufficient conditions for the bound to hold with equality are derived. This paper also illustrates some conditions under which the incidence matrix of a balanced incomplete block design is equivalent to a pilot design achieving the minimum total noise variance. So the results in block design theory can be used to construct optimal schemes for channel gain estimation in VLC and VLP systems. Methods for constructing pilot sequences, which satisfy an arbitrary average power constraint, are shown.