Coding and Bounds for Channel Estimation in Visible Light Communications and Positioning

Abstract

In visible light communications (VLC) and visible light positioning (VLP), it is essential to obtain accurate estimates of the channel gains between receiver and multiple light sources. When there are multiple transmitters, time-division multiple access (TDMA) is typically used in the channel estimation phase of radio frequency systems. However, the estimation performance of TDMA-based schemes in VLC and VLP systems is substantially impacted by the maximum power constraint and desired average power constraint that are unique to visible light systems. Under these constraints, this paper explores coding schemes for the simultaneous channel gain estimations of multiple light sources such that the total and maximum noise variances of the channel estimates by the receiver are minimized. Although the minimization problem is non-convex, criteria for optimal codes are found by using majorization theory. Coding scheme satisfying these criteria is proposed that helps to characterize the fundamental tradeoff between noise variance and codeword length.