Effect of optimal Lambertian order for cellular indoor optical wireless communication and positioning systems

We propose and analyze an optimized Lambertian order (OLO) of light-emitting diode for both indoor cellular optical wireless communication and positioning systems. We carry out analysis for the system consisting of a Lambertian source and a tilted optical receiver, and develop an expression for OLO for four-, six-, and nine-cell configurations. We investigate the channel characteristics including the optical path loss, impulse response, transmission bandwidth, and positioning accuracy for the proposed systems with and without OLO, showing that there is a significant improvement in the transmission bandwidth as well as the positioning accuracy when employing OLO. For example, for a four-cell configuration with the optimum Lambertian order, 99% of cumulative distribution function of the estimation errors is within the Cramer–Rao bound (CRB) accuracy of 6.7 to 26.7 cm, compared to the CRB accuracy of 12.8 to 29.7 cm for the Lambertian order of m=1.