Theoretical limits on localization in single input multiple output (SIMO) visible light systems

In this work, a theoretical accuracy analysis is conducted for position estimation in visible light systems based on received signal strength (RSS) measurements. Considering a single light emitting diode (LED) at the transmitter and multiple photo-detectors (PDs) at the receiver, the Cramér-Rao lower bound (CRLB) is derived for both a generic three-dimensional scenario and specific configurations of the PDs at the receiver. For the special case in which the height of the receiver is known, a compact expression is derived for the CRLB, considering a uniform circular layout and the same elevation angle for all the PDs. In addition, the optimal placement of the PDs at the receiver is investigated by taking the effects of the elevation angle parameter of the PDs into consideration. The optimal values are obtained theoretically and also verified by simulations. Numerical examples are provided to illustrate the impacts of various system parameters on localization accuracy and to compare the theoretical limits against the maximum likelihood estimator (MLE) for the receiver position.