LED Selection and Orientation and Power Adaptation for Visible Light Positioning Systems

We investigate a visible light positioning (VLP) system in which a number of light emitting diode (LED) transmitters emit signals over a certain number of time intervals for localizing a visible light communication (VLC) receiver. We formulate the problem of LED selection and orientation adaptation, with the aim of optimally determining the LED transmitter and its orientation vector to be employed in each time interval for minimizing the average Cramér-Rao lower bound (CRLB) on position estimation. Due to the complexity of the proposed problem, we take a discretization approach in which the orientation vector of each LED transmitter is confined to a finite set as in digital implementations. Then, we obtain a convex problem via relaxation and propose a solution approach based on the relaxed solution and a swap algorithm. We also formulate the problem of joint LED selection, orientation adaptation, and power allocation. For this problem, we extend the discretization approach by generating a power vector corresponding to each LED orientation. Then, we develop a convex formulation over all the design parameters via relaxation, and propose a low-complexity algorithm using the convex problem and a swap algorithm. We present numerical examples to illustrate the effectiveness of the proposed approaches. In particular, it is shown that, in some cases, instead of employing multiple LEDs over a number of time intervals, using the same LED with different orientations can be more desirable for accurate localization. Moreover, the proposed joint optimization approach can significantly reduce the average CRLB compared to the uniform power allocation approach.