## 3 Results
### The Experiment of Receiver's Circle Radius and Height  
Figure 4 shows the block diagram and experimental setup to test the receiver's circle radius and height, respectively. In this system, a microcontroller control unit (MCU) (STM32F103 RCT6) in the transmitter part firstly generates the origin data, then adds a frame header to mark the beginning of each frame. A CRC (cyclic redundancy check) is also added to ensure the correctness of the data transmission. Finally, the original bit sequence is mapped into OOK (on-off keying). Four commercially available PINs (HAMAMATSU S10784, HAMAMATSU, Beijing, China, effective photosensitive area: 7 mm\({}^{2}\), and 0.45 A/W sensitivity with a -3 dB bandwidth of 300 MHz at 660 nm) are used for detecting the light signal. At the receiver part, a MCU (STM32F103 RCT6) is used to compare the received power of four PINs after ADC (analog-to-digital conversion), demodulation, CRC recovery and frame header (FH) synchronization. The radius of the PIN circle is \(r\) and the distance between the LED and the center of the receiver is \(d\). Since the received power of each PIN is different, we can compare different ADC values by the MCU to calculate angles. In this system, the minimum ADC value that the MCU can distinguish is 0.1 when the ADC value is normalized. In this experiment, we fix the LED and change \(r\) (up to 0.5 m) and \(d\) (up to 1.8 m) to investigate the position performance. Moreover, in Figure 4, O is the center of the receiver. The sliding rail and the LED are in the same horizontal direction, so we can change the position of the sliding rail to change the x-offset of the receiver. In Figure 5a, Pin1_2 represents the different ADC values of PIN1 and PIN2. It is obvious that the ADC differences of two adjacent PINs are the same if the center of the receiver and LED are in the same horizontal direction. In order to estimate the positioning performance in a more complex environment, we change the x-offset of the receiver. As shown in Figure 5a, with the increase of the radius, the difference of the ADC values of two adjacent PINs also gradually increases. Besides, the value of Pin1_2 is bigger than Pin1_4 because of the square relationship of the power with distance. Since the MCU can distinguish a 0.1 normalized ADC value, we obtain the minimum radius of the PINs' circle which is 0.16 m. In Figure 5b, the ADC value difference of two adjacent PINs decreases with the increase of the height because when we change the distance, the received signal strength of each PIN changes a lot. That makes the decrease of the received signal strength the main factor in the ADC value difference. From this experiment, we obtain the maximum distance of the transmitter-receiver plane which is 1.8 m, and the maximum radius is 0.2 m. To sum up, the radius of the PIN circle is between 0.16 m and 0.2 m.  
Figure 3: The BER distribution of two receivers when vertical distance is 0.5 m, 1 m and 1.8 m.  
Table 1 is the estimated normalized ADC value of the difference at different x-offsets when the radius of the PIN circle is 0.2 m and the distance is 1.1 m. It is shown in the table that the power of PIN4 is the largest because it is nearest to the LED. On the contrary, PIN2 obtains the minimum value. The values of PIN1 and PIN3 are almost the same due to the symmetric distribution of the LED illumination. We are most concerned about the max_difference of the two adjacent PINs. The result shows that when the x-offset is 0.05 m, the max_difference is less than 0.1, which means the MCU cannot work out the angle. Furthermore, the max_difference is increasing with the increasing x-offset, so the system is more effective when the LED is far away from the center of the receivers.