## 3 Approach and Methodology  
The VLC system considered in this paper has two transmitters, Tx1 and Tx2, which are the taillights of the vehicle traveling in front of another vehicle carrying a photodiode receiver, as illustrated in Figure 1. \(L_{1}\) is the distance between Tx1 and Rx, and \(L_{2}\) is the distance between Tx2 and Rx.  
From Equations (3) and (7), it is known that when the LED transmitter of a VLC system has a narrow FOV, its Lambertian emission coefficient (\(m\)) increases, resulting in a larger DC channel gain \(H(0)\). However, vehicle taillights are designed with wide FOVs. To address this, we employ LED arrays of various geometrical shapes, where each individual LED has a narrow FOV. This approach allows the array transmitters to illuminate the same area as a wide-FOV LED while benefiting from the narrow FOVs of each LED.  
LED arrays are commonly used in vehicle headlights and taillights. For instance, Figure 2 presents Samsung's PixCell LED headlight design, which features a light-emitting surface that is just \(1/16\) the size of a traditional one, making it one of the smallest lighting solutions in the automotive industry. The design incorporates 4 rows of 100 LEDs in total, covering an area of 15.4 mm \(\times\) 2.74 mm [42].  
To evaluate the effect of using LED arrays as transmitters in a V2V VLC system on system performance, we consider six different configurations. The first one, established as a reference, uses two single LEDs with power \(P_{0}\) for each transmitter, Tx1, and Tx2. The irradiance distribution provided by these transmitters in the plane \(y=1\) m serves as the reference. All the proposed LED array configurations are intended to yield this reference irradiance distribution in the plane \(y=1\) m.  
The second configuration has \(3\times 3\) square LED arrays, with each LED in the transmitter array having a power of \(P_{0}/9\). The third configuration uses single hexagonal-shaped arrays consisting of 9 LEDs, each with a power of \(P_{0}/9\). The fourth configuration has  
Figure 1: The road scenario for the proposed vehicle-to-vehicle (V2V) system.  
octagonal array transmitters, again consisting of 9 LEDs each with a power of \(P_{0}/9\). Since these three configurations have the same number of LEDs, it will be possible to observe the difference in system performance resulting from the geometry of the LED arrays.  
Additionally, the fifth configuration has \(5\times 5\) square LED arrays, with each LED having a power of \(P_{0}/25\). Finally, the last one has honeycomb-like hexagonal arrays consisting of 25 LEDs. Again, each LED has a power of \(P_{0}/25\). Since the geometries of the \(3\times 3\) and \(5\times 5\) square array transmitters are the same except for the number of elements, it will be possible to evaluate the effect of increasing the number of elements and, thus, the size of the array on system performance. Furthermore, by comparing the fifth and sixth configurations, we can determine whether using a more complex geometry than a simple square, hexagon, or octagon has any advantage in terms of system performance.  
In Figure 1, the vehicles are traveling in the negative y direction. The separation between the transmitters, Tx1 and Tx2, is fixed at \(D=1.5\) m, their height from the road is 70 cm, and the lane width is 3.5 m. The midpoint between the transmitters is selected as the origin. The transmitter and receiver coordinates are given in Table 1. The coordinates show that the receiver has a 75 cm lateral misalignment from each transmitter, but no vertical misalignment.