## 3 System Description
### Proposed LED Design Layout  
Most of the VLC based studies in the literature typically employ a room size of \(5\times 5\times 3\) m\({}^{3}\), wherein CLQ is generally employed for the placement of four transmitters [11]. Other studies utilize complex optimization routines to determine optimal locations for six or more transmitters. However, practically the room dimensions may vary, where CLQ based arrangements may not always provide optimum results and optimization-based algorithms are computationally intensive. Therefore, in this study, we propose the CoIQ technique and heuristically derive a simple design formula to obtain optimum transmitter locations that offer link availability at all points in the room with minimum BER of \(10^{-9}\).  
To determine the coordinates for a generalized VLC set-up with five transmitters, let \(L_{x}\), \(L_{y}\), and \(L_{z}\) specify the length, width, and height of the room along the x-,y-, and z-axes, respectively. The entire 3D space is then assumed to be divided into four quadrants, such that the origin lies at the geometrical centre of the room (see Figure 4). This creates x-,y-, and z-axes that range between [\(-L_{x}/2\), \(L_{x}/2\)], [\(-L_{y}/2\), \(L_{y}/2\)], and, [\(-L_{z}/2\), \(L_{z}/2\)], respectively. The XY-plane of each quadrant is then further divided into several segments with a resolution (\(\triangle r\)) of 0.25 m, for instance, if the length of the room is 5m then a 0.25 m resolution implies that the x- and y- axes have been virtually divided into 20 equal parts. Now, let there be five transmitters to cover the entire room where each transmitter is denoted by its transmitter position \(TP_{n}(x_{n},y_{n},z_{n})\) and '\(n\)' refers to the number of each transmitter. \(TP_{o}\) is placed at the origin with coordinates (0,0, \(L_{z}/2\)). However, the remainingtransmitters can be defined by the diagonal points \(DP_{x}\) and \(DP_{y}\) along the x- and y-directions, respectively, which are calculated as:  
\[DP_{x} =((L_{x})*\sqrt{2})/4 \tag{17}\] \[DP_{y} =((L_{y})*\sqrt{2})/4 \tag{18}\]  
Subsequently, exploiting the symmetry of the square room, the transmitters can be placed along the diagonals passing through origin with a tolerance of \(\pm\triangle r\), such that:  
\[TP_{1} =[-DP_{x}\pm\triangle r,\ \ -DP_{y}\pm\triangle r,\ \ L_{z}/2] \tag{19}\] \[TP_{2} =[-DP_{x}\pm\triangle r,\ \ \ DP_{y}\pm\triangle r,\ \ L_{z}/2]\] \[TP_{3} =[\ \ DP_{x}\pm\triangle r,\ \ \ DP_{y}\pm\triangle r,\ \ L_{z}/2]\] \[TP_{4} =[\ \ DP_{x}\pm\triangle r,\ \ -DP_{y}\pm\triangle r,\ \ L_{z}/2]\]  
Further steps for heuristically obtaining the optimized coordinates have been summarized in Algorithm 1, which takes room dimensions \(L_{x}\), \(L_{y}\) and \(L_{z}\) as the input. Instead of performing exhaustive iterations to acquire optimized coordinates, the algorithm then uses (17) and (18) to calculate one diagonal point (\(TP(DP_{x},DP_{y})\). Next, it exploits the room symmetry to define (\(TP_{0}\), \(TP_{1}\), \(TP_{2}\), \(TP_{3}\), and \(TP_{4}\)) as given in (19) and calculates the illuminance and \(SNR\) uniformities. Because (17) and (18) were devised heuristically to calculate the coordinates, it was observed that for room lengths lower than 5m, optimum results were obtained at (\(DP_{x}+\Delta r\), \(DP_{y}+\Delta r\)), while for lengths greater than 5m, (\(DP_{x}-\Delta r\), \(DP_{y}-\Delta r\)) produced better uniformity results. Based on these observations, steps 3 and 4 were repeated for \(TP_{n}(x_{n},y_{n})+\Delta r\) and \(TP_{n}(x_{n},y_{n})-\Delta r\), respectively. Accordingly, the conditional statements were used next to output the optimized coordinates based on minimum \(SNR\) deviation.