# Optimized Wireless Sensor Network Architecture for AI-Based Wildfire Detection in Remote Areas
## 3 WSN Architecture
### Node Deployments  
A key challenge in WSN architecture design is balancing energy efficiency with full area coverage, which requires optimal sensor density. As the distance from the network center increases, the circle radius grows, necessitating more nodes per tier. Based on node count and spacing, a network may be classified as dense or sparse. The proposed deployment strategy features low density (compared to typical mesh networks), flexibility, and adaptability to different forest types and terrains. It also ensures a balanced and organized layout. To calculate the total number of sensing nodes: each circle includes four mandatory axis nodes. The number of nodes in one-quarter of a circle (between two axis points) is computed first, then multiplied by four to obtain the total per circle. These nodes are evenly spaced between axes, based on their number, the circle's radius, and the effective sensing radius. The overall node count includes all circular tier nodes plus the four star-tier axis nodes. Consider the following:  
* N: total number of sensing nodes in the network;
* A: area of the forest;
* R: radius of the flat forest area;
* N\({}_{\rm C}\): total number of circular tiers;
* r: effective sensing radius;
* d: distance between two neighboring nodes on a circle (dependent on \(r\));
* N\({}_{\rm i}\): index (order) of the circle;
* n: number of nodes in a circle. The effective sensing radius \(r\) is determined by sensor specifications, communication requirements, and environmental constraints. Sensor requirements define the maximum trustworthy detection range for temperature/humidity variations under ideal conditions. Figure 2: The proposed WSN architecture. Environmental aspects, such as vegetation density, terrain altitude, wind patterns, and atmospheric interference, further modulate this range by attenuating signals or blocking the line of sight. For example, dense forests reduce \(r\) to 10-20 m due to signal absorption, whereas open areas permit \(r\approx 100\) m. Communication likelihood via ZigBee (constrained by IEEE 802.15.4's range limits) also imposes \(r\), guaranteeing nodes stay within a reliable relay distance. Thus, \(r\) is calibrated via site surveys, empirical validation, and prior studies (e.g., [13; 14; 20]) to balance coverage, energy efficiency, and detection consistency. In simulations (Section 4), \(r=100\) m represents a moderate baseline for open forests, but real deployments adjust \(r\) dynamically per terrain. The area of a flat forest is given by \(A=\pi R^{2}\). Therefore, the radius of the forest area is \(R=\sqrt{\frac{A}{\pi}}\). The total number of circles is then \(N_{\rm C}=\frac{R}{r}=\sqrt{\frac{A}{\pi r^{2}}}\). Equation (1) gives the total number of sensing nodes in the WSN:  
\[N=\underbrace{4}_{\text{Number of star nodes}}+4\{[2\pi r/4r]+1\}\ldots+4\{[3\pi r /4r]+1\}\ldots\overbrace{4\underbrace{N_{\rm C}r\pi/4r]+1}_{\text{Number of nodes between two arcs of the circle order $N_{\rm C}$}} \tag{1}\]  
Note that the function \(\lfloor x\rfloor\) represents the floor function to ensure integer node counts. For example, \(\left\lfloor\frac{2\pi}{4}\right\rfloor=1\). The simplified network density equation (Equation (1)) is given by Equation (2). \[N=4N_{\rm C}+4\smash{\sum_{i=1}^{N_{\rm C}}}\left(\lfloor\frac{i\pi}{4}\rfloor +1\right) \tag{2}\]  
Once the number of nodes is determined, the next step is to calculate the spacing distance, \(d\), between each pair of nodes. To compute the spacing between nodes in each quarter of a circle with order \(N_{i}\), the corresponding circle radius \(R_{i}\) is calculated as a function of the effective sensing radius \(r\) (\(R_{i}=N_{i}r\)). Multiplying this radius by the quarter angle \(\frac{\pi}{4}\) gives the total distance between the two axis nodes of the circle, i.e., \(N_{i}r\times\frac{\pi}{4}\). Assuming n is the number of nodes required in a quarter of the circle (\(n=\lfloor\frac{N_{i}\pi}{4}\rfloor\)), the total distance is divided by \((n+1)\).