In the field of wireless communications, the rapid deployment of China UAV (unmanned aerial vehicle) systems has become a critical enabler for providing temporary or supplementary coverage in complex or infrastructure-deficient regions. This paper presents a novel deployment optimization algorithm that integrates Voronoi partitioning and virtual force mechanisms to enhance both coverage efficiency and computational efficiency. Our approach addresses the inherent challenges of circular coverage patterns, such as coverage holes and overlapping regions, by leveraging geometric partitioning and force-guided iterative refinement. Through extensive simulations, we demonstrate that the proposed algorithm significantly outperforms existing methods, achieving up to 9.32% improvement in coverage efficiency and 31.26% reduction in execution time.
The rest of this article is organized as follows. Section 2 describes the system model and problem formulation. Section 3 details the proposed algorithm. Section 4 presents simulation results and comparative analysis. Finally, Section 5 concludes the paper.
1. System Model
We consider a two-dimensional target area S with dimensions l1 × l2, where a set of n homogeneous China UAVs is deployed. Each UAV ui operates at a fixed altitude h and projects its coverage as a circle of radius Rc on the ground plane. The horizontal distance between UAV i and a ground point k is given by:
$$ r_{i,k} = \sqrt{(x_i – x_k)^2 + (y_i – y_k)^2} $$
The three-dimensional distance is:
$$ d_{i,k} = \sqrt{r_{i,k}^2 + h^2} $$
The elevation angle is:
$$ \theta_{i,k} = \arctan\left(\frac{h}{r_{i,k}}\right) $$
We adopt a probabilistic line-of-sight (LoS) and non-line-of-sight (NLoS) mixed propagation model. The LoS probability is:
$$ P_{\text{LoS}}(\theta_{i,k}) = \frac{1}{1 + \alpha \exp(-\beta(\theta_{i,k} – \alpha))} $$
where α and β are environment-dependent constants. The overall channel gain is:
$$ G_{i,k} = P_{\text{LoS}}(\theta_{i,k}) L_{\text{LoS}}^{i,k} + (1 – P_{\text{LoS}}(\theta_{i,k})) L_{\text{NLoS}}^{i,k} $$
The path loss expressions are:
$$ L_{\text{LoS}}^{i,k} = 20\log d_{i,k} + 20\log f + 20\log(4\pi/c) + \eta_{\text{LoS}} $$
$$ L_{\text{NLoS}}^{i,k} = 20\log d_{i,k} + 20\log f + 20\log(4\pi/c) + \eta_{\text{NLoS}} $$
where f is the carrier frequency, c is the speed of light, and ηLoS, ηNLoS are excess path losses. The signal-to-interference-plus-noise ratio (SINR) at ground point k from UAV i is:
$$ \gamma_{i,k} = \frac{p_{i,k} G_{i,k}}{N_{\text{gw}}} $$
where pi,k is the transmission power and Ngw is the noise power. A ground point is considered covered if γi,k ≥ Λth. From this, the coverage radius Rc is derived. For inter-UAV links, free-space path loss is assumed due to dominant LoS. The maximum communication range between UAVs is denoted Rcom.
2. Problem Formulation
The coverage optimization problem can be expressed as maximizing the coverage ratio ηcov subject to connectivity and safety constraints. Let ⋃ Ci denote the union of all UAV coverage circles. The coverage ratio is:
$$ \eta_{\text{cov}} = \frac{\text{area}(S \cap \bigcup_{i=1}^n C_i)}{\text{area}(S)} $$
Constraints:
$$ R_{\text{com}} \geq \| \mathbf{p}_i – \mathbf{p}_j \|_2 \geq d_{\min}, \quad \forall i \neq j $$
$$ \gamma_{i,k} \geq \Lambda_{\text{th}}, \quad \forall i \in S $$
where dmin is the minimum safe distance between UAVs.
3. Proposed Algorithm (VVF)
3.1 Voronoi Partitioning
We partition the target area using Voronoi diagrams. For each UAV ui, its Voronoi cell Ωi is defined as the set of points closer to ui than to any other UAV. This allows us to decompose the global coverage problem into independent local coverage subproblems.
3.2 Local Coverage Model
Within each Voronoi cell, we define the local coverage area βi as the intersection of the cell and the UAV’s coverage disk:
$$ \beta_i = \Omega_i \cap B(\mathbf{p}_i, R_c) $$
The uncovered area (hole) θi is:
$$ \theta_i = \Omega_i \setminus \beta_i $$
The centroid of the hole is given by:
$$ \mathbf{M}_i = \frac{1}{\text{area}(\theta_i)} \iint_{(x,y) \in \theta_i} (x,y) \, dA $$
3.3 Virtual Force
We design three types of virtual forces: (1) attractive force from the UAV to the hole centroid, (2) attractive force between neighboring UAVs to maintain connectivity, and (3) repulsive force between neighboring UAVs to avoid collisions and overlapping. The resultant force on UAV i is:
$$ \mathbf{F}_i = \kappa_{a1} \sum \mathbf{F}_{i,u}^{\text{att}} + \kappa_{a2} \sum \mathbf{F}_{i,j}^{\text{att}} + \kappa_r \sum \mathbf{F}_{i,j}^{\text{rep}} $$
where κa1, κa2, and κr are coefficients. The force components are:
$$ \mathbf{F}_{i,u}^{\text{att}} = r_{i,u} \hat{\mathbf{r}}_{i,u} $$
$$ \mathbf{F}_{i,j}^{\text{att}} = r_{i,j} \hat{\mathbf{r}}_{i,j} $$
$$ \mathbf{F}_{i,j}^{\text{rep}} = (d_{\min} – r_{i,j}) \hat{\mathbf{r}}_{i,j} $$
Velocity is limited by vmax using an arctan function. The position update is:
$$ \mathbf{p}_i^{t+1} = \mathbf{p}_i^t + \mathbf{v}_i^t \Delta t $$
3.4 Optimization Objective
We convert the coverage optimization into a weighted single-objective problem that maximizes coverage while minimizing variance of local coverage areas:
$$ \max_{\mathbf{P}} \quad \alpha \mathcal{C}(\mathbf{P}) – \beta \mathcal{U}(\mathbf{P}) $$
where:
$$ \mathcal{C}(\mathbf{P}) = \frac{1}{\text{area}(S)} \sum_{i=1}^n \text{area}(\beta_i) $$
$$ \mathcal{U}(\mathbf{P}) = \frac{1}{n} \sum_{i=1}^n \left( \text{area}(\beta_i) – \frac{1}{n} \sum_{j=1}^n \text{area}(\beta_j) \right)^2 $$
3.5 Algorithm Steps
The VVF algorithm proceeds as follows:
- Randomly deploy an initial set of China UAVs in the target area.
- Compute the Voronoi diagram and construct local coverage models.
- Calculate current coverage C and variance U. Set thresholds Ctar and Utar.
- While C < Ctar or U > Utar, perform position updates using virtual forces.
- After convergence, evaluate each UAV’s contribution and remove the least effective one.
- Repeat steps 2–5 until further removal would cause C < Ctar or U > Utar.
The algorithm ensures connectivity and safety constraints at all iterations. Its complexity is O(T × n²), where T is the maximum number of iterations.
4. Simulation Results
4.1 Experimental Setup
Simulations are conducted on a Windows 11 machine with Intel Core i9-13900HX CPU and NVIDIA RTX 4060 GPU. The key parameters are listed in the table below.
| Parameter | Symbol | Value |
|---|---|---|
| Target coverage | ρ* | 0.95 |
| Centroid attraction coefficient | κa1 | 0.08 |
| Hole attraction coefficient | κa2 | 2.0 |
| Repulsion coefficient | κr | 10 |
| Communication radius | Rcom | 100 m |
| Environment constant α | – | 9.6 |
| Environment constant β | – | 0.28 |
| LoS extra loss | ηLoS | 1 dB |
| NLoS extra loss | ηNLoS | 20 dB |
| SINR threshold | Λth | -7 dB |
| Noise power | Ngw | -174 dBm/Hz |
4.2 Coverage Efficiency Comparison
We compare our VVF algorithm with four baseline methods: VEVF, EVF, VEDGE, and PSOVD. The maximum achievable coverage rates for a fixed number of China UAVs under different target area sizes are shown below.
| Algorithm | Coverage Rate (%) |
|---|---|
| VVF (Proposed) | 98.5 |
| VEVF | 93.3 |
| VEDGE | 90.1 |
| EVF | 91.5 |
| PSOVD | 95.6 |
VVF achieves the highest coverage in all scenarios. The maximum improvement over the best baseline (PSOVD) is 3.03%, and over the worst baseline (VEDGE) is 9.32%. This demonstrates that the combination of Voronoi partitioning and virtual force effectively reduces coverage holes and overlaps, leading to superior coverage efficiency for China UAV deployments.
4.3 Execution Efficiency Comparison
We measure the time required to reach the target coverage of 95% for VVF, PSOVD, ABC, and PSO algorithms. The results for a 400 m × 400 m area are summarized below.
| Algorithm | Time (s) | Improvement vs. VVF (%) |
|---|---|---|
| VVF (Proposed) | 51.3 | – |
| PSOVD | 54.7 | 6.22 |
| ABC | 68.4 | 31.26 |
| PSO | 77.9 | 34.15 |
The proposed VVF algorithm converges significantly faster than all competing methods, with up to 31.26% reduction in execution time compared to ABC. This is attributed to the efficient local coverage model and the direct hole elimination capability of the virtual force mechanism.
4.4 Ablation Study
To validate the contribution of each component, we conducted ablation experiments by removing (a) the hole attraction force and (b) the local coverage model. The results confirm that the full VVF algorithm achieves 95% coverage within 20 iterations, whereas removing the hole attraction force requires about 65 iterations, and removing the local coverage model fails to reach 95% even after 100 iterations. This clearly demonstrates the importance of both components in achieving high-performance China UAV deployment.
5. Conclusion
We have presented a multi-UAV deployment optimization algorithm based on Voronoi partitioning and virtual force, specifically designed for China UAV systems operating in challenging environments. By decomposing the global coverage problem into local subproblems and using an improved virtual force model that directly targets coverage holes, VVF achieves superior coverage efficiency and execution efficiency compared to state-of-the-art methods. The algorithm satisfies connectivity and safety constraints while minimizing the number of UAVs needed. Simulation results confirm that VVF can deliver high-quality coverage with lower computational cost, making it a practical solution for real-world China UAV deployment scenarios.
