Rapid Deployment Method for Multi-Scene UAV Base Stations for Disaster Emergency Communications

Abstract

The collaborative deployment of multiple UAVs is a crucial issue in UAV-supported disaster emergency communication networks, as utilizing these UAVs as air base stations can greatly assist in restoring communication networks within disaster-stricken areas. In this paper, the problem of rapid deployment of randomly distributed UAVs in disaster scenarios is studied, and a distributed rapid deployment method for UAVs´ emergency communication network is proposed; this method can cover all target deployment points while maintaining connectivity and provide maximum area coverage for the emergency communication network. To reduce the deployment complexity, we decoupled the three-dimensional UAV deployment problem into two dimensions: vertical and horizontal. For this small-area deployment scenario, a small area UAVs deployment improved-Broyden–Fletcher–Goldfarb–Shanno (SAIBFGS) algorithm is proposed via improving the Iterative step size and search direction to solve the high computational complexity of the traditional Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm. In a large area deployment scenario, aiming at the problem of the premature convergence of the standard genetic algorithm (SGA), the large-area UAVs deployment elitist strategy genetic algorithm (LAESGA) is proposed through the improvement of selection, crossover, and mutation operations. The adaptation function of connectivity and coverage is solved by using SAIBFGS and LAESGA, respectively, in the horizontal dimension to obtain the optimal UAV two-dimensional deployment coordinates. Then, the transmitting power and height of the UAV base station are dynamically adjusted according to the channel characteristics and the discrete coefficients of the ground users to be rescued in different environments, which effectively improves the power consumption efficiency of the UAV base station and increases the usage time of the UAV base station, realizing the energy-saving deployment of the UAV base station. Finally, the effectiveness of the proposed method is verified via data transmission rate simulation results in different environments.

1. Introduction

In recent decades, the frequency of all kinds of natural disasters has been increasing year by year, especially earthquakes, floods, and debris flows, which often bring incalculable losses to the affected areas [1]. In these disasters, the ground communication facilities in the accident area are often destroyed, which can make it difficult for information on the disaster situation in the accident area to be transmitted in time and makes the post-disaster relief work difficult to carry out effectively. Unmanned aerial vehicles (UAVs), which are characterized by their low cost, high flexibility, and high line-of-sight link probability [2], can be utilized to establish low altitude platforms (LAP) for emergency communication purposes [3], satisfying post-disaster communication needs [4,5,6,7,8].

However, given the urgency and timeliness of disasters, a UAV-assisted emergency communications network must be deployed in a timely manner [9], and the key challenges are the following. First, UAVs have limited computing power [10], and the dynamic tracking of disaster areas to rescue ground users will consume a lot of computing resources, increasing the deployment time of UAVs. Second, the UAV’s energy storage is limited [11]; the dynamic adjustment of the height of the UAV will further increase energy consumption, reducing the UAV emergency communications service time.

A reasonable channel model can improve the deployment effect of UAVs, minimizing the path loss, expanding the coverage area, and reducing the deployment time of the UAVs. In [12], the authors assumed that UAVs are fixed in a two-dimensional plane without seeking a balance between deployment range and link loss. In [13], the authors derived the air-to-air channel model among UAVs while considering height factors. In [14], the authors incorporated the characteristics of the air-to-ground propagation channel, the impact of co-channel interference from other UAV base stations, and energy constraints of the UAV base stations. In [15], the authors proposed a framework for evaluating flight height and area coverage using a fixed number of drones and area dimensions. In [16], the authors presented a distributed deployment algorithm specifically designed for line-of-sight (LoS) scenarios which allowed UAV base stations to determine their motion based solely on local information, making it suitable for large area UAVs deployments.

By integrating considerations of connectivity and coverage, the communication connectivity and area coverage challenges in the deployment of emergency communication UAVs can be effectively addressed, thereby enhancing the efficiency and accuracy of the emergency response. In [17], the authors proposed a three-dimensional UAV deployment scheme based on the improved genetic algorithm (IGA), which ensured the connectivity of the UAV network in both static and dynamic user scenarios. In [18], the authors investigated the maximum coverage deployment problem while maintaining connectivity conditions in the absence of user location information. In [19], the authors presented a combined approach using the steepest descent method and genetic algorithm to optimize the deployment scheme of wireless sensor nodes, aiming to achieve network connectivity while meeting coverage constraints. In [20], the authors proposed a graphic coalition formation game that combines UAV time-varying topology with a coalition formation game.

To reduce the complexity of the UAV deployment problem, some scholars have pursued some interesting research. In [21], the authors took into consideration the complexity of 3D UAV deployment by decoupling the UAV deployment problem into vertical and horizontal dimensions. In [22], the authors demonstrated the existence of an optimal vertical height that achieves a maximum coverage range for UAV energy efficiency.

Due to the limited endurance of UAVs, researchers have investigated the power allocation problem for UAVs. In [23], the authors proposed a new analysis model to study the key factors affecting UAV power consumption. In [24], the authors proposed a joint power allocation and deployment scheme in UAV-based IoT networks, aiming to optimize the deployment locations and power allocation of UAVs by maximizing network coverage and minimizing network interference. In [25], the authors proposed an adaptive UAV deployment scheme with the objective of optimizing UAV positions to cover as many navigation grids as possible while reducing communication energy consumption. In [26], the authors analyzed the effects of wind speed, wind direction, and turbulence on the endurance of UAVs. In [27], the authors studied the use of hybrid precoding to reduce hardware complexity and energy consumption in UAVs.

Applying the meta-heuristic optimization algorithm to solve the UAV deployment optimization problem can simplify the solution process, improve the deployment efficiency, and optimize the deployment effectiveness. The most common meta-heuristic methods include real-coded genetic algorithm (RCGA-rdn) [28], water strider algorithm (WSA) [29], thermal exchange optimization algorithm (TEO) [30], and so on.

Moreover, there exist several intriguing research directions. In [31], the authors presented a UAV emergency communication system architecture based on 5G and its subsequent technologies. This system exploits UAVs as communication relay nodes to provide communication services within disaster-stricken areas. In [32], the authors proposed a relay deployment and network optimization framework based on non-orthogonal multiple access. The framework aims to maximize network coverage and service quality by optimizing the deployment locations and power allocation of relay nodes. In [33], the authors considered a facility location problem with drones. In [34], the authors proposed a new UAV or UAV platform that can connect a network of sensors and actuators on demand. In [35], the authors proposed a base station interference management method for UAVs based on affinity propagation and machine learning. In [36], the authors proposed a lightweight, privacy-preserving protocol for UAV internet environments. In [37], the authors developed a multi-UAV cooperative search model (MCSM) with communication cost and formation benefit as an optimization function to ensure the effectiveness of multi-UAV search.

The above research focuses on solving the problems of UAV energy consumption and UAV communication effect but does not consider the efficiency of UAV deployment. In view of the urgency and timeliness of disaster emergency communication, we design the rapid deployment method for UAV base stations which is suitable for small areas and large areas, respectively. Then, according to different disaster scenarios, the launch power and deployment height of the UAVs are dynamically adjusted to provide emergency communications for different disaster scenarios.

The main contributions of this paper are as follows:

• First, we decouple the UAV deployment problem for disaster emergency communication into two sub-problems: horizontal deployment and height regulation. We extract the horizontal deployment problem into the solution of UAV coverage rate and connectivity rate and calculate the optimal horizontal deployment coordinates of the UAV base stations, which effectively improves the deployment speed of UAV base stations after disasters. Then, the transmitting power and deployment height of the UAV base station are adjusted according to the channel model of urban, suburban, and rural environments and the distribution characteristics of the users waiting for rescue on the ground; in this way, energy-saving communication for the UAV base station is realized effectively.
• Secondly, we proposed the small-area UAV deployment improved-Broyden–Fletcher–Goldfarb–Shanno algorithm (SAIBFGS) to solve the UAV two-dimensional deployment problem for small-scale disaster scenarios, which reduces the complexity of the algorithm by improving the iterative step size and search direction. For large-scale disaster scenarios, we proposed a large area UAV deployment elitist strategy genetic algorithm (LAESGA) to solve the UAV two-dimensional deployment problem. By improving the selection, crossover, and mutation operations, the premature convergence of genetic algorithm is avoided. Simulation results show the convergence of the algorithm.

The remaining sections of this paper are as follows: Section 2 presents the system model and problem-solving approach for the rapid deployment of disaster emergency communication UAVs. Section 3 proposes deployment methods for unmanned UAVs applicable to different scales of disaster scenarios, along with the validation of the proposed algorithms’ effectiveness in problem solving. Section 4 provides simulation results and analysis. Finally, Section 5 concludes the paper.

2. System Model

The present paper primarily investigates a UAVs-assisted model for disaster emergency communication networks, as depicted in Figure 1. We consider a disaster scenario with a square area of $S$. The system comprises $I_{UAV}$ of UAVs, $J_{person}$ of ground users awaiting rescue, and $L$ target deployment points are located, the sets $I_{UAV}=\left\{1,2,\dots i\right\}$, $J_{person}=\left\{1,2\dots j\right\}$ and $L=\left\{1,2\dots l\right\}$. In the disaster scenario described in this paper, the target deployment point represents the damaged ground communication base station, and the UAV base stations replace these damaged ground communication base stations to provide emergency communications services for the rescue ground users. The communication links depicted in Figure 1 include UAV-to-UAV communication (U2U) and UAV-to-ground communication (U2G) for interaction between unmanned aerial vehicles and ground users in need of rescue. In addition,

Table 1. Table of notations.

Notations	Description
$I_{UAV}$	UAVs’ set
$J_{person}$	Sets of ground users awaiting rescue
$D$	The horizontal distance between the user’s equipment antenna on the rescue surface and the UAV´s station antenna
$\mathbb{Z}(h_{msta})$	The antenna parameter calibration factor
$\mathbb{k}$	The scenario type calibration factor
$R_{u_i,l_i}$	Euclid distance between UAVs and target deployment points
$R_{u_i,Z_i}$	Euclid distance between a UAV and any point
$u_i$	The horizontal coordinates of a UAV
$l_i$	The horizontal coordinates of the target deployment points
$Z_i$	The coordinates of any point in the rectangular area
$f_1$	The connectivity fitness function
$f_2$	The coverage fitness function
$fi{t}_{final}$	Fitness function
$P_{loss}$	Pathloss
$\vartheta$	Random variable
$a_k$	Step size
$d_k$	The search direction
$N$	Number of UAVs
$L$	Number of target deployment points
$M$	Number of the ground users awaiting rescue
$d_{min}$	UAVs safe distance
$d_{max}$	Maximum communication distance of UAVs
$f_0$	Carrier frequency
$T_1$	Path loss threshold
$h_{msta}$	The effective height of the user equipment antenna on the rescue surface
$h_{sta}$	The effective height of the UAVs station antenna
$\omega$	The number of chromosomes
$C_i$	The offspring chromosome
$F_i$	The parent chromosome
$⊲$	The crossover probability
$⊳$	The mutation probability
${\gamma }_1,{\gamma }_2$	Number of iterations
$P_t$	UAVs launch power
$P_r$	Power received by ground users to be rescued
$C_{target}$	The coordinates of the target deployment points
$C_{final}$	The final deployment coordinates
$M_i$	The number of users in need of rescue within the coverage range of the UAVs
$M_{COV}$	The user coverage ratio
$\mathbb{S}$	The accuracy of deployment
$F_{BW}$	Bandwidth frequency
$\mathfrak{M}$	Data transmission rate
$SINR$	The signal-to-noise ratio of the communication.
$\sigma$,$\tau$	Random variable
$erf$	Error function
$U$	A random number uniformly distributed over an interval (0,1)
$C_D$	The discrete coefficient of user distribution on the ground to be rescued
$Z_{Jperson}$	The coordinates of the ground users to be rescued
$P_{extra}$	A power loss function

summarizes the main notations used in this paper.

2.1. Channel Model

For the recovery of UAV communications in the disaster area, we assume that the people who survived in the disaster area can still use their smartphones, but because the ground base stations in the disaster area are overloaded or damaged, it makes it impossible for smartphones to communicate with the outside world. At this time, UAV can be used as a mobile node in the communication network to provide emergency communications for disaster areas. We hypothesized two scenarios that would require UAVs deployment. One scenario would be a large event space, where the large number of user communications requests exceed the load of the ground base station, and the UAVs would overcome geographic barriers that limit communication at the event horizon, providing temporary emergency communications to the region. In the other scenario, where ground base stations are damaged by a disaster such as an earthquake or mudslide [5], UAVs are deployed immediately to provide a temporary emergency communications network in open areas. The Hata–Okumura model [38] is employed to evaluate path loss and signal enhancement. This model enables the assessment of path loss in urban, suburban, and rural environments, and can be represented as follows:

$$P_{loss}=69.55+26.16{\mathit{lg}(f}_o)-13.82{\mathit{lg}(h}_{{}_{sta}})-\mathbb{Z}(h_{msta})+(44.9-6.55{\mathit{lg}(h}_{sta}\left)\right)\times \mathit{lg}\left(D\right)+\mathbb{k}$$

(1)

$$\mathbb{Z}(h_{msta})=\{\begin{array}{c}3.2\times {\left(\mathit{lg}\right(11.75\times h_{msta}\left)\right)}^2-4.97f_0>300MHz\\ 8.29\times {\left(\mathit{lg}\right(1.54\times h_{msta}\left)\right)}^2-1.1f_0\le 300MHz\\ (1.11{\mathit{lgf}}_0-0.7{)h}_{msta}-1.56{\mathit{lgf}}_0+0.8\mathit{others}\end{array}$$

(2)

$$\mathbb{k}=\{\begin{array}{cc}\hspace{1em}\hspace{1em}0\hfill & urban\hfill \\ -2\times {{\left(\mathit{lg}\right(f}_0/28\left)\right)}^2-5.4\hfill & suburban\hfill \\ \hspace{1em}\hspace{1em}-4.78\times {{\left(\mathit{lg}\right(f}_0\left)\right)}^2+18.33\times {\mathit{lg}(f}_0)-40.98\hfill & \mathit{rural}\hfill \end{array}$$

(3)

In the equation, $h_{msta}$ represents the effective height of the user equipment antenna on the rescue surface, $h_{sta}$ represents the effective height of the UAVs station antenna, $D$ represents the horizontal distance between the users equipment antenna on the rescue surface and the UAVs station antenna, $\mathbb{Z}(h_{msta})$ is the antenna parameter calibration factor, $\mathbb{k}$ is the scenario type calibration factor, and $f_0$ is the carrier frequency of the U2U channel. Due to the requirement of setting a certain redundancy value for path loss in disaster scenarios, this paper does not consider the path loss generated by the transmission and reception signals between the UAV and the ground user equipment. The relationship curve between path loss $P_{loss}$ and horizontal distance $D$ is plotted using Equations (1) to (3), as shown in Figure 2:

When the path loss $P_{loss}$ is less than or equal $T_1$ to the threshold, it can be inferred that the quality of customer service (QoS) of all ground users [39] under the coverage of UAV $i_{th}$ in need of rescue is ensured.

2.2. Connectivity and Coverage Model

Assume a rectangular area R, within which $L$ target deployment points are located, denoted by the set $L=\left\{1,2\dots l\right\}$, $l_i=(l{x}_l,l{y}_l)$ representing the horizontal coordinates of the target deployment points. Let $N$ UAVs be distributed within this area, $u_i=(x_i,y_i)$ representing the horizontal coordinates of the $i_{th}$ UAV. $R_i$ represent the communication radius of the $i_{th}$ UAV. Let $Z_i=(z{x}_i,z{y}_i)$ represent the coordinates of any point in the rectangular area. The distance between any two UAVs must not be less than the UAVs safe distance, nor exceed the maximum communication distance. The distance between UAVs can be expressed as follows:

$$d_{i,k}=\sqrt{{(h_{sta}-h_k)}^2+{(u_i-u_k)}^2}\ge d_{min}$$

(4)

where $d_{min}$ represents the UAVs safe distance.

Modeling the connectivity rate as a function of Euclid distance $R_{u_i,l_i}$ between UAVs $u_i$ and target deployment points $l_i$: max

$$P_{u_i,l_i}=\{\begin{array}{l}1,0\le R_{u_i,l_i}\le d_{max}\\ 0,R_{u_i,l_i}>d_{max}\end{array}$$

(5)

$$R_{u_i,l_i}=\sqrt{h_{sta}{}^2+{(lxi-xi)}^2+{(lyi-yi)}^2}$$

(6)

where $d_{max}$ represented the maximum communication distance of UAVs.

The connectivity fitness function is:

$$f_1={\displaystyle {\sum }_{l_i\in R}{P}_{u_i,l_i}}$$

(7)

Modeling coverage as the Euclid distance $R_{u_i,l_i}$ between a UAV $u_i$ and any point $Z_i$ within a given region:

$$P_{u_i,Z_i}=\{\begin{array}{l}1,0\le R_{u_i,Z_i}\le d_{max}\\ 0,R_{u_i,Z_i}>d_{max}\end{array}$$

(8)

$$R_{u_i,Z_i}=\sqrt{{(zxi-xi)}^2+{(zyi-yi)}^2}$$

(9)

The coverage fitness function is:

$$f_2={\displaystyle {\sum }_{Z_i\in R}{P}_{u_i,Z_i}}$$

(10)

The connectivity fitness function and the coverage fitness function are specified as follows:

$$Maximize:fi{t}_{final}=\left[\vartheta \times \frac{f_1}{L\times L}+(1-\vartheta )\times \frac{f_2}{S}\right],\vartheta \in (0,1)$$

(11)

3. UAVs Deployment Methods for Disaster Scenarios of Different Scales

According to the requirement in disaster emergency response that UAVs must be deployed precisely and timely at the target point, this paper designs SAIBFGS, which is suitable for small-area UAV deployment, and LAESGA, which applies to large area UAV deployment.

3.1. Small Area UAVs Deployment Improved-Broyden–Fletcher–Goldfarb–Shanno

The quasi-Newton method is one of the most efficient approaches for solving nonlinear optimization problems, initially proposed by American physicist W. C. Davidon in the 1950s. Presently, the prevalent variants of the quasi-Newton method are the well-established Broyden–Fletcher–Goldfarb–Shanno (BFGS) method. Additionally, the steepest descent methods (SD) are frequently employed to tackle nonlinear optimization problems [19].

The conventional BFGS quasi-Newton method, due to its excessive computational demands, is not suitable for application in disaster emergency communications UAV deployment tasks. Therefore, this paper proposes the low-complexity and low-storage-demand SAIBFGS method. The SAIBFGS algorithm process is defined in Algorithm 1.

The standard iterative form of the BFGS algorithm is as follows:

$$x_{k+1}=x_k+a_k{d}_k=x_k-a_k{b}_k{g}_k$$

(12)

From the above equation, it can be observed that the computational burden of the standard BFGS algorithm primarily lies in the search direction $d_k$ and iteration step $a_k$. In order to cater to the exigent communication scenarios during disaster emergencies, improvements need to be made in these two aspects.

Firstly, we consider the iteration step size $a_k$. In the quasi-Newton method, in order to ensure the convergence of the function, it is required that the line search be monotonic. Considering the requirement of conserving computational resources in disaster emergency communication, we made the following improvements.

Exact search step size:

$$a_k=\frac{{(d_k)}^T(g_k)}{{(d_k)}^{T}B(d_k)}$$

(13)

Simplify the direction of the search:

$$d_{k+1}=-g_{k+1}+\frac{(a_k{d}_k){(a_{k}B{d}_k)}^T}{{(a_k{d}_k)}^T(a_{k}B{d}_k)}{g}_{k+1}$$

(14)

In the equation, $B$ is a positive definite matrix.

Compared to the standard BFGS algorithm, the SAIBFGS algorithm obviates the need for direct calculation of the inverse Hessian matrix $b_k$, thereby effectively reducing computational complexity. The computational complexity of the standard BFGS algorithm is $L(6k^2+6k)$, while that of the SAIBFGS algorithm is $L(2k^2+7k)$.

Algorithm 1 Small-Area UAV Deployment Improved-Broyden–Fletcher–Goldfarb–Shanno (SAIBFGS)

Input: The starting coordinates of the UAV and the coordinates of the ground users awaiting rescue. Output: The final coordinates for the deployment of the unmanned aerial vehicle. Step1: Initialize the two-dimensional coordinate points for the unmanned aerial vehicle, initialize the step size, and store the data of the nearest m iterations. Step2: While it is less than the iteration number and greater than the error, do the following. Step3:   Calculate the iterative step size: $a_k$. Step4:   Modify and refine key points: $x_{k+1}=x_k+a_k{d}_k$ Step5:   Compute the correction operator: $p_k=a_k{d}_k,q_k=a_{k}B{d}_k$. Step6:   Calculate the updated gradient value: $g_{k+1}=g_k+q_k$. Step7:   Compute a novel trajectory for the search: $d_{k+1}$. Step8:   Update: $k=k+1$ Step9: End

The accuracy of SAIBFGS is high, but as the number of UAVs increases and the deployment range expands, it is prone to getting trapped in local optima. Additionally, SAIBFGS further reduces computational complexity, making it suitable for small-scale UAV deployment.

3.2. Large Area UAVs Deployment Elitist Strategy Genetic Algorithm

The standard genetic algorithm (SGA), proposed by John Holland of the United States in the 1970s, is a computational technique that utilizes mathematical methods and computer simulations to transform the problem-solving process into a series of chromosome-based genetic operations such as selection, crossover, and mutation, similar to biological evolution. Genetic algorithms can be encoded using either binary or real-number representations, and this article adopts the real-number encoding scheme. The LAESGA algorithm process is defined as shown in Algorithm 2.

Selection operation: The common selection method for genetic algorithms is binary tournament selection; because only two individuals are compared at a time, the mechanism of this method is simple, reducing diversity. In view of the defects of the binary tournament, we made some improvements to the selection operation. First, the fitness function values of each individual in the population are calculated and ranked from large to small. Then, an elite strategy is applied to the first two ranked individuals, which are preserved and directly copied to the next generation; the remaining ranked individuals were equally divided into two groups, and the individuals with the same rank in each group were cross-operated, thus avoiding limiting the population to a local optimal solution. Since only a comparison between two individuals is involved at a time, the calculation is simple and fast. To understand the selection operation more clearly, below is a schematic of a selection operation with a chromosome number of 10, as shown in Figure 3:

The chromosome before ranking is $X=(X_1,X_2,\dots ,X_{\omega })$; after ranking, it becomes $X^{*}=(X_1^{*},X_2^{*},\dots ,X_{\omega }^{*})$ and satisfies $fi{t}_{final}(X_1^{*})\ge fi{t}_{final}(X_2^{*})\ge \dots \ge fi{t}_{final}(X_{\omega }^{*})$.

Crossover operation: The uniform crossover operation based on random weights is adopted. In each crossover process, two parent individuals are selected from the mating pool, denoted as $F_i$ and $F_{i+1}$ respectively. Then, the decision of whether to perform crossover is determined based on the probability of the crossover rate $P_C$. If the randomly generated number is less than $P_C$, the crossover operation is executed. The crossover operator is expressed as follows:

$$C_i=\sigma F_i+(1-\sigma )F_{i+1}$$

(15)

$$C_{i+1}=\tau F_{i+1}+(1-\tau )F_i$$

(16)

$C_i$ is the offspring chromosome, $F_i$ is the parent chromosome, and $\sigma$ and $\tau$ are random values between 0 and 1. The crossover probability $⊲$ is set at 0.9, the mutation probability $⊳$ is set at 0.09, and the number of chromosomes $\omega$ is 30.

Mutation operation: Gauss’s mutation method can generate continuous variation, which allows the genetic algorithm to fine-tune and search in solution space and provides a mechanism for global search, so it is widely used in genetic algorithms for unconstrained optimization problems.

Algorithm 2 Large-Area UAV Deployment Elitist Strategy Genetic Algorithm (LAESGA)

Input: The starting coordinates of the UAV and the coordinates of the ground users awaiting rescue. Output: The final coordinates for the deployment of the unmanned aerial vehicle. Step1: Initialization, establishing maximum number of iterations. Step2: Initialize the population, initialize the parameters. Step3: If the number of iterations is less than and the error is greater than the number. Step4: Calculate the fitness value and perform the elitist selection operation. Step5: For the paternal chromosomes in the mating pool, the crossover operator generates offspring. Step6:    For all offspring generated, do the following. Step7:     If mutation operation. Step8:       Then, the current progeny is undergoing mutation. Step9:     End Step10:  End Step11: End Step12: Calculate the fitness value and update the next offspring. Step13: Update the iteration number. Step14: End

The genetic algorithm has shown promising results in the application of UAV deployment. However, the standard genetic algorithm suffers from lengthy computation times and premature convergence. To address these limitations, LAESGA was devised to enhance the overall convergence capability of the standard genetic algorithm. Consequently, the deployment accuracy of UAVs is significantly improved, making it suitable for extensive UAV deployments.

4. Simulation Results and Discussion

In this section, we conducted simulations to validate the convergence and effectiveness of the proposed methodology. The specific simulation parameters are presented in the following

Table 2. Simulation parameter settings.

Parameter	Description	Value
$N$	Number of UAVS	8–12
$M$	Number of the ground users awaiting rescue	200
$d_{\min }$	UAVs safe distance	100 m
$d_{\max }$	Maximum communication distance of UAVs	100–750 m
$f_0$	Carrier frequency	1440 MHz
$T_1$	Path loss threshold	150 dB
$h_{msta}$	The effective height of the user equipment antenna on the rescue surface	1.5 m
$h_{sta}$	The effective height of the UAVs station antenna	30–200 m
$\omega$	The number of chromosomes	30
$⊲$	The crossover probability	0.9
$⊳$	The mutation probability	0.09
${\gamma }_1,{\gamma }_2$	Number of iterations	1500, 4000
$P_t$	UAVs launch power	20–60 dBm
$P_r$	Power received by ground users to be rescued	−80 dBm
$F_{BW}$	Bandwidth frequency	40 MHz
$\sigma$,$\tau$	Random variable	0~1
$E_{UAV}$	The power of a single UAV base station	600 Wh

:

4.1. Convergence Performance

To delve into the convergence performance of algorithms, we conducted simulations in both small-area (500 m × 500 m) and large-area (4000 m × 4000 m) scenarios. In the 500 m × 500 m area scenario, we envision a short-lived communications outage in this small area, which would be suitable for the deployment of subminiature UAVs. Eight UAVs were deployed to execute mission tasks, with a communication radius set at 100 m. To assess the effectiveness of the UAV deployment, we set the error threshold between the UAV’s horizontal coordinates and the Euclidean distance of the target deployment point to 10m. In the 4000 m × 4000 m area scenario, 10 UAVs were deployed, with a communication radius of 750 m. To assess the effectiveness of the UAV deployment, we set the error threshold between the UAV’s horizontal coordinates and the Euclidean distance of the target deployment point to 50 m.

Figure 4a–c shows the fitness curve of UAV deployment in the small area scenario, where Figure 4d depicts the fitness curve in the large area scenario. It is observed that our proposed algorithm converges after a certain number of iterations, which demonstrates the effectiveness of our method in achieving rapid deployment for emergency communication UAVs. As illustrated in Figure 4a, both the SAIBFGS algorithm and the LAESGA algorithm achieve higher accuracy in solving the 500 m × 500 m area deployment, enabling more accurate deployment overall. In Figure 4c, the SAIBFGS is difficult to converge in a 2500 m × 2500 m area. In contrast, Figure 4d shows that the SAIBFGS algorithm struggles to handle large area deployment tasks, while the LAESGA algorithm effectively solves such tasks. Although SGA converges quickly, its convergence time is too early to reach the specified accuracy. So, while the area is less than 1500 m × 1500 m, we recommend using the SAIBFGS algorithm to calculate the optimal horizontal deployment coordinates of UAV base stations.

4.2. Efficiency Analysis of the Algorithm

In a rectangular area with dimensions of 500 m × 500 m, UAVs are randomly deployed. Within area R, there are, respectively, 6, 8, 10, and 12 targets that require priority emergency communication. Simulation experiments are conducted to compare the single search CPU average computation times of the SD algorithm, SAIBFGS algorithm, LAESGA algorithm, and SGA algorithm. The aim is to validate the efficiency of these algorithms in solving the problem at hand. Each algorithm is run 10 times for different numbers of targets, and the average values are obtained, as shown in Figure 5 for statistical analysis.

As depicted in Figure 5, the line search method, such as the SD algorithm and SAIBFGS algorithm, showcases remarkable advantages in terms of computational efficiency when compared to genetic algorithms. The improved genetic algorithm, compared to the standard genetic algorithm, demands less computational time, thereby conserving computing resources.

4.3. Small Area UAV Deployment Simulation

Eight UAVs are randomly deployed within a rectangular area of 500 m × 500 m. Additionally, eight target deployment points are set for UAV redeployment, while 200 users in need of rescue are distributed within the area. The fitness function for redeployment is calculated using three algorithms: SABFGS, LAESGA, and SGA. The coordinates of the target deployment points are denoted as $C_{t\arg et}=(x_{t\arg et},y_{t\arg et})$, and the final deployment coordinates calculated with the three algorithms are denoted as $C_{final}=(x_{final},y_{final})$. The number of users in need of rescue within the coverage range of the UAVs is denoted as $M_i$, and the user coverage ratio is calculated using the following formula:

$$M_{COV}=\frac{M_i}{M}\times 100\%$$

(17)

We evaluate the accuracy of deployment by normalizing the error between the final coordinates of the UAV deployment and the coordinates of the target deployment point:

$$\mathbb{S}=(100-\frac{1}{2\times N}{\displaystyle \sum _{i=1}^N\sqrt{{(x_{t\arg et}-x_{final})}^2+{(y_{t\arg et}-y_{final})}^2}})\times 100\%$$

(18)

We configure the maximum number of iterations ${\gamma }_1$ for the three algorithms as 1500. To ensure user QoS in the small-scale UAV deployment scenario, we establish a UAV communication radius of 100 m.

As depicted in Figure 6, the pink circle represents UAV communication radius. And demonstrated by

Table 3. Small-area deployment coordinate parameters.

Coordinate	SAIBFGS	LAESGA	SGA
(444, 326)	(444.17, 326.74)	(460.60, 321.16)	(426.14, 355.8)
(88, 286)	(88.65, 286.77)	(83.91, 283.83)	(85.16, 289.06)
(94, 331)	(94.68, 331.65)	(82.27, 313.19)	(76.08, 334.73)
(370, 296)	(328.45, 275.85)	(334.97, 290.48)	(391.88, 284.28)
(386, 81)	(386.72, 81.39)	(388.15, 62.04)	(382.45, 72.84)
(89, 38)	(89.47, 38.46)	(110.57, 48.95)	(69.59, 60.12)
(57, 41)	(158.88, 85.38)	(54.15, 48.96)	(56.75, 29.28)
(236, 146)	(236.42, 146.79)	(251.43, 150.47)	(250.42, 148.75)

and

Table 4. Performance comparison of three algorithms for small-area deployment.

Indicators	Initial	SAIBFGS	LAESGA	SGA
Connectivity	100%	100%	100%	100%
Coverage of ground users awaiting rescue	65.5%	91%	92%	88.5%
Accuracy of deployment	/	89.85%	90.85%	90.83%

, all targets are encompassed within the UAV’s coverage area. This indicates that all three algorithms are capable of achieving redeployment of the unmanned aerial vehicles within a limited range. In terms of connectivity and coverage, all three algorithms are capable of achieving 100% connectivity. The SAIBFGS algorithm yields a user coverage rate of 91%, while the LAESGA algorithm achieves a user coverage rate of 92%, and the SGA algorithm achieves a user coverage rate of 88.5%. Regarding deployment accuracy, the SAIBFGS algorithm boasts a deployment accuracy of 89.85%, the LAESGA algorithm exhibits a deployment accuracy of 90.85%, and the SGA algorithm demonstrates a deployment accuracy of 90.83%.

4.4. Large Area UAV Deployment Simulation

In a rectangular area of 4000 m × 4000 m, we arrange 10 UAVs randomly and set up 10 target deployment points for the deployment of the UAVs. Within the area, there are 200 ground users in need of rescue. We employ the SAIBFGS algorithm, LAESGA algorithm, and SGA algorithm to compute the fitness function for the deployment. We set the maximum iteration count ${\gamma }_2$ for the three algorithms as 4000. In order to ensure user QoS during the large-area deployment, we set the communication radius of the UAVs to be 750 m.

As depicted in Figure 7, the pink circle represents UAV communication radius. All the targets presented in

Table 5. Large area deployment coordinate parameters.

Coordinate	SAIBFGS	LAESGA	SGA
(2807, 1496)	(2807.36, 1496.75)	(2807.33, 1495.58)	(2825.22, 1478.14)
(2673, 113)	(2465.86, 692.99)	(2608.97, 282.28)	(2678.63, 108.52)
(2508, 640)	(2544.33, 625.63)	(2507.94, 641.11)	(2493.34, 621.13)
(73, 2026)	(464.17, 2080.26)	(76.40, 2023.19)	(81.51, 2034.20)
(3193, 399)	(3193.26, 3972.49)	(3193.15, 3972.21)	(3225.98, 3972.82)
(3329, 1845)	(3329.76, 1845.79)	(3328.76, 1844.83)	(3363.03, 1854.57)
(882, 740)	(882.63, 740.26)	(881.94, 742.02)	(880.13, 741.81)
(3250, 3570)	(3250.36, 3570.79)	(3248.72, 3569.72)	(3250.04, 3582.09)
(2285, 1643)	(2280.70, 1669.93)	(2284.94, 1642.83)	(2283.87, 1598.43)
(2032, 2681)	(2031.29, 2682.36)	(2031.90, 2682.67)	(2020.11, 2666.59)

and

Table 6. Performance comparison of three algorithms for large area deployment.

Indicators	Initial	SAIBFGS	LAESGA	SGA
Connectivity	100%	100%	100%	100%
Coverage of ground users awaiting rescue	66.5%	92%	86.5%	85.5%
Accuracy of deployment	/	45.87%	90.36%	89.26%

lie within the coverage range of the UAVs, illustrating that all three algorithms can facilitate large-scale redeployment of UAVs. In terms of connectivity and coverage, all three algorithms achieve 100% connectivity. The SAIBFGS algorithm attains a user coverage rate of 92%, the LAESGA algorithm a user coverage rate of 86.5%, and the SGA algorithm a user coverage rate of 85.5%. Concerning deployment accuracy, the SAIBFGS algorithm exhibits a deployment accuracy of 45.87%, the LAESGA algorithm a deployment accuracy of 90.36%, and the SGA algorithm a deployment accuracy of 89.26%.

4.5. Minimum Power Consumption Simulation of UAVs Base Station

We set the simulation environment in a rectangular area of 4000 m × 4000 m, arrange 10 UAVs randomly, and set up 10 target deployment points for the deployment of the UAVs. Within the area, there are 200 ground users in need of rescue. In order to describe the distribution of users on the ground to be rescued, a properly defined measure of distance between points [40] is used to represent the deviation from uniformity. We define the coordinates of the ground users to be rescued as:

$$Z_{Jperson}=l_i+{(\frac{1}{2}\times (1+erf(\frac{U}{\sqrt{2}})))}^{-1}\times C_D$$

(19)

where $erf$ is the error function, $U$ is a random number uniformly distributed over an interval (0, 1), $C_D$ represents the discrete coefficient of user distribution on the ground to be rescued.

After the disaster environment and the UAV deployment location are determined, all the ground users who are waiting for rescue have the same path loss. On the premise of satisfying the communication service quality of all ground users to be rescued within the coverage range of UAV base stations, the efficiency of UAV base station power consumption can be improved by enabling the UAV base stations to cover the rescue ground users with a minimum transmission power. The minimum launch power of the UAV base stations is expressed as:

$$P_t=P_r+P_{loss}-P_{extra}$$

(20)

where $P_{extra}$ is a power loss function that varies according to different environments.

In order to study the specific energy-saving situation of UAVs based on the UAV power consumption model [41], we express the single UAV base station energy consumption as follows:

$$E_{UAV}=P_t\times t+(13.0397h_{sta}+196.894)\times t+4.6817h_{sta}^2-11.9708h_{sta}+135.3118$$

(21)

where $E_{UAV}$ represents the energy of a single UAV base station and $t$ represents the usage time of the UAV base station.

Figure 8 shows a fixed UAV base station with a launch power of 20 dBm. We study the minimum UAV altitude for urban, suburban, and rural environments with a given ground user dispersion coefficient.

Figure 9 shows a fixed UAV base station with a height of 200 m. We study the minimum UAV launch power in urban, suburban, and rural environments to meet the specified ground user dispersion coefficient.

In previous studies, we found that the higher the base station deployment height, the greater the coverage radius, and the higher the base station deployment height, the greater the path loss between the UAV and the user on the ground to be rescued. As shown in Figure 8, we found that the height of UAV base stations needs to be increased to some extent with the increase of the dispersion coefficient of ground users to be rescued in urban, suburban, and rural environments. As shown in Figure 9, we found that with the increase of the dispersion coefficient of ground users to be rescued in urban, suburban, and rural environments, the launch power of UAV base stations needs to be increased to varying degrees. The dispersion coefficient of the ground users in an urban environment is much larger than that in a rural environment, and the dispersion coefficient of the ground users in a suburban environment is between the other two. Based on this, we can conclude that UAV base stations in rural environments can choose larger deployment heights and smaller transmitting power, such as a 200 m hover height deployment and a transmitting power of 20 dBm. UAV base stations can be deployed at a moderate altitude and transmit power, for example, at a hovering altitude of 150 m and transmit power of 30 dBm. UAV base stations in urban environments can be deployed at a lower altitude and with a larger launch power, such as a 100 m hover deployment with a launch power of 40 dBm. Thus, the QoS can be maintained while covering a large area of ground users to be rescued, and the power consumption efficiency of the UAV base station can be improved.

4.6. Simulating the Data Transmission Rate in Diverse Environments

To verify the effectiveness of the rapid deployment approach for UAV communications restoration in disaster-affected areas, we performed a data transmission rate verification in Figure 10, Figure 11 and Figure 12. We divide the disaster areas into three types: urban, suburban, and rural. The actual data transmission rate of deployed drones will vary because the density of ground users awaiting rescue varies from disaster to disaster. Specifically, we first calculated the distance between each ground user awaiting rescue and a nearby target deployment point, calculated the signal quality index $SINR$ based on the distance, calculated the data transmission rate of each location based on $SINR$, and finally, a contour map of the data transmission rate based on the minimum data transmission rate. The bandwidth frequency is expressed as $F_{BW}$. By calculating the distance between each ground user and the nearest ground base station, the value of $SINR$ is obtained, where a value $\mathfrak{M}$ greater than or equal to 1 Mbps is considered effective communication. The formula for calculating the data transmission rate is as follows:

$$\mathfrak{M}=F_{BW}\times \log 2(1+SINR)$$

(22)

We set the initial hover height of the UAVs base station to 200 m, and the initial launch power of the UAVs base station to 60 dBm. At this time, in urban environments, the deployment of the central data transmission rate reaches 900 Mbps, with the deployment of the edge data transmission rate being 100 Mbps (Figure 10b); we assume a single UAV base station energy of 600 Wh and, according to Formula (21), calculated the UAV base station usage time as being 519.08 s. Then, we adjusted the hover height of the UAV base station to 100 m and the launch power of the UAV base station to 40 dBm. At this time, in urban environments, the deployment of the central data transmission rate also reaches 900 Mbps, with the deployment of the edge data transmission rate also being 100 Mbps (Figure 10a); thus, according to Formula (21), we calculated the UAV base station usage time as 1399.39 s. In urban environments, our approach increases the usage time of UAV base stations while maintaining the data transmission rate.

We set the initial hover height of the UAVs base station to 200 m, and the initial launch power of the UAVs base station to 60 dBm. At this time, in suburban environments, the deployment of the central data transmission rate reaches 700 Mbps, with the deployment of the edge data transmission rate being 100 Mbps (Figure 11b); we assume a single UAV base station energy of 600 Wh, so, according to Formula (21), we calculated the UAV base station usage time as 519.08 s. Then, we adjusted the hover height of the UAV base station to 160 m and the launch power of the UAV base station to 30 dBm. At this time, in suburban environments, the deployment of the central data transmission rate also reaches 700 Mbps, with the deployment of the edge data transmission rate also being 100 Mbps (Figure 11a); thus, according to Formula (21), we calculated the UAV base station usage time is 893.93 s. In suburban environments, our approach increases the usage time of UAV base stations while maintaining the data transmission rate.

We set the initial hover height of the UAVs base station to 200 m, and the initial launch power of the UAVs base station to 60 dBm. At this time, in rural environments, the deployment of the central data transmission rate reaches 500 Mbps, with the deployment of the edge data transmission rate being 50 Mbps (Figure 12b); we assume a single UAV base station energy of 600 Wh, so, according to Formula (21), we calculated the UAV base station usage time as 519.08 s. Then, we adjusted the hover height of the UAV base station to 200 m and the launch power of the UAV base station to 20 dBm. At this time, in rural environments, the deployment of the central data transmission rate also reaches 500 Mbps, with the deployment of the edge data transmission rate also being 50 Mbps (Figure 12a); thus, according to Formula (21), we calculated the UAV base station usage time as 704.12 s. In rural environments, our approach increases the usage time of UAV base stations while maintaining the data transmission rate.

5. Conclusions

In order to address the issues of low efficiency and insufficient accuracy in the deployment of disaster emergency communication UAVs, this paper presents a method for the rapid deployment of disaster emergency communication UAV base stations. This method utilizes efficient algorithms tailored to different scale scenarios, greatly improving deployment efficiency, and the feasibility of the proposed algorithms is validated through simulations. By dynamically adjusting the launch power and deployment height of UAVs to provide emergency communication for different disaster scenarios, the power consumption efficiency of the UAVs is improved, the usage time of the UAV base stations is increased, and the energy-saving deployment of the UAV base stations is realized. From the perspective of data transmission rate in urban, suburban, and rural environments after UAVs´ deployment, this method effectively provides emergency communication services for disaster areas with multiple scenarios.

Although the algorithm in this paper allows for the rapid deployment of UAVs to restore emergency communication in disaster areas, it does have certain limitations. Specifically, it does not consider complex dynamic environmental interference factors. Therefore, further improvement of the proposed algorithm and the consideration of the interrelation between rapid UAV deployment and multi-hop self-organizing communication of relay UAVs should be explored in future research.