A Method of Relay Node Selection for UAV Cluster Networks Based on Distance and Energy Constraints

Abstract

Cooperative communication is a key technology to improve the stability of UAV swarm communication. To reduce the energy consumption in cooperative communication, this study proposes a method for selecting relay nodes based on distance and energy constraints. First, a two-stage communication model was designed to explain the signal forwarding communication process. Subsequently, cluster head nodes were filtered through a competition mechanism to be used for forwarding source signals. The minimum communication capacity of the link contained the distance parameter of the relay link. Lastly, under energy and distance constraints, the optimal solution of the minimum interrupt function for the cluster head was found, and was defined as the best relay node. The experimental results show that the two parameters of network coverage and residual energy of the improved method were higher than those of other mainstream algorithms. Furthermore, the actual UAV networking test results show that the proposed relay selection method had the most residual energy. It is concluded that the relay selection method proposed in this study has good practicality and advancement in UAV cluster communication.

1. Introduction

Unmanned aerial vehicle (UAV) cluster networks have a wide range of applications in industry, agriculture, and forestry. Cooperative communication is a key technology to increase communication stability in UAV networks [1,2]. As the number of communication nodes in a cluster network increases, the selection of the optimal relay node will consume a large amount of energy. However, the energy provided by UAVs for communication is limited, so UAV communication requires low energy consumption [3]. Relay node selection method optimization is used as an effective method to reduce the energy consumption. Therefore, the method of selecting relay nodes in collaborative communication has become the focus of scholars’ research.

Relay selection methods are an important part of research in cooperative communication. Scholars have been working on reducing the complexity of the methods. After more than a decade of development, the conducted research has formed several schools of thought based on node topology information, instantaneous channel information, and link evaluation. In 2003, Sendonaris was the first to propose a two-stage research model for relay node forwarding [4], and the model applied cooperative communication to the research of wireless communication. Since then, scholars have been keen on the study of relay selection for wireless communication.

In recent years, the focus of research on relay node methods has started to shift towards cluster networks. In 2020, Cao D et al. proposed a relay selection method based on spatial node location information [5]. In order to reduce the complexity of obtaining dynamic information, this research used the spatial location data of nodes to calculate the probability of link disruption. Although the results of the study improve the stability of the communication link, the calculation process requires knowledge of the state information of all nodes, which is difficult to achieve in practice. In 2020, Lei H et al. proposed a relay selection method based on the average signal-to-noise ratio [6]. To simplify the complexity of the computational process, the research used the signal-to-noise ratio of the link to construct the optimal function. The improved method reduced the energy consumption of the communication process. However, the method will become computationally intensive if the communication link is interrupted. In 2020, Ji B et al. improved the relay selection algorithm using the maximum–minimum principle [7]. Under the energy constraint, the optimal communication quality function was studied by minimizing the link information to constitute the optimal communication quality function. The optimal function was solved by the gradient descent method and used to determine the best relay node. The proposed method discards the information of interrupted links, and the process of solving for link information is simplified. In the same year, the scope of the communication process was extended. In 2020, Dy Peng M et al. proposed the relay packet routing (RS-CPR) scheme to reduce channel contention conflicts and decrease energy consumption [8]. The proposed method improves the throughput of the network system; however, the system complexity of the algorithm will be high when the number of relays is high. Cao D et al. improved a distance-based robust relay selection method for eliminating interference in the communication process [9]. The improved strategy enhances the stability of the network link, but the method requires a large storage space. In 2021, C Huang et al. proposed a selection algorithm based on instantaneous channel state information [10]. The algorithm improves the accuracy of the selection method. However, the algorithm is limited by the number of nodes. When the number of nodes of the network increases, the energy consumption of the system will become gradually larger. By comparing the above-mentioned research results, it is apparent that the focus of research on clustered networks is how to reduce the energy consumption of node communication.

Low-power communication has achieved many results in the research of collaborative communication, and the research results focus on two methods of clustering grouping and power allocation. In 2020, Martinaa et al. designed a network protocol for subcluster communication [11]. It assisted in dividing the network into several cluster heads according to grouping, which reduced the communication between groups. Later, Ngang-bam R et al. proposed a low-energy adaptive clustering network structure for wireless sensor networks [12]. The algorithm was autonomously divided into several cluster heads according to the size of the network. The network can be divided automatically to reduce the energy consumption of the algorithm. For the problem of irregular networks, in which size is irregular, Agrawal D et al. proposed an unequal clustering method [13]. The research effectively solves the problem of energy consumption of equipartition groups. However, the method is only applicable to sensor networks.

Due to the rise of machine learning, researchers started to use machine learning to solve the energy allocation problem. Suriya Praba T et al. designed a pendulum water wave transmission mechanism to solve the energy imbalance problem of multi-hop networks [14]. The network automatically formed hierarchical clusters by a quadratic clustering algorithm to solve the hierarchical problem of large-scale communication. Therefore, Benmahdi M B et al. proposed an infinite sensor network cluster head approach [15]. The study designed a distributed K-means method to accomplish adaptive clustering network partitioning. The improved method showed better performance in terms of energy consumption and network lifetime. Ren Q et al. proposed an energy-efficient cluster head selection scheme called EECHS [16]. The study concluded with the energy allocation problem of subclusters. In 2021, Nagendranth MVSS et al. proposed a fuzzy-based two-class clustering routing protocol for solving the energy overload problem of data transmission in MANETs [17]. Zhi Lin et al. proposed an improved optimization algorithm to solve the energy allocation problem for long-distance communication [18]. In 2022, Kandali K integrated density peak clustering (DPC) and particle swarm optimization (PSO) into a single algorithm to improve the stability of mobile networks [19]. Inspired by this, Tabatabaei S et al. proposed a new algorithm similar to bacterial foraging and movement [20]. Although the above methods improve the efficiency of energy allocation, larger memory is required. Nowadays, how to calculate the energy allocation method for small amounts of information is an important direction for cooperative communication.

The UAV cluster network consists of movable UAVs. The network nodes and links are mobile. However, the existing studies have not been able to address the low-power communication needs of UAVs. Therefore, some studies have shown that sufficient attention needs to be paid to relay selection methods for mobile networks with regard to the energy consumption of cooperative communications [21,22]. In order to reduce the energy consumption in communication, a relay selection method based on distance and energy constraints is proposed in our study. A competing method used to determine the subclusters is proposed to partition the network. Link information based on node distances is computed by solving for spatial node coordinates. The outage probability function under the energy constraint is studied, and the optimal solution of the function is the best relay node information. The comparison of experimental results proves that the method proposed in this study has better network coverage and energy allocation efficiency than the mainstream algorithms. Furthermore, practical tests show that the proposed method has good practicality. It is concluded that the relay selection method proposed in this study can be used in the low-power communication of UAV clusters.

2. Multi-Relay Selection Theory Based on Energy Allocation

2.1. Cluster Head Selection Method Based on Competition Mechanism

Cooperative communication consists of a two-stage signal broadcast process. Figure 1 illustrates the working process of collaborative communication. In the first stage, the source node transmits the source signal to the surrounding nodes in the form of broadcast. The surrounding nodes obtain the diversity gain from the source node. In the second stage, the system selects the best relay node to forward the gain to the destination node, and also forwards the gain signal in broadcast form. The destination node sends back information to the relay node on whether to decode the gain or not [23]. Since the communication process is a broadcast signal, other nodes also receive the gain forwarded by different nodes. The signal expressions for these two phases are shown in the following equations.

Relay node receives the signal

$${\mathrm{y}}_{\mathrm{s}\mathrm{r}}={\mathrm{h}}_{\mathrm{s}\mathrm{r}}\sqrt{{\mathrm{E}}_{\mathrm{s}}}\mathrm{x}+{\mathrm{z}}_{\mathrm{s}\mathrm{r}}$$

(1)

Destination node receives signal

$${\mathrm{y}}_{\mathrm{r}\mathrm{d}}={\mathrm{h}}_{\mathrm{r}\mathrm{d}}\sqrt{{\mathrm{E}}_{\mathrm{r}}}{\mathrm{y}}_{\mathrm{s}\mathrm{r}}+{\mathrm{z}}_{\mathrm{r}\mathrm{d}}$$

(2)

In the formula, s denotes source node, r denotes relay node, d denotes destination node, y denotes the signal received by the node, h denotes the link channel gain, E denotes the energy consumed by the transmission, and Z denotes the noise.

In order to solve the complex problem of randomly distributed relay node computation, a novel reorder selection algorithm has been proposed in the research. The improvement in the method arises through the use of a competition mechanism to reduce the information transmission without nodes and select the best communication link for cooperative communication. In the two-stage process of the cooperative communication packet, the whole link channel quality is taken as the minimum of the two links channel quality, after determining the two-stage communication link channel quality, the research determines the best relay competition method according to the link quality maximum competition method, and the relay competition rules designed in the research are as follows.

Reducing the energy consumption of multiple nodes is the first problem addressed by cooperative communication. A novel cluster selection algorithm is proposed in the study. The cluster head node competition mechanism is designed to reduce the message transmission between packets. The cluster head node of the cluster network is responsible for forwarding the information. The research calculates the channel quality of the entire link by identifying the minimum channel quality value in both phases. The optimal solution of the link function is the best relay node information. The cluster head is selected based on the relay competition method with the maximum link quality. The relay competition rule formula is as follows.

$${\mathrm{q}}_{\mathrm{i}}=\min \left({\left|{\mathrm{h}}_{\mathrm{S},\mathrm{i}}\right|}^2,{\left|{\mathrm{h}}_{\mathrm{i},\mathrm{D}}\right|}^2\right)$$

(3)

In the formula, h is the channel coefficient of a communication link, Si is the link between the source and the relay, iD is the link between the relay and the destination.

The competition weights of each relay node are defined in the competition rules of the cluster head. When a competition cycle T starts, each node decreases its count by the same unit. When the count reaches zero, the node is selected as the best relay node. At this point, the best relay node notifies the other nodes that the competition has ended by broadcasting. The expression for the weights is presented as

$${\mathrm{w}}_{\mathrm{i}}=\frac{\mathrm{\lambda }}{{\mathrm{q}}_{\mathrm{i}}}$$

(4)

Here, λ is a constant with a value of 0.01 T.

The research uses a method based on the joint application of maximum channel quality and minimum link quality to design the optimal relay competition rule. The expression is as follows.

$${\mathrm{h}}_{\mathrm{sd}}={\max }_{\mathrm{j}}\left\{\min \left({\left|{\mathrm{h}}_{\mathrm{S},\mathrm{i}}\right|}^2,{\left|{\mathrm{h}}_{\mathrm{i},\mathrm{D}}\right|}^2\right)\right\}$$

(5)

Here, j denotes the number of channels, j = (1,2,3,..., n), and i denotes the number of relays, i = (1,2,3,..., n).

The clustered network is divided into subgroups by means of a competition mechanism. Cluster heads are responsible for exchanging information about the subgroup network. The cluster head controls the nodes within the subgroups to communicate with each other. Cluster head communication reduces the information exchange between the nodes of different groups. The collaborative communication contains two phases of communication, and the study establishes the minimum channel capacity instead of complex channel computation. Because the minimum channel only needs to obtain the spatial location of nodes, the selection of relay nodes within the group can avoid interrupted communication over long-distance links. The stability of the communication link is enhanced.

2.2. Alternative Set of Link Distances

In the cooperative communication process of UAV clusters, the process of relay nodes forwarding signals occurs in the second phase of work. The definition of interruption probability was proposed to represent the channel capacity [24]. The mutual information I of the links in the definition of interruption probability is expressed as

$$\mathrm{I}=\frac{1}{\mathrm{n}+1}\log \left[1+{\mathrm{E}}_{\mathrm{s}}{\left|{\mathrm{h}}_{\mathrm{s}\mathrm{d}}\right|}^2\mathrm{S}\mathrm{N}\mathrm{R}+\left.{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{n}}\mathrm{f}}\left({\mathrm{E}}_{\mathrm{s}}{\left|{\mathrm{h}}_{\mathrm{s}\mathrm{r}}\right|}^2\mathrm{S}\mathrm{N}\mathrm{R},{\mathrm{E}}_{\mathrm{r}}{\left|{\mathrm{h}}_{\mathrm{r}\mathrm{d}}\right|}^2\mathrm{S}\mathrm{N}\mathrm{R}\right)\right]\right.$$

(6)

Here, SNR is the signal to noise ratio, and f is a formula that calculates $\mathrm{f}(\mathrm{x},\mathrm{y})=\frac{\mathrm{x}\mathrm{y}}{\mathrm{x}+\mathrm{y}+1}$.

Since the two-stage communication process is dynamic, the above equation-solving process is complicated. The research proposes an improvement using the signal-to-noise ratio instead of a dynamic link. The improvement is easier to solve because of the stability of the signal-to-noise ratio. The research defines the parameters for $\mathrm{\Gamma }=\mathrm{K}·\mathrm{S}·{\mathrm{d}}^{-\mathsf{\beta }}·\mathrm{S}\mathrm{N}\mathrm{R}$, in which K is the link loss parameter, S is the shadow fading parameter, d is the distance of the link, and $\mathsf{\beta }$ is a constant factor.

$$\mathrm{I}=\frac{1}{\mathrm{n}+1}\log \left[1+{\mathrm{E}}_{\mathrm{s}}{\left|{\mathrm{a}}_{\mathrm{s}\mathrm{d}}\right|}^2{\mathrm{\Gamma }}_{\mathrm{s}\mathrm{d}}+\left.{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{n}}\mathrm{f}}\left({\mathrm{E}}_{\mathrm{s}}{\left|{\mathrm{a}}_{\mathrm{s}\mathrm{r}}\right|}^2{\mathrm{\Gamma }}_{\mathrm{s}\mathrm{r}},{\mathrm{E}}_{\mathrm{r}}{\left|{\mathrm{a}}_{\mathrm{r}\mathrm{d}}\right|}^2{\mathrm{\Gamma }}_{\mathrm{r}\mathrm{d}}\right)\right]\right.$$

(7)

From the improved formula, it is clear that the amount of mutual information is related to the distance and energy between nodes. The research puzzle is transformed into an optimal problem based on distance and energy allocation constraints.

The Kalman filter algorithm is used to predict the position of the UAV at the next moment [25,26,27]. Assuming a constant flight speed, the distance of the UAV can be obtained iteratively, the research calculates the link distance of relay forwarding and selects the nodes whose link distance d_xi is less than the average distance d to form the relay alternative set J.

$$\mathrm{J}=\mathrm{\{}{\mathrm{x}}_{\mathrm{i}}\mathrm{|}{\mathrm{d}}_{\mathrm{xi}}<\overline{\mathrm{d}}\mathrm{\}}$$

(8)

2.3. Energy Allocation Strategy in Cooperative Communication Process

When the mutual information of nodes is less than the set threshold, the minimum interruption probability (P_out) of cooperative communication is formulated as follows [12,28].

$$\begin{array}{cc}\hfill {\mathrm{P}}_{\mathrm{out} }& ={\mathrm{P}}_{\mathrm{r}}[\mathrm{I}<\mathrm{R}]\hfill \\ & ={\mathrm{P}}_{\mathrm{r}}\left[{\mathrm{E}}_{\mathrm{s}}{\left|{\mathrm{a}}_{\mathrm{s}\mathrm{d}}\right|}^2{\mathrm{\Gamma }}_{\mathrm{sd}}+{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{n}}\mathrm{f}}\left({\mathrm{E}}_{\mathrm{s}}{\left|{\mathrm{a}}_{\mathrm{s}\mathrm{r}}\right|}^2{\mathrm{\Gamma }}_{\mathrm{sr}},{\mathrm{E}}_{\mathrm{r}}{\left|{\mathrm{a}}_{\mathrm{r}\mathrm{d}}\right|}^2{\mathrm{\Gamma }}_{\mathrm{rd}}\right)\right.\left.<\left(2^{(\mathrm{n}+1)\mathrm{R}}-1\right)\right]\hfill \\ & =\mathrm{C}\left(\mathrm{n}\right)\frac{1}{{\mathrm{E}}_{\mathrm{s}}{\mathrm{\Gamma }}_{\mathrm{sd}}{\mathsf{\sigma }}_{\mathrm{sd}}^2}{\displaystyle \prod _{\mathrm{i}=1}^{\mathrm{n}}\left(\frac{1}{{\mathrm{E}}_{\mathrm{s}}{\mathrm{\Gamma }}_{\mathrm{sd}}{\mathsf{\sigma }}_{\mathrm{si}}^2}+\frac{1}{{\mathrm{E}}_{\mathrm{i}}{\mathrm{\Gamma }}_{\mathrm{rd}}{\mathsf{\sigma }}_{\mathrm{id}}^2}\right)}\hfill \end{array}$$

(9)

Here, $\mathrm{C}(\mathrm{n})={\left(2^{(\mathrm{n}+1)\mathrm{R}}-1\right)}^{\mathrm{n}+1}/(\mathrm{n}+1)$!

Considering that the energy of the UAV is limited, the rational allocation of energy for transmitting and forwarding is studied. The energy allocation scheme is as follows.

Assume the source node energy is ${\mathrm{E}}_{\mathrm{S}}={\mathsf{\beta }}_0{\mathrm{E}}_{\mathrm{t}}$, and the i relay node energy is ${\mathrm{E}}_{\mathrm{i}}={\mathsf{\beta }}_{\mathrm{i}}{\mathrm{E}}_{\mathrm{t}}$, where E_t is the total transmit power of the system, β₀ is the power allocation factor of the source node, and β_i is the i relay node power allocation factor.

$${\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{n}}{\mathsf{\beta }}_{\mathrm{i}}}=1$$

(10)

With the introduction of the energy allocation scheme, the average interruption probability is expressed as

$${\mathrm{P}}_{\mathrm{o}\mathrm{u}\mathrm{t}}=\mathrm{C}(\mathrm{n})\frac{1}{{\mathsf{\beta }}_0{\mathsf{\sigma }}_{\mathrm{s}\mathrm{d}}^2{\mathrm{\Gamma }}_{\mathrm{sd}}{({\mathrm{E}}_{\mathrm{t}})}^{\mathrm{n}+1}}{\displaystyle \prod _{\mathrm{i}=1}^{\mathrm{n}}\left(\frac{1}{{\mathsf{\beta }}_0{\mathrm{\Gamma }}_{\mathrm{sd}}{\mathsf{\sigma }}_{\mathrm{s}\mathrm{i}}^2}+\frac{1}{{\mathsf{\beta }}_{\mathrm{i}}{\mathrm{\Gamma }}_{\mathrm{id}}{\mathsf{\sigma }}_{\mathrm{i}\mathrm{d}}^2}\right)}$$

(11)

Both sides of the formula are logarithmically transformed to obtain

$$\begin{array}{l}\log {\mathrm{P}}_{\mathrm{o}\mathrm{u}\mathrm{t}}=-(\mathrm{n}+1)\log {\mathsf{\beta }}_0+{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{n}}\log ({\mathsf{\beta }}_0{\mathrm{\Gamma }}_{\mathrm{sd}}{\mathsf{\sigma }}_{\mathrm{s}\mathrm{i}}^2+{\mathsf{\beta }}_{\mathrm{i}}{\mathrm{\Gamma }}_{\mathrm{id}}{\mathsf{\sigma }}_{\mathrm{i}\mathrm{d}}^2)-}\\ {\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{n}}[\log {\mathsf{\beta }}_{\mathrm{i}}+2\log ({\mathsf{\sigma }}_{\mathrm{s}\mathrm{i}}{\mathsf{\sigma }}_{\mathrm{d}\mathrm{i}}{\mathrm{\Gamma }}_{\mathrm{sd}}{\mathrm{\Gamma }}_{\mathrm{id}})]+}\log \left[\mathrm{C}(\mathrm{n})\frac{1}{{\mathrm{\Gamma }}_{\mathrm{sd}}{\mathsf{\sigma }}_{\mathrm{s}\mathrm{d}}^2}·\frac{1}{{({\mathrm{E}}_{\mathrm{t}})}^{\mathrm{n}+1}}\right]\end{array}$$

(12)

Solving the energy allocation problem with minimum interruption probability can be transformed into solving the optimal problem [29], thus constructing the Lagrangian function (L) as

$$\begin{array}{cc}\hfill \mathrm{L}=& -(\mathrm{n}+1)\log {\mathsf{\beta }}_0+{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{n}}\log ({\mathsf{\beta }}_0{\mathrm{\Gamma }}_{\mathrm{sd}}{\mathsf{\sigma }}_{\mathrm{s}\mathrm{i}}^2+{\mathsf{\beta }}_{\mathrm{i}}{\mathrm{\Gamma }}_{\mathrm{id}}{\mathsf{\sigma }}_{\mathrm{i}\mathrm{d}}^2)}\hfill \\ & -{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{n}}{[\log \mathsf{\beta }}_{\mathrm{i}}{+2\log (\mathsf{\sigma }}_{\mathrm{si}}{\mathsf{\sigma }}_{\mathrm{di}}{\mathsf{\Gamma }}_{\mathrm{sd}}{\mathsf{\Gamma }}_{\mathrm{id}}\left)\right]+}\mathsf{\lambda }\left[{\displaystyle \sum _{\mathrm{i}=0}^{\mathrm{n}}{\mathsf{\beta }}_{\mathrm{i}}}-1\right]\hfill \end{array}$$

(13)

The research takes the derivative of the optimal function with respect to the energy distribution factor, and the equation is as follows.

$$\frac{\partial \mathrm{L}}{\partial {\mathsf{\beta }}_0}=-(\mathrm{n}+1)\frac{1}{{\mathsf{\beta }}_0}+{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{n}}\frac{{\mathrm{\Gamma }}_{\mathrm{sd}}{\mathsf{\sigma }}_{\mathrm{s}\mathrm{i}}^2}{({\mathsf{\beta }}_0{\mathrm{\Gamma }}_{\mathrm{sd}}{\mathsf{\sigma }}_{\mathrm{s}\mathrm{i}}^2+{\mathsf{\beta }}_{\mathrm{i}}{\mathrm{\Gamma }}_{\mathrm{id}}{\mathsf{\sigma }}_{\mathrm{i}\mathrm{d}}^2)}}+\mathrm{\lambda }=0$$

(14)

$$\frac{\partial \mathrm{L}}{\partial {\mathsf{\beta }}_{\mathrm{i}}}={\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{n}}\frac{{\mathrm{\Gamma }}_{\mathrm{id}}{\mathsf{\sigma }}_{\mathrm{i}\mathrm{d}}^2}{({\mathsf{\beta }}_0{\mathrm{\Gamma }}_{\mathrm{sd}}{\mathsf{\sigma }}_{\mathrm{s}\mathrm{i}}^2+{\mathsf{\beta }}_{\mathrm{i}}{\mathrm{\Gamma }}_{\mathrm{id}}{\mathsf{\sigma }}_{\mathrm{i}\mathrm{d}}^2)}-\frac{1}{{\mathsf{\beta }}_{\mathrm{i}}}}+\mathrm{\lambda }=0$$

(15)

$$\frac{\partial \mathrm{L}}{\partial \mathrm{\lambda }}={\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{n}}{\mathsf{\beta }}_{\mathrm{i}}-1}=0$$

(16)

This is solved using the steepest descent method.

$$\begin{gathered} {\mathsf{\beta }}_0={\mathsf{\beta }}_0-\frac{1}{2}\mathsf{\mu }\frac{\partial \mathrm{L}}{\partial {\mathsf{\beta }}_0}+\Delta ({\mathrm{\Gamma }}_{\mathrm{sd}}) \\ {\mathsf{\beta }}_{\mathrm{i}}={\mathsf{\beta }}_{\mathrm{i}}-\frac{1}{2}\mathsf{\mu }\frac{\partial \mathrm{L}}{\partial {\mathsf{\beta }}_{\mathrm{i}}}+\Delta ({\mathrm{\Gamma }}_{\mathrm{sd}})+\Delta ({\mathrm{\Gamma }}_{\mathrm{id}}) \end{gathered}$$

(17)

2.4. Optimal Solution of Interruption Probability

Since the outage probability P_out is related to the power allocation factor β_i, equivalent signal-to-noise ratio Γ_i, and σ_i [30], and σ_i is an exponential random variable, the probability density satisfies $\mathrm{p}\left(\mathrm{x}\right)=\mathrm{e}-\mathrm{x}$. Thus, the outage probability of the relay node ${\mathrm{P}}_{\mathrm{rs} }^{{\mathrm{r}}_{\mathrm{i}}}$ at this time is as follows.

$${\mathrm{P}}_{\mathrm{rs} }^{{\mathrm{r}}_{\mathrm{i}}}={\mathrm{P}}_{\mathrm{s}\mathrm{d}}·{\mathrm{P}}_{{\mathrm{sr}}_{\mathrm{i}}}+{\mathrm{P}}_{\mathrm{s}\mathrm{d}\mathrm{r}}·\left(1-{\mathrm{P}}_{{\mathrm{s},\mathrm{r}}_{\mathrm{i}}}\right)$$

(18)

$$\mathrm{Here}: {\mathrm{P}}_{\mathrm{s} {\mathrm{r}}_{\mathrm{i}}}=\mathrm{P}\left[\frac{1}{2}{\log }_2\left(1+{\mathsf{\beta }}_{\mathrm{i}}{\mathrm{\Gamma }}_{{\mathrm{sr}}_{\mathrm{i}}}{\left|{\mathrm{a}}_{{\mathrm{sr}}_{\mathrm{i}}}\right|}^2\right)<\mathrm{R}\right]=1-\exp \left(-\frac{2^{2\mathrm{R}}-1}{{\mathsf{\beta }}_{\mathrm{i}}{\mathrm{\Gamma }}_{{\mathrm{sr}}_{\mathrm{i}}}}\right)$$

(19)

$${\mathrm{P}}_{\mathrm{sd}}=\mathrm{P}\left[\frac{1}{2}{\log }_2\left(1+{\mathsf{\beta }}_0{\mathrm{\Gamma }}_{\mathrm{sd}}{\left|{\mathrm{h}}_{\mathrm{sd}}\right|}^2\right)<\mathrm{R}\right]=1-\exp \left(-\frac{2^{2\mathrm{R}}-1}{{\mathsf{\beta }}_0{\mathrm{\Gamma }}_{\mathrm{sd}}}\right)$$

(20)

$$\begin{array}{l}{\mathrm{P}}_{\mathrm{srd}}=\mathrm{P}\left[\frac{1}{2}{\log }_2\left(1+{\mathsf{\beta }}_0{\mathrm{\Gamma }}_{\mathrm{sd}}{\left|{\mathrm{h}}_{\mathrm{sd}}\right|}^2+{\mathsf{\beta }}_{\mathrm{i}}{\mathrm{\Gamma }}_{{\mathrm{r}}_{\mathrm{id}}}{\left|{\mathrm{h}}_{{\mathrm{r}}_{\mathrm{rd}}}\right|}^2\right)<\mathrm{R}\right]\\ =\frac{1}{{\mathsf{\beta }}_0{\mathrm{\Gamma }}_{\mathrm{sd}}-{\mathsf{\beta }}_{\mathrm{i}}{\mathrm{\Gamma }}_{{\mathrm{r}}_{\mathrm{rd}}}}\times \left[{\mathsf{\beta }}_{\mathrm{i}}{\mathrm{\Gamma }}_{{\mathrm{r}}_{\mathrm{r}}\mathrm{d}}\exp \left(-\frac{2^{2\mathrm{R}}-1}{{\mathsf{\beta }}_{\mathrm{i}}{\mathrm{\Gamma }}_{{\mathrm{r}}_{\mathrm{rd}}}}\right)-{\mathsf{\beta }}_0{\mathrm{\Gamma }}_{\mathrm{sd}}\exp \left(-\frac{2^{2\mathrm{R}}-1}{{\mathsf{\beta }}_0{\mathrm{\Gamma }}_{\mathrm{sd}}}\right)\right]+1\end{array}$$

(21)

The research establishes the set of disruption probabilities using the disruption probabilities of all nodes. Under the energy constraint, the research solves the optimal function of system interruption probability and screens the best relay nodes by energy allocation coefficients. The optimal function constructed by the research is as follows.

$${\mathrm{p}}_{\mathrm{o}\mathrm{u}\mathrm{t}}=\arg \min \left\{{\mathrm{P}}_{\mathrm{o}\mathrm{u}\mathrm{t}}^{\mathrm{i}}\right\}$$

(22)

$$\mathrm{St}: {\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{n}}{\mathsf{\beta }}_{\mathrm{i}}}=1$$

$${\mathsf{\beta }}_0={\mathsf{\beta }}_0-\frac{1}{2}\mathsf{\mu }\frac{\partial \mathrm{L}}{\partial {\mathsf{\beta }}_0}+\Delta ({\mathrm{\Gamma }}_{\mathrm{sd}})$$

$${\mathsf{\beta }}_{\mathrm{i}}={\mathsf{\beta }}_{\mathrm{i}}-\frac{1}{2}\mathsf{\mu }\frac{\partial \mathrm{L}}{\partial {\mathsf{\beta }}_{\mathrm{i}}}+\Delta ({\mathrm{\Gamma }}_{\mathrm{sd}})+\Delta ({\mathrm{\Gamma }}_{\mathrm{id}})$$

3. Algorithm Design

Since the energy of the UAV is limited and the location is constantly changing, the algorithm first predicts the spatial location. The communication system establishes the alternative set by screening the link distance. After the energy allocation factor is set, the minimum interruption probability function is determined through the distance and energy parameters. The optimal solution of the function is the information of the relay node. The algorithm 1 that procedure for competitive clustering is designed according to the following steps.

Step 1, Prediction of node locations. The node positions at each moment are predicted by an improved Kalman filtering algorithm

Step 2, Building alternative sets. The spatial distances of the links are obtained and formed into alternative sets J.

Step 3, Energy allocation strategy. According to the energy allocation factor, the source and relay nodes are allocated different amounts of energy for communication.

Step 4, Solve for the optimal disruption probability. In the alternative set J, the optimal outage probability of the solved system is studied according to the power allocation constraint.

Step 5, Solve for the best relay nodes. The solved best relays are sorted by different times to obtain the minimum set of relay nodes.

The pseudo-code design of the algorithm is as follows.

Algorithm 1: Procedure for competitive clustering (n: integer)

var temp, i, j, t;

begin

for t = 1:k;

for i = 1:n;

Ft = f(xi,yi,vt)

Function Competitive clustering (n: integer);

{ qi = min (hsr,hrd);

wi = λ/qi;

Time(i) = time(i)-1;

Q = max(qi;)}

Function ENGRY (n: integer)

{ for j = 1:n

arg (psd(j) + βi prd(j));

$\mathrm{St}: {\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{n}}{\mathsf{\beta }}_{\mathrm{i}}}=1$;}

End

4. Simulation Verification

To verify the practicality and advancement of the improved algorithm, a simulation experiment was carried out by software simulation. The results of three sets of simulation experiments were compared to verify the performance of the improved algorithm. At the same time, 20 UAVs were networked for practical testing to verify the results of the simulation. Through simulation experiments and practical tests, the research results are proven to have good practicality and advancement in UAV clustering networks.

4.1. Parameter Settings

The simulation simulates the cooperative communication process of the cluster network. The simulation parameters are shown in

Table 1. Simulation parameter setting.

Parameter	Parameter Value
Network coverage area	100 × 100 m
Number of UAVs	20
Signal transmission stage	2
Broadcast energy consumption	0.75 J
Forwarding energy consumption	0.5 J
Maximum number of rounds	1000 round
System energy	100 J

. The simulation results contain three metrics: network topology, operational complexity, and energy surplus [31]. During the simulation, the source node sends the signal to the destination node. The signal needs to be forwarded through the relay node. The distance of the network nodes in the simulation is calculated through the location parameter. The optimal solution of the interrupt function is the location information of the relay node. The performance of different algorithms is compared by comparing the magnitude of the three metrics.

4.2. Communication Link Topology Simulation Comparison

The simulation simulates the network topology process with three different algorithms. The first algorithm is a communication process, in which all nodes act as relay nodes. The second algorithm is a relay selection method based on distance and energy constraints. The third algorithm is the process of selecting relay nodes based on the minimum outage probability. The network topology is a measure of the distance of cooperative communication. Both broadcast communications of source nodes and relay nodes forwarding communication affect the network topology range. Figure 2 shows the network topology simulation of the first method. Figure 3 is the network topology simulation of the second method. Figure 4 is the network topology simulation effect of the first method.

4.3. Simulation Comparison of Cooperative Communication Process

The simulation simulates the communication complexity of the three different algorithms. The communication complexity is measured by the number of remaining rounds of communication. Figure 5 shows the cumulative number of rounds after forwarding the signal for the three methods. To accurately compare the energy consumption of the algorithms for each round, Figure 6 shows the number of relays chosen for each round for the three schemes.

Figure 5 shows that the cumulative number of rounds for the first method is larger than the other two methods. The second method and the third method have the same large number of rounds. Figure 6 shows the difference between the number of rounds for the three methods. The first method has the largest number of rounds because the number of relays is the number of drones. The other two methods in the first phase have the same number of rounds. However, after one phase of communication, the number of rounds calculated by method two is less than that of method three. The difference between the number of rounds of the two methods gradually increases.

4.4. Comparative Simulation of System Residual Energy

To verify the effectiveness of the energy constraint of the improved algorithm, Figure 7 compares the residual energy of the three algorithms. It can be seen from the figure that method 1 has the least residual energy during signal forwarding. This is due to the fact that all nodes are involved in relay forwarding, and the network consumes more energy. By comparing the curve trends, the values of method two and method three are similar at the beginning. As the computation process increases, the improved algorithm reduces the number of computations of the nodes, and the energy consumed by method 2 decreases. However, method three has no energy constraint, and the energy consumed in the communication process increases. Figure 8 illustrates that method two outperforms method three in terms of energy constraint comparison.

4.5. Testing of UAV Cluster Networking

A physical test of 20 UAV networks was used to verify the results of the software simulation. The test follows different relay selection algorithms to achieve network communication. Figure 8 shows the results of the experimental test with 20 images transmitted.

Table 2. Statistics of the average remaining energy values of the network for the three groups of algorithms (Unit/J).

	5 min	10 min	15 min	20 min	25 min	30 min
Method 1	95.5	88.8	79.1	65.8	40.6	30.5
Method 2	95.9	90.3	84.4	77.3	58.7	44.1
Method 3	95.4	89.2	81.9	71.5	51.2	38.9

shows the statistical values of the remaining battery power for different algorithms in 30 min. The results show that the network with the improved algorithm has a higher residual power than the other two algorithms. Using the residual energy as a measure, the improved algorithm communication achieves stable communication with low power consumption.

The actual test was conducted using a network of Chinese DJI-branded drones. Three different relay selection algorithms were used for the communication of each of the 20 UAVs. The test recorded battery residual values every 5 min. The Table 2 values are the average of the remaining battery power for the 30-min network, the algorithm with the most energy remaining has good low-power communication.

The research calculates three types of parameters in a network of 20 UAVs through simulations. Physical tests are used to verify the accuracy of the simulation results. The simulation experiments were conducted by comparing the three algorithms in terms of coverage, residual energy, and other parameters. The simulation results show that the improved method has the largest values of the number of communication rounds and residual energy. By comparing the values of residual energy of the three algorithms through physical tests, the improved method has the largest value of residual energy. By comparing the two sets of experiments through simulation and physical tests, the improved algorithm has better application value in UAV swarm network communication.

5. Conclusions

To address the problem of excessive energy consumption of cooperative communication in large-scale UAV population networks, our research proposes an improved relay selection method based on distance and power constraints. In the two-stage communication model developed in this study, cluster heads are identified through a competition mechanism of nodes. Moreover, the network is divided into several broadcast groups for communication. This study indicates that grouping can effectively reduce information interaction of discrete nodes, thereby reducing energy consumption of information transmission.

Furthermore, UAV node information is predicted by utilizing the Kalman filtering method. Link distances are calculated by node information. The link-based mutual information of cooperative communication is simplified. On this basis, the idea for a minimum interruption probability of the link in one cycle is presented. Thus, the problem of solving the network link is transformed into the problem of solving the minimum interruption probability. The optimal dynamic equation, constrained by the energy distribution coefficient, consists of the minimum interruption function, and information about the optimal relay link and relay node is filtered according to the optimal solution of this equation. At the testing and validation stage, the design scheme for this study was carried out on an actual UAV, and the test results were used as parameters for the simulation experiments. The simulation results show that the network’s improved method is optimal in terms of algorithm complexity and residual energy. It demonstrates that our research results have greater advantages in large-scale UAV communication. In addition, the improved method of relay node selection proposed in this study is a theoretical innovation for large-scale intra-UAV communication, and has significant performance in physical simulations.

Future research needs to consider remote communication between UAV swarms and the ground based on this study. Dual-channel communication between ground-based base station communication and UAV air communication is not only a future research direction, but also an important means to solve mutual interference between base stations and UAVs. It is found that the method proposed in this study is suitable for application in large-scale UAV swarms, and that the improved algorithm has good practicality and generality.

6. Patents

A patent entitled “Heterogeneous cognitive wireless sensor network cluster routing method” is disclosed under CN110708735B.