CN114173304A - A trade-off method for throughput and delay of 3D UAV communication network - Google Patents

Abstract

The invention relates to the technical field of unmanned aerial vehicle communication, and specifically discloses a method for weighing the throughput and time delay of a three-dimensional unmanned aerial vehicle communication network. The weighted sum of rates is the optimization objective, and the original optimization problem is determined by jointly optimizing the 3D UAV trajectory, communication time and rate allocation; given the UAV height, the original optimization problem is simplified into the first sub-problem, and the first sub-problem is The subproblem is transformed into a first convex optimization problem; given the two-dimensional trajectory and resource allocation of any UAV, the original optimization problem is reduced to a second subproblem, and the second subproblem is transformed into a second convex optimization problem; The first and second convex optimization problems are solved to obtain a suboptimal solution to the original optimization problem. Simulation results show that this method achieves a trade-off between throughput, latency, and height-dependent angle-distance on 3D UAV communication networks.

Description

A trade-off method for throughput and delay of 3D UAV communication network

technical field

The invention relates to the technical field of unmanned aerial vehicle communication, in particular to a method for weighing throughput and time delay of a three-dimensional unmanned aerial vehicle communication network.

Background technique

Due to the characteristics of mobility, low cost, and easy deployment, unmanned aerial vehicles (UAVs) are expected to be widely used as aerial wireless platforms in the beyond fifth generation (B5G) and sixth generation (6G) wireless communication networks. Specifically, when the ground base station (GBS) is paralyzed due to natural disasters, the UAV can be used as an air base station (ABS) for backup transmission, or as an auxiliary communication platform to supplement the ground base station to unload the hotspot base station network data. Unlike traditional terrestrial wireless communication systems, UAVs are easier to establish a line-of-sight (LoS) communication link due to their maneuverability and flexibility, helping to improve the performance of the communication system.

On the other hand, multimedia services such as video are becoming more and more popular, such as virtual reality, online games, etc. The huge amount of data brings huge pressure on the service capability of existing wireless networks, resulting in low quality of service (QoS) for users. Therefore, B5G and 6G networks are expected to provide different quality of service guarantees for media applications on various networks in network design. For example, when a user downloads a file with latency requirements, others may play a high-definition (HD) movie at the same time, which requires a minimum playback rate limit. Therefore, these different types of services should be optimized at the same time to maximize system throughput while meeting the heterogeneous latency requirements of different applications. Intuitively, for applications that support UAV communication, UAVs can serve a specific user by getting closer to better channel quality to increase throughput. But this situation will cause the drone to move away from other users, causing those users to have poor channel quality and violating their latency requirements. Therefore, for the user, there is a fundamental trade-off between throughput and latency requirements, due to which the mobility of the drone may be limited. At present, some work has studied the trade-off between throughput and access delay in UAV communication. UAVs fly along a fixed straight line and communicate with users in a cyclic multiple access mode. There is also work to study the UAV communication system considering the delay, by optimizing the UAV trajectory and power and bandwidth allocation to maximize the minimum value of the average throughput of all users. There is also work that divides transmissions with delay requirements into two categories, namely delay-limited transmissions and delay-tolerant transmissions, and maximizes the throughput of the system on this basis. However, these works above only consider UAVs to fly in a straight line or perform horizontal flight, while ignoring that UAVs can move freely in three-dimensional (3D) space.

Compared with ground communication, the modeling of air-to-ground (A2G) communication channel is more challenging due to the location of UAV in 3D free space, such as A2G communication contains more model parameters. Obstacles (like buildings, trees, etc.) can obstruct the transmitted signal or reduce its power, the impact of which is the main difficulty to be solved in A2G channels. Generally speaking, line-of-sight (LoS) channels and non-line-of-sight (NLoS) channels are two common channel states in A2G channels, and each state is characterized by different models. At present, a probabilistic LoS channel model has been proposed, which uses the function of the elevation angle between the UAV and the ground user to describe the probability of occurrence of the LoS/NLoS channel state. Intuitively, by increasing the altitude of the drone, the LoS probability increases as the drone-ground elevation angle increases. However, if the drone height increases, the distance between the drone and the user will increase, which will result in a larger path loss, which reflects the channel gain angle-distance trade-off associated with altitude. On the other hand, when considering that the drone is flying in three-dimensional space, the greater the height of the drone, the greater the elevation angle between the drone and all the users, which is approximately the same, then the distance between the drone and all the users can be realized. Fairer communication achieves similar latency at the same time. However, increasing the drone height results in an increase in the distance between the drone and the user, which reduces the throughput of the user. In fact, the effect of drone height on throughput and latency is unknown, which has not been studied in previous work.

SUMMARY OF THE INVENTION

The invention provides a method for weighing the throughput and delay of a three-dimensional unmanned aerial vehicle communication network, and the technical problem to be solved is: how to realize the throughput, delay and the angle-distance relationship related to the height on the three-dimensional unmanned aerial vehicle communication network. compromise balance.

In order to solve the above technical problems, the present invention provides a method for weighing the throughput and delay of a three-dimensional unmanned aerial vehicle communication network, comprising the steps of:

S1. To maximize the user throughput of the 3D UAV communication system and the weighted sum of the required minimum rate as the optimization goal, determine the original optimization problem by jointly optimizing the 3D UAV trajectory, communication time and rate allocation;

S2. Given the height of the UAV, simplify the original optimization problem into the first sub-problem, and transform the first sub-problem into the first convex optimization problem based on the differential convex function optimization framework and successive convex approximation;

S3. Given the two-dimensional trajectory and resource allocation of any UAV, simplify the original optimization problem into a second sub-problem, and transform the second sub-problem into a second convex optimization problem based on the differential convex function optimization framework and successive convex approximation ;

S4. Solve the first convex optimization problem and the second convex optimization problem based on an iterative algorithm and a convex optimization solver, and obtain a suboptimal solution of the original optimization problem.

Further, in step S1, the three-dimensional UAV communication system includes 1 UAV and K ground users, wherein the UAV serves as an air base station for K ground users; the original optimization problem is described as:

(P1):

q[1]=q[N], z[1]=z[N], (8)

分别表示无人机水平和垂直方向的最大速度，总时间T分成N个等长时隙δ_t，即T＝Nδ_t；式(8)表示无人机周期性地为地面用户服务；式(7)表示任意时隙无人机在最小飞行高度H_min和最大飞行高度H_max之间飞行；式(6)表示地面用户s_k到无人机的仰角的定义，其中w_k表示地面用户s_k的水平位置，K个地面用户的集合表示为

式(5)中，r_k表示地面用户s_k的最小速率，x_k[n]表示时隙n时无人机与地面用户s_k通信的时间分配，满足式(2)的条件，

表示时隙n时无人机与地面用户s_k通信的近似期望速率，由期望速率

近似而来；式(3)表示无人机每个时刻最多和一个地面用户进行通信；式(4)中，

表示无人机对地面用户s_k的总吞吐量，m表示加权系数，0≤m≤1，mD_k+(1-m)r_kN表示地面用户s_k的总吞吐量和所需最小速率的加权和，μ表示三维无人机通信系统的用户吞吐量和所需速率的加权和的最小值；

Among them, equations (9) and (10) represent the speed limit of the UAV, q[n], z[n] represent the horizontal position and height of the UAV at time slot n, respectively,

respectively represent the maximum speed of the UAV in the horizontal and vertical directions, and the total time T is divided into N equal-length time slots δ _t , namely T=Nδ _t ; Equation (8) indicates that the UAV serves ground users periodically; Equation ( 7) Indicates that the UAV flies between the minimum flight height H _min and the maximum flight height H _max in any time slot; Equation (6) represents the definition of the elevation angle from the ground user s _k to the UAV, where w _k represents the ground user s The horizontal position of _k , the set of K ground users is expressed as

In equation (5), r _k represents the minimum rate of ground user _sk , x _k [n] represents the time allocation of the communication between the UAV and the ground user _sk in time slot n, which satisfies the condition of equation (2),

Represents the approximate expected rate of communication between the UAV and the ground user _sk at time slot n, given by the expected rate

Approximate; Equation (3) indicates that the UAV communicates with at most one ground user at each moment; in Equation (4),

represents the total throughput of the UAV to the ground user _sk , m represents the weighting coefficient, 0≤m≤1, mD _k +(1-m)r _k N represents the total throughput of the ground user _sk and the required minimum rate The weighted sum of , μ represents the minimum value of the weighted sum of the user throughput and the required rate of the 3D UAV communication system;

地面用户s_k和无人机之间的LoS信道概率

表示为地面用户s_k到无人机仰角θ_k[n]的函数：Further, the distance between the UAV and the ground user _sk at time slot n

LoS channel probability between ground user _sk and UAV

Expressed as a function of the ground user s _k to the UAV elevation angle θ _k [n]:

表示为LoS通信链路表达式

以概率

表示为NLoS通信链路表达式

其中β₀是在参考距离1m时的信道功率增益，ε表示由于NLoS通信链路传播导致的附加衰减因子，ε＜1；LoS信道链路和NLoS信道链路的路径损耗指数分别表示成α_L和α_N。where B _a < 0, B _b > 0, B _d > 0, B _c =1-B _d , the values of these four constants are determined by the specific environment; at time slot n, the UAV and the ground user s The channel power gain _{βk[n] between k with} probability

Expressed as a LoS communication link expression

with probability

Expressed as an NLoS communication link expression

where β ₀ is the channel power gain at a reference distance of 1 m, ε represents the additional attenuation factor due to the propagation of the NLoS communication link, ε <1; the path loss exponents of the LoS channel link and the NLoS channel link are respectively expressed as α _L and α _N .

其中B表示信号带宽，P表示无人机的发射功率，σ²表示噪声功率；Further, the achievable rate between the UAV and the ground user _sk at time slot n is

where B represents the signal bandwidth, P represents the transmit power of the UAV, and σ ² represents the noise power;

Further, the step S2 specifically includes the steps:

S21. Given the UAV height Z, simplify the original optimization problem (P1) into the first sub-problem:

(P2):

s.t.(2)-(6),(10),

q[1]=q[N] (11)

S22. Introduce slack variables Y={y _k [n]}, Θ={θ _k [n]}, and further transform the problem (P2) into:

(P3):

s.t.(2)-(4),(10),(11),

S23. Based on the differential convex function optimization framework, the non-convex constraint equations (4), (12)-(14) are transformed into convex constraints, and the problem (P3) is further transformed into a standard convex optimization problem (P4).

Further, the step S23 specifically includes the steps:

S231. Rewrite the non-convex term x _k [n]y _k [n] in equation (13) as a differential convex function:

用一阶泰勒展开求近似，得到：S232, matching item

Approximation with first-order Taylor expansion, we get:

where _Qk [n] ^lb is the joint concave function with respect to _xk [n] and _yk [n];

函数应用一阶泰勒展开求近似，得到：S233. For formula (14), when q _k [n] ^l is given, by applying

The function is approximated by a first-order Taylor expansion, and we get:

in,

函数用一阶泰勒展开求近似，得到：S234. For equations (4) and (12), given q _k [n] ^l and θ _k [n] ^l , for

The function is approximated by a first-order Taylor expansion, and we get:

in,

替换式(15)-(17)，将问题(P3)进一步转化为标准的第一凸优化问题：S235, using the derived lower limit Q _k [n] ^lb , v _k [n] ^lb ,

Substituting equations (15)-(17), the problem (P3) is further transformed into a standard first convex optimization problem:

(P4):

s.t.(2),(3),(10),(11),

In all first-order Taylor expansions, a parameter with a superscript l indicates the value corresponding to that parameter at the lth iteration.

Further, the step S3 specifically includes the steps:

S31. Given the two-dimensional trajectory and resource allocation {Q, X, R} of any UAV, reduce the original optimization problem (P1) to the second sub-problem:

(P5):

s.t.(4)-(7),(9),

z[1]=z[N] (22)

S32, the second sub-problem (P5) is further equivalent to:

(P6):

s.t.(4),(5),(7),(9),(14),(22);

应用一阶泰勒展开求近似，得到：S33. Given θ _k [n] ^l and z[n] ^l , for

Applying the first-order Taylor expansion for approximation, we get:

in,

S34. Based on equation (23), the problem (P6) is further approximated as a standard second convex optimization problem:

(P7):

s.t.

(7), (9), (14), (22).

Further, the step S4 specifically includes the steps:

具体包括步骤：S41. Solve the first sub-problem based on an iterative algorithm and a convex optimization solver, and obtain {x _k [n], y _k [n], q[n] when the target value of the first sub-problem converges to a predefined precision } target value

Specifically include steps:

设迭代次数l＝0；S411. Initialization

Set the number of iterations l = 0;

使用凸优化求解器求解第一凸优化问题(P4)获得当前最优解

S412. Given a local point

Use a convex optimization solver to solve the first convex optimization problem (P4) to obtain the current optimal solution

S413. Update the local point of the l-th iteration:

S414, update l=l+1;

作为求解第一子问题(P2)的最优解；S415, until the target value of the first sub-problem (P2) converges to a predefined precision, and output the current optimal solution

as the optimal solution for solving the first sub-problem (P2);

S42. Solve the second sub-problem (P5) based on steps similar to steps S411 to S415, and obtain the target value of z[n] when the target value of the second sub-problem (P5) converges to a predefined precision z ^{^} [ n].

Further, the step S4 specifically includes the steps:

设迭代次数l＝0；S401, initialization

Set the number of iterations l = 0;

与步骤S412～S413相同步骤求解第一凸优化问题(P4)获得

S402, a given local point

Solve the first convex optimization problem (P4) in the same steps as steps S412-S413 to obtain

与步骤S412～S413相似步骤求解第二凸优化问题(P7)获得{z^l+1[n]}；S403, given

Similar to steps S412-S413, solve the second convex optimization problem (P7) to obtain {z ^l+1 [n]};

S404, update l=l+1;

作为求解原始优化问题(P1)的次优解。S405, until the target value of the optimization problem (P1) converges to the pre-defined precision, and output the current optimal solution

as a suboptimal solution to the original optimization problem (P1).

The present invention provides a method for weighing the throughput and delay of a three-dimensional unmanned aerial vehicle communication network, which has the following effects:

1. In order to realize the trade-off between throughput and delay in the 3D UAV communication network, the minimum rate required by the user is introduced, and the 3D UAV trajectory and the communication time and rate allocation are jointly optimized to make each user The minimum value of the weighted sum of the throughput and the required rate is maximized, and the optimization problem is constructed taking into account the LoS probability channel model based on the elevation angle and the fairness among all users;

2. Since the optimization problem cannot be solved directly, the optimization problem is further decomposed into two sub-problems, and the successive convex approximation (SCA) and differential convex function optimization framework are used to solve the sub-problems in each iteration, and the sub-optimal solution of the optimization problem is obtained. ;

3. The simulation results show that this method is better than the benchmark schemes, and achieves a trade-off between throughput, delay and height-related angle-distance on the 3D UAV communication network.

Description of drawings

1 is a flow chart of steps of a method for weighing throughput and delay of a 3D UAV communication network according to an embodiment of the present invention;

2 is an optimized trajectory diagram of an unmanned aerial vehicle in a simulation provided by an embodiment of the present invention;

Fig. 3 is the communication time allocation diagram of unmanned aerial vehicle to different ground users in the simulation provided by the embodiment of the present invention;

4 is a trade-off diagram of throughput and required minimum rate in a simulation provided by an embodiment of the present invention;

FIG. 5 is a comparison diagram of the average allocation time and the maximum-minimum weight sum between the scheme proposed in this paper and each benchmark scheme in the simulation provided by the embodiment of the present invention.

Detailed ways

The embodiments of the present invention will be explained in detail below in conjunction with the accompanying drawings. The examples are given only for the purpose of illustration and should not be construed as a limitation of the present invention. The accompanying drawings are only used for reference and description, and do not constitute a limitation on the protection scope of the patent of the present invention. limitation, since many changes may be made in the present invention without departing from the spirit and scope of the invention.

A method for weighing throughput and delay of a 3D UAV communication network provided by an embodiment of the present invention, as shown in FIG. 1 , includes steps:

S1. To maximize the user throughput of the 3D UAV communication system and the weighted sum of the required minimum rate as the optimization goal, determine the original optimization problem by jointly optimizing the 3D UAV trajectory, communication time and rate allocation;

S2. Given the height of the UAV, simplify the original optimization problem into the first sub-problem, and transform the first sub-problem into the first convex optimization problem based on the differential convex function optimization framework and successive convex approximation;

S3. Given the two-dimensional trajectory and resource allocation of any UAV, simplify the original optimization problem into a second sub-problem, and transform the second sub-problem into a second convex optimization problem based on the differential convex function optimization framework and successive convex approximation ;

S4. Solve the first convex optimization problem and the second convex optimization problem based on an iterative algorithm and a convex optimization solver, and obtain a suboptimal solution of the original optimization problem.

地面用户s_k(简称用户s_k)的水平位置用

表示。为了简化分析，本例将总时间T分成N个等长时隙δ_t，即T＝Nδ_t。在任意时隙n时，无人机的水平位置可以近似用

来表示。本例定义z[n]为在时隙n时无人机的高度，则H_min≤z[n]≤H_max,

其中H_min和H_max为无人机的最小以及最大飞行高度。因此，时隙n时的无人机3D位置可表示为(q[n],z[n])。本例还假设q[1]＝q[N]和z[1]＝z[N]，使得无人机可以周期性地为地面用户服务。由于无人机的速度限制，有

2≤n≤N，

分别是无人机水平和垂直方向的最大速度。无人机和用户s_k之间在时隙n的距离可以由

表示。In step S1, a three-dimensional (3D) UAV communication system (ie, a three-dimensional UAV communication network) includes 1 UAV and K ground users, wherein the UAV acts as an air base station (ABS) for K ground users (GUs) to provide services. Among them, the set of K ground users can be expressed as

The horizontal position of ground user _sk (referred to as user _sk ) is used as

express. To simplify the analysis, this example divides the total time T into N equal-length time slots δ _t , that is, T=Nδ _t . At any time slot n, the horizontal position of the UAV can be approximated by

To represent. In this example, z[n] is defined as the height of the UAV at time slot n, then H _min ≤z[n]≤H _max ,

where H _min and H _max are the minimum and maximum flying heights of the UAV. Therefore, the 3D position of the drone at time slot n can be expressed as (q[n], z[n]). This example also assumes that q[1]=q[N] and z[1]=z[N], so that the UAV can periodically serve ground users. Due to the speed limit of the drone, there are

2≤n≤N,

are the maximum speeds of the drone in the horizontal and vertical directions, respectively. The distance between the UAV and user _sk at time slot n can be given by

express.

可以表示为用户到无人机的仰角θ_k[n]的函数，其中仰角定义为

具体来说，In general, A2G channels include large and small scale fading coefficients, which depend on whether the A2G channel is a LoS channel or an NLoS channel. Although each slot may contain multiple small-scale fading blocks, their effects can be averaged by using a sufficiently long channel code. LoS channel probability between user _sk and UAV at slot n

can be expressed as a function of the user-to-UAV elevation angle _θk [n], where the elevation angle is defined as

Specifically,

表示为LoS通信链路表达式

以概率

表示为NLoS通信链路表达式

其中β₀是在参考距离1m时的信道功率增益，ε表示由于NLoS通信链路传播导致的附加衰减因子，ε＜1。此外，LoS信道链路和NLoS信道链路的路径损耗指数可以分别表示成α_L和α_N。Wherein B _a < 0, B _b > 0, B _d > 0, B _c =1-B _d , the values of these four constants are determined by specific circumstances. At slot n, the channel power gain _βk [n] between the UAV and user _sk is calculated with probability

Expressed as a LoS communication link expression

with probability

Expressed as an NLoS communication link expression

where β ₀ is the channel power gain at a reference distance of 1 m, ε represents the additional attenuation factor due to the propagation of the NLoS communication link, and ε < 1. Furthermore, the path loss exponents of the LoS channel link and the NLoS channel link can be expressed as α _L and α _N , respectively.

定义P表示无人机的发射功率，则无人机和用户s_k之间的可达速率可以表示为

其中B表示信号带宽，而σ²表示噪声功率。从上述表达式中可以看出R_k[n]依赖于β_k[n]，并且β_k[n]取决于链路是否为LoS通信链路。根据LoS概率模型推导出期望速率

并推导出其近似的表达式

即：The variable x _k [n] is defined to represent the time allocation for the time slot n UAV to communicate with the user s _k , _0≤xk [n]≤1. This example assumes that the drone communicates with at most one user at a time, then

Define P to represent the launch power of the UAV, then the achievable rate between the UAV and the user _sk can be expressed as

where B represents the signal bandwidth and ^σ2 represents the noise power. From the above expression, it can be seen that R _k [n] depends on _βk [n], and _βk [n] depends on whether the link is a LoS communication link or not. Deriving the expected rate from the LoS probability model

and derive its approximate expression

which is:

其中中间变量

本例用

进行无人机轨迹设计。因此，无人机对地面用户s_k的总吞吐量可表述为

where the intermediate variable

This example uses

Carry out UAV trajectory design. Therefore, the total throughput of the UAV to the ground user _sk can be expressed as

其中r_k可以解释为用户s_k播放视频流的播放速率，如果满足最低播放速率，则视频播放不会卡顿。因此，

代表的用户s_k在每个时刻的时延需求。直观地说，更大的吞吐量和更小的时延可以为每个地面用户s_k提供更好的服务质量(QoS)保障。因此，本发明的目标是对每个用户s_k同时最大化D_k和r_k。为了实现D_k和r_k之间的权衡，本例将D_k和r_k与加权系数m相关联，0≤m≤1，并最大化加权和mD_k+(1-m)r_kN。其中，让r_k乘以N，使r_kN的大小与吞吐量的大小可以达到可比较的量级。定义

为了实现所有地面用户之间的公平性，本例通过优化无人机的3D轨迹以及通信时间和速率分配，最大化所有地面用户加权和的最小值。基于上述设定，优化问题可以写成：Considering service applications with limited user delay, such as video applications, each user _sk has a minimum rate _rk requirement, that is

where r _k can be interpreted as the playback rate at which the user _sk plays the video stream. If the minimum playback rate is met, the video playback will not be stuck. therefore,

The latency requirement of the representative user _sk at each moment. Intuitively, larger throughput and smaller delay can provide better quality of service (QoS) guarantee for each terrestrial user _sk . Therefore, the goal of the present invention is to maximize _Dk and _{rk simultaneously for each user sk .} To achieve the trade-off between Dk and _rk , this example associates Dk and _rk with a weighting coefficient m, _0≤m≤1 , and maximizes the weighted sum _{mDk +} (1-m) _rkN . Among them, multiply r _k by N, so that the size of r _k N and the size of the throughput can reach a comparable order of magnitude. definition

In order to achieve fairness among all ground users, this example maximizes the minimum value of the weighted sum of all ground users by optimizing the 3D trajectory of the UAV and the allocation of communication time and rate. Based on the above settings, the optimization problem can be written as:

(P1):

q[1]=q[N], z[1]=z[N], (8)

Among them, the non-convex constraints in (4)-(6) make the problem (P1) a non-convex optimization problem with coupled variables and complex rate expressions, and it is very difficult to solve the optimal solution. In this example, the sub-optimal solution of the problem (P1) is obtained through steps S2-S4 to effectively solve the problem (P1).

Firstly, the problem (P1) is simplified into the first sub-problem and transformed into the first convex optimization problem through step S2, which specifically includes the following steps:

S21. Given the UAV height Z, simplify the original optimization problem (P1) into the first sub-problem:

(P2):

s.t.(2)-(6),(10),

q[1]=q[N] (11)

S22. Introduce slack variables Y={y _k [n]}, Θ={θ _k [n]}, and further transform the problem (P2) into:

(P3):

s.t.(2)-(4),(10),(11),

It can be seen that in the optimal solution of (P3), equations (12) and (14) must hold. Otherwise, _θk [n] and _yk [n] can always be increased until the equations hold and the optimal solution still satisfies the other constraints without changing the target value. Therefore, problem (P3) is equivalent to problem (P2). However, since (4), (12)-(14) are non-convex constraints, problem (P3) is still a non-convex optimization problem, and the non-convex constraints in problem (P3) are transformed into convex constraints below.

S23. Convert the non-convex constraint equations (4), (12)-(14) into convex constraints based on the differential convex function optimization framework, and further convert the problem (P3) into a standard convex optimization problem (P4); this step S23 Specifically include steps:

S231. Rewrite the non-convex term x _k [n]y _k [n] in equation (13) as a differential convex function:

用一阶泰勒展开求近似，得到：S232, matching item

Approximation with first-order Taylor expansion, we get:

where Q _k [n] ^lb is the joint concave function with respect to x _k [n] and y _k [n], in this first-order Taylor expansion process, a parameter with a superscript l indicates that at the l-th iteration The value corresponding to this parameter is also expressed in the following first-order Taylor expansion process;

是关于x＞0的凸函数；故，在给定q_k[n]^l时，通过对

函数应用一阶泰勒展开求近似，得到：S233. For formula (14), it can be verified that

is a convex function with respect to x>0; therefore, given q _k [n] ^l , by

The function is approximated by a first-order Taylor expansion, and we get:

in,

是联合x和y的凸函数；故，对于式(4)和(12)，给定q_k[n]^l和θ_k[n]^l，对

函数用一阶泰勒展开求近似，得到：S234. For (4) and (12), the function can be verified

is a convex function of the joint x and y; therefore, for equations (4) and (12), given q _k [n] ^l and θ _k [n] ^l , for

The function is approximated by a first-order Taylor expansion, and we get:

in,

替换式(15)-(17)，将问题(P3)进一步转化为标准的第一凸优化问题(P4)：S235, using the derived lower limit Q _k [n] ^lb , v _k [n] ^lb ,

Substituting equations (15)-(17), the problem (P3) is further transformed into a standard first convex optimization problem (P4):

(P4):

s.t.(2),(3),(10),(11),

It can be verified that (P4) is a standard convex optimization problem and can be solved by standard convex optimization solvers such as CVX. Therefore, the problem (P2) can be solved by the differential convex function (DC) optimization framework and the SCA method. The details of the solution are reflected in step S4, and its complexity can be expressed as O((NK) ^3.5 log(1/κ)), κ is the solution accuracy.

Then, the problem (P1) is reduced to a second sub-problem and transformed into a second convex optimization problem through step S3, which specifically includes steps:

S31. Given the two-dimensional trajectory and resource allocation {Q, X, R} of any UAV, reduce the original optimization problem (P1) to the second sub-problem:

(P5):

s.t.(4)-(7),(9),

z[1]=z[N] (22)

S32, the second sub-problem (P5) is further equivalent to:

(P6):

s.t.(4),(5),(7),(9),(14),(22);

应用一阶泰勒展开求近似，得到：S33. Given θ _k [n] ^l and z[n] ^l , for

Applying the first-order Taylor expansion for approximation, we get:

in,

S34. Based on equation (23), the problem (P6) is further approximated as a standard second convex optimization problem:

(P7):

s.t.

(7), (9), (14), (22).

It can be verified that problem (P7) is a standard convex optimization problem and can be solved efficiently by CVX. Therefore, the iterative algorithm for solving problem (P5) is similar to solving problem (P2) by applying the SCA method iteratively given θk[n] _l and z[n] ^{l .}

Next, step S4 is used to solve the two sub-problems, which specifically includes steps:

具体包括步骤：S41. Solve the first sub-problem based on an iterative algorithm and a convex optimization solver, and obtain {x _k [n], y _k [n], q[n] when the target value of the first sub-problem converges to a predefined precision } target value

Specifically include steps:

设迭代次数l＝0；S411. Initialization

Let the number of iterations l = 0;

使用凸优化求解器求解第一凸优化问题(P4)获得当前最优解

S412. Given a local point

Use a convex optimization solver to solve the first convex optimization problem (P4) to obtain the current optimal solution

S413. Update the local point of the l-th iteration:

S414, update l=l+1;

作为求解第一子问题(P2)的最优解；S415, until the target value of the first sub-problem (P2) converges to a predefined precision, and output the current optimal solution

as the optimal solution for solving the first sub-problem (P2);

S42. Solve the second sub-problem (P5) based on steps similar to steps S411 to S415, and obtain the target value of z[n] when the target value of the second sub-problem (P5) converges to a predefined precision z ^{^} [ n].

On the whole, the process of solving the problem P1 in step S4 includes the steps:

设迭代次数l＝0；S401, initialization

Set the number of iterations l = 0;

与步骤S412～S413相同步骤求解第一凸优化问题(P4)获得

S402, a given local point

Solve the first convex optimization problem (P4) in the same steps as steps S412-S413 to obtain

与步骤S412～S413相似步骤求解第二凸优化问题(P7)获得{z^l+1[n]}；S403, given

Similar to steps S412-S413, solve the second convex optimization problem (P7) to obtain {z ^l+1 [n]};

S404, update l=l+1;

作为求解原始优化问题(P1)的次优解。S405, until the target value of the optimization problem (P1) converges to the pre-defined precision, and output the current optimal solution

as a suboptimal solution to the original optimization problem (P1).

和

无人机的初始轨迹可以设置为高度H_min＝50m的圆形轨迹，其圆心位于所有地面用户坐标的几何中心。通信参数设置为P＝0.1W，β₀＝-60dB，B＝1MHz，σ²＝-110dBm，α_L＝2.5。In order to evaluate the effectiveness of the optimization scheme proposed in this example, simulation experiments are carried out below. Assume that K terrestrial users are randomly distributed in an 800m×800m square area and K=5. The parameters in the communication model can be set as Ba= _-0.4568 , Bb _{= 0.0470} , Bc=-0.63, _Bd =-1.63. The minimum and maximum flying heights of the UAV are H _min =50m and _Hmax =100m, respectively. Assume that the maximum horizontal and vertical flight speeds of the UAV are respectively

and

The initial trajectory of the UAV can be set as a circular trajectory with a height of H _min =50m, the center of which is located at the geometric center of all ground user coordinates. The communication parameters are set as P=0.1W, β0 ₌ -60dB, B=1MHz, ^σ2 =-110dBm, αL ₌ 2.5.

Figure 2 shows the optimized trajectories of the UAV under different weight factors m when T=60s. Figure 2(a) depicts the UAV flight trajectory moving in 3D space, and Figure 2(b) and Figure 2(c) depict the UAV trajectory and UAV height changes projected on a 2D plane, respectively. It can be seen from Figure 2 that the optimized UAV trajectory changes with the change of m value, from which it can be concluded that when the m value is close to 1, maximizing the throughput of each ground user has a greater impact on the target value. Larger, so the drone will fly close to each ground user to get better channel quality. In addition, when the UAV is close to the ground user, the flying height of the UAV decreases, which can further reduce the distance between the UAV and the ground user and improve the communication efficiency, as shown in Figure 2(c). Interestingly, the drone flies up and down frequently, and tends to stay at a higher altitude during flight between adjacent users, until it approaches the ground user and then lowers again. The main reason why the drone will fly higher after leaving the user is that the LoS channel probability between the drone and the ground user depends on the elevation angle. The higher the altitude, the higher the LoS channel probability. Therefore, in different periods, the main factors affecting the channel quality are different. When the drone is close to the ground user, reducing the distance has a greater impact on the communication quality than the elevation angle, so the altitude of the drone is reduced. Conversely, when the UAV leaves the ground user, increasing the elevation angle between the UAV and the user has a more significant effect on increasing the communication quality, so the UAV height increases. Another reason for the increase in the height of the drone is to ensure the fairness of the data transmission between the drone and the user. The drone can increase the elevation angle of each user by increasing its height, so that the elevation angle of each user is different. Not much.

On the other hand, when m is close to 0, an increase in the minimum rate required by each terrestrial user has a greater impact on system performance than an increase in system throughput. So the 2D UAV trajectory shrinks and stays at a higher place, as shown in Figure 2(b) and Figure 2(c). In other words, drones tend to hover over and away from all ground users. The reason is that in each time slot where m is small, the demand rate of each terrestrial user should be larger. If the drone is far from a particular ground user, the demand rate for that ground user may not be reached.

Fig. 3 shows the communication time allocation of five ground users (S ₁ to S ₅ ) when m=0.9. In this case, the impact of maximizing system throughput on increasing communication quality is more significant than maximizing the minimum demand rate of users on increasing system performance, so UAVs are more inclined to be close enough to ground users and When the channel quality is better, communicate with terrestrial users to improve communication efficiency.

Figure 4 depicts the trade-off between throughput and minimum rate required by users for different values of m. It can be seen from Figure 2 that when m is large and close to 1, although the UAV will reduce the minimum demand rate, the throughput of the UAV will increase. In practical applications, m can be appropriately selected according to specific requirements to balance the trade-off between throughput and delay. To demonstrate the superiority of the joint optimization design scheme, this example compares the target value of the proposed scheme with the following schemes:

(1) Two-dimensional trajectory fixed reference scheme, in which the UAV is kept at the geometric center of all ground users, and only the height is optimized;

(2) The altitude fixed reference scheme, in which the UAV is kept flying at the altitude H _max ;

(3) The benchmark plan is evenly distributed, and the communication time is equally distributed to all ground users;

(4) A stationary reference scheme, in which the UAV is always kept at the geometric center of all ground users, and the height is fixed as H _max .

Figure 5 shows the minimum value of the weighted sum of the throughput of the system and the minimum demand rate of the user in different time periods T when m=0.9. It can be observed that the weighted sum increases as time T increases as expected. Compared with other benchmark schemes, the minimum value of the weighted sum of the proposed scheme is the largest, which is most beneficial to the data communication between the UAV and the ground user. The performance gap between the solution proposed in this example and the evenly allocated benchmark shows the benefits of communication time allocation. This example demonstrates the additional gain brought by the UAV's maneuverability in three-dimensional space by comparing the two-dimensional trajectory fixed reference scheme, the height fixed reference scheme and the stationary reference scheme, which improves the effectiveness of information transmission.

To sum up, the embodiment of the present invention studies the trade-off between throughput and delay in the 3D UAV communication network, introduces the minimum demand rate of each ground user, and jointly optimizes the UAV trajectory in 3D space, Communication time and rate allocation, maximizing the minimum of the weighted sum of each user's throughput and the required rate, obtains the joint design optimization problem, and models the optimization problem as a non-convex optimization problem. Finally, the suboptimal solution is obtained by an iterative algorithm based on coordinate descent, differential convex optimization and SCA method. The simulation results illustrate the significant gains of the proposed solution and reveal the fundamental trade-off between throughput and latency in 3D UAV communication networks.

The above-mentioned embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited by the above-mentioned embodiments, and any other changes, modifications, substitutions, combinations, The simplification should be equivalent replacement manners, which are all included in the protection scope of the present invention.

Claims (9)

1. A method for balancing throughput and time delay of a three-dimensional unmanned aerial vehicle communication network is characterized by comprising the following steps:

s1, determining an original optimization problem by jointly optimizing the three-dimensional unmanned aerial vehicle track, the communication time and the rate distribution by taking the weighted sum of the user throughput and the required minimum rate of the three-dimensional unmanned aerial vehicle communication system as an optimization target;

s2, setting the height of the unmanned aerial vehicle, simplifying the original optimization problem into a first sub-problem, and converting the first sub-problem into a first convex optimization problem based on a differential convex function optimization framework and successive convex approximation;

s3, given the two-dimensional track and resource allocation of any unmanned aerial vehicle, simplifying the original optimization problem into a second sub-problem, and converting the second sub-problem into a second convex optimization problem based on a difference convex function optimization framework and successive convex approximation;

s4, solving the first convex optimization problem and the second convex optimization problem based on the iterative algorithm and the convex optimization solver to obtain a suboptimal solution of the original optimization problem.

2. The method of claim 1, wherein the method comprises the following steps: in step S1, the three-dimensional drone communication system includes 1 drone and K ground users, where the drone serves as an aerial base station to provide services for the K ground users; the original optimization problem is described as:

(P1):

q[1]＝q[N],z[1]＝z[N], (8)

wherein equations (9) and (10) represent the speed limit of the drone, q [ n ]]、z[n]Respectively representing the horizontal position and height of the drone at time slot n,

individual watchShowing the maximum speed of the unmanned aerial vehicle in the horizontal and vertical directions, and dividing the total time T into N equal-length time slots delta_tI.e. T ═ N δ_t(ii) a Equation (8) represents that the drone serves the ground users periodically; formula (7) represents that the unmanned aerial vehicle in any time slot has the minimum flying height H_minAnd a maximum flying height H_maxFly in the air; equation (6) represents a ground user s_kDefinition of elevation angle to drone, w_kRepresenting terrestrial users s_kA set of K ground users as

In the formula (5), r_kRepresenting terrestrial users s_kMinimum rate of (x)_k[n]Unmanned aerial vehicle and ground user s when representing time slot n_kThe time allocation of communication satisfies the condition of the formula (2),

unmanned aerial vehicle and ground user s when representing time slot n_kApproximate desired rate of communication, from desired rate

Approximation is carried out; formula (3) represents that the unmanned aerial vehicle communicates with at most one ground user at each moment; in the formula (4), the reaction mixture is,

representing unmanned aerial vehicle to ground user s_kM represents a weighting coefficient, m is 0. ltoreq. m.ltoreq.1, mD_k+(1-m)r_kN denotes a terrestrial user s_kMu represents the minimum value of the weighted sum of the user throughput and the required rate of the three-dimensional unmanned aerial vehicle communication system;

3. the method of claim 2, wherein the method comprises the following steps:

unmanned aerial vehicle and ground user s in time slot n_kThe distance between

Ground user s_kAnd LoS channel probability between drones

Denoted as terrestrial users s_kAngle of elevation theta to unmanned aerial vehicle_k[n]Function of (c):

wherein B is_a＜0，B_b＞0，B_d＞0，B_c＝1-B_dThe values of the four constants are determined by specific environments; at time slot n, unmanned aerial vehicle and ground user s_kChannel power gain beta in between_k[n]By probability

Expressed as LoS communication link expressions

By probability

Expressed as NLoS communication link expression

Wherein beta is₀Is the channel power gain at a reference distance of 1m, epsilon represents an additional attenuation factor due to NLoS communication link propagation, epsilon < 1; the path loss exponent of the LoS channel link and the NLoS channel link are respectively expressed as alpha_LAnd alpha_N。

4. The method of claim 3, wherein the method comprises the following steps:

unmanned aerial vehicle and ground user s in time slot n_kAchievable rate in between

Where B denotes the signal bandwidth, P denotes the transmit power of the drone, σ²Representing the noise power;

5. the method for trading off throughput and latency of a communication network of a three-dimensional unmanned aerial vehicle according to claim 4, wherein the step S2 specifically comprises the steps of:

s21, given the unmanned aerial vehicle height Z, simplifying the original optimization problem (P1) into a first sub-problem:

(P2):

s.t.(2)-(6),(10),

q[1]＝q[N] (11)

s22, introducing relaxation variable Y ═ Y_k[n]},Θ＝{θ_k[n]The question (P2) is further converted into:

(P3):

s.t.(2)-(4),(10),(11),

s23, converting the non-convex constrained expressions (4), (12) to (14) into convex constraints based on the differential convex function optimization framework, and further converting the problem (P3) into a standard convex optimization problem (P4).

6. The method for trading off throughput and latency of a communication network of a three-dimensional unmanned aerial vehicle according to claim 5, wherein the step S23 specifically comprises the steps of:

s231, converting the non-convex term x in the formula (13)_k[n]y_k[n]Rewrite as a difference convex function:

s232, item pairing

Approximation with a first order Taylor expansion yields:

wherein Q is_k[n]^lbIs about x_k[n]And y_k[n]A joint concave function of (a);

s233, for the formula (14), given q_k[n]^lWhen passing through

The function applies a first order Taylor expansion to approximate, yielding:

wherein,

s234, for the formulae (4) and (12), q is given_k[n]^lAnd theta_k[n]^lTo, for

The function is approximated with a first order Taylor expansion to yield:

wherein,

s235, using derived lower limit Q_k[n]^lb、v_k[n]^lb、

Replacing equations (15) - (17), further transforming the problem (P3) into a standard first convex optimization problem:

(P4):

s.t.(2),(3),(10),(11),

in all first-order Taylor expansions, a parameter is indicated with a superscript l to the value corresponding to the parameter at the i-th iteration.

7. The method for trading off throughput and latency of a communication network of a three-dimensional unmanned aerial vehicle according to claim 6, wherein the step S3 specifically comprises the steps of:

s31, given the two-dimensional trajectory and resource allocation { Q, X, R } of any unmanned aerial vehicle, simplifying the original optimization problem (P1) into a second subproblem:

(P5):

s.t.(4)-(7),(9),

z[1]＝z[N]

(22)

s32, further equating the second sub-problem (P5) as:

(P6):

s.t.(4),(5),(7),(9),(14),(22)；

s33, given theta_k[n]^lAnd z [ n ]]^lTo, for

Approximation is solved by applying first order Taylor expansion to obtain:

wherein,

s34, further approximating the problem (P6) as a standard second convex optimization problem based on equation (23):

(P7):

(7),(9),(14),(22)。

8. the method for trading off throughput and latency of a communication network of a three-dimensional unmanned aerial vehicle according to claim 7, wherein the step S4 specifically includes the steps of:

s41, solving the first subproblem based on the iterative algorithm and the convex optimization solver, and obtaining { x ] when the target value of the first subproblem converges to the predefined precision_k[n],y_k[n],q[n]Target value of }

The method specifically comprises the following steps:

s411, initialization

Setting the iteration number l as 0;

s412, giving local points

Solving a first convex optimization problem (P4) using a convex optimization solver to obtain a current optimal solution

S413, updating the local point of the ith iteration:

s414, updating l + 1;

s415, until the target value of the first subproblem (P2) converges to the predefined precision, outputting the current optimal solution

As an optimal solution to solve the first sub-problem (P2);

s42, solving the second sub-problem (P5) based on steps similar to steps S411 to S415, and obtaining the purpose of the second sub-problem (P5)Z [ n ] when the scalar converges to a predefined precision]Target value z of^{^}[n]。

9. The method for trading off throughput and latency of a communication network of a three-dimensional unmanned aerial vehicle according to claim 8, wherein the step S4 specifically includes the steps of:

s401, initialization

Setting the iteration number l as 0;

s402, giving local points

The same steps as the steps S412 to S413 are carried out to solve the first convex optimization problem (P4) to obtain

S403, give

Similar to steps S412-S413, the second convex optimization problem (P7) is solved to obtain { z^l+1[n]}；

S404, updating l + 1;

s405, until the target value of the optimization problem (P1) converges to the predefined precision, outputting the current optimal solution

As a sub-optimal solution to solve the original optimization problem (P1).

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