CN115665775A - Air-ground integrated communication network coverage method based on multiple time scales - Google Patents

Air-ground integrated communication network coverage method based on multiple time scales Download PDF

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CN115665775A
CN115665775A CN202211332474.7A CN202211332474A CN115665775A CN 115665775 A CN115665775 A CN 115665775A CN 202211332474 A CN202211332474 A CN 202211332474A CN 115665775 A CN115665775 A CN 115665775A
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resource allocation
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base station
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李建东
张艺如
刘俊宇
盛敏
史琰
赵晨曦
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Xidian University
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Abstract

The invention provides an air-ground integrated communication network coverage method based on multiple time scales, belongs to the technical field of communication networks, and solves the problem that how to maximize the transmission information quantity of each unit of unmanned aerial vehicle energy consumption to realize optimal energy efficiency in the prior art; initializing relevant parameters, associating strategies, resource allocation and flight trajectories; solving a first subproblem of given flight trajectory and resource allocation to obtain an association strategy; solving a second subproblem of the given flight trajectory and the associated strategy based on the result of the first subproblem to obtain resource allocation; solving a subproblem three of the given resource allocation and association strategy based on the results of the subproblems one and two to obtain a flight trajectory; obtaining a final association strategy, resource allocation and flight trajectory by repeating the iterative optimization process until the result is converged; the method jointly optimizes user association, resource allocation and flight path of the aerial base station in a multi-time scale mode, so that the method is more practical and the application effect is greatly improved.

Description

Air-ground integrated communication network coverage method based on multiple time scales
Technical Field
The invention belongs to the technical field of communication networks, relates to a process of air-ground integrated communication network coverage, and particularly relates to an air-ground integrated communication network coverage method based on multiple time scales.
Background
Since the 80 s of the 20 th century, mobile communication systems have changed tremendously; the demand of the communication industry is continuously increased, new applications are continuously emerging, and innovation is breaking the bottleneck of traditional communication. With the explosive growth of mobile data traffic, the current communication networks are not enough to respond to new challenges, and new communication architectures should be established to break through the traditional data exchange limitations. The 5G network brings the concept of everything interconnection, and the 6G network is expected to evolve into an intelligent everything interconnection platform; by integrating the satellite network and the near-earth network into the ground network, the 6G network can achieve true global coverage, maintaining high availability and robustness even in the event of a natural disaster. Therefore, the air-ground integrated communication network draws great attention from the academic world.
In the existing communication network technical scheme, an Unmanned Aerial Vehicle (UAV) is an economical and convenient airborne platform and can carry a communication base station to serve a ground terminal. Because the unmanned aerial vehicle is located at low altitude, the maneuverability and flexibility of the unmanned aerial vehicle can bring the advantages of larger coverage range and faster deployment, and therefore the unmanned aerial vehicle can be applied to various scenes, particularly rural areas, emergency deployment, disaster relief and other scenes. Unmanned planes can be divided into rotor-wing unmanned planes and fixed-wing unmanned planes; the rotor unmanned aerial vehicle has the characteristics of small volume and easy control, can vertically lift, but has very limited power; compare in rotor unmanned aerial vehicle, fixed wing unmanned aerial vehicle can be in high-speed flight in the air, and has stronger payload ability. Although drones play a great role in air-ground scenarios, the challenges of energy-saving drone deployment are still faced due to their limited onboard energy. Maximizing the amount of information transmitted per unit of energy consumption of the drone to achieve optimal energy efficiency within the flight time of the drone is a crucial issue.
The prior art provides some communication network coverage methods, but each type of method has its limitations, as follows:
1. by jointly optimizing regional scheduling, a flight trajectory of a space-based access point and transmitting power, the energy efficiency of the system is maximized, but limited return capacity of the unmanned aerial vehicle, which is not suitable for actual single time scale and does not take into account rate, is used;
2. under the condition of limited cache capacity and flight time, the minimum achievable throughput of each ground user is maximized by jointly optimizing cache layout, unmanned aerial vehicle resource allocation and track; the same time scale is used when the air base station trajectory planning and the resource allocation are carried out, and the condition that the 5G base station has the fixed time slot length in practice is not considered; and the system energy efficiency is not involved in the optimization, and the green coverage of the air-ground integrated communication network cannot be supported.
3. A communication system optimization method for multi-unmanned aerial vehicle auxiliary communication mainly comprises the following steps: (1) Forming a downlink communication link of time division multiple access by a plurality of unmanned aerial vehicles and user communication equipment; (2) Establishing a target optimization problem by taking the maximum system communication rate as an optimization target; (3) Under the condition that the position and the transmitting power of the unmanned aerial vehicle are assumed to be fixed, determining the optimal communication connection allocation between the user equipment and the unmanned aerial vehicle by using a continuous convex approximation algorithm and an optimization function with a penalty term; (4) The hovering position of the unmanned aerial vehicle and the communication power distribution of the unmanned aerial vehicle are optimized by adopting a block coordinate optimization method and utilizing a continuous convex approximation algorithm with a local stable solution, so that the communication construction with the return link capacity limitation of the multiple unmanned aerial vehicles is realized; in the method, unmanned aerial vehicles are not dynamically deployed, the optimization problem of system energy efficiency is not considered, and the method has limitation in the aspect of green coverage of the air-ground integrated communication network.
4. An unmanned aerial vehicle auxiliary communication method based on resource allocation and track optimization; the method comprises the steps of firstly planning a flight track of the unmanned aerial vehicle according to the distribution condition of users, wherein the flight track is a circular track, secondly decomposing the non-convex problem into two subproblems by using a block coordinate descent method, and optimizing a beam forming matrix of unmanned aerial vehicle communication under the condition of the circular track based on the flight of the unmanned aerial vehicle; under the condition of fixed beam forming, the flight speed of the unmanned aerial vehicle is optimized and adjusted, and finally the beam forming and the flight speed of the unmanned aerial vehicle are alternately optimized through a two-layer alternating optimization algorithm to maximize the total transmission rate of the system; however, the unmanned aerial vehicle trajectory planning is not considered in the method, and the optimization problem of energy efficiency is not involved.
5. In the prior art, in an air-ground scene, the achievable throughput of an intelligent vehicle is maximized by jointly optimizing user association, base station/unmanned aerial vehicle transmission power distribution and unmanned aerial vehicle track, and meanwhile, different limitations and quality of service (QoS) constraints are considered; however, this technique does not consider the power consumption of the air base station, nor does it involve an optimization problem of energy efficiency in an air-to-ground network supporting the air base station.
In summary, in the prior art, how to implement association between a user and a base station, resource allocation, and trajectory planning of an air base station in an air-ground integrated scenario, and improve the energy efficiency of a system while satisfying the user service quality is a problem that still needs to be solved; when the problem is solved, the algorithm complexity is too high to be practically applied due to the same time scale, which is a bottleneck to be broken through.
Disclosure of Invention
Therefore, the invention provides a new method for solving the limitation problem of various methods in the background technology and breaking through the communication network coverage problem; by integrating the satellite and the near-earth network into the ground network, an air-ground integrated communication architecture is established, and the traditional data exchange limit is broken through; the method aims at maximizing the energy efficiency of the whole system, and jointly optimizes the user association, the resource allocation and the flight path of the aerial base station, so that the method is more practical, and the optimization effect of practical application can be greatly improved in a multi-time scale mode.
The invention adopts the following technical scheme to realize the purpose:
a multi-time scale-based air-ground integrated communication network coverage method comprises the following steps:
s1, initializing parameters of a system, wherein the parameters comprise ground user parameters, air base station parameters and other auxiliary parameters;
s2, initializing an association strategy, resource allocation and a flight track; during initialization, resource allocation is that resources are allocated to each user evenly, and a flight track is that the aerial base station starts from an initial position and flies in a straight line along a specific direction;
s3, carrying out iterative optimization calculation, solving a first subproblem of the given flight trajectory and resource allocation, wherein the objective function of the first subproblem is the maximized system efficiency, and solving to obtain a correlation strategy;
s4, solving a second subproblem of the given track and the association strategy, wherein in the solving process of the second subproblem, the time scales used by the association strategy and the resource allocation are different, so that in the solving process, a multi-time scale homogenization method is applied, and the resource allocation is obtained by solving according to the association strategy obtained by the first subproblem;
s5, solving a third subproblem of the given resource allocation and association strategy, and solving to obtain a flight trajectory according to the association strategy obtained by the first subproblem and the resource allocation obtained by the second subproblem;
and S6, repeating the iterative optimization calculation process from the step S3 to the step S5 until the solving results of the first subproblem, the second subproblem and the third subproblem are converged, obtaining a final association strategy, resource allocation and flight trajectory, and finishing the joint optimization of the air-ground integrated communication network coverage.
Further, the specific initialization content of step S1 is as follows:
s1-1, initializing the number K of ground users, the number U of aerial base stations, the number N of time slots for flight path planning, and the length delta of time slots for flight path planning t The number M of time slots for resource allocation, and the length tau of the time slots for resource allocation t (ii) a And represents a set of airborne base stations as
Figure BDA0003914091490000047
The set of terrestrial users is represented as
Figure BDA0003914091490000048
S1-2, initializing the position of a ground user, the position of a satellite and the position of an air base station, wherein the steps comprise:
the positions of ground users are randomly distributed, a satellite is at an initial position, and an air base station is at an initial position, wherein the air base station is in return connection through the satellite; the horizontal coordinate of the kth ground user is
Figure BDA0003914091490000041
The horizontal position of the satellite in the nth time slot is represented as
Figure BDA0003914091490000042
Figure BDA0003914091490000043
The height of the satellite is H, and the fixed height of the u-th air base station is
Figure BDA0003914091490000044
Each ground user is only associated with one air base station;
s1-3, initializing other auxiliary parameters in the system, including W US 、W GU 、
Figure BDA0003914091490000045
Number of iterations j =0, v, κ 1 ，κ 2 (ii) a Wherein, W US Represents the bandwidth of the backhaul link transmitting data during time slot n; w GU Represents the total bandwidth of the access link for transmitting data during time slot n;
Figure BDA0003914091490000046
respectively representing the maximum transmission power of the access link and the backhaul link in the nth time slot; v is the flight rate of the unmanned aerial vehicle; k is a radical of 1 And k 2 Is a fixed parameter related to air density, unmanned aerial vehicle weight, wing area, etc.
Specifically, during initialization, the flight path is that the aerial base station starts from the initial position and flies along a straight line at 45 degrees in the southwest direction.
Further, the specific content of step S3 includes:
s3-1, defining an association strategy: defining an airborne base station to be capable of simultaneously having a maximum of k th A ground user providing communication service, where k th K is less than or equal to K; introducing a binary variable a ku [n]Indicating whether the kth terrestrial user is connected to the u-th airborne base station in the nth time slot, and if so, a ku [n]=1, otherwise a ku [n]=0; deriving an association policy as follows:
Figure BDA0003914091490000051
a ku [n]∈{0，1}
s3-2, an objective function of the first subproblem is specified, the objective function of the first subproblem is the same as the objective functions of the second subproblem and the third subproblem, and the objective functions are the objective functions for maximizing the system efficiency, and the following steps are performed:
Figure BDA0003914091490000052
s3-3, solving the first sub-problem, which comprises the following steps:
the optimization problem of the first subproblem is as follows:
maxη EE
s.t.C1：s[0]＝i
C2：
Figure BDA0003914091490000053
C3：
Figure BDA0003914091490000054
C4：
Figure BDA0003914091490000055
C5：
Figure BDA0003914091490000056
relaxing the binary dependent variable into a continuous variable, rewriting the sub-problem one as:
maxη EE
s.t.C1：s[0]＝i
C2：
Figure BDA0003914091490000061
C3：
Figure BDA0003914091490000062
C4：
Figure BDA0003914091490000063
C5：
Figure BDA0003914091490000064
introducing a penalty function F (a) ku [n])＝a ku [n](a ku [n]-1), the penalty function being a convex function, the sub-problem one being further rewritten as:
maxη EE +κF(a ku [n])
s.t.C1：s[0]＝i
C2：
Figure BDA0003914091490000065
C3：
Figure BDA0003914091490000066
C4：
Figure BDA0003914091490000067
C5：
Figure BDA0003914091490000068
wherein K > 0 is a penalty factor, the objective function eta EE +κF(a ku [n]) Is the difference of the concave function, i.e. eta EE -(-k F(a ku [n]) ); in the j +1 th iteration, F (a) in the target is added ku [n]) The substitution is a first order taylor expansion as follows:
Figure BDA0003914091490000069
and gives the following:
Figure BDA00039140914900000610
according to the above process, the sub-problem is converted into a linear program as follows:
Figure BDA0003914091490000071
s.t.C1：s[0]＝i
C2：
Figure BDA0003914091490000072
C3：
Figure BDA0003914091490000073
C4：
Figure BDA0003914091490000074
C5：
Figure BDA0003914091490000075
at this time, the CVX tool is used for solving a first subproblem by substituting the given flight trajectory and resource allocation, and the solving variable of the first subproblem is the correlation strategy.
Further, the specific content of step S4 includes:
s4-1, stipulated resource allocation: resource allocation at an over-the-air base stationIn the air, the base station uses a fixed time slot length tau t Updating in units; use of b ku [m]Represents the proportion of bandwidth allocated to the kth terrestrial user by the access link within time slot m, which is a discrete value between 0 and 1; each subcarrier is allocated to only one terrestrial user, if the number of subcarriers is large enough, b ku [m]Approximately continuous between 0 and 1; based on the above specification, a resource allocation is derived as follows:
Figure BDA0003914091490000076
Figure BDA0003914091490000077
s4-2, establishing and applying a time scale unification model; in the optimization solving process of the second subproblem, the association strategy a ku [n]And resource allocation b ku [m]The used time scales are different, and the time scale normalization model and the association strategy a under different conditions ku [n]Obtaining the resource allocation after time scale homogenization
Figure BDA0003914091490000078
S4-3, solving a second subproblem, which comprises the following steps:
the optimization problem of the second subproblem is as follows:
max η FE
s.t.C1：s[0]＝i
C2：
Figure BDA0003914091490000081
C3：
Figure BDA0003914091490000082
C4：
Figure BDA0003914091490000083
C5：
Figure BDA0003914091490000084
C6：
Figure BDA0003914091490000085
unified time scale a ku [n]And b ku [m]B is to be ku [m]Conversion into
Figure BDA0003914091490000086
The objective function at this time is as follows:
Figure BDA0003914091490000087
and solving a second subproblem by using a CVX tool through the association strategy and the given flight trajectory which can be solved by substituting the first subproblem, wherein the solving variable of the second subproblem is the resource allocation.
Further, in the step S4-2, the model and the association policy a are normalized according to the time scale under different conditions ku [n]Obtaining the resource allocation after time scale homogenization
Figure BDA0003914091490000088
The method is specifically divided into the following five conditions:
in case one, if the resource allocation characteristics can be reflected by the median of the resource allocation, τ with smaller slot length is used t Delta larger than slot length t Division, i.e. c = δ t /τ t Obtaining the corresponding relation of two different time scale lengths; then every c b ku [m]The value of (A) is obtained by taking the median of the bits
Figure BDA0003914091490000089
Case two, if the resource allocation has been for a certain period of timeIn case of representativeness or insufficient memory, the time slot length is reduced to be tau t Delta larger than slot length t Division, i.e. c = δ t /τ t Obtaining the corresponding relation of two different time scale lengths; then every c b ku [m]Taking out a representative value of the value of (A) and averaging the value
Figure BDA0003914091490000091
And in the third case, if the whole time of resource allocation is representative, the time slot length is smaller tau t Delta larger than slot length t Division, i.e. c = δ t /τ t Obtaining the corresponding relation of two different time scale lengths; then b is mixed ku [m]Is averaged every c times to obtain
Figure BDA0003914091490000092
And in case of the maximum value of the resource allocation can embody the resource allocation characteristics, the time slot length is reduced to be tau t Delta larger than slot length t Division, i.e. c = δ t /τ t Obtaining the corresponding relation of two different time scale lengths; then b is mixed ku [m]The value of (c) is obtained by taking the maximum value of each c
Figure BDA0003914091490000093
Case five, if the resource allocation has randomness, the time slot length is smaller tau t Delta larger than slot length t Division, i.e. c = δ t /τ t Obtaining the corresponding relation of two different time scale lengths; then every c b ku [m]The value of (A) is obtained by randomly taking a plurality of values and then averaging the values
Figure BDA0003914091490000094
Further, the specific content of step S5 includes:
the optimization problem of the third subproblem is as follows:
maxη EE
s.t.C1：
Figure BDA0003914091490000095
C2：
Figure BDA0003914091490000096
C3：s[0]＝i
C4：
Figure BDA0003914091490000097
C5：
Figure BDA0003914091490000098
C6：
Figure BDA0003914091490000099
the objective function of the sub-problem three at this time is as follows:
Figure BDA00039140914900000910
Figure BDA0003914091490000101
wherein eta EE And
Figure BDA0003914091490000102
is non-convex, such that
Figure BDA0003914091490000103
Introducing a relaxation variable:
(H u 2 +||q u [n]-w k [n]|| 2 )≤Q ku [n]
Figure BDA0003914091490000104
obtaining:
Figure BDA0003914091490000105
Figure BDA0003914091490000106
the sub-problem three is therefore rewritten as:
max η EE
s.t.C1：
Figure BDA0003914091490000111
C2：
Figure BDA0003914091490000112
C3：s[0]＝i
C4：
Figure BDA0003914091490000113
C5：
Figure BDA0003914091490000114
C6：
Figure BDA0003914091490000115
C7：
Figure BDA0003914091490000116
C8：
Figure BDA0003914091490000117
the expansion is performed using first order Taylor, obtaining the lower bound of f (x) at a given feasible point xj:
Figure BDA0003914091490000118
order to
Figure BDA0003914091490000119
x＝Qku[n]And obtaining the following data at the j +1 th iteration:
Figure BDA00039140914900001110
Figure BDA00039140914900001111
Figure BDA00039140914900001112
through the above process, the sub-problem three can be further rewritten as:
maxη EE
s.t.C1：
Figure BDA0003914091490000121
C2：
Figure BDA0003914091490000122
C3：s[0]＝i
C4：
Figure BDA0003914091490000123
C5：
Figure BDA0003914091490000124
C6：
Figure BDA0003914091490000125
C7：
Figure BDA0003914091490000126
C8：
Figure BDA0003914091490000127
and solving a third subproblem by using a CVX tool through substituting the association strategy solved by the first subproblem and the resource allocation solved by the second subproblem, wherein the solving variable of the third subproblem is the flight track.
In summary, due to the adoption of the technical scheme, the invention has the following beneficial effects:
the satellite and the near-earth network are integrated into the ground network, the air-ground integrated communication architecture is established, and the traditional data exchange limit is broken through; when the flight path, user association and resource allocation of the aerial base station are jointly optimized, because the same time scale used in the existing research cannot be realized in practice, an optimization method based on multiple time scales is innovatively provided, so that the method is more practical.
The invention establishes an air-ground integrated communication network system model, wherein the system comprises a satellite and a plurality of air base stations, and the air base stations can carry out return trip through the satellite; the satellite and the plurality of aerial base stations in the combined deployment system provide communication service for ground users in the area, and simultaneously, the communication power consumption and the flight power consumption of the aerial base stations are considered, so that the energy efficiency of the whole system is maximized, the user association, the resource allocation and the flight track of the aerial base stations are jointly optimized, the communication network coverage method is complete and effective, all conditions are fully considered, and the practical value is extremely high.
Drawings
Fig. 1 is a schematic diagram of a communication network architecture according to the method of the present invention;
FIG. 2 is a graph of total throughput versus time slot;
FIG. 3 is a diagram of system energy efficiency versus number of ground users.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all embodiments of the present invention. The components of embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations.
Thus, the following detailed description of the embodiments of the present invention, presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be obtained by a person skilled in the art without inventive step based on the embodiments of the present invention, are within the scope of protection of the present invention.
A multi-time scale-based air-ground integrated communication network coverage method comprises the following steps:
s1, initializing parameters of a system, wherein the parameters comprise ground user parameters, air base station parameters and other auxiliary parameters;
s2, initializing an association strategy, resource allocation and a flight track; during initialization, resource allocation is that resources are evenly allocated to each user, and a flight track is that the aerial base station starts from an initial position and flies in a straight line along a specific direction; in the initialization process, the flight path is that the aerial base station starts from the initial position and flies along a straight line in the southwest direction 45;
s3, carrying out iterative optimization calculation, solving a first subproblem of given flight trajectory and resource allocation, wherein an objective function of the first subproblem is the maximized system efficiency, and solving to obtain an association strategy;
s4, solving a second subproblem of the given track and the association strategy, wherein in the solving process of the second subproblem, the time scales used by the association strategy and the resource allocation are different, so that the resource allocation is obtained by solving according to the association strategy obtained by the first subproblem by using a multi-time scale homogenization method in the solving process;
s5, solving a third subproblem of the given resource allocation and association strategy, and solving to obtain a flight trajectory according to the association strategy obtained by the first subproblem and the resource allocation obtained by the second subproblem;
and S6, repeating the iterative optimization calculation process from the step S3 to the step S5 until the solving results of the first subproblem, the second subproblem and the third subproblem are converged, obtaining a final association strategy, resource allocation and flight trajectory, and finishing the joint optimization of the air-ground integrated communication network coverage.
A schematic diagram of a system architecture for performing communication network coverage by using the method is shown in fig. 1.
In this embodiment, the specific initialization content of step S1 is as follows:
s1-1, initializing the number K of ground users, the number U of aerial base stations, the number N of time slots for flight path planning, and the length delta of time slots for flight path planning t The number of time slots M of resource allocation and the time slot length tau of resource allocation t (ii) a And represents a collection of over-the-air base stations as
Figure BDA0003914091490000141
The set of terrestrial users is represented as
Figure BDA0003914091490000142
S1-2, initializing the position of a ground user, the position of a satellite and the position of an aerial base station, comprising:
the method comprises the following steps that positions of ground users are randomly distributed, a satellite is at an initial position, and an air base station is at an initial position, wherein the air base station is in backhaul connection through the satellite; the horizontal coordinate of the kth ground user is
Figure BDA0003914091490000143
The horizontal position of the satellite at the nth time slot is represented as
Figure BDA0003914091490000144
Figure BDA0003914091490000145
The height of the satellite is H, and the fixed height of the u-th aerial base station is
Figure BDA0003914091490000146
Each ground user is only associated with one air base station;
s1-3, initializing other auxiliary parameters in the system, including W US 、W GU 、
Figure BDA0003914091490000147
Number of iterations j =0, v, κ 1 ，κ 2 . Wherein, W US Represents a bandwidth of the backhaul link to transmit data during slot n; w GU Represents the total bandwidth of the access link for transmitting data during time slot n;
Figure BDA0003914091490000148
respectively representing the maximum transmission power of the access link and the backhaul link in the nth time slot; v is the flight rate of the unmanned aerial vehicle; k is a radical of 1 And k 2 Is a fixed parameter related to air density, unmanned aerial vehicle weight, wing area, etc.
In this embodiment, the specific content of step S3 includes:
s3-1, defining an association strategy:
since terrestrial users may be very dense in practice, it is not possible for an airborne base station to provide communication services to all users in the coverage area at the same time. Thus, it is specified that one airborne base station can be simultaneously up to k th A ground user providing communication service, where k th K is less than or equal to K; introducing a binary variable a ku [n]Indicating whether the kth terrestrial user is connected to the u-th airborne base station in the nth slot, and if so, a ku [n]=1, otherwise a ku [n]=0; deriving an association policy as follows:
Figure BDA0003914091490000151
a ku [n]∈{0，1}
s3-2, an objective function of the first subproblem is specified, the objective function of the first subproblem is the same as the objective functions of the second subproblem and the third subproblem, and the objective functions are the objective functions for maximizing the system efficiency, and the following steps are performed:
Figure BDA0003914091490000152
s3-3, solving the first subproblem, comprising:
the optimization problem of the first subproblem is as follows:
maxη EE
s.t.C1：s[0]＝i
C2：
Figure BDA0003914091490000153
C3：
Figure BDA0003914091490000154
C4：
Figure BDA0003914091490000155
C5：
Figure BDA0003914091490000156
the first subproblem is non-convex, relaxing the binary-related variable into a continuous variable, and the first subproblem is rewritten as:
max η EE
s.t.C1：s[0]＝i
C2：
Figure BDA0003914091490000161
C3：
Figure BDA0003914091490000162
C4：
Figure BDA0003914091490000163
C5：
Figure BDA0003914091490000164
it is easy to conclude that the above problem is convex. But since the associated variable is relaxed to a continuous value between 0 and 1, it cannot be guaranteed that it can converge to 0 or 1; therefore, a penalty function F (a) is introduced ku [n])＝a ku [n](a ku [n]-1), the penalty function being a convex function, the subproblem one being further rewritten as:
maxη EE +κF(a ku [n])
s.t.C1：s[0]＝i
C2：
Figure BDA0003914091490000165
C3：
Figure BDA0003914091490000166
C4：
Figure BDA0003914091490000167
C5：
Figure BDA0003914091490000168
where k > 0 is a penalty factor, the objective function η EE +κF(a ku [n]) Is the difference of the concave function, i.e. eta EE -(-kF(a ku [n]) ); therefore, the problem becomes a DC programming problem (DCP); to convert the problem to a convex problem, in the j +1 th iteration, F (a) in the target is added ku [n]) The substitution is a first order Taylor expansion as follows:
Figure BDA0003914091490000169
and gives:
Figure BDA00039140914900001610
according to the above process, the sub-problem is converted into a linear program as follows:
Figure BDA0003914091490000171
s.t.C1：s[0]＝i
C2：
Figure BDA0003914091490000172
C3：
Figure BDA0003914091490000173
C4：
Figure BDA0003914091490000174
C5：
Figure BDA0003914091490000175
at this time, the CVX tool is used for solving a sub-problem one by substituting the given flight trajectory and resource allocation, and the solving variable of the sub-problem one is the correlation strategy.
Further, the specific content of step S4 includes:
s4-1, stipulate resource allocation:
in the resource allocation of the air base station, the air base station is in a fixed time slot length tau t Updating in units; use of b ku [m]Represents the proportion of bandwidth allocated to the kth terrestrial user by the access link within time slot m, which is a discrete value between 0 and 1; each subcarrier is allocated to only one terrestrial user, if the number of subcarriers is large enough, b ku [m]Approximately continuous between 0 and 1; based on the above specification, a resource allocation is derived as follows:
Figure BDA0003914091490000176
Figure BDA0003914091490000177
s4-2, establishing and applying a time scale unification model; in the optimization solving process of the second sub-problem, the strategy a is associated ku [n]And resource allocation b ku [m]The used time scales are different, and the normalization model and the association strategy a are based on the time scales under different conditions ku [n]To obtain resource allocation after time scale homogenization
Figure BDA0003914091490000178
In practice, the resource allocation is updated in the 5G base station on board the drone, the 5G base station having its update slot of fixed length. Because the time slot length of resource allocation updating is very small, if the time slot length of the 5G base station is adopted for optimizing the flight path and the resource allocation, the operation complexity is multiplied. Therefore, the present embodiment proposes a time scale unification model, and deals with the case of multiple time scales.
S4-3, solving a second subproblem, comprising:
the optimization problem of the second subproblem is as follows:
max η FE
s.t.C1：s[0]＝i
C2：
Figure BDA0003914091490000181
C3：
Figure BDA0003914091490000182
C4：
Figure BDA0003914091490000183
C5：
Figure BDA0003914091490000184
C6：
Figure BDA0003914091490000185
in calculating energy efficiency, a ku [n]And b ku [m]At different time scales. Therefore, it needs to be converted into a uniform time scale, and thus the uniform time scale a ku [n]And b ku [m]In particular to b ku [m]Conversion into
Figure BDA0003914091490000186
It is easy to see that the objective function at this time is as follows:
Figure BDA0003914091490000187
the objective function of the above formula is a concave function, and the constraints of the second subproblem are both convex constraints, so the problem is convex programming. And at the moment, solving a second sub-problem by using a CVX tool through substituting the association strategy and the given flight trajectory which are solved by the first sub-problem, wherein the solving variable of the second sub-problem is the resource allocation.
In the step S4-2, when a model is built by using multiple time scales, how to resolve conflicts brought by different time scales in the optimization problem needs to be considered, which is a challenge brought by the multiple time scales. In sub-problem two, associate policy a ku [n]And resource allocation b ku [m]The time scales used are different, and time scale conflict problems arise when computing throughput and energy efficiency. Therefore, the embodiment innovatively provides a multi-time scale homogenization method, which not only considers the characteristics of resource allocation, but also reduces the complexity of the algorithm.
Normalizing model and associated strategy according to time scale under different conditions ku [n]Is characterized byTo obtain the resource allocation after the time scale is unified
Figure BDA0003914091490000191
The method is specifically divided into the following five cases, and the processing method is selected according to the technical background:
in case one, if the resource allocation characteristics can be reflected by the median of the resource allocation, τ with smaller slot length is used t Delta larger than slot length t Division, i.e. c = δ t /τ t Obtaining the corresponding relation of two different time scale lengths; then every c b ku [m]The value of (A) is obtained by taking the median of the bits
Figure BDA0003914091490000192
In case two, if the resource allocation is representative or insufficient in memory for a certain period of time, the time slot length is smaller τ t Delta larger than slot length t Division, i.e. c = δ t /τ t Obtaining the corresponding relation of two different time scale lengths; then every c b ku [m]Taking out a representative value of the value of (A) and averaging the value
Figure BDA0003914091490000193
Case three, if the resource allocation total time is representative, the time slot length is smaller tau t Delta larger than slot length t Division, i.e. c = δ t /τ t Obtaining the corresponding relation of two different time scale lengths; then b is ku [m]Is averaged every c times to obtain
Figure BDA0003914091490000194
And fourthly, if the maximum value of the resource allocation can embody the resource allocation characteristics, the time slot length is shortened to be smaller tau t Delta larger than slot length t Division, i.e. c = δ t /τ t Obtaining the corresponding relation of two different time scale lengths; then b is ku [m]Is taken every c timesThe maximum value is obtained
Figure BDA0003914091490000195
Case five, if the resource allocation has randomness, the time slot length is smaller tau t Delta larger than slot length t Division, i.e. c = δ t /τ t Obtaining the corresponding relation of two different time scale lengths; then every c b ku [m]The value of (A) is obtained by randomly taking a plurality of values and then averaging the values
Figure BDA0003914091490000209
In this embodiment, the specific content of step S5 includes:
the optimization problem of the third subproblem is as follows:
max η EE
s.t.C1：
Figure BDA0003914091490000201
C2：
Figure BDA0003914091490000202
C3：s[0]＝i
C4：
Figure BDA0003914091490000203
C5：
Figure BDA0003914091490000204
C6：
Figure BDA0003914091490000205
the objective function of the sub-problem three at this time is as follows:
Figure BDA0003914091490000206
wherein eta EE And
Figure BDA0003914091490000207
is non-convex, and
Figure BDA0003914091490000208
introducing a relaxation variable:
(H u 2 +||q u [n]-w k [n]|| 2 )≤Q ku [n]
Figure BDA0003914091490000211
obtaining:
Figure BDA0003914091490000212
Figure BDA0003914091490000213
sub-problem three is therefore rewritten as:
maxη EE
s.t.C1：
Figure BDA0003914091490000214
C2：
Figure BDA0003914091490000215
C3：s[0]＝i
C4：
Figure BDA0003914091490000216
C5：
Figure BDA0003914091490000217
C6：
Figure BDA0003914091490000218
C7：
Figure BDA0003914091490000219
C8：
Figure BDA00039140914900002110
it is easy to see that the problem remains non-convex. Since when x > 0
Figure BDA00039140914900002111
Is convex and is unfolded using a first order Taylor at a given feasible point x j To obtain a lower bound of f (x):
Figure BDA00039140914900002112
order to
Figure BDA00039140914900002113
x＝Qku[n]And obtaining the following data at the j +1 th iteration:
Figure BDA0003914091490000221
Figure BDA0003914091490000222
Figure BDA0003914091490000223
through the above process, the sub-problem three can be further rewritten as:
maxη EE
s.t.C1：
Figure BDA0003914091490000224
C2：
Figure BDA0003914091490000225
C3：s[0]＝i
C4：
Figure BDA0003914091490000226
C5：
Figure BDA0003914091490000227
C6：
Figure BDA0003914091490000228
C7：
Figure BDA0003914091490000229
C8：
Figure BDA00039140914900002210
and solving a third subproblem by using a CVX tool through substituting the association strategy solved by the first subproblem and the resource allocation solved by the second subproblem, wherein the solving variable of the third subproblem is the flight track.
After the above method process of this embodiment, the final association strategy, resource allocation and flight trajectory are obtained, and then the joint optimization of the air-ground integrated communication network coverage can be completed.
The embodiment simultaneously provides the comparison data of the method and the single time scale algorithm and the random algorithm, wherein the single time scale algorithm is used for carrying out the track optimization and the resource allocation of the air base station in the same time scale, and the time slot length is 0.5s. The random algorithm is to randomly perform association and trajectory planning of the aerial base station and the user under the condition of resource average allocation. The parameters of the simulation experiment scenario of the embodiment are as follows:
TABLE 1 simulation parameters
Parameter(s) Value of Parameter(s) Value of
Number of flight time slots N 60 Flight time slot length 0.5s
Number of resource allocation slots M 3000 Resource allocation slot length 0.01s
Number of unmanned aerial vehicles 2 Number of users 50
Total bandwidth of access link 1 30Mhz Access link 2 total bandwidth 30Mhz
Unmanned plane
1 height 1.2km 2 altitude of unmanned plane 1km
Total bandwidth of backhaul link 50Mhz Satellite transmission power 62dBm
Flying speed 50m/s Maximum number of connectable users 10
Initial position of satellite [-345，0]km Altitude of satellite 2000km
Unmanned aerial vehicle 1 initial position [1，0.7]km 2 initial position of unmanned aerial vehicle [1，1]km
κ 1 9.26×10 -4 kg/m κ 2 2.250kg·m 3 /s 4
In the simulation experiment scene of the embodiment, a large number of ground users are randomly distributed in a ground area under a network scene with a simulation area of 1000m × 1000 m. In this simulation, the multi-time scale normalization method uses averaging of each c of the three cases. B1 (N, K), b2 (N, K) are initially set to be a matrix of N rows and K columns with the numerical value of 1/K, the unmanned aerial vehicle 1 flies along a line y = x-300 from the initial position, and the unmanned aerial vehicle 2 flies along a line y = x from the initial position. The moving speed of each airborne base station is v =50m/s. And carrying out multiple iterations to obtain a final result. The performance comparison of the multi-time scale algorithm, the single time scale algorithm, and the random algorithm is given below:
fig. 2 is a line graph showing the total system throughput changes with the increase of time slots when the terrestrial users are randomly distributed, where the number of terrestrial users is 50, the number of air base stations is 2, and the number of satellites is 1. The total time length is not changed, and obviously, as the number of time slots in the system increases, the throughput of the system also increases. It can be seen from the figure that the total throughput of the system obtained by the multi-time scale algorithm is highest, the next time of the single-time scale algorithm is lowest, and the random algorithm is lowest. Moreover, compared with a single time scale algorithm, when the number of the time slots is 40, the total throughput of the system is improved by 11.7 percent by using the multi-time scale algorithm. Compared with the random algorithm, the total throughput of the system is improved by 301.8% when the number of the time slots is 40.
Because the flight time of the air base station is fixed, the flight energy consumption of the air base station is the same in different algorithms. And because the energy consumption of the carried 5G base station is fixed, the total energy consumption is the same. The multi-time scale algorithm has relatively higher total system throughput under the condition of the same energy consumption, and realizes higher performance, because the algorithm adopts different time scales to carry out air base station resource allocation and track planning, the multi-time scale algorithm can better provide service for ground users.
Fig. 3 is a line graph showing the total throughput change of the system every time the number of users increases when the ground users are randomly distributed, where the number of air base stations is 2, the number of satellites is 1, and the total time length is constant. The influence of the change of the number of the ground users in the system on the energy efficiency of the system is obtained by only changing the number of the ground users which are respectively 30, 40, 50, 60 and 70. As can be seen from the figure, the system energy efficiency obtained by the multi-time scale algorithm is highest, the single-time scale algorithm is next to the next, and the random algorithm is lowest. Moreover, compared with a single time scale algorithm, when the number of users is 50, the system energy efficiency is improved by 10.2% by using the multi-time scale algorithm. Compared with a random algorithm, when the number of users is 50, the system energy efficiency is improved by 305.3%. Single time scale algorithms are not practical, while multi-time scale algorithms can not only achieve higher performance but also be practical. The superiority of the multi-time scale algorithm in the invention is embodied.

Claims (7)

1. A space-ground integrated communication network coverage method based on multiple time scales is characterized by comprising the following steps:
s1, initializing parameters of a system, wherein the parameters comprise ground user parameters, air base station parameters and other auxiliary parameters;
s2, initializing an association strategy, resource allocation and a flight track; during initialization, resource allocation is that resources are evenly allocated to each user, and a flight track is that the aerial base station starts from an initial position and flies in a straight line along a specific direction;
s3, performing iterative optimization calculation, solving a first subproblem of given flight trajectory and resource allocation, wherein an objective function of the first subproblem is the maximum system efficiency, and solving to obtain an association strategy;
s4, solving a second subproblem of the given track and the association strategy, wherein in the solving process of the second subproblem, the time scales used by the association strategy and the resource allocation are different, so that in the solving process, a multi-time scale homogenization method is applied, and the resource allocation is obtained by solving according to the association strategy obtained by the first subproblem;
s5, solving a third subproblem of the given resource allocation and association strategy, and solving to obtain a flight trajectory according to the association strategy obtained by the first subproblem and the resource allocation obtained by the second subproblem;
and S6, repeating the iterative optimization calculation process from the step S3 to the step S5 until the solving results of the first subproblem, the second subproblem and the third subproblem are converged, obtaining a final association strategy, resource allocation and flight trajectory, and finishing the joint optimization of the air-ground integrated communication network coverage.
2. The air-ground integrated communication network coverage method based on multiple time scales according to claim 1, wherein specific initialization contents of the step S1 are as follows:
s1-1, initializing the number K of ground users, the number U of aerial base stations, the number N of time slots of flight path planning and the time slot length delta of flight path planning t The number M of time slots for resource allocation, and the length tau of the time slots for resource allocation t (ii) a And represents a set of airborne base stations as
Figure FDA0003914091480000011
The set of terrestrial users is represented as
Figure FDA0003914091480000012
S1-2, initializing the position of a ground user, the position of a satellite and the position of an air base station, wherein the steps comprise:
the method comprises the following steps that positions of ground users are randomly distributed, a satellite is at an initial position, and an air base station is at an initial position, wherein the air base station is in backhaul connection through the satellite; the horizontal coordinate of the kth ground user is
Figure FDA0003914091480000021
The horizontal position of the satellite in the nth time slot is represented as
Figure FDA0003914091480000022
Figure FDA0003914091480000023
The height of the satellite is H, and the fixed height of the u-th aerial base station is
Figure FDA0003914091480000024
Each ground user is only associated with one air base station;
s1-3, initializing other auxiliary parameters in the system, including W US 、W GU 、
Figure FDA0003914091480000025
Number of iterations j =0, v, κ 1 、κ 2 。
3. The air-ground integrated communication network coverage method based on multiple time scales of claim 2, wherein: when initialization is carried out, the flying track is that the aerial base station starts from the initial position and flies along a straight line at 45 degrees in the southwest direction.
4. The method for overlaying the air-ground integrated communication network based on the multiple time scales according to claim 3, wherein the specific contents of the step S3 comprise:
s3-1, defining an association strategy: defining an airborne base station to be capable of simultaneously having a maximum of k th A ground user providing communication service, wherein k th K is less than or equal to K; introducing a binary variable a ku [n]Indicating whether the kth terrestrial user is connected to the u-th airborne base station in the nth slot, and if so, a ku [n]=1, otherwise a ku [n]=0; deriving an association policy as follows:
Figure FDA0003914091480000026
a ku [n]∈{0,1}
s3-2, an objective function of the first subproblem is specified, the objective function of the first subproblem is the same as the objective functions of the second subproblem and the third subproblem, and the objective functions are the objective functions for maximizing the system efficiency, and the following steps are performed:
Figure FDA0003914091480000027
Figure FDA0003914091480000031
s3-3, solving the first subproblem, comprising:
the optimization problem of the first subproblem is as follows:
maxη EE
s.t.C1:s[0]＝i
C2:
Figure FDA0003914091480000032
C3:
Figure FDA0003914091480000033
C4:
Figure FDA0003914091480000034
C5:
Figure FDA0003914091480000035
relaxing the binary associated variable into a continuous variable, and rewriting the subproblem one as:
maxη EE
s.t.C1:s[0]＝i
C2:
Figure FDA0003914091480000036
C3:
Figure FDA0003914091480000037
C4:
Figure FDA0003914091480000038
C5:
Figure FDA0003914091480000039
introducing a penalty function F (a) ku [n])＝a ku [n](a ku [n]-1), the penalty function being a convex function, the subproblem one being further rewritten as:
maxη EE +κF(a ku [n])
s.t.C1:s[0]＝i
C2:
Figure FDA0003914091480000041
C3:
Figure FDA0003914091480000042
C4:
Figure FDA0003914091480000043
C5:
Figure FDA0003914091480000044
wherein, κ>0 is a penalty factor, the objective function η EE +κF(a ku [n]) Is the difference of the concave function, i.e. eta EE -(-κF(a ku [n]) ); in the j +1 th iteration, F (a) in the target is added ku [n]) The substitution is a first order Taylor expansion as follows:
Figure FDA0003914091480000045
Figure FDA0003914091480000046
and gives the following:
Figure FDA0003914091480000047
according to the above process, the subproblem is transformed into a linear program as follows:
Figure FDA0003914091480000048
s.t.C1:s[0]＝i
C2:
Figure FDA0003914091480000049
C3:
Figure FDA00039140914800000410
C4:
Figure FDA00039140914800000411
C5:
Figure FDA00039140914800000412
at this time, the CVX tool is used for solving a sub-problem one by substituting the given flight trajectory and resource allocation, and the solving variable of the sub-problem one is the correlation strategy.
5. The method for overlaying the air-ground integrated communication network based on the multiple time scales according to claim 4, wherein the specific contents of the step S4 comprise:
s4-1, stipulate resource allocation: in the resource allocation of the air base station, the air base station is in a fixed time slot length tau t Updating in units; use of b ku [m]Represents the proportion of bandwidth allocated to the kth terrestrial user by the access link within time slot m, which is a discrete value between 0 and 1; each subcarrier is allocated to only one terrestrial user, if the number of subcarriers is large enough, b ku [m]Approximately continuous between 0 and 1; based on the above specification, a resource allocation is derived as follows:
Figure FDA0003914091480000051
Figure FDA0003914091480000052
s4-2, establishing and applying a time scale unification model; in the optimization solving process of the second subproblem, the association strategy a ku [n]And resource allocation b ku [m]The used time scales are different, and the normalization model and the association strategy a are based on the time scales under different conditions ku [n]To obtain resource allocation after time scale homogenization
Figure FDA0003914091480000053
S4-3, solving a second subproblem, which comprises the following steps:
the optimization problem of the second subproblem is as follows:
maxη EE
s.t.C1:s[0]＝i
C2:
Figure FDA0003914091480000054
C3:
Figure FDA0003914091480000055
C4:
Figure FDA0003914091480000056
C5:
Figure FDA0003914091480000057
C6:
Figure FDA0003914091480000058
unified time scale a ku [n]And b ku [m]B is to be ku [m]Conversion into
Figure FDA0003914091480000059
The objective function at this time is as follows:
Figure FDA0003914091480000061
and solving a second subproblem by using a CVX tool through the association strategy and the given flight trajectory which can be solved by substituting the first subproblem, wherein the solving variable of the second subproblem is the resource allocation.
6. The air-ground integrated communication network coverage method based on multiple time scales of claim 5, wherein: in the step S4-2, the time scale normalization model and the association strategy a under different conditions are adopted ku [n]To obtain resource allocation after time scale homogenization
Figure FDA0003914091480000062
The method is specifically divided into the following five conditions:
in case one, if the resource allocation characteristics can be reflected by the median of the resource allocation, τ with smaller slot length is used t Delta larger than slot length t Division, i.e. c = δ t /τ t Obtaining the corresponding relation of two different time scale lengths; then every c b ku [m]Is obtained by taking the median of the values
Figure FDA0003914091480000063
In case two, if the resource allocation is representative or insufficient in memory for a certain period of time, the time slot length is smaller τ t Delta larger than slot length t Division, i.e. c = δ t /τ t Obtaining the corresponding relation of two different time scale lengths; then every c b ku [m]Taking out a representative value of the value of (A) and averaging the values
Figure FDA0003914091480000064
Case three, if the resource allocation total time is representative, the time slot length is smaller tau t Delta larger than slot length t Division, i.e. c = δ t /τ t Obtaining the corresponding relation of two different time scale lengths; then b is mixed ku [m]Is averaged every c times to obtain
Figure FDA0003914091480000065
And fourthly, if the maximum value of the resource allocation can embody the resource allocation characteristics, the time slot length is shortened to be smaller tau t Delta larger than slot length t Division, i.e. c = δ t /τ t Obtaining the corresponding relation of two different time scale lengths; then b is ku [m]The value of (c) is obtained by taking the maximum value of each c
Figure FDA0003914091480000066
Case five, if the resource allocation has randomness, the time slot length is smaller tau t Delta larger than slot length t Division, i.e. c = δ t /τ t Obtaining the corresponding relation of two different time scale lengths; then every c b ku [m]The value of (A) is obtained by randomly taking a plurality of values and then averaging the values
Figure FDA0003914091480000071
7. The air-ground integrated communication network coverage method based on multiple time scales according to claim 5, wherein the specific content of the step S5 comprises:
the optimization problem of the third subproblem is as follows:
maxη EE
s.t.C1:
Figure FDA0003914091480000072
C2:
Figure FDA0003914091480000073
C3:s[0]＝i
C4:
Figure FDA0003914091480000074
C5:
Figure FDA0003914091480000075
C6:
Figure FDA0003914091480000076
the objective function of the subproblem three at this time is as follows:
Figure FDA0003914091480000077
wherein eta EE And
Figure FDA0003914091480000078
is non-convex, such that
Figure FDA0003914091480000079
Introducing a relaxation variable:
(H u 2 +‖q u [n]-w k [n]‖ 2 )≤Q ku [n]
Figure FDA0003914091480000081
obtaining:
Figure FDA0003914091480000082
Figure FDA0003914091480000083
the sub-problem three is therefore rewritten as:
maxη EE
s.t.C1:
Figure FDA0003914091480000084
C2:
Figure FDA0003914091480000085
C3:s[0]＝i
C4:
Figure FDA0003914091480000086
C5:
Figure FDA0003914091480000087
C6:
Figure FDA0003914091480000088
C7:
Figure FDA0003914091480000089
C8:
Figure FDA00039140914800000810
the expansion is performed using a first order Taylor, at a given feasible point x j To obtain a lower bound of f (x):
Figure FDA00039140914800000811
order to
Figure FDA00039140914800000812
x＝Q ku [n]And obtaining the following data at the j +1 th iteration:
Figure FDA00039140914800000813
Figure FDA0003914091480000091
Figure FDA0003914091480000092
through the above process, the sub-problem three can be further rewritten as:
maxη EE
s.t.C1:
Figure FDA0003914091480000093
C2:
Figure FDA0003914091480000094
C3:s[0]＝i
C4:
Figure FDA0003914091480000095
C5:
Figure FDA0003914091480000096
C6:
Figure FDA0003914091480000097
C7:
Figure FDA0003914091480000098
C8:
Figure FDA0003914091480000099
and solving a third subproblem by using a CVX tool through substituting the association strategy solved by the first subproblem and the resource allocation solved by the second subproblem, wherein the solving variable of the third subproblem is the flight track.
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