CN107094044B - Unmanned aerial vehicle relay communication track planning method based on space-time block coding - Google Patents

Unmanned aerial vehicle relay communication track planning method based on space-time block coding Download PDF

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CN107094044B
CN107094044B CN201710201116.5A CN201710201116A CN107094044B CN 107094044 B CN107094044 B CN 107094044B CN 201710201116 A CN201710201116 A CN 201710201116A CN 107094044 B CN107094044 B CN 107094044B
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aerial vehicle
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CN107094044A (en
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刘海涛
赵文强
李春鸣
王磊
李冬霞
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Civil Aviation University of China
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    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04BTRANSMISSION
    • H04B7/00Radio transmission systems, i.e. using radiation field
    • H04B7/14Relay systems
    • H04B7/15Active relay systems
    • H04B7/185Space-based or airborne stations; Stations for satellite systems
    • H04B7/18502Airborne stations
    • H04B7/18504Aircraft used as relay or high altitude atmospheric platform
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04BTRANSMISSION
    • H04B7/00Radio transmission systems, i.e. using radiation field
    • H04B7/02Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/06Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station
    • H04B7/0613Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04BTRANSMISSION
    • H04B7/00Radio transmission systems, i.e. using radiation field
    • H04B7/02Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/08Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station
    • H04B7/0837Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station using pre-detection combining
    • H04B7/0842Weighted combining
    • H04B7/0848Joint weighting
    • H04B7/0857Joint weighting using maximum ratio combining techniques, e.g. signal-to- interference ratio [SIR], received signal strenght indication [RSS]
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00Arrangements for detecting or preventing errors in the information received
    • H04L1/02Arrangements for detecting or preventing errors in the information received by diversity reception
    • H04L1/06Arrangements for detecting or preventing errors in the information received by diversity reception using space diversity
    • H04L1/0618Space-time coding
    • H04L1/0637Properties of the code
    • H04L1/0643Properties of the code block codes

Abstract

A space-time block coding unmanned aerial vehicle relay communication track planning method comprises the following steps: the model for establishing the unmanned aerial vehicle relay communication system of the space-time block coding comprises the following steps: at time t, transmitting signals through two transmitting antennas in a space-time block coding mode at two continuous time slots by a certain power at the mobile access node; the unmanned aerial vehicle receives signals from the movable access node in a first time slot and a second time slot, and forwards the received signals with certain power; the base station node receives signals transmitted by the unmanned aerial vehicle in the third time slot and the fourth time slot, and a receiver of the base station node performs relevant combination processing on the received signals; the method for establishing the flight path planning model of the unmanned aerial vehicle relay communication system comprises the following steps: solving the traversal capacity of the relay communication system of the unmanned aerial vehicle at the time t; respectively calculating the distance from the movable access node to the unmanned aerial vehicle and the distance from the unmanned aerial vehicle to the base station node; and establishing a flight path planning model of the unmanned aerial vehicle relay communication system. The method effectively improves the reliability of the relay communication link transmission of the point-to-point unmanned aerial vehicle.

Description

Unmanned aerial vehicle relay communication track planning method based on space-time block coding
Technical Field
The invention relates to a method for planning a relay communication track of an unmanned aerial vehicle. In particular to a space-time block coding unmanned aerial vehicle relay communication track planning method.
Background
Unmanned aerial vehicle relay communication is an important technical means for realizing remote point-to-point wireless communication. Compared with fixed relay communication, the unmanned aerial vehicle relay communication has the advantages of long communication distance, convenience in deployment, flexible and controllable relay position, rapidness in system construction, low maintenance cost and the like, so that the unmanned aerial vehicle relay communication is widely applied to the military and civil fields [1-2 ]. Meanwhile, due to the characteristics of high-speed maneuverability of the unmanned aerial vehicle, limited energy of the unmanned aerial vehicle and the like, in order to guarantee the connectivity and reliability of the relay communication system of the unmanned aerial vehicle, the problem of unmanned aerial vehicle track planning inevitably occurs.
The problem of planning the flight path around the relay communication unmanned aerial vehicle is related to the following research: for the performance optimization problem of the unmanned aerial vehicle relay communication system accessed by multiple users, document [3] provides an unmanned aerial vehicle track planning method based on the criterion of the maximization of the normalized transmission rate of each epoch, however, only single-hop links from user nodes to the unmanned aerial vehicle are considered when the unmanned aerial vehicle track is optimized, and the influence of the unmanned aerial vehicle to a base station link on the overall system performance is not considered. Also aiming at the problem of optimization of relay communication of an unmanned aerial vehicle accessed by multiple users, document [4] proposes two unmanned aerial vehicle track planning methods based on the criterion of average and rate maximization and the criterion of user minimum rate maximization, however, the article only considers the single-hop link from the user node to the unmanned aerial vehicle, and does not consider the influence of the links from the unmanned aerial vehicle to the base station on the performance. For the problem of flight path planning of an unmanned aerial vehicle relay broadcast communication system, document [5] proposes a low-complexity unmanned aerial vehicle flight path planning method based on the criterion of maximizing the link capacity of the minimum individual history, and the method is mainly characterized in that the position information of each user does not need to be accurately known. For the problem of flight path planning of point-to-point unmanned aerial vehicle relay communication, document [6] proposes an unmanned aerial vehicle relay transmission method based on transmit beam forming and receive beam forming, and provides an unmanned aerial vehicle flight path planning method based on the criterion of signal-to-noise ratio maximization, however, the method requires that both an access node transmitter and a base station receiver need to accurately know fading information of a channel, and the transmitter is difficult to acquire fading information of the channel in practical application, so that the method is very difficult to apply to a practical system.
The point-to-point unmanned aerial vehicle relay communication transmission scheme mainly comprises the following steps: the drawbacks and deficiencies of the techniques are described below, respectively, for a single-transmit, single-receive transmission scheme and a beamforming transmission scheme.
The basic idea of the single-transmission single-reception transmission scheme is as follows: the single-transmitting single-receiving unmanned aerial vehicle relay communication system is composed of a source node provided with an antenna, a relay unmanned aerial vehicle provided with 1 antenna and a destination node provided with an antenna, and LOS does not exist between the source node and the destination node. The signal is divided into two time slots in the whole relay transmission process, and in the 1 st time slot, the source node sends the sent signal to the unmanned aerial vehicle; in the 2 nd time slot, the relay drone first multiplies the received signal by an amplification factor with a fixed gain, and then forwards the signal to the destination node with a certain power. In practical application, the method has the following defects: the channel capacity is small, the interruption probability is high, and the reliability is poor.
Basic idea of beamforming transmission scheme: the unmanned aerial vehicle relay communication system based on the beam forming transmission scheme is composed of a source node provided with a plurality of antennas, an unmanned aerial vehicle provided with one antenna and a destination node provided with a plurality of antennas, and a direct communication link does not exist between the source node and the destination node. In order to realize the communication between the source node and the destination node, the communication between the source node and the destination node must be realized through unmanned aerial vehicle relay. The signal is divided into two time slots in the whole relay transmission process. In the 1 st time slot, the source node performs beam forming on the sent signal and then transmits the signal; in the 2 nd time slot, the unmanned aerial vehicle amplifies and forwards the received signal to the destination node, and then the destination node performs beam forming processing on the received signal. The most important defects of the scheme are as follows: both the source node transmitter and the destination node receiver need to accurately know the fading information of the channel, and in practical application, the transmitter is difficult to acquire the fading information of the channel, so that the method is very difficult to apply in a practical system.
Disclosure of Invention
The invention aims to solve the technical problem of providing an unmanned aerial vehicle relay communication track planning method which can effectively improve the reliability of point-to-point unmanned aerial vehicle relay communication link transmission and realize space-time block coding of remote point-to-point wireless communication.
The technical scheme adopted by the invention is as follows: a space-time block coding unmanned aerial vehicle relay communication track planning method comprises the following steps:
1) the model for establishing the unmanned aerial vehicle relay communication system of the space-time block coding comprises the following steps:
(1) at time t, at the mobile access node, a certain power P1Transmitting signals through two transmitting antennas in a space-time block coding mode in two continuous time slots;
(2) the unmanned aerial vehicle receives signals from the mobile access node in a first time slot and a second time slot respectively, and then the signals are transmitted with a certain power P2Adopting an amplification forwarding mode to forward the received signal transmitted by the movable access node;
(3) the base station node receives signals transmitted by the unmanned aerial vehicle in the third time slot and the fourth time slot respectively, a receiver of the base station node accurately obtains fading coefficients of all channels through channel estimation, and a maximum ratio combining method is adopted to carry out relevant combining processing on the signals received by the two time slots;
2) the method for establishing the flight path planning model of the unmanned aerial vehicle relay communication system according to the traversal capacity maximization criterion comprises the following steps:
(1) solving the traversal capacity of the relay communication system of the unmanned aerial vehicle at the time t;
(2) respectively calculating the distance from the movable access node to the unmanned aerial vehicle and the distance from the unmanned aerial vehicle to the base station node;
(3) and establishing a flight path planning model of the unmanned aerial vehicle relay communication system.
Step 1) of step (1)The signal is transmitted by two transmitting antennas in a space-time block coding mode, and a first transmitting antenna in the movable access node transmits a symbol s in a first time slot1The second transmitting antenna transmits a symbol s2Second time slot, 1 st transmitting antenna sends symbol
Figure BDA0001258582960000021
Figure BDA0001258582960000021
2 nd transmitting antenna transmitting symbol
Figure BDA0001258582960000022
Wherein represents complex conjugate operation, and the transmitted symbol satisfies E { | si|21, wherein i is 1, 2; e is the desired operation.
In step 1), the unmanned aerial vehicle in step (2) receives signals from the mobile access node in the first time slot and the second time slot respectively, and the signals are represented as follows:
Figure BDA0001258582960000023
wherein the content of the first and second substances,
Figure BDA0001258582960000025
representing the reception of the signal transmitted from the mobile access node by the receiving antenna of the drone in the 1 st time slot, r1 2Receiving a signal transmitted from the mobile access node at a2 nd time slot by the receiving antenna of the unmanned aerial vehicle; p1Representing the power of each transmit antenna of the mobile access node transmitting a signal;
Figure BDA0001258582960000024
the mean value of the receiving antenna of the unmanned aerial vehicle at the 1 st time slot is 0, and the variance is
Figure BDA0001258582960000031
The complex white gaussian noise of (1) is,
Figure BDA0001258582960000032
representing the receiving antenna receiving in the 2 nd time slotReceived mean of 0 and variance of
Figure BDA0001258582960000033
The complex white Gaussian noise is independent in the statistics of noise signals in different time slots;
Figure BDA0001258582960000034
representing the channel fading coefficients from the 1 st transmit antenna of the mobile access node to the 1 st receive antenna of the drone,
Figure BDA0001258582960000035
representing channel fading coefficients of a2 nd transmitting antenna of the mobile access node to a1 st receiving antenna of the drone, the channel fading coefficients being modeled as:
Figure BDA0001258582960000036
wherein i is 1; j is 1, 2;
Figure BDA0001258582960000037
representing the small-scale fading coefficient of the channel from the jth transmitting antenna of the movable access node to the ith receiving antenna of the unmanned aerial vehicle, wherein the small-scale fading coefficient is modeled into a complex Gaussian random variable with the mean value of 0 and the variance of 1, α represents a path loss factor, dAURepresenting the distance of the mobile access node to the drone.
Step 1) in step (2) with a certain power P2The signal transmitted by the mobile access node and forwarded by adopting the amplification forwarding mode is as follows: after receiving the signal sent by the movable access node, the unmanned aerial vehicle multiplies the received signal by a gain factor G in an amplification forwarding mode:
Figure BDA0001258582960000038
the step (3) in the step 1) comprises the following steps:
a) in the third time slot, the signals transmitted by the drone and received by the two receiving antennas of the base station node are respectively represented as:
Figure BDA0001258582960000039
in the fourth time slot, the signals received by the two receiving antennas of the base station node and transmitted by the drone are respectively represented as:
Figure BDA00012585829600000310
in the formula (I), the compound is shown in the specification,
Figure BDA00012585829600000311
the 1 st receiving antenna (B1) of the base station node receives the signal transmitted by the unmanned aerial vehicle in the third time slot;
Figure BDA00012585829600000312
a2 nd receiving antenna (B2) representing the base station node receiving the signal transmitted from the drone in a third time slot;
Figure BDA00012585829600000313
the 1 st receiving antenna of the base station node receives the signal transmitted by the unmanned aerial vehicle in the fourth time slot;
Figure BDA00012585829600000314
the 2 nd receiving antenna of the base station node receives the signal transmitted by the unmanned aerial vehicle in the fourth time slot; p2Representing the drone transmit signal power;
Figure BDA00012585829600000315
represents that the mean value of the 1 st receiving antenna of the base station node in the third time slot is 0 and the variance is
Figure BDA00012585829600000316
Complex white gaussian noise of (a);
Figure BDA00012585829600000317
the mean value of the received signal of the 2 nd receiving antenna of the base station node in the third time slot is 0, and the variance is
Figure BDA00012585829600000318
Complex white gaussian noise of (a);
Figure BDA00012585829600000319
represents that the mean value received by the 1 st receiving antenna of the base station node in the fourth time slot is 0 and the variance is
Figure BDA00012585829600000320
Complex white gaussian noise of (a);
Figure BDA0001258582960000041
represents that the mean value received by the 2 nd receiving antenna of the base station node in the fourth time slot is 0 and the variance is
Figure BDA0001258582960000042
Complex white gaussian noise of (a);
Figure BDA0001258582960000043
representing the channel fading coefficient from the 1 st transmitting antenna of the unmanned aerial vehicle to the 1 st receiving antenna of the base station node;
Figure BDA0001258582960000044
representing the channel fading coefficient from the 1 st transmitting antenna of the unmanned aerial vehicle to the 2 nd receiving antenna of the base station node, wherein the channel fading coefficient is modeled as:
Figure BDA0001258582960000045
wherein n is 1, 2; m is 1;
Figure BDA0001258582960000046
the small-scale fading coefficient represents a channel from the mth transmitting antenna of the unmanned aerial vehicle to the nth receiving antenna of the base station node, and the small-scale fading coefficient is modeled into a complex Gaussian random variable with the mean value of 0 and the variance of 1; dUBRepresent unmanned aerial vehicle to the distance of base station node, for convenient simplification, introduced the following parameter in the above formula:
Figure BDA0001258582960000047
Figure BDA0001258582960000048
b) the receiver of the base station node accurately obtains the fading coefficients of all channels through channel estimation:
c) the base station node adopts a maximum ratio combining method to carry out relevant combining processing on signals received by two time slots:
the receiver of the base station node performs correlation combination processing on the signals received by the two time slots of the base station node according to the following formula:
Figure BDA0001258582960000049
will be provided with
Figure BDA00012585829600000410
And
Figure BDA00012585829600000411
respectively substituting into the formula to obtain after simplification:
Figure BDA00012585829600000412
in the formula (I), the compound is shown in the specification,
Figure BDA00012585829600000413
the step (1) in the step 2) comprises the following steps:
the traversal capacity of the relay communication system of the unmanned aerial vehicle at the time t is represented as follows:
Figure BDA00012585829600000414
wherein r isout,tThe instantaneous snr of the receiver demodulator input representing the base station node at time t is specifically:
Figure BDA00012585829600000415
wherein the content of the first and second substances,
Figure BDA00012585829600000416
||·||Frepresents the Frobenius norm;
Figure BDA00012585829600000417
Figure BDA00012585829600000418
observed from the above formula: distance d from mobile access node to unmanned aerial vehicle of instantaneous signal-to-noise ratio input by receiver demodulator of base station nodeAUDistance d from unmanned aerial vehicle to base station nodeUBSmall-scale attenuation of movable access node-unmanned aerial vehicle link
Figure BDA0001258582960000051
And jointly determining the small-scale attenuation of the unmanned aerial vehicle-base station node.
The step (2) in the step 2) comprises the following steps:
establishing a three-dimensional rectangular coordinate for accurately giving the distance from the movable access node to the unmanned aerial vehicle and the distance from the unmanned aerial vehicle to the base station node, and assuming that the position coordinate of the fixed base station node is (x)B,yB0), the position coordinate of the movable access node at the time t is (x)A,t,yA,t0), the position coordinates of the drone are (x)t,yt,ht) And the distances between the unmanned aerial vehicle at the time t and the movable access node and the base station node are calculated by using the position coordinates of each node and are respectively as follows:
Figure BDA0001258582960000052
further assuming that the flying height of the unmanned aerial vehicle is always kept at h and the unmanned aerial vehicle flies at a constant speed v, the position of the unmanned aerial vehicle at the time t is determined according to the position information of the unmanned aerial vehicle at the time t-delta t, and by using the following equation:
Figure BDA0001258582960000053
updating to obtain:
Figure BDA0001258582960000054
wherein the content of the first and second substances,trepresenting the course angle of the unmanned plane at the moment t, and meeting the requirementt-Δt-maxtt-Δt+maxWhereinmaxRepresenting a maximum heading angle of the drone; Δ t represents the time interval of the unmanned plane position update;
the above formula shows that: after the position of the unmanned aerial vehicle is given at the time t-delta t, the distance between the movable access node and the unmanned aerial vehicle at the time t and the distance between the unmanned aerial vehicle and the base station node are only determined by the course angle of the unmanned aerial vehicle at the time tt
The step (3) in the step 2) comprises the following steps:
carrying out Taylor series expansion on a traversal capacity formula of the relay communication system of the unmanned aerial vehicle at the time t, and taking a first term of the expansion as follows:
Figure BDA0001258582960000055
wherein, E { rout,tRepresents the average signal-to-noise ratio of the receiver demodulator input at the base station node at time t, expressed as:
Figure BDA0001258582960000056
considering that the formula (17) is still difficult to calculate, the above formula is expanded again by using taylor series, and the first term in the expansion formula is taken as:
Figure BDA0001258582960000061
will dAU,tAnd dUB,tSubstituting the above formula, the following conclusions were observed: under the condition that the position of the unmanned aerial vehicle is given at the moment t-delta t, the input average signal-to-noise ratio of a receiver demodulator of a base station node of the relay communication system of the unmanned aerial vehicle at the moment t is only determined by the course angle of the unmanned aerial vehicle at the moment ttIn order to maximize the link capacity of the relay communication system of the unmanned aerial vehicle at the time t, the course angle of the unmanned aerial vehicle is optimized based on the traversal capacity maximization criterion, and the optimization problem of optimizing the course angle of the unmanned aerial vehicle is expressed as follows:
Figure BDA0001258582960000062
further consider log in addition2(. to) is a monotonically increasing function, and the problem of optimizing the heading angle of the drone is finally expressed as
Figure BDA0001258582960000063
Wherein the content of the first and second substances,
Figure BDA0001258582960000064
representing the optimal course angle of the unmanned aerial vehicle at the time t; the solution of the course angle problem of the optimized unmanned aerial vehicle is solved by a one-dimensional linear search method.
The unmanned aerial vehicle relay communication track planning method based on space-time block coding can effectively improve the reliability of point-to-point unmanned aerial vehicle relay communication link transmission and realize long-distance point-to-point wireless communication; compared with the single-transmitting single-receiving unmanned aerial vehicle relay communication method, the method has the advantages that the obtained system has smaller interruption probability and larger traversal channel capacity; compared with the unmanned aerial vehicle relay transmission scheme of beam forming, the transmitter does not need to accurately know the fading information of the channel, and the flight path planning method is simple and easy to implement, and the system is simple to realize in the practical application process.
Drawings
Fig. 1 is a space-time block coded drone relay communication system;
FIG. 2 is a graph of UAV optimal trajectory as a function of AP motion path;
FIG. 3 is a graph of the effect of maximum heading angle on the flight path of a UAV;
FIG. 4 is a graph of system outage probability over time;
FIG. 5 is a graph of system traversal capacity over time;
FIG. 6 is a graph of the effect of maximum heading angle on system outage probability performance;
FIG. 7 is a graph of the effect of maximum heading angle on system traversal capacity performance.
Detailed Description
The following describes in detail a space-time block coded unmanned aerial vehicle relay communication track planning method according to the present invention with reference to the following embodiments and accompanying drawings.
In order to solve the problem of reliability of link transmission of a point-to-point unmanned aerial vehicle relay communication system, the invention provides an unmanned aerial vehicle amplification forwarding relay communication transmission scheme based on space-time block coding, and provides an unmanned aerial vehicle optimal track planning method based on a double-hop link traversal capacity maximization criterion. The invention can effectively improve the reliability of the relay communication link transmission of the point-to-point unmanned aerial vehicle and realize remote point-to-point wireless communication.
Fig. 1 shows a model of a space-time block coded unmanned aerial vehicle relay communication system. The system is composed of a movable Access Point (AP), a high-speed motion Unmanned Aerial Vehicle (UAV) and a Base Station node (BS). Assuming that the distance between the AP and the BS is far, a direct communication link between the AP and the BS does not exist in the system, and in order to implement the mutual communication between the AP and the BS node, the communication between the AP and the BS must be implemented by a UAV relay. In order to improve the link transmission reliability of the UAV relay communication system and reduce the complexity of system implementation, the invention adopts a space-time block coding UAV relay communication scheme, AP adopts a two-antenna space-time block coding transmit diversity mode to transmit signals, UAV adopts a single-antenna amplifying and forwarding protocol to relay signals, and BS adopts a multi-antenna maximum ratio combining method to combine signals so as to improve the link transmission reliability.
The invention discloses a space-time block coding unmanned aerial vehicle relay communication track planning method, which comprises the following steps:
1) the model for establishing the unmanned aerial vehicle relay communication system of the space-time block coding comprises the following steps:
(1) at time t, a mobile Access Point (AP) is in a certain power P1Transmitting signals through two transmitting antennas in a space-time block coding mode in two continuous time slots;
the signal is transmitted by two transmitting antennas in a space-time block coding mode, and a first transmitting antenna (A1) in the mobile access node transmits a symbol s in a first time slot1The second transmitting antenna (A2) transmits a symbol s2Second time slot, 1 st transmitting antenna sends symbol
Figure BDA0001258582960000071
Figure BDA0001258582960000071
2 nd transmitting antenna transmitting symbol
Figure BDA0001258582960000072
Wherein represents complex conjugate operation, and the transmitted signal satisfies E { | si|21 (i-1, 2), and E is the desired operation.
(2) An Unmanned Aerial Vehicle (UAV) receives signals from a mobile access node in a first time slot and a second time slot respectively, and then the signals are transmitted with a certain power P2Adopting an amplification forwarding mode to forward the received signal transmitted by the movable access node;
the signals received by the unmanned aerial vehicle from the mobile access node in the first time slot and the second time slot are respectively expressed as:
Figure BDA0001258582960000073
wherein r is1 1The unmanned aerial vehicle receiving antenna receives a signal transmitted from the mobile access node in the 1 st time slot; r is1 2Representing unmanned aerial vehicle receiving skyThe line receives the signal transmitted from the mobile access node in the 2 nd time slot; p1Representing the power of each transmit antenna of the mobile access node transmitting a signal;
Figure BDA0001258582960000074
the mean value of the receiving antenna of the unmanned aerial vehicle at the 1 st time slot is 0, and the variance is
Figure BDA0001258582960000075
The complex white gaussian noise of (1) is,
Figure BDA0001258582960000076
represents that the receiving antenna receives the mean value of 0 and the variance of
Figure BDA0001258582960000077
The complex white Gaussian noise is independent in the statistics of noise signals in different time slots;
Figure BDA0001258582960000078
representing the channel fading coefficients from the 1 st transmit antenna of the mobile access node to the 1 st receive antenna of the drone,
Figure BDA0001258582960000079
representing channel fading coefficients of a2 nd transmitting antenna of the mobile access node to a1 st receiving antenna of the drone, the channel fading coefficients being modeled as:
Figure BDA0001258582960000081
wherein i is 1; j is 1, 2;
Figure BDA0001258582960000082
representing the small-scale fading coefficient of the channel from the jth transmitting antenna of the movable access node to the ith receiving antenna of the unmanned aerial vehicle, wherein the small-scale fading coefficient is modeled into a complex Gaussian random variable with the mean value of 0 and the variance of 1, α represents a path loss factor, dAURepresenting a movable typeDistance of access node to drone.
Said constant power P2The signal transmitted by the mobile access node and forwarded by adopting the amplification forwarding mode is as follows: after receiving the signal sent by the movable access node, the unmanned aerial vehicle multiplies the received signal by a gain factor G in an amplification forwarding mode:
Figure BDA0001258582960000083
(3) receiving signals transmitted by the unmanned aerial vehicle at a third time slot and a fourth time slot respectively at a base station node (BS), accurately obtaining fading coefficients of all channels by a receiver of the base station node through channel estimation, and performing related combination processing on the signals received by the two time slots by adopting a maximum ratio combination method; the method comprises the following steps:
a) in the third time slot, the signals received by the two receiving antennas of the base station node (for convenience of description, the BS uses two receiving antennas, and the method is easily popularized to the case where the BS uses multiple receiving antennas) are respectively expressed as:
Figure BDA0001258582960000084
in the fourth time slot, the signals received by the two receiving antennas of the base station node and transmitted by the drone are respectively represented as:
Figure BDA0001258582960000085
in the formula (I), the compound is shown in the specification,
Figure BDA0001258582960000086
the 1 st receiving antenna (B1) of the base station node receives the signal transmitted by the unmanned aerial vehicle in the third time slot;
Figure BDA0001258582960000087
a2 nd receiving antenna (B2) representing the base station node receiving the signal transmitted from the drone in a third time slot;
Figure BDA0001258582960000088
the 1 st receiving antenna of the base station node receives the signal transmitted by the unmanned aerial vehicle in the fourth time slot;
Figure BDA0001258582960000089
the 2 nd receiving antenna of the base station node receives the signal transmitted by the unmanned aerial vehicle in the fourth time slot; p2Representing the drone transmit signal power;
Figure BDA00012585829600000810
represents that the mean value of the 1 st receiving antenna of the base station node in the third time slot is 0 and the variance is
Figure BDA00012585829600000811
Complex white gaussian noise of (a);
Figure BDA00012585829600000812
the mean value of the received signal of the 2 nd receiving antenna of the base station node in the third time slot is 0, and the variance is
Figure BDA00012585829600000813
Complex white gaussian noise of (a);
Figure BDA00012585829600000814
represents that the mean value received by the 1 st receiving antenna of the base station node in the fourth time slot is 0 and the variance is
Figure BDA00012585829600000815
Complex white gaussian noise of (a);
Figure BDA00012585829600000816
represents that the mean value received by the 2 nd receiving antenna of the base station node in the fourth time slot is 0 and the variance is
Figure BDA0001258582960000091
Complex white gaussian noise of (a);
Figure BDA0001258582960000092
representing the channel fading coefficient from the 1 st transmitting antenna of the unmanned aerial vehicle to the 1 st receiving antenna of the base station node;
Figure BDA0001258582960000093
representing the channel fading coefficient from the 1 st transmitting antenna of the unmanned aerial vehicle to the 2 nd receiving antenna of the base station node, wherein the channel fading coefficient is modeled as:
Figure BDA0001258582960000094
wherein n is 1, 2; m is 1;
Figure BDA0001258582960000095
the small-scale fading coefficient represents a channel from the mth transmitting antenna of the unmanned aerial vehicle to the nth receiving antenna of the base station node, and the small-scale fading coefficient is modeled into a complex Gaussian random variable with the mean value of 0 and the variance of 1; dUBRepresent unmanned aerial vehicle to the distance of base station node, for convenient simplification, introduced the following parameter in the above formula:
Figure BDA0001258582960000096
Figure BDA0001258582960000097
b) the receiver of the base station node accurately obtains the fading coefficients of all channels through channel estimation:
c) the base station node adopts a maximum ratio combining method to carry out relevant combining processing on signals received by two time slots:
the receiver of the base station node performs correlation combination processing on the signals received by the two time slots of the base station node according to the following formula:
Figure BDA0001258582960000098
substituting the formulas (4) and (5) into the formulas respectively to obtain the following products:
Figure BDA0001258582960000099
in the formula (I), the compound is shown in the specification,
Figure BDA00012585829600000910
2) establishing an unmanned aerial vehicle relay system track planning model according to a traversal capacity maximization criterion, wherein the method comprises the following steps:
(1) solving the traversal capacity of the relay communication system of the unmanned aerial vehicle at the time t;
the method comprises the following steps:
the traversal capacity of the unmanned aerial vehicle relay communication system at the time t is represented as [8 ]:
Figure BDA00012585829600000911
wherein r isout,tThe instantaneous snr of the receiver demodulator input representing the base station node at time t is specifically:
Figure BDA00012585829600000912
wherein the content of the first and second substances,
Figure BDA00012585829600000913
||·||Frepresents the Frobenius norm;
Figure BDA00012585829600000914
observed from the above formula: distance d from mobile access node to unmanned aerial vehicle of instantaneous signal-to-noise ratio input by receiver demodulator of base station nodeAUDistance d from unmanned aerial vehicle to base station nodeUBSmall-scale attenuation of movable access node-unmanned aerial vehicle link
Figure BDA0001258582960000101
And jointly determining the small-scale attenuation of the unmanned aerial vehicle-base station node.
(2) Respectively calculating the distance from the movable access node to the unmanned aerial vehicle and the distance from the unmanned aerial vehicle to the base station node; the method comprises the following steps:
establishing a three-dimensional rectangular coordinate for accurately giving the distance from the movable access node to the unmanned aerial vehicle and the distance from the unmanned aerial vehicle to the base station node, and assuming that the position coordinate of the fixed base station node is (x)B,yB0), the position coordinate of the movable access node at the time t is (x)A,t,yA,t0), the position coordinates of the drone are (x)t,yt,ht) And the distances between the unmanned aerial vehicle at the time t and the movable access node and the base station node are calculated by using the position coordinates of each node and are respectively as follows:
Figure BDA0001258582960000102
further assuming that the flying height of the unmanned aerial vehicle is always kept at h, and the unmanned aerial vehicle flies at a constant speed v, the position of the unmanned aerial vehicle at the time t is determined according to the position information of the unmanned aerial vehicle at the time t- Δ t, and by using the following equation [7 ]:
Figure BDA0001258582960000103
updating to obtain:
Figure BDA0001258582960000104
wherein the content of the first and second substances,trepresenting the course angle of the unmanned plane at the moment t, and meeting the requirementt-Δt-maxtt-Δt+maxWhereinmaxRepresenting a maximum heading angle of the drone; Δ t represents the time interval of the unmanned plane position update;
the above formula shows that: after the position of the unmanned aerial vehicle is given at the time t-delta t, the distance between the movable access node and the unmanned aerial vehicle at the time t and the distance between the unmanned aerial vehicle and the base station node are only determined by the course angle of the unmanned aerial vehicle at the time tt
(3) And establishing a flight path planning model of the unmanned aerial vehicle relay system. The method comprises the following steps:
because it is very difficult to directly carry out statistical average operation on the ergodic capacity formula of the relay communication system of the unmanned aerial vehicle at the time t, the taylor series expansion is carried out on the ergodic capacity formula of the relay communication system of the unmanned aerial vehicle at the time t, and the first term of the expansion is taken as:
Figure BDA0001258582960000105
wherein, E { rout,tRepresents the average signal-to-noise ratio of the receiver demodulator input at the base station node at time t, expressed as:
Figure BDA0001258582960000106
considering that the formula (17) is still difficult to calculate, the above formula is expanded again by using taylor series, and the first term in the expansion formula is taken as:
Figure BDA0001258582960000111
substituting equation (15) into the above equation, the following observations were made: under the condition that the position of the unmanned aerial vehicle is given at the moment t-delta t, the input average signal-to-noise ratio of a receiver demodulator of a base station node of the relay communication system of the unmanned aerial vehicle at the moment t is only determined by the course angle of the unmanned aerial vehicle at the moment ttIn order to maximize the link capacity of a relay communication system of the unmanned aerial vehicle at the time t, optimizing the course angle of the unmanned aerial vehicle based on a traversal capacity maximization criterion, wherein the course angle of the optimized unmanned aerial vehicle is expressed as:
Figure BDA0001258582960000112
further consider log in addition2(. to) is a monotonically increasing function, and the problem of optimizing the heading angle of the drone is finally expressed as
Figure BDA0001258582960000113
Wherein the content of the first and second substances,
Figure BDA0001258582960000114
representing the optimal course angle of the unmanned aerial vehicle at the time t; the solution of the course angle problem of the optimized unmanned aerial vehicle is solved by a one-dimensional linear search method.
Fig. 2 shows a curve of the UAV optimal path along the movement path of the AP, where the abscissa and ordinate in fig. 2 represent the x-axis and y-axis, respectively, of a rectangular coordinate system, the solid curve represents the movement path of the AP, the dashed curve represents the optimal path of the UAV, the symbol "#" represents the initial position of the AP, the symbol "+" represents the initial position of the UAV, and the symbol "□" represents the fixed position of the BS. The comparison of the curves in the figure shows that: 1) when the AP moves, the UAV enables the UAV to fly along the change of the AP path by adjusting the course angle of the UAV; 2) when the UAV flies following the AP movement, the trajectory of the UAV appears circular for the following reasons: since the flight speed of the UAV is greater than the moving speed of the AP and UAV flight is limited by the maximum heading angle, the UAV must fly in a circle-around manner at certain times in order to ensure that the performance of the UAV relay communication system is optimal.
FIG. 3 shows the effect of maximum heading angle on the UAV flight path (10 and 15 for maximum heading angle, respectively), where marked as the dashed curve is the UAV best flight path at 15 for maximum heading angle, marked as the solid curve is the UAV best flight path at 10 for maximum heading angle, marked as "Δ" represents the path of movement of the AP, marked as "diamond" represents the initial position of the AP, marked as "+" represents the initial position of the UAV, and marked as "□" represents the fixed position of the BS. The comparison of the curves in the figure shows that: when the maximum course angle value is small, the radius of the unmanned aerial vehicle flying around the circle is large; when the maximum course angle value is large, the radius of the unmanned aerial vehicle flying around the circle is small. The reasons why the above phenomena occur are: when the flight speed of the unmanned aerial vehicle is given, the increase of the maximum course angle means that the range of the optimal course angle which can be selected by the unmanned aerial vehicle is increased, so that the radius of the unmanned aerial vehicle flying around the circle is reduced.
Fig. 4 and 5 respectively show the interruption probability and the traversal capacity of the unmanned aerial vehicle relay communication system as time-varying curves. Fig. 4 and 5 include four curves: the curve marked as a solid line represents an interrupt probability performance curve of the unmanned aerial vehicle relay communication system obtained by theoretical analysis of a single-transmitter single-receiver method, the curve marked as a dotted curve represents the interrupt probability performance curve of the unmanned aerial vehicle relay communication system obtained by theoretical analysis of a space-time block coding method, the curve marked as "o" represents the interrupt probability performance curve obtained by Monte Carlo simulation when the single-transmitter single-receiver method is adopted, and the curve marked as "it" is the interrupt probability performance curve obtained by Monte Carlo simulation when the space-time block coding method is adopted. The comparison of the curves shows that: 1) the curve obtained by theoretical calculation is completely consistent with the curve obtained by Monte Carlo simulation, and the correctness of the flight path planning method proposed by the thesis is shown; 2) the scheme of space-time block coding unmanned aerial vehicle relay communication proposed by the thesis is significantly superior to the scheme of single-transmitting single-receiving unmanned aerial vehicle relay communication system, and the effectiveness of the method proposed by the thesis is shown.
Fig. 6 and 7 show the effect of the maximum heading angle on the UAV relay communication system outage probability and traversal capacity performance (maximum heading angles of 10 ° and 15 °, respectively). The comparison of the curves shows that: 1) under the condition of different maximum course angles, the space-time block coding unmanned aerial vehicle relay communication scheme is still superior to the single-transmitting single-receiving unmanned aerial vehicle relay communication scheme; 2) the maximum course angle of the UAV has little influence on the interruption probability and the channel traversal capacity of the UAV relay communication system.
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Claims (5)

1. a space-time block coding unmanned aerial vehicle relay communication track planning method is characterized by comprising the following steps:
1) the model for establishing the unmanned aerial vehicle relay communication system of the space-time block coding comprises the following steps:
(1) at time t, at the mobile access node, a certain power P1Transmitting signals through two transmitting antennas in a space-time block coding mode in two continuous time slots;
(2) the unmanned aerial vehicle receives signals from the mobile access node in a first time slot and a second time slot respectively, and then the signals are transmitted with a certain power P2Adopting an amplification forwarding mode to forward the received signal transmitted by the movable access node;
(3) receiving signals transmitted by the unmanned aerial vehicle at a third time slot and a fourth time slot respectively at a base station node, accurately obtaining fading coefficients of all channels by a receiver of the base station node through channel estimation, and performing related combination processing on the signals received by the two time slots by adopting a maximum ratio combination method; the method comprises the following steps:
a) in the third time slot, the signals transmitted by the drone and received by the two receiving antennas of the base station node are respectively represented as:
Figure FDA0002504982060000011
in the fourth time slot, the signals received by the two receiving antennas of the base station node and transmitted by the drone are respectively represented as:
Figure FDA0002504982060000012
in the formula, s1A symbol is sent by a1 st transmitting antenna (A1) in the 1 st time slot movable access node; s2A2 nd transmitting antenna (A2) in the movable access node representing the 1 st time slot transmits symbols;
Figure FDA0002504982060000013
transmitting a symbol representing a1 st transmitting antenna (a1) in a2 nd time slot mobile access node;
Figure FDA0002504982060000014
transmitting symbols representing the 2 nd transmitting antenna in the 2 nd time slot movable access node, wherein the symbol represents complex conjugate operation; r is1 1The unmanned aerial vehicle receiving antenna receives a signal transmitted from the mobile access node in the 1 st time slot;
Figure FDA0002504982060000015
receiving a signal transmitted from the mobile access node at a2 nd time slot by the receiving antenna of the unmanned aerial vehicle; g represents a gain factor;
Figure FDA0002504982060000016
the 1 st receiving antenna (B1) of the base station node representing the reception of the signal transmitted from the drone in the third time slot;
Figure FDA0002504982060000017
A2 nd receiving antenna (B2) representing the base station node receiving the signal transmitted from the drone in a third time slot;
Figure FDA0002504982060000018
the 1 st receiving antenna of the base station node receives the signal transmitted by the unmanned aerial vehicle in the fourth time slot;
Figure FDA0002504982060000019
the 2 nd receiving antenna of the base station node receives the signal transmitted by the unmanned aerial vehicle in the fourth time slot; p2Representing the drone transmit signal power;
Figure FDA00025049820600000110
represents that the mean value of the 1 st receiving antenna of the base station node in the third time slot is 0 and the variance is
Figure FDA00025049820600000111
Complex white gaussian noise of (a);
Figure FDA00025049820600000112
the mean value of the received signal of the 2 nd receiving antenna of the base station node in the third time slot is 0, and the variance is
Figure FDA0002504982060000021
Complex white gaussian noise of (a);
Figure FDA0002504982060000022
represents that the mean value received by the 1 st receiving antenna of the base station node in the fourth time slot is 0 and the variance is
Figure FDA0002504982060000023
Complex white gaussian noise of (a);
Figure FDA0002504982060000024
represents that the mean value received by the 2 nd receiving antenna of the base station node in the fourth time slot is 0 and the variance is
Figure FDA0002504982060000025
Complex white gaussian noise of (a);
Figure FDA0002504982060000026
representing the channel fading coefficient from the 1 st transmitting antenna of the unmanned aerial vehicle to the 1 st receiving antenna of the base station node;
Figure FDA0002504982060000027
representing the channel fading coefficient from the 1 st transmitting antenna of the unmanned aerial vehicle to the 2 nd receiving antenna of the base station node, wherein the channel fading coefficient is modeled as:
Figure FDA0002504982060000028
wherein n is 1, 2; m is 1;
Figure FDA0002504982060000029
the small-scale fading coefficient represents a channel from the mth transmitting antenna of the unmanned aerial vehicle to the nth receiving antenna of the base station node, and the small-scale fading coefficient is modeled into a complex Gaussian random variable with the mean value of 0 and the variance of 1; dUBRepresent unmanned aerial vehicle to the distance of base station node, for convenient simplification, introduced the following parameter in the above formula:
Figure FDA00025049820600000210
Figure FDA00025049820600000211
b) the receiver of the base station node accurately obtains the fading coefficients of all channels through channel estimation:
c) the base station node adopts a maximum ratio combining method to carry out relevant combining processing on signals received by two time slots:
the receiver of the base station node performs correlation combination processing on the signals received by the two time slots of the base station node according to the following formula:
Figure FDA00025049820600000212
will be provided with
Figure FDA00025049820600000213
And
Figure FDA00025049820600000214
respectively substituting into the formula to obtain after simplification:
Figure FDA00025049820600000215
in the formula (I), the compound is shown in the specification,
Figure FDA00025049820600000216
2) the method for establishing the flight path planning model of the unmanned aerial vehicle relay communication system according to the traversal capacity maximization criterion comprises the following steps:
(1) solving the traversal capacity of the relay communication system of the unmanned aerial vehicle at the time t; the method comprises the following steps:
the traversal capacity of the relay communication system of the unmanned aerial vehicle at the time t is represented as follows:
Figure FDA00025049820600000217
wherein r isout,tThe instantaneous snr of the receiver demodulator input representing the base station node at time t is specifically:
Figure FDA00025049820600000218
wherein the content of the first and second substances,
Figure FDA0002504982060000031
||·||Frepresents the Frobenius norm;
Figure FDA0002504982060000032
Figure FDA0002504982060000033
dAUα represents the path loss factor;
Figure FDA0002504982060000034
representing the variance of complex white Gaussian noise received by the receiving antenna of the unmanned aerial vehicle at the time t;
Figure FDA0002504982060000035
representing the variance of complex white Gaussian noise received by a receiving antenna of the base station node;
observed from the above formula: distance d from mobile access node to unmanned aerial vehicle of instantaneous signal-to-noise ratio input by receiver demodulator of base station nodeAUDistance d from unmanned aerial vehicle to base station nodeUBSmall-scale attenuation of mobile access node to unmanned aerial vehicle link
Figure FDA0002504982060000036
Jointly determining the small-scale attenuation from the unmanned aerial vehicle to the base station node;
(2) respectively calculating the distance from the movable access node to the unmanned aerial vehicle and the distance from the unmanned aerial vehicle to the base station node;
(3) establishing a flight path planning model of the unmanned aerial vehicle relay communication system; the method comprises the following steps:
the traversal capacity formula of the unmanned aerial vehicle relay communication system at the time t is represented as follows:
Figure FDA0002504982060000037
carrying out Taylor series expansion on a traversal capacity formula of the relay communication system of the unmanned aerial vehicle at the time t, and taking a first term of the expansion as follows:
Figure FDA0002504982060000038
wherein, E { rout,tRepresents the average signal-to-noise ratio of the receiver demodulator input at the base station node at time t, expressed as:
Figure FDA0002504982060000039
wherein the content of the first and second substances,
Figure FDA00025049820600000310
dAU,trepresenting the distance from the movable access node to the unmanned aerial vehicle at the moment t; dUB,tRepresenting the distance from the unmanned aerial vehicle to the base station node at the time t;
considering that the formula (17) is still difficult to calculate, the above formula is expanded again by using taylor series, and the first term in the expansion formula is taken as:
Figure FDA00025049820600000311
will dAU,tAnd dUB,tSubstituting the above formula, the following conclusions were observed: under the condition that the position of the unmanned aerial vehicle is given at the moment t-delta t, the input average signal-to-noise ratio of a receiver demodulator of a base station node of the relay communication system of the unmanned aerial vehicle at the moment t is only determined by the course angle of the unmanned aerial vehicle at the moment ttIn order to maximize the link capacity of the relay communication system of the unmanned aerial vehicle at the time t, the course angle of the unmanned aerial vehicle is optimized based on the traversal capacity maximization criterion, and the optimization problem of optimizing the course angle of the unmanned aerial vehicle is expressed as follows:
Figure FDA0002504982060000041
further consider log in addition2(. 2) is a monotone increasing function, and the optimization is noneThe problem of the heading angle of the human machine is finally expressed as:
Figure FDA0002504982060000042
wherein the content of the first and second substances,
Figure FDA0002504982060000043
representing the optimal course angle of the unmanned aerial vehicle at the time t; the solution to the problem of optimizing the course angle of the unmanned aerial vehicle is solved by a one-dimensional linear search method.
2. A space-time block coded unmanned aerial vehicle relay communication track planning method according to claim 1, wherein in step 1), the signal is transmitted by two transmitting antennas in a space-time block coded manner in step (1), and in a first time slot, a first transmitting antenna (a1) in the mobile access node sends a symbol s1The second transmitting antenna (A2) transmits a symbol s2Second time slot, 1 st transmitting antenna sends symbol
Figure FDA0002504982060000044
2 nd transmitting antenna transmitting symbol
Figure FDA0002504982060000045
Wherein represents complex conjugate operation, and the transmitted symbol satisfies E { | si|21, wherein i is 1, 2; e is the desired operation.
3. A space-time block coded unmanned aerial vehicle relay communication track planning method according to claim 1, wherein the unmanned aerial vehicle in step 1) (2) receives signals from the mobile access node in the first time slot and the second time slot respectively as follows:
Figure FDA0002504982060000046
wherein the content of the first and second substances,
Figure FDA0002504982060000047
the mean value of the receiving antenna of the unmanned aerial vehicle at the 1 st time slot is 0, and the variance is
Figure FDA0002504982060000048
The complex white gaussian noise of (1) is,
Figure FDA0002504982060000049
represents that the receiving antenna receives the mean value of 0 and the variance of
Figure FDA00025049820600000410
The complex white Gaussian noise is independent in the statistics of noise signals in different time slots;
Figure FDA00025049820600000411
representing the channel fading coefficients from the 1 st transmit antenna of the mobile access node to the 1 st receive antenna of the drone,
Figure FDA00025049820600000412
representing channel fading coefficients of a2 nd transmitting antenna of the mobile access node to a1 st receiving antenna of the drone, the channel fading coefficients being modeled as:
Figure FDA00025049820600000413
wherein i is 1; j is 1, 2;
Figure FDA00025049820600000414
representing the small-scale fading coefficient of the channel from the jth transmitting antenna of the movable access node to the ith receiving antenna of the unmanned aerial vehicle, wherein the small-scale fading coefficient is modeled into a complex Gaussian random variable with the mean value of 0 and the variance of 1, α represents a path loss factor, dAURepresenting the distance of the mobile access node to the drone.
4. A space-time block coded unmanned aerial vehicle relay communication track planning method according to claim 1, wherein step 1) is performed at a certain power P in step (2)2The signal transmitted by the mobile access node and forwarded by adopting the amplification forwarding mode is as follows: after receiving the signal sent by the movable access node, the unmanned aerial vehicle multiplies the received signal by a gain factor G in an amplification forwarding mode:
Figure FDA0002504982060000051
5. a space-time block coded unmanned aerial vehicle relay communication flight path planning method according to claim 1, wherein the step (2) in the step 2) includes:
establishing a three-dimensional rectangular coordinate for accurately giving the distance from the movable access node to the unmanned aerial vehicle and the distance from the unmanned aerial vehicle to the base station node, and assuming that the position coordinate of the fixed base station node is (x)B,yB0), the position coordinate of the movable access node at the time t is (x)A,t,yA,t0), the position coordinates of the drone are (x)t,yt,ht) And the distances between the unmanned aerial vehicle at the time t and the movable access node and the base station node are calculated by using the position coordinates of each node and are respectively as follows:
Figure FDA0002504982060000052
further assuming that the flying height of the unmanned aerial vehicle is always kept at h and the unmanned aerial vehicle flies at a constant speed v, the position of the unmanned aerial vehicle at the time t is determined according to the position information of the unmanned aerial vehicle at the time t-delta t, and by using the following equation:
Figure FDA0002504982060000053
updating to obtain:
Figure FDA0002504982060000054
wherein the content of the first and second substances,trepresenting the course angle of the unmanned plane at the moment t, and meeting the requirementt-Δt-maxtt-Δt+maxWhereinmaxRepresenting a maximum heading angle of the drone; Δ t represents the time interval of the unmanned plane position update;
the above formula shows that: after the position of the unmanned aerial vehicle is given at the time t-delta t, the distance between the movable access node and the unmanned aerial vehicle at the time t and the distance between the unmanned aerial vehicle and the base station node are only determined by the course angle of the unmanned aerial vehicle at the time tt
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