CN111541473B - Array antenna unmanned aerial vehicle base station-oriented track planning and power distribution method - Google Patents

Array antenna unmanned aerial vehicle base station-oriented track planning and power distribution method Download PDF

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CN111541473B
CN111541473B CN202010357428.7A CN202010357428A CN111541473B CN 111541473 B CN111541473 B CN 111541473B CN 202010357428 A CN202010357428 A CN 202010357428A CN 111541473 B CN111541473 B CN 111541473B
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aerial vehicle
unmanned aerial
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power distribution
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CN111541473A (en
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蔡曙
张卫东
张军
郭永安
陈龙
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Nanjing University of Posts and Telecommunications
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/14—Relay systems
    • H04B7/15—Active relay systems
    • H04B7/185—Space-based or airborne stations; Stations for satellite systems
    • H04B7/18502—Airborne stations
    • H04B7/18504—Aircraft used as relay or high altitude atmospheric platform
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • G05D1/10—Simultaneous control of position or course in three dimensions
    • G05D1/101—Simultaneous control of position or course in three dimensions specially adapted for aircraft
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B17/00—Monitoring; Testing
    • H04B17/30—Monitoring; Testing of propagation channels
    • H04B17/391—Modelling the propagation channel
    • H04B17/3911—Fading models or fading generators
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/0413—MIMO systems
    • H04B7/0456—Selection of precoding matrices or codebooks, e.g. using matrices antenna weighting
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
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    • H04W16/18—Network planning tools
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W52/00—Power management, e.g. TPC [Transmission Power Control], power saving or power classes
    • H04W52/04—TPC
    • H04W52/06—TPC algorithms
    • H04W52/14—Separate analysis of uplink or downlink
    • H04W52/143—Downlink power control
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W52/00—Power management, e.g. TPC [Transmission Power Control], power saving or power classes
    • H04W52/04—TPC
    • H04W52/18—TPC being performed according to specific parameters
    • H04W52/26—TPC being performed according to specific parameters using transmission rate or quality of service QoS [Quality of Service]
    • H04W52/267—TPC being performed according to specific parameters using transmission rate or quality of service QoS [Quality of Service] taking into account the information rate

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Abstract

The invention discloses a flight path planning and power distribution method for an array antenna unmanned aerial vehicle base station, which is suitable for scenes such as unmanned aerial vehicle emergency communication and the like. The method comprises the following steps: establishing a channel fading model by utilizing an air-ground wireless channel model of the array antenna according to the geographical positions of the unmanned aerial vehicle and the user; establishing a user reachable rate model of the array antenna unmanned aerial vehicle base station communication system based on a precoding technology adopted by an array antenna transmitting end; based on a user reachable rate model, under the condition that the flight state and the transmitting power of the unmanned aerial vehicle are limited, a joint optimization problem of flight path planning and user power distribution is established by taking the maximum system transmission rate as a target; and transforming and solving the optimization problem by using a block coordinate rotation descent and continuous convex approximation method to obtain an unmanned aerial vehicle path planning and power distribution scheme based on the precoding technology. The method has important guiding significance for the deployment of the array antenna unmanned aerial vehicle base station communication system.

Description

Array antenna unmanned aerial vehicle base station-oriented track planning and power distribution method
Technical Field
The invention belongs to the technical field of wireless communication, and particularly relates to a flight path planning and power distribution method for an array antenna unmanned aerial vehicle base station.
Background
Unmanned aerial vehicle technology has developed rapidly in recent years. Because unmanned aerial vehicle has characteristics such as high flexibility and high controllability, unmanned aerial vehicle assisted wireless communication system has extensive application prospect, especially faces all kinds of emergency communication demands. For example, in a large sudden disaster, or a large activity, the ground communication facilities may not provide communication assurance. At the moment, the unmanned aerial vehicle is used as an aerial base station, and a wireless communication network can be quickly and flexibly established, so that information transmission is guaranteed.
At present, a great deal of research is carried out at home and abroad aiming at the problem of auxiliary wireless communication of the unmanned aerial vehicle, but the existing research mainly considers the single-antenna unmanned aerial vehicle and rarely relates to an array antenna technology. Very little research has been directed at array antenna drones, involving only the deployment of the drone's location, without considering its trajectory planning. Considering that the drone provides communication services during the flight, research on the flight path planning of the drone is necessary. As a high-altitude base station, since the total energy carried by the drone is fixed, optimization of power resources is also particularly important. Therefore, the method has important significance for planning the flight path and the communication resources of the unmanned aerial vehicle.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the blank of the prior art, the invention provides a flight path planning and power distribution method facing to an array antenna unmanned aerial vehicle base station, and provides high-reliability technical guidance for the deployment of a communication system of the array antenna unmanned aerial vehicle base station.
The technical scheme is as follows: a flight path planning and power distribution method facing an array antenna unmanned aerial vehicle base station is disclosed, wherein the unmanned aerial vehicle base station is loaded with a group of array antennas to realize space diversity multiplexing, and precoding is carried out on a Transmission symbol by adopting Maximum Ratio Transmission (MRT) and Zero Forcing (ZF) precoding technologies respectively, and the flight path planning and power distribution method maximizes a system Transmission rate by adjusting flight path and power distribution of the unmanned aerial vehicle under the condition that the flight state and flight time of the unmanned aerial vehicle are limited, so that an optimal flight path and power distribution scheme is obtained, and the method specifically comprises the following steps:
(1) establishing a channel fading model by utilizing an air-ground wireless channel model of the array antenna according to the geographical positions of the unmanned aerial vehicle and the ground user;
(2) establishing a user reachable rate model of the array antenna unmanned aerial vehicle base station communication system based on a precoding technology adopted by an array antenna transmitting end;
(3) based on a user reachable rate model, under the condition that the flight state and the transmitting power of the unmanned aerial vehicle are limited, a joint optimization problem of flight path planning and user power distribution is established by taking the maximum system transmission rate as a target;
(4) and transforming and solving the optimization problem by using a block coordinate rotation descent and continuous convex approximation method to obtain an unmanned aerial vehicle path planning and power distribution scheme based on the precoding technology.
When the precoding technology adopted by the array antenna transmitting end is the MRT precoding technology, the step 2 establishes a user reachable rate model of the array antenna unmanned aerial vehicle base station communication system based on the MRT precoding technology, and the step 3 establishes a flight path planning and power distribution joint optimization problem (1) based on the MRT precoding technology; when the precoding technology adopted by the array antenna transmitting end is ZF precoding technology, the step 2 establishes a user reachable rate model of the array antenna unmanned aerial vehicle base station communication system based on the ZF precoding technology, and the step 3 establishes a flight path planning and power distribution joint optimization problem (2) based on the ZF precoding technology.
Assuming that the flight altitude of the unmanned aerial vehicle is large enough, the channel between the unmanned aerial vehicle and the user is a Line of Sight (LOS) channel; then in time slot m, the channel fading model between the drone and user i is:
Figure BDA0002473968740000021
wherein d isi[m]Is the distance between the drone and the ith user in the mth time slot; beta is a0Representing the power gain when the distance between the unmanned aerial vehicle and the user is 1 m; b (theta)i[m]) Representing a steering vector; when the array is a uniform linear array,
Figure BDA0002473968740000022
n is the number of antennas, θi[m]Representing the included angle between the array normal vector and the user direction; for an arbitrary array, the steering vector is represented as
Figure BDA0002473968740000023
τiAnd receiving the time delay of the signal relative to the original point signal for the ith array element.
Based on MRT precoding technology, a user reachable rate model of the array antenna unmanned aerial vehicle base station communication system is established as follows:
Figure BDA0002473968740000024
wherein,
Figure BDA0002473968740000025
representing the achievable rate of user i in time slot m; n represents the number of array elements in the array antenna; p is a radical ofi[m]The power distributed to the user I by the unmanned aerial vehicle in the time slot m is represented, and I represents the total number of the users; sigma2Is the received noise power of the terrestrial user.
Based on the user reachable rate model, under the condition that the flight state and the transmitting power of the unmanned aerial vehicle are limited, the flight path planning and power distribution joint optimization problem (1) is established by taking the maximum system transmission rate as a target as follows:
Figure BDA0002473968740000031
Figure BDA0002473968740000032
Figure BDA0002473968740000033
q0＝q[0],qF＝q[M], (1.d)
Figure BDA0002473968740000034
wherein
Figure BDA0002473968740000035
"max" represents a maximization operation; "s.t." means a constraint; m represents the total time slot number; (1.b) and (1.c) represent the transmit power constraint per time slot, P represents the drone maximum transmit power; (1.d) and (1.e) are unmanned aerial vehicle flight state constraints, q0And q isFRespectively representing the starting and ending positions of the drone, qm]The position of the unmanned plane in the mth time slot is shown, and delta represents the size of the time slot; vmaxRepresenting the maximum flight speed of the drone.
Based on the ZF precoding technology, a user reachable rate model of the array antenna unmanned aerial vehicle base station communication system is established as follows:
Figure BDA0002473968740000036
wherein, γi[m]＝1/[(Hi[m]HH[m])-1]ii，H[m]＝[bT(θi[m]),...,bT(θI[m])]TWhere I denotes the total number of users, σ2Is the received noise power of the terrestrial user.
Based on the user reachable rate model, under the condition that the flight state and the transmitting power of the unmanned aerial vehicle are limited, the flight path planning and power distribution joint optimization problem (2) is established by taking the maximum system transmission rate as a target as follows:
Figure BDA0002473968740000037
Figure BDA0002473968740000038
Figure BDA0002473968740000039
q0＝q[0],qF＝q[M], (2.d)
Figure BDA0002473968740000041
wherein,
Figure BDA0002473968740000042
"max" represents a maximization operation; "s.t." means a constraint; m represents the total time slot number; p represents the drone maximum transmit power, (2.b) and (2.c) are transmit power constraints; (2.d) and (2.e) represent unmanned aerial vehicle flight state constraints, q0And q isFRespectively representing the starting and ending positions of the drone, qm]The position of the unmanned plane in the mth time slot is shown, and delta represents the size of the time slot; vmaxRepresenting the maximum flight speed of the drone.
Has the advantages that: the invention provides a method for planning a flight path and distributing power for an array antenna unmanned aerial vehicle base station for the first time, a user reachable rate model is established according to a pre-coding technology adopted by an antenna transmitting end, and the flight path and the user power distribution of the unmanned aerial vehicle are adjusted to optimize the system transmission rate under the condition that the flight state and the flight time of the unmanned aerial vehicle are limited. The invention can provide high-reliability technical guidance for the deployment of the array antenna unmanned aerial vehicle base station communication system.
Drawings
Fig. 1 is a schematic diagram of a wireless communication system based on an array antenna unmanned aerial vehicle base station in the invention;
FIG. 2 is a flow chart of a method for planning a flight path and distributing power for an array antenna-oriented unmanned aerial vehicle base station according to the present invention;
FIG. 3 is a diagram of the trend of the optimal system speed of the invention along with the change of the flying height of the unmanned aerial vehicle;
fig. 4 is a graph of the variation trend of λ corresponding to ZF precoding with time slot when the flying height H of the drone is 100m and H is 400m in the present invention;
fig. 5 is a graph of the system and velocity of the present invention as a function of the number of drone antennas, time of flight and maximum transmit power.
Detailed Description
The technical scheme of the invention is further explained by combining the attached drawings.
As shown in fig. 1, this example provides a schematic diagram of a wireless communication system based on an array antenna drone base station, in which a communication system with a single drone as an aerial base station is considered, and the drone provides downlink transmission service for a plurality of users on the ground while flying from a starting position to a predetermined end position. The base station of the unmanned aerial vehicle is provided with a group of array antennas to realize space diversity multiplexing, and the transmission symbols are precoded by adopting Maximum Ratio Transmission (MRT) and Zero Forcing (ZF) precoding technologies respectively. For convenience of description, it is assumed that the unmanned aerial vehicle flies from a starting point to an end point along a straight line, that is, the direction of the array antenna is always the same as the flight direction, and under the condition that the flight state and the flight time of the unmanned aerial vehicle are limited, the system transmission rate is maximized by adjusting the flight path and the user power distribution of the unmanned aerial vehicle. Referring to fig. 2, the specific steps are as follows:
step 1, establishing a channel fading model according to the geographical positions of an unmanned aerial vehicle and a user and an air-ground wireless channel model based on an array antenna:
Figure BDA0002473968740000051
wherein,
Figure BDA0002473968740000052
indicating the distance between the unmanned plane and the ith user in the mth time slot; the horizontal coordinate of the unmanned plane at the mth time slot is q [ m ]]＝[x[m],0]THeight H; the height of user i is zero and the horizontal coordinate is
Figure BDA0002473968740000053
β0Representing the power gain when the distance between the unmanned aerial vehicle and the user is 1 m; b (theta)i[m]) Representing a steering vector; when the array is a uniform linear array,
Figure BDA0002473968740000054
n is the number of antennas, θi[m]Representing the included angle between the array normal vector and the user direction; for an arbitrary array, the steering vector is represented as
Figure BDA0002473968740000055
τiAnd receiving the time delay of the signal relative to the original point signal for the ith array element.
Assuming that the channel information is known, the signal received by the ith user in the mth slot can be expressed as:
Figure BDA0002473968740000056
wherein, (.)HDenotes a conjugate transpose operation, niIs that the mean is zero and the variance is sigma2The white gaussian noise of (a) is,
Figure BDA0002473968740000057
indicating the precoded signal transmitted at the m-th slot.
In step 2, based on MRT precoding technique, in the mth slot, the transmitted signal s [ m ] is specifically represented as:
Figure BDA0002473968740000058
wherein,
Figure BDA0002473968740000059
and pi[m]Respectively represents the precoding vector and the transmission power of the array antenna relative to the user i in the mth time slot, si[m]Is user data and satisfies | si[m]1. Substituting expression (3) into expression (2) yields:
Figure BDA0002473968740000061
wherein, aik[m]＝bH(θi[m])b(θk[m]),i≠k,
Figure BDA0002473968740000062
Therefore, in the mth slot, the received Signal-to-Noise ratio (SINR) of user i can be expressed as:
Figure BDA0002473968740000063
therefore, the user reachable rate model of the array antenna unmanned aerial vehicle base station communication system based on the MRT precoding technology is as follows:
Figure BDA0002473968740000064
in step 3, the problem of flight path planning and power joint optimization based on the MRT precoding technology is as follows:
Figure BDA0002473968740000065
Figure BDA0002473968740000066
Figure BDA0002473968740000067
q0＝q[0],qF＝q[M], (7.d)
Figure BDA0002473968740000068
wherein,
Figure BDA0002473968740000069
"max" represents a maximization operation; "s.t." means a constraint; i represents the total number of users; m represents the total time slot number; (7.b) and (7.c) denote a transmit power constraint for each slot, P denotesMaximum transmitting power of the unmanned aerial vehicle; (7.d) and (7.e) are unmanned aerial vehicle flight state constraints, q0And q isFRespectively representing the starting and ending positions of the drone, qm]The position of the unmanned plane in the mth time slot is shown, and delta represents the size of the time slot; vmaxRepresenting the maximum flight speed of the drone.
In step 4, for the optimization problem (7) based on MRT precoding in step 3, the solving process is as follows:
aiming at the problem, the original problem is decomposed into two sub-problems by adopting a block coordinate rotation descending method to solve.
1) Fixed track optimized power: when the track is given, the target problem (7) is simplified into a power distribution sub-problem:
Figure BDA0002473968740000071
s.t.(7.b),(7.c), (8.b)
the objective function in problem (8) is still non-convex with respect to power variations, according to the user achievable rate definitions in equations (5) and (6). Therefore, the present invention first derives
Figure BDA0002473968740000072
And then continuously maximizing the lower bound by using an iterative method, thereby optimizing the original problem. The optimization concept is called Sequential Convex Approximation (SCA) [ Razaviyayn M. ] 'sequential convex approximation: analysis and applications', Ph.D. discovery, University of Minnesota,2014]. Following derivation of the function
Figure BDA0002473968740000073
The lower concave boundary of (2) is obtained from the formula (6)
Figure BDA0002473968740000074
Wherein,
Figure BDA0002473968740000075
and
Figure BDA0002473968740000076
are all concave functions with respect to variable transmit power. By definition, the first order Taylor expansion of the concave function at any point is its global upper limit. In accordance with this characteristic, the liquid crystal display device,
Figure BDA0002473968740000077
at the transmission power
Figure BDA0002473968740000078
The global upper bound of (c) is:
Figure BDA0002473968740000081
where μ represents the number of iterations. Due to the fact that
Figure BDA0002473968740000082
For any given
Figure BDA0002473968740000083
Is provided with
Figure BDA0002473968740000084
The SCA iteration subproblem of the problem (8) is the convex-down optimization problem:
Figure BDA0002473968740000085
s.t.(7.b),(7.c), (11.b)
solving the problem by using an optimization algorithm such as an interior point method and the like, and expressing the optimal solution as
Figure BDA0002473968740000086
And as an initial value for the (μ +1) th iteration. When the absolute value of the difference between the target functions of the two previous iterations is less than
Figure BDA0002473968740000087
Then the iteration is terminated and the resulting transmit power is output.
2) Fixed power optimization track: given the transmission power allocation of each time slot unmanned aerial vehicle, the following path planning sub-problems are obtained:
Figure BDA0002473968740000088
s.t.(7.d),(7.e), (12.b)
wherein,
Figure BDA0002473968740000089
is a non-convex function of the variable q, so the problem (12) is non-convex. In order to solve the problem, the invention adopts an SCA thought, firstly deduces the global concave lower bound of the objective function, and then continuously maximizes the lower bound by using an iterative method, thereby optimizing the original problem. In that
Figure BDA00024739687400000810
In, | aik[m]|2Is q [ m ]]Resulting in a problem that is difficult to optimize. Therefore, at | aik[m]|2Using the output of the previous iteration
Figure BDA00024739687400000811
To approximate q [ m ]]Thus will | aik[m]|2Becomes constant to simplify the problem. To make it possible to
Figure BDA0002473968740000091
Is true, introduce a regularization term
Figure BDA0002473968740000092
Where alpha is an adjustable parameter. Optimal q [ m ] in problem (12) as α increases continuously]Will be continuously close to
Figure BDA0002473968740000093
In the epsilon iteration, order
Figure BDA0002473968740000094
Figure BDA0002473968740000095
And is in Qε[m]Is aligned with
Figure BDA0002473968740000096
First order taylor expansion is performed to obtain its concave lower bound:
Figure BDA0002473968740000097
wherein,
Ei[m]＝β0N2pi[m], (14)
Figure BDA0002473968740000098
thus resulting in an SCA iteration sub-problem for the problem (12):
Figure BDA0002473968740000099
s.t. (7.d), (7.e), (16.b) the above problem (16) is a convex problem that can be solved quickly by an optimization method such as the interior point method, and the optimal solution is expressed as
Figure BDA00024739687400000910
As an initial point for the next iteration. And when the iteration converges, outputting the unmanned aerial vehicle track plan.
The solution algorithm of the flight path planning and power joint optimization problem (7) based on the MRT precoding technology is summarized as follows:
algorithm A:
1: initializing the unmanned aerial vehicle track q according to the constraint conditions in the problemk[m]And power
Figure BDA00024739687400000911
The iteration number k is 0;
2: fixing the unmanned aerial vehicle track, and iteratively optimizing the transmitting power by using continuous convex approximation until convergence;
3: fixing the inter-user power distribution obtained in step 2, iteratively optimizing the unmanned aerial vehicle track by using a continuous convex approximation algorithm,
until convergence;
4: and (5) iteratively executing 1 and 2 based on the block coordinate rotation descent method until convergence.
In step 5, when ZF precoding is employed, there is no interference between users. According to equation (2), in the mth slot, the received signal of user i is:
Figure BDA0002473968740000101
wherein,
Figure BDA0002473968740000102
Figure BDA0002473968740000103
Figure BDA0002473968740000104
wherein p isi[m]The transmission power of the unmanned plane to the user i in the time slot m is represented, and the conditions are met
Figure BDA0002473968740000105
P is the maximum transmit power of the drone,
Figure BDA0002473968740000106
is the precoding vector for user i. Defining a channel state matrix as
Figure BDA0002473968740000107
Then when ZF pre-coding is used,
Figure BDA0002473968740000108
wherein,
Figure BDA0002473968740000109
is a matrix
Figure BDA00024739687400001010
The (c) th column of (a),
V[m]＝HH[m](H[m]HH[m])-1 (20)
therefore, the user reachable rate model of the array antenna unmanned aerial vehicle base station communication system based on the ZF precoding technology is as follows:
Figure BDA00024739687400001011
wherein λ isi[m]＝τi[m]γi[m]/σ2，γi[m]＝1/[(Hi[m]HH[m])-1]ii。
In step 6, the problem of flight path planning and power distribution joint optimization based on the ZF precoding technology is as follows:
Figure BDA00024739687400001012
Figure BDA00024739687400001013
Figure BDA00024739687400001014
q0＝q[0],qF＝q[M], (22.d)
Figure BDA0002473968740000111
wherein (22.b) and (22.c) are transmit power constraints; (22.d) and (22.e) represent drone flight state constraints.
In step 7, because the optimization problem (22) in step 6 is non-convex, the invention adopts the idea of block coordinate rotation reduction and continuous convex approximation to solve the problem, and the specific process is as follows:
based on the thought of block coordinate rotation descent, the unmanned aerial vehicle track q [ m ] is given first]Update power pi[m](ii) a The power allocation for a given user then updates the track. The specific process is as follows:
1) fixed track optimized Power when the drone track is given, the problem (22) can be written as the following sub-problem:
Figure BDA0002473968740000112
s.t.(22.b),(22.c), (23.b)
the problem can be solved by a Convex optimization method, such as an interior point method, and the optimal power distribution can be obtained by referring to [ s.p.boyd and l.vandenberghe, convention optimization. Cambridge, u.k.: Cambridge univ.press,2004 ].
2) And when power is distributed to timing, the sub-problem of the track planning of the unmanned aerial vehicle is as follows:
Figure BDA0002473968740000113
s.t.(22.d),(22.e), (24.b)
wherein,
Figure BDA0002473968740000114
is q [ m ]]Is not a convex function of (a) a,
Figure BDA0002473968740000115
is a regularization term, and its role is the same as in the problem (18).
The problem (24) is non-convex, here solved by the SCA idea, i.e. continuously maximized by an iterative method
Figure BDA0002473968740000116
The concave lower boundary of (2) can be obtained by expanding the formula (21)
Figure BDA0002473968740000117
When the power is given, the power is supplied,
Figure BDA0002473968740000118
is a constant. Thus, for any given
Figure BDA0002473968740000119
Is provided with
Figure BDA00024739687400001110
Concave lower boundary of (2):
Figure BDA0002473968740000121
wherein,
Figure BDA0002473968740000122
Figure BDA0002473968740000123
thus, the SCA iteration sub-problem of problem (24) is
Figure BDA0002473968740000124
s.t.(22.d),(22.e), (29.b)
The problem (29) is a convex optimization problem, which can be solved by an optimization method such as an interior point method, and the optimal solution is expressed as
Figure BDA0002473968740000125
As an initial value for the next iteration. And when the SCA iteration converges, outputting the obtained optimal power distribution.
The solution algorithm for the track planning and power allocation optimization problem (22) based on ZF precoding is summarized as follows:
and algorithm B:
1: initializing the trajectory q of the drone according to constraints in the problemk[m]The iteration number k is 0;
2: fixing the flight path of the unmanned aerial vehicle, and optimizing power distribution among users by using an interior point method;
3: fixing the power distribution among the users obtained in step 2, and iteratively optimizing the flight path of the unmanned aerial vehicle by using continuous convex approximation until the algorithm is converged;
4: iterations 2 and 3 are performed down based on the block coordinate rotation until convergence.
It should be understood that the method described in the above description of steps 1 to 7 is only for the purpose of clearly and completely explaining the technical solution of the present invention, and does not limit that the method must be executed in the order of steps 1 to 7, and only a part of the steps may be executed, or some steps may be executed in parallel, or executed in the reverse order, without departing from the spirit of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Based on the detailed step description of the power distribution method for the track planning of the array antenna unmanned aerial vehicle base station, the performance of the method is verified through a simulation example. Matlab software is adopted for system simulation in the embodiment, and a CVX software package is adopted for solving the optimization problem. In the whole simulation, the unmanned aerial vehicle flies along a straight line all the time and provides data transmission service for ground users. The following simulations are not specifically described, and the relevant parameters are set as follows: the flying height H of the unmanned aerial vehicle is 150 m; the initial position and the final position are [0,0, H ] respectively]And [1500,0, H](ii) a Maximum flying speed Vmax40 m/s; the number of array elements of the linear array antenna is N-4; the horizontal coordinates of three ground users are w respectively1＝[300,0]，w2＝[800,50]And w3＝[1200,0](ii) a The total power of the unmanned aerial vehicle is P0.1W; noise power of sigma2-110 dBm; channel power gain beta relative to reference distance0-50 dBm; the total time T of flight is 50s, and it is assumed that the length of each time slot is δ is 0.1s, so the total number of time slots is M500.
Fig. 3 is a graph of the trend of optimal system and velocity as a function of flying height of the drone. As can be seen from the figure, in ZF precoding based systems, the system and rate increase first and then decrease as the elevation increases. Where the system and rate increase with height is counter intuitive. When the height of the unmanned aerial vehicle is smaller, the unmanned aerial vehicle is close to the user, so that the reachable speed of the user is higher; when the height of the unmanned aerial vehicle increases, the reachable rate is gradually reduced away from the user. However, when the height is too small, the incident angles of the short-distance user (U1) and the long-distance user (U2) are greatly different, and | b at this timeH(θ1)b(θ2) | ≈ 0; at the same time, to serve the short-range user U1, the corresponding steering vectors x and bH(θ1) Strong correlation, i.e. x ≈ bH(θ1) Thus | xb (θ)2) I ≈ 0, resulting in a small λ for distant users (as shown in fig. 4), i.e., a small achievable rate. So when the height is too low, the overall rate will drop. When the height exceeds a certain value, the signal fading is large, and the signal-to-noise ratio and the system and rate are reduced. In MRT-based precoding systems, the system and rate gradually decrease with increasing altitude, because the distance between the drone and the user increases, causing the signal attenuation to increase, and thus the system and rate to decrease.
Fig. 5 shows the relationship between the system and the rate and the flight time of the drone, the number of antennas, and the total transmission power in the MRT and ZF based precoding systems, respectively. At a certain total time, as the number of antennas increases, the system and the rate also increase; at a given number of antennas, the system and rate will increase as the total time increases. In addition, when the number of antennas, the total transmission power and the total time are the same, the system and the rate obtained by using the ZF precoding are larger than those obtained by the MRT precoding, because in the system, the main factor influencing the system performance during interference, and the ZF precoding eliminates the interference among users. The method has important guiding significance for the deployment of the array antenna unmanned aerial vehicle base station communication system.

Claims (3)

1. A flight path planning and power distribution method facing an array antenna unmanned aerial vehicle base station is characterized by comprising the following steps:
(1) according to the geographical positions of the unmanned aerial vehicle and the ground user, an air-ground wireless channel model of the array antenna is utilized to establish a channel fading model as follows:
Figure FDA0002853910350000011
wherein d isi[m]Is the distance between the drone and the ith user in the mth time slot; beta is a0Representing the power gain when the distance between the unmanned aerial vehicle and the user is 1 m; b (theta)i[m]) Representing a steering vector; when the array is a uniform linear array,
Figure FDA0002853910350000012
n is the number of antennas, θi[m]Representing the included angle between the array normal vector and the user direction; for an arbitrary array, the steering vector is represented as
Figure FDA0002853910350000013
τiThe time delay of the signal received by the ith array element relative to the original point signal;
(2) based on a precoding technology adopted by an array antenna transmitting end, a user reachable rate model of an array antenna unmanned aerial vehicle base station communication system is established, and the method specifically comprises the following steps:
when the precoding technology adopted by the array antenna transmitting end is MRT precoding technology, a user reachable rate model of the array antenna unmanned aerial vehicle base station communication system based on the MRT precoding technology is established as follows:
Figure FDA0002853910350000014
wherein,
Figure FDA0002853910350000015
representing the achievable rate of user i in time slot m; p is a radical ofi[m]The power distributed to the user I by the unmanned aerial vehicle in the time slot m is represented, and I represents the total number of the users; sigma2Is the received noise power of the user;
when the precoding technology adopted by the array antenna transmitting end is ZF precoding technology, establishing a user reachable rate model of the array antenna unmanned aerial vehicle base station communication system based on the ZF precoding technology as follows:
Figure FDA0002853910350000016
wherein, γi[m]＝1/[(Hi[m]HH[m])-1]ii，H[m]＝[bT(θi[m]),...,bT(θI[m])]T；
(3) Based on a user reachable rate model, under the condition that the flight state and the transmitting power of the unmanned aerial vehicle are limited, a joint optimization problem of flight path planning and user power distribution is established by taking the maximum system transmission rate as a target, wherein,
the flight path planning and power joint optimization problem based on the MRT precoding technology (1) is as follows:
Figure FDA0002853910350000021
Figure FDA0002853910350000022
Figure FDA0002853910350000023
q0＝q[0],qF＝q[M], (1.d)
Figure FDA0002853910350000024
wherein
Figure FDA0002853910350000025
max represents a maximization operation; s.t. represents a constraint; m represents the total time slot number; (1.b) and (1.c) represent the transmit power constraint per time slot, P represents the drone maximum transmit power; (1.d) and (1.e) are unmanned aerial vehicle flight state constraints, q0And q isFRespectively representing the starting and ending positions of the drone, qm]The position of the unmanned plane in the mth time slot is shown, and delta represents the size of the time slot; vmaxRepresenting the maximum flight speed of the unmanned aerial vehicle;
the flight path planning and power distribution joint optimization problem (2) based on the ZF precoding technology is as follows:
Figure FDA0002853910350000026
Figure FDA0002853910350000027
Figure FDA0002853910350000028
q0＝q[0],qF＝q[M], (2.d)
Figure FDA0002853910350000029
wherein,
Figure FDA00028539103500000210
max represents a maximization operation; s.t. represents a constraint; m represents the total time slot number; p represents the drone maximum transmit power, (2.b) and (2.c) are transmit power constraints; (2.d) and (2.e) represent unmanned aerial vehicle flight state constraints, q0And q isFRespectively representing the starting and ending positions of the drone, qm]The position of the unmanned plane in the mth time slot is shown, and delta represents the size of the time slot; vmaxRepresenting the maximum flight speed of the unmanned aerial vehicle;
(4) and transforming and solving the optimization problem by using a block coordinate rotation descent and continuous convex approximation method to obtain an unmanned aerial vehicle path planning and power distribution scheme based on the precoding technology.
2. The array antenna-oriented unmanned aerial vehicle base station track planning and power distribution method according to claim 1, wherein in the step 4, the problem (1) is converted and solved by using a block coordinate rotation descent and continuous convex approximation method, and the specific steps are as follows:
step 1), initializing the flight path of the unmanned aerial vehicle according to the constraint conditions in the problem (1);
step 2), fixing the flight path of the unmanned aerial vehicle, and optimizing the transmitting power by using continuous convex approximation until the algorithm is converged;
step 3), fixing power distribution among users, and iteratively optimizing the flight path of the unmanned aerial vehicle by using a continuous convex approximation algorithm until the algorithm is converged;
and 4) iteratively executing the step 2) and the step 3) based on the block coordinate rotation descent method until convergence.
3. The array antenna-oriented unmanned aerial vehicle base station track planning and power distribution method according to claim 1, wherein in the step 4, the problem (2) is converted and solved by using a block coordinate rotation descent and continuous convex approximation method, and the specific steps are as follows:
step 1), initializing the flight path of the unmanned aerial vehicle according to the constraint conditions in the problem (2);
step 2), fixing the flight path of the unmanned aerial vehicle, and optimizing power distribution among users by using an interior point method;
step 3), fixing power distribution among users, and optimizing the flight path of the unmanned aerial vehicle by utilizing continuous convex approximation iteration until the algorithm is converged;
and 4) iterating the step 2) and the step 3) based on the block coordinate rotation descent method until convergence.
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