CN114584192A - Anti-jitter robust beamforming optimization method for millimeter wave unmanned aerial vehicle communication system - Google Patents

Anti-jitter robust beamforming optimization method for millimeter wave unmanned aerial vehicle communication system Download PDF

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CN114584192A
CN114584192A CN202210181193.XA CN202210181193A CN114584192A CN 114584192 A CN114584192 A CN 114584192A CN 202210181193 A CN202210181193 A CN 202210181193A CN 114584192 A CN114584192 A CN 114584192A
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欧阳键
倪单福
潘阳阳
衡晟玥
王雪薇
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Nanjing University of Posts and Telecommunications
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Abstract

The invention discloses an anti-jitter robust beamforming optimization method for a millimeter wave unmanned aerial vehicle communication system, which comprises the steps that the millimeter wave communication system of an unmanned aerial vehicle receives feedback information of a GPS positioning channel and a user return channel in real time, obtains an unmanned aerial vehicle transmitting beamforming vector, and obtains pitch angle and azimuth angle information between the unmanned aerial vehicle and a ground user, so that an upper limit value of a jitter error of the unmanned aerial vehicle is obtained; a jitter error model is introduced, the downlink transmission capacity sum of a plurality of ground users is calculated according to the unmanned aerial vehicle transmitting beam forming vector and the noise power, and the transmitting beam forming optimization problem is determined; and (3) carrying out deterministic transformation on the optimization problem of the jitter error model based on a convex hull theory, and solving by using a continuous convex approximation method to obtain beam forming vector parameters. The unmanned aerial vehicle millimeter wave communication system with the optimal anti-jitter robust wave performance is determined based on the unmanned aerial vehicle millimeter wave transmitting beam forming optimization problem model with known vector parameters, and the anti-jitter capability of the unmanned aerial vehicle millimeter wave communication system is improved.

Description

Anti-jitter robust beamforming optimization method for millimeter wave unmanned aerial vehicle communication system
Technical Field
The invention relates to the technical field of millimeter wave communication of an unmanned aerial vehicle, in particular to an anti-jitter robust beamforming optimization method of a millimeter wave unmanned aerial vehicle communication system.
Background
In recent years, the implementation of unmanned aerial vehicle data communication by using millimeter wave technology has become a research hotspot in academia and industry. On the one hand, the characteristic of millimeter wave signal short wavelength high frequency provides a feasible scheme for solving the problems of unmanned aerial vehicle load limitation and frequency spectrum resource shortage, and is favorable for improving the information transmission rate. On the other hand, the unmanned aerial vehicle can be flexibly arranged in the air, and the high flying position enables a line-of-sight path to exist in the communication process, so that the coverage range of millimeter wave communication can be greatly expanded, the network connectivity can be improved, and the unmanned aerial vehicle becomes an excellent carrying platform of the millimeter wave communication technology. However, unlike the ground cellular network with a stable infrastructure, the drone is susceptible to airflow and self-vibration due to the limitations of atmospheric turbulence and flight control capability, and random jitter such as yaw jitter in the horizontal direction or pitch jitter in the vertical direction is generated, so that the beam pointing direction is angularly deviated, thereby causing inefficient and unstable information transmission of the air-ground transmission link.
The millimeter wave is more susceptible to the influence of angle errors caused by unmanned aerial vehicle jitter due to the characteristic of directional narrow beams, and the performance of a communication system can generate more adverse influence due to beam angle deviation. Therefore, the negative impact of the jitter characteristic of the drone in the millimeter wave drone communication system is more negligible.
Disclosure of Invention
The purpose of the invention is as follows: in order to overcome the defects in the prior art, the invention provides an anti-jitter robust beamforming optimization method for a millimeter wave unmanned aerial vehicle communication system; by optimizing the millimeter wave transmitting beam forming vector of the unmanned aerial vehicle, the sum of downlink transmission capacity of multiple users under the worst condition is maximized, so that the millimeter wave communication system of the unmanned aerial vehicle has stronger robustness to the shaking of the unmanned aerial vehicle.
The technical scheme is as follows: the invention provides a jitter-resistant robust beamforming optimization method for a millimeter wave unmanned aerial vehicle communication system, which comprises the following steps:
receiving feedback information of GPS positioning and user return channels in real time through an unmanned aerial vehicle millimeter wave communication system, analyzing millimeter wave transmitting beams transmitted to a plurality of ground users by a multi-antenna unmanned aerial vehicle base station in the feedback information, obtaining unmanned aerial vehicle transmitting beam forming vectors according to the millimeter wave transmitting beams, and extracting position data of the unmanned aerial vehicle and the ground users from the feedback information;
calculating based on the position data of the unmanned aerial vehicle and the ground user, determining pitch angle and azimuth angle information between the unmanned aerial vehicle and the ground user, calculating all pitch angle and azimuth angle information between the unmanned aerial vehicle and the ground user in the whole flying process of the unmanned aerial vehicle, and obtaining an upper limit value of a jitter error in the flying process of the unmanned aerial vehicle;
inputting the upper limit value of the jitter error into a jitter error model of a millimeter wave air-ground channel of the unmanned aerial vehicle, calculating the sum of downlink transmission capacities of a plurality of ground users according to the transmitted beam forming vector of the unmanned aerial vehicle and the noise power from the unmanned aerial vehicle to the ground users, and determining the optimization problem of the millimeter wave transmitted beam forming of the unmanned aerial vehicle; the unmanned aerial vehicle millimeter wave air-ground channel jitter error model is constructed according to the communication characteristics of the unmanned aerial vehicle millimeter wave air-ground channel;
carrying out deterministic transformation on the jitter error model on the unmanned aerial vehicle millimeter wave emission beam forming optimization problem based on a convex hull theory to obtain a deterministic problem;
solving the certainty problem by using a continuous convex approximation method to obtain vector parameters of the unmanned aerial vehicle millimeter wave transmission beam forming optimization problem;
and determining the unmanned aerial vehicle millimeter wave communication system with the optimal anti-jitter robust wave performance based on the unmanned aerial vehicle millimeter wave transmitting beam forming optimization problem model with known vector parameters.
In a further embodiment, the pitch angle and azimuth angle information calculation formulas between the drone and the ground user are respectively:
Figure BDA0003521018740000021
in the formula, qu＝(xu，yu)TAnd q isk(xk，yk)THorizontal coordinates, x, representing unmanned aerial vehicle and ground user, respectivelyτAnd yττ ∈ { u, k } denotes the coordinates of the horizontal x-direction and y-direction of the drone (ground user), respectively,
Figure BDA0003521018740000022
h is the flying height of the unmanned aerial vehicle, and T is the transposed symbol of the vector.
In a further embodiment, the formula for calculating the millimeter wave air-ground channel jitter error model of the drone is as follows:
Figure BDA0003521018740000023
in the formula, hkIs a vector of the channel to be transmitted,
Figure BDA0003521018740000024
is a constant, c is the speed of light, fcIs the carrier center frequency and is the carrier center frequency,
Figure BDA0003521018740000025
Figure BDA0003521018740000026
the distance between the drone and the ground user,
Figure BDA0003521018740000027
is an antenna array vector, θkAnd
Figure BDA0003521018740000028
pitch and azimuth angles between the drone and the ground user,
Figure BDA0003521018740000029
and
Figure BDA00035210187400000210
respectively, an estimated value of a pitch angle and an estimated value of an azimuth angle between the unmanned aerial vehicle and a ground user, delta thetakAnd
Figure BDA00035210187400000211
respectively a pitching angle shaking error and an azimuth angle shaking error caused by the shaking of the unmanned aerial vehicle,
Figure BDA00035210187400000212
and
Figure BDA00035210187400000213
respectively an upper limit value of a pitching angle jitter error and an upper limit value of an azimuth angle jitter error;
wherein the antenna array vector
Figure BDA00035210187400000214
The expression of (a) is:
Figure BDA0003521018740000031
wherein d is the distance between adjacent antenna elements of the uniform planar array, λ is the carrier wavelength, and m is not less than 1x≤Mx，1≤my≤My，MxAnd MyThe number of the row antennas and the number of the column antennas of the uniform planar array are respectively.
In a further embodiment, the expression for determining the millimeter wave transmission beamforming optimization problem of the unmanned aerial vehicle is as follows:
Figure BDA0003521018740000032
Figure BDA0003521018740000033
in the formula (I), the compound is shown in the specification,
Figure BDA0003521018740000034
is the upper limit value of the transmitting power of the unmanned aerial vehicle,
Figure BDA0003521018740000035
for multi-user downlink transmission of capacity sum, wkTransmitting a beamforming vector for the drone;
wherein the downlink transmission capacity of multiple users is
Figure BDA0003521018740000036
The calculation formula of (2) is as follows:
Figure BDA0003521018740000037
in the formula, HkFor a channel matrix, ΛkIs HkIs determined by the uncertainty set of (a),
Figure BDA0003521018740000038
representing the noise power of the drone to ground user communication link,
Figure BDA0003521018740000039
for the kth beamforming vector wkThe conjugate of (a) the transposed vector (v),
Figure BDA00035210187400000310
for the ith ≠ k beamforming vectors wiThe conjugate transpose vector of (1);
wherein HkUncertain set Λ ofkThe calculation expression of (a) is:
Figure BDA00035210187400000311
in the formula, hkFor the purpose of the channel vector,
Figure BDA00035210187400000312
is hkThe conjugate of (2) is transposed the vector.
In a further embodiment, the method of obtaining a deterministic problem is:
according to the convex hull theory, the uncertain channel matrix containing the jitter error can be expressed as a deterministic form of the weighted sum of finite or infinite discrete samples in an uncertain set, and the expression of the uncertain channel matrix is as follows:
Figure BDA00035210187400000313
in the formula, LkThe number of the total samples is the number of the samples,
Figure BDA00035210187400000314
is the weighting coefficient for the jth sample,
Figure BDA00035210187400000315
determining the jth sample according to the discretized angle information; by using
Figure BDA00035210187400000316
Substitute HkThe problem (P1) is approximately represented as a deterministic problem (P2) and the calculation formula is:
Figure BDA00035210187400000317
s.t. (4b) (8b)
in a further embodiment, the deterministic problem is solved using a continuous convex approximation method as follows:
the non-convex problem is converted into a convex optimization problem by using a continuous convex approximation method,
the conversion calculation formula is:
maxwk，a，fk，pka (9a)
Figure BDA0003521018740000041
Figure BDA0003521018740000042
Figure BDA0003521018740000043
(4b) (9e)
in the formula (I), the compound is shown in the specification,
Figure BDA0003521018740000044
Figure BDA0003521018740000045
representing the real part, a, f, of Ak，pkRepresents the auxiliary variables introduced in the optimization problem,
Figure BDA0003521018740000046
is wk，fk，pkIs possible.
In a further embodiment, the method for obtaining the vector parameters of the unmanned aerial vehicle millimeter wave transmission beam forming optimization problem includes:
initializing a beam forming vector, and presetting an auxiliary variable and iteration precision in an unmanned aerial vehicle air-ground channel jitter error model;
substituting the beamforming vector and the auxiliary variable into a formula of a continuous convex approximation method for comparison, and selecting and outputting the beamforming vector and the auxiliary variable which meet the value range of the formula of the continuous convex approximation method;
and judging whether the difference between the iteration values of the two previous and next multi-user downlink transmission capacity sums is smaller than the iteration precision or not according to the multi-user downlink transmission capacity sums, outputting a beam forming vector if the difference is smaller than the iteration precision, and circularly comparing whether the beam forming vector and the auxiliary variable meet the value range of a convex approximation method or not if the difference is larger than the iteration precision.
Has the advantages that: compared with the prior art, the invention has the following advantages:
the advantages of the unmanned aerial vehicle communication system and the millimeter wave technology are complementary by combining the unmanned aerial vehicle communication system and the millimeter wave technology, and meanwhile, a deterministic conversion method of a jitter error model based on a convex hull theory is provided for the jitter characteristic of unmanned aerial vehicle jitter, so that the problem of uncertain angle errors caused by unmanned aerial vehicle jitter is effectively solved, and the jitter resistance of the unmanned aerial vehicle millimeter wave communication system is improved.
Aiming at the problem of multi-user downlink transmission capacity and maximization of an unmanned aerial vehicle millimeter wave system under the worst condition, an iterative solution algorithm based on continuous convex approximation is provided, a non-convex problem is converted into a convex form, the optimal suboptimal solution of an original problem is obtained through optimization of a beam forming vector and convergence under finite iterations, and the service quality requirement of unmanned aerial vehicle millimeter wave downlink data transmission in a task window is guaranteed.
Drawings
Fig. 1 is a system model diagram of an anti-jitter robust beamforming optimization method of a millimeter wave unmanned aerial vehicle communication system according to the present invention;
fig. 2 is a schematic diagram of the unmanned aerial vehicle dithering of the anti-dithering robust beamforming optimization method for the millimeter wave unmanned aerial vehicle communication system according to the present invention;
FIG. 3 is a flowchart of an algorithm of the anti-jitter robust beamforming optimization method of the millimeter wave unmanned aerial vehicle communication system according to the present invention;
FIG. 4 is a beam diagram of a beamforming vector w _1 under the robust beamforming scheme for anti-jitter proposed in the present invention;
fig. 5 is a graph of the multi-user downlink transmission capacity and the variation trend with the maximum value of jitter error under the anti-jitter robust beamforming scheme and the non-robust beamforming scheme.
Detailed Description
In order to more fully understand the technical content of the present invention, the technical solution of the present invention will be further described and illustrated with reference to the following specific embodiments, but not limited thereto.
The invention provides a jitter-resistant robust beamforming optimization method for a millimeter wave unmanned aerial vehicle communication system, which comprises the following steps:
receiving feedback information of GPS positioning and user return channels in real time through an unmanned aerial vehicle millimeter wave communication system, analyzing millimeter wave transmitting beams transmitted to a plurality of ground users by a multi-antenna unmanned aerial vehicle base station in the feedback information, obtaining unmanned aerial vehicle transmitting beam forming vectors according to the millimeter wave transmitting beams, and extracting position data of the unmanned aerial vehicle and the ground users from the feedback information;
calculating based on the position data of the unmanned aerial vehicle and the ground user, determining pitch angle and azimuth angle information between the unmanned aerial vehicle and the ground user, calculating all pitch angle and azimuth angle information between the unmanned aerial vehicle and the ground user in the whole flying process of the unmanned aerial vehicle, and obtaining an upper limit value of a jitter error in the flying process of the unmanned aerial vehicle;
inputting the upper limit value of the jitter error into a jitter error model of a millimeter wave air-ground channel of the unmanned aerial vehicle, calculating the sum of downlink transmission capacities of a plurality of ground users according to the transmitted beam forming vector of the unmanned aerial vehicle and the noise power from the unmanned aerial vehicle to the ground users, and determining the optimization problem of the millimeter wave transmitted beam forming of the unmanned aerial vehicle; the unmanned aerial vehicle millimeter wave air-ground channel jitter error model is constructed according to the communication characteristics of the unmanned aerial vehicle millimeter wave air-ground channel;
carrying out deterministic conversion on the jitter error model on the problem of optimization of millimeter wave transmitting beam forming of the unmanned aerial vehicle based on a convex hull theory to obtain a deterministic problem;
solving the certainty problem by using a continuous convex approximation method to obtain vector parameters of the unmanned aerial vehicle millimeter wave transmission beam forming optimization problem;
and determining the unmanned aerial vehicle millimeter wave communication system with the optimal anti-jitter robust wave performance based on the unmanned aerial vehicle millimeter wave transmitting beam forming optimization problem model with known vector parameters.
In a further embodiment, the pitch angle and azimuth angle information between the drone and the ground user are calculated by the following formulas:
Figure BDA0003521018740000061
in the formula, qu＝(xu，yu)TAnd q isk(xk，yk)THorizontal coordinates, x, representing unmanned aerial vehicle and ground user, respectivelyτAnd yττ ∈ { u, k } denotes the coordinates of the horizontal x-direction and y-direction of the drone (ground user), respectively,
Figure BDA0003521018740000062
h is the flying height of the unmanned aerial vehicle, and T is the transposed symbol of the vector.
In a further embodiment, the formula for calculating the millimeter wave air-ground channel jitter error model of the drone is as follows:
Figure BDA0003521018740000063
in the formula, hkFor the purpose of the channel vector,
Figure BDA0003521018740000064
is a constant, c is the speed of light, fcIs the carrier center frequency and is the carrier center frequency,
Figure BDA0003521018740000065
Figure BDA0003521018740000066
the distance between the drone and the ground user,
Figure BDA0003521018740000067
is an antenna array vector, θkAnd
Figure BDA0003521018740000068
pitch and azimuth angles between the drone and the ground user,
Figure BDA0003521018740000069
and
Figure BDA00035210187400000610
respectively between unmanned aerial vehicle and ground userEstimated values of pitch and azimuth angles, Delta thetakAnd
Figure BDA00035210187400000611
respectively a pitching angle shaking error and an azimuth angle shaking error caused by the shaking of the unmanned aerial vehicle,
Figure BDA00035210187400000612
and
Figure BDA00035210187400000613
respectively an upper limit value of a pitching angle jitter error and an upper limit value of an azimuth angle jitter error;
wherein the antenna array vector
Figure BDA00035210187400000614
The expression of (a) is:
Figure BDA00035210187400000615
wherein d is the distance between adjacent antenna elements of the uniform planar array, λ is the carrier wavelength, and m is not less than 1x≤Mx，1≤my≤My，MxAnd MyThe number of the row antennas and the number of the column antennas of the uniform planar array are respectively.
In a further embodiment, an optimization algorithm expression for establishing the unmanned aerial vehicle millimeter wave transmission beam forming optimization problem is as follows:
Figure BDA00035210187400000616
Figure BDA0003521018740000071
in the formula (I), the compound is shown in the specification,
Figure BDA0003521018740000072
is the upper limit value of the transmitting power of the unmanned aerial vehicle,
Figure BDA0003521018740000073
for multi-user downlink transmission of capacity sum, wkTransmitting a beamforming vector for the drone;
wherein the downlink transmission capacity of multiple users is
Figure BDA0003521018740000074
The calculation formula of (c) is:
Figure BDA0003521018740000075
in the formula, HkFor a channel matrix, ΛkIs HkIs determined by the uncertainty set of (a),
Figure BDA0003521018740000076
representing the noise power of the drone to ground user communication link,
Figure BDA0003521018740000077
for the kth beamforming vector wkThe conjugate of the transposed vector of (a),
Figure BDA0003521018740000078
for the ith ≠ k beamforming vectors wiThe conjugate transpose vector of (1);
wherein HkUncertain set Λ ofkThe calculation expression of (a) is:
Figure BDA0003521018740000079
in the formula, hkFor the purpose of the channel vector,
Figure BDA00035210187400000710
is hkThe conjugate of (2) transposes the vector.
In a further embodiment, the optimization algorithm combines the convex hull theory to perform deterministic transformation on the jitter error model, and the method for obtaining the deterministic problem comprises the following steps:
according to the convex hull theory, the uncertain channel matrix containing the jitter error can be expressed as a deterministic form of the weighted sum of finite or infinite discrete samples in an uncertain set, and the expression of the uncertain channel matrix is as follows:
Figure BDA00035210187400000711
in the formula, LkTo be the total number of samples,
Figure BDA00035210187400000712
is the weighting coefficient for the jth sample,
Figure BDA00035210187400000713
determining the jth sample according to the discretized angle information; by using
Figure BDA00035210187400000714
Substitute HkThe problem (P1) is approximately represented as a deterministic problem (P2) with the calculation formula:
Figure BDA00035210187400000715
s.t. (4b) (8b)
in a further embodiment, the deterministic problem is solved using a continuous convex approximation method as follows:
the non-convex problem is converted into a convex optimization problem by using a continuous convex approximation method,
the conversion calculation formula is:
Figure BDA00035210187400000716
Figure BDA00035210187400000717
Figure BDA00035210187400000718
Figure BDA0003521018740000081
(4b) (9e)
in the formula (I), the compound is shown in the specification,
Figure BDA0003521018740000082
Figure BDA0003521018740000083
representing the real part, a, f, of Ak，pkRepresents the auxiliary variables introduced in the optimization problem,
Figure BDA0003521018740000084
is wk，fk，pkIs possible.
In a further embodiment, the method for outputting the millimeter wave drone anti-jitter robust beamforming vector parameters comprises:
initializing a beam forming vector, and presetting an auxiliary variable and iteration precision in an unmanned aerial vehicle air-ground channel jitter error model;
substituting the beamforming vector and the auxiliary variable into a formula of a continuous convex approximation method for comparison, and selecting and outputting the beamforming vector and the auxiliary variable which meet the value range of the formula of the continuous convex approximation method;
and judging whether the difference of the iteration values of the multi-user downlink transmission capacity sums in the previous and subsequent times is smaller than the iteration precision or not according to the multi-user downlink transmission capacity sum, outputting a beam forming vector if the difference is smaller than the iteration precision, and circularly comparing whether the beam forming vector and the auxiliary variable meet the value range of a convex approximation method or not if the difference is larger than the iteration precision.
The output vector parameters are in a multi-antenna millimeter wave unmanned aerial vehicle system, and the signal weighted value of each array element in the antenna array is adjusted in a self-adaptive manner according to the beam forming technology; and then the transmission beam direction of the millimeter wave unmanned aerial vehicle is adjusted, so that the main lobe direction of the beam is aligned to the target user, and other users are in the null space of the target user, the interference among users is reduced, and the anti-jitter capability of the millimeter wave communication system of the unmanned aerial vehicle is effectively improved.
The invention is further illustrated with reference to example 1:
as shown in fig. 1, the system model of the present invention considers an unmanned plane millimeter wave downlink communication system, which includes an unmanned plane base station and K ground users. The unmanned aerial vehicle adopts a uniform plane antenna array, and is equipped with M-MxMyThe ground user is equipped with a single antenna.
Assuming that an air-ground node transmission channel is a line-of-sight transmission channel, considering the communication characteristics of a millimeter wave air-ground channel of the unmanned aerial vehicle, establishing an unmanned aerial vehicle air-ground channel model based on angle jitter errors as follows: +
Figure BDA0003521018740000085
Wherein
Figure BDA0003521018740000086
c is the speed of light, fcIs the carrier center frequency, qu＝(xu，yu)TAnd q isk＝(xk，yk)THorizontal coordinates representing the drone and the ground user respectively,
Figure BDA0003521018740000087
h is the flying height of the unmanned aerial vehicle, akAs an antenna array vector, it can be expressed as:
Figure BDA0003521018740000091
wherein d is the distance between adjacent antenna elements of the uniform planar array, λ is the carrier wavelength, 1 ≦ mx≤Mx，1≤my≤My，M＝Mx×MyIs the total antenna number of the uniform planar array. ThetakAnd
Figure BDA0003521018740000092
representing the pitch and azimuth angles between the drone and the ground user, respectively. The angle information between the drone and the ground user may be expressed as:
Figure BDA0003521018740000093
different from ground cellular network, because do not have fixed ground support facility, unmanned aerial vehicle's stability can't be guaranteed, lead to its vertical direction and horizontal direction to appear the angle shake error. The unmanned aerial vehicle shaking model is shown in fig. 2, the left figure is a schematic diagram of millimeter wave emission beams of an unmanned aerial vehicle with a vertical section, and the right figure is a schematic diagram of millimeter wave emission beams of an unmanned aerial vehicle with a horizontal section. Considering the jitter characteristics of the unmanned aerial vehicle, an angle jitter error model based on the unmanned aerial vehicle jitter can be established as follows:
Figure BDA0003521018740000094
Figure BDA0003521018740000095
wherein
Figure BDA0003521018740000096
And
Figure BDA0003521018740000097
respectively, an estimated value of a pitch angle and an estimated value of an azimuth angle between the unmanned aerial vehicle and a ground user, delta thetakAnd
Figure BDA0003521018740000098
respective pitch angle jitter error and azimuth caused by unmanned aerial vehicle jitterThe error in the angular jitter is a function of,
Figure BDA0003521018740000099
and
Figure BDA00035210187400000910
the maximum value of the pitching angle jitter error and the maximum value of the azimuth angle jitter error are respectively. The uncertainty angle jitter error model is used to characterize the uncertainty channel matrix, which can be expressed as:
Figure BDA00035210187400000911
Figure BDA00035210187400000912
wherein
Figure BDA00035210187400000913
Assuming that the drone transmit signal can be expressed as:
Figure BDA00035210187400000914
wherein s iskThe information sent for the drone is sent by the drone,
Figure BDA00035210187400000915
Figure BDA00035210187400000916
representing unmanned aerial vehicle millimeter wave transmit beamforming vectors. Thus, the signal received by the kth terrestrial user can be specifically expressed as:
Figure BDA00035210187400000917
wherein
Figure BDA00035210187400000918
Is additive white gaussian noise for the unmanned aerial vehicle to ground user communication link. The signal-to-interference-and-noise ratio of the k-th ground user from the drone obtained by the above equation can be expressed as follows:
Figure BDA0003521018740000101
according to equations (1-8), considering the worst case, the sum of the multi-user downlink transmission capacities can be expressed as:
Figure BDA0003521018740000102
further constructing an optimization problem of millimeter wave transmission beam forming of the unmanned aerial vehicle containing angle jitter errors, maximizing the downlink transmission capacity of multiple users, and specifically modeling as follows:
Figure BDA0003521018740000103
Figure BDA0003521018740000104
wherein
Figure BDA0003521018740000105
Representing the drone transmit power maximum.
Next, the optimization problem (1-10) is processed and converted into a form that can be solved. Firstly, a deterministic conversion method of a jitter error model based on a convex hull theory is provided. According to convex hull theory, the uncertain channel matrix containing the jitter error can be expressed in a deterministic fashion as a weighted sum of a finite or infinite number of discrete samples in an uncertain set, i.e.
Figure BDA0003521018740000106
Wherein L iskTo be the total number of samples,
Figure BDA0003521018740000107
is the weighting coefficient for the jth sample,
Figure BDA0003521018740000108
is the jth sample.
Figure BDA0003521018740000109
By
Figure BDA00035210187400001010
It is determined that,
Figure BDA00035210187400001011
discretizing by the following formula:
Figure BDA00035210187400001012
Figure BDA00035210187400001013
thus, adopt
Figure BDA00035210187400001014
Substitute HkThe problem (P1) can be equivalently represented as a deterministic problem (P2):
Figure BDA00035210187400001015
s.t. (10b) (1-13b)
the objective function in the optimization problem (1-13) is non-convex, by introducing auxiliary variables a, fk，pkIts equivalence is converted into the following form:
Figure BDA00035210187400001016
Figure BDA00035210187400001017
Figure BDA00035210187400001018
Figure BDA00035210187400001019
(10b) (1-14e)
since the constraints (1-14c) are non-convex and difficult to solve, we apply the continuous convex approximation method to convert it into a convex form by first-order Taylor expansion. Given a
Figure BDA0003521018740000111
Is provided with
Figure BDA0003521018740000112
Whereby (1-14c) can be converted into:
Figure BDA0003521018740000113
to this end, the original non-convex optimization problem can be equivalently transformed into the following form:
Figure BDA0003521018740000114
s.t. (10b)，(14b)，(14d)，(16) (1-17b)
finally, an anti-jitter robust beamforming algorithm of the millimeter wave communication system of the unmanned aerial vehicle is designed, and an unmanned aerial vehicle transmitting beamforming vector which enables downlink transmission capacity of multiple users to be maximized is obtained through continuous convex approximation iterative solution, wherein the specific algorithm is shown in fig. 3, and the process is as follows:
step 1: initializing beamforming vectors
Figure BDA0003521018740000115
Auxiliary variable
Figure BDA0003521018740000116
And
Figure BDA0003521018740000117
let n equal to 0 and epsilon equal to 10-4。
Step 2: in the beamforming vector
Figure BDA0003521018740000118
And auxiliary variables
Figure BDA0003521018740000119
Based on the formula (1-17) to calculate the beam forming vector
Figure BDA00035210187400001110
And auxiliary variables
Figure BDA00035210187400001111
And step 3: and judging whether the objective function value of the formula (1-9) converges on epsilon or not, namely whether the difference between the iteration values of the previous iteration and the next iteration is smaller than the iteration precision or not. If yes, continue step 4, otherwise, go to step 2 after making n ═ n + 1.
And 4, step 4: obtaining a beamforming vector optimal solution
Figure BDA00035210187400001112
The output vector parameters are in a multi-antenna millimeter wave unmanned aerial vehicle system, and the signal weighted value of each array element in the antenna array is adjusted in a self-adaptive manner according to the beam forming technology; further adjusting the transmission beam direction of the millimeter wave unmanned aerial vehicle to ensure thatThe main lobe direction of the obtained wave beam is aligned to the target user, and meanwhile, other users are in the null space of the target user, so that the interference among the users is reduced. Further described with reference to FIG. 4; FIG. 4 shows a beamforming vector w under the robust beamforming scheme for anti-jitter proposed in the present invention1The beam pattern of (a). The rectangular area in the figure is an angle jitter error range caused by unmanned aerial vehicle jitter. As can be seen from the figure, w1The main lobe of (1) points to the direction of the user 1, and the normalized transmission power is higher than-0.1 dB. At the same time, w1The null space aligns to the uncertain areas where the users 2 and 3 are located, and the normalized transmitting power of the null space is lower than-50 dB, which means that the anti-jitter robust beamforming scheme provided by the invention can effectively improve the anti-jitter capability of the millimeter wave communication system of the unmanned aerial vehicle, and simultaneously reduces the interference between the users.
Fig. 5 is a graph of a multi-user downlink transmission and a capacity variation trend with a maximum value of an angle error under an anti-jitter robust beamforming scheme and a non-robust beamforming scheme. As can be seen from the figure, as the maximum value of the pitch angle jitter error and the maximum value of the azimuth angle jitter error increase, the downlink transmission and capacity of the robust and non-robust schemes are continuously reduced. However, the descending rate of the robust scheme is obviously slower than that of the non-robust scheme, because the robust scheme considers the angle jitter error caused by the unmanned aerial vehicle jitter during optimization and has robustness on the jitter error, and the non-robust scheme does not consider the influence of the unmanned aerial vehicle jitter, so that the beam pointing direction is deviated, and the performance of the millimeter wave system of the unmanned aerial vehicle is rapidly reduced.
Therefore, the advantages of the unmanned aerial vehicle communication system and the millimeter wave technology are complemented by combining the two technologies, and meanwhile, a deterministic conversion method of a jitter error model based on a convex hull theory is provided for the jitter characteristic of the unmanned aerial vehicle jitter, so that the problem of uncertain angle errors caused by the unmanned aerial vehicle jitter is effectively solved, and the jitter resistance of the unmanned aerial vehicle millimeter wave communication system is improved.
Aiming at the problem of multi-user downlink transmission capacity and maximization of an unmanned aerial vehicle millimeter wave system under the worst condition, an iterative solution algorithm based on continuous convex approximation is provided, a non-convex problem is converted into a convex form, the optimal suboptimal solution of an original problem is obtained through optimization of a beam forming vector and convergence under finite iterations, and the service quality requirement of unmanned aerial vehicle millimeter wave downlink data transmission in a task window is guaranteed.
Embodiments of the present application may be provided as methods, systems, or computer program products. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
Embodiments of the present application may be provided as methods, systems, or computer program products. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The above description is only a preferred embodiment of the present invention, and several modifications and variations can be made without departing from the technical principle of the present invention, and these modifications and variations should also be regarded as the protection scope of the present invention.

Claims (7)

1. A jitter-resistant robust beamforming optimization method for a millimeter wave unmanned aerial vehicle communication system is characterized by comprising the following steps:
receiving feedback information of GPS positioning and user return channels in real time through an unmanned aerial vehicle millimeter wave communication system, analyzing millimeter wave transmitting beams transmitted to a plurality of ground users by a multi-antenna unmanned aerial vehicle base station in the feedback information, obtaining unmanned aerial vehicle transmitting beam forming vectors according to the millimeter wave transmitting beams, and extracting position data of the unmanned aerial vehicle and the ground users from the feedback information;
calculating based on the position data of the unmanned aerial vehicle and the ground user, determining pitch angle and azimuth angle information between the unmanned aerial vehicle and the ground user, calculating all pitch angle and azimuth angle information between the unmanned aerial vehicle and the ground user in the whole flying process of the unmanned aerial vehicle, and obtaining an upper limit value of a jitter error in the flying process of the unmanned aerial vehicle;
inputting the upper limit value of the jitter error into a jitter error model of a millimeter wave air-ground channel of the unmanned aerial vehicle, calculating the sum of downlink transmission capacities of a plurality of ground users according to the transmitted beam forming vector of the unmanned aerial vehicle and the noise power from the unmanned aerial vehicle to the ground users, and determining the optimization problem of the millimeter wave transmitted beam forming of the unmanned aerial vehicle; the unmanned aerial vehicle millimeter wave air-ground channel jitter error model is constructed according to the communication characteristics of the unmanned aerial vehicle millimeter wave air-ground channel;
carrying out deterministic conversion on the jitter error model on the problem of optimization of millimeter wave transmitting beam forming of the unmanned aerial vehicle based on a convex hull theory to obtain a deterministic problem;
solving the certainty problem by using a continuous convex approximation method to obtain vector parameters of the unmanned aerial vehicle millimeter wave transmission beam forming optimization problem;
and determining the unmanned aerial vehicle millimeter wave communication system with the optimal anti-jitter robust wave performance based on the unmanned aerial vehicle millimeter wave transmitting beam forming optimization problem model with known vector parameters.
2. The method of claim 1, wherein the calculation formulas for pitch angle and azimuth angle information between the drone and the ground user are respectively:
Figure RE-FDA0003595257310000011
in the formula, qu＝(xu，yu)TAnd q isk(xk，yk)THorizontal coordinates, x, representing unmanned aerial vehicle and ground user, respectivelyτAnd yττ ∈ { u, k } denotes the coordinates of the horizontal x-direction and y-direction of the drone (ground user), respectively,
Figure RE-FDA0003595257310000012
h is the flying height of the unmanned aerial vehicle, and T is the transposed symbol of the vector.
3. The method of claim 1, wherein the formula for calculating the millimeter wave space-ground channel jitter error model of the drone is as follows:
Figure RE-FDA0003595257310000013
Figure RE-FDA0003595257310000021
in the formula, hkFor the purpose of the channel vector,
Figure RE-FDA0003595257310000022
is a constant, c is the speed of light, fcIs the carrier center frequency and is the carrier center frequency,
Figure RE-FDA0003595257310000023
Figure RE-FDA0003595257310000024
the distance between the drone and the ground user,
Figure RE-FDA0003595257310000025
is an antenna array vector, θkAnd
Figure RE-FDA0003595257310000026
pitch and azimuth angles between the drone and the ground user,
Figure RE-FDA0003595257310000027
and
Figure RE-FDA0003595257310000028
respectively, an estimated value of a pitch angle and an estimated value of an azimuth angle between the unmanned aerial vehicle and a ground user, delta thetakAnd
Figure RE-FDA0003595257310000029
respectively a pitching angle shaking error and an azimuth angle shaking error caused by the shaking of the unmanned aerial vehicle,
Figure RE-FDA00035952573100000210
and
Figure RE-FDA00035952573100000211
respectively an upper limit value of a pitching angle jitter error and an upper limit value of an azimuth angle jitter error;
wherein the antenna array vector
Figure RE-FDA00035952573100000212
The expression of (a) is:
Figure RE-FDA00035952573100000213
wherein d is the distance between adjacent antenna elements of the uniform planar array, λ is the carrier wavelength, and m is greater than or equal to 1x≤Mx，1≤my≤My，MxAnd MyThe number of the row antennas and the number of the column antennas of the uniform planar array are respectively.
4. The method of claim 1, wherein the determining an expression of the drone millimeter wave transmit beamforming optimization problem is:
Figure RE-FDA00035952573100000214
Figure RE-FDA00035952573100000215
in the formula (I), the compound is shown in the specification,
Figure RE-FDA00035952573100000216
is the upper limit value of the transmitting power of the unmanned aerial vehicle,
Figure RE-FDA00035952573100000217
for multiple users downlink transmission capacity sum, wkTransmitting a beamforming vector for the drone;
wherein the downlink transmission capacity of multiple users is
Figure RE-FDA00035952573100000218
The calculation formula of (2) is as follows:
Figure RE-FDA00035952573100000219
in the formula, HkFor a channel matrix, ΛkIs HkIs determined by the uncertainty set of (a),
Figure RE-FDA00035952573100000220
representing the noise power of the drone to ground user communication link,
Figure RE-FDA00035952573100000221
for the kth beamforming vector wkThe conjugate of (a) the transposed vector (v),
Figure RE-FDA00035952573100000222
for the i ≠ k beamforming vectors wiThe conjugate transpose vector of (1);
wherein HkUncertain set Λ ofkThe calculation expression of (a) is:
Figure RE-FDA00035952573100000223
Figure RE-FDA00035952573100000224
in the formula, hkFor the purpose of the channel vector,
Figure RE-FDA0003595257310000031
transpose the vector for the conjugate of hk.
5. The method for optimizing anti-jitter robust beamforming for a millimeter wave drone communication system of claim 1, wherein the method for obtaining the deterministic problem is:
according to the convex hull theory, the uncertain channel matrix containing the jitter error is expressed as a deterministic form of the weighted sum of finite or infinite discrete samples in an uncertain set, and the expression of the uncertain channel matrix is as follows:
Figure RE-FDA0003595257310000032
in the formula, LkTo be the total number of samples,
Figure RE-FDA0003595257310000033
is the weighting coefficient for the jth sample,
Figure RE-FDA0003595257310000034
determining the jth sample according to the discretized angle information; by using
Figure RE-FDA0003595257310000035
Substitute HkThe problem (P1) is approximately represented as a deterministic problem (P2) and the calculation formula is:
Figure RE-FDA0003595257310000036
s.t. (4b) (8b)。
6. the method for optimizing anti-jitter robust beamforming for a millimeter wave drone communication system of claim 1, wherein the method for solving the deterministic problem using the continuous convex approximation method is:
the non-convex problem is converted into a convex optimization problem by using a continuous convex approximation method,
the conversion calculation formula is:
Figure RE-FDA0003595257310000037
Figure RE-FDA0003595257310000038
Figure RE-FDA0003595257310000039
Figure RE-FDA00035952573100000310
(4b) (9e)
in the formula (I), the compound is shown in the specification,
Figure RE-FDA00035952573100000311
representing the real part, a, f, of Ak，pkRepresents the auxiliary variables introduced in the optimization problem,
Figure RE-FDA00035952573100000312
is wk，fk，pkIs possible.
7. The method of claim 1, wherein the method for obtaining vector parameters of the unmanned aerial vehicle millimeter wave transmission beamforming optimization problem comprises:
initializing a beam forming vector, and presetting an auxiliary variable and iteration precision in an unmanned aerial vehicle air-ground channel jitter error model;
substituting the beamforming vector and the auxiliary variable into a formula of a continuous convex approximation method for comparison, and selecting and outputting the beamforming vector and the auxiliary variable which meet the value range of the formula of the continuous convex approximation method;
and judging whether the difference of the iteration values of the multi-user downlink transmission capacity sums in the previous and subsequent times is smaller than the iteration precision or not according to the multi-user downlink transmission capacity sum, outputting a beam forming vector if the difference is smaller than the iteration precision, and circularly comparing whether the beam forming vector and the auxiliary variable meet the value range of a convex approximation method or not if the difference is larger than the iteration precision.
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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115685067A (en) * 2022-11-07 2023-02-03 江西理工大学 Normal-mode signal blind estimation method and system for positioning and tracking of multi-rotor unmanned aerial vehicle
CN115842582A (en) * 2022-11-24 2023-03-24 南通大学 Wireless transmission method and device for resisting random jitter of unmanned aerial vehicle

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115685067A (en) * 2022-11-07 2023-02-03 江西理工大学 Normal-mode signal blind estimation method and system for positioning and tracking of multi-rotor unmanned aerial vehicle
CN115842582A (en) * 2022-11-24 2023-03-24 南通大学 Wireless transmission method and device for resisting random jitter of unmanned aerial vehicle
CN115842582B (en) * 2022-11-24 2023-09-15 南通大学 Wireless transmission method and device for resisting random jitter of unmanned aerial vehicle

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