CN115190448A - Intelligent reflecting surface assisted cognitive unmanned aerial vehicle communication network design method - Google Patents

Intelligent reflecting surface assisted cognitive unmanned aerial vehicle communication network design method Download PDF

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CN115190448A
CN115190448A CN202210666768.7A CN202210666768A CN115190448A CN 115190448 A CN115190448 A CN 115190448A CN 202210666768 A CN202210666768 A CN 202210666768A CN 115190448 A CN115190448 A CN 115190448A
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unmanned aerial
aerial vehicle
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邓茜
虞广成
梁小朋
束锋
刘世豪
李太君
林志阳
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Hainan University
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    • H04W4/40—Services specially adapted for particular environments, situations or purposes for vehicles, e.g. vehicle-to-pedestrians [V2P]
    • H—ELECTRICITY
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W16/00—Network planning, e.g. coverage or traffic planning tools; Network deployment, e.g. resource partitioning or cells structures
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W4/00—Services specially adapted for wireless communication networks; Facilities therefor
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Abstract

The invention provides a method for designing an intelligent reflector assisted cognitive unmanned aerial vehicle communication network, which is applied to a network model, when a leader unmanned aerial vehicle senses that a frequency spectrum state is an idle state within a frame duration T, a Following Unmanned Aerial Vehicle (FUAV) provides communication service for the leader unmanned aerial vehicle by utilizing the sensed idle frequency spectrum, and meanwhile, the intelligent reflector enhances the communication between the unmanned aerial vehicles by passive beam forming.

Description

Intelligent reflecting surface assisted cognitive unmanned aerial vehicle communication network design method
Technical Field
The invention relates to the technical field of unmanned aerial vehicle communication, in particular to a cognitive unmanned aerial vehicle communication network design method assisted by an intelligent reflecting surface.
Background
With the continuous progress of manufacturing technology, the integration of Unmanned Aerial Vehicles (UAVs) and civil applications is receiving attention, such as disaster relief, traffic control, aerial survey, and the like. Among them, drone-enabled wireless communication is one of the most attractive hot spot applications at present. For example, due to their high mobility and low cost deployment, drones can be flexibly deployed on a large scale to perform efficient tasks, effectively relieving the pressure of terrestrial cellular networks. In addition, the unmanned aerial vehicle is used as an aerial base station, and a line-of-sight link can be established between the unmanned aerial vehicle and a ground base station and between the unmanned aerial vehicle and a ground user, so that high data rate and high reliability transmission are realized. Based on the above advantages, in order to meet the demand of B5G/6G mobile communication networks, unmanned aerial vehicle communication is rapidly developing. In order to fully exploit the potential of unmanned aerial vehicle communication, the development of innovative wireless transmission technology is at the forefront.
In an actual communication scenario, due to the fact that the transmission power of the drone is limited and the propagation environment between the drone and the receiver is not controllable, network performance of drone communication is inevitably limited. However, an Intelligent Reflecting Surface (IRS) is considered as an important solution to this problem, which can enhance the signal strength by reconstructing the propagation environment. In particular, the intelligent reflecting surface is an element surface consisting of a large number of passive reflecting elements, and each element on the reflecting surface can intelligently adjust the amplitude and phase change of an incident signal by using an embedded intelligent controller. Thus, with the aid of the intelligent reflecting surface, signals from different communication links can be added in the same direction at desired receivers to increase the signal strength or in anti-phase at undesired receivers to avoid undesired information leakage and thus shape the radio propagation environment in an advantageous manner.
On the other hand, in the unmanned aerial vehicle communication process, the authorized spectrum band of the unmanned aerial vehicle is extremely limited, such as IEEE S band, IEEE L band, and Industrial band, which undoubtedly causes the problem that the unmanned aerial vehicle communication will face the spectrum scarcity. To alleviate this problem, cognitive Radio (CR) technology is introduced as a promising solution. CR techniques allow secondary users to access the primary network by ensuring that the primary user is adequately protected or by detecting unoccupied frequency bands in the primary user. Therefore, by applying the cognitive radio technology, the frequency spectrum resources can be efficiently utilized, and the frequency spectrum utilization rate of unmanned aerial vehicle communication is further improved.
In summary, the problems of the prior art are as follows: (1) The performance of the unmanned aerial vehicle communication network is low due to the limited transmitting power of the unmanned aerial vehicle and the uncontrollable propagation environment of the unmanned aerial vehicle communication link; (2) The authorized spectrum of unmanned aerial vehicle communication is extremely limited, and the utilization rate of the authorized spectrum of the existing ground master user is low; (3) The existing scheme rarely relates to the combination of an unmanned aerial vehicle network and an intelligent reflector technology + cognitive radio technology.
Disclosure of Invention
Therefore, the invention aims to provide a method for designing an intelligent reflector-assisted cognitive unmanned aerial vehicle communication network, so as to at least solve the problems.
The technical scheme adopted by the invention is as follows:
the intelligent reflector assisted cognitive unmanned aerial vehicle communication network design method comprises the following steps:
step 1, constructing an unmanned aerial vehicle system model, an unmanned aerial vehicle channel model and an unmanned aerial vehicle transmission model;
step 2, establishing an unmanned aerial vehicle optimization problem by determining objective functions and relevant constraints in an unmanned aerial vehicle system model, an unmanned aerial vehicle channel model and an unmanned aerial vehicle transmission model;
step 3, solving an optimization problem under a single unmanned aerial vehicle through an algorithm;
and 4, solving the optimization problem under multiple unmanned aerial vehicles through a design algorithm.
Further, in step 1, constructing the model of the unmanned aerial vehicle system specifically includes:
step 11, deploying M = M on the intelligent reflecting surface r ×M c A passive reflection element, wherein K leading unmanned aerial vehicles and one following unmanned aerial vehicle are all single antenna, and the main transmitter is single antennaThe passive reflective elements being arranged in a uniform planar array, M r And M c The number of elements in each row and column of the intelligent reflecting surface is respectively, and the phase shift matrix of the intelligent reflecting surface is expressed as
Figure BDA0003693222140000031
Wherein
Figure BDA0003693222140000032
The phase shift value of the mth reflecting element is represented, the frame is divided into a leader unmanned aerial vehicle frequency spectrum sensing duration tau and a following unmanned aerial vehicle data transmission duration T-tau, the following unmanned aerial vehicle adopts a time division multiplexing mode to transmit data in an uplink transmission process, and in a three-dimensional Cartesian coordinate system, a main transmitter, an intelligent reflecting surface and a jth following unmanned aerial vehicle coordinate are respectively fixed on q P ＝[x P ,y P ,z P ] T 、q R ＝[x R ,y R ,z R ] T And
Figure BDA0003693222140000033
wherein
Figure BDA0003693222140000034
Representing a set of following drones, let q L ＝[x,y,z] T Leading unmanned aerial vehicle coordinates needing to be optimized;
in step 1, the method for constructing the unmanned aerial vehicle channel model specifically comprises the following steps:
step 12, a line-of-sight channel model and a free space path loss model are respectively adopted for the intelligent reflecting surface auxiliary link and the direct link, the intelligent reflecting surface auxiliary link comprises a link from the following unmanned aerial vehicle to the intelligent reflecting surface and a link from the intelligent reflecting surface to the leading unmanned aerial vehicle, wherein the gain of a channel from the following unmanned aerial vehicle j to the intelligent reflecting surface is represented as:
Figure BDA0003693222140000035
where ρ represents a reference distance d 0 Path loss at =1, α representsThe intelligent reflective surface assists the path loss exponent of the link,
Figure BDA0003693222140000036
indicating the distance from the following drone j to the intelligent reflective surface,
Figure BDA0003693222140000037
a deterministic line-of-sight channel component representing the link, wherein
Figure BDA0003693222140000038
And
Figure BDA0003693222140000039
respectively, the elevation and azimuth angles of the intelligent reflecting surface following the unmanned plane j, and g (x, y) represents the function of the line-of-sight channel component expressed as
Figure BDA00036932221400000310
Wherein d represents the spacing between two adjacent elements on the intelligent reflective surface, λ represents the carrier wavelength,
Figure BDA00036932221400000311
representing the kronecker product, the channel gain from the intelligent reflecting surface to the leading drone is represented as:
Figure BDA00036932221400000312
wherein, d RL ＝||q R -q L | | represents the distance from the intelligent reflecting surface to the leading drone,
Figure BDA0003693222140000041
a deterministic line-of-sight channel component representing the link, wherein
Figure BDA00036932221400000410
And xi RL Respectively representing intelligent reflecting surfaces to leadershipThe elevation and azimuth of the machine, for the direct link, i.e., the link from the following drone j to the leading drone and the link from the leading drone to the main transmitter, the channel gain from the following drone j to the leading drone is expressed as:
Figure BDA0003693222140000042
wherein
Figure BDA0003693222140000043
Denotes the distance of the following drone j to the leader drone, κ denotes the corresponding path loss exponent, and the channel gain from the leader drone to the main transmitter is expressed as:
Figure BDA0003693222140000044
wherein d is LP ＝||q L -q P | represents the distance from the leader drone to the main transmitter, μ represents the corresponding path loss exponent;
in step 1, the construction of the unmanned aerial vehicle transmission model specifically comprises:
step 13, setting P (H) 0 ) And P (H) 1 ) Respectively representing the probability of the main transmitter being in an idle and busy state, P d And P f Respectively representing detection and false alarm probabilities, at a given P d ，P f Can be expressed as
Figure BDA0003693222140000045
Wherein
Figure BDA0003693222140000046
The function of the gaussian Q is represented by,
Figure BDA0003693222140000047
f s which is indicative of the sampling frequency, is,
Figure BDA0003693222140000048
representing leader unmanned aerial vehicle receiving ownerSignal-to-noise ratio of transmitter signal, where P T Is the transmission power of the main transmitter,
Figure BDA0003693222140000049
representing the noise power at the leading drone.
Further, in step 2, the problem of optimizing the drone by determining the objective function and the relevant constraints in the drone system model, the drone channel model, and the drone transmission model is specifically:
through the sensing time length tau of the leader unmanned aerial vehicle and the phase shift matrix theta of the intelligent reflecting surface j And a three-dimensional position q of the leading drone L Joint optimization, which maximizes the network reachable rate, the optimization problem can be expressed as:
Figure BDA0003693222140000051
s.t.C 1 :P d ≥P d0 ,
C 2 :(ω 2 /ω 1 ) 2 ≤τ≤T,
Figure BDA0003693222140000052
C 4 :||q L -q R || 2 ≥ζ 2 ,
C 5 :||q L -q P || 2 ≥ζ 2 ,
Figure BDA0003693222140000053
wherein, C 1 Representing the detection probability constraint, C 2 Representing a bounded perceived duration constraint, C 3 Representing the phase shift constraint of each reflective element on the intelligent reflective surface, where r,j Denotes the r-th diagonal element, C, following the phase shift matrix under drone j 4 -C 6 Unmanned plane for representation leaderWhere ζ represents the minimum safe distance between the leader drone and the primary transmitter, the intelligent reflecting surface, and the following drone.
Further, solving the optimization problem under the single unmanned aerial vehicle through an algorithm specifically comprises:
decomposing the optimization problem of the single unmanned aerial vehicle into optimal values of three sub-problems by utilizing binary search, semi-definite relaxation, continuous convex approximation and convex difference, and then optimizing the three sub-problems alternately by an alternate iterative algorithm, namely K =1, until the algorithm converges, wherein the method comprises the following specific steps:
step 31, optimizing sensing duration tau of leading unmanned aerial vehicle
Given phase shift matrix Θ j And leader unmanned aerial vehicle three-dimensional position q L Then sub-problem of sensing duration optimization
Figure BDA0003693222140000054
Can be expressed as:
Figure BDA0003693222140000055
s.t.C 2 ,
wherein
Figure BDA0003693222140000056
To analyze R j (τ) Property, R j (τ) the second derivative with respect to τ is as follows:
Figure BDA0003693222140000057
wherein
Figure BDA0003693222140000058
Analyzed by
Figure BDA0003693222140000059
Thus R is j (τ) is a pseudo-concave function with respect to τ, which can be solved by a binary search method;
step 32, phase shift matrix theta of intelligent reflecting surface j Is optimized
Giving a sensing time length tau and leading the three-dimensional position q of the unmanned aerial vehicle L Sub-problem of optimization of the phase shift matrix
Figure BDA0003693222140000061
It can be abbreviated as:
Figure BDA0003693222140000062
s.t.C 3
due to sub-problems
Figure BDA0003693222140000063
The constraint with a medium modulus value of 1 is non-convex, so a semi-definite relaxation technique is to be applied to relax the constraint, and the objective function also translates into a tracing problem, so a sub-problem
Figure BDA0003693222140000064
Can be equivalently rewritten as:
Figure BDA0003693222140000065
s.t.V≥0,
V r,r ＝1,r＝1,2,…,M+1,
rank(V)＝1,
where Tr (-) denotes the trace of the matrix, V r,r The (r, r) bit elements of the matrix V are represented, and since the solution with rank one is difficult to obtain, the relaxed rank one constraint is selected, and the problem is a standard semi-definite programming problem and can be solved by a convex optimization tool CVX, and then, by using a gaussian randomization method, a phase shift vector V can be recovered from the solved V;
step 33, leading the three-dimensional position q of the drone L Optimization
Given a perceptual duration tau and a phase-shift matrix theta j And then leader of the sub-problem of three-dimensional position optimization of the unmanned aerial vehicle
Figure BDA0003693222140000066
Can be abbreviated as:
Figure BDA0003693222140000067
s.t.C 4 -C 6 ,
wherein C is 0 ＝P(H 0 )(T-τ)，
Figure BDA0003693222140000068
And
Figure BDA0003693222140000069
due to h RL With respect to the position variable q L Is complex and non-linear, which makes the position optimization difficult to design, for which the leader drone position variable at the (l-1) th iteration is used to approximate h of the l-th iteration RL Thus H Q Is shown as
Figure BDA0003693222140000071
Consider the sub-problem
Figure BDA0003693222140000072
Is a non-convex optimization problem by introducing auxiliary variables
Figure BDA0003693222140000073
This non-convex problem can be equivalently translated into:
Figure BDA0003693222140000074
s.t log 2 (1+ρC 1 r d )≥w,
1-Q(h)≥k,
h≥0,
Figure BDA0003693222140000075
Figure BDA0003693222140000076
Figure BDA0003693222140000077
γ s ≥t,
Figure BDA0003693222140000078
Figure BDA0003693222140000079
C 4 -C 6 ,
converting the constraints into an upper mirror graph form, namely epi f = { (x, t) | x ∈ dom f, f (x) ≦ t }, wherein concave functions exist in the upper mirror graph forms of the constraints, and because concave functions exist in the upper mirror graph form of the constraints, the concave functions in the upper mirror graph form are expanded by one-order Taylor at feasible points by applying a continuous convex approximation method, so that the constraints are approximately converted into convex constraints, the constraints are converted into convex constraints by utilizing continuous convex approximation, the constraints can be converted into second-order cone constraints, and the second-order cone constraints can be converted into the following steps after convex difference and continuous convex approximation:
Figure BDA00036932221400000710
wherein k is 0 ，w 0 Given a feasible point, thereby, a sub-problem
Figure BDA00036932221400000814
Is converted into a convex problem;
step 34, firstly, solving the optimal spectrum sensing duration by using a binary search method, then solving the optimal phase shift matrix by using a semi-definite relaxation method and gaussian randomization, and finally solving the optimal leading unmanned aerial vehicle deployment position by using a continuous convex approximation function and a convex difference function, wherein the specific flow is as follows:
(1) Setting an initial spectrum sensing duration tau (0) Intelligent reflecting surface phase shift matrix theta (0) Leader drone's three-dimensional position
Figure BDA0003693222140000081
Iteration number l =1, auxiliary variable { u } 0 ,e 0 ,t 0 ,k 0 ,w 0 }, objective function value
Figure BDA0003693222140000082
And an iteration end threshold epsilon.
(2) Given a
Figure BDA0003693222140000083
And Θ (l-1) Calculating the optimal spectrum sensing time length
Figure BDA00036932221400000815
；
(3) Given the
Figure BDA0003693222140000084
And τ (l) Calculating the optimal phase shift matrix theta (l) ；
(4) Given Θ (l) ,τ (l) And { u } 0 ,e 0 ,t 0 ,k 0 ,w 0 Calculate { u }, calculate (l) ,e (l) ,t (l) ,k (l) ,w (l) } and optimal leader unmanned plane deployment position
Figure BDA0003693222140000085
(5) Updating the auxiliary variable: u. u 0 ＝u (l) ,e 0 ＝e (l) ,t 0 ＝t (l) ,k 0 ＝k (l) And w 0 ＝w (l) Updating the objective function value
Figure BDA0003693222140000086
(6) If it is
Figure BDA0003693222140000087
The iteration is terminated and output
Figure BDA0003693222140000088
If it is
Figure BDA0003693222140000089
The number of update iterations l = l +1 and jumps to step (2).
Further, in step 4, solving the optimization problem under multiple unmanned aerial vehicles through a design algorithm specifically comprises:
the optimization problem of the multiple unmanned aerial vehicles is solved by designing an achievable rate weighting sum algorithm and a position weighting sum algorithm, namely K >1,
the achievable rate weighting sum algorithm is specifically:
by weighting
Figure BDA00036932221400000810
The optimization problem can be restated as:
Figure BDA00036932221400000811
Figure BDA00036932221400000812
Figure BDA00036932221400000813
C 4 -C 6 ,
wherein
Figure BDA0003693222140000091
To follow the optimal objective function value, ω, under drone j j Is a weighting coefficient;
the position weighting sum algorithm specifically comprises:
to minimize
Figure BDA0003693222140000092
To each q Lj The Euclidean distance of (a) is,
Figure BDA0003693222140000093
can be obtained by weighting q Lj The method is specifically obtained as follows:
Figure BDA0003693222140000094
wherein q is Lj To follow the optimal leader drone position under drone j,
Figure BDA0003693222140000095
and leading the final position of the unmanned aerial vehicle under the position weighting and algorithm.
Further, when the main transmitter is in idle state and correctly sensed, the probability of the occurrence of the condition is P (H) 0 )(1-P f ) At this time, the transmission rate of the following unmanned plane j is
Figure BDA0003693222140000096
Wherein
Figure BDA0003693222140000097
The receiving signal-to-noise ratio of the leading unmanned aerial vehicle under the following unmanned aerial vehicle j is represented, and the specific calculation is as follows:
Figure BDA0003693222140000098
wherein, P F Indicating the transmit power of the following drone,
Figure BDA0003693222140000099
representing a phase-shift matrix that follows the smart reflective surface under drone j,
Figure BDA00036932221400000910
and representing a distance-dependent path loss model of the following unmanned plane j to the leading unmanned plane link through the intelligent reflecting surface.
Furthermore, when the main transmitter is in a busy state but is sensed by error, the detection probability needs to satisfy P d ≥P d0 In which P is d0 Is a predefined threshold for detection probability, the achievable rate of following a drone can be expressed as:
Figure BDA00036932221400000911
compared with the prior art, the invention has the beneficial effects that:
compared with the traditional unmanned aerial vehicle network, the intelligent reflecting surface and cognitive radio scheme is introduced, and the application scenes of multiple unmanned aerial vehicles are considered. Compared with the traditional optimization method, the invention provides a joint optimization method of sensing time length, a phase shift matrix of an intelligent reflecting surface and a three-dimensional deployment position of an unmanned aerial vehicle.
Firstly, the method for assisting the unmanned aerial vehicle by the intelligent reflecting surface can enhance the communication between the unmanned aerial vehicles and improve the uncontrollable propagation environment between the unmanned aerial vehicle and the receiving end in a favorable mode, thereby greatly improving the frequency spectrum efficiency.
Secondly, when the main network is in a busy state, the access of the unmanned aerial vehicle not only enables the data transmission rate of the unmanned aerial vehicle to be low, but also generates strong interference on a main user in the network; when the main network is in an idle state, the frequency spectrum of the unallocated traffic is also in the idle state, which causes a waste phenomenon of the frequency spectrum resources of the main network. The invention provides a cognitive radio technology applied to an unmanned aerial vehicle network, and the unmanned aerial vehicle can be accessed into the main network according to the sensing result of the state of the main network, so that the interference to a main user is controlled and the frequency spectrum resources are fully utilized.
And thirdly, when the number of the following unmanned aerial vehicles is more than 1, under different following unmanned aerial vehicles, the phase shift matrix of the intelligent reflecting surface and the position of the leading unmanned aerial vehicle need to be optimized simultaneously, so that the established optimization problem is difficult to solve. The reachable rate weighting and algorithm provided by the invention can equivalently convert the original optimization problem into a more manageable weighting and problem, so that the complexity of the reachable rate weighting and algorithm is further reduced.
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In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings needed to be used in the description of the embodiments will be briefly introduced below, and it is apparent that the drawings in the following description are only preferred embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained based on these drawings without inventive efforts.
Fig. 1 is a scene and frame structure schematic diagram of an unmanned aerial vehicle network of an intelligent reflector assisted cognitive unmanned aerial vehicle communication network design method provided by an embodiment of the present invention.
Fig. 2 is a schematic diagram of a relationship between an achievable rate and a transmission power of a following unmanned aerial vehicle in a single following unmanned aerial vehicle network according to the intelligent reflector-assisted cognitive unmanned aerial vehicle communication network design method provided by the embodiment of the present invention.
Fig. 3 is a schematic diagram illustrating a relationship between an achievable rate and a transmission power of a following unmanned aerial vehicle in a multi-following unmanned aerial vehicle network according to the method for designing an intelligent reflector-assisted cognitive unmanned aerial vehicle communication network provided by the embodiment of the present invention.
Detailed Description
The principles and features of this invention are described below in conjunction with the following drawings, which are set forth to illustrate the invention and are not intended to limit the scope of the invention.
Referring to fig. 1, the invention provides a method for designing an intelligent reflector assisted cognitive unmanned aerial vehicle communication network, comprising the following steps:
step 1, constructing an unmanned aerial vehicle system model, an unmanned aerial vehicle channel model and an unmanned aerial vehicle transmission model;
step 2, establishing an unmanned aerial vehicle optimization problem by determining objective functions and relevant constraints in an unmanned aerial vehicle system model, an unmanned aerial vehicle channel model and an unmanned aerial vehicle transmission model;
step 3, solving an optimization problem under a single unmanned aerial vehicle through an algorithm;
and 4, solving the optimization problem under the multiple unmanned aerial vehicles through a design algorithm.
In step 1, the construction of the model of the unmanned aerial vehicle system specifically comprises:
step 11, deploying M = M on the intelligent reflecting surface r ×M c A passive reflection component, wherein K lead unmanned aerial vehicle and one follow unmanned aerial vehicle and be the single antenna, main transmitter is the single antenna, passive reflection component arranges with even plane array, M r And M c The number of elements in each row and column of the intelligent reflecting surface is respectively, and the phase shift matrix of the intelligent reflecting surface is expressed as
Figure BDA0003693222140000111
Wherein
Figure BDA0003693222140000112
The frame is divided into a frequency spectrum sensing duration tau of the leading unmanned aerial vehicle and a data transmission duration T-tau of the following unmanned aerial vehicle, the following unmanned aerial vehicle adopts a time division multiplexing mode to transmit data in an uplink transmission process, and in a three-dimensional Cartesian coordinate system, a main transmitter, an intelligent reflecting surface and a jth following unmanned aerial vehicle are respectively fixed on q coordinate of the main transmitter, the intelligent reflecting surface and the jth following unmanned aerial vehicle in a three-dimensional Cartesian coordinate system P ＝[x P ,y P ,z P ] T 、q R ＝[x R ,y R ,z R ] T And
Figure BDA0003693222140000113
wherein
Figure BDA0003693222140000114
Representing a set of following drones, let q L ＝[x,y,z] T Leading unmanned aerial vehicle coordinates needing to be optimized;
illustratively, the positions of the intelligent reflective surface and the main emitter are fixed to [0,0 ] respectively,50] T And [130,0,10] T For a single-trailing drone scenario, the position of the trailing drone is fixed at [0,150,100] T For a scene with multiple following unmanned aerial vehicles, the following unmanned aerial vehicles are randomly distributed at 250 multiplied by 250m under the condition of safe obstacle avoidance distance 2 And hovers at a height of 100 meters. The monte carlo simulation runs 10000 times at different locations following the drone.
Other simulation parameters were set as follows: the frame duration T =20ms, the number K =4 of following unmanned aerial vehicles, the safe obstacle avoidance distance ζ =1, and the sampling frequency f s =1MHz, detection probability P d0 =0.95, main transmitter transmit power P T =30mw, probability of master transmitter idle state P (H) 0 ) =0.7, reference position d 0 =1 path loss ρ = -80dB, pathloss index α =2 for the intelligent reflector assisted link, pathloss index β =2 for the following drone to the leader drone, pathloss index μ =3 for the leader drone to the main transmitter, and noise power
Figure BDA0003693222140000121
In step 1, the channel model of the unmanned aerial vehicle is specifically constructed as follows:
step 12, a line-of-sight channel model and a free space path loss model are respectively adopted for the intelligent reflecting surface auxiliary link and the direct link, the intelligent reflecting surface auxiliary link comprises a link from the following unmanned aerial vehicle to the intelligent reflecting surface and a link from the intelligent reflecting surface to the leading unmanned aerial vehicle, wherein the gain of a channel from the following unmanned aerial vehicle j to the intelligent reflecting surface is represented as:
Figure BDA0003693222140000122
where ρ represents the reference distance d 0 A path loss at =1, a denotes a path loss exponent of the intelligent reflector auxiliary link,
Figure BDA0003693222140000123
indicating following unmanned plane j to intelligent reflecting surfaceThe distance between the first and second electrodes,
Figure BDA0003693222140000124
a deterministic line-of-sight channel component representing the link, wherein
Figure BDA0003693222140000125
And
Figure BDA0003693222140000126
respectively, the elevation angle and the azimuth angle of the j following unmanned aerial vehicle to the intelligent reflecting surface, and g (x, y) represents a view distance channel component function expressed as
Figure BDA0003693222140000127
Wherein d represents the spacing between two adjacent elements on the intelligent reflective surface, λ represents the carrier wavelength,
Figure BDA0003693222140000128
representing the kronecker product, the channel gain from the intelligent reflecting surface to the leading drone is represented as:
Figure BDA0003693222140000129
wherein d is RL ＝||q R -q L The | | represents the distance from the intelligent reflecting surface to the leader drone,
Figure BDA0003693222140000131
a deterministic line-of-sight channel component representing the link, wherein
Figure BDA00036932221400001310
And xi RL The elevation angle and the azimuth angle from the intelligent reflecting surface to the leading unmanned aerial vehicle are respectively represented, and for a direct link, namely a link from the following unmanned aerial vehicle j to the leading unmanned aerial vehicle and a link from the leading unmanned aerial vehicle to the main transmitter, the channel gain from the following unmanned aerial vehicle j to the leading unmanned aerial vehicle is represented as follows:
Figure BDA0003693222140000132
wherein
Figure BDA0003693222140000133
Representing the distance of the following drone j from the leader drone, k represents the corresponding path loss exponent, and the channel gain of the leader drone from the main transmitter is represented as:
Figure BDA0003693222140000134
wherein d is LP ＝||q L -q P | represents the distance from the leader drone to the main transmitter, μ represents the corresponding path loss exponent;
exemplarily, since the intelligent reflector and the unmanned aerial vehicle are both deployed at high altitude, and the air-to-ground and air-to-air wireless channels are dominated by line-of-sight links, it is assumed that the intelligent reflector auxiliary link and the direct link respectively adopt a line-of-sight channel model and a free space path loss model.
In step 1, the construction of the unmanned aerial vehicle transmission model specifically comprises:
step 13, setting P (H) 0 ) And P (H) 1 ) Respectively representing the probability of the main transmitter being in an idle and busy state, P d And P f Respectively representing detection and false alarm probabilities, at a given P d ，P f Can be expressed as
Figure BDA0003693222140000135
Wherein
Figure BDA0003693222140000136
The function of Q of a gaussian is represented,
Figure BDA0003693222140000137
f s which is indicative of the sampling frequency, is,
Figure BDA0003693222140000138
representing the signal-to-noise ratio of the leading drone receiving the primary transmitter signal, where P T Is the transmission power of the main transmitter and,
Figure BDA0003693222140000139
representing the noise power at the lead drone.
In step 2, the unmanned aerial vehicle optimization problem is constructed by determining objective functions and related constraints in an unmanned aerial vehicle system model, an unmanned aerial vehicle channel model and an unmanned aerial vehicle transmission model, and specifically comprises the following steps:
through the sensing time length tau of the leader unmanned aerial vehicle and the phase shift matrix theta of the intelligent reflecting surface j And a three-dimensional position q of the leader drone L Joint optimization, which maximizes the network reachable rate, the optimization problem can be expressed as:
Figure BDA0003693222140000141
s.t.C 1 :P d ≥P d0 ,
C 2 :(ω 2 /ω 1 ) 2 ≤τ≤T,
Figure BDA0003693222140000142
C 4 :||q L -q R || 2 ≥ζ 2 ,
C 5 :||q L -q P || 2 ≥ζ 2 ,
Figure BDA0003693222140000143
wherein, C 1 Representing a detection probability constraint, C 2 Representing a bounded perceptual time constraint, C 3 Representing the phase shift constraint of each reflective element on the intelligent reflective surface, where r,j Representing the r-th diagonal element following the phase shift matrix under drone j，C 4 -C 6 Represents a collision avoidance constraint for the lead drone, where ζ represents a minimum safe distance between the lead drone and the main transmitter, the intelligent reflective surface, and the following drone.
Solving the optimization problem under the single unmanned aerial vehicle through an algorithm specifically comprises the following steps:
decomposing the optimization problem of the single unmanned aerial vehicle into optimal values of three sub-problems by utilizing binary search, semi-definite relaxation, continuous convex approximation and convex difference, and then optimizing the three sub-problems alternately by an alternate iterative algorithm, namely K =1, until the algorithm converges, wherein the method comprises the following specific steps:
step 31, optimizing sensing duration tau of leading unmanned aerial vehicle
Given phase shift matrix Θ j And leader unmanned aerial vehicle three-dimensional position q L Then sub-problem of sensing time optimization
Figure BDA0003693222140000144
Can be expressed as:
Figure BDA0003693222140000145
s.t.C 2 ,
wherein
Figure BDA0003693222140000146
To analyze R j (τ) Properties, R j (τ) the second derivative with respect to τ is as follows:
Figure BDA0003693222140000147
wherein
Figure BDA0003693222140000148
Is analyzed by
Figure BDA0003693222140000149
Thus R j (τ) is a pseudo-concave function with respect to τ, which can be solved by a binary search methodJudging;
step 32, phase shift matrix theta of intelligent reflecting surface j Is optimized
Giving sensing duration tau and leading unmanned aerial vehicle three-dimensional position q L Sub-problem of phase-shift matrix optimization
Figure BDA0003693222140000151
It can be abbreviated as:
Figure BDA0003693222140000152
s.t.C 3
due to sub-problems
Figure BDA0003693222140000153
The constraint with a medium modulus value of 1 is non-convex, so a semi-definite relaxation technique is to be applied to relax the constraint, and the objective function is also transformed into the tracking problem, so the subproblems
Figure BDA0003693222140000154
Can be equivalently rewritten as:
Figure BDA0003693222140000155
s.t.V≥0,
V r,r ＝1,r＝1,2,…,M+1,
rank(V)＝1,
wherein Tr (-) denotes the trace of the matrix, V r,r The (r, r) bit elements of the matrix V are represented, and since the solution with rank one is difficult to obtain, the relaxed rank one constraint is selected, and the problem is a standard semi-definite programming problem and can be solved by a convex optimization tool CVX, and then, by using a gaussian randomization method, a phase shift vector V can be recovered from the solved V;
step 33, leading the three-dimensional position q of the drone L Optimization
Given a perceptual duration tau and a phase-shift matrix theta j Then lead to noneSub-problem of human-machine three-dimensional position optimization
Figure BDA0003693222140000156
It can be abbreviated as:
Figure BDA0003693222140000157
s.t.C 4 -C 6 ,
wherein C is 0 ＝P(H 0 )(T-τ)，
Figure BDA0003693222140000158
And
Figure BDA0003693222140000159
due to h RL With respect to the position variable q L Is complex and non-linear, which makes the position optimization difficult to design, for which the leader drone position variable at the (l-1) th iteration is used to approximate h of the l-th iteration RL Thus H is Q Is shown as
Figure BDA0003693222140000161
Consider the sub-problem
Figure BDA0003693222140000162
Is a non-convex optimization problem by introducing auxiliary variables
Figure BDA0003693222140000163
This non-convex problem can be equivalently converted into:
Figure BDA0003693222140000164
s.t log 2 (1+ρC 1 r d )≥w,
1-Q(h)≥k,
h≥0,
Figure BDA0003693222140000165
Figure BDA0003693222140000166
Figure BDA0003693222140000167
γ s ≥t,
Figure BDA0003693222140000168
Figure BDA0003693222140000169
C 4 -C 6 ,
converting the constraints into an upper mirror graph form, namely epi f = { (x, t) | x ∈ dom f, f (x) ≦ t }, wherein concave functions exist in the upper mirror graph forms of the constraints, and because concave functions exist in the upper mirror graph form of the constraints, the concave functions in the upper mirror graph form are expanded by one-order Taylor at feasible points by applying a continuous convex approximation method, so that the constraints are approximately converted into convex constraints, the constraints are converted into convex constraints by utilizing continuous convex approximation, the constraints can be converted into second-order cone constraints, and the second-order cone constraints can be converted into the following steps after convex difference and continuous convex approximation:
Figure BDA00036932221400001610
wherein k is 0 ，w 0 Given a feasible point, from which a sub-problem
Figure BDA00036932221400001715
Is converted into a convex problem;
step 34, firstly, solving the optimal spectrum sensing duration by using a binary search method, then solving the optimal phase shift matrix by using a semi-definite relaxation method and gaussian randomization, and finally solving the optimal deployment position of the leading unmanned aerial vehicle by using a continuous convex approximation function and a convex difference function, wherein the specific flow is as follows:
(1) Setting an initial spectrum sensing duration tau (0) Intelligent reflector phase shift matrix theta (0) Leader drone's three-dimensional position
Figure BDA0003693222140000171
Iteration number l =1, auxiliary variable { u } 0 ,e 0 ,t 0 ,k 0 ,w 0 Value of objective function
Figure BDA0003693222140000172
And an iteration end threshold epsilon.
(2) Given a
Figure BDA0003693222140000173
And Θ (l-1) Calculating the optimal spectrum sensing duration
Figure BDA00036932221400001716
；
(3) Given the
Figure BDA0003693222140000174
And τ (l) Calculating the optimal phase shift matrix theta (l) ；
(4) Given Θ (l) ,τ (l) And { u 0 ,e 0 ,t 0 ,k 0 ,w 0 Calculate { u }, calculate (l) ,e (l) ,t (l) ,k (l) ,w (l) } and optimal leader unmanned plane deployment position
Figure BDA0003693222140000175
(5) Updating the auxiliary variable: u. of 0 ＝u (l) ,e 0 ＝e (l) ,t 0 ＝t (l) ,k 0 ＝k (l) And w 0 ＝w (l) Updating the objective function value
Figure BDA0003693222140000176
(6) If it is
Figure BDA0003693222140000177
The iteration is terminated and output
Figure BDA0003693222140000178
If it is
Figure BDA0003693222140000179
The number of update iterations l = l +1 and jumps to step (2).
In step 4, solving the optimization problem under multiple unmanned aerial vehicles through a design algorithm specifically comprises:
the optimization problem of the multiple unmanned aerial vehicles is solved by designing an achievable rate weighting sum algorithm and a position weighting sum algorithm, namely K >1,
the achievable rate weighting sum algorithm is specifically:
by weighting
Figure BDA00036932221400001710
The optimization problem can be restated as:
Figure BDA00036932221400001711
Figure BDA00036932221400001712
Figure BDA00036932221400001713
C 4 -C 6 ,
wherein
Figure BDA00036932221400001714
For following the optimal objective function under unmanned plane jValue, ω j Is a weighting coefficient;
the position weighting sum algorithm specifically comprises:
to minimize
Figure BDA0003693222140000181
To each q Lj The Euclidean distance of (a) is,
Figure BDA0003693222140000182
can be obtained by weighting q Lj The method is specifically obtained as follows:
Figure BDA0003693222140000183
wherein q is Lj To follow the optimal leader drone position under drone j,
Figure BDA0003693222140000184
and leading the final position of the unmanned aerial vehicle under the position weighting and algorithm.
When the main transmitter is in idle state and correctly sensed, the probability of the situation is P (H) 0 )(1-P f ) At this time, the transmission rate of the following unmanned plane j is
Figure BDA0003693222140000185
Wherein
Figure BDA0003693222140000186
The receiving signal-to-noise ratio of the leading unmanned aerial vehicle under the following unmanned aerial vehicle j is represented, and the specific calculation is as follows:
Figure BDA0003693222140000187
wherein, P F Indicating the transmit power of the following drone,
Figure BDA0003693222140000188
representing a phase shift matrix that follows the intelligent reflective surface under drone j,
Figure BDA0003693222140000189
and representing a distance-dependent path loss model of the following unmanned plane j to the leading unmanned plane link through the intelligent reflecting surface.
When the main transmitter is in busy state but is sensed wrongly, the detection probability needs to satisfy P d ≥P d0 In which P is d0 Is a predefined threshold for detection probability, the achievable rate of following a drone can be expressed as:
Figure BDA00036932221400001810
illustratively, to further reduce the complexity of the reachable rate weighting sum algorithm, the present application further provides a low-complexity location weighting sum algorithm, where the flow of the weighting sum algorithm implementation is specifically as follows:
(1) Inputting the optimal objective function value and the optimal leading unmanned aerial vehicle position under each following unmanned aerial vehicle:
Figure BDA00036932221400001811
(2) Calculating suboptimal solution tau, q under reachable rate weighting sum algorithm L And Θ j And an objective function value R.
(3) Calculating a suboptimal solution of the position of the leader unmanned aerial vehicle under the position weighting sum algorithm
Figure BDA00036932221400001812
(4) Given the
Figure BDA0003693222140000191
By passing
Figure BDA0003693222140000193
And
Figure BDA0003693222140000194
respectively calculate tau opt And τ opt 。
(5) Given a
Figure BDA0003693222140000192
τ opt And τ opt And then the objective function value R is calculated.
Illustratively, fig. 2 shows the variation of the reachable rate with the transmission power of the following drone in the network of single following drones, and it can be seen from fig. 2 that the transmission power P with the following drones F The achievable rates are all increased, more importantly, at P F =0.3w, the achievable rate is improved by about 95% compared with the scheme without the aid of the intelligent reflector, which further proves that the aid of the intelligent reflector can greatly improve the performance of the unmanned aerial vehicle network.
Illustratively, fig. 3 shows the variation of the achievable rate with the transmission power of the following drones in a network of multiple following drones. As can be seen from fig. 3, no matter the position weighted sum algorithm or the reachable rate weighted sum algorithm, the reachable rate of the present application without the assistance of the intelligent reflector follows the transmitting power P of the drone F Is increased. More importantly, at the transmission power P, compared with the assistance of no intelligent reflector F At the position of =0.3w, the achievable rate of the application is improved by more than 60%. In addition, the achievable rate weighting sum algorithm performs slightly better than the position weighting sum algorithm. When P is F When the power consumption is not larger than 0.3w, the achievable rate of the application is remarkably improved; the performance penalty of the low complexity position weighted sum algorithm is small compared to the achievable rate weighted sum algorithm.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.

Claims (7)

1. The intelligent reflector assisted cognitive unmanned aerial vehicle communication network design method is characterized by comprising the following steps:
step 1, constructing an unmanned aerial vehicle system model, an unmanned aerial vehicle channel model and an unmanned aerial vehicle transmission model;
step 2, establishing an unmanned aerial vehicle optimization problem by determining objective functions and relevant constraints in an unmanned aerial vehicle system model, an unmanned aerial vehicle channel model and an unmanned aerial vehicle transmission model;
step 3, solving an optimization problem under a single unmanned aerial vehicle through an algorithm;
and 4, solving the optimization problem under the multiple unmanned aerial vehicles through a design algorithm.
2. The intelligent reflector assisted cognitive unmanned aerial vehicle communication network design method according to claim 1, wherein in step 1, building an unmanned aerial vehicle system model specifically comprises:
step 11, deploying M = M on the intelligent reflecting surface r ×M c A passive reflection component, wherein K lead unmanned aerial vehicle and one follow unmanned aerial vehicle are the single antenna, and main transmitter is the single antenna, and passive reflection component arranges with even plane array, M r And M c The number of elements in each row and column of the intelligent reflecting surface is respectively, and the phase shift matrix of the intelligent reflecting surface is expressed as
Figure FDA0003693222130000011
Wherein
Figure FDA0003693222130000012
The phase shift value of the mth reflecting element is represented, the frame is divided into a leader unmanned aerial vehicle frequency spectrum sensing duration tau and a following unmanned aerial vehicle data transmission duration T-tau, the following unmanned aerial vehicle adopts a time division multiplexing mode to transmit data in an uplink transmission process, and in a three-dimensional Cartesian coordinate system, a main transmitter, an intelligent reflecting surface and a jth following unmanned aerial vehicle coordinate are respectively fixed on q P ＝[x P ,y P ,z P ] T 、q R ＝[x R ,y R ,z R ] T And
Figure FDA0003693222130000013
wherein
Figure FDA0003693222130000014
Representing a set of following drones, let q L ＝[x,y,z] T Leading unmanned aerial vehicle coordinates needing to be optimized;
in step 1, the channel model of the unmanned aerial vehicle is specifically constructed as follows:
step 12, a line-of-sight channel model and a free space path loss model are respectively adopted for the intelligent reflector auxiliary link and the direct link, the intelligent reflector auxiliary link comprises a link from the following unmanned aerial vehicle to the intelligent reflector and a link from the intelligent reflector to the leading unmanned aerial vehicle, wherein channel gains from the following unmanned aerial vehicle j to the intelligent reflector are expressed as:
Figure FDA0003693222130000021
where ρ represents a reference distance d 0 =1, α represents the path loss exponent of the intelligent reflector auxiliary link,
Figure FDA0003693222130000022
indicating the distance from the following drone j to the intelligent reflective surface,
Figure FDA0003693222130000023
a deterministic line-of-sight channel component representing the link, wherein
Figure FDA0003693222130000024
And
Figure FDA0003693222130000025
respectively, the elevation and azimuth angles of the intelligent reflecting surface following the unmanned plane j, and g (x, y) represents the function of the line-of-sight channel component expressed as
Figure FDA0003693222130000026
Wherein d represents the Smart inverseThe spacing of two adjacent elements on the incident plane, λ represents the carrier wavelength,
Figure FDA0003693222130000027
representing the kronecker product, the channel gain from the intelligent reflecting surface to the leading drone is represented as:
Figure FDA0003693222130000028
wherein d is RL ＝||q R -q L | | represents the distance from the intelligent reflecting surface to the leading drone,
Figure FDA0003693222130000029
a deterministic line-of-sight channel component representing the link, where θ RL And xi RL The elevation angle and the azimuth angle from the intelligent reflecting surface to the leading unmanned aerial vehicle are respectively represented, and for a direct link, namely a link from the following unmanned aerial vehicle j to the leading unmanned aerial vehicle and a link from the leading unmanned aerial vehicle to the main transmitter, the channel gain from the following unmanned aerial vehicle j to the leading unmanned aerial vehicle is represented as follows:
Figure FDA00036932221300000210
wherein
Figure FDA00036932221300000211
Representing the distance of the following drone j from the leader drone, k represents the corresponding path loss exponent, and the channel gain of the leader drone from the main transmitter is represented as:
Figure FDA00036932221300000212
wherein d is LP ＝||q L -q P | | represents the distance from the leading drone to the primary transmitter, μ represents the corresponding path loss exponent;
in step 1, the construction of the unmanned aerial vehicle transmission model specifically comprises:
step 13, setting P (H) 0 ) And P (H) 1 ) Respectively representing the probability of the main transmitter being in idle and busy states, P d And P f Respectively representing detection and false alarm probabilities, at a given P d ，P f Can be expressed as
Figure FDA0003693222130000031
Wherein
Figure FDA0003693222130000032
The function of the gaussian Q is represented by,
Figure FDA0003693222130000033
f s which is indicative of the sampling frequency, is,
Figure FDA0003693222130000034
representing the signal-to-noise ratio of the leading drone receiving the primary transmitter signal, where P T Is the transmission power of the main transmitter,
Figure FDA0003693222130000035
representing the noise power at the leading drone.
3. The intelligent reflector assisted cognitive unmanned aerial vehicle communication network design method of claim 2, wherein in step 2, constructing the unmanned aerial vehicle optimization problem by determining objective functions and related constraints in an unmanned aerial vehicle system model, an unmanned aerial vehicle channel model and an unmanned aerial vehicle transmission model is specifically:
through the sensing time length tau of the leader unmanned aerial vehicle and the phase shift matrix theta of the intelligent reflecting surface j And a three-dimensional position q of the leading drone L Joint optimization, which maximizes the network reachable rate, the optimization problem can be expressed as:
Figure FDA0003693222130000036
s.t.C 1 :P d ≥P d0 ,
C 2 :(ω 2 /ω 1 ) 2 ≤τ≤T,
Figure FDA0003693222130000037
C 4 :||q L -q R || 2 ≥ζ 2 ,
C 5 :||q L -q P || 2 ≥ζ 2 ,
Figure FDA0003693222130000038
wherein, C 1 Representing a detection probability constraint, C 2 Representing a bounded perceptual time constraint, C 3 Representing the phase shift constraint of each reflective element on the intelligent reflective surface, where r,j Denotes the r-th diagonal element, C, following the phase shift matrix under drone j 4 -C 6 Represents a collision avoidance constraint for the lead drone, where ζ represents a minimum safe distance between the lead drone and the main transmitter, the intelligent reflective surface, and the following drone.
4. The intelligent reflector assisted cognitive unmanned aerial vehicle communication network design method according to claim 3, wherein the optimization problem under a single unmanned aerial vehicle solved by an algorithm is specifically:
decomposing the optimization problem of the single unmanned aerial vehicle into optimal values of three sub-problems by utilizing binary search, semi-definite relaxation, continuous convex approximation and convex difference, and then optimizing the three sub-problems by an alternating iterative algorithm, namely K =1, until the algorithm is converged, wherein the method comprises the following specific steps:
step 31, leading the optimization of the sensing time length tau of the unmanned aerial vehicle
Given a phase shift matrix Θ j And leader unmanned aerial vehicleThree-dimensional position q L Then sub-problem of sensing duration optimization
Figure FDA0003693222130000041
Can be expressed as:
Figure FDA0003693222130000042
Figure FDA0003693222130000043
s.t.C 2 ,
wherein
Figure FDA0003693222130000044
For analysis of R j (τ) Properties, R j (τ) the second derivative with respect to τ is as follows:
Figure FDA0003693222130000045
wherein
Figure FDA0003693222130000046
Analyzed by
Figure FDA0003693222130000047
Thus R is j (τ) is a pseudo-concave function with respect to τ, which can be solved by a binary search method;
step 32, phase shift matrix theta of intelligent reflecting surface j Is optimized
Giving sensing duration tau and leading unmanned aerial vehicle three-dimensional position q L Sub-problem of phase-shift matrix optimization
Figure FDA0003693222130000048
Can be abbreviated as:
Figure FDA0003693222130000049
Figure FDA00036932221300000410
s.t.C 3
due to sub-problems
Figure FDA00036932221300000411
The constraint with a medium modulus value of 1 is non-convex, so a semi-definite relaxation technique is to be applied to relax the constraint, and the objective function is also transformed into the tracking problem, so the subproblems
Figure FDA00036932221300000412
Can be equivalently rewritten as:
Figure FDA00036932221300000413
s.t.V≥0,
V r,r ＝1,r＝1,2,…,M+1,
rank(V)＝1,
wherein Tr (-) denotes the trace of the matrix, V r,r The (r, r) bit elements of the matrix V are represented, and since the solution with rank one is difficult to obtain, the relaxed rank one constraint is selected, and the problem is a standard semi-definite programming problem and can be solved by a convex optimization tool CVX, and then, by using a gaussian randomization method, a phase shift vector V can be recovered from the solved V;
step 33, leading the three-dimensional position q of the drone L Optimization of
Given a perceptual duration tau and a phase-shift matrix theta j And then leader of the sub-problem of three-dimensional position optimization of the unmanned aerial vehicle
Figure FDA00036932221300000512
Can be abbreviated as:
Figure FDA0003693222130000051
Figure FDA0003693222130000052
s.t.C 4 -C 6 ,
wherein C 0 ＝P(H 0 )(T-τ)，
Figure FDA0003693222130000053
And
Figure FDA0003693222130000054
due to h RL With respect to the position variable q L Is complex and non-linear, which makes the position optimization difficult to design, for which the leader drone position variable at the (l-1) th iteration is used to approximate h of the l-th iteration RL Thus H is Q Is shown as
Figure FDA0003693222130000055
Consider the subproblem
Figure FDA0003693222130000056
Is a non-convex optimization problem by introducing auxiliary variables
Figure FDA0003693222130000057
This non-convex problem can be equivalently translated into:
Figure FDA0003693222130000058
s.t log 2 (1+ρC 1 r d )≥w,
1-Q(h)≥k,
h≥0,
Figure FDA0003693222130000059
Figure FDA00036932221300000510
Figure FDA00036932221300000511
γ s ≥t,
Figure FDA0003693222130000061
Figure FDA0003693222130000062
C 4 -C 6 ,
converting the constraints into an upper mirror graph form, namely epi f = { (x, t) | x ∈ domf, f (x) ≦ t }, wherein concave functions exist in the upper mirror graph forms of the constraints, and the concave functions in the upper mirror graph form are expanded in a first order Taylor mode at feasible points by applying a continuous convex approximation method, so that the constraints are approximately converted into convex constraints, the convex constraints are converted into continuous convex approximations, the constraints can be converted into second-order cone constraints, and the second-order cone constraints can be converted into the following steps after convex difference and continuous convex approximations:
Figure FDA0003693222130000063
wherein k is 0 ，w 0 Given a feasible point, thereby, a sub-problem
Figure FDA0003693222130000064
Is converted into a convex problem;
step 34, firstly, solving the optimal spectrum sensing duration by using a binary search method, then solving the optimal phase shift matrix by using a semi-definite relaxation method and gaussian randomization, and finally solving the optimal deployment position of the leading unmanned aerial vehicle by using a continuous convex approximation function and a convex difference function, wherein the specific flow is as follows:
(1) Setting an initial spectrum sensing duration tau (0) Intelligent reflecting surface phase shift matrix theta (0) Leader drone's three-dimensional position
Figure FDA0003693222130000065
Iteration number l =1, auxiliary variable { u } 0 ,e 0 ,t 0 ,k 0 ,w 0 Value of objective function
Figure FDA0003693222130000066
And an iteration end threshold epsilon.
(2) Given a
Figure FDA0003693222130000067
And Θ (l-1) And calculating the optimal spectrum sensing time length tau (l) ；
(3) Given the
Figure FDA0003693222130000068
And τ (l) Calculating the optimal phase shift matrix theta (l) ；
(4) Given Θ (l) ,τ (l) And { u } 0 ,e 0 ,t 0 ,k 0 ,w 0 Calculate { u }, calculate (l) ,e (l) ,t (l) ,k (l) ,w (l) } and optimal leader unmanned plane deployment position
Figure FDA0003693222130000069
(5) Updating the auxiliary variable: u. u 0 ＝u (l) ,e 0 ＝e (l) ,t 0 ＝t (l) ,k 0 ＝k (l) And w 0 ＝w (l) Updating the object letterNumerical value
Figure FDA00036932221300000610
(6) If it is
Figure FDA00036932221300000611
The iteration is terminated and output
Figure FDA00036932221300000612
If it is
Figure FDA00036932221300000613
The number of update iterations l = l +1 and jumps to step (2).
5. The intelligent reflector assisted cognitive unmanned aerial vehicle communication network design method according to claim 4, wherein in step 4, solving the optimization problem under multiple unmanned aerial vehicles through a design algorithm specifically comprises:
the optimization problem of the multiple unmanned aerial vehicles is solved by designing an achievable rate weighting sum algorithm and a position weighting sum algorithm, namely K >1,
the achievable rate weighting sum algorithm is specifically:
by weighting
Figure FDA0003693222130000071
The optimization problem can be restated as:
Figure FDA0003693222130000072
Figure FDA0003693222130000073
Figure FDA0003693222130000074
C 4 -C 6 ,
wherein
Figure FDA0003693222130000075
To follow the optimal objective function value, ω, under drone j j Is a weighting coefficient;
the position weighting sum algorithm is specifically as follows:
to minimize
Figure FDA0003693222130000076
To each q Lj The euclidean distance of (c) is,
Figure FDA0003693222130000077
can be obtained by weighting q Lj The method is specifically obtained as follows:
Figure FDA0003693222130000078
wherein q is Lj To follow the optimal leader drone position under drone j,
Figure FDA0003693222130000079
and leading the final position of the unmanned aerial vehicle under the position weighting and algorithm.
6. The method as claimed in claim 2, wherein when the main transmitter is in idle state and correctly sensed, the probability of occurrence of the situation is P (H) 0 )(1-P f ) At this time, the transmission rate of the following drone j is
Figure FDA00036932221300000710
Wherein
Figure FDA00036932221300000711
Show following the leader under unmanned plane jThe receiving signal-to-noise ratio of the unmanned aerial vehicle is specifically calculated as follows:
Figure FDA0003693222130000081
wherein, P F Indicating the transmit power of the following drone,
Figure FDA0003693222130000082
representing a phase-shift matrix that follows the smart reflective surface under drone j,
Figure FDA0003693222130000083
and the distance-dependent path loss model represents the distance from the following unmanned aerial vehicle j to the leading unmanned aerial vehicle link through the intelligent reflecting surface.
7. The design method of intelligent reflector assisted cognitive unmanned aerial vehicle communication network according to claim 2, wherein when the main transmitter is in busy state but is sensed wrongly, the detection probability needs to satisfy P d ≥P d0 In which P is d0 Is a predefined threshold for detection probability, the achievable rate of following the drone can be expressed as:
Figure FDA0003693222130000084
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CN116074848A (en) * 2023-04-04 2023-05-05 南京邮电大学 Reconfigurable intelligent surface-assisted cognitive transmission time slot allocation method

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