A joint optimization method for obstacle-assisted UAV covert communication in three-dimensional urban environment

Abstract

The present invention discloses a joint optimization method for obstacle-assisted covert communication of unmanned aerial vehicles (UAVs) in a three-dimensional urban environment, comprising the following steps: (1) designing an urban communication environment with obstacles; (2) setting parameters of the UAV and the environment and their ranges; channel modeling; (3) calculating the optimal flight position and transmission power of the UAV using a joint optimization method based on the channel modeling; including: testing a binary hypothesis of the eavesdropper Willie; obtaining the monotonicity relationship of the objective function to the spatial position variable by solving the SNR function of the receiver Bob; converting the monotonicity relationship into a mathematical problem and solving it; the present invention can better utilize the performance of the UAV and the resources of the dispatching communication system, and is suitable for the application of UAV covert communication in actual urban environments.

Description

Technical Field

[0001] The present invention relates to the field of communication and information engineering technology, and in particular to an obstacle-assisted unmanned aerial vehicle covert communication joint optimization method for a three-dimensional urban environment. Background Art

[0002] With the development of UAV communication technology and the increasing prominence of wireless communication information security issues in urban environments, it has become necessary to study the joint optimization method of UAV covert communication in three-dimensional urban environments.

[0003] In terms of urban ground-to-air channels, there are various interfering objects in the urban environment, such as tall and stationary buildings, moving pedestrians and vehicles, and obstacles with irregular shapes and irregular motion trajectories. Therefore, it is often necessary to introduce scatterers to simulate complex communication scenarios in the urban environment. Basic urban channel modeling is an extension of the basic channel fading model. The Clark model, which is extended from the Rayleigh fading channel, is suitable for urban areas.

[0004] Covert communication aims to hide the existence of the signal transmitter (usually denoted as Alice) transmitting to the legitimate user (usually denoted as Bob) without being detected by the monitor (usually denoted as Willie), thereby meeting higher confidentiality and security protection requirements.

[0005] In terms of UAV covert communication, when performing confidential missions, UAVs can be used as air base stations to maintain emergency connections with existing ground users. The concealment of the ground-to-air communication system can be improved through optimization of UAV trajectory and communication. In addition, UAVs can also be used as relay receivers. Since the Line-of-Sight (LoS) link has a low transmission power requirement, it is conducive to covert communication. Therefore, it is particularly important to design a reasonable optimization algorithm considering various factors that affect the performance of UAV covert communication, such as UAV trajectory, transmission power, user scheduling, and jammers. Summary of the invention

[0006] Purpose of the invention: The purpose of the present invention is to provide an obstacle-assisted UAV covert communication joint optimization method for three-dimensional urban environments, aiming to jointly optimize the flight position and signal transmission power of the UAV, so as to improve the communication quality of wireless communication between the UAV and the receiver while ensuring concealment, thereby solving the problem of low signal-to-noise ratio at the receiver in traditional covert communication scenarios.

[0007] Technical solution: The obstacle-assisted UAV covert communication joint optimization method for a three-dimensional urban environment described in the present invention comprises the following steps:

[0008] (1) Designing an urban communication environment with obstacles;

[0009] (2) Setting UAV and environment parameters and their ranges; channel modeling;

[0010] (3) Based on channel modeling, the optimal flight position and transmission power of the UAV are calculated using a joint optimization method; including: binary hypothesis testing for the eavesdropper Willie; obtaining the monotonicity of the objective function on the spatial position variable by solving the SNR function of the receiver Bob; converting the monotonicity into a mathematical problem and solving it.

[0011] Furthermore, step (2) is as follows: Assume that the distance between the legitimate receiver Bob and the eavesdropper Willie is , the distances between drone Alice and the legitimate receiver Bob and eavesdropper Willie are , ; The azimuths of drone Alice to the legitimate receiver Bob and eavesdropper Willie are and ; The angle between the vertical plane where the drone Alice and the eavesdropper Willie are located and the vertical plane where the legal receiver Bob and the eavesdropper Willie are located is ; The variances of the additive white Gaussian noise signal AWGN at the legitimate receiver Bob and the eavesdropper Willie are , ; The signal transmission power of the drone is , the path loss of the LoS channel is ;

[0012] Suppose that the obstacles near the eavesdropper Willie are Abstracted in space, it is a linear body with no thickness or width but only height, and is perpendicular to the horizontal plane; let its height be , the angle between the highest point and the horizontal plane of the line connecting the eavesdropper Willie is , the angle between its horizontal projection and the line connecting the eavesdropper Willie and the plumb plane where the legal receiver Bob and the eavesdropper Willie are located is ;

[0013] Alice's position in three-dimensional space is determined by be uniquely identified; , , The possible regions where Alice's optimal position can exist are restricted as follows:

[0014] (S1) : Drone Alice cannot fly too close to the eavesdropper Willie to prevent being detected by radar or observed by human eyes. There is a minimum distance limit Due to the limited resolution of the drone, in order to better monitor the area where the eavesdropper Willie is located, there is a maximum distance limit. ;

[0015] (S2) :UAV Alice needs to have an acceptable viewing angle of the monitoring area, thus requiring Cannot be too small, there is a minimum angle limit ;

[0016] (S3) :UAV Alice flies away from the vertical plane where the legitimate receiver Bob and the eavesdropper Willie are located, through Uniquely determine the position of the drone Alice in three-dimensional space; due to symmetry, only consider Half of the three-dimensional space;

[0017] (S4) : The drone can adjust the signal transmission power, and its maximum transmission power is ;

[0018] (S5) : The distance between the drone and the receiver is greater than the distance between the drone and the eavesdropper; among them, is a very small angle, so the above equation always holds true.

[0019] Furthermore, in step (2), the channel modeling formula is as follows:

[0020] set up is the additional path loss coefficient of the NLoS channel; Less than 1; is a random variable that follows a Rayleigh distribution, Less than 1; Since the environment near Willie does not change with time, As an environmental parameter close to Willie , is a constant; then the average intensity is After the signal is scattered by the scatterers around Willie, the average intensity that finally reaches Willie is:

[0021] ;

[0022] in, It is the average strength of the wireless signal transmitted from the UAV to the monitor when obstacles block the air-to-ground line-of-sight communication link; The average strength of the wireless signal transmitted by the drone to the scatterers around the monitor; is the line-of-sight channel probability between the UAV and the monitor, which is given by the line-of-sight channel probability formula, is the path loss index of the line-of-sight channel;

[0023] satisfy:

[0024] ;

[0025] If Alice is Inside, there are:

[0026] ;

[0027] in, By obstacles M and the two-dimensional plane determined by the monitor Willie;

[0028] If Alice is not here If M has no significant effect on the probabilistic LoS channel between Alice and Willie, then:

[0029] .

[0030] Furthermore, in step (3), the binary hypothesis test for the eavesdropper Willie is as follows: There is no behavior of drones transmitting signals; There is an act of drone transmitting signals; among them, the event Correspondingly, Willie believes that the received signal strength is ,event Correspondingly, Willie believes that the received signal strength is , every time Willie makes a judgment, and Choose between the two times, where the prior probabilities of the two times are the same; let the probability of Willie's misdetection be , the false positive behavior includes Alice not transmitting a signal and Willie choosing to accept the hypothesis Alice is transmitting and Willie chooses to accept the hypothesis ;

[0031] Assume that the privacy required by Alice's covert communication is ,in, is a Small positive number in the range; in any case Not less than ;set up The minimum value of , then the following formula holds: ;

[0032] in, In binary hypothesis testing, the probability of Willie's false positive is The minimum probability of Willie's false positive in binary hypothesis testing; The value is given by the likelihood function, which is transformed into a stricter constraint by the KL divergence, as follows: ;

[0033] Right now ;

[0034] in, For binary hypothesis testing, right Information entropy of is used to quantify the concealment;

[0035] in, ;

[0036] Where n is the maximum block length.

[0037] Furthermore, in step (3), the monotonicity relationship of the objective function to the spatial position variable is obtained by solving the SNR function of the receiver Bob, as follows: The signal-to-noise ratio function at the legitimate receiver Bob is:

[0038] ;

[0039] in, The distance between drone Alice and eavesdropper Willie, The elevation angle between drone Alice and eavesdropper Willie, The azimuth between drone Alice and eavesdropper Willie, The distance between the legitimate receiver Bob and the eavesdropper Willie;

[0040] According to geometric relations and formulas: in, a and b is the S-curve parameter that depends on the communication environment and is determined by the building density and average height in the urban environment. Enter the angle value; we get:

[0041] ;

[0042] in, The distance between drone Alice and eavesdropper Willie, The elevation angle between drone Alice and eavesdropper Willie, The azimuth between drone Alice and eavesdropper Willie, The distance between the legitimate receiver Bob and the eavesdropper Willie; Taking partial derivative, we get right It increases first and then decreases, and has a unique maximum point; it is recorded as , the following conditions are met:

[0043] ;

[0044] Its exact value is determined by the following formula:

[0045] ;

[0046] right Taking partial derivative, we get hour right It increases first and then decreases, and has a unique maximum point, which is recorded as , the following conditions are met:

[0047] in:

[0048] The exact value is determined by:

[0049] ;

[0050] when hour, right Monotonically increasing.

[0051] Furthermore, in step (3), the monotonicity relationship is converted into a mathematical problem and solved as follows: first, the dimension of the feasible domain of the UAV is reduced, and then after the dimension reduction of the feasible domain, the optimization problem can be converted into a mathematical description, and the mathematical description is solved, wherein the mathematical description formula is as follows:

[0052] .

[0053] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages: Actively utilizing urban ground obstacles to design an example of a joint optimization method for the flight position and transmission power of a UAV. In the ground-to-air channel modeling part of a UAV in a three-dimensional urban environment, the present invention innovatively introduces an obstacle model into the traditional model and integrates the Rayleigh fading channel to describe the channel characteristics of a complex urban environment, overcoming the problem of poor accuracy of the traditional channel model in an urban environment, and being able to better utilize the performance of the UAV and the resources of the dispatching communication system, which is suitable for the application of UAV covert communication in an actual urban environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 A flow chart for designing the urban ground-to-air channel model of the present invention;

[0055] Figure 2 It is a schematic diagram of the urban ground-to-air channel model of the present invention;

[0056] Figure 3 A schematic diagram of the UAV flight area in a three-dimensional free space of the present invention;

[0057] Figure 4 It is a schematic diagram of the two-dimensional feasible domain of the UAV flight feasible domain after dimensionality reduction of the present invention;

[0058] Figure 5 The Clarke model schematic diagram of the present invention;

[0059] Figure 6 It is a transmission flow chart of the signal transmitted by the UAV of the present invention;

[0060] Figure 7 This is a schematic diagram of further narrowing the two-dimensional feasible domain of the UAV of the present invention;

[0061] Figure 8 It is a flow chart of the present invention. DETAILED DESCRIPTION

[0062] The technical solution of the present invention is further described below in conjunction with the accompanying drawings.

[0063] like Figure 8 As shown, an embodiment of the present invention provides an obstacle-assisted UAV covert communication joint optimization method for a three-dimensional urban environment, comprising the following steps:

[0064] Step 1: Design the urban ground-to-air channel model as follows:

[0065] (11) Designing a hidden communication environment in an urban area with obstacles, such as Figure 1As shown in the figure, the details are as follows: The traditional three-point model of UAV covert communication includes the UAV Alice, the legal receiver Bob, and the eavesdropper Willie. Alice, Bob, and Willie are all equipped with a single antenna. Alice attempts to secretly transmit signals to Bob in real time and continuously without Willie discovering the occurrence of this behavior. Willie determines whether the UAV's monitoring behavior is occurring by detecting whether the signal-to-noise ratio it receives is abnormal. Bob requires that the highest possible signal-to-noise ratio be received to ensure reliable communication quality. Bob and Willie are both ground receivers, and their activity ranges are known and can be regarded as fixed points. Alice can clarify or change their positions in real time through means such as GPS, and assumes that the frequency of the radio wave signals it transmits is fixed in a short time. In traditional scenarios, fixed ground obstacles are introduced to simulate urban environments, such as Figure 2 As shown in the figure, typical tall buildings in the city are considered as fixed ground obstacles in the urban ground-to-air channel model. The width of these obstacles ranges from a few meters to tens of meters, and the length ranges from more than ten meters to hundreds of meters. The common frequencies of radio waves emitted by drones are 2.4GHz, 5.8GHz, etc., and the corresponding wavelengths are 5.2cm and 12.5cm, which are much smaller than the size of the above obstacles. The radio waves emitted by drones are difficult to diffract these obstacles, that is, these obstacles can cut off the drone's ground-to-air line-of-sight (LoS) channel.

[0066] (12) Set the drone and environment parameters and their ranges as follows: Assume that the distance between the legitimate receiver Bob and the eavesdropper Willie is , the distances between drone Alice and the legitimate receiver Bob and eavesdropper Willie are , ; The azimuths of drone Alice to the legitimate receiver Bob and eavesdropper Willie are and ; The angle between the plumb plane where the drone Alice and the eavesdropper Willie are located and the plumb plane where the legal receiver Bob and the eavesdropper Willie are located is ; The variances of the additive white Gaussian noise signal AWGN at the legitimate receiver Bob and the eavesdropper Willie are , ; The signal transmission power of the drone is , the path loss of the LoS channel is ;

[0067] Suppose that the obstacles near the eavesdropper Willie are Abstracted in space, it is a linear body with no thickness or width but only height, and is perpendicular to the horizontal plane; let its height be , the angle between the highest point and the horizontal plane of the line connecting the eavesdropper Willie is , the angle between its horizontal projection and the line connecting the eavesdropper Willie and the plumb plane where the legal receiver Bob and the eavesdropper Willie are located is ;

[0068] Alice's position in three-dimensional space is determined by be uniquely identified; , , Limit the possible area where Alice's optimal position can exist, such as Figure 3 As shown, the details are as follows:

[0069] (S1) : Drone Alice cannot fly too close to the eavesdropper Willie to prevent being detected by radar or observed by human eyes. There is a minimum distance limit Due to the limited resolution of the drone, in order to better monitor the area where the eavesdropper Willie is located, there is a maximum distance limit. ;

[0070] (S2) :UAV Alice needs to have an acceptable viewing angle of the monitoring area, thus requiring Cannot be too small, there is a minimum angle limit ;

[0071] (S3) :UAV Alice flies away from the vertical plane where the legitimate receiver Bob and the eavesdropper Willie are located, through Uniquely determine the position of the drone Alice in three-dimensional space; due to symmetry, only consider Half of the three-dimensional space;

[0072] (S4) : The drone can adjust the signal transmission power, and its maximum transmission power is ;

[0073] (S5) : The distance between the drone and the receiver is greater than the distance between the drone and the eavesdropper; among them, is a very small angle, so the above equation always holds true.

[0074] (13) Channel modeling, as follows:

[0075] (131) Considering the presence of other obstacles and interference in the urban low-altitude environment, the channel between Alice and Willie (Bob) or its surrounding scatterers is modeled as a probabilistic LoS channel: Assume that the average intensity of the signal transmitted by Alice to Willie (or its surrounding scatterers) is The average power of the signal transmitted by Alice to Bob (or its surrounding scatterers) is , the model formula under the probabilistic LoS channel is as follows:

[0076] (1);

[0077] (2);

[0078] in, is the probability that there is a LoS component in the channel between Alice, Bob and Willie, The average strength of the wireless signal transmitted by the drone to the scatterers around the monitor; is the probability of line-of-sight channel between drone Alice and eavesdropper Willie; is the line-of-sight channel probability between drone Alice and the legitimate receiver Bob; is the distance between drone Alice and the legal receiver Bob; is the distance between drone Alice and eavesdropper Willie; is the path loss exponent of the line-of-sight (LoS) channel; The calculation formula is as follows:

[0079] (3);

[0080] in, a and b is an S-curve parameter that depends on the communication environment and is determined by factors such as building density and average height in an urban environment. Measured in degrees.

[0081] (132) Construct deep fading and Rayleigh fading channels, as follows: Specifically: The communication scenario considered by the present invention is that Alice transmits radio waves at a constant frequency in a short period of time, Willie is far away from Alice and is in a densely populated area of ​​scatterers, and the scatterers around him are all close to Willie and the distance difference is not large, but they are far away from Alice. Figure 4 (In the figure, As an example, let’s assume that the line connecting Alice and Willie passes through obstacle M, and Alice’s flight area is limited to the shaded part in the figure, which is denoted as . At this time, M blocks the line-of-sight transmission path between Alice and Willie. There is no LoS ​​component in the channel between Alice and Willie, but there may be LoS components in the channel between Alice and the scatterers around Willie. Assume that there are N (micro) paths from the reflectors around Willie to Willie, and N is very large. The distances from these N paths to Willie differ by several wavelengths of the electromagnetic waves emitted by the drones. When they are transmitted to Willie, they experience similar fading, that is, the amplitude of the radio waves on each path is equal but the phase is random, which conforms to the Clarke model of flat fading. N The combined amplitude of the (micro)paths follows the Rayleigh distribution.

[0082] In the same period, the signal transmitted from Alice reaches Willie through a similar fading in the non-line-of-sight channel, which meets the characteristics of flat fading. When there is no line-of-sight channel between Alice and Willie, the channel between the scatterers around Alice and Willie is modeled as a probabilistic LoS channel, as follows: Figure 5 As shown in the figure, according to the Clarke model, the channel between Willie and its surrounding scatterers is modeled as a Rayleigh channel. Due to the large number of scatterers (micro-scatterers), the received signal strength at Willie must conform to the statistical characteristics of the Rayleigh fading channel. The formula is as follows:

[0083] set up is the additional path loss coefficient of the NLoS channel; Less than 1; is a random variable that follows a Rayleigh distribution, Less than 1; Since the environment near Willie does not change with time, As an environmental parameter close to Willie , is a constant; then the average intensity is After the signal is scattered by the scatterers around Willie, the average intensity that finally reaches Willie is:

[0084] (4);

[0085] in, It is the average strength of the wireless signal transmitted from the UAV to the monitor when obstacles block the air-to-ground line-of-sight communication link; The average strength of the wireless signal transmitted by the drone to the scatterers around the monitor; is the line-of-sight channel probability between the UAV and the monitor, which is given by the line-of-sight channel probability formula, is the path loss index of the line-of-sight channel;

[0086] satisfy:

[0087] (5);

[0088] If Alice is Inside, there are:

[0089] (6);

[0090] in, By obstacles M and the two-dimensional plane determined by the monitor Willie;

[0091] If Alice is not here If M has no significant effect on the probabilistic LoS channel between Alice and Willie, then:

[0092] (7) The flow chart of the signal transmitted by the drone to the monitor through the channel is as follows Figure 6 shown.

[0093] Step 2: Joint Optimization Method for Obstacle Assistance

[0094] (21) Willie's binary hypothesis test is as follows: There is no behavior of drones transmitting signals; There is an act of drone transmitting signals; among them, the event Correspondingly, Willie believes that the received signal strength is ,event Correspondingly, Willie believes that the received signal strength is , every time Willie makes a judgment, and Choose between the two times, where the prior probabilities of the two times are the same; let the probability of Willie's misdetection be , the false positive behavior includes Alice not transmitting a signal and Willie choosing to accept the hypothesis Alice is transmitting and Willie chooses to accept the hypothesis ;

[0095] Assume that the privacy required by Alice's covert communication is ,in, is a Small positive number in the range; in any case Not less than ;set up The minimum value of , then the following formula holds: (8);

[0096] in, In binary hypothesis testing, the probability of Willie's false positive is The minimum probability of Willie's false positive in binary hypothesis testing; The value is given by the likelihood function, which is transformed into a stricter constraint by the KL divergence, as follows: (9);

[0097] Right now (10);

[0098] in, For binary hypothesis testing, right Information entropy of is used to quantify the concealment;

[0099] in, (11);

[0100] Where n is the maximum block length. Formula (11) is the concealment constraint.

[0101] (22) By solving the SNR function of the receiver Bob, the monotonicity relationship of the objective function to the spatial position variable is obtained as follows:

[0102] The signal-to-noise ratio function at the legitimate receiver Bob is:

[0103] (12);

[0104] in, The distance between drone Alice and eavesdropper Willie, The elevation angle between drone Alice and eavesdropper Willie, The azimuth between drone Alice and eavesdropper Willie, The distance between the legitimate receiver Bob and the eavesdropper Willie;

[0105] From the geometric relationship and formula (3), we can get:

[0106] (13);

[0107] in, The distance between drone Alice and eavesdropper Willie, The elevation angle between drone Alice and eavesdropper Willie, The azimuth between drone Alice and eavesdropper Willie, The distance between the legitimate receiver Bob and the eavesdropper Willie; Taking partial derivative, we get right It increases first and then decreases, and has a unique maximum point; it is recorded as , the following conditions are met:

[0108] (14);

[0109] Its exact value is determined by the following formula:

[0110] (15);

[0111] right Taking partial derivative, we get hour right It increases first and then decreases, and has a unique maximum point, which is recorded as , the following conditions are met: ;

[0112] in: (16);

[0113] The exact value is determined by:

[0114] (17);

[0115] when hour, right Monotonically increasing.

[0116] (23) The specific dimension reduction of the feasible domain of the drone is as follows: Alice chooses to fly to an appropriate position so that there is a line-of-sight channel between her and Bob, but there is no line-of-sight channel between her and Willie. The present invention proposes that, compared with other positions, since the line-of-sight detection channel between Alice and Willie is blocked by obstacles, Alice can transmit signals with a higher transmission power while ensuring concealment. This is mainly based on equations (6) and (7), that is, when other conditions are the same, Alice is In and out of plane Compared with the situation in the plane, the intensity of the signal emitted by it at Willie is F times different. In the scenario discussed in this invention, the distance between Bob and Willie is much greater than the distance between Alice and Willie. When the drone changes its position in the area around Willie, The change of the function is gentle, rather than a large change of deep fading. If Alice flies to the right position so that there is no obstacle between her and Bob, but there is an obstacle between her and Willie (this is often easy to do in an urban environment with relatively dense buildings), then Alice can achieve stronger concealment. Therefore, on the basis of ensuring concealment, Alice can transmit signals with a higher transmission power, thereby achieving a higher signal-to-noise ratio at Bob. Therefore, assuming that Alice chooses to use obstacle M to cut off the LoS channel with Willie, then:

[0117] (18);

[0118] Right now can be Alice's feasible domain is completely determined, and is reduced to a two-dimensional region determined by the following formula:

[0119] ;

[0120] ;

[0121] (19);

[0122] Right now Figure 7 The area shown in This achieves dimensionality reduction of the feasible domain.

[0123] (24) After reducing the dimension of the feasible domain, the optimization problem can be described as follows:

[0124] (20);

[0125] in, right and The monotonicity of is reflected in equations (15) to (20), and the derivative is: For P, right , The monotonicity relationship with P is:

[0126] (twenty one);

[0127] In order to further reduce the two-dimensional feasible domain of the UAV, (That is, the relative position of the obstacle and Willie ) is divided into three cases:

[0128] Case 1: ;

[0129] Case 2: ;

[0130] Case 3: ;

[0131] Among them, the results of Case 2 and Case 3 are obtained by simulation experiments; according to the SNR function analysis and constraints, the two-dimensional feasible domain of the UAV in Case 1 is further reduced. On point Let it be point N, point Denoted as point G, point For point K Figure 7 As shown. Based on the monotonicity and hidden constraints of the SNR function, the optimal search area and related conclusions in three cases are obtained:

[0132] Case I: For each , give the definitions of region A, region B, and region C:

[0133] ;

[0134] ;

[0135] ;

[0136] The search area is: ,when or , the search area becomes completely one-dimensional.

[0137] Case II: The search area is .

[0138] Scenario III: Searching the entire area In particular, when the drone is always able to maintain its concealment in this area (i.e., it can always achieve maximum power ), the feasible region is reduced to the line segment KN, and only then the optimal point can be obtained by one-dimensional search.

[0139] Among them, in case II and case III, the search domain of joint optimization is usually the entire two-dimensional area, and the solution of the optimization result is difficult to obtain directly, and it is often necessary to use the interior point algorithm to iteratively approximate it. For case I, the search domain of joint optimization can often be reduced to one dimension. The present invention provides explicit solutions for joint optimization of four different constraint combinations when the search domain is one-dimensional in case I, as follows:

[0140] Combination A: The constraint combination is , , the corresponding solution is .

[0141] Combination B: The constraint combination is , , the corresponding solution is .

[0142] Combination C: Constraint combination is , , the corresponding solution is .

[0143] Combination D: The constraint combination is , , the corresponding solution is .

[0144] in, and Respectively meet: ; ;in, The value of is determined by formula (19), in combination D and The following optimization problem is solved:

[0145] ;

[0146] in, Determined by the following formula: .

[0147] The parameters in the formula of the present invention are explained as follows:

[0148] is the distance between the legitimate receiver Bob and the eavesdropper Willie;

[0149] is the distance between drone Alice and the legal receiver Bob;

[0150] is the distance between drone Alice and eavesdropper Willie;

[0151] is the elevation angle between the drone Alice and the legal receiver Bob;

[0152] is the elevation angle between the drone Alice and the eavesdropper Willie;

[0153] is the azimuthal angle between the drone Alice and the eavesdropper Willie, that is, the angle between the plumb plane where the drone Alice and the eavesdropper Willie are located and the plumb plane where the legitimate receiver Bob and the eavesdropper Willie are located;

[0154] is the variance of the additive white Gaussian noise signal (AWGN) at the legitimate receiver Bob;

[0155] is the variance of the additive white Gaussian noise signal (AWGN) at the eavesdropper Willie;

[0156] is the path loss exponent of the line-of-sight (LoS) channel;

[0157] For obstacles Height;

[0158] For obstacles The angle between the highest point of and the horizontal plane of Willie;

[0159] For obstacles The angle between its horizontal projection and the line connecting Willie and the plumb plane where Bob and Willie are located;

[0160] is the signal transmission power of the UAV, and its maximum value is ;

[0161] All are events of binary hypothesis testing;

[0162] When obstacles block the air-to-ground line-of-sight communication link, the average strength of the wireless signal transmitted by the drone to the monitor;

[0163] Environmental parameters represent the loss of the wireless signal transmitted by the drone during the process of being scattered by the scatterer and then reaching the monitor through the Rayleigh channel;

[0164] The average strength of the wireless signal transmitted by the drone to the scatterers around the monitor;

[0165] is the probability of line-of-sight channel between drone Alice and eavesdropper Willie;

[0166] is the line-of-sight channel probability between drone Alice and the legitimate receiver Bob;

[0167] The average strength of the wireless signal transmitted from the drone to the monitor;

[0168] is the probability of Willie's false positive in binary hypothesis testing;

[0169] is the minimum probability of Willie's false positive in binary hypothesis testing;

[0170] To meet the need for concealed communication;

[0171] For binary hypothesis testing, right The information entropy of is used to quantify the concealment;

[0172] is the signal-to-noise ratio function at the legitimate receiver Bob, the objective function of the optimization problem;

[0173] As the basic restriction ( ) Under this condition, the feasible flight area of ​​the UAV;

[0174] is the Rayleigh factor;

[0175] It is an average measure of the scattering loss of the signal caused by scattering of the object.

Claims

1. A joint optimization method for obstacle-assisted UAV covert communication in a three-dimensional urban environment, characterized in that: The following steps are involved: (1) Designing an urban communication environment with obstacles; (2) Set the parameters of the drone and the environment and their ranges; model the channel; assume that the distance between the legitimate receiver Bob and the eavesdropper Willie is , the distances between drone Alice and the legitimate receiver Bob and eavesdropper Willie are , ; The azimuths of drone Alice to the legitimate receiver Bob and eavesdropper Willie are and ; The angle between the plumb plane where the drone Alice and the eavesdropper Willie are located and the plumb plane where the legal receiver Bob and the eavesdropper Willie are located is ; The variances of the additive white Gaussian noise signal AWGN at the legitimate receiver Bob and the eavesdropper Willie are , ; The signal transmission power of the drone is , the path loss of the LoS channel is ; Suppose that the obstacles near the eavesdropper Willie are Abstracted in space, it is a linear body with no thickness or width but only height, and is perpendicular to the horizontal plane; let its height be , the angle between the highest point and the horizontal plane of the line connecting the eavesdropper Willie is , the angle between its horizontal projection and the line connecting the eavesdropper Willie and the plumb plane where the legal receiver Bob and the eavesdropper Willie are located is ; Alice's position in three-dimensional space is determined by be uniquely identified; , , The possible areas where Alice's optimal position can exist are restricted as follows: (S1) : Drone Alice cannot fly too close to the eavesdropper Willie to prevent being detected by radar or observed by human eyes. There is a minimum distance limit ; Due to the limited resolution of the drone, in order to have a better monitoring effect on the area where the eavesdropper Willie is located, there is a maximum distance limit ; (S2) :UAV Alice needs to have an acceptable viewing angle of the monitoring area, thus requiring Cannot be too small, there is a minimum angle limit ; (S3) :UAV Alice flies away from the vertical plane where the legitimate receiver Bob and the eavesdropper Willie are located, through Uniquely determine the position of the drone Alice in three-dimensional space; due to symmetry, only consider Half of the three-dimensional space; (S4) : The drone can adjust the signal transmission power, and its maximum transmission power is ; (S5) : The distance between the drone and the receiver is greater than the distance between the drone and the eavesdropper; among them, is a very small angle, so the above equation always holds true; The channel modeling formula is as follows: is the additional path loss coefficient of the NLoS channel; Less than 1; is a random variable that follows a Rayleigh distribution, Less than 1; Since the environment near Willie does not change with time, As an environmental parameter close to Willie , is a constant; then the average intensity is After the signal is scattered by the scatterers around Willie, the average intensity that finally reaches Willie is: ； in, It is the average strength of the wireless signal transmitted from the UAV to the monitor when obstacles block the air-to-ground line-of-sight communication link; The average strength of the wireless signal transmitted by the drone to the scatterers around the monitor; is the line-of-sight channel probability between the UAV and the monitor, which is given by the line-of-sight channel probability formula, is the path loss index of the line-of-sight channel; satisfy: ; If Alice is Inside, then ;in, By obstacles M and the two-dimensional plane determined by the observer Willie; if Alice is not Inside, then , it is believed that M has no significant impact on the probabilistic LoS channel between Alice and Willie; (3) Based on channel modeling, the optimal flight position and transmission power of the UAV are calculated using a joint optimization method; including: binary hypothesis testing for the eavesdropper Willie; obtaining the monotonicity relationship of the objective function to the spatial position variable by solving the SNR function of the receiver Bob; converting the monotonicity relationship into a mathematical problem and solving it; The binary hypothesis test for the eavesdropper Willie is as follows: There is no behavior of drones transmitting signals; There is an act of drone transmitting signals; among them, the event Correspondingly, Willie believes that the received signal strength is ,event Correspondingly, Willie believes that the received signal strength is , every time Willie makes a judgment, and Choose between the two times, where the prior probabilities of the two times are the same; let the probability of Willie's misdetection be , the false positive behavior includes Alice not transmitting a signal and Willie choosing to accept the hypothesis Alice is transmitting and Willie chooses to accept the hypothesis ; Assume that the privacy required by Alice's covert communication is ,in, is a Small positive number in the range; in any case Not less than ;set up The minimum value of , then the following formula holds: ; in, In binary hypothesis testing, the probability of Willie's false positive is The minimum probability of Willie's false positive in binary hypothesis testing; The value is given by the likelihood function, which is transformed into a stricter constraint by the KL divergence, as follows: ; Right now ; in, For binary hypothesis testing, right Information entropy of is used to quantify the concealment; in, ; Where n is the maximum block length; By solving the SNR function of the receiver Bob, the monotonic relationship of the objective function to the spatial position variable is obtained, as follows: The signal-to-noise ratio function at the legitimate receiver Bob is: ； in, The distance between drone Alice and eavesdropper Willie, The elevation angle between drone Alice and eavesdropper Willie, The azimuth between drone Alice and eavesdropper Willie, The distance between the legitimate receiver Bob and the eavesdropper Willie; According to geometric relations and formulas: in, a and b is the S-curve parameter that depends on the communication environment and is determined by the building density and average height in the urban environment. Enter the angle value; we get: ； in, The distance between drone Alice and eavesdropper Willie, The elevation angle between drone Alice and eavesdropper Willie, The azimuth between drone Alice and eavesdropper Willie, The distance between the legitimate receiver Bob and the eavesdropper Willie; Taking partial derivative, we get right It increases first and then decreases, and has a unique maximum point; it is recorded as , the following conditions are met: ； Its exact value is determined by the following formula: ； right Taking partial derivative, we get hour right It increases first and then decreases, and has a unique maximum point, which is recorded as , the following conditions are met: in: The exact value is determined by: ； when hour, right Monotonically increasing; The monotonicity relationship is converted into a mathematical problem and solved as follows: first, the dimension of the feasible domain of the UAV is reduced, and then after the dimension reduction of the feasible domain, the optimization problem can be converted into a mathematical description, and the mathematical description is solved. The mathematical description formula is as follows: 。

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