Fixed-wing unmanned aerial vehicle assisted uninterrupted covert communication optimization method

Abstract

The invention provides an uninterrupted covert communication optimization method assisted by a fixed-wing unmanned aerial vehicle. The method comprises the following steps: acquiring system information; the distance d0 between the ground detection node Willie and the ground target node Bob is calculated; according to different conditions met by the distance d0 between the Willie and the Bob, different methods are adopted to calculate the maximum information rate, and uninterrupted covert communication between the unmanned aerial vehicle and the ground node is achieved. According to the method, the flight position, the flight radius and the transmitting power of the unmanned aerial vehicle are jointly optimized by using the position information of the ground destination node and the ground detection node, the noise uncertainty statistical information and the constraint information of the flight speed, the height, the inclination angle and the transmitting power of the unmanned aerial vehicle; and maximizing the information rate from the unmanned aerial vehicle to the ground destination node under the conditions that the communication outage probability requirement from the unmanned aerial vehicle to the ground destination node is met and the total error rate of the ground detection node is greater than a given threshold.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technology, and in particular to an optimization method for uninterrupted covert communication assisted by a fixed-wing unmanned aerial vehicle (UAV). Background Art

[0002] In recent years, due to its controllable mobility, on-demand deployment ability, and high probability of providing line-of-sight air-ground links, UAVs have been widely used in wireless communication networks. Compared with rotary-wing UAVs, fixed-wing UAVs play an increasingly important role in military reconnaissance, disaster monitoring, border patrol and other fields with their advantages of long endurance, long flight range, and strong load capacity. During the mission execution of UAVs, real-time communication with ground stations or other UAVs is required to transmit control commands, status information, and mission data. It should be noted that traditional UAV communication mostly uses public frequency bands, which are vulnerable to detection, interference, and interception, seriously threatening the security of UAV systems. Covert communication or low-detection-probability communication, as a new wireless transmission technology, can effectively solve the privacy and security problems in communication. Traditional ground transmitters are generally located at a fixed point on a two-dimensional plane or move on a two-dimensional plane. However, UAVs can move freely in three-dimensional space, providing more degrees of freedom for covert communication. On the other hand, compared with rotary-wing UAVs, fixed-wing UAVs cannot hover and must always fly forward to obtain the necessary lift. Therefore, for covert communication assisted by fixed-wing UAVs, the flight trajectory and attitude of the UAV need to be considered. In addition, there are also basic communication quality requirements for covert communication behaviors, such as requirements for outage probability, information rate, bit error rate, etc. These problems are often overlooked in existing research work. Therefore, how to utilize the mobility of fixed-wing UAVs to achieve covert communication that guarantees basic communication requirements in three-dimensional space is an urgent problem to be studied. Summary of the Invention

[0003] The present invention provides an optimization method for uninterrupted covert communication assisted by a fixed-wing UAV. Considering the uncertainty of noise existing in the ground destination node and the ground detection node, by using the position information of the ground destination node and the ground detection node, the statistical information of noise uncertainty, and the constraint information of the flight speed, altitude, tilt angle, and transmit power of the UAV, the flight position, flight radius, and transmit power of the UAV are jointly optimized to maximize the information rate from the UAV to the ground destination node under the condition that the communication outage probability requirement from the UAV to the ground destination node is satisfied and the total error rate of the ground detection node is greater than a given threshold.

[0004] To achieve the above object, the present invention provides an optimization method for uninterrupted covert communication assisted by a fixed-wing UAV, including the following steps:

[0005] Step 1: Obtain system information; obtain the location information q of Willie w , the location information q of Bob B , the minimum flight altitude h of the drone min and the maximum flight altitude h max , the minimum flight speed V of the drone min and the maximum flight speed V max , the minimum transmission power P of the drone min and the maximum transmission power P max , the maximum tilt angle φ of the drone max , the channel power per unit distance β0, the total detection error rate limit for Willie the communication interruption probability limit Θ between the drone and Bob B , the standard noise power expressed in dB and the noise uncertainty parameter ρ expressed in dB;

[0006] Step 2: Initialize the gravitational acceleration g, calculate the distance d0 between Willie and Bob according to their location information, calculate the lower limit value of the minimum distance between the drone and Willie that can achieve covert communication and the upper limit value Calculate the optimal flight radius of the drone Calculate the lower limit value of the maximum distance between the drone and Bob that can achieve non-interrupted communication

[0007] Step 3: If holds; the center of the circular trajectory of the drone is h * = h min , the optimal transmission power of the drone is Calculate the maximum information rate R B [n], and then jump to Step 11;

[0008] Step 4: If and hold; the center of the circular trajectory of the drone is h * = h min , calculate the optimal transmission power of the drone and the maximum information rate R B [n], and then jump to Step 11;

[0009] Step 5: If and hold; the center of the circular trajectory of the drone is the optimal transmission power of the drone is Calculate the maximum information rate R B [n], and then jump to step 11;

[0010] Step 6: When and hold. The center of the UAV's circular trajectory is h * = h max , and the optimal transmission power of the UAV is Calculate the maximum information rate R B [n], and then jump to step 11;

[0011] Step 7: If and hold; The center of the UAV's circular trajectory is The optimal transmission power of the UAV is Calculate the maximum information rate R B [n], and then jump to step 11;

[0012] Step 8: If and hold; The center of the UAV's circular trajectory is h * = h max , calculate the optimal transmission power and the maximum information rate R B [n], and then jump to step 11;

[0013] Step 9: If and hold. The center of the UAV's circular trajectory is h * = h max , the optimal transmission power of the UAV is Calculate the maximum information rate R B [n], and then jump to step 11;

[0014] Step 10: If holds, it is impossible to achieve un-interrupted covert communication; Step 11: The algorithm ends.

[0015] Furthermore, the specific steps of step 2 are as follows:

[0016] According to Willie's position information q w and Bob's position information q B , calculate the distance d0 = ||q w - q B ||;

[0017] Calculate the lower limit and upper limit of the minimum UAV-Willie distance that can achieve covert communication according to Equation (21) and the minimum and maximum transmission powers of the UAV and the upper limit

[0018]

[0019] Calculate the optimal flight radius of the UAV according to Equation (23) Calculate the lower limit of the maximum UAV-Bob distance that can achieve uninterrupted communication

[0020]

[0021] Furthermore, in step 3, calculate the maximum information rate R B The formula for [n] is:

[0022]

[0023] Furthermore, in step 4, calculate the optimal transmission power of the UAV The formula for it is:

[0024]

[0025] Calculate the maximum information rate R B The formula for [n] is

[0026]

[0027] Furthermore, in step 5, calculate the maximum information rate R B The formula for [n] is:

[0028]

[0029] In steps 6 and 9, calculate the maximum information rate R B The formula for [n] is:

[0030]

[0031] In step 7, calculate the maximum information rate R B The formula for [n] is:

[0032]

[0033] Furthermore, in step 8, calculate the optimal transmission power of the UAV The formula for it is:

[0034]

[0035] Calculate the maximum information rate RB [n] is expressed as:

[0036]

[0037] According to one aspect of the present invention, a storage medium is provided. Instructions are stored in the storage medium, and when a computer reads the instructions, the computer is caused to execute the fixed-wing UAV-assisted uninterrupted covert communication optimization method described in any one of the above.

[0038] According to another aspect of the present invention, an electronic device is provided, including a processor and the above storage medium, and the processor executes the instructions in the storage medium.

[0039] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0040] The present invention utilizes the three-dimensional mobility of the fixed-wing UAV, jointly considers the concealment requirements of the communication behavior between the UAV and the ground destination node and the performance requirements of the communication interruption probability between the UAV and the ground destination node, and utilizes the position information of the ground destination node and the ground detection node, the statistical information of noise uncertainty, and the constraint information of the UAV's flight speed, altitude, tilt angle, and transmission power to jointly optimize the flight position, flight radius, and transmission power of the UAV. Under the condition of meeting the requirements of the communication interruption probability from the UAV to the ground destination node and the total error rate of the ground detection node being greater than a given threshold, the information rate from the UAV to the ground destination node is maximized. Simulation experiments also show that this optimization method can achieve uninterrupted covert communication from the UAV to the ground destination node at a given maximum information transfer rate. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 is a schematic diagram of the UAV-assisted uninterrupted covert communication system of the present invention;

[0042] Figure 2 is the flight altitude of the UAV when Willie and Bob are 6 to 12 meters apart;

[0043] Figure 3 is the flight altitude of the UAV when Willie and Bob are 12 to 40 meters apart;

[0044] Figure 4 is the flight altitude of the UAV when Willie and Bob are 40 to 400 meters apart;

[0045] Figure 5 is the flight altitude of the UAV when Willie and Bob are 400 to 800 meters apart;

[0046] Figure 6For the horizontal coordinates (x0, y0) of the center of the UAV trajectory when Willie and Bob are 6 to 12 meters apart;

[0047] Figure 7 For the horizontal coordinates (x0, y0) of the center of the UAV trajectory when Willie and Bob are 12 to 40 meters apart;

[0048] Figure 8 For the horizontal coordinates (x0, y0) of the center of the UAV trajectory when Willie and Bob are 40 to 400 meters apart;

[0049] Figure 9 For the horizontal coordinates (x0, y0) of the center of the UAV trajectory when Willie and Bob are 400 to 800 meters apart;

[0050] Figure 10 For the UAV transmission power when Willie and Bob are 6 to 12 meters apart;

[0051] Figure 11 For the UAV transmission power when Willie and Bob are 12 to 40 meters apart;

[0052] Figure 12 For the UAV transmission power when Willie and Bob are 40 to 400 meters apart;

[0053] Figure 13 For the UAV transmission power when Willie and Bob are 400 to 800 meters apart;

[0054] Figure 14 For the UAV information transmission rate when Willie and Bob are 6 to 12 meters apart;

[0055] Figure 15 For the UAV information transmission rate when Willie and Bob are 12 to 40 meters apart;

[0056] Figure 16 For the UAV information transmission rate when Willie and Bob are 40 to 400 meters apart;

[0057] Figure 17 For the UAV information transmission rate when Willie and Bob are 400 to 800 meters apart;

[0058] Figure 18 For the probability of interruption at Bob's end when the UAV flies one week when Willie and Bob are 6 meters apart;

[0059] Figure 19It is the outage probability at the Bob side when the drone flies one week with Willie and Bob being 40 meters apart;

[0060] Figure 20 It is the outage probability at the Bob side when the drone flies one week with Willie and Bob being 400 meters apart;

[0061] Figure 21 It is the outage probability at the Bob side when the drone flies one week with Willie and Bob being 800 meters apart;

[0062] Figure 22 It is the total detection error rate of Willie when the drone flies one week with Willie and Bob being 6 meters apart;

[0063] Figure 23 It is the total detection error rate of Willie when the drone flies one week with Willie and Bob being 40 meters apart;

[0064] Figure 24 It is the total detection error rate of Willie when the drone flies one week with Willie and Bob being 400 meters apart;

[0065] Figure 25 It is the total detection error rate of Willie when the drone flies one week with Willie and Bob being 800 meters apart. Detailed implementation manners

[0066] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0067] Embodiment 1: As Figure 1-25 shown, an optimization method for uninterrupted covert communication assisted by a fixed-wing drone according to an embodiment of the present invention includes the following steps:

[0068] As Figure 1 shown, an airborne fixed-wing drone R serves as a mobile transmitter to covertly transmit signals to Bob (a ground destination node). At the same time, Willie (a ground detection node) detects whether the drone R transmits signals to Bob. Assume that the positions of Bob and Willie are known, and Willie is located at q w =(0, 0, 0) in a three-dimensional coordinate system, and Bob is located at q B =(d0, 0, 0), where d0 = ||qw - q B || is the distance between Willie and Bob; the drone R makes a horizontal uniform circular motion in the air, and the center of its flight trajectory is (x0, y0, h) and the radius is r R, the linear velocity is v and the flight altitude is h. For a fixed-wing UAV, due to the limitations of the overall mechanism and the need to obtain lift, there are maximum and minimum flight speed limits, that is, the flight speed of the UAV needs to satisfy

[0069] V min ≤v≤V max (1)

[0070] where V min and V max are the minimum and maximum flight speed limits of UAV R respectively. According to the research results of 3GPP (3rd Generation Partnership Project), when the UAV flies above 40 meters in a rural environment, the probability of having a line-of-sight (LoS) link between the air and ground communication nodes is 100%. On the other hand, due to the limitations of UAV design, its flight altitude is also restricted. Therefore, to ensure the existence of an LoS link and flight safety between the air and ground users, the flight altitude of the UAV should satisfy

[0071] h min ≤h≤h max (2)

[0072] where h min and h max are the minimum and maximum flight altitudes of the UAV respectively. In addition, considering that the UAV can only fly between Willie and Bob, that is, the central coordinate of the circular trajectory of the UAV not only needs to satisfy the constraint of formula (2), but also needs to satisfy r R ≤x0≤d0 - r R .

[0073] Denote the time for the UAV to fly one week along the circular trajectory as T, and divide it into N equal-length time slots, and the length of each time slot is T N = T / N. Since the length of each time slot is small enough, within one time slot, the UAV can be regarded as approximately stationary. Use P R [n] to represent the transmission power of the UAV in the nth time slot, where n ∈ {1, 2,..., N}. The transmission power of the UAV is also restricted, that is, the transmission power P R [n] in the nth time slot needs to satisfy

[0074] P min ≤P R [n]≤P max (3)

[0075] where P min and P max are the minimum and maximum transmission power limits respectively.

[0076] Suppose Willie uses a power detector as the detector. For the nth time slot, Willie conducts m signal detections and uses the average value of the m detected signal powers as the decision basis for whether there is communication behavior. Let H1 represent the situation where the UAV sends hidden information, and H0 represent the situation where the UAV does not send signals. In the nth time slot, the signal detected by Willie for the ith time can be written as

[0077]

[0078] where \(i\in\{1,\ldots,m\}\), \(n\) W [i] is the Gaussian white noise with a mean of 0 and a variance of \(\delta\) W at the ith detection, \(P\) R [n] is the transmission power of the UAV R in the nth time slot, is the power-normalized signal transmitted by the UAV R detected at the ith time in the nth time slot, \(h\) RW is the channel gain from the UAV R to Willie. Considering that there is a LoS link between the UAV R and Willie, then where \(\beta_0\) represents the channel power gain at a reference distance of 1 meter, \(d\) RW is the distance between the UAV R and Willie.

[0079] In the nth time slot, when the average power \(T\) W [n] detected by Willie is greater than a certain threshold, it is considered that there is communication behavior; otherwise, it is considered that there is no communication behavior. That is, Willie's decision rule is

[0080]

[0081] where \(T\) W [n] is the average power of the signal detected by Willie in the nth time slot, is the signal power detected by Willie for the ith time, \(m\) is the number of signal detections in the nth time slot, \(\lambda[n]\) is the detection threshold in the nth time slot, \(D_0\) is the determination that Willie believes the UAV R has not sent a signal; \(D_1\) is the determination that Willie believes the UAV has sent a signal.

[0082] Suppose that in each time slot, Willie conducts an infinite number of detections, that is, \(m\rightarrow\infty\), then \(T\) W [n] can be rewritten as

[0083]

[0084] where \(\delta\) W is the variance (average power) of the Gaussian white noise at Willie's location, \(h\) RWis the channel gain from the UAV R to Willie, and P R [n] is the transmission power of the UAV R in the n-th time slot.

[0085] In practice, the transceiver cannot exactly know the power of the noise. Therefore, the noise uncertainty situation is considered, that is, the variance δ W of the Gaussian white noise is a random variable with a known distribution. Let Then δ WdB obeys a uniform distribution in the interval . Here, is the standard noise power expressed in dB, and ρ is the noise uncertainty parameter expressed in dB, satisfying ρ > 0. Therefore, the probability density function of δ W can be written as

[0086]

[0087] Here, use and to represent the false alarm rate and the miss detection rate of Willie in the n-th time slot respectively, which can be specifically given by equations (8) and (9).

[0088]

[0089] In the n-th time slot, the total error rate ε[n] of Willie can be written as

[0090] ε[n] = P F [n] + P M [n] (10)

[0091] Consider the case where the sum of the false alarm rate and the miss detection rate of Willie is minimized, that is, the total error rate ε[n] is minimized. In this case, if the UAV R can send signals safely, then in other cases, the UAV R can also send signals safely. According to equations (8) and (9), the false alarm rate and the miss detection rate of Willie in the n-th time slot can be rewritten as

[0092]

[0093] where In this way, the total error rate ε[n] of Willie can be written as

[0094]

[0095] It should be noted that: if holds, that is, holds, then the situation where the total error rate ε[n] is 0 may occur. Therefore, from the perspective of covert communication, it is necessary to ensure that holds. It can be proved that when When ε[n] reaches its minimum value.

[0096] In summary, from the perspective of covert communication, to ensure is satisfied, at this time, Willie's minimum total error rate is

[0097]

[0098] From the perspective of the UAV and Bob, in order to achieve covert communication, it is necessary to communicate when Willie's total error rate is not less than a certain threshold ( is a positive decimal close to 1). From it can be obtained that As mentioned above, the condition for achieving covert communication is Since is satisfied, therefore, from the perspective of the UAV and Bob, communication is only carried out when the distance between Willie and the UAV satisfies equation (15), otherwise communication will not be carried out.

[0099]

[0100] That is to say, the minimum d for achieving covert communication RW is Therefore, in order to achieve covert communication, the distance d between the UAV and Willie RW needs to be greater than or equal to

[0101] Observing equation (15), it can be found that: ρ, β0 and are constants, P R [n] is the transmission power of the UAV in the nth time slot, d RW is the distance between the UAV and Willie; in the nth time slot, in order to satisfy equation (15), appropriate P R [n] and d RW need to be found; when P R [n] is fixed, only by finding an appropriate distance d RW to make equation (15) hold can covert communication be achieved. Next, the constraint given by equation (15) is called the covert constraint.

[0102] To enable the UAV and Bob to communicate normally under covert conditions, the outage constraint at Bob also needs to be considered.

[0103] In the nth time slot, n ∈ {1, 2, …, N}, the received signal at Bob can be written as: where, P R [n] is the transmission power of the UAV R in the nth time slot, hRB is the channel gain between the UAV R and Bob, x R [n] is the power-normalized signal transmitted by the UAV R in the n-th time slot, n B [n] is the Gaussian white noise with mean 0 and variance δ at Bob B . Similarly, Bob has uncertainty about δ B , and its probability density function can be given by Equation (7). Similarly, considering the case where there is a LoS link between the UAV R and Bob, then where β0 represents the channel power gain at a reference distance of 1 meter, and d RB is the distance between the UAV R and Bob. At this time, the received signal-to-noise ratio at Bob is where δ B is a random variable, and its probability density function can be given by Equation (7).

[0104] Assume that the UAV R and Bob require the communication outage probability to be less than or equal to Θ B , that is, Equation (16) needs to be satisfied.

[0105] Pr{log2(1 + γ B [n]) < R B [n]} ≤ Θ B (16)

[0106] In Equation (16), R B [n] is the information rate from the UAV R to Bob in the n-th time slot, Pr{log2(1 + γ B [n]) < R B [n]} represents the probability of outage, and Θ B is the outage probability limit required by Bob. Substitute into Pr{log2(1 + γ B [n]) < R B [n]} and according to Equation (7), the outage probability expression for the communication between the UAV R and Bob in the n-th time slot can be obtained, specifically

[0107]

[0108] According to the outage probability limit Θ B required by Bob and Equation (17), the condition for the UAV R and Bob to achieve non-outage communication is that Equation (18) holds.

[0109]

[0110] Furthermore, by combining the two inequality constraints in Equation (18), the constraint of Equation (19) can be obtained.

[0111]

[0112] That is, the maximum d for which uninterrupted communication can be achieved between the UAV R and Bob RB is Therefore, in order to achieve uninterrupted communication, the distance d between the UAV and Bob RB needs to be less than or equal to Below, Equation (19) is referred to as the outage constraint.

[0113] It should be noted that when the UAV flies horizontally along a circular trajectory with a radius of r R , an inclination angle φ is generated, and the inclination angle φ satisfies tanφ = v 2 / gr R , where g is the acceleration due to gravity and v is the flight speed of the UAV; to ensure flight safety, the inclination angle φ needs to satisfy φ ≤ φ max , where φ max is the maximum inclination angle of the UAV. Therefore, to ensure flight safety, the flight radius of the UAV needs to satisfy r R ≥ v 2 / (gtanφ max ).

[0114] Assume that during one circle of the UAV flying along the circular trajectory, that is, in N time slots, the transmit power P R [n] for sending data information to Bob remains constant, and the information rate R B [n] also remains constant, where n ∈ {1, 2,..., N}. Below, with the goal of maximizing the uninterrupted covert communication rate, an optimization problem is established as follows.

[0115]

[0116] r R ≤ x0 ≤ d0 - r R (20d)

[0117] h min ≤ h ≤ h max (20e)

[0118] P min ≤ P R [n] ≤ P max (20f)

[0119]

[0120] Equation (20a) gives the optimization objective, that is, to maximize the information transmission rate R of uninterrupted covert communication B[n] and the optimization variables are: the coordinates of the center of the circular trajectory of the UAV R (x0, y0, h), the radius r of the circular trajectory R and the transmission power P of the UAV R [n], and are the optimization variables x0, y0, h, r R and P R [n]. Equation (20b) gives the concealment constraint, that is, the distance between the UAV and Willie at any point on the circular trajectory must satisfy the constraint given by Equation (15), where, (x0 - r R cosθ) 2 +(y0 + r R sinθ) 2 +h 2 is the square of the distance between the UAV and Willie at any point on the circular trajectory, θ ∈ [0, 2π), is the minimum distance between the UAV and Willie that can achieve covert communication, which can be specifically given by Equation (21).

[0121]

[0122] Equation (20c) gives the non - interruption communication constraint, that is, the distance between the UAV and Bob at any point on the circular trajectory must satisfy the constraint given by Equation (19), where, (d0 - x0 + r R cosθ) 2 +(y0 + r R sinθ) 2 +h 2 is the square of the distance between the UAV and Bob at any point on the circular trajectory, θ ∈ [0, 2π), is the maximum distance between the UAV and Bob that can achieve non - interruption communication, which can be specifically given by Equation (22).

[0123]

[0124] Equation (20d) gives the UAV flight area restriction, that is, the UAV flies between Willie and Bob. Equation (20e) gives the UAV flight altitude restriction. Equation (20f) gives the UAV transmission power restriction. Equation (20g) gives the UAV flight tilt angle restriction, where the flight speed v of the UAV is within the range given by Equation (1), that is, V min ≤v≤V max .

[0125] It can be proved that the optimization problem (20), that is, the optimization problem composed of equations (20a), (20b), (20c), (20d), (20e), (20f) and (20g), will reach the optimal value at , that is, the optimal flight radius is

[0126]

[0127] In addition, in order to obtain the non - interrupted communication condition as much as possible, the UAV should be as close to Bob as possible. Therefore, the center of the UAV's circular trajectory should be as close to Bob as possible. To solve the optimization problem (20), when P R [n]=P min , the minimum is denoted as Specifically, it can be obtained by substituting P R [n]=P min into equation (21); when P R [n]=P max , the maximum is denoted as Specifically, it can be obtained by substituting P R [n]=P max into equation (21). In addition, since the minimum flight altitude of the UAV is h min , and the optimal flight radius is Therefore, the minimum value of is denoted as At this time, the coordinates of the center of the UAV flight trajectory are That is to say, the minimum and maximum hidden - ball radii are and The minimum interruption - ball radius is Next, the specific solution process of problem (20) is given.

[0128] Case 1: If holds. At this time, the maximum hidden - ball and the minimum interruption - ball have no intersection or the ordinate of the intersection is less than or equal to h min . To maximize the information rate, the UAV should transmit signals with the maximum transmit power P max , and fly with the center , that is, h * =h min , The information rate at this time is

[0129]

[0130] Case 2: If It holds. At this time, the largest hidden sphere and the smallest interruption sphere have an intersection point, and the ordinate of the intersection point is greater than h min Or the largest hidden sphere contains the smallest interruption sphere. It can be proved that when the UAV should fly at the lowest possible altitude; when the UAV should fly at the highest possible altitude; when it is impossible to achieve non - interrupted covert communication. Next, for case 2, it is discussed in 7 sub - cases.

[0131] (2.1) When and hold. At this time, the UAV can fly at the lowest flight altitude, that is, h * = h min and In this way, the maximum distance between the UAV and Bob that can achieve non - interrupted communication is The minimum distance between the UAV that can achieve covert communication and Willie is According to and equation (21), the optimal transmit power of the UAV can be calculated as

[0132]

[0133] According to and equations (22) and (25), the information rate at this time can be calculated as

[0134]

[0135] (2.2) When and hold. At this time, the UAV should transmit signals with the minimum transmit power because this can make the flight altitude of the UAV the lowest, that is, In this way, the maximum distance between the UAV and Bob that can achieve non - interrupted communication is According to and equation (22), the information rate at this time can be calculated as

[0136]

[0137] (2.3) When and hold. At this time, the UAV can only transmit signals with the minimum power, and the center of the UAV's circular trajectory cannot be on the horizontal line between Willie and Bob and needs to be offset along the horizontal vertical axis, that is, h * = h maxIn this way, the maximum distance between the UAV and Bob that can achieve uninterrupted communication is According to and Equation (22), the information rate at this time can be calculated as

[0138]

[0139] If holds. At this time, the flight altitude of the UAV should be as high as possible to be optimal. For this reason, the UAV should transmit signals with the maximum transmit power P max to maximize the hidden ball and thus increase the flight altitude. The maximum possible value of its flight altitude is

[0140] (2.4) When and hold. The optimal transmit power of the UAV is The optimal flight altitude is And In this way, the maximum distance between the UAV and Bob that can achieve uninterrupted communication is According to and Equation (22), the information rate at this time can be calculated as

[0141]

[0142] (2.5) When and hold, the optimal flight altitude of the UAV should be h * = h max And In this way, the maximum distance between the UAV and Bob that can achieve uninterrupted communication is The minimum distance between the UAV and Willie that can achieve covert communication is According to and Equation (21), the optimal transmit power of the UAV can be calculated as

[0143]

[0144] According to and Equation (30), Equation (22), the information rate at this time can be calculated as

[0145]

[0146] (2.6) When and hold. At this time, the UAV can only transmit signals with the minimum power, and the center of the UAV's circular trajectory cannot be on the horizontal line between Willie and Bob, and needs to be offset in the direction of the horizontal vertical axis, that is, h * =h max In this way, the maximum distance between the UAV and Bob that can achieve uninterrupted communication is According to and Equation (22), the information rate at this time can be calculated, which can be specifically given by Equation (28).

[0147] (2.7) If holds. At this time, it is impossible to achieve uninterrupted covert communication, that is, there is no feasible solution to Problem (20).

[0148] Summarizing the above solution process, an optimization method for uninterrupted covert communication that can maximize the information rate is given below, as follows.

[0149] Step 1: Obtain system information, including: the position information q of Willie w , the position information q of Bob B , the minimum flight altitude h of the UAV min and the maximum flight altitude h max , the minimum flight speed V of the UAV min and the maximum flight speed V max , the minimum transmission power P of the UAV min and the maximum transmission power P max , the maximum tilt angle φ of the UAV max , the channel power per unit distance β0, the total detection error rate limit for Willie the communication outage probability limit Θ between the UAV and Bob B , the standard noise power expressed in dB and the noise uncertainty parameter ρ expressed in dB;

[0150] Step 2: Initialize the gravitational acceleration g, calculate the distance d0 = ||q w -q B || between Willie and Bob, and calculate the lower limit value and the upper limit value of the minimum distance between the UAV and Willie that can achieve covert communication according to Equation (21) and the minimum and maximum transmission powers of the UAV Calculate the optimal flight radius of the UAV according to Equation (23) Calculate the lower limit value of the maximum distance between the UAV and Bob that can achieve uninterrupted communication

[0151] Step 3: If holds. The center of the circular trajectory of the UAV is h * =h min, the optimal transmission power of the UAV is Calculate the maximum information rate R B [n], and then jump to step 11;

[0152] Step 4: If and hold. The center of the UAV's circular trajectory is h * = h min , calculate the optimal transmission power of the UAV according to Equation (25) Calculate the maximum information rate R B [n], and then jump to step 11;

[0153] Step 5: If and hold. The center of the UAV's circular trajectory is The optimal transmission power of the UAV is Calculate the maximum information rate R B [n], and then jump to step 11;

[0154] Step 6: When and hold. The center of the UAV's circular trajectory is h * = h max , the optimal transmission power of the UAV is Calculate the maximum information rate R B [n], and then jump to step 11;

[0155] Step 7: If and hold. The center of the UAV's circular trajectory is The optimal transmission power of the UAV is Calculate the maximum information rate R B [n], and then jump to step 11;

[0156] Step 8: If and hold. The center of the UAV's circular trajectory is h * = h max , calculate the optimal transmission power of the UAV according to Equation (30) as Calculate the maximum information rate R B [n], and then jump to step 11;

[0157] Step 9: If and is established. The center of the circular trajectory of the UAV is h * = h max , and the optimal transmission power of the UAV is Calculate the maximum information rate R B [n] according to Equation (28), and then jump to Step 11;

[0158] Step 10: If is established. At this time, it is impossible to achieve un-interrupted covert communication. Step 11: The algorithm ends.

[0159] Example 1: As Figure 1 shown, the UAV R flies along a circular trajectory and sends data information to the ground destination node Bob at a certain information rate and transmission power during the flight.

[0160] Before the UAV R officially flies, it obtains system information, including: the position information q of Willie w , the position information q of Bob B , the minimum flight altitude h of the UAV min and the maximum flight altitude h max , the minimum flight speed V of the UAV min and the maximum flight speed V max , the minimum transmission power P of the UAV min and the maximum transmission power P max , the maximum tilt angle φ of the UAV max , the channel power per unit distance β0, the detection error rate limit for Willie the communication interruption probability limit Θ between the UAV and Bob B , the standard noise power expressed in dB and the noise uncertainty parameter ρ expressed in dB; then, initialize the gravitational acceleration g, calculate the distance d0 = ||q w - q B || between Willie and Bob, and calculate the lower limit value and the upper limit value of the minimum distance between the UAV and Willie that can achieve covert communication according to Equations (21) and the minimum and maximum transmission powers of the UAV Calculate the optimal flight radius of the UAV according to Equation (23) Calculate the lower limit value of the maximum distance between the UAV and Bob that can achieve un-interrupted communication Next, for the optimization problem composed of equations (20a), (20b), (20c), (20d), (20e), (20f), and (20g), the drone R obtains the center position and radius of the optimal circular trajectory, the optimal transmission power, and the maximum information transmission rate through the method of the present invention; finally, the drone R moves in a circular motion with the optimal center position and optimal radius, and at the same time, sends data information to the ground destination node Bob with the optimal transmission power and maximum information rate.

[0161] For the optimization method proposed by the present invention, the present invention conducts a simulation experiment, and the experimental environment is the Matlab environment. Table 1 gives the parameter values in the simulation experiment.

[0162] Table 1

[0163]

[0164] In the experiment, three noise uncertainty parameters are considered, namely, ρ = 0.5 dB, ρ = 1 dB, and ρ = 1.5 dB; different situations where Willie and Bob may be 6 to 800 meters apart are considered. In addition, in order to verify the correctness of the proposed optimization method, the "SQP" algorithm in the Matlab optimization toolbox is used to solve problem (20). In the simulation result graph, the solution obtained by the "SQP" algorithm is marked with "simulation".

[0165] Figure 2 、 Figure 3 、 Figure 4 and Figure 5 show the relationship between the flight altitude of the drone and the distance d0 between Willie and Bob. It is found through observation that when the distance d0 between Willie and Bob is less than 10 meters, in order to achieve uninterrupted covert communication, the drone needs to fly very high; when d0 = 10.4 meters, the flight altitude of the drone will drop suddenly, and then decrease as d0 increases; when d0 is greater than 200 meters, the flight altitude of the drone will tend to the minimum value h min ; the flight altitude of the drone will decrease as ρ increases, that is to say, when the uncertainty of the noise increases, the drone can fly lower. In addition, Figure 2 、 Figure 3 、 Figure 4 and Figure 5 show that the solution given by the "SQP" algorithm is in good agreement with the solution given by the method of the present invention, which proves the correctness of the method of the present invention.

[0166] Figure 6 、 Figure 7 、 Figure 8 and Figure 9The relationship between the horizontal coordinates (x0, y0) of the center of the circular trajectory of the UAV and the distance d0 between Willie and Bob is given. It is found through observation that the vertical coordinate y0 of the horizontal coordinates of the center of the circular trajectory of the UAV is always 0, and the horizontal coordinate is always It shows that the center of the circle should be on the line connecting Willie and Bob and closer to Bob; the horizontal coordinates (x0, y0) of the center of the circular trajectory of the UAV are independent of the value of ρ. In addition, Figure 6 、 Figure 7 、 Figure 8 and Figure 9 show that the solutions given by the "SQP" algorithm are in good agreement with the solutions given by the method of the present invention, proving the correctness of the method of the present invention.

[0167] Figure 10 、 Figure 11 、 Figure 12 and Figure 13 The relationship between the transmission power of the UAV and the distance d0 between Willie and Bob is given. When the distance d0 between Willie and Bob is less than 10 meters, in order to achieve uninterrupted covert communication, the UAV needs to fly very high, so a relatively high transmission power is required; when d0 = 10.4 meters, the flight altitude and transmission power of the UAV will drop sharply and quickly tend to the minimum transmission power P min , until d0 increases to about 200 meters, the transmission power of the UAV will increase accordingly; the transmission power of the UAV will increase with the increase of ρ, indicating that the greater the uncertainty of the noise, the greater the transmission power required. In addition, Figure 10 、 Figure 11 、 Figure 12 and Figure 13 show that the solutions given by the "SQP" algorithm are in good agreement with the solutions given by the method of the present invention, proving the correctness of the method of the present invention.

[0168] Figure 14 、 Figure 15 、 Figure 16 and Figure 17 The relationship between the transmission information rate of the UAV and the distance d0 between Willie and Bob is given. It is observed that the transmission information rate of the UAV first increases slowly with the increase of d0; when d0 increases to about 200 meters, the transmission information rate of the UAV will increase rapidly with the increase of d0; when d0 increases to about 300 meters, the transmission information rate of the UAV will increase with the increase of d0, but the increasing trend will slightly decline; the transmission information rate of the UAV will increase with the increase of ρ, because the larger ρ is, the larger the detection error rate of Willie is, so that the UAV can communicate with Bob at a higher rate. In addition, Figure 14 、 Figure 15 、 Figure 16 and Figure 17It is shown that the solution given by the "SQP" algorithm is in good agreement with the solution given by the method of the present invention, which proves the correctness of the method of the present invention.

[0169] Figure 18 , Figure 19 , Figure 20 and Figure 21 give the communication outage probability at the Bob side when the UAV flies for one week (i.e., θ ranges from 0° to 360°). Here, four cases of d0 values are considered, namely, d0 = 6m, d0 = 40m, d0 = 400m, and d0 = 800m. It can be found from the figure that the communication outage probabilities at the Bob side are all less than the required value of 0.01, which proves the correctness of the method of the present invention; when θ = 180°, the UAV is closest to Bob, so there will be the minimum outage probability. Figure 20 and Figure 21 In, when θ is in the middle region, the outage probability at the Bob side tends to 0, so there is no outage probability curve; as d0 increases, the overall outage probability at the Bob side decreases, because when d0 is large, the flight altitude of the UAV is at the minimum value, which is beneficial to the communication between the UAV and Bob; as the noise uncertainty parameter ρ increases, the outage rate at the Bob side also increases, because a large ρ value means large noise uncertainty, making it impossible for Bob to accurately estimate the noise power, resulting in the overestimation or underestimation of the actual signal-to-noise ratio, and finally manifested as an increase in the outage probability.

[0170] Figure 22 , Figure 23 , Figure 24 and Figure 25 give the total detection error rate at the Willie side when the UAV flies for one week (i.e., θ ranges from 0° to 360°). Similarly, four cases of d0 values are considered here, namely, d0 = 6m, d0 = 40m, d0 = 400m, and d0 = 800m. The figure shows that the total error rates at the Willie side are all greater than the set value of 0.95, which proves the correctness of the method of the present invention; when d0 = 40m, d0 = 400m, and d0 = 800m, θ = 180° means that the UAV is closest to Bob and farthest from Willie, so the maximum total error rate will be generated; when d0 = 6m, the total error rate hardly changes with the change of θ, because the UAV flies very high at this time, resulting in the distance between the UAV and Willie hardly changing with the change of the θ value; as the noise uncertainty parameter ρ increases, the total error rate at the Willie side also increases, because a large ρ value means large noise uncertainty, making it more difficult for Willie to make a correct decision.

[0171] It should be noted that in all the above cases considered, the optimal flight radius of the UAV is equal to And it coincides with the solution given by the "SQP" algorithm, which proves the correctness of the method of the present invention.

[0172] Embodiment 2:

[0173] The computer-readable storage medium of this embodiment stores a computer program, and when the program is executed by a processor, it implements the steps in the optimized method for uninterrupted covert communication assisted by a fixed-wing UAV in Embodiment 1.

[0174] The computer-readable storage medium of this embodiment can be an internal storage unit of the terminal, such as the hard disk or memory of the terminal; the computer-readable storage medium of this embodiment can also be an external storage device of the terminal, such as a plug-in hard disk, a smart memory card, a secure digital card, a flash card, etc. equipped on the terminal; further, the computer-readable storage medium can also include both the internal storage unit and the external storage device of the terminal.

[0175] The computer-readable storage medium of this embodiment is used to store the computer program and other programs and data required by the terminal, and the computer-readable storage medium can also be used to temporarily store the data that has been output or will be output.

[0176] Embodiment 3:

[0177] The computer device of this embodiment includes a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the program, it implements the steps of the optimized method for uninterrupted covert communication assisted by a fixed-wing UAV in Embodiment 1.

[0178] In this embodiment, the processor can be a central processing unit, or other general-purpose processors, digital signal processors, application-specific integrated circuits, off-the-shelf programmable gate arrays, or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor, or the processor can also be any conventional processor, etc.; the memory can include a read-only memory and a random access memory, and provide instructions and data to the processor. A part of the memory can also include a non-volatile random access memory. For example, the memory can also store information about the device type.

[0179] Those skilled in the art should understand that the content disclosed in the embodiments can be provided as a method, a system, or a computer program product. Therefore, this solution can be in the form of a hardware embodiment, a software embodiment, or an embodiment combining software and hardware aspects. Moreover, this solution can be in the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage and optical storage, etc.) containing computer-usable program code.

[0180] This solution is described with reference to the flowcharts and / or block diagrams of methods and computer program products according to embodiments of this solution. It should be understood that each process and / or block in the flowchart and / or block diagram, and the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions; these computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing devices generate a device for implementing the functions specified in one process Figure 1 one process or multiple processes and / or blocks Figure 1 or a device for implementing the functions specified in multiple blocks.

[0181] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer-readable memory generate a manufactured article including an instruction device, and the instruction device implements the functions specified in one process Figure 1 one process or multiple processes and / or blocks Figure 1 or a device for implementing the functions specified in multiple blocks.

[0182] These computer program instructions can also be loaded onto a computer or other programmable data processing device, so that a series of operation steps are executed on the computer or other programmable device to generate a computer-implemented process, and thus the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in one process Figure 1 one process or multiple processes and / or blocks Figure 1 or a device for implementing the functions specified in multiple blocks.

[0183] Those of ordinary skill in the art can understand that all or part of the processes in the above-described embodiment methods can be completed by instructing relevant hardware through a computer program. The program can be stored in a computer-readable storage medium. When the program is executed, it can include the processes of the above-described method embodiments. Among them, the storage medium can be a magnetic disk, an optical disk, a read-only memory (ROM), or a random access memory (RAM), etc.

[0184] The examples described in the present invention are only descriptions of the preferred embodiments of the present invention, and do not limit the concept and scope of the present invention. Without departing from the design concept of the present invention, various deformations and improvements made by those skilled in the art to the technical solutions of the present invention should all fall within the protection scope of the present invention.

Claims

1. A fixed-wing UAV-assisted uninterrupted covert communication optimization method, characterized in that: The steps include: Step 1: Get system information; get Willie's location information w , Bob's location information q B 、Minimum flight altitude of drone h min and maximum flight altitude h max 、Minimum flight speed of drone V min and maximum flight speed V max 、Minimum transmission power of drone P min and the maximum transmit power P max 、UAV maximum tilt angle φ max , unit distance channel power β0, detection total error rate limit for Willie θ, communication interruption probability limit Θ between the drone and Bob B , Standard noise power expressed in dB and the noise uncertainty parameter ρ expressed in dB; Step 2: Initialize gravity acceleration g, calculate the distance d0 between Willie and Bob based on their position information, and calculate the minimum distance between the drone and Willie that can achieve covert communication The lower limit of and upper limit Calculate the optimal flight radius of a drone Calculate the lower limit of the maximum distance between the drone and Bob that can achieve uninterrupted communication Step 3: If Established; the center of the circular trajectory of the drone is h * =h min , the optimal transmission power of the UAV is Calculate the maximum information rate R B [n], then jump to step 11; Step 4: If and Established; the center of the circular trajectory of the drone is Calculating the optimal transmit power for drones and the maximum information rate R B [n], then jump to step 11; Step 5: If and Established; the center of the circular trajectory of the drone is The optimal transmission power of the UAV is Calculate the maximum information rate R B [n], then jump to step 11; Step 6: When and Established; the center of the circular trajectory of the drone is The optimal transmission power of the UAV is Calculate the maximum information rate R B [n], then jump to step 11; Step 7: If and Established; the center of the circular trajectory of the drone is The optimal transmission power of the UAV is Calculate the maximum information rate R B [n], then jump to step 11; Step 8: If and Established; the center of the circular trajectory of the drone is Calculating the optimal transmit power for drones and the maximum information rate R B [n], then jump to step 11; Step 9: If and Established; the center of the circular trajectory of the drone is The optimal transmission power of the UAV is Calculate the maximum information rate R B [n], then jump to step 11; Step 10: If Established; Uninterrupted covert communication cannot be achieved; Step 11: The algorithm ends.

2. The method according to claim 1, characterized in that The specific steps of step 2 are: According to Willie's location information w and Bob’s location information q B , calculate the distance between them d0 = ||q w -q B ||; According to formula (21) and the minimum and maximum transmission power of the UAV, the minimum distance between the UAV and Willie that can achieve covert communication is calculated: The lower limit of and upper limit According to formula (23), the optimal flight radius of the UAV is calculated Calculate the lower limit of the maximum distance between the drone and Bob that can achieve uninterrupted communication 3. The method according to claim 2, characterized in that In step 3, the maximum information rate R is calculated B The formula for [n] is:

4. The method according to claim 3, characterized in that In step 4, calculate the optimal transmission power of the drone The formula is: Calculate the maximum information rate R B The formula for [n] is:

5. The method according to claim 4, characterized in that In step 5, the maximum information rate R is calculated B The formula for [n] is: In steps 6 and 9, the maximum information rate R is calculated B The formula for [n] is: In step 7, the maximum information rate R is calculated B The formula for [n] is:

6. The method according to claim 1, characterized in that In step 8, calculate the optimal transmission power of the drone The formula is: Calculate the maximum information rate R B The formula for [n] is:

7. A storage medium, characterized in that: The storage medium stores instructions, and when a computer reads the instructions, the computer executes the fixed-wing UAV-assisted uninterrupted covert communication optimization method as described in any one of claims 1-6.

8. An electronic device, characterized in that: The invention comprises a processor and the storage medium as claimed in claim 7, wherein the processor executes instructions in the storage medium.

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