A Covert Communication Method for Cooperative Dual Unmanned Aerial Vehicles

Abstract

The present application provides a covert communication method for dual unmanned aerial vehicle (UAV) cooperation. The method includes: Step 1, representing the initial parameters of each node of the dual-UAV cooperative covert communication system and constructing a model of the dual-UAV cooperative covert communication system; Step 2, a ground illegal eavesdropper uses a likelihood ratio detection method to determine whether a ground transmitter and a UAV relay transmit signals to a ground receiver, and derives the covertness constraint of the system; Step 3, analyzing the covert performance of the system, using the minimum value of the two-stage transmission effective throughput to describe the overall performance and taking it as the optimization objective to construct an optimization problem; Step 4, processing the constraint terms in the optimization problem, using a multi-objective sparrow search algorithm to solve the optimization problem to obtain an optimal deployment location and power design scheme. The present application improves the effective covert communication rate in the UAV relay covert communication system.

Description

Technical Field

[0001] This application relates to the field of wireless communication technologies, and particularly relates to a covert communication method for cooperative operation of two unmanned aerial vehicles (UAVs). Background Art

[0002] In the field of wireless communication, UAVs, as an important auxiliary tool, have very wide applications. One important and common application is to act as a relay to assist both communication transceiver parties in long-distance transmission, thereby effectively increasing the communication range (reference: Zeng Y, Zhang R, Lim T J. Throughput maximization for UAV-enabled mobile relaying systems[J]. IEEE Transactions on Communications, 2016, 64(12): 4983-4996.). Compared with traditional ground relays, UAV relays have the advantages of strong flexibility, fast deployability, and the ability to change positions or flight trajectories according to mission requirements. UAV relays transfer the channels of communication users from the ground to the air. Compared with the fading channels on the ground, the high-probability line-of-sight channels between the relay UAV and the ground provide more reliable and higher-quality communication while also increasing the risk of communication being eavesdropped. Therefore, it is necessary to improve the security performance of UAV relay communication. The rapidly developing low probability of detection (LPD) transmission technology in recent years can well solve this problem (reference: Yan S, Zhou X, Hu J, et al. Low probability of detection communication: Opportunities and challenges[J]. IEEE Wireless Communications, 2019, 26(5): 19-25.). LPD communication is also known as covert communication. Usually, some uncertain parameters are introduced at the illegal listener to make it unable to correctly judge whether the communication between legitimate receivers is occurring, reduce the probability of successful detection, and achieve covert transmission at a certain positive rate.

[0003] In existing research on UAV-assisted covert communication, the roles of UAVs are mainly considered as relays or friendly jammers. When using a relay UAV alone, due to the openness of the air-ground channel, the UAV is prone to being detected by illegal listeners on the ground when forwarding signals, resulting in a relatively small achievable covert transmission rate. When using a jamming UAV alone, the ground transmitter needs to send signals with a large power, thereby increasing the risk of communication exposure. Moreover, if the distance between the ground transceiver is far or there are obstacles in the middle, effective information transmission cannot be achieved. Summary of the Invention

[0004] The present application provides a covert communication method for dual-UAV collaboration, which can be used to solve the technical problem that when using a relay or a jamming UAV alone, it is impossible to ensure communication security under the premise of high transmission rate.

[0005] The present application provides a covert communication method for dual-UAV collaboration, and the method includes:

[0006] Step 1: Represent the initial parameters of each node of the dual-UAV collaborative covert communication system and construct a dual-UAV collaborative covert communication system model; wherein, the nodes include a ground transmitter, a ground illegal eavesdropper, a ground receiver, a UAV relay, and a UAV jammer; the initial parameters include the position information of three nodes, namely the ground transmitter, the ground illegal eavesdropper, and the ground receiver, the deployment position range, the working power range of the two UAVs, and the background noise.

[0007] Step 2: The ground illegal eavesdropper uses the likelihood ratio detection method to determine whether the ground transmitter and the UAV relay transmit signals to the ground receiver, and derives the covertness constraint of the system.

[0008] Step 3: Analyze the covert performance of the system, use the minimum value of the two-stage transmission effective throughput to describe the overall performance, and use it as the optimization goal to construct an optimization problem.

[0009] Step 4: Process the constraint terms in the optimization problem, and use the multi-objective sparrow search algorithm to solve the optimization problem to obtain the optimal deployment position and power design scheme.

[0010] Further, Step 1: Represent the initial parameters of each node of the dual-UAV collaborative covert communication system and construct a dual-UAV collaborative covert communication system model, including:

[0011] The set initial parameters include: the horizontal position coordinate (m) of the ground transmitter: q a =[0, 500]; the horizontal position coordinate (m) of the ground listener: q w =[400, 450]; the horizontal position coordinate (m) of the ground receiver: q b =[500, 500]; the working power range (W) of the ground transmitter: 0 ≤ P a ≤ 0.01, the working power range (W) of the UAV relay: 0 ≤ P r ≤ 0.1, the working power range (W) of the UAV jammer: 0 ≤ P j ≤ 1, the horizontal position range (m) of the UAV relay: 0 ≤ x r ≤ 1000, 0 ≤ y r≤1000, height range (m): 300 ≤ Hr ≤ 500; horizontal position range of the UAV jammer (m): 0 ≤ x j ≤1000, 0 ≤ y j ≤1000, height range (m): 300 ≤ H j ≤500; environmental background noise (dBm): σ w 2 = σ b 2 = σ r 2 = -120; channel gain at a reference distance of 1m (dB): β 0 = -60; unknown parameters to be solved are: the optimal horizontal position q of the UAV relay r = [x r , y r , the optimal horizontal position q of the UAV jammer j = [x j , y j , the optimal heights H r 、H j , the optimal operating powers P a 、P r 、P j ;

[0012] The positions of each node are represented in a three - dimensional Cartesian coordinate system. The horizontal positions of the UAV relay, UAV jammer, ground transmitter, ground receiver, and ground illegal listener are respectively represented as: q r = [x r , y r 、q j = [x j , y j 、q a = [x a , y a 、q b = [x b , y b 、q w = [x w , y w ; the heights of the UAV relay and UAV jammer are respectively represented as H r and H j； Considering that the transmission channels from both UAVs to the ground are line - of - sight channels, the channel power gains from the ground transmitter to the UAV relay, from the UAV relay to the ground receiver and ground illegal listener, and from the UAV jammer to the ground receiver and ground illegal listener are respectively denoted as h ar , h rb , h rw, h jb , h jw denotes:

[0013]

[0014] where β 0 denotes the channel power gain when the reference distance is 1 m; the ground channel from the ground transmitter to the ground illegal listener is expressed as:

[0015]

[0016] where, g aw is a quasi-static Rayleigh fading obeying CN(0,1), d aw denotes the distance between the ground transmitter and the ground illegal listener, and α is the path loss exponent.

[0017] Furthermore, in step 2, the ground illegal listener uses the likelihood ratio detection method to determine whether the ground transmitter and the UAV relay transmit signals to the ground receiver, and derives the concealment constraints of the system, including:

[0018] The UAV relay operates in a half-duplex mode, and the signal sent by the ground transmitter undergoes two-stage transmission: the first stage is from the ground transmitter to the UAV relay in the air, and the second stage is from the UAV relay to the ground receiver;

[0019] In the i-th coherence period of the first stage of transmission, the signal received at the ground illegal listener is expressed as:

[0020]

[0021] where, i = 1,..., N, N is the finite block length of this transmission, x a [i], x j [i] respectively denote the symbols sent by the ground transmitter and the UAV jammer, n w [i] ~ CN(0, σ w 2 ) denotes the background noise at the ground illegal listener, P a , P j are the transmission powers of the ground transmitter and the UAV jammer respectively; means that the UAV relay does not forward information, means that the UAV relay forwards information;

[0022] means that the ground illegal listener judges that the ground transmitter does not send information, means that the ground illegal listener judges that the ground transmitter sends information; then the false alarm probability of the ground illegal listener at this time is expressed as The probability of missed detection is expressed as Then the total detection error probability of the ground illegal listener is expressed as:

[0023] ξ 1 =π 0 P FA1 +π 1 P MD1

[0024] where π 0 and π 1 represent the prior transmission probabilities of the UAV relay. Take π 0 =π 0 =0.5, that is, equal prior transmission probabilities; the optimal detection threshold of the ground illegal listener and the corresponding minimum detection error probability ξ * The optimal detection is likelihood ratio detection, and the likelihood ratio function is expressed as follows:

[0025]

[0026] where λ = π 0 / π 1 =1, P 1aw and P 0aw are respectively and the likelihood functions under the conditions. According to Pinsker's inequality, ξ 1 has a lower bound, and the lower bound of ξ 1 is expressed as:

[0027]

[0028] where, D(P 0aw |P 1aw ) is the KL divergence from P 0aw to P 1aw The KL divergence is the relative entropy, which is used to measure the degree of non - approximation of the P 0aw and P 1aw distributions. The smaller the value, the more approximate the two distributions are, and the corresponding detection error probability ξ of the ground illegal listener will increase; the expression of the KL divergence is:

[0029]

[0030] where γ w1 is the signal - to - interference - plus - noise ratio at the ground illegal listener in the first stage of transmission, expressed as:

[0031]

[0032] In covert communication, ξ 1 ≥1 - ε is adopted, where ε is an arbitrarily small value, and from ξ 1From the lower bound, the relative entropy constraint D(P 0aw |P 1aw ) ≤ 2ε 2 is a more stringent constraint than ξ 1 ≥ 1 - ε. Therefore, the covert constraint in the first stage of transmission is expressed as:

[0033] D(P 0aw |P 1aw ) ≤ 2ε 2

[0034] In the second stage of transmission, the UAV relay decodes and forwards the signal from the ground transmitter. Then, at the i-th coherence interval, the signal received by the ground illegal listener is expressed as:

[0035]

[0036] where x r [i] represents the symbol decoded and forwarded by the UAV relay, and P r is the forwarding power of the UAV relay; indicates that the UAV relay does not forward information, indicates that the UAV relay forwards information; the ground illegal listener needs to determine whether the UAV relay has sent a signal. Let represent that the ground illegal listener determines that the UAV relay has not sent information, represent that the ground illegal listener determines that the UAV relay has sent information; then the false alarm probability of the ground illegal listener is expressed as and the missed detection probability is expressed as The total detection error probability of the ground illegal listener is expressed as:

[0037] ξ 2 = π 0 P FA2 + π 1 P MD2

[0038] Using the relative entropy constraint D(P 0rw |P 1rw ) ≤ 2ε 2 as the covert constraint for the second stage of transmission; and the expression of D(P 0rw |P 1rw ) is:

[0039]

[0040] where γ w2 is the signal-to-interference-plus-noise ratio at the ground illegal listener during the second stage of transmission, and is expressed as:

[0041]

[0042] The covert constraint in the second stage of transmission is expressed as:

[0043] D(P 0rw |P 1rw ) ≤ 2ε 2 .

[0044] Furthermore, in step 3, analyze the covert performance of the system. Use the minimum value of the two-stage transmission effective throughput to describe the overall performance and take it as the optimization objective to construct an optimization problem, including:

[0045] In the first stage of transmission, the signal received at the UAV relay in the i-th symbol period is expressed as:

[0046]

[0047] where x a [i] represents the symbol sent by the ground transmitter, n r [i] ~ CN(0, σ r 2 ) represents the background noise at the UAV relay, P a represents the transmission power of the ground transmitter, and the signal-to-noise ratio at the UAV relay is expressed as:

[0048]

[0049] In the second stage of transmission, the signal received at the ground receiver in the i-th symbol period is expressed as:

[0050]

[0051] where n b [i] ~ CN(0, σ b 2 ) represents the background noise at the ground receiver. Due to the interference of the UAV jammer at the ground receiver, the signal-to-interference-plus-noise ratio at the ground receiver is expressed as:

[0052]

[0053] Considering short-packet covert communication, for the transmission of N finite-length messages, the value of the decoding error probability of the receiver is determined by the following method:

[0054]

[0055] where is the Q function, k ∈ {r, b}, R k is the transmission rate, and the effective throughput is expressed as:

[0056] η k = NRk (1 - δ)

[0057] To measure the performance of covert communication, the minimum value of the achievable effective throughput in the two - stage transmission from the ground transmitter to the ground receiver is used as the performance metric, which is defined as:

[0058] η = min(η ar , η rb )

[0059] η k is a monotonically increasing function of γ k . Optimizing the effective throughput η k is equivalent to optimizing γ k . The optimization objective is: γ = min(γ ar , γ rb ). Therefore, the constructed optimization problem is expressed as:

[0060]

[0061] where C1 represents the covert constraint in the first stage of transmission, C2 represents the covert constraint in the second stage of transmission. Both of them must be satisfied simultaneously to achieve covert information transmission; C3, C4, and C5 respectively represent the working power ranges of the ground transmitter, the UAV relay, and the UAV jammer; C6 and C7 respectively represent the altitude ranges of the UAV relay and the UAV jammer.

[0062] Furthermore, step 4: Process the constraint terms in the optimization problem, and use the multi - objective sparrow search algorithm to solve the optimization problem to obtain the optimal deployment location and power design scheme.

[0063] The constraint terms are processed using the multi - objective optimization method, that is, the original constraint optimization problem is converted into a multi - objective optimization problem with two objectives; the covert constraint is written in the standard form in the optimization problem as: D(P 0aw |P 1aw ) - 2ε 2 ≤0; D(P 0rw |P 1rw ) - 2ε 2 ≤0;

[0064] where objective 1 is the objective function of the original constraint optimization problem, that is: f(x) = - min(γ ar , γ rb ), and objective 2 is the degree of individual constraint violation, that is:

[0065] G(x) = max{0, D(P 0aw |P 1aw ) - 2ε 2 , D(P 0rw |P 1rw ) - 2ε2}

[0066] where \(x\) represents the decision variable; the problem is transformed into a multi-objective optimization problem \(F(x)\) with two objectives:

[0067] \(F(x)=F(f(x),G(x))\)

[0068] Then the optimization problem is transformed into the following form of multi-objective optimization:

[0069]

[0070] Finally, the multi-objective sparrow search algorithm is used to solve this problem, and the optimal deployment positions and working powers of the two UAVs are obtained, so as to maximize the effective covert throughput from the ground transmitter to the ground receiver.

[0071] Compared with the prior art, the significant advantages of this application are as follows: (1) The proposed covert transmission scheme in the present invention can enable the ground transmitter to send signals with a lower power through the relay forwarding of the relay UAV, and at the same time can increase the covert communication distance between the ground transmitter and receiver. In addition, by adding the jamming UAV, interference is implemented on the detection of ground illegal eavesdroppers to assist the information forwarding of the relay UAV. Through the cooperation of the two UAVs, the effective covert throughput in the UAV relay covert communication system is significantly improved; (2) In the process of solving the optimization problem, by dealing with the constraint terms, the multi-constrained non-convex optimization problem is transformed into a multi-objective unconstrained optimization problem, and then the multi-objective search algorithm is used to solve the problem. Compared with the traditional approximate processing method of non-convex optimization, the computational complexity is lower and the convergence speed is faster, and the optimization result can be obtained quickly and accurately. That is, after obtaining the initial parameters, the optimal deployment positions and optimal transmission powers of the two UAVs for cooperative covert communication can be quickly obtained. Description of the Drawings

[0072] Figure 1 is a system model diagram of a method for cooperative covert communication between two UAVs provided by an embodiment of this application.

[0073] Figure 2 is a schematic flowchart of a method for cooperative covert communication between two UAVs provided by an embodiment of this application.

[0074] Figure 3 is an algorithm flowchart for solving the optimal deployment position and optimal working power provided by an embodiment of this application.

[0075] Figure 4 is the optimal deployment position of the UAV calculated and obtained by an embodiment of this application.

[0076] Figure 5 is the optimal working powers of the two UAVs calculated and obtained by an embodiment of this application.

[0077] Figure 6 This is the comparative analysis of the concealment performance between the solution provided by the embodiments of this application and the benchmark solution. Detailed implementation manners

[0078] To make the objectives, technical solutions, and advantages of this application clearer, the following will further describe the embodiments of this application in detail with reference to the accompanying drawings.

[0079] This application considers the scenario of two unmanned aerial vehicles (UAVs) collaborating to achieve covert communication. One UAV acts as a relay to assist two transceiver nodes on the ground that are far apart in distance to communicate, and the other UAV acts as a friendly jammer to actively jam the illegal eavesdroppers on the ground, transmitting artificial noise to confuse the opponent's detection and providing signal cover for the relay UAV, thereby effectively improving the covert communication performance.

[0080] This application provides a covert communication method for two UAVs to collaborate. The method includes:

[0081] Step 1: Represent the initial parameters of each node in the two-UAV collaborative covert communication system and construct a two-UAV collaborative covert communication system model. Among them, the nodes include a ground transmitter, a ground illegal eavesdropper, a ground receiver, a UAV relay, and a UAV jammer; the initial parameters include the position information of the three nodes of the ground transmitter, the ground illegal eavesdropper, and the ground receiver, the deployment position range, working power range, and background noise of the two UAVs; among them, the three-dimensional positions and transmission powers of the two UAVs are used as unknown parameters;

[0082] Step 2: The ground illegal eavesdropper uses the likelihood ratio detection method to determine whether the ground transmitter and the UAV relay transmit signals to the ground receiver, and derives the concealment constraint of the system;

[0083] Step 3: Analyze the concealment performance of the system, use the minimum value of the two-stage transmission effective throughput to describe the overall performance, and use it as the optimization objective to construct an optimization problem;

[0084] Step 4: Process the constraint terms in the optimization problem, and use the multi-objective sparrow search algorithm (Multi-objective Sparrow Search Algorithm, MSSA) to solve the optimization problem to obtain the optimal deployment position and power design scheme.

[0085] Step 1: Represent the initial parameters of each node in the two-UAV collaborative system and construct a two-UAV collaborative covert communication system model. It includes:

[0086] The set initial parameters include: the horizontal position coordinate (m) of the ground transmitter: q a= [0, 500]; Horizontal position coordinate (m) of the ground listener: q w = [400, 450]; Horizontal position coordinate (m) of the ground receiver: q b = [500, 500]; Operating power range (W) of the ground transmitter: 0 ≤ P a ≤ 0.01, Operating power range (W) of the UAV relay: 0 ≤ P r ≤ 0.1, Operating power range (W) of the UAV jammer: 0 ≤ P j ≤ 1, Horizontal position range (m) of the UAV relay: 0 ≤ x r ≤ 1000, 0 ≤ y r ≤ 1000, Altitude range (m): 300 ≤ Hr ≤ 500; Horizontal position range (m) of the UAV jammer: 0 ≤ x j ≤ 1000, 0 ≤ y j ≤ 1000, Altitude range (m): 300 ≤ H j ≤ 500; Environmental background noise (dBm): σ w 2 = σ b 2 = σ r 2 = -120; Channel gain (dB) at a reference distance of 1 m: β 0 = -60; Unknown parameters to be solved are: Optimal horizontal position q of the UAV relay r = [x r , y r , Optimal horizontal position q of the UAV jammer j = [x j , y j , Optimal altitudes H of the UAV relay and the UAV jammer r 、H j , Optimal operating powers P of the ground transmitter, the UAV relay, and the UAV jammer a 、P r 、P j ;

[0087] The positions of each node are represented in a three-dimensional Cartesian coordinate system. The horizontal positions of the UAV relay, the UAV jammer, the ground transmitter, the ground receiver, and the ground illegal listener are respectively represented as: q r = [x r , y r , q j = [x j , y j , q a = [x a , y a , q b = [xb , y b , q w = [x w , y w ; The heights of the UAV relay and the UAV jammer are respectively denoted as H r and H j； Considering that the transmission channels from both UAVs to the ground are line-of-sight channels, the channel power gains from the ground transmitter to the UAV relay, from the UAV relay to the ground receiver and the ground illegal eavesdropper, and from the UAV jammer to the ground receiver and the ground illegal eavesdropper are respectively denoted by h ar , h rb , h rw , h jb , h jw :

[0088]

[0089] where β 0 represents the channel power gain at a reference distance of 1 m; The ground channel from the ground transmitter to the ground illegal eavesdropper consists of a large-scale path loss and a small-scale fading, and is expressed as:

[0090]

[0091] where, g aw is a quasi-static Rayleigh fading obeying CN(0, 1), d aw represents the distance between the ground transmitter and the ground illegal eavesdropper, and α is the path loss exponent.

[0092] Step 2: The ground illegal eavesdropper uses the likelihood ratio detection method to determine whether the ground transmitter and the UAV relay are transmitting signals to the ground receiver, and derives the secrecy constraint of the system;

[0093] The UAV relay operates in a half-duplex mode. The signal sent by the ground transmitter undergoes two-stage transmission: the first stage is from the ground transmitter to the UAV relay in the air, and the second stage is from the UAV relay to the ground receiver;

[0094] In the i-th coherence period of the first stage of transmission, the signal received at the ground illegal eavesdropper is expressed as:

[0095]

[0096] where, i = 1,..., N, N is the finite block length of this transmission, x a [i], x j [i] respectively represent the symbols sent by the ground transmitter and the UAV jammer, n w [i] ~ CN(0, σw 2 ) represents the background noise at the ground illegal listener, P a 、P j are the transmission powers of the ground transmitter and the UAV jammer respectively; indicates that the UAV relay did not forward the information, indicates that the UAV relay forwarded the information;

[0097] The ground illegal listener needs to determine whether the ground transmitter has sent a signal, using to indicate that the ground illegal listener determines that the ground transmitter did not send information, to indicate that the ground illegal listener determines that the ground transmitter has sent information; then the false alarm probability of the ground illegal listener at this time is expressed as The miss detection probability is expressed as Then the total detection error probability of the ground illegal listener is expressed as:

[0098] ξ 1 = π 0 P FA1 + π 1 P MD1

[0099] where π 0 and π 1 represent the prior transmission probabilities of the UAV relay, taking π 0 = π 0 = 0.5, that is, equal prior transmission probabilities; the optimal detection threshold of the ground illegal listener and the corresponding minimum detection error probability ξ * The optimal detection is likelihood ratio detection, and the likelihood ratio function is expressed as follows:

[0100]

[0101] where λ = π 0 / π 1 = 1, P 1aw and P 0aw are respectively and under the conditions of the likelihood functions. According to Pinsker's inequality, ξ 1 has a lower bound, and subsequent research is based on this lower bound, and the lower bound of ξ 1 is expressed as:

[0102]

[0103] where, D(P 0aw |P 1aw ) is from P 0aw to P 1awThe Kullback-Leibler (KL) divergence. The KL divergence is the relative entropy and is used to measure P 0aw and P 1aw The degree of non-approximation of the distributions. The smaller the value, the more approximate the two distributions are. When D(P 0aw |P 1aw ) is very small, it means that the distance between P 0aw and P 1aw is very small, and the detection error probability ξ of the corresponding ground illegal listener will increase; The expression of the KL divergence is:

[0104]

[0105] where γ w1 is the signal-to-interference-plus-noise ratio at the ground illegal listener in the first stage of transmission, expressed as:

[0106]

[0107] In covert communication, ξ 1 ≥ 1 - ε is adopted, where ε is an arbitrarily small value. From the lower bound of ξ 1 , it can be seen that the relative entropy constraint D(P 0aw |P 1aw ) ≤ 2ε 2 is a more stringent constraint than ξ 1 ≥ 1 - ε. Therefore, the covert constraint in the first stage of transmission is expressed as:

[0108] D(P 0aw |P 1aw ) ≤ 2ε 2

[0109] In the second stage of transmission, the UAV relay decodes and forwards the signal from the ground transmitter. Then, at the i-th coherence period, the signal received at the ground illegal listener is expressed as:

[0110]

[0111] where x r [i] represents the symbol decoded and forwarded by the UAV relay, and P r is the forwarding power of the UAV relay; means that the UAV relay does not forward information, means that the UAV relay forwards information; The ground illegal listener needs to judge whether the UAV relay has sent a signal. Use to indicate that the ground illegal listener judges that the UAV relay has not sent information, to indicate that the ground illegal listener judges that the UAV relay has sent information; Then the false alarm probability of the ground illegal listener is expressed as The undetected probability is expressed as The total detection error probability of the ground illegal listener is expressed as:

[0112] ξ 2 =π 0 P FA2 +π 1 P MD2

[0113] Similar to the analysis of the first-stage transmission, a more stringent relative entropy constraint is used as the covert constraint for the second-stage transmission; and the expression of D(P 0rw |P 1rw ) is:

[0114]

[0115] where γ w2 is the signal-to-interference-plus-noise ratio at the ground illegal listener during the second stage of transmission, and is expressed as:

[0116]

[0117] In summary, the covert constraint during the second stage of transmission is expressed as:

[0118] D(P 0rw |P 1rw ) ≤ 2ε 2

[0119] Step 3: Analyze the covert performance of the system. The minimum value of the effective throughput of the two-stage transmission is used to describe the overall performance and is used as the optimization objective to construct an optimization problem, including:

[0120] During the first stage of transmission, the signal received at the UAV relay in the i-th symbol period is expressed as:

[0121]

[0122] where x a [i] represents the symbol sent by the ground transmitter, and n r [i] ~ CN(0,σ r 2 ) represents the background noise at the UAV relay, and P a represents the transmission power of the ground transmitter. The signal-to-noise ratio at the UAV relay is expressed as:

[0123]

[0124] During the second stage of transmission, the signal received at the ground receiver in the i-th symbol period is expressed as:

[0125]

[0126] where n b [i]~CN(0,σ b 2 ) represents the background noise at the ground receiver. Due to the interference of the UAV jammer at the ground receiver, the signal-to-interference-plus-noise ratio at the ground receiver is expressed as:

[0127]

[0128] Considering short-packet covert communication, for the transmission of N pieces of information with a finite code length, the value of the decoding error probability of the receiver is determined by the following method:

[0129]

[0130] where is the Q function, k ∈ {r, b}, R k is the transmission rate, and the effective throughput is expressed as:

[0131] η k = NR k (1 - δ)

[0132] In the UAV relay communication model constructed in the present invention, in order to measure the performance of covert communication, the minimum value of the effective throughput achievable in the two-stage transmission from the ground transmitter to the ground receiver is used as a performance index, defined as:

[0133] η = min(η ar , η rb )

[0134] Existing literature has proven that η k is a monotonically increasing function of γ k . Optimizing the effective throughput η k is equivalent to optimizing γ k . The optimization objective is: γ = min(γ ar , γ rb ). Therefore, the constructed optimization problem is expressed as:

[0135]

[0136] where C1 represents the covert constraint in the first stage of transmission, C2 represents the covert constraint in the second stage of transmission. Both must be satisfied simultaneously to achieve covert information transmission; C3, C4, and C5 respectively represent the working power ranges of the ground transmitter, the UAV relay, and the UAV jammer; C6 and C7 respectively represent the height ranges of the UAV relay and the UAV jammer.

[0137] There are multiple optimization variables in this problem, and these variables are coupled with each other, making it difficult to solve directly. Therefore, an intelligent heuristic algorithm can be considered to solve the problem. However, most intelligent heuristic algorithms are used to solve unconstrained optimization problems. Therefore, the constraints of the problem need to be processed first.

[0138] Step 4: Process the constraints in the optimization problem, and use the Multi-objective Sparrow Search Algorithm (MSSA) to solve the optimization problem to obtain the optimal deployment location and power design scheme.

[0139] The main inequality constraints in the problem are hidden constraints, and the rest are the upper and lower limit ranges of parameters. For the processing of the constraints in the constrained problem, common methods include the penalty function method, the multi-objective optimization method, etc. Among them, the penalty function method is more dependent on the selection of parameters, while the multi-objective optimization method does not require additional parameter setting, successfully avoiding the imbalance problem between the objective function and the constraints, and having good performance in dealing with constrained optimization.

[0140] Therefore, this application uses the multi-objective optimization method to process the constraints, that is, converts the original constrained optimization problem into a multi-objective optimization problem with two objectives; the hidden constraint is written in the standard form of the optimization problem as: D(P 0aw |P 1aw ) - 2ε 2 ≤ 0; D(P 0rw |P 1rw ) - 2ε 2 ≤ 0;

[0141] Among them, objective 1 is the objective function of the original constrained optimization problem, that is: f(x) = -min(γ ar , γ rb ), and objective 2 is the degree of individual constraint violation, that is:

[0142] G(x) = max{0, D(P 0aw |P 1aw ) - 2ε 2 , D(P 0rw |P 1rw ) - 2ε 2}

[0143] Where x represents the decision variable; the problem is converted into a multi-objective optimization problem F(x):

[0144] F(x) = F(f(x), G(x))

[0145] Then the optimization problem is converted into the following form of multi-objective optimization:

[0146]

[0147] Finally, the multi-objective sparrow search algorithm is used to solve this problem, and the optimal deployment positions and working powers of the two UAVs are obtained, so as to maximize the effective covert throughput from the ground transmitter to the ground receiver.

[0148] In the constraints of the optimization problem, there are only upper and lower limit ranges. The objective function is to solve the minimum value of two functions, which can be regarded as a multi-objective unconstrained non-convex optimization problem. For this type of problem, using traditional non-convex optimization approximation methods to solve the problem will result in a high computational complexity and a slow convergence speed. Therefore, an intelligent heuristic algorithm is considered for solving. The sparrow search algorithm is a new intelligent optimization algorithm proposed in recent years. It has the advantages of few adjustable parameters, fast convergence speed, and strong search ability, and can well solve problems such as UAV trajectory planning and image segmentation. The multi-objective sparrow search algorithm divides the sparrow population into two categories. One is the discoverer, which is responsible for finding food and providing the foraging area and direction. The other is the predator, which follows the discoverer and obtains the food of the discoverer. Among all the sparrow populations, a certain proportion of individuals are also selected as scouts, which are responsible for sending alarm signals when the predator encounters danger, so that the sparrow population can make corresponding responses. To apply the sparrow search algorithm to the multi-objective optimization problem, the non-dominated sorting method in the non-dominated sorting genetic algorithm (NSGA-II) is used to sort the sparrow population, so as to distinguish the discoverer and the predator, and an external archive is introduced to store the non-dominated solutions obtained in each iteration of the algorithm. By using the multi-objective sparrow search algorithm to solve the optimization problem, the optimal deployment positions and working powers of the two UAVs are obtained, so as to maximize the effective covert throughput of the information sent by the ground transmitter relayed by the UAV to the ground receiver. For the specific algorithm flow, please refer to Figure 3 。

[0149] The solution results of this example are shown in Figure 4 、 Figure 5 ,from Figure 4 it can be seen the relationship between the optimal deployment positions of the two UAVs and the position change of the ground illegal monitor. The optimal horizontal position projection of the UAV jammer is located on the extension line of the connection line between the ground receiver and the ground illegal monitor, and the abscissa of the optimal horizontal position of the UAV relay is located between the ground transmitter and the ground receiver. From Figure 5 the optimal powers of the UAV relay and the UAV jammer under different covert constraints can be seen.

[0150] Refer to Figure 6 It can be seen that the maximum effective covert throughput obtained by the proposed dual-UAV cooperative covert communication method of the present invention is significantly better than the benchmark scheme that only uses the relay UAV without using the cooperative interference UAV. The present invention can significantly improve the effective covert throughput.

[0151] The present invention first analyzes the detection performance of ground illegal eavesdroppers, and on this basis, derives the concealment constraint and the expression for describing the concealment transmission performance. Under the satisfaction of all constraint conditions, an optimization problem is established with the effective throughput as the objective function and the three-dimensional deployment positions and working powers of two unmanned aerial vehicles as decision variables. Finally, the sparrow search algorithm based on multi-objective optimization is used to solve the optimization problem, and the optimal position deployment and power design scheme are obtained.

[0152] The implementation manners of the present application described above do not constitute a limitation on the protection scope of the present application.

Claims

1. A dual-UAV cooperative covert communication method, characterized in that: The method comprises: Step 1, represents the initial parameters of each node of the dual-UAV cooperative covert communication system and constructs a dual-UAV cooperative covert communication system model; wherein the nodes include ground transmitters, ground illegal eavesdroppers, ground receivers, UAV relays and UAV jammers; the initial parameters include the location information of the three nodes of the ground transmitter, the ground illegal eavesdropper and the ground receiver, the deployment position range, working power range and background noise of the two UAVs; Step 2: The ground illegal eavesdropper uses the likelihood ratio detection method to determine whether the ground transmitter and the UAV relay transmit signals to the ground receiver, and derives the concealment constraint of the system; Step 3: Analyze the concealment performance of the system, use the minimum value of the effective throughput of the two-stage transmission to describe the overall performance, and use it as the optimization target to construct the optimization problem; Step 4: Process the constraints in the optimization problem and use a multi-objective sparrow search algorithm to solve the optimization problem and obtain the optimal deployment location and power design solution; Step 1: Express the initial parameters of each node of the dual-UAV cooperative covert communication system and build a dual-UAV cooperative covert communication system model, including: The initial parameters to be set include: horizontal position coordinates of the ground transmitter (m): q a = [0,500]; horizontal position coordinate of the ground listener (m): q w =[400,450]; horizontal position coordinate of ground receiver (m):q b =[500,500]; Ground transmitter operating power range (W): 0≤P a ≤0.01, UAV relay working power range (W): 0≤P r ≤0.1, UAV jammer operating power range (W): 0≤P j ≤1, UAV relay horizontal position range (m): 0≤x r ≤1000,0≤y r ≤1000, height range (m): 300≤Hr≤500; UAV jammer horizontal position range (m): 0≤x j ≤1000,0≤y j ≤1000, height range (m): 300≤H j ≤500; Environmental background noise (dBm): σ w 2 =σ b 2 =σ r 2 =-120; Channel gain (dB) at a reference distance of 1m: β0 = -60; The unknown parameters to be solved are: The optimal horizontal position q of the drone relay r =[x r ,y r ], the optimal horizontal position of the UAV jammer q j =[x j ,y j ], the optimal height H of the UAV relay and UAV jammer r , H j , the optimal operating power P of the ground transmitter, UAV relay, and UAV jammer a , P r , P j ; The position of each node is represented by a three-dimensional Cartesian coordinate system. The horizontal positions of the drone relay, drone jammer, ground transmitter, ground receiver and ground illegal eavesdropper are respectively expressed as: q r =[x r ,y r ], q j =[x j ,y j ], q a =[x a ,y a ], q b =[x b ,y b ], q w =[x w ,y w ]; the heights of the UAV relay and the UAV jammer are denoted as H r and H j； Considering that the transmission channels from the two drones to the ground are all line-of-sight channels, the channel power gains from the ground transmitter to the drone relay, from the drone relay to the ground receiver and the ground illegal eavesdropper, and from the drone jammer to the ground receiver and the ground illegal eavesdropper are expressed as h ar ,h rb ,h rw ,h jb ,h jw express: Where β0 represents the channel power gain when the reference distance is 1m; the ground channel from the ground transmitter to the ground illegal eavesdropper is expressed as: Among them, g aw is the quasi-static Rayleigh fading subject to CN(0,1), d aw represents the distance between the ground transmitter and the illegal ground monitor, and α is the path loss index; Step 2: The ground-based illegal eavesdropper uses a likelihood ratio detection method to determine whether the ground transmitter and the drone relay transmit signals to the ground receiver, and derives the system's concealment constraints, including: The drone relay works in half-duplex mode, and the signal from the ground transmitter goes through two stages of transmission: the first stage is from the ground transmitter to the drone relay in the air, and the second stage is from the drone relay to the ground receiver; In the i-th coincidence period of the first stage of transmission, the signal received by the illegal ground monitor is expressed as: Where i = 1, ..., N, N is the finite block length of this transmission, x a [i], x j [i] represents the symbols sent by the ground transmitter and the UAV jammer, respectively, n w [i]~CN(0,σ w 2 ) represents the background noise at the illegal ground monitor, P a , P j are the transmission powers of the ground transmitter and the UAV jammer respectively; Indicates that the drone relay does not forward information. It means that the drone relayed the information; It means that the illegal ground monitor judges that the ground transmitter does not send any information. It means that the illegal ground monitor judges that the ground transmitter has sent information. Then the false alarm probability of the illegal ground monitor is expressed as The probability of missed detection is expressed as Then the total detection error probability of illegal ground monitors is expressed as: ξ1=π0P FA1 +π1P MD1 Where π0 and π1 represent the prior transmission probability of the drone relay, and π0=π1=0.5, that is, equal prior transmission probability; the optimal detection threshold of the ground illegal eavesdropper and the corresponding minimum detection error probability ξ * The optimal detection is the likelihood ratio detection, and the likelihood ratio function is expressed as follows: Where λ=π0 / π1=1, P 1aw and P 0aw They are and According to Pinsker inequality, the likelihood function under the condition has a lower bound, and the lower bound of ξ1 is expressed as: Among them, D(P 0aw |P 1aw ) is P 0aw To P 1aw KL divergence, KL divergence is the relative entropy, used to measure P 0aw and P 1aw The smaller the value of the distribution dissimilarity, the more similar the two distributions are, and the corresponding detection error probability ξ of the illegal ground eavesdropper will increase; the expression of KL divergence is expressed as: where γ w1 The signal-to-interference-to-noise ratio at the illegal ground monitor in the first stage of transmission is expressed as: In covert communication, ξ1≥1-ε is used, where ε is an arbitrarily small value. From the lower bound of ξ1, we can see that the relative entropy constraint D(P 0aw |P 1aw )≤2ε 2 is a stricter constraint than ξ1≥1-ε, so the hidden constraint in the first stage of transmission is expressed as: D(P 0aw |P 1aw )≤2ε 2 In the second stage of transmission, the UAV relay decodes and forwards the signal from the ground transmitter. At this time, in the i-th coincidence period, the signal received by the illegal ground eavesdropper is expressed as: Among them, x r [i] indicates the symbol of the UAV relay decoding and forwarding, P r is the forwarding power of the drone relay; It means that the drone relay does not forward information. It means that the drone relay has forwarded the information; illegal ground eavesdroppers need to determine whether the drone relay has sent a signal. It means that the illegal ground monitors judged that the drone relay did not send any information. It means that the illegal ground monitor judges that the UAV relay sends information; then the false alarm probability of the illegal ground monitor is expressed as The probability of missed detection is expressed as The total detection error probability of illegal ground monitors is expressed as: ξ2=π0P FA2 +π1P MD2 Using the relative entropy constraint D(P 0rw |P 1rw )≤2ε 2 As the second-stage transmission concealment constraint; and D(P 0rw |P 1rw ) is: where γ w2 is the signal-to-interference-to-noise ratio at the ground illegal eavesdropper in the second stage of transmission, expressed as: The hidden constraint in the second stage of transmission is expressed as: D(P 0rw |P 1rw )≤2ε 2 Step 3: Analyze the concealment performance of the system, use the minimum value of the effective throughput of the two-stage transmission to describe the overall performance, and use it as the optimization target to construct the optimization problem; including: In the first stage of transmission, the signal received at the drone relay in the i-th symbol period is expressed as: Among them, x a [i] represents the symbol sent by the ground transmitter, n r [i]~CN(0,σ r 2 ) represents the background noise at the UAV relay, P a represents the transmission power of the ground transmitter, and the signal-to-noise ratio at the UAV relay is expressed as: In the second stage of transmission, the signal received by the ground receiver in the i-th symbol period is expressed as: Among them, n b [i]~CN(0,σ b 2 ) represents the background noise at the ground receiver. Since the ground receiver is affected by the interference of the UAV jammer, the signal-to-interference-noise ratio at the ground receiver is expressed as: Considering short packet covert communication, for information transmission with N finite code lengths, the value of the receiver's decoding error probability is determined by the following method: in is the Q function, k∈{r,b}, R k is the transmission rate, then the effective throughput is expressed as: or k =NR k (1-d) In order to measure the performance of covert communication, the minimum effective throughput that can be achieved in the two-stage transmission from the ground transmitter to the ground receiver is used as the performance indicator, which is defined as: η=min(η ar ,or rb ) η k About γ k A monotonically increasing function that optimizes the effective throughput η k Equivalent to optimizing γ k , the optimization goal is: γ=min(γ ar ,γ rb ), so the constructed optimization problem is expressed as: Among them, C1 represents the concealment constraint of the first stage of transmission, and C2 represents the concealment constraint of the second stage of transmission. Both must be met at the same time to realize covert information transmission; C3, C4, and C5 represent the operating power ranges of ground transmitters, UAV relays, and UAV jammers, respectively; C6 and C7 represent the altitude ranges of UAV relays and UAV jammers, respectively.

2. The method according to claim 1, characterized in that Step 4: Process the constraints in the optimization problem and use the multi-objective sparrow search algorithm to solve the optimization problem and obtain the optimal deployment location and power design solution; The constraints are processed by using multi-objective optimization method, that is, the original constraint optimization problem is converted into a multi-objective optimization problem with two objectives; The hidden constraints are written in the standard form of the optimization problem: D(P 0aw |P 1aw )-2ε 2 ≤0; D(P 0rw |P 1rw )-2ε 2 ≤0; Where objective 1 is the objective function of the original constrained optimization problem, that is, f(x) = -min(γ ar ,γ rb ), and goal 2 is the degree of individual constraint violation, namely: G(x)=max{0,D(P 0aw |P 1aw )-2ε 2 ,D(P 0rw |P 1rw )-2ε 2 } Where x represents the decision variable; the problem is transformed into a multi-objective optimization problem F(x) with two objectives: F(x)=F(f(x),G(x)) The optimization problem is then transformed into the following multi-objective optimization form: Finally, the multi-objective sparrow search algorithm is used to solve the problem and obtain the optimal deployment position and working power of the two UAVs, so as to maximize the effective covert throughput from the ground transmitter to the ground receiver.

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