Unmanned aerial vehicle position optimization method under NOMA covert communication system

Abstract

The invention discloses an unmanned aerial vehicle position optimization method under an NOMA covert communication system, and relates to the technical field of unmanned aerial vehicle communication. An unmanned aerial vehicle base station sends two kinds of signals to two ground users by adopting a superposition coding technology, the two ground users access the system in a non-orthogonal multiple access mode, and on the premise of meeting the concealment and reliability of communication between an unmanned aerial vehicle and a near-end user, an improved marine predator algorithm is adopted to search for the optimal position of the unmanned aerial vehicle base station, so that the unmanned aerial vehicle base station is optimized. And the hidden throughput of the system is maximized. According to the method, a marine predator algorithm is improved on the basis of a self-adaptive search strategy and a sine and cosine optimization algorithm, the defect that the marine predator algorithm is prone to falling into local optimum is effectively overcome, and the convergence speed is increased.

Description

Technical Field

[0001] The present invention belongs to the technical field of unmanned aerial vehicle communication, and in particular relates to a method for optimizing the position of an unmanned aerial vehicle in a NOMA covert communication system. Background Art

[0002] With the rapid development of wireless communication technology, human beings' dependence on wireless networks has grown rapidly, and an unprecedented amount of confidential and sensitive information is being transmitted through wireless media. At the same time, issues such as security and privacy are increasingly receiving attention from most people. Today, unmanned aerial vehicles (UAVs) play an important role in target positioning, environmental monitoring, military communications and other fields. However, due to the broadcast nature of wireless media and the long-distance transmission characteristics of line of sight (LOS) air-to-ground links, UAV communication systems are more vulnerable to communication security threats than ground wireless networks. As a physical layer information security technology, covert communication fundamentally protects user privacy by confusing listeners so that they cannot determine whether the user sends information. At the same time, covert communication technology provides an innovative solution for improving the security defense and privacy protection capabilities of UAV communications. The idea of ​​covert communication is to make it impossible for illegal monitors to detect the wireless transmission between wireless devices. It directly realizes low-probability detection of wireless signals at the physical layer. Unlike physical layer security technology that focuses on protecting the content of communication, covert communication focuses more on protecting the legitimacy of communication behavior. Combining covert communication with non-orthogonal multiple access (NOMA) technology improves the transmission rate of covert communication and further improves the system security performance.

[0003] Non-orthogonal multiple access technology can ensure the communication fairness of access users, so as to ensure the access and communication of low-speed service users. When the user channel conditions are uneven or have large differences, NOMA technology has significantly improved spectrum utilization efficiency, throughput performance and user fairness compared with traditional orthogonal frequency division multiple access (OFDMA). In the 5G communication system and the future 6G network deployment, NOMA technology will continue to receive attention as a core technology. Summary of the invention

[0004] In view of this, the present invention provides a method for optimizing the position of a UAV in a NOMA covert communication system. The present invention improves the marine predator algorithm based on an adaptive search strategy and a sine-cosine optimization algorithm, thereby improving the convergence speed and accuracy of the marine predator algorithm and effectively avoiding falling into a local optimum.

[0005] In order to achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is:

[0006] A method for optimizing the position of a drone in a NOMA covert communication system, wherein the NOMA covert communication system includes a drone, a user, and an eavesdropper. The drone sends a high-power signal to a remote user, and the communication between the two continues. The drone uses the high-power signal to cover up the low-power signal between the drone and the near-end user to ensure that it is not discovered by the eavesdropper. The eavesdropper uses a power detector to passively detect whether the drone sends covert information to the near-end user. The method includes the following steps:

[0007] S1: construct the objective function, set hidden constraints and interrupt constraints, and determine the range of variables;

[0008] S2: Initialize the population and generate a set of random candidate solutions for UAV positions;

[0009] S3: Determine the population fitness value and construct the elite matrix and predator matrix;

[0010] S4: Adopting an adaptive search strategy, by collecting information feedback during the search process, introducing an adaptive search factor to control the adjustment of the step size and the update intensity of the individual position during the iteration process;

[0011] S5: Calculate the fitness value, update the predator position, and measure the pros and cons of the current drone position; use the sine-cosine optimization algorithm to achieve the jump of candidate solutions in the solution space, and fine-tune the prey position again;

[0012] S6: Using the FADs fish school effect, introducing environmental factors, updating the best predator position, and continuously optimizing the drone position through multiple rounds of iterations;

[0013] S7: Determine whether the stop condition is met. If so, output the optimal fitness value, i.e., the position of the drone. Otherwise, repeat steps S4-S7.

[0014] Further, step S1 includes:

[0015] S101: In the set UAV covert communication scenario, the UAV sends two signals, one is a high-power signal sent to the remote user, and the other is a superposition-coded signal sent to the near-end user and the remote user at the same time in a specific time slot; in a specific time slot, the UAV uses superposition coding to send information to two users at the same time, and its expression is:

[0016]

[0017] The received signal at the near-end user Bob is expressed as:

[0018]

[0019] Where n = 1, 2, ..., N represents the total number of channels used, P a Represents the total transmission power of the drone, Represents the power allocation factor, considering system performance and user fairness factors, set d ab is the distance between the drone and Bob, α is the path loss factor, represents the additive white Gaussian noise at Bob, and the channel gain coefficient between the drone and Bob is Where β0 represents the unit distance channel power gain, L a and L b denote the horizontal coordinates of the drone and Bob, respectively, H denotes the flight altitude of the drone, ‖·‖ denotes the Euclidean norm operation, and x 1 and x 2 They represent the signals sent by the drone to the remote user Carl and the local user Bob respectively;

[0020] S102: Willie performs a binary hypothesis test to determine whether the drone sends a covert signal to Bob. The received signal expression is:

[0021]

[0022] Among them, H 0 is the null hypothesis, indicating that the drone does not send covert information to Bob, H 1 is the alternative hypothesis, indicating that there is communication between the drone and Bob, d aw is the distance between the drone and the listener, Indicates that the mean at the listener is 0 and the variance is The channel gain coefficient between the drone and the listener is Where L w Indicates the horizontal coordinate of the listener;

[0023] The listener uses a power detector to analyze the received signal, and its decision rule expression is:

[0024]

[0025] Among them, D 0 and D 1 represents the listener's binary decision on whether the drone sends covert information, Y w represents the average power received by the listener in a time slot, M represents the total transmission time slot, and τ represents the detection threshold of the listener;

[0026] The total detection error probability of the listener is denoted by ξ, which is given by the false alarm probability P FA =Pr(D 1 |H 0 ) and the probability of missed detection P MD =Pr(D 0 |H 1 ), the expression is:

[0027] ξ=P FA +P MD

[0028] S103: According to the transmission criteria of the NOMA covert communication system, SIC decoding is used at the receiving end; Bob first demodulates the high-power signal, then filters it out, and finally demodulates his own signal; the remote user Carl filters out Bob's signal as noise; the interruption probability at Bob is:

[0029]

[0030] The outage probability at Carl is:

[0031]

[0032] in, The channel gain coefficient between the drone and Carl is Where L c represents Carl's horizontal coordinate, and R 1 and R 2 Represent the signal transmission rates at Carl and Bob respectively;

[0033] S104: In a two-dimensional rectangular coordinate system, the optimal position of the drone is optimized. The positions L of the near-end user Bob, the far-end user Carl, and the listener Willie are known. Under the premise of satisfying the system's concealment constraints and reliability constraints, the system's concealment throughput is maximized to achieve the optimal position of the drone. The optimization problem is as follows:

[0034]

[0035]

[0036] P out,C ≤P th

[0037] Among them, Γ 1 represents the concealed throughput, represents the hidden constraints of the system, P th represents the maximum interruption probability allowed by Carl; where, represents the average detection error probability of the listener Willie, ε represents an arbitrarily small positive number, when When it was established, it was believed that covert communication between the drone and Bob could be achieved.

[0038] Further, step S2 includes:

[0039] S201: Define the search space of the drone position as:

[0040] S = {((x, y)|x min ≤x≤x max ,y min ≤y≤y max )}

[0041] S202: Randomly generate R candidate solutions in the search space, each candidate solution represents the initial position of a UAV and is represented by a vector; on the two-dimensional plane, each solution P i It is expressed as:

[0042] P i =(x i ,y i ), i = 1, 2, ..., R

[0043] x i =x min +(x max -x min )*rand(i)

[0044] y i =y min +(y max -y min )*rand(i)

[0045] Here, rand(i) represents a random function that generates a uniform distribution in the interval [0, 1].

[0046] Further, in step S4, the adaptive search factor is:

[0047]

[0048] Among them, λ, μ, k are constant coefficients, θ is a random number between the interval [0, 1], t is the current iteration number, T max is the maximum number of iterations, and e is Euler's constant.

[0049] Furthermore, in step S5, the sine-cosine algorithm is used to optimize the prey link of the marine predator algorithm, so as to realize the jump of the candidate solution in the solution space, and fine-tune the prey position again to avoid falling into the local optimum. The specific expression is:

[0050]

[0051]

[0052] in, is the position of the current individual in the tth generation of the i-th dimension, h is a constant, t is the current iteration number, and T is the maximum iteration number; r 2 represents the angle, which is a random number between 0 and 2π; r 3 is a random number between 0 and 2; r 4 is a random number between 0 and 1; represents the position of the i-th dimension of the optimal individual position variable at the tth iteration; r 1 Indicates that the location area of ​​the next solution is between or outside the current solution and the optimal solution; r 2 , r 3 , r 4 is a random factor, r 2 Defines the distance of the current solution close to or away from the optimal solution; r 3 Provide a random weight for the optimal solution, randomly emphasize or ignore the effect of the optimal solution in defining the moving distance of the candidate solution, r 4 Switching the sine and cosine functions equally allows one solution to be relocated around the other, ensuring that the space between two solutions is searched.

[0053] Furthermore, in step S6, the specific method of optimizing the position of the drone is:

[0054]

[0055] Among them, FADs represents the probability of affecting the algorithm optimization process, CF is the predator Brownian motion adaptive parameter, P max and P min represents the upper and lower limits of the individual prey positions, r is a random number between 0 and 1, U is a binary vector matrix containing 0 and 1, and the random indices of all prey matrices are r1 and r2 respectively.

[0056] The beneficial effects of the present invention are:

[0057] 1. Compared with the original marine predator algorithm, the improved marine predator algorithm of the present invention has a faster convergence speed and global optimization ability, which effectively avoids the problem that the original algorithm is prone to fall into the local optimum.

[0058] 2. The improved ocean predator algorithm is applied to the NOMA covert communication system to optimize the position of the UAV. Under the premise of satisfying the concealment constraints and interruption constraints, the system covert throughput is maximized, which confirms the effectiveness of the proposed algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0060] Figure 1 This is a schematic diagram of the NOMA-based covert communication system.

[0061] Figure 2 It is a flow chart of the improved marine predator algorithm of the present invention.

[0062] Figure 3 This is a comparison chart of the convergence speed of the SCA-MPA algorithm and the MPA algorithm.

[0063] Figure 4 It is a schematic diagram of the optimal position of the UAV under the concealment constraint and interruption constraint.

[0064] Figure 5 This is a comparison chart of the hidden throughput of the SCA-MPA algorithm and the MPA algorithm system. DETAILED DESCRIPTION

[0065] The specific implementation modes of the present invention are described below so that those skilled in the art can understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific implementation modes. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations utilizing the concept of the present invention are protected.

[0066] A method for optimizing the position of a UAV in a NOMA covert communication system comprises the following steps:

[0067] S1: Design the NOMA downlink covert communication system, construct the objective function, set the covert constraints and interruption constraints, and determine the range of variables. The UAV (Unmanned Aerial Vehicle) sends a high-power signal to the remote user, and the communication between the two continues. The high-power signal is used to cover the low-power signal between the UAV and the near-end user to ensure that it is not discovered by the eavesdropper Willie. Willie uses a power detector to passively detect whether the UAV sends covert information to the near-end user;

[0068] S2: Population initialization, generating a set of random candidate solutions (i.e., drone positions);

[0069] S3: Determine the population fitness value and construct the elite matrix and predator matrix;

[0070] S4: Adopt an adaptive search strategy, collect information feedback during the search process, introduce an adaptive search factor, and control the adjustment of the algorithm's step size and the update intensity of individual positions during the iteration process. Specifically, in the early stages of the algorithm, the adaptive factor value is large, and the algorithm's search behavior is more random, which is conducive to global search to jump out of the local optimal solution. In the later stages of the algorithm, as the iteration proceeds, the adaptive factor value gradually decreases, the algorithm's search behavior becomes more detailed, the search step size is reduced, and a fine search is performed in the search space;

[0071] S5: Calculate the fitness value, update the predator position, and measure the pros and cons of the current drone position. Use the sine-cosine optimization algorithm to achieve the jump of candidate solutions in the solution space, and fine-tune the prey position again to avoid falling into the local optimum;

[0072] S6: Using FADs (Fish Aggregating Devices) fish school effect, introducing environmental factors, updating the best predator position, and continuously optimizing the drone position through multiple rounds of iterations;

[0073] S7: Determine whether the stop condition is met. If so, output the optimal fitness value, i.e., the location of the drone base station. Otherwise, repeat the above steps.

[0074] Furthermore, in step S1, building the NOMA covert communication system includes the following steps:

[0075] S101: For the set UAV covert communication scenario, the UAV sends two signals, one is a high-power signal sent to the remote user, and the other is a superposition coded signal sent to the near-end user and the remote user at the same time in a specific time slot. Considering a specific time slot, the UAV uses superposition coding technology (SC) to send information to two users at the same time, and its expression is

[0076]

[0077] The received signal at the near-end user Bob is expressed as

[0078]

[0079] Where n = 1, 2, ..., N represents the total number of channels used, P a Represents the total transmission power of the drone, Represents the power allocation factor, considering factors such as system performance and user fairness, and setting d abis the distance between the drone and Bob, α is the path loss factor, represents the additive white Gaussian noise (AWGN) at Bob, and the channel gain coefficient between the drone and Bob where β 0 Represents the unit distance channel power gain, L a and L b denote the horizontal coordinates of the drone and Bob, respectively; H denotes the flight altitude of the drone; ||·|| denotes the Euclidean norm operation; x 1 and x 2 They represent the signals sent by the drone to the remote user Carl and the local user Bob respectively.

[0080] S102: Willie performs a binary hypothesis test to determine whether the drone sends a covert signal to Bob. The received signal expression is:

[0081]

[0082] Among them, H 0 is the null hypothesis, indicating that the drone does not send covert information to Bob, H 1 is the alternative hypothesis, indicating that there is communication between the drone and Bob, d aw is the distance between the drone and Willie, Indicates that the mean at Willie is 0 and the variance is AWGN, channel gain coefficient between drone and Willie Where L w Indicates Willie's horizontal coordinate.

[0083] Willie uses a power detector to analyze the received signal, and its decision rule expression is:

[0084]

[0085] Among them, D 0 and D 1 represents Willie’s binary decision on whether the drone sends covert information, Y w represents the average power received by Willie in a time slot, M represents the total transmission time slot, and τ represents the detection threshold of Willie.

[0086] Willie's total detection error probability is represented by ξ, which is given by the false alarm probability P FA =Pr(D 1 |H 0 ) and the probability of missed detection P MD =Pr(D 0 |H 1), the expression is

[0087] ξ=P FA +P MD (5)

[0088] S103: According to the NOMA transmission criteria, SIC technology is used for decoding at the receiving end. Bob needs to demodulate the high-power signal first, then filter it out, and finally demodulate his own signal; while Carl only needs to filter out Bob's signal as noise. The outage probability at Bob is expressed as:

[0089]

[0090] The outage probability at Carl is expressed as:

[0091]

[0092] in, Channel gain coefficient between the drone and Carl Where L c represents Carl's horizontal coordinate, and R 1 and R 2 Represent the signal transmission rates at Carl and Bob respectively.

[0093] S104: When the drone base station hovers at a certain height, the three-dimensional problem can be regarded as a two-dimensional problem, and the optimal position of the drone is optimized in a two-dimensional rectangular coordinate system. In the covert communication scenario proposed by the present invention, the positions of the near-end user Bob, the remote user Carl and the listener Willie are known. Under the premise of satisfying the system's concealment constraints and reliability constraints, the system's concealment throughput is maximized to achieve the optimal position of the drone. The optimization problem is as follows:

[0094]

[0095] P out,C ≤P th (10)

[0096] Among them, Γ 1 represents the concealed throughput, represents the hidden constraints of the system, P th represents the maximum interruption probability allowed by Carl. represents the average detection error probability of the listener Willie, ε represents an arbitrarily small positive number, when When it was established, it was believed that covert communication between the drone and Bob could be achieved.

[0097] Furthermore, step S2 includes the following steps:

[0098] S201: Define the spatial range where the drone base station can be deployed. The search area is:

[0099] S = {((x, y)|x min ≤x≤x max ,y min ≤y≤y max )} (11)

[0100] S202: Randomly generate R candidate solutions in the defined search space. Each candidate solution represents the initial position of a UAV and is represented by a vector. On the two-dimensional plane, each solution P i It can be expressed as:

[0101] P i =(x i ,y i ), i = 1, 2, ..., R (12)

[0102] x i =x min +(x max -x min )*rand(i) (13)

[0103] y i =y min +(y max -y min )*rand(i) (14)

[0104] Here, rand(i) represents a random function that generates a uniform distribution in the interval [0, 1].

[0105] Further, in step S4, an adaptive search strategy is used to improve the marine predator algorithm, including the following steps:

[0106] The adaptive search factor is introduced to control the adjustment of the step size and the update intensity of the individual position during the iteration process of the algorithm. Its function is to dynamically adjust the parameters of the algorithm according to the progress of the current iteration, so that the algorithm can perform more global exploration in the early stage, and gradually turn to local development in the later stage, focusing on finding the optimal solution in a smaller range of the search space. Its expression is as follows:

[0107]

[0108] Among them, λ, μ, k are constant coefficients. θ is a random number between the interval [0, 1], t is the current iteration number, T max is the maximum number of iterations, and e is Euler's constant.

[0109] Further, in step S5, the sine-cosine optimization algorithm optimizes the post-development stage of the marine predator algorithm, including the following steps:

[0110] The sine-cosine algorithm is used to optimize the hunting link of the marine predator algorithm, so that the candidate solution can jump in the solution space, and the prey position is fine-tuned again to avoid falling into the local optimum. The specific expression is:

[0111]

[0112]

[0113] in, is the position of the current individual in the tth generation of the i-th dimension, h is a constant, t is the current iteration number, and T is the maximum iteration number; r 2 represents the angle, which is a random number between 0 and 2π; r 3 is a random number between 0 and 2; r 4 is a random number between 0 and 1; Represents the position of the i-th dimension of the optimal individual position variable at the tth iteration. 1 Indicates that the location of the next solution is between or outside the current solution and the optimal solution, r 1 When the value is small, it helps to enhance the local development ability of the algorithm. 1 When the value is large, it helps to improve the global search ability of the algorithm; r 2 , r 3 , r 4 is a random factor, r 2 Defines the distance of the current solution close to or away from the optimal solution; r 3 Provide a random weight for the optimal solution, randomly emphasize (r 3 >1) or ignore (r 3 <1) The influence of the optimal solution on the definition of the moving distance of the candidate solution, r 4 Switching the sine and cosine functions equally allows a solution to be relocated around other solutions, ensuring that searching the space between two solutions can converge to the global optimum faster.

[0114] Furthermore, in step S6, the FADs effect is used to update the optimal predator position, and the drone position is continuously optimized through multiple rounds of iterations. The expression is as follows:

[0115]

[0116] Among them, FADs represents the probability of affecting the algorithm optimization process, CF is the predator Brownian motion adaptive parameter, P max and P minrepresents the upper and lower limits of the individual prey positions, r is a random number between 0 and 1, U is a binary vector matrix containing 0 and 1, and the random indices of all prey matrices are r1 and r2 respectively.

[0117] Finally, the optimal position is input to the drone, and the drone flies directly to that position.

[0118] This method can optimize the position of the UAV and maximize the system's concealed throughput while satisfying the system's concealed constraints and interruption constraints.

[0119] Here is a more specific example, including the following steps:

[0120] S1: Figure 1 As shown in the figure, the NOMA covert communication system model is established. The drone maintains a fixed altitude H = 50. The initial positions of the near-end user Bob, the far-end user Carl, and the listener Willie are fixed. Bob's position is (-100, 0), Carl's position is (200, 0), and the listener's position is (50, -50). The transmission power of the drone is P a =30dB.

[0121] S2: Figure 2 As shown, this method uses an adaptive search strategy and a sine-cosine optimization algorithm to improve the marine predator algorithm, which mainly includes the following steps:

[0122] S201: Initialize the population and generate a set of random candidate solutions (i.e., drone positions).

[0123] Defines the spatial range in which the drone base station can be deployed. The search area is:

[0124] S = {((x, y)|x min ≤x≤x max ,y min ≤y≤y max )} (1)

[0125] S202: Randomly generate R candidate solutions in the defined search space. Each candidate solution represents the initial position of a UAV and is represented by a vector. On the two-dimensional plane, each solution P i It can be expressed as:

[0126] P i =(x i ,y i ), i = 1, 2, ..., R (2)

[0127] x i =x min +(x max -x min)*rand(i) (3)

[0128] y i =y min +(y max -y min )*rand(i) (4)

[0129] Here, rand(i) represents a random function that generates a uniform distribution in the interval [0, 1].

[0130] S3: Construct the Prey matrix and the Elite matrix. The dimensions of the prey matrix Prey and the elite matrix Elite are the same. The predator is updated based on the Prey matrix. At the end of each iteration, if a predator with a higher fitness value appears, the top predator will be replaced and the elite matrix will be updated accordingly. The Prey matrix and the Elite matrix are expressed as:

[0131]

[0132]

[0133] Among them, n is the population size, that is, the number of drone locations, and d is the dimension.

[0134] S4: Introduce an adaptive search factor to control the adjustment of the step size or the update intensity of individual positions during the iteration process. Its function is to dynamically adjust the algorithm parameters according to the progress of the current iteration, so that the algorithm can perform more global exploration in the early stage, and gradually turn to local development in the later stage, focusing on finding the optimal solution in a smaller range of the search space. Its expression is as follows:

[0135]

[0136] Among them, λ, μ, k are constant coefficients. θ is a random number between the interval [0, 1], t is the current iteration number, T max is the maximum number of iterations, and e is Euler's constant.

[0137] S5: Use the sine and cosine algorithms to optimize the hunting link of the marine predator algorithm, realize the jump of candidate solutions in the solution space, and fine-tune the prey position again to avoid falling into the local optimum. The specific expression is:

[0138]

[0139]

[0140] in, is the position of the current individual in the tth generation of the i-th dimension, h is a constant, t is the current iteration number, and T is the maximum iteration number; r2 represents the angle, which is a random number between 0 and 2π; r 3 is a random number between 0 and 2; r 4 is a random number between 0 and 1; Represents the position of the i-th dimension of the optimal individual position variable at the tth iteration. 1 Indicates that the location of the next solution is between or outside the current solution and the optimal solution, r 1 When the value is small, it helps to enhance the local development ability of the algorithm. 1 When the value is large, it helps to improve the global search ability of the algorithm. 1 The value decreases gradually with the number of iterations, balancing the algorithm's local development and global search capabilities; r 2 , r 3 , r 4 is a random factor, r 2 Defines the distance of the current solution close to or away from the optimal solution; r 3 Provide a random weight for the optimal solution, randomly emphasize (r 3 >1) or ignore (r 3 <1) The influence of the optimal solution on the definition of the moving distance of the candidate solution, r 4 Switching the sine and cosine functions equally allows a solution to be relocated around other solutions, ensuring that searching the space between two solutions can converge to the global optimum faster.

[0141] S6: Using FADs (Fish Aggregating Devices) fish school effect, introduce environmental factors to update the prey matrix. FADs represents the probability of affecting the algorithm optimization process, CF is the predator Brownian motion step length adaptive parameter, P max and P min represents the upper and lower limits of the individual prey positions, r is a random number between 0 and 1, U is a binary vector matrix containing 0 and 1, and the random indexes of all prey matrices are r1 and r2 respectively. The expression is as follows:

[0142]

[0143] S7: Determine whether the maximum number of iterations has been reached. If not, return to the above step. If so, output the optimal fitness value, i.e., the location of the drone base station.

[0144] like Figure 3 As shown in the figure, the improved algorithm of the present invention and the MPA algorithm are used simultaneously to optimize the position of the UAV. It can be seen that the improved algorithm converges faster, which proves the effectiveness of the improved algorithm of the present invention. Figure 4As shown, the result of optimizing the location of the drone base station using the improved algorithm is shown. In the NOMA downlink covert communication system set by the present invention, the horizontal distance between the drone base station and Carl must be greater than the horizontal distance with Bob. The blue dotted line and the red dotted line in the figure represent the new coordinate axis. The second and third quadrants represent the location area where the drone can be distributed if the distance constraint is satisfied. The green dotted circle with Carl as the center and the distance α between Carl and the origin of the new coordinate axis as the radius indicates that the range of the drone base station Alice can move satisfies r>α. The area inside the pink solid circle indicates the area that satisfies the concealment constraint. and the interruption constraint P out，C ≤P th Under the premise of , the range of Alice's activities. The optimization algorithm proposed in this paper accurately realizes the position optimization in the feasible area, and the coordinates of the best drone position are displayed as (-124.367, 37.6185).

[0145] like Figure 5 As shown in the figure, the improved algorithm (SCA-MPA) and MPA algorithm are used to optimize the position of the UAV, and the changes in the system concealed throughput are compared based on the best UAV positions found by the two algorithms. It is obvious that the algorithm proposed in the present invention is superior to the MPA algorithm in terms of convergence speed and accuracy, which improves the system concealed throughput and proves the effectiveness of the proposed algorithm.

[0146] In this method, the UAV base station uses superposition coding technology to send two signals to two ground users. The two ground users access the system in a non-orthogonal multiple access mode. Under the premise of meeting the concealment and reliability of the communication between the UAV and the near-end user, the improved marine predator algorithm is used to find the optimal location of the UAV base station to maximize the system's concealed throughput. This method can be used in the NOMA downlink communication system. When the original ground base station is damaged due to force majeure, a UAV is required to serve as a temporary base station to maintain communication with the ground users. By optimizing the location of the UAV base station, the system's concealed throughput is maximized while meeting the concealment and reliability requirements.

[0147] This method improves the Marine Predators Algorithm (MPA) based on an adaptive search strategy and the Sine-Cosine Algorithm (SCA), effectively improving the MPA algorithm's tendency to fall into local optimality and increasing the convergence speed.

[0148] In summary, the present invention adopts an adaptive search strategy and a sine-cosine optimization algorithm to improve the marine predator algorithm and obtain the optimal position of the UAV. Compared with the original algorithm, the method of the present invention has better effects in terms of convergence speed, accuracy, system throughput, etc.

[0149] Those skilled in the art can understand that the above are only preferred examples of the invention and are not intended to limit the invention. Although the invention is described in detail with reference to the above examples, those skilled in the art can still modify the technical solutions recorded in the above examples or replace some of the technical features therein with equivalents. Any modification, equivalent replacement, etc. made within the spirit and principle of the invention shall be included in the protection scope of the invention.

Claims

1. A method for optimizing the position of a UAV in a NOMA covert communication system, characterized in that: The NOMA covert communication system includes a drone, a user and an eavesdropper. The drone sends a high-power signal to a remote user, and the communication between the two continues. The drone uses the high-power signal to cover the low-power signal between the drone and the near-end user to ensure that it is not discovered by the eavesdropper. The eavesdropper uses a power detector to passively detect whether the drone sends covert information to the near-end user. The method includes the following steps: S1: Construct the objective function, set hidden constraints and interrupt constraints, and determine the range of variables; S2: Initialize the population and generate a set of random candidate solutions for UAV positions; S3: Determine the population fitness value and construct the elite matrix and predator matrix; S4: Adopting an adaptive search strategy, by collecting information feedback during the search process, introducing an adaptive search factor to control the adjustment of the step size and the update intensity of the individual position during the iteration process; S5: Calculate the fitness value, update the predator position, and measure the pros and cons of the current drone position; use the sine-cosine optimization algorithm to achieve the jump of candidate solutions in the solution space, and fine-tune the prey position again; S6: Using the FADs fish school effect, introducing environmental factors, updating the best predator position, and continuously optimizing the drone position through multiple rounds of iterations; S7: Determine whether the stop condition is met. If so, output the optimal fitness value, i.e., the position of the drone. Otherwise, repeat steps S4-S7.

2. The method for optimizing the position of a drone in a NOMA covert communication system according to claim 1, characterized in that: Step S1 includes: S101: In the set UAV covert communication scenario, the UAV sends two signals, one is a high-power signal sent to the remote user, and the other is a superposition-coded signal sent to the near-end user and the remote user at the same time in a specific time slot; in a specific time slot, the UAV uses superposition coding to send information to two users at the same time, and its expression is: The received signal at the near-end user Bob is expressed as: Where n = 1, 2…, N represents the total number of channels used, P a Represents the total transmission power of the UAV, Represents the power allocation factor, considering system performance and user fairness factors, set d ab is the distance between the drone and Bob, α is the path loss factor, represents the additive white Gaussian noise at Bob, and the channel gain coefficient between the drone and Bob is Where β0 represents the unit distance channel power gain, L a and L b denote the horizontal coordinates of the drone and Bob, respectively; H denotes the flight altitude of the drone; ∥·∥ denotes the Euclidean norm operation; x1 and x2 denote the signals sent by the drone to the remote user Carl and the local user Bob, respectively; S102: Willie performs a binary hypothesis test to determine whether the drone sends a covert signal to Bob. The received signal expression is: Among them, H0 is the null hypothesis, indicating that the drone does not send covert information to Bob, H1 is the alternative hypothesis, indicating that there is communication between the drone and Bob, d aw is the distance between the drone and the listener, Indicates that the mean at the listener is 0 and the variance is The channel gain coefficient between the drone and the listener is Where L w Indicates the horizontal coordinate of the listener; The listener uses a power detector to analyze the received signal, and its decision rule expression is: Among them, D0 and D1 represent the binary judgment of the monitor on whether the drone sends covert information, and Y w represents the average power received by the listener in a time slot, M represents the total transmission time slot, and τ represents the detection threshold of the listener; The total probability of detection error of the listener is denoted by ξ, which is given by the false alarm probability P FA =Pr(D1|H0) and missed detection probability P MD =Pr(D0|H1), the expression is: ξ=P FA +P MD S103: According to the transmission criteria of the NOMA covert communication system, SIC decoding is used at the receiving end; Bob first demodulates the high-power signal, then filters it out, and finally demodulates his own signal; the remote user Carl filters out Bob's signal as noise; the interruption probability at Bob is: The outage probability at Carl is: in, The channel gain coefficient between the drone and Carl is Where L c represents Carl's horizontal coordinate, and R1 and R2 represent the signal transmission rates at Carl and Bob respectively; S104: In a two-dimensional rectangular coordinate system, the optimal position of the drone is optimized. The positions of the near-end user Bob, the far-end user Carl, and the listener Willie are known. Under the premise of satisfying the system's concealment constraints and reliability constraints, the system's concealment throughput is maximized to achieve the optimal position of the drone. The optimization problem is as follows: P out,c ≤P th Where Γ1 represents the concealed throughput, represents the hidden constraints of the system, P th represents the maximum interruption probability allowed by Carl; where, represents the average detection error probability of the listener Willie, ε represents an arbitrarily small positive number, when When it was established, it was believed that covert communication between the drone and Bob could be achieved.

3. The method for optimizing the position of a drone in a NOMA covert communication system according to claim 2, characterized in that: Step S2 includes: S201: Define the search space of the drone position as: S={((x,y)|x min ≤x≤x max ,and min ≤y≤y max )} S202: Randomly generate R candidate solutions in the search space, each candidate solution represents the initial position of a UAV and is represented by a vector; on the two-dimensional plane, each solution P i It is expressed as: P i =(x i ,y i ),i=1,2,…,R x i =x min +(x max -x min )*rand(i) and i =and min +(and max -and min )*rand(i) Here, rand(i) represents a random function that generates a uniform distribution in the interval [0, 1].

4. The method for optimizing the position of a drone in a NOMA covert communication system according to claim 3, characterized in that: In step S4, the adaptive search factor is: Among them, λ, μ, k are constant coefficients, θ is a random number between the interval [0, 1], t is the current iteration number, T max is the maximum number of iterations, and e is Euler's constant.

5. The method for optimizing the position of a drone in a NOMA covert communication system according to claim 4, characterized in that: In step S5, the sine-cosine algorithm is used to optimize the hunting link of the marine predator algorithm, so as to realize the jump of the candidate solution in the solution space and fine-tune the prey position again to avoid falling into the local optimum. The specific expression is: in, is the position of the current individual in the tth generation of the i-th dimension, h is a constant, t is the current iteration number, and T is the maximum iteration number; r2 represents the angle, which is a random number between 0 and 2π; r3 is a random number between 0 and 2; r4 is a random number between 0 and 1; Represents the position of the i-th dimension of the optimal individual position variable at the tth iteration; r1 indicates that the location area of ​​the next solution is between or outside the current solution and the optimal solution; r2, r3, and r4 are random factors, and r2 defines the distance that the current solution is close to or away from the optimal solution; r3 provides a random weight for the optimal solution, randomly emphasizing or ignoring the influence of the optimal solution in defining the moving distance of the candidate solution, and r4 switches the sine and cosine functions equally, allowing a solution to be repositioned around other solutions, ensuring that the space between two solutions is searched.

6. The method for optimizing the position of a drone in a NOMA covert communication system according to claim 5, characterized in that: In step S6, the specific method of optimizing the position of the drone is: Among them, FADs represents the probability of affecting the algorithm optimization process, CF is the predator Brownian motion adaptive parameter, P max and P min represents the upper and lower limits of the individual prey positions, r is a random number between 0 and 1, U is a binary vector matrix containing 0 and 1, and the random indices of all prey matrices are r1 and r2 respectively.

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