Power control method and system for anti-interference networking radar system

Abstract

A power control method for an anti-interference networking radar system comprises the following steps: S1, for the networking radar system executing a target detection task in a countermeasure environment with a plurality of jammers, acquiring path propagation loss according to actual operation environment prior information; s2, respectively constructing a utility function of the networking radar system about target detection and a utility function of the networking radar system about each interference node of suppressing interference; s3, respectively establishing a non-cooperative game joint beam forming and power control model related to target detection and a non-cooperative game joint beam transmitting and power distribution model related to suppressing interference; s4, solving the model about suppressing interference by adopting a matched filtering theory and a Lagrange multiplier method, and predicting an optimal interference strategy; and S5, substituting the interference strategy obtained in the step S4 into a model about target detection, and carrying out iterative solution on the model by adopting an alternating optimization method. According to the invention, the purpose of improving the radio frequency stealth performance and the anti-interference performance of the networking radar system is achieved.

Description

Technical Field

[0001] The present invention belongs to the technical field of radar signal processing, and specifically proposes a combined beamforming and game power control method for a networked radar system for anti-jamming. Background Technique

[0002] Beamforming is a technology that realizes signal enhancement by controlling multiple antenna elements. Compared with a single antenna, an array antenna using beamforming technology has higher signal gain, longer detection range, and stronger anti-jamming performance. A radar system needs to actively transmit signals and receive the signals reflected by the target, so as to complete tasks such as target detection, positioning, and recognition. In a radar system, beamforming technology can not only be used at the receiving end to suppress interference signals, but also be used at the transmitting end to form higher directional gain and meet specific low intercept performance requirements, thereby improving the radio frequency stealth performance of the system. Radio frequency stealth is a technology that reduces the perception ability of passive detection systems to radio frequency radiation sources. Passive detection systems use electronic reconnaissance equipment to receive electromagnetic waves from radiation sources and complete the positioning and recognition of radiation sources through signal processing technology. Radio frequency radiation sources improve their own radio frequency stealth performance by controlling the characteristics of radiation signals and reducing the probability of interception, sorting, and recognition by passive detection systems.

[0003] However, for a networked radar system that performs target detection tasks in a countermeasure environment with multiple jammers, the active interference of multiple jammers increases the sidelobe level and total transmission power of the transmitting beam of the networked radar system, thereby weakening the anti-jamming performance and radio frequency stealth performance of the networked radar system. Summary of the Invention

[0004] The technical problem to be solved by the present invention is how to improve the anti-jamming performance and radio frequency stealth performance of a networked radar system.

[0005] The present invention solves the above technical problems through the following technical means: A power control method for a networked radar system for anti-jamming, including the following steps:

[0006] S1. For a networked radar system that performs target detection tasks in a countermeasure environment with multiple jammers, according to the prior information of the actual operating environment, obtain the path propagation losses between each radar node and the target, between each radar node and each jammer node, and between each radar node;

[0007] S2. Respectively construct the utility function of the networked radar system for target detection and the utility functions of each interference node for suppressing interference;

[0008] S3. Respectively establish a non - cooperative game joint beamforming and power control model for target detection and a non - cooperative game joint transmit beam and power allocation model for jamming suppression;

[0009] S4. Use the matched - filtering theory and the Lagrange multiplier method to solve the non - cooperative game joint transmit beam and power allocation model for jamming suppression, and predict the optimal jamming strategy;

[0010] S5. Substitute the jamming strategy obtained in S4 into the non - cooperative game joint beamforming and power control model for target detection, and use the alternating optimization method to iteratively solve the model to obtain the receiving beam weight vector that maximizes the output signal - to - interference - plus - noise ratio and the transmit beam weight vector that minimizes the total transmit power of the networked radar system and the peak sidelobe level of each radar node's transmit beam under the constraint of meeting the pre - set target detection signal - to - interference - plus - noise ratio threshold, thereby determining the transmit power of each radar.

[0011] As a further optimized technical solution, in S2, construct the utility function of the networked radar system for target detection as follows:

[0012]

[0013] In formula (1), \(P = [P_1,\cdots,P_{ M \) represents the transmit power of all radar nodes, where \(P_{ m}=\|u_{ m}\|_{ 2}\), \(m = 1,\cdots,M\) represents the transmit power of the \(m\) - th radar node, \(M\) represents the number of radar nodes, \(u_{ m}\) represents the transmit beam weight vector of the \(m\) - th radar node, \(\|\cdot\|\) represents the Euclidean norm, \((\cdot)^{ H}\) represents the conjugate transpose operation, \(\tau_{ m}\) represents the cumulative sidelobe power weight of the \(m\) - th radar node, \(\mathbf{R}_{m}^{s}\) represents the path propagation loss matrix in the sidelobe region of the \(m\) - th radar node, where the interval \([s_{ m ,S_{ m}]\) represents the sidelobe range of the \(m\) - th radar node, \(\mathbf{A}_{m}^{s}\) represents the array response matrix in the sidelobe direction, \(\mathbf{a}_{r}\) and \(\mathbf{a}_{t}\) respectively represent the receive and transmit steering vectors, \(\theta^{s}\) represents the angle sampling value in the sidelobe region, \((\cdot)^{ T}\) represents the transpose operation, \(v_{ m}\) represents the receive beam weight vector of the \(m\) - th radar node.

[0014] As a further optimized technical solution, in S2, construct the utility function of the \(n\) - th jammer node for jamming suppression as follows:

[0015]

[0016] where h m,m is the path propagation loss between the m-th radar node and the target, and g n,m is the path propagation loss between the n-th jammer node and the m-th radar node, and J n = [J n,1 , …, J n,M represents the interference power of the n-th jammer node on all radar nodes, represents the normalization of the interference beam weight vector t n,m of the n-th jammer node on the m-th radar node, and J n,m = ||t n,m || 2 represents the interference power of the n-th jammer node on the m-th radar node, and C n represents the interference power cost of the n-th jammer node.

[0017] As a further optimized technical solution, in S3, aiming at minimizing the total transmission power of all radar nodes and the peak sidelobe level of the transmission beam of each radar node, and taking the satisfaction of the signal-to-interference-plus-noise ratio threshold value of the preset target detection performance of each radar node as a constraint condition, a non-cooperative game joint beamforming and power control model for target detection is established; aiming at minimizing the signal-to-interference-plus-noise ratio of the target detection performance of all radar nodes and taking the total interference power as a constraint condition, a non-cooperative game joint transmission beamforming and power allocation model for suppressing interference is constructed.

[0018] As a further optimized technical solution, in S3, a non-cooperative game joint beamforming and power control model for target detection is established as follows:

[0019]

[0020] where is the preset signal-to-interference-plus-noise ratio threshold value of the target detection performance of the m-th radar node, and SINR m represents the signal-to-interference-plus-noise ratio of the target detection performance of the m-th radar node, which is expressed as:

[0021]

[0022] where h m,j is the path propagation loss between the m-th radar node and the j-th radar node, N represents the number of jammer nodes, represents the radar node receiver noise power, represents the target path propagation loss matrix of the m-th radar node, where θ mRepresents the angle of the target relative to the m-th radar node, Represents the mutual interference covariance matrix between radars, Represents the path propagation loss matrix of the l-th radar node - target - m-th radar node, Represents the suppression interference covariance matrix, Represents the path propagation loss matrix of the n-th jammer node - m-th radar node, where θ m,n Represents the angle of the n-th jammer node relative to the m-th radar node, Represents the angle of the m-th radar node relative to the n-th jammer node, and I represents the identity matrix.

[0023] As a further optimized technical solution, a non - cooperative game joint transmission beam and power allocation model for suppression interference is established as follows:

[0024]

[0025] In the formula, Is the total interference power of the n-th jammer node.

[0026] As a further optimized technical solution, S4 is to solve the model (5), which specifically includes:

[0027] First, consider that the n-th jammer node uses the matched filtering algorithm to optimize the transmission beam weight vector t n,m , and its expression is:

[0028]

[0029] Then, substitute (6) into the optimization model (5), and use the Lagrange multiplier method to solve. The Lagrange function is defined as:

[0030]

[0031] In the formula, ξ represents the Lagrange multiplier. Take the first - order partial derivative of with respect to J n,m :

[0032]

[0033] By setting The interference power expression of the n-th jammer node on the m-th radar node is obtained as:

[0034]

[0035] In the formula, [a] + = max{0, a}.

[0036] As a further optimized technical solution, in S5, the interference strategy obtained in S4 is brought into the optimization model (3), and it is solved. The optimization model (3) is decomposed into two sub-problems: transmit beam optimization and receive beam optimization, and the alternating optimization method is used to solve them.

[0037] As a further optimized technical solution, S5 specifically includes: First, fix the transmit beam weight vector u m , and optimize the receive beam weight vector v m . Taking maximizing the output signal-to-interference-plus-noise ratio as the goal, establish the receive beamforming optimization model as follows:

[0038]

[0039] In the formula, represents the normalized transmit beam weight vector of the m-th radar node. Using the Lagrange multiplier method, the optimal receive beam weight vector is obtained as follows:

[0040]

[0041] Then, fix the receive beam weight vector v m , and optimize the transmit beam weight vector u m . Expand the signal-to-interference-plus-noise ratio constraint in formula (3) to obtain the equivalent optimization model as follows:

[0042]

[0043] In the formula, represents the interference and noise power received by the m-th radar node. Using the Lagrange dual method, define the Lagrangian function as:

[0044]

[0045] In the formula, λ = [λ1,…,λ M represents the vector composed of the Lagrange multipliers corresponding to the M signal-to-interference-plus-noise ratio constraints, where, Q m = I + τ m A m . Take the first-order partial derivative of formula (13) with respect to u m and set it equal to 0 to get:

[0046]

[0047] That is

[0048]

[0049] Multiply both sides of the equation by on the left at the same time to get:

[0050]

[0051] is a constant. Eliminating this term on both sides of Equation (16) gives an iterative expression for λ m as follows:

[0052]

[0053] wherein, After that, by solving the dual problem of the optimization model (12), the optimal transmit beam weight vector u m is obtained. As can be seen from Equation (13), the dual problem is expressed as:

[0054]

[0055] wherein, A μ B means that A - B is a positive semi - definite matrix. The solution of this problem is obtained by solving the equivalent optimization problem of the dual problem (18). The dual problem (18) is equivalent to the receive beam optimization problem as follows:

[0056]

[0057] wherein, w m represents the equivalent radar receive beam weight vector, Q m = I + τ m A m . The optimal receive beam weight vector maximizes the output signal - to - interference - plus - noise ratio. As can be seen from Equations (10) and (11), the optimal receive beam weight vector is expressed as:

[0058]

[0059] The transmit beam weight vector u m and the receive beam weight vector w m are linearly related as follows:

[0060]

[0061] wherein, δ m is a constant. By substituting Equation (21) into the signal - to - interference - plus - noise ratio constraint of Equation (12) and setting the inequality constraint to an equality, we get:

[0062] δ = F -1 r, (22)

[0063] wherein, δ = [δ1,…,δ M T , represents the element of matrix F located at the m - th row and m - th column, ​Denote the element of matrix F at the m-th row and j-th column, r = [I1, …, I M T ;

[0064] Finally, alternately optimize the transmit beam weight vector u m and the receive beam weight vector v m until convergence.

[0065] The present invention also provides a system corresponding to the power control method of the anti-jamming-oriented networking radar system as described above, including:

[0066] A path propagation loss acquisition module, which is used for a networking radar system performing target detection tasks in an anti-jamming environment with multiple jammers. According to the prior information of the actual operating environment, it acquires the path propagation losses between each radar node and the target, between each radar node and each jammer node, and between each radar node;

[0067] A utility function construction module, which is used to respectively construct the utility function of the networking radar system for target detection and the utility functions of each interference node for suppressing interference;

[0068] A model establishment module, which is used to respectively establish a non-cooperative game joint beamforming and power control model for target detection and a non-cooperative game joint transmit beam and power allocation model for suppressing interference;

[0069] A solution module for the interference suppression model, which is used to solve the non-cooperative game joint transmit beam and power allocation model for suppressing interference by using the matched filtering theory and the Lagrange multiplier method, and predict the optimal interference strategy;

[0070] A solution module for the target detection model, which is used to substitute the interference strategy obtained by the solution module of the interference suppression model into the non-cooperative game joint beamforming and power control model for target detection, and use an iterative optimization algorithm to solve the model, and obtain the receive beam weight vector that maximizes the output signal-to-interference-plus-noise ratio and the transmit beam weight vector that minimizes the total transmit power of the networking radar system and the peak sidelobe level of each radar node's transmit beam and the lowest peak sidelobe level of each radar node's transmit beam under the constraint of satisfying the preset target detection signal-to-interference-plus-noise ratio threshold value, so as to determine the transmit power of each radar.

[0071] The advantages of the present invention are as follows:

[0072] ​1. The present invention proposes a combined beamforming and game power control method for a networking radar system oriented to anti-interference. The main task of this method is for a networking radar system performing target detection tasks in a confrontation environment with multiple jammers. According to the prior information of the actual operating environment, the path propagation losses between each radar node and the target, between each radar node and each jammer node, and between each radar node are obtained. Then, a utility function of the networking radar system for target detection and a utility function of each jammer node for suppressing interference are respectively constructed. On this basis, with the goal of minimizing the signal-to-interference-plus-noise ratio (SINR) of the target detection performance of all radar nodes and with the total interference power as the constraint condition, a non-cooperative game joint transmit beamforming and power allocation model for suppressing interference is established. On the basis of optimizing the design of each interference beam, the interference resources of each jammer to the networking radar system are effectively allocated to achieve the purpose of reducing its target detection performance. Finally, with the goal of minimizing the total transmit power of all radar nodes and the peak sidelobe level of the transmit beam of each radar node, and with the SINR threshold value of the target detection performance preset for each radar node as the constraint condition, a non-cooperative game joint beamforming and power control model for target detection is established, so as to effectively predict and suppress the active interference from the jammer and control the radio frequency radiation of the networking radar system, in order to achieve the purpose of improving the anti-interference performance and radio frequency stealth performance of the system.

[0073] The advantages of this invention are that it not only meets the requirements of the SINR threshold values of the target detection performance preset for each radar node, but also, on the basis of controlling the total transmit power of the networking radar, effectively suppresses the peak sidelobe level of the transmit beam of each radar node for the first time. At the same time, it predicts the possible interference beam and interference power allocation strategy, achieving the purpose of improving the radio frequency stealth performance and anti-interference performance of the networking radar system. The reason for this advantage is that the present invention comprehensively considers the actual operating requirements of the networking radar system and the jammer, and respectively establishes a non-cooperative game joint beamforming and power control model for target detection and a non-cooperative game joint transmit beam and power allocation model for suppressing interference. Among them, the cumulative sidelobe power cost of each radar node is first introduced into the utility function of the non-cooperative game model for target detection, enabling the radar networking system to not only have a low transmit power but also have the ability to suppress the peak sidelobe level of the transmit beam of each radar node. The disclosed inventions only consider transmit power control and do not involve suppressing the sidelobe level. By using the alternating optimization algorithm to iteratively solve the model, the transmit and receive beam weight vectors that minimize the total transmit power value of the networking radar system and the peak sidelobe level of the transmit beam of each radar node under the constraint of meeting the preset SINR threshold value of the target detection performance are selected as the optimal solutions, thus effectively improving the anti-interference performance and radio frequency stealth performance of the networking radar system.

[0074] 2. Compared with the prior art, the proposed joint beamforming and game power control method for anti-jamming networked radar systems in the present invention not only meets the requirements of the preset signal-to-interference-plus-noise ratio (SINR) threshold for the target detection performance of each radar node, but also effectively suppresses the total transmission power of the networked radar and the peak sidelobe level of the transmission beam of each radar node. At the same time, it predicts possible interference radiation strategies, achieving the purpose of improving the radio frequency stealth performance and anti-jamming performance of the networked radar system. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] Figure 1 It is a flowchart of the joint beamforming and game power control method for anti-jamming networked radar systems according to an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0076] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention. Apparently, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0077] Refer to Figure 1 As shown, the present invention provides a joint beamforming and game power control method for anti-jamming networked radar systems, including the following steps:

[0078] S1. Determine the composition of the networked radar system and the game relationship between the system and multiple jammers, and obtain the prior information of path propagation loss:

[0079] For a networked radar system composed of multiple radar nodes that are interfered by multiple jammers and operate in the same frequency band, according to the prior information of the actual operating environment, obtain the path propagation loss h m,m between the m-th radar node and the target, the path propagation loss h m,j between the m-th radar node and the j-th radar node, and the path propagation loss g n,m between the n-th jammer node and the m-th radar node.

[0080] S2. Construct the utility function of the networked radar system for target detection and the utility function of each jammer node for suppressing interference respectively:

[0081] Construct the utility function of the networked radar system for target detection as follows:

[0082]

[0083] In Equation (1), P = [P1,..., P Mdenotes the transmission power of all radar nodes, where P m = ||u m || 2 , m = 1, …, M, represents the transmission power of the m-th radar node, M represents the number of radar nodes, and u m represents the transmission beam weight vector of the m-th radar node, ||·|| represents the Euclidean norm, and (·) H represents the conjugate transpose operation, and τ m represents the cumulative sidelobe power weight of the m-th radar node, represents the path propagation loss matrix in the sidelobe region of the m-th radar node, where the interval [s m , S m represents the sidelobe range of the m-th radar node, represents the array response matrix in the sidelobe direction, and respectively represent the receive and transmit steering vectors, represents the angle sampling values in the sidelobe region, and (·) T represents the transpose operation, and v m represents the receive beam weight vector of the m-th radar node.

[0084] Construct the utility function of the n-th jammer node for suppressing jamming as follows:

[0085]

[0086] In the formula, J n = [J n,1 , …, J n,M represents the interference power of the n-th jammer node on all radar nodes, represents the normalization of the interference beam weight vector t n,m of the n-th jammer node on the m-th radar node, and J n,m = ||t n,m || 2 represents the interference power of the n-th jammer node on the m-th radar node, and C n represents the interference power cost of the n-th jammer node.

[0087] S3. Respectively establish a non-cooperative game joint beamforming and power control model for target detection and a non-cooperative game joint transmit beam and power allocation model for suppressing jamming:

[0088] According to the pre-set signal-to-interference-plus-noise ratio threshold of the target detection performance of the m-th radar node, establish a non-cooperative game joint beamforming and power control model for target detection as follows:

[0089]

[0090] In the formula, SINR m represents the signal-to-interference-plus-noise ratio for target detection performance of the m-th radar node, and can be expressed as:

[0091]

[0092] In the formula, N represents the number of jammer nodes, represents the radar node receiver noise power, represents the target path propagation loss matrix of the m-th radar node, where θ m represents the angle of the target relative to the m-th radar node, represents the mutual interference covariance matrix between radars, represents the path propagation loss matrix of the l-th radar node - target - m-th radar node, represents the suppression interference covariance matrix, represents the path propagation loss matrix of the n-th jammer node - m-th radar node, where θ m,n represents the angle of the n-th jammer node relative to the m-th radar node, represents the angle of the m-th radar node relative to the n-th jammer node, and I represents the identity matrix.

[0093] According to the total interference power of the n-th jammer node, a non-cooperative game joint transmission beam and power allocation model for suppression interference is established as follows:

[0094]

[0095] S4. Solve the optimization model (27):

[0096] First, consider that the n-th jammer node uses the matched filtering algorithm to optimize the transmission beam weight vector t n,m , and its expression is:

[0097]

[0098] Then, substitute (6) into the optimization model (5), and use the Lagrange multiplier method to solve. The Lagrangian function is defined as:

[0099]

[0100] In the formula, ξ represents the Lagrange multiplier. Substitute for J n,m to find the first-order partial derivative:

[0101]

[0102] By setting The expression for obtaining the interference power of the nth jammer node on the mth radar node is as follows:

[0103]

[0104] In the formula, [a] + = max{0, a}.

[0105] S5. Substitute the interference strategy obtained in S4 into the optimization model (25) and solve it:

[0106] Decompose the optimization model (25) into two sub-problems of transmit beam optimization and receive beam optimization, and solve them using the alternating optimization method.

[0107] First, fix the transmit beam weight vector u m , and optimize the receive beam weight vector v m . With the goal of maximizing the output signal-to-interference-plus-noise ratio, establish the receive beamforming optimization model as follows:

[0108]

[0109] In the formula, represents the normalized transmit beam weight vector of the mth radar node. Using the Lagrange multiplier method, the optimal receive beam weight vector can be obtained as follows:

[0110]

[0111] Then, fix the receive beam weight vector v m , and optimize the transmit beam weight vector u m . Expand the signal-to-interference-plus-noise ratio constraint in formula (25) to obtain an equivalent optimization model as follows:

[0112]

[0113] In the formula, represents the interference and noise power received by the mth radar node. Using the Lagrange dual method, define the Lagrangian function as:

[0114]

[0115] In the formula, λ = [λ1,…,λ M represents the vector composed of the Lagrange multipliers corresponding to the M signal-to-interference-plus-noise ratio constraints, where, Q m = I + τ m A m . For formula (35) with respect to u mBy finding the first-order partial derivatives and setting them equal to zero, we can obtain:

[0116]

[0117] That is

[0118]

[0119] Left-multiplying both sides of the equation by we can get:

[0120]

[0121] Since is a constant, canceling this term on both sides of equation (38) gives an iterative expression for λ m as follows:

[0122]

[0123] where After that, by solving the dual problem of the optimization model (34), the optimal transmit beam weight vector u m is obtained. From equation (35), the dual problem is expressed as:

[0124]

[0125] where A μ B means that A - B is a positive semi-definite matrix. The solution to this problem is obtained by solving the equivalent optimization problem of the dual problem (40), and the dual problem (40) is equivalent to the receive beam optimization problem as follows:

[0126]

[0127] where w m represents the equivalent radar receive beam weight vector, and Q m = I + τ m A m The optimal receive beam weight vector maximizes the output signal-to-interference-plus-noise ratio. From equations (32) and (33), the optimal receive beam weight vector can be expressed as:

[0128]

[0129] The transmit beam weight vector u m and the receive beam weight vector w m are linearly related as follows:

[0130]

[0131] where δ mis a constant. By substituting Equation (43) into the signal-to-interference-plus-noise ratio constraint of Equation (34) and setting the inequality constraint to an equality, we can obtain:

[0132] δ = F -1 r, (44)

[0133] where δ = [δ1, …, δ M T , represents the element of matrix F in the m-th row and m-th column, represents the element of matrix F in the m-th row and j-th column, r = [I1, …, I M T .

[0134] Finally, alternately optimize the transmit beam weight vector u m and the receive beam weight vector v m until convergence.

[0135] The present invention also provides a power control system for a networking radar system for anti-interference corresponding to any of the above solutions, including:

[0136] A path propagation loss acquisition module, which is used for a networking radar system performing target detection tasks in a countermeasure environment with multiple jammers. According to the prior information of the actual operating environment, it acquires the path propagation losses between each radar node and the target, between each radar node and each jammer node, and between each radar node;

[0137] A utility function construction module, which is used to respectively construct the utility function of the networking radar system regarding target detection and the utility functions of each interference node regarding suppressing interference;

[0138] A model establishment module, which is used to respectively establish a non-cooperative game joint beamforming and power control model regarding target detection and a non-cooperative game joint transmit beam and power allocation model regarding suppressing interference;

[0139] A solving module for the interference suppression model, which is used to solve the non-cooperative game joint transmit beam and power allocation model regarding suppressing interference by using the matched filtering theory and the Lagrange multiplier method to predict the optimal interference strategy;

[0140] A solving module for the target detection model, which is used to substitute the interference strategy obtained by the solving module of the interference suppression model into the non-cooperative game joint beamforming and power control model regarding target detection, and use an iterative optimization algorithm to solve the model to obtain the receive beam weight vector that maximizes the output signal-to-interference-plus-noise ratio and the transmit beam weight vector that minimizes the total transmit power of the networking radar system and the peak sidelobe level of the transmit beam of each radar node under the constraint of satisfying the preset target detection signal-to-interference-plus-noise ratio threshold value, so as to determine the transmit power of each radar.​​

[0141] The execution of tasks in each module adopts the specific steps in the power control method of the above anti-interference-oriented networking radar system.

[0142] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A power control method for an anti-interference networking radar system, characterized in that, It includes the following steps: S1. For a networking radar system performing target detection tasks in a countermeasure environment with multiple jammers, based on the prior information of the actual operating environment, obtain the path propagation losses between each radar node and the target, between each radar node and each jammer node, and between each radar node; S2. Respectively construct the utility function of the networking radar system for target detection and the utility functions of each jammer node for suppressing interference; S3. Respectively establish a non-cooperative game joint beamforming and power control model for target detection and a non-cooperative game joint transmit beam and power allocation model for suppressing interference; S4. Use the matched filtering theory and the Lagrange multiplier method to solve the non-cooperative game joint transmit beam and power allocation model for suppressing interference, and predict the optimal interference strategy; S5. Substitute the interference strategy obtained in S4 into the non-cooperative game joint beamforming and power control model for target detection, and use the alternating optimization method to iteratively solve the model to obtain the receiving beam weight vector that maximizes the output signal-to-interference-plus-noise ratio and the transmit beam weight vector that minimizes the total transmit power of the networking radar system and the peak sidelobe level of the transmit beam of each radar node under the constraint of meeting the pre-set target detection signal-to-interference-plus-noise ratio threshold, so as to determine the transmit power of each radar.

2. The power control method for an anti-interference-oriented networking radar system according to claim 1, characterized in that, In S2, the utility function of the networking radar system for target detection is constructed as follows: In Equation (1), \(P = [P_1,\ldots,P M \) represents the transmission power of all radar nodes, \(P m =\|u m \| 2 , m = 1,\ldots,M\), represents the transmission power of the \(m\)-th radar node, \(M\) represents the number of radar nodes, \(u m \) represents the transmission beam weight vector of the \(m\)-th radar node, \(\|\cdot\|\) represents the Euclidean norm, \((\cdot) H \) represents the conjugate transpose operation, \(\tau m \) represents the cumulative sidelobe power weight of the \(m\)-th radar node, \) represents the path propagation loss matrix in the sidelobe region of the \(m\)-th radar node, where the interval \([s m ,S m \) represents the sidelobe range of the \(m\)-th radar node, \) represents the array response matrix in the sidelobe direction, \) and \) respectively represent the receive and transmit steering vectors, \) represents the angle sampling value in the sidelobe region, \((\cdot) T \) represents the transpose operation, \(v m \) represents the receive beam weight vector of the \(m\)-th radar node.

3. The power control method of the anti-interference-oriented networking radar system according to claim 2, wherein, In S2, the utility function of the nth jammer node for suppressing interference is constructed as follows: Where h m,m is the path propagation loss between the m-th radar node and the target, and g n,m is the path propagation loss between the n-th jammer node and the m-th radar node. J n = [J n,1 , …, J n,M represents the interference power of the n-th jammer node on all radar nodes. represents the normalization of the interference beam weight vector t n,m of the n-th jammer node on the m-th radar node. J n,m = ||t n,m || 2 represents the interference power of the n-th jammer node on the m-th radar node, and C n represents the interference power cost of the n-th jammer node.

4. The power control method of the anti-interference-oriented networking radar system according to claim 3, wherein In S3, with the goal of minimizing the total transmit power of all radar nodes and the peak sidelobe level of the transmit beam of each radar node, and with the constraint of meeting the pre-set target detection performance signal-to-interference-plus-noise ratio threshold of each radar node, establish a non-cooperative game joint beamforming and power control model for target detection; with the goal of minimizing the target detection performance signal-to-interference-plus-noise ratio of all radar nodes and with the total interference power as the constraint condition, construct a non-cooperative game joint transmit beamforming and power allocation model for suppressing interference.

5. The power control method for an anti-interference-oriented networking radar system according to claim 4, characterized in that, In S3, the non-cooperative game joint beamforming and power control model for target detection is established as follows: In the formula, is the target detection performance signal-to-interference-plus-noise ratio threshold of the m-th radar node preset in advance, and SINR m represents the target detection performance signal-to-interference-plus-noise ratio of the m-th radar node, which is expressed as: where h m,j is the path propagation loss between the m-th radar node and the j-th radar node, N represents the number of jammer nodes, represents the radar node receiver noise power, represents the target path propagation loss matrix of the m-th radar node, where θ m represents the angle of the target relative to the m-th radar node, represents the mutual interference covariance matrix between radars, represents the path propagation loss matrix of the l-th radar node - target - m-th radar node, represents the suppression interference covariance matrix, represents the path propagation loss matrix of the n-th jammer node - m-th radar node, where θ m,n represents the angle of the n-th jammer node relative to the m-th radar node, represents the angle of the m-th radar node relative to the n-th jammer node, and I represents the identity matrix.

6. The power control method for an anti-interference oriented networking radar system as claimed in claim 5, wherein The non-cooperative game joint transmit beam and power allocation model for suppressing interference is established as follows: wherein, is the total interference power of the nth jammer node.

7. The power control method for an anti-interference-oriented networking radar system according to claim 6, wherein S4 is to solve model (5), specifically including: First, consider that the nth jammer node uses the matched filtering algorithm to optimize the transmit beam weight vector t n,m , and its expression is: Then, substitute (6) into the optimization model (5), and use the Lagrange multiplier method to solve. The Lagrangian function is defined as: where ξ represents the Lagrange multiplier, and taking the first-order partial derivative of n,m J: By setting The expression for obtaining the interference power of the nth jammer node on the mth radar node is as follows: where [a] + = max{0, a}.

8. The power control method for an anti-interference-oriented networking radar system according to claim 7, characterized in that, In S5, substitute the interference strategy obtained in S4 into the optimization model (25), and solve it. Decompose the optimization model (25) into two sub-problems of transmit beam optimization and receive beam optimization, and use the alternating optimization method to solve.

9. The power control method for an anti-interference oriented networking radar system according to claim 8, characterized in that, S5 specifically includes: First, fix the transmit beam weight vector u m , and optimize the receive beam weight vector v m . Taking the maximization of the output signal-to-interference-plus-noise ratio as the goal, establish a receive beamforming optimization model as follows: In the formula, represents the normalized transmit beam weight vector of the m-th radar node. Using the Lagrange multiplier method, the optimal receive beam weight vector is obtained as follows: Then, fix the received beam weight vector v m , optimize the transmit beam weight vector u m , expand the signal-to-interference-plus-noise ratio (SINR) constraint in Equation (25) to obtain the following equivalent optimization model: Wherein, represents the interference and noise power received by the m-th radar node. Using the Lagrange dual method, the Lagrange function is defined as: where λ = [λ1,…,λ M represents a vector composed of Lagrange multipliers corresponding to M signal-to-interference-plus-noise ratio constraints, where Q m = I + τ m A m , taking the first-order partial derivative of Equation (35) with respect to u m and setting it equal to 0, we obtain: That is Multiply both sides of the equation on the left by We get: is a constant. Canceling this term on both sides of Equation (38) gives an iterative expression for λ m as follows: wherein, After that, by solving the dual problem of the optimization model (34), the optimal transmit beam weight vector u is obtained m , as can be seen from Equation (35), the dual problem is expressed as: In the formula, A μ B means that A - B is a positive semi-definite matrix. The solution of this problem is obtained by solving the equivalent optimization problem of the dual problem (40). The dual problem (40) is equivalent to the receive beam optimization problem, as follows: where, w m represents the equivalent radar receiving beam weight vector, Q m = I + τ m A m , the optimal receiving beam weight vector maximizes the output signal-to-interference-plus-noise ratio. From Eqs. (32) and (33), it can be seen that the optimal receiving beam weight vector is expressed as: while the transmit beam weight vector u m is linearly related to the receive beam weight vector w m as follows: where δ m is a constant. By substituting Equation (43) into the signal-to-interference-plus-noise ratio constraint of Equation (34) and setting the inequality constraint to an equality, we obtain: δ = F -1 r, (66) where δ = [δ1, …, δ M T , denotes the element of matrix F at the m-th row and m-th column, denotes the element of matrix F at the m-th row and j-th column, r = [I1, …, I M T ;​​ Finally, alternately optimize the transmit beam weight vector $\mathbf{u}$ m and the receive beam weight vector $\mathbf{v}$ m until convergence.

10. A power control system for a networking radar system oriented to anti-interference, characterized in that, It includes: A path propagation loss acquisition module, which is used for a networking radar system that performs target detection tasks in a countermeasure environment with multiple jammers. According to the prior information of the actual operation environment, it acquires the path propagation losses between each radar node and the target, between each radar node and each jammer node, and between each radar node; A utility function construction module, which is used to construct the utility function of the networking radar system for target detection and the utility functions of each jammer node for suppressing interference respectively; A model establishment module, which is used to establish a non-cooperative game joint beamforming and power control model for target detection and a non-cooperative game joint transmit beam and power allocation model for suppressing interference respectively; A solving module for the suppression interference model, which is used to solve the non-cooperative game joint transmit beam and power allocation model for suppressing interference by using the matched filtering theory and the Lagrange multiplier method to predict the optimal interference strategy; A solving module for the target detection model, which is used to substitute the interference strategy obtained by the solving module of the suppression interference model into the non-cooperative game joint beamforming and power control model for target detection, and use the iterative optimization algorithm to solve the model to obtain the receiving beam weight vector that maximizes the output signal-to-interference-plus-noise ratio and the transmit beam weight vector that minimizes the total transmit power of the networking radar system and the peak sidelobe level of the transmit beam of each radar node under the constraint of meeting the preset target detection signal-to-interference-plus-noise ratio threshold, so as to determine the transmit power of each radar.

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