Antenna power control method for multi-target tracking oriented radar network system

Abstract

The present application belongs to the technical field of radar signal processing, and proposes a radar networking system power control method and system for multi-target tracking. The method and system are directed to a radar networking system composed of multiple single-base radars performing multi-target tracking tasks, by obtaining the path propagation loss between each radar node and multiple targets, the clutter scattering matrix prior information between each radar node and clutter, and modeling the path propagation loss as a function of the radar transmitting beam and receiving beam weight vector; the signal-to-interference-and-noise ratio of each radar node for the target is calculated; then, a non-cooperative game joint optimization model for antenna power control is established with the minimum maximum antenna power of each radar node as the target and the desired target signal-to-interference-and-noise ratio threshold value as the constraint condition; a distributed iterative algorithm is used to solve the model to obtain the optimal solution, thereby achieving the purpose of improving the radio frequency stealth performance and radio frequency front end stability of the system.

Description

Technical Field

[0001] This invention belongs to the technical field of radar signal processing, specifically relating to a power control method and system for radar networking systems oriented towards multi-target tracking. Background Technology

[0002] Beamforming is a technique that enhances signals by controlling multiple antenna elements. Compared to a single antenna, an array antenna employing beamforming technology has higher signal gain, longer tracking range, and stronger anti-jamming performance. Radar systems need to actively transmit signals and receive signals reflected back from targets to perform tasks such as target detection, localization, and identification. In radar systems, beamforming technology is used not only at the receiver to suppress interference signals but also at the transmitter to generate higher directional gain and meet specific low-intercept performance requirements, thereby improving the system's radio frequency stealth performance. Therefore, antenna power control in radar network systems is crucial. For example, Chinese invention patent application CN108260198A discloses a radar network power control method based on non-cooperative game theory under spectrum sharing. The method obtains the path propagation loss between each radar and the target in the network system and the RCS of the target relative to each radar based on prior knowledge; with the goal of minimizing the transmit power of each radar in the radar network system, and under the conditions of satisfying certain target detection performance and the maximum acceptable interference power threshold of the communication system, a radar network power control model based on non-cooperative game theory is established, and the model is solved by a distributed power iterative algorithm.

[0003] However, the power control model of the above method is based on tracking a single target, and the path propagation loss does not take into account the influence of beam gain. In practical applications, when facing the need for multi-target tracking, the electromagnetic interference faced by radar network systems is more complex, and the limitations of the above method are more prominent. Summary of the Invention

[0004] The technical problem to be solved by this invention is to propose an antenna power control method for radar networking systems that meets practical applications, in the context of multi-target tracking requirements and more complex path propagation loss and electromagnetic interference.

[0005] The present invention solves the above-mentioned technical problems through the following technical means:

[0006] This invention discloses an antenna power control method for a radar networking system oriented towards multi-target tracking, the method comprising the following steps:

[0007] S1. Obtain the path propagation loss between each radar node and multiple targets, and the prior information of the clutter scattering matrix between each radar node and clutter.

[0008] S2. Model the path propagation loss as a matrix composed of the weight vectors of the radar transmit beam and the receive beam.

[0009] S3. Calculate the signal-to-interference-plus-noise ratio (SIR) of each radar node for multiple targets.

[0010] S4. Construct an optimization model for antenna radiation power control of a radar networking system based on non-cooperative game theory.

[0011] S5. A distributed iterative algorithm is used to solve the antenna radiation power control optimization model of the radar network system.

[0012] Furthermore, step S1 specifically includes:

[0013] In a radar network system composed of multiple monostatic radars, the first... The radar node and the first Between the goals regarding the first Path propagation loss of the transmitted waveform from each radar node , No. The relationship between the radar node and clutter regarding the first... The radar node is used to detect the first... Clutter scattering matrix of the emitted waveform of each target .

[0014] Step S2 specifically involves:

[0015] use Indicates the first The radar node tracks the first... The matrix formed by the transmitted beam weight vectors of each target is: ;use Indicates the first The radar node tracks the first... The matrix formed by the received beam weight vectors of each target is: .

[0016] Step S3 involves calculating the signal-to-interference-plus-noise ratio (SIR) of each radar node for multiple targets. The specific calculation formula is as follows:

[0017] (1)

[0018] In the above formula, ,in, Indicates the target reflectance coefficient. , Indicates the first The first objective is relative to the second objective. The angle of each radar node and These represent the radar transmitting and receiving arrays respectively. Directional guide vector, Indicates transpose. This represents the clutter covariance matrix generated by the transmitted waveforms of other radar nodes. Represents the clutter scattering matrix. Indicates by the first The clutter covariance matrix generated by the transmitted waveforms of each radar node;

[0019] Let represent the target crosstalk covariance matrix of other radar nodes, where Indicates the first The radar node tracks the first... The transmission waveform of each target With the The radar node tracks the first... The transmission waveform of each target The correlation coefficient between them , Represents the identity matrix. , This indicates the noise power of the radar receiver.

[0020] Step S4, which involves constructing an antenna radiation power control optimization model for a radar networking system based on non-cooperative game theory, specifically involves:

[0021] (2)

[0022] In the above formula, Indicates the upper limit of the transmit power of each antenna. This indicates the conjugate transpose. Representation matrix The Line number List the elements, Indicates the number of transmitting antenna elements in a radar node. Indicates the first For the radar node of the _th The signal-to-interference-plus-noise ratio threshold value for each target. Indicates the number of targets.

[0023] Step S5 includes the following steps:

[0024] S51. Solving the radar network system antenna radiation power control optimization model described in step 4 is equivalent to solving the problem of maximizing the diagonal matrix formed by the Lagrange multipliers corresponding to each antenna power constraint and minimizing the vector matrix formed by the Lagrange multipliers corresponding to the signal-to-interference-plus-noise ratio constraint. Furthermore, step S51 specifically involves:

[0025] First, fix the transmit beam weight vector. The receiving beam weight vector is optimized using a diagonal loading method. To maximize the first The radar node tracks the first... Taking the signal-to-interference-plus-noise ratio (SIR) of a target as the objective, the receiving beam optimization model is established as follows:

[0026] (3)

[0027] In the formula, The diagonal loading coefficients are represented; the optimal receiving beam weight vector is obtained using the Lagrange multiplier method. The expression is as follows:

[0028] (4)

[0029] Then, fix the receiving beam weight vector and optimize the transmitting beam weight vector; rewrite the signal-to-interference-plus-noise ratio constraint in equation (1) as follows:

[0030] (5)

[0031] In the formula, ;

[0032] Then, the first The optimal model for the transmit beam of a radar node can be expressed in the following form:

[0033] (6)

[0034] The above problem is a convex optimization problem. The Lagrange duality method is used to solve this problem, and the Lagrange function can be defined as follows:

[0035] (7)

[0036] In the formula, Let (6) represent the diagonal matrix formed by the Lagrange multipliers corresponding to the antenna power constraints in (6). The vector is composed of the Lagrange multipliers corresponding to the SNR constraint in (6). ;

[0037] The Lagrange dual problem corresponding to optimization problem (6) can be expressed in the following form:

[0038] (8)

[0039] In the formula, express It is a positive semi-definite matrix; the problem is solved by solving the equivalent problem of optimization problem (8), which is equivalent to the receiving beamforming optimization problem, as shown below:

[0040] (9)

[0041] In the formula, This represents the virtual receive beam weight vector.

[0042] S52. Solve the problem of maximizing the diagonal matrix formed by the Lagrange multipliers corresponding to the power constraints of each antenna. More specifically, step S52 involves:

[0043] Define about function As shown below:

[0044] (10)

[0045] Among them, the function about It is a concave function;

[0046] It is a function The subgradient, Represented by matrix A diagonal matrix consisting of diagonal elements;

[0047] definition On the constraint set The subgradient projection; for a fixed radar transmit beam weight vector The solution is obtained by iteratively solving the subgradient projection algorithm. The iteration expression is as follows:

[0048] (11)

[0049] In the formula, Indicates the number of iterations. Indicates the first The iteration matrix The value of , This represents the iteration step size, which satisfies the square summability criterion.

[0050] S53. Solve the problem of minimizing the vector matrix formed by the Lagrange multipliers corresponding to the signal-to-interference-plus-noise ratio constraint. More specifically, step S53 involves:

[0051] First, regarding (7) Find the first-order partial derivatives, and then perform mathematical transformations to obtain the Lagrange multipliers. The fixed-point iteration expression is as follows:

[0052] (12)

[0053] In the formula, Indicates the number of iterations. ;

[0054] Then, based on the minimum variance distortionless response criterion, the optimal virtual receive beam weight vector is obtained. The expression is as follows:

[0055] (13)

[0056] According to the transmitted beam weight vector and The coefficient relationship is used to obtain the solution. The expression is as follows:

[0057] (14)

[0058] In the formula, Since is a constant, substituting (14) into the signal-to-interference-plus-noise ratio constraint in (5) and setting it to be equal, we get:

[0059] (15)

[0060] therefore, It can be obtained through the following expression:

[0061] (16)

[0062] In the formula, , , , .

[0063] S54, Alternating optimization of receive beam weight vector and the transmitted beam weight vector Until the set accuracy requirement is achieved.

[0064] This invention also provides an antenna power control system for a radar networking system oriented towards multi-target tracking. The system specifically employs the above-described method and includes the following modules:

[0065] The path propagation loss prior module is used to obtain the path propagation loss between each radar node and multiple targets, and the prior information of the clutter scattering matrix between each radar node and clutter.

[0066] The path propagation loss modeling module is used to model the path propagation loss as a matrix composed of the weight vectors of the radar transmit beam and the receive beam.

[0067] The signal-to-interference-plus-noise ratio (SINR) calculation module is used to calculate the SINR of each radar node for multiple targets.

[0068] The model building module is used to build an optimization model for antenna radiation power control of a radar networking system based on non-cooperative game theory.

[0069] The model solving module is used to solve the optimization model for antenna radiation power control in radar networking systems.

[0070] The advantages of this invention are:

[0071] (1) This invention targets a radar network system composed of multiple monostatic radars performing multi-target tracking tasks. Based on prior information about the actual combat environment, it obtains the path propagation loss between each radar node and multiple targets, and the prior information about the clutter scattering matrix between each radar node and clutter. The path propagation loss is modeled as a function of the radar transmit beam and the receive beam weight vector. Then, the signal-to-interference-plus-noise ratio (SIR) of each radar node relative to the target is calculated. Based on this, with the goal of minimizing the maximum antenna power of each radar node and with the desired target SIR threshold value as a constraint, a non-cooperative game-theoretic joint transmit and receive beamforming optimization model for antenna power control is established. By solving the model, the stability of the radar system's radio frequency front-end and the total radiated power of the system are improved. Among these, the above-mentioned modeling of the path propagation loss as a function of the radar transmit beam and the receive beam weight vector makes the optimization model created by this invention more closely aligned with practical applications when facing multi-target tracking requirements, more complex path propagation loss, and electromagnetic interference.

[0072] (2) This invention addresses the power control problem of transmitting antenna elements in multi-target tracking of radar network systems under complex electromagnetic environments. It proposes an optimization model that minimizes the maximum radiated power of antenna elements under target detection performance constraints for each radar. In the model solution process, the optimization problem is decomposed into two sub-problems, and iterative algorithms are designed to efficiently solve the optimization model. This not only meets the pre-set signal-to-interference-plus-noise ratio threshold requirement for target tracking performance, but also effectively controls the radio frequency radiation of the radar network system and the peak antenna power of each radar node, thereby achieving the goal of improving the radio frequency stealth performance and radio frequency front-end stability of the system. Attached Figure Description

[0073] Figure 1 This is a schematic flowchart of the antenna power control method for a radar networking system for multi-target tracking, according to Embodiment 1 of the present invention.

[0074] Figure 2 This is a schematic diagram of the antenna power control system module of the radar networking system for multi-target tracking in Embodiment 2 of the present invention. Detailed Implementation

[0075] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0076] Example 1

[0077] Embodiment 1 of the present invention provides an antenna power control method for a radar networking system oriented towards multi-target tracking, such as... Figure 1 As shown, the method includes the following steps:

[0078] S1. Obtain the path propagation loss between each radar node and multiple targets, and the prior information of the clutter scattering matrix between each radar node and clutter.

[0079] S2. Model the path propagation loss as a matrix composed of the weight vectors of the radar transmit beam and the receive beam.

[0080] S3. Calculate the signal-to-interference-plus-noise ratio (SIR) of each radar node for multiple targets.

[0081] S4. Construct an optimization model for antenna radiation power control of a radar networking system based on non-cooperative game theory.

[0082] S5. A distributed iterative algorithm is used to solve the antenna radiation power control optimization model of the radar network system.

[0083] Furthermore, step S1 specifically includes:

[0084] In a radar network system composed of multiple monostatic radars, the first... The radar node and the first Between the goals regarding the first Path propagation loss of the transmitted waveform from each radar node , No. The relationship between the radar node and clutter regarding the first... The radar node is used to detect the first... Clutter scattering matrix of the emitted waveform of each target .

[0085] Step S2 specifically involves:

[0086] use Indicates the first The radar node tracks the first... The matrix formed by the transmitted beam weight vectors of each target is: ;use Indicates the first The radar node tracks the first... The matrix formed by the received beam weight vectors of each target is: .

[0087] Step S3 involves calculating the signal-to-interference-plus-noise ratio (SIR) of each radar node for multiple targets. The specific calculation formula is as follows:

[0088] (1)

[0089] Indicates the first For the radar node of the _th The signal-to-interference-plus-noise ratio (SIR) of each target is given in the formula above. ,in, Indicates the target reflectance coefficient. , Indicates the first The first objective is relative to the second objective. The angle of each radar node and These represent the radar transmitting and receiving arrays respectively. Directional guide vector, Indicates transpose. This represents the clutter covariance matrix generated by the transmitted waveforms of other radar nodes. Represents the clutter scattering matrix. Indicates by the first The clutter covariance matrix generated by the transmitted waveforms of each radar node;

[0090] Let represent the target crosstalk covariance matrix of other radar nodes, where Indicates the first The radar node tracks the first... The transmission waveform of each target With the The radar node tracks the first... The transmission waveform of each target The correlation coefficient between them , Represents the identity matrix. , This indicates the noise power of the radar receiver.

[0091] Step S4, which involves constructing an antenna radiation power control optimization model for a radar networking system based on non-cooperative game theory, specifically involves:

[0092] (2)

[0093] In the above formula, Indicates the upper limit of the transmit power of each antenna. This indicates the conjugate transpose. Representation matrix The Line number List the elements, Indicates the number of transmitting antenna elements in a radar node. Indicates the first For the radar node of the _th The signal-to-interference-plus-noise ratio threshold value for each target. Indicates the number of targets.

[0094] Step S5 includes the following steps:

[0095] S51. Solving the radar network system antenna radiation power control optimization model described in step 4 is equivalent to maximizing the diagonal matrix formed by the Lagrange multipliers corresponding to each antenna power constraint and minimizing the vector matrix formed by the Lagrange multipliers corresponding to the signal-to-interference-plus-noise ratio constraint. Furthermore, S51 specifically involves:

[0096] First, fix the transmit beam weight vector. The receiving beam weight vector is optimized using a diagonal loading method. To maximize the first The radar node tracks the first... Taking the signal-to-interference-plus-noise ratio (SIR) of a target as the objective, the receiving beam optimization model is established as follows:

[0097] (3) In the formula, The diagonal loading coefficients are represented; the optimal receiving beam weight vector is obtained using the Lagrange multiplier method. The expression is as follows:

[0098] (4)

[0099] Then, fix the receiving beam weight vector and optimize the transmitting beam weight vector; rewrite the signal-to-interference-plus-noise ratio constraint in equation (1) as follows:

[0100] (5)

[0101] In the formula, ;

[0102] Then, the first The optimal model for the transmit beam of a radar node can be expressed in the following form:

[0103] (6)

[0104] The above problem is a convex optimization problem. The Lagrange duality method is used to solve this problem, and the Lagrange function can be defined as follows:

[0105] (7)

[0106] In the formula, Let (6) represent the diagonal matrix formed by the Lagrange multipliers corresponding to the antenna power constraints in (6). The vector is composed of the Lagrange multipliers corresponding to the SNR constraint in (6). ;

[0107] The Lagrange dual problem corresponding to optimization problem (6) can be expressed in the following form:

[0108] (8)

[0109] In the formula, express It is a positive semi-definite matrix; the problem is solved by solving the equivalent problem of optimization problem (8), which is equivalent to the receiving beamforming optimization problem, as shown below:

[0110] (9) In the formula, This represents the virtual receive beam weight vector.

[0111] Thus, optimization problem (9) contains two sub-problems: (1) about Maximizing the outermost optimization problem; (2) Regarding Minimize the inner layer optimization problem.

[0112] S52. Solve the problem of maximizing the diagonal matrix formed by the Lagrange multipliers corresponding to each antenna power constraint. Furthermore, step S52 is to solve subproblem (1), specifically:

[0113] Define about function As shown below:

[0114] (10)

[0115] Among them, the function about It is a concave function;

[0116] It is a function The subgradient, Represented by matrix A diagonal matrix consisting of diagonal elements;

[0117] definition On the constraint set The subgradient projection; for a fixed radar transmit beam weight vector The solution is obtained by iteratively solving the subgradient projection algorithm. The iteration expression is as follows:

[0118] (11)

[0119] In the formula, Indicates the number of iterations. Indicates the first The iteration matrix The value of , This represents the iteration step size, which satisfies the square summability criterion.

[0120] S53. Solve the problem of minimizing the vector matrix formed by the Lagrange multipliers corresponding to the signal-to-interference-plus-noise ratio constraint. Furthermore, step S53, in order to solve sub-problem (2), specifically involves:

[0121] First, regarding (7) Find the first-order partial derivatives, and then perform mathematical transformations to obtain the Lagrange multipliers. The fixed-point iteration expression is as follows:

[0122] (12)

[0123] In the formula, Indicates the number of iterations. ;

[0124] Then, based on the minimum variance distortionless response criterion, the optimal virtual receive beam weight vector is obtained. The expression is as follows:

[0125] (13)

[0126] According to the transmitted beam weight vector and The coefficient relationship is used to obtain the solution. The expression is as follows:

[0127] (14)

[0128] In the formula, Since is a constant, substituting (14) into the signal-to-interference-plus-noise ratio constraint in (5) and setting it to be equal, we get:

[0129] (15)

[0130] therefore, It can be obtained through the following expression:

[0131] (16)

[0132] In the formula, , , , .

[0133] S54, Alternating optimization of receive beam weight vector and the transmitted beam weight vector Until the set accuracy requirement is achieved.

[0134] Embodiment 1 of this invention first targets a radar network system composed of multiple monostatic radars performing multi-target tracking tasks. Based on prior information about the actual combat environment, it obtains the path propagation loss between each radar node and multiple targets, and the clutter scattering matrix prior information between each radar node and clutter. The path propagation loss is then modeled as a function of the radar transmit beam and receive beam weight vector. Next, the signal-to-interference-plus-noise ratio (SIR) of each radar node relative to the target is calculated. Based on this, with the goal of minimizing the maximum antenna power of each radar node and the constraint of satisfying the desired target SIR threshold, a non-cooperative game-theoretic joint transmit and receive beamforming optimization model for antenna power control is established. Finally, a distributed iterative joint transmit and receive beamforming algorithm is used to solve the model, and the transmit beam and receive beam weight vector that minimizes the maximum antenna power of each radar node under the pre-set target tracking SIR performance constraint are selected as the optimal solution. This achieves the goal of improving the system's radio frequency stealth performance and radio frequency front-end stability.

[0135] Example 2

[0136] It should be further explained that, based on the same inventive concept as Embodiment 1, the present invention also provides an antenna power control system for a radar networking system oriented towards multi-target tracking, wherein the system executes the method described in Embodiment 1 during operation. Figure 2 As shown, the system includes the following modules:

[0137] The path propagation loss prior module is used to obtain the path propagation loss between each radar node and multiple targets, and the prior information of the clutter scattering matrix between each radar node and clutter.

[0138] The path propagation loss modeling module is used to model path propagation loss as a matrix composed of the weight vectors of the radar transmit beam and receive beam.

[0139] The signal-to-interference-plus-noise ratio (SIR / NOT) calculation module is used to calculate the SIR / NOT of each radar node for multiple targets.

[0140] The model building module is used to construct an optimization model for antenna radiation power control of a radar networking system based on non-cooperative game theory.

[0141] The model solving module is used to solve the optimization model for antenna radiation power control in radar networking systems.

[0142] Furthermore, the specific execution method of the path propagation loss prior module is as follows:

[0143] In a radar network system composed of multiple monostatic radars, the first... The radar node and the first Between the goals regarding the first Path propagation loss of the transmitted waveform from each radar node , No. The relationship between the radar node and clutter regarding the first... The radar node is used to detect the first... Clutter scattering matrix of the emitted waveform of each target .

[0144] The specific execution method of the path propagation loss modeling module is as follows:

[0145] use Indicates the first The radar node tracks the first... The matrix formed by the transmitted beam weight vectors of each target is: ;use Indicates the first The radar node tracks the first... The matrix formed by the received beam weight vectors of each target is: .

[0146] The specific calculation formula executed by the signal-to-interference-plus-noise ratio (SINR) calculation module is as follows:

[0147] (1)

[0148] Indicates the first For the radar node of the _th The signal-to-interference-plus-noise ratio (SIR) of each target is given in the formula above. ,in, Indicates the target reflectance coefficient. , Indicates the first The first objective is relative to the second objective. The angle of each radar node and These represent the radar transmitting and receiving arrays respectively. Directional guide vector, Indicates transpose. This represents the clutter covariance matrix generated by the transmitted waveforms of other radar nodes. Represents the clutter scattering matrix. Indicates by the first The clutter covariance matrix generated by the transmitted waveforms of each radar node;

[0149] Let represent the target crosstalk covariance matrix of other radar nodes, where Indicates the first The radar node tracks the first... The transmission waveform of each target With the The radar node tracks the first... The transmission waveform of each target The correlation coefficient between them , Represents the identity matrix. , This indicates the noise power of the radar receiver.

[0150] The optimized model constructed by the model building module is specifically as follows:

[0151] (2)

[0152] In the above formula, Indicates the upper limit of the transmit power of each antenna. This indicates the conjugate transpose. Representation matrix The Line number List the elements, Indicates the number of transmitting antenna elements in a radar node. Indicates the first For the radar node of the _th The signal-to-interference-plus-noise ratio threshold value for each target. Indicates the number of targets.

[0153] The specific execution method of the model solving module is as follows:

[0154] 1. Solving the radar network system antenna radiation power control optimization model constructed by the model building module is equivalent to solving the problem of maximizing the diagonal matrix formed by the Lagrange multipliers corresponding to each antenna power constraint and minimizing the vector matrix formed by the Lagrange multipliers corresponding to the signal-to-interference-plus-noise ratio constraint. Specifically:

[0155] First, fix the transmit beam weight vector. The receiving beam weight vector is optimized using a diagonal loading method. To maximize the first The radar node tracks the first... Taking the signal-to-interference-plus-noise ratio (SIR) of a target as the objective, the receiving beam optimization model is established as follows:

[0156] (3) In the formula, The diagonal loading coefficients are represented; the optimal receiving beam weight vector is obtained using the Lagrange multiplier method. The expression is as follows:

[0157] (4)

[0158] Then, fix the receiving beam weight vector and optimize the transmitting beam weight vector; rewrite the signal-to-interference-plus-noise ratio constraint in equation (1) as follows:

[0159] (5)

[0160] In the formula, ;

[0161] Then, the first The optimal model for the transmit beam of a radar node can be expressed in the following form:

[0162] (6)

[0163] The above problem is a convex optimization problem. The Lagrange duality method is used to solve this problem, and the Lagrange function can be defined as follows:

[0164] (7)

[0165] In the formula, Let (6) represent the diagonal matrix formed by the Lagrange multipliers corresponding to the antenna power constraints in (6). The vector is composed of the Lagrange multipliers corresponding to the SNR constraint in (6). ;

[0166] The Lagrange dual problem corresponding to optimization problem (6) can be expressed in the following form:

[0167] (8)

[0168] In the formula, express It is a positive semi-definite matrix; the problem is solved by solving the equivalent problem of optimization problem (8), which is equivalent to the receiving beamforming optimization problem, as shown below:

[0169] (9) In the formula, This represents the virtual receive beam weight vector.

[0170] Thus, optimization problem (9) contains two sub-problems: (1) about Maximizing the outermost optimization problem; (2) Regarding Minimize the inner layer optimization problem.

[0171] 2. Solve the problem of maximizing the diagonal matrix formed by the Lagrange multipliers corresponding to the power constraints of each antenna. Specifically:

[0172] Define about function As shown below:

[0173] (10)

[0174] Among them, the function about It is a concave function;

[0175] It is a function The subgradient, Represented by matrix A diagonal matrix consisting of diagonal elements;

[0176] definition On the constraint set The subgradient projection; for a fixed radar transmit beam weight vector The solution is obtained by iteratively solving the subgradient projection algorithm. The iteration expression is as follows:

[0177] (11)

[0178] In the formula, Indicates the number of iterations. Indicates the first The iteration matrix The value of , This represents the iteration step size, which satisfies the square summability criterion.

[0179] 3. Solve the problem of minimizing the vector matrix formed by the Lagrange multipliers corresponding to the signal-to-interference-plus-noise ratio (SINR) constraint. Specifically:

[0180] First, regarding (7) Find the first-order partial derivatives, and then perform mathematical transformations to obtain the Lagrange multipliers. The fixed-point iteration expression is as follows:

[0181] (12)

[0182] In the formula, Indicates the number of iterations. ;

[0183] Then, based on the minimum variance distortionless response criterion, the optimal virtual receive beam weight vector is obtained. The expression is as follows:

[0184] (13)

[0185] According to the transmitted beam weight vector and The coefficient relationship is used to obtain the solution. The expression is as follows:

[0186] (14)

[0187] In the formula, Since is a constant, substituting (14) into the signal-to-interference-plus-noise ratio constraint in (5) and setting it to be equal, we get:

[0188] (15)

[0189] therefore, It can be obtained through the following expression:

[0190] (16)

[0191] In the formula, , , , .

[0192] 4. Alternately optimize the received beam weight vector and the transmitted beam weight vector Until the set accuracy requirement is achieved.

[0193] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. An antenna power control method for a radar network system for multi-target tracking, characterized in that, The method includes the following steps: S1. Obtain the path propagation loss between each radar node and multiple targets, and the prior information of the clutter scattering matrix between each radar node and clutter. S2. Model the path propagation loss as a matrix composed of the weight vectors of the radar transmit beam and the receive beam. S3. Calculate the signal-to-interference-plus-noise ratio (SIR) of each radar node for multiple targets. The specific calculation formula is as follows: (1) In the above formula, ,in, Indicates the target reflectance coefficient. , Indicates the first The first objective is relative to the second objective. The angle of each radar node and These represent the radar transmitting and receiving arrays respectively. Directional guide vector, Indicates transpose. This represents the clutter covariance matrix generated by the transmitted waveforms of other radar nodes. Represents the clutter scattering matrix. Indicates by the first The clutter covariance matrix generated by the transmitted waveforms of each radar node; Let represent the target crosstalk covariance matrix of other radar nodes, where Indicates the first The radar node tracks the first... The transmission waveform of each target With the The radar node tracks the first... The transmission waveform of each target The correlation coefficient between them , , Indicates the noise power of the radar receiver; S4. Construct an optimization model for antenna radiation power control of a radar networking system based on non-cooperative game theory; S5. A distributed iterative algorithm is used to solve the antenna radiation power control optimization model of the radar network system.

2. The antenna power control method for a radar networking system for multi-target tracking according to claim 1, characterized in that, Step S1 specifically involves: In a radar network system composed of multiple monostatic radars, the first... The radar node and the first Between the goals regarding the first Path propagation loss of the transmitted waveform from each radar node , No. The relationship between the radar node and clutter regarding the first... The radar node is used to detect the first... Clutter scattering matrix of the emitted waveform of each target .

3. The antenna power control method for a radar networking system for multi-target tracking according to claim 1, characterized in that, Step S2 specifically involves: use Indicates the first The radar node tracks the first... The matrix formed by the transmitted beam weight vectors of each target is: ;use Indicates the first The radar node tracks the first... The matrix formed by the received beam weight vectors of each target is: .

4. The antenna power control method for a radar networking system for multi-target tracking according to claim 3, characterized in that, Step S4, which involves constructing an antenna radiation power control optimization model for a radar networking system based on non-cooperative game theory, specifically involves: (2) In the above formula, Indicates the upper limit of the transmit power of each antenna. This indicates the conjugate transpose. Representation matrix The Line number List the elements, Indicates the number of transmitting antenna elements in a radar node. Indicates the first For the radar node of the _th Signal-to-interference-plus-noise ratio threshold for each target Indicates the number of targets.

5. The antenna power control method for a radar networking system for multi-target tracking according to claim 4, characterized in that, Step S5 includes the following steps: S51. Solving the radar networking system antenna radiation power control optimization model described in step 4 is equivalent to solving the problem of maximizing the diagonal matrix formed by the Lagrange multipliers corresponding to each antenna power constraint and minimizing the vector matrix formed by the Lagrange multipliers corresponding to the signal-to-interference-plus-noise ratio constraint. S52. Solve the problem of maximizing the diagonal matrix formed by the Lagrange multipliers corresponding to the power constraints of each antenna; S53. Solve the problem of minimizing the vector matrix formed by the Lagrange multipliers corresponding to the signal-to-interference-plus-noise ratio constraint; S54, Alternating optimization of receive beam weight vector and the transmitted beam weight vector Until the set accuracy requirement is achieved.

6. The antenna power control method for a radar networking system for multi-target tracking according to claim 5, characterized in that, Step S51 specifically involves: First, fix the transmit beam weight vector. The receiving beam weight vector is optimized using a diagonal loading method. To maximize the first The radar node tracks the first... Taking the signal-to-interference-plus-noise ratio (SIR) of a target as the objective, the receiving beam optimization model is established as follows: (3) In the formula, Indicates the diagonal loading coefficient; The optimal receiving beam weight vector is obtained by using the Lagrange multiplier method. The expression is as follows: (4) Then, fix the receiving beam weight vector and optimize the transmitting beam weight vector; rewrite the signal-to-interference-plus-noise ratio constraint in equation (1) as follows: (5) In the formula, ; Then, the first The optimal model for the transmit beam of a radar node can be expressed in the following form: (6) The above problem is a convex optimization problem. The Lagrange duality method is used to solve this problem, and the Lagrange function is defined as follows: (7) In the formula, Let (6) represent the diagonal matrix formed by the Lagrange multipliers corresponding to the antenna power constraints in (6). The vector is composed of the Lagrange multipliers corresponding to the SNR constraint in (6). ; The Lagrange dual problem corresponding to optimization problem (6) can be expressed in the following form: (8) In the formula, express It is a positive semi-definite matrix; the problem is solved by solving the equivalent problem of optimization problem (8), which is equivalent to the receiving beamforming optimization problem, as shown below: (9) In the formula, This represents the virtual receive beam weight vector.

7. The antenna power control method for a radar networking system for multi-target tracking according to claim 6, characterized in that, Step S52 specifically involves: Define about function As shown below: (10) Among them, the function about It is a concave function; It is a function The subgradient, Represented by matrix A diagonal matrix consisting of diagonal elements; definition On the constraint set The subgradient projection; for a fixed radar transmit beam weight vector The solution is obtained by iteratively solving the subgradient projection algorithm. The iteration expression is as follows: (11) In the formula, Indicates the number of iterations. Indicates the first The iteration matrix The value of , This represents the iteration step size, which satisfies the square summability criterion.

8. The antenna power control method for a radar networking system for multi-target tracking according to claim 6, characterized in that, Step S53 specifically involves: First, regarding (7) Find the first-order partial derivatives, and then perform mathematical transformations to obtain the Lagrange multipliers. The fixed-point iteration expression is as follows: (12) In the formula, Indicates the number of iterations. ; Then, based on the minimum variance distortionless response criterion, the optimal virtual receive beam weight vector is obtained. The expression is as follows: (13) According to the transmitted beam weight vector and The coefficient relationship is used to obtain the solution. The expression is as follows: (14) In the formula, Since is a constant, substituting (14) into the signal-to-interference-plus-noise ratio constraint in (5) and setting it to be equal, we get: (15) therefore, It can be obtained through the following expression: (16) In the formula, , , , .

9. An antenna power control system for a radar network system for multi-target tracking, characterized in that, The system includes the following modules: The path propagation loss prior module is used to obtain the path propagation loss between each radar node and multiple targets, and the prior information of the clutter scattering matrix between each radar node and clutter. The path propagation loss modeling module is used to model the path propagation loss as a matrix composed of the weight vectors of the radar transmit beam and the receive beam. The signal-to-interference-plus-noise ratio (SIR) calculation module is used to calculate the SIR of each radar node for multiple targets. The specific calculation formula is as follows: (1) In the above formula, Indicates the first One radar node, Indicates the first One goal, ,in, Indicates the target reflectance coefficient. , Indicates the first The first objective is relative to the second objective. The angle of each radar node and These represent the radar transmitting and receiving arrays respectively. Directional guide vector, Indicates transpose. This represents the clutter covariance matrix generated by the transmitted waveforms of other radar nodes. Represents the clutter scattering matrix. Indicates the first The radar node tracks the first... The transmitted beam weight vector of each target. Indicates by the first The clutter covariance matrix generated by the transmitted waveforms of each radar node; Let represent the target crosstalk covariance matrix of other radar nodes, where Indicates the first The radar node tracks the first... The transmission waveform of each target With the The radar node tracks the first... The transmission waveform of each target The correlation coefficient between them , , Indicates the noise power of the radar receiver; The model building module is used to build an optimization model for antenna radiation power control of a radar networking system based on non-cooperative game theory. The model solving module is used to solve the optimization model for antenna radiation power control in radar networking systems.

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