A method for improving the radio frequency stealth performance of a phased array radar system

Abstract

The application discloses a method for improving the radio frequency stealth performance of a phased array radar system, which comprises the following steps: firstly, constructing a scene of fighter searching M targets based on guidance information; secondly, taking minimization of total radiation power as an objective function, taking radar search performance, system hardware configuration and resource natural attribute as constraint conditions, and establishing a multi-region search aperture and power joint optimization model of the phased array radar based on the guidance information; thirdly, continuously using convex relaxation on the optimization model, and then using the Lagrange multiplier method to analytically solve the continuous optimization model; and finally, rounding the aperture value and then performing power distribution. Under the constraint of detection performance, the method optimizes the apertures and powers used in different search regions, minimizes the total consumed power of the multi-region search of the phased array radar, improves the energy utilization rate, minimizes the total transmitting power of the system, and improves the radio frequency stealth performance of the phased array radar system.

Description

TECHNICAL FIELD

[0001] The present application relates to a method for improving the radio frequency stealth performance of a phased array radar system, belonging to the technical field of radar resource allocation. BACKGROUND

[0002] Radar is the main sensor for battlefield environment perception, and information exchange between different types of radars is also essential. For example, the most common early warning aircraft guides the fighter aircraft to search for enemy targets, so that the fighter aircraft can quickly and accurately search for enemy formations, thereby achieving the purpose of discovering and attacking the enemy first. Since the fighter aircraft carries limited fuel, it is necessary to effectively manage its radar radiation resources, thereby prolonging its working time and increasing its combat radius and deterrent range. In addition, radiation resource management technology reduces the radiation power of the radar, increasing the difficulty of the enemy sensor intercepting the radar signal, i.e., improving the stealth performance of the radar signal. At present, in the aspect of target search, the common resource management techniques include search parameter optimization such as dwell time, wave position arrangement, and frame period. In addition to radar search parameter optimization, scholars have proposed optimizing other parameters to improve the search performance or radio frequency stealth performance of the radar system. Common parameters include radar radiation power, number of subarrays for antenna division, and array element deployment. When there is prior information for guidance, the search space of the guided radar is greatly reduced, and the main task of the radar system is to detect the target and determine whether it exists.

[0003] For example, application number 202010504069.3 is a frequency control array radar radiation power control method based on radio frequency stealth. This method not only meets the pre-set target azimuth angle parameter estimation performance and target distance parameter estimation performance requirements, but also effectively reduces the radiation power of the frequency control array radar, thereby improving the radio frequency stealth performance of the frequency control array radar system. For example, application number 201911343282.4 is a networking radar residence time optimization control method based on radio frequency stealth. The networking of airborne radars includes N airborne two-coordinate phased array radars that are synchronized in space, time and frequency. The Q uniformly moving targets in the two-dimensional plane are tracked, and the observation model of the airborne radar networking and the motion model of the target are constructed accordingly. The BCRLB of the target state estimation error during uniform motion target tracking is obtained, and the lower bound of the target position estimation mean square error is extracted as a measure of target tracking accuracy. The predicted detection probability of the airborne radar networking for the tracked target is calculated according to the predicted echo signal-to-noise ratio. An optimization control model is constructed to minimize the residence time of the airborne radar networking. Under the premise that the predicted tracking accuracy and the predicted detection probability of all targets meet the constraint conditions, the total residence time of the airborne radar networking is minimized. A two-step decomposition method is used to solve the optimization control model. By jointly optimizing the residence time and radar allocation index of the airborne radar networking when tracking multiple targets, the total residence time of the airborne radar networking illuminating all targets during target tracking can be shortened, effectively improving the radio frequency stealth performance of the airborne radar networking, and ensuring the tracking accuracy and detection probability of all targets.

[0004] In general, the above method proposes the idea of radar power optimization design and improvement of radar signal stealth performance, but at this time, the search parameter optimization is no longer significant for improving the performance of the radar system. At this time, the main technical problems to be solved include: how does the phased array radar search multiple regions with the lowest power under the constraints of radar search performance, system hardware configuration and resource natural properties when the fighter simultaneously searches M targets. SUMMARY

[0005] The main purpose of the present application is to provide a method for improving the radio frequency stealth performance of a phased array radar system. In the context of multi-target search by an airborne phased array radar, a method of joint optimization of aperture and power is proposed. Under the constraint of detection performance, the total consumed power of multi-region search of the phased array radar is minimized by optimizing the aperture and power used to search different regions, reducing system resource consumption, and improving the radio frequency stealth performance of the phased array radar system.

[0006] To achieve the above object, the technical scheme adopted by the present application is as follows: a method for improving the radio frequency stealth performance of a phased array radar system, steps as follows: first, constructing a scene of a fighter searching M targets based on guidance information; second, establishing a multi-region search aperture and power joint optimization model of a phased array radar based on guidance information, taking the minimization of total radiation power as an objective function, and taking radar search performance, system hardware configuration and resource natural attributes as constraint conditions; third, using convex relaxation to continuously optimize the optimization model, and then using the Lagrange multiplier method to analytically solve the continuous optimization model; and finally, rounding the aperture numerical value and then performing power distribution.

[0007] Considering the beam agility characteristics of the phased array radar, the optimization configuration of the radar system radiation and hardware resources is focused on, and when performing multi-target search, detection and tracking and other tasks, if the radar system radiation and the number of array elements of the subarray are optimized at the same time, the performance of the phased array radar system will be greatly improved, or the system power consumption will be reduced when the same performance is achieved.

[0008] Further, the construction of the scene of the fighter searching M targets based on guidance information refers to that it is assumed that a warning plane discovers M targets in a certain airspace in a three-dimensional space, and then sends the measured radar reflection cross-sectional area, position and speed information of each target to the fighter through a data link, and according to the guidance information of the warning plane, the fighter searches the M targets.

[0009] Further, the establishment of the multi-region search aperture and power joint optimization model of the phased array radar based on guidance information is as shown in formula (1):

[0010]

[0011] In the formula, P=[p1, p2, …, p M ] is a power vector, the mth element of which is p m , representing the power emitted by the multifunction phased array radar when searching the mth target; A=[A1, A2, …, A M ] is a radar aperture vector, the mth element of which is A m , representing the radar aperture allocated by the multifunction phased array radar when searching the mth target; , representing the minimization of the objective function by optimizing variables P and A; P m , representing the detection probability of the radar when searching the mth target; , representing the given radar detection probability threshold for the mth target; , representing any certain element; n m , representing the number of array elements when the aperture area is A m ; N total , representing the total number of array elements of the phased array radar; p m≥0 means that the power is non-negative, M means that the fighter searches M targets; n m ∈{1, …, N total} means that the number of array elements must be a natural number from 1 to N total .

[0012] Further, the utilization of the convex relaxation to continuously the optimization model means that the discrete constraint of the array element is converted into a continuous constraint, i.e. n m ∈{1, …, N total} is replaced by the constraint of formula (2):

[0013] n m ≥0 (2)

[0014] Then the detection probability constraint is converted into a signal-to-noise ratio constraint, and the continuous optimization model is converted into formula (3):

[0015]

[0016] In the formula, the signal-to-noise ratio required for the radar to search the mth target to reach a given radar detection probability; σ m is the RCS of the mth target; L represents the total loss of the system; k is the Boltzmann constant; T e is the temperature of the radar system; B is the spectral width of the radar signal; F r is the noise figure of the radar system; R m is the distance between the mth target and the radar; and λ is the wavelength of the radar signal.

[0017] Further, the utilization of the Lagrange multiplier method to analytically solve the continuous optimization model means:

[0018]

[0019] In the formula,

[0020] Further, the numerical aperture is rounded and then the power is distributed, and by solving the optimization model, the aperture resource A m and the transmitted power p m of the phased array radar searching the mth target are obtained under the constraint conditions of satisfying the radar search performance, the system hardware configuration and the natural properties of resources, and the total radiant energy of the system is the lowest.

[0021] The beneficial effect of the present application is that the method minimizes the total consumed power of the phased array radar multi-region search under the constraint of the detection performance, the phased array radar multi-region search aperture and power joint optimization based on the guidance information, the objective function is to minimize the total radiation power, the radar search performance, the system hardware configuration and the natural attribute of the resource are constraints, the phased array radar multi-region search aperture and power joint optimization model based on the guidance information is established, not only the energy utilization rate is improved, but also the total transmitting power of the system is minimized, and the radio frequency stealth performance of the radar system is improved. BRIEF DESCRIPTION OF DRAWINGS

[0022] The present application is further described below in conjunction with the accompanying drawings and embodiments.

[0023] Figure 1 The flow chart of the phased array radar multi-region search aperture and power joint optimization based on the guidance information. DETAILED DESCRIPTION

[0024] The present application is further described below in conjunction with the accompanying drawings and embodiments, wherein the drawings are only used for exemplary description, and the representation is only a schematic diagram, not a physical diagram, and cannot be understood as a limitation of the present patent, in order to better illustrate the specific embodiments of the present application, some components of the drawings are omitted, enlarged or reduced, and do not represent the size of the actual product, and it is understandable for those skilled in the art that some known structures and their descriptions in the drawings can be omitted, based on the specific embodiments in the present application, all other specific embodiments obtained by those skilled in the art without creative labor fall within the scope of the present application.

[0025] In order to make the technical means, creative features, purposes and effects of the present application easy to understand, in the description of the present application, it should be noted that the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer" and the like indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, and are only for the convenience of describing the present application and simplifying the description, and therefore cannot be understood as indicating or implying that the devices or elements referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as a limitation of the present application, in addition, the terms "first", "second", "third" are only for the purpose of description, and cannot be understood as indicating or implying relative importance, the present application is further described below in conjunction with the specific embodiments.

[0026] In the description of the present application, the description of the terms "an embodiment", "an example" and the like means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present application, in the present application, the illustrative description of the above terms does not necessarily refer to the same embodiment or example.

[0027] Furthermore, it should be understood that although the specification is described in terms of embodiments, not every embodiment contains only one independent technical solution, and the specification is described in this way only for the sake of clarity, and those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can be appropriately combined to form other embodiments that those skilled in the art can understand.

[0028] A method for improving the radio frequency stealth performance of a phased array radar system, comprising the following steps:

[0029] First, based on the guidance information, a scene of the fighter searching M targets is constructed; assuming that the early warning aircraft discovers M targets in a certain airspace, and then sends the measured radar cross section (RCS), position and speed information of each target to the fighter through the data link, according to the guidance information of the early warning aircraft, the fighter searches for M targets.

[0030] Secondly, taking the minimization of total radiation power as the objective function, and taking the radar search performance, system hardware configuration and resource natural attribute as the constraints, a phased array radar multi-region search aperture and power joint optimization model based on guidance information is established as follows (1):

[0031]

[0032] In the formula, P=[p1,p2,…,p M ] is a power vector, the mth element of which is p m , which represents the power emitted by the multi-functional phased array radar when searching for the mth target; A=[A1,A2,…,A M ] is a radar aperture vector, the mth element of which is A m , which represents the radar aperture allocated by the multi-functional phased array radar when searching for the mth target; minimize the objective function by optimizing variables P and A; P m represents the detection probability of the radar searching for the mth target; represents the given radar detection probability threshold for the mth target; represents any certain element; n m is the number of array elements corresponding to the aperture area A m ; N total is the total number of array elements of the phased array radar; p m ≥0 represents that the power is non-negative, and M represents that the fighter searches for M targets; n m , ∈{1,…,N total} represents that the number of array elements must be a natural number between 1 and N total .

[0033] Because the first constraint expression of formula (1) is complex, it is difficult to solve the problem. The search performance constraint can be transformed into the signal-to-noise ratio constraint, that is The constraint of formula (5) can be replaced by

[0034]

[0035] In the formula, S m represents the signal-to-noise ratio of the target echo signal when the radar searches the mth target; represents the signal-to-noise ratio required by the radar to search the mth target to achieve a given radar detection probability. In the search mode, the expression of the signal-to-noise ratio can be expressed as formula (6):

[0036]

[0037] In the formula, G m is the aperture A m allocated for searching the mth target; G m is the transmit gain of the formed beam; σ e is the RCS of the mth target; L represents the total loss of the system; k is the Boltzmann constant; T r is the temperature of the radar system; B is the frequency spectrum width of the radar signal; F m is the noise figure of the radar system; R m is the distance between the mth target and the radar. In addition, the transmit beam gain of the radar and its corresponding aperture also have the following relationship formula (7):

[0038]

[0039] In the formula, λ is the wavelength of the radar signal. Substituting it into formula (6) gives formula (8):

[0040]

[0041] For a phased array radar with a half-wavelength interval between adjacent elements, When n m >> 1, Substituting it into formula (8) gives formula (9):

[0042]

[0043] Substituting it into formula (5) and then into formula (1) gives the simplified optimization model formula (10):

[0044]

[0045] Then, it is still difficult to solve the optimization model, mainly because the model is a non-continuous, non-linear and non-convex optimization model. The last constraint is changed to a weaker constraint by convex relaxation, and the optimization model is transformed into equation (3):

[0046]

[0047] The continuous optimization model is solved by Lagrange multiplier method, and equation (4) is obtained: The Lagrange function of the optimization problem is shown in equation (11):

[0048]

[0049] In equation (11), λ m , μ, ν m and η m are Lagrange multipliers.

[0050] Since the distance R m of the target from the radar cannot be equal to 0, the power and aperture allocated to each target cannot be 0. According to the KKT condition, equation (12) is obtained:

[0051]

[0052] Therefore, the Lagrange function of the optimization problem can be simplified as equation (13):

[0053]

[0054] The sufficient condition of extreme point is equation (14) according to the KKT condition:

[0055]

[0056] In equation (14), L , p m , n m , λ m and μ respectively represent the partial derivatives of L g with respect to p m , n m , λ m and μ, that is, equation (15):

[0057]

[0058] Equation (4) is obtained by solving equation (15):

[0059]

[0060] In equation (4), p m , n m , λ m and μ are respectively the power, aperture, Lagrange multiplier of power and Lagrange multiplier of aperture.

[0061] Since formula (15) has only one extreme point, the extreme point is also the optimal value point, formula (4) is the optimal solution of the optimization problem formula (3), finally, the aperture numerical value is rounded and then power distribution is performed.

[0062] Although the specific embodiments of the present application are described and illustrated in detail above, it should be obvious to those skilled in the art that various equivalent changes and modifications can be made to the above-described embodiments without departing from the spirit and scope of the present application.

Claims

1. A method for improving the radio frequency stealth performance of a phased array radar system, comprising the following steps: First, constructing a fighter jet search system based on guidance information. M The scenario of multiple targets; secondly, with minimizing the total radiated power as the objective function, and with radar search performance, system hardware configuration and resource natural attributes as constraints, a joint optimization model of multi-area search aperture and power based on guidance information phased array radar is established; then, the optimization model is made continuous by using convex relaxation, and then the continuous optimization model is solved analytically by using the Lagrange multiplier method; finally, the aperture value is rounded and then the power is allocated; the establishment of the joint optimization model of multi-area search aperture and power based on guidance information phased array radar is as shown in equation (1): （1） where is the power vector whose m th element is p m , representing the power transmitted by the multi-function phased array radar to search the m th target; is the radar aperture vector whose m th element is A m , representing the radar aperture allocated by the multi-function phased array radar to search the m th target; represents minimizing the objective function by optimizing the variables P and A; p m represents the detection probability of the radar searching the m th target; represents the given radar detection probability threshold for the m th target; represents any arbitrary element; n m is the number of array elements corresponding to the aperture area of A m ; and N total is the total number of array elements of the phased array radar; p m ≥ 0 represents that the power is non-negative, M represents that the fighter jointly searches M targets; represents that the number of array elements must be a natural number from 1 to N total .

2. The method of claim 1, wherein: The scene of constructing the fighter search based on the guidance information refers to: assuming that the early warning aircraft discovers some targets in a space in three-dimensional space, then sends the information of radar cross section, position and speed of each target to the fighter through data link, and the fighter searches the targets according to the guidance information of the early warning aircraft. M M M The scene of constructing the fighter search based on the guidance information refers to: assuming that the early warning aircraft discovers some targets in a space in three-dimensional space, then sends the information of radar cross section, position and speed of each target to the fighter through data link, and the fighter searches the targets according to the guidance information of the early warning aircraft.​​ 3. The method of claim 1, wherein: The continuous optimization model by convex relaxation refers to converting the discrete constraint of the array element into a continuous constraint, i.e. Replace the constraint with formula (2): n m ≥0 (2) Then the detection probability constraint is converted into the signal-to-noise ratio constraint, and the continuous optimization model is converted into equation (3): wherein represents the signal-to-noise ratio required by the radar to detect the m first target to a given radar detection probability; is the RCS of the m first target; L represents the total loss of the system; k is the Boltzmann constant; T e is the temperature of the radar system; B is the spectral width of the radar signal; F r is the noise figure of the radar system; R m is the distance between the m th target and the radar; is the wavelength of the radar signal.

4. The method of claim 3, wherein: The continuous optimization model is solved by using the Lagrange multiplier method, which is referred to as: In the formulae, , .

5. The method of claim 1, wherein: The aperture number is rounded and then power is allocated, by solving the optimization model, to obtain the aperture resource allocated by the phased array radar search for a target under the constraint conditions of satisfying radar search performance, system hardware configuration and resource natural attributes, and the lowest total radiant energy of the system m A m and the power of the transmitted p m .​

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