A method and system for generating a low observable waveform for an airborne radar facing uncertain target scattering characteristics

Abstract

The application discloses a kind of methods and systems for generating airborne radar low observable waveform facing uncertain target scattering characteristics, the method includes: based on spatial information interaction theory, the expected interaction information amount between target scattering signal and radar receiving signal of maneuvering target in state transition angle interval is constructed, from the angle of intercept receiver signal processing link, with the log-likelihood ratio expected value of intercepted signal and the interaction information amount between intercept receiver input and output signal, fusion construction intercept-identification joint performance evaluation index;Under the given transmitting power constraint, the frequency domain waveform multi-objective optimization model with the maximum radar expected interaction information amount and the minimum intercept-identification joint performance index as target is constructed, and is converted into convex optimization problem for solving;Based on random sequence step frequency modulation signal, the time domain waveform implementation mode satisfying the frequency domain optimization result is designed, and the performance of the designed waveform is verified;The application satisfies radar resolution performance.

Description

Technical Field

[0001] This invention relates to the field of radar waveform design technology, specifically to a method and system for generating low-observable waveforms for airborne radar that addresses the scattering characteristics of uncertain targets. Background Technology

[0002] The LPI (Low Interception Performance) technology path mainly includes low sidelobe antenna design, low radiated power control, and anti-interception waveform design. Since the diversity of radar waveforms directly affects the processing gain of intercept receivers, anti-interception waveform design has become one of the most important technical approaches for radar to achieve low intercept performance. Anti-interception waveforms designed using broadband modulation techniques include frequency / phase modulation signals, frequency hopping signals, phase shift / frequency shift keying signals, spurious noise modulation signals, and intra-pulse / inter-pulse modulation signals. These anti-interception waveforms disperse energy in the frequency domain, making them difficult to intercept and identify using conventional power spectrum analysis. However, such anti-interception waveform designs do not consider target characteristic matching detection gain and intercept receiver performance, failing to achieve optimal design for both radar detection and anti-interception performance. Summary of the Invention

[0003] Purpose of the invention: The purpose of this invention is to provide a method and system for generating low-observable waveforms for airborne radar based on the scattering characteristics of uncertain targets. The method is based on waveform frequency domain power optimization and time domain implementation based on the matching of uncertain target characteristics, which solves the problem that traditional anti-interception waveforms cannot achieve optimal radar detection performance and low interception performance.

[0004] Technical solution: The present invention provides a method for generating low-observable waveforms for airborne radar based on the scattering characteristics of uncertain targets, comprising the following steps:

[0005] (1) Based on the theory of spatial information interaction, the expected interactive information quantity between the target scattering signal and the radar received signal in the state transition angle interval of the maneuvering target is constructed as the radar detection performance evaluation index under the condition of uncertainty of target scattering characteristics.

[0006] (2) From the perspective of the intercept receiver signal processing link, the expected value of the log likelihood ratio of the intercepted signal and the amount of interactive information between the input and output signals of the intercept receiver are used as the interception capability evaluation index and the recognition capability evaluation index, respectively, and the interception-recognition joint performance evaluation index is constructed by fusion.

[0007] (3) Under the given transmit power constraint, construct a frequency domain waveform multi-objective optimization model with the goal of maximizing the radar expected interactive information and minimizing the interception-identification joint performance index, and transform the model into a convex optimization problem for solution;

[0008] (4) Based on the random sequence step frequency modulation signal, design a time-domain waveform implementation method that satisfies the frequency domain optimization result, and verify the detection performance, resolution performance, anti-interception performance and anti-identification performance of the designed waveform.

[0009] Further, the specific process of step (1) is as follows: model the discrete frequency domain response of the target as a random vector; under the given frequency domain response of the target, calculate the amount of interactive information between the radar received signal and the target scattered signal; by taking the expectation of this amount of interactive information, obtain the radar detection performance quantification index for waveform optimization.

[0010] Further, step (2) is as follows: use the log-likelihood ratio of the intercepted signal to test the expected value to quantify the interception performance; use the amount of interactive information between the input and output signals of the intercepted receiver to quantify the recognition performance; and weight and fuse the two to form a joint interception-recognition performance evaluation index.

[0011] Further, step (3) specifically involves: under the constraint of transmit power, establishing an optimization model with the goal of maximizing the radar interaction information expectation and minimizing the interception-identification joint index; by setting a radar detection performance threshold, transforming the multi-objective problem into a single-objective constrained optimization problem; further transforming the model into a convex quadratic programming problem and solving it using the effective set algorithm.

[0012] Further, step (4) specifically involves: using a random sequence step frequency modulation signal as the basis for realizing the time-domain waveform, adjusting the pulse width of each pulse to maintain the pulse amplitude consistency, thereby maintaining the waveform resolution performance; the generated signal is called a random step frequency signal with uneven pulse width, which is used for final waveform synthesis and performance verification.

[0013] The present invention discloses an airborne radar low-observable waveform generation system for uncertain target scattering characteristics, comprising: The detection performance evaluation index module is used to construct the expected interactive information between the target scattering signal and the radar received signal within the state transition angle range of the maneuvering target based on the spatial information interaction theory, and to serve as the radar's detection performance evaluation index under the condition of uncertainty in target scattering characteristics. Joint performance evaluation index module: From the perspective of the intercept receiver signal processing link, it uses the expected value of the log-likelihood ratio of the intercepted signal and the amount of interactive information between the input and output signals of the intercept receiver as interception capability evaluation index and recognition capability evaluation index respectively, and integrates them to construct a joint interception-recognition performance evaluation index. The solution module is used to construct a frequency domain waveform multi-objective optimization model under a given transmit power constraint, with the goal of maximizing the radar's expected interactive information content and minimizing the intercept-identification joint performance index, and to transform the model into a convex optimization problem for solution. Waveform Implementation Module: Used to design a time-domain waveform implementation method that satisfies the frequency domain optimization results based on a random sequence step frequency modulation signal, and to verify the detection performance, resolution performance, anti-interception performance and anti-identification performance of the designed waveform.

[0014] Furthermore, in the detection performance evaluation index module, the specific process is as follows: the discrete frequency domain response of the target is modeled as a random vector; given the target frequency domain response, the amount of interactive information between the radar received signal and the target scattered signal is calculated; by taking the expectation of this amount of interactive information, a quantitative index of radar detection performance for waveform optimization is obtained.

[0015] Furthermore, in the joint performance evaluation index module, the following are specific details: the interception performance is quantified by testing the expected value of the log-likelihood ratio of the intercepted signal; the recognition performance is quantified by the amount of interactive information between the input and output signals of the intercepted receiver; and the two are weighted and fused to form a joint interception-recognition performance evaluation index.

[0016] Furthermore, in the solution module, specifically: under the constraint of transmit power, an optimization model is established with the objectives of maximizing the expected radar interaction information and minimizing the joint interception-identification index; by setting a radar detection performance threshold, the multi-objective problem is transformed into a single-objective constrained optimization problem; the model is further transformed into a convex quadratic programming problem and solved using the effective set algorithm.

[0017] Furthermore, in the waveform implementation module, a random sequence step frequency modulation signal is used as the basis for time-domain waveform implementation. The pulse amplitude is kept consistent by adjusting the pulse width of each pulse, thereby maintaining the waveform resolution performance. The generated signal is called a random step frequency signal with uneven pulse width, which is used for final waveform synthesis and performance verification.

[0018] Beneficial Effects: Compared with existing technologies, this invention has the following significant advantages: Based on spatial information theory, this invention establishes optimal performance indices for radar detection under uncertain target characteristics and integrated interception and identification performance indices for interception receivers. On this basis, a frequency domain design optimization model for radar anti-interception waveforms is established to maximize radar detection performance and minimize interception receiver performance under a certain transmit power, and this optimization model is transformed into a convex problem for solution. Furthermore, to ensure that the optimized anti-interception waveform meets radar resolution requirements, a time-domain implementation method for the radar anti-interception waveform that satisfies the ambiguity function requirement is designed based on a random sequence stepped-frequency signal. The designed waveform, under the condition of optimal matching detection of uncertain target characteristics, satisfies the lower bound of the interception and identification performance of the interception receiver through frequency domain power allocation, and the time-domain implementation method satisfies radar resolution requirements. Attached Figure Description

[0019] Figure 1 This is a flowchart of the present invention;

[0020] Figure 2 The power spectral density diagram of the radar waveform under different radar detection performance index values ​​is shown in the present invention.

[0021] Figure 3 This is a time-domain diagram showing the optimized radar waveform of the present invention under different radar detection performance index values.

[0022] Figure 4 This is a diagram showing the received signal-to-noise ratio before radar matched filtering at different azimuth angles according to the present invention.

[0023] Figure 5 The normalized time delay diagram and normalized Doppler frequency shift diagram of the ambiguity function of the SPD-RS-SF signal and the RS-SF signal of this invention are shown below; wherein, Figure 5 (a) and Figure 5 In the diagram, (b) represents the normalized time delay diagram and normalized Doppler frequency shift of the ambiguity function of the SPD-RS-SF signal and the RS-SF signal, respectively;

[0024] Figure 6 The curve showing the change in the number of frequency channels that the intercept receiver can identify according to the present invention. Detailed Implementation

[0025] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0026] like Figure 1 As shown, this embodiment of the invention provides a method for generating low-observable waveforms for airborne radar based on the scattering characteristics of uncertain targets, comprising the following steps:

[0027] (1) Based on the spatial mutual information theory, the expected mutual information between the target scattered signal and the received signal within the range of the state transition angle of the maneuvering target is established as a radar performance optimization index for uncertain target characteristics;

[0028] Establish radar performance optimization indices based on uncertain target characteristics Specifically, assuming the target's discrete frequency response is... This frequency response can form a random vector. .

[0029] Response at a given target frequency At that time, the mutual information between the radar received signal and the scattered signal It can be represented as:

[0030] (1)

[0031] in, Indicates the energy decay coefficient. It is the frequency domain form of the radar transmitted signal. Indicates the frequency sampling interval. It is the one-sided power spectral density of radar receiver noise.

[0032] Mutual Information It can be considered as a response to the target frequency. Let the random variable be a random vector. probability distribution It is a known random variable. The expected value, i.e., the expected mutual information. It can be calculated as:

[0033] (2)

[0034] Combining equations (1) and (2), we expect mutual information. It can be specifically expressed as

[0035] (3)

[0036] Based on Taylor expansion, expected mutual information It can be approximated as:

[0037] (4)

[0038] in, , .

[0039] To further simplify the expected mutual information in equation (4), let

[0040] (5)

[0041] (6)

[0042] (7)

[0043] Then the expected mutual information can be simplified to

[0044] (8)

[0045] (2) From the perspective of the interception receiver's interception signal processing information flow, the expected value of the log-likelihood ratio test of the interception signal and the mutual information between the input and output signals of the interception receiver are respectively used as the interception performance and recognition performance optimization indicators. Based on this, an integrated interception and recognition performance optimization index is established.

[0046] To measure the average interception capability of an intercepting receiver for unknown signals, the interception likelihood ratio test statistic is used. The logarithmic expectation of the intercept receiver, used as an indicator of its interception performance, can be expressed in the form of relative entropy, i.e.

[0047] (9)

[0048] Among them, the test statistic of the intercept likelihood ratio test Can be defined as

[0049] (10)

[0050] in, To intercept the receiver's intercepted signal, and These represent the assumptions of the absence and presence of the radar transmitted signal in the intercepted signal, respectively. Here is the probability density function; for ease of notation, and Marked as and ; Indicates the use of probability density Find the expected value.

[0051] Intercept the receiver output signal With input signal Mutual information between As an identification performance indicator of the interception receiver. Therefore, the interception performance indicator in the combined equation (9) Performance optimization indicators of the interception and identification integration of the interception receiver It can be calculated by the sum of the two, specifically:

[0052] (11)

[0053] in, Indicates the use of joint probability density function Find the expected value. To capture the signal attenuation coefficient.

[0054] (3) A multi-target optimization design problem in the frequency domain of anti-interception waveform was established to maximize the radar expected mutual information and minimize the interception and identification performance under certain power constraints, and it was transformed into a convex optimization problem for solution;

[0055] Under the constraint of a fixed transmission power, the mutual information is expected by simultaneously maximizing the radar detection performance optimization index. And minimize the integrated interception and identification performance optimization index of the interception receiver A multi-objective optimization model for anti-interception waveform frequency domain is constructed. This optimization model can be expressed as:

[0056] (12)

[0057] in, , , , For signal power, Represents a standard unit vector, its first... One element is equal to 1, and the rest are 0.

[0058] The optimization model of equation (12) can be further expressed as the problem of minimizing the integrated interception and identification performance of the interception receiver under the condition of making certain concessions on radar detection performance, that is:

[0059] (13)

[0060] in, It meets the requirements of radar detection performance. Indicator values. For different scenarios, It can be set to various different values.

[0061] Assuming the radar transmitted signal is a small signal, the performance optimization index of the interception and identification integrated system of the interception receiver is as follows: It can be approximated as:

[0062] (14)

[0063] in,

[0064] (15)

[0065] It is the one-sided power spectral density of the intercepted receiver noise.

[0066] Therefore, the optimization model in equation (13) can be specifically expressed as:

[0067] (16)

[0068] The optimization problem in equation (16) is a convex quadratic programming problem, which can be solved by the effective set method.

[0069] (4) Considering the resolution performance of the designed waveform, a time-domain implementation method for anti-interception frequency domain optimized waveform is designed based on random sequence step frequency signal, and the detection performance, resolution performance, anti-interception performance and anti-identification performance of the designed waveform are verified.

[0070] Because the random sequence stepped-frequency (RS-SF) signal possesses a near-ideal thumbtack-shaped ambiguity function, using the RS-SF signal as the time-domain implementation method for the optimized anti-interception frequency domain waveform offers superior resolution performance. The time-domain form of the anti-interception frequency domain waveform can be expressed as:

[0071] (17)

[0072] in,

[0073] (18)

[0074] (19)

[0075] (20)

[0076] Indicates the pulse repetition period. Indicates the pulse width.

[0077] Because the amplitude of each pulse in equation (17) The amplitudes of these pulses are not equal, which would disrupt the pin-shaped ambiguity function of traditional RS-SF signals. Therefore, the amplitudes of each pulse can be made equal by changing the pulse width of each pulse. It can be represented as:

[0078] (twenty one)

[0079] This modified RS-SF signal can be called a staggered pulse width random sequence stepped frequency (SPD-RS-SF) signal, specifically expressed as:

[0080] (twenty two)

[0081] in, It is a gate function. .

[0082] Based on the above steps, the frequency domain and time domain forms of the designed anti-interception waveform are simulated, and the detection performance, resolution performance, anti-interception performance and anti-identification performance of the anti-interception waveform are verified.

[0083] The present invention proposes an airborne radar anti-interception waveform design method under the condition of target characteristic uncertainty. The detection performance, resolution performance, anti-interception performance and anti-identification performance of the radar waveform are analyzed and verified through experiments. The simulation parameter settings are shown in Table 1.

[0084] Table 1 Simulation Parameter Settings

[0085] ;

[0086] The specific implementation steps are as follows:

[0087] Step 1: Design the anti-interception radar optimized waveform by combining the radar's optimal detection performance optimization index, expected mutual information, and the interception receiver's integrated interception and identification performance optimization index. Based on the optimization model in equation (16), set the threshold required for the radar's detection performance. and observe different Optimize the power spectral density of the radar waveform under the given value, such as Figure 2 As shown.

[0088] Step 2: Implement the anti-interception frequency domain waveform optimized in Step 1 using the SPD-RS-SF signal in the time domain. Simulations were performed to compare the real parts of the time domain forms of the optimized anti-interception signal based on the RS-SF signal and the SPD-RS-SF signal, as shown below. Figure 3 As shown.

[0089] Step 3: To verify the effectiveness of the optimized anti-interception radar waveforms in Steps 1 and 2, as well as the correctness of the proposed optimal radar detection performance index and the integrated interception and identification performance index of the interception receiver, simulations were used to verify the radar's detection and resolution performance.

[0090] Figure 2 This reflects the threshold required for different radar detection performances. The optimized results of the radar waveform power spectral density under the given value. When near At this point, the optimization problem approximately degenerates into waveform design without considering radar detection performance, and the optimized radar waveform is: Figure 2 The blue curve in the image. When... near At this point, the optimization problem approximately degenerates into waveform design without considering the performance of the intercepting receiver; that is, the optimized radar waveform should be weighted relative to the target. The matching is represented by the yellow curve. For the intermediate threshold... The optimized waveform should be in and Between waveforms, such as Figure 2 As shown by the red curve in the figure, this waveform not only possesses the required radar detection performance, but also has superior anti-interception and anti-identification performance.

[0091] Figure 3 Reflects the parameter as Optimized radar waveform time domain diagram. Figure 3 The real parts of the optimized wave time-domain signals based on RS-SF and SPD-RS-SF signals are given respectively. The amplitudes of the pulses based on RS-SF signals are not equal, while the amplitudes of the pulses based on SPD-RS-SF signals are constant across all pulses. This makes them superior to traditional RS-SF signals in terms of velocity and range resolution.

[0092] Figure 4 The received signal-to-noise ratio (SNR) before matched filtering at different azimuth angles can be considered a performance indicator of radar detection capabilities. For example... Figure 4 As shown, at each azimuth angle, with the increase of radar detection performance constraints, i.e. As the value decreases, the received signal-to-noise ratio gradually increases, thus improving the radar's detection performance, which aligns with the proposed radar waveform design principles. Furthermore, for any optimized waveform, the higher the probability of the azimuth angle, the better the received signal-to-noise ratio, i.e., the better the detection performance, which also aligns with the proposed radar waveform design principles.

[0093] Figure 5 (a) and Figure 5 Figure (b) shows the normalized time delay and normalized Doppler frequency shift plots of the ambiguity functions for the SPD-RS-SF and RS-SF signals, respectively. These two figures show that the peak values ​​of the range and velocity ambiguity functions based on the SPD-RS-SF signal (represented by the red line) are smaller than those based on the RS-SF signal (represented by the blue line). Therefore, the waveform optimized based on the SPD-RS-SF signal exhibits superior range and velocity resolution performance compared to the waveform optimized based on the RS-SF signal. Furthermore, the SPD-RS-SF-based waveform possesses random frequencies and interleaved pulse durations, which can further improve the anti-interception and anti-identification performance of the optimized radar waveform.

[0094] like Figure 6 As shown, when the intercepted signal-to-noise ratio threshold is less than At that time, with An increase in the value, i.e., a decrease in radar detection performance constraints, means that the number of identifiable channels gradually decreases until it reaches zero, which implies a deterioration in recognition performance. When the interception signal-to-noise ratio threshold is greater than or equal to... When the parameter is and The optimized radar waveform has zero identifiable channels; however, for radars with strong performance constraints... Even in such cases, the number of identifiable targets remains large. Therefore, by reducing the constraints on radar detection performance, the optimized radar waveform can achieve anti-identification performance.

[0095] In summary, the airborne radar anti-interception waveform design method under uncertain target characteristics solves the problem that traditional anti-interception waveforms cannot achieve optimal radar detection performance and low interception performance. Simulation analysis results show that this method realizes the frequency domain design and time domain implementation of anti-interception radar waveforms, effectively improving the radar detection and resolution performance for uncertain target characteristic matching, and effectively improving the anti-interception and anti-identification performance of the designed waveform while satisfying optimal target detection performance.

[0096] The physical meanings of all parameters are shown in Tables 2-4. Table 2 Physical Meaning of Parameters 1 ;

[0097] Table 3 Physical Meaning of Parameters 2 ; Table 4 Physical Meaning of Parameters 3 .

Claims

1. A method for generating low-observable waveforms for airborne radar based on the scattering characteristics of uncertain targets, characterized in that, Includes the following steps: (1) Based on the spatial information interaction theory, the expected interaction information between the target scattering signal and the radar received signal in the state transition angle interval of the maneuvering target is constructed as the radar detection performance evaluation index under the condition of uncertainty of the target scattering characteristics; the specific process is as follows: the discrete frequency domain response of the target is modeled as a random vector; under the condition of the given target frequency domain response, the interaction information between the radar received signal and the target scattering signal is calculated; by taking the expectation of the interaction information, the radar detection performance quantification index for waveform optimization is obtained. (2) From the perspective of the intercept receiver signal processing link, the expected value of the log-likelihood ratio of the intercepted signal and the amount of interactive information between the input and output signals of the intercept receiver are used as the interception capability evaluation index and the recognition capability evaluation index, respectively, and the interception-recognition joint performance evaluation index is constructed by fusion; specifically as follows: the expected value of the log-likelihood ratio of the intercepted signal is used to quantify the interception performance; the amount of interactive information between the input and output signals of the intercept receiver is used to quantify the recognition performance; the two are weighted and fused to form the interception-recognition joint performance evaluation index; (3) Under the given transmit power constraint, construct a frequency domain waveform multi-objective optimization model with the goal of maximizing the radar expected interactive information and minimizing the interception-identification joint performance index, and transform the model into a convex optimization problem for solution; specifically: under the transmit power constraint, establish an optimization model with the goal of maximizing the radar interactive information expectation and minimizing the interception-identification joint performance index; by setting the radar detection performance threshold, transform the multi-objective problem into a single-objective constraint optimization problem; further transform the model into a convex quadratic programming problem, and solve it using the effective set algorithm; (4) Based on the random sequence step frequency modulation signal, design a time-domain waveform implementation method that satisfies the frequency domain optimization result, and verify the detection performance, resolution performance, anti-interception performance and anti-identification performance of the designed waveform; specifically: use the random sequence step frequency modulation signal as the basis for time-domain waveform implementation, and maintain the waveform resolution performance by adjusting the pulse width of each pulse to keep the pulse amplitude consistent; the generated signal is called the random step frequency signal with uneven pulse width, which is used for final waveform synthesis and performance verification.

2. A low-observable waveform generation system for airborne radar based on the scattering characteristics of uncertain targets, implemented using the method described in claim 1, characterized in that, include: The detection performance evaluation index module is used to construct the expected interactive information between the target scattering signal and the radar received signal within the state transition angle range of the maneuvering target based on the spatial information interaction theory, and to serve as the radar's detection performance evaluation index under the condition of uncertainty in target scattering characteristics. Joint performance evaluation index module: From the perspective of the intercept receiver signal processing link, it uses the expected value of the log-likelihood ratio of the intercepted signal and the amount of interactive information between the input and output signals of the intercept receiver as interception capability evaluation index and recognition capability evaluation index respectively, and integrates them to construct a joint interception-recognition performance evaluation index. The solution module is used to construct a frequency domain waveform multi-objective optimization model under a given transmit power constraint, with the goal of maximizing the radar's expected interactive information content and minimizing the intercept-identification joint performance index, and to transform the model into a convex optimization problem for solution. Waveform Implementation Module: Used to design a time-domain waveform implementation method that satisfies the frequency domain optimization results based on a random sequence step frequency modulation signal, and to verify the detection performance, resolution performance, anti-interception performance and anti-identification performance of the designed waveform.

3. The airborne radar low-observable waveform generation system for uncertain target scattering characteristics according to claim 2, characterized in that, The specific process in the detection performance evaluation index module is as follows: the discrete frequency domain response of the target is modeled as a random vector; given the target frequency domain response, the amount of interactive information between the radar received signal and the target scattered signal is calculated; by taking the expectation of this amount of interactive information, a quantitative index of radar detection performance for waveform optimization is obtained.

4. The airborne radar low-observable waveform generation system for uncertain target scattering characteristics according to claim 2, characterized in that, The joint performance evaluation index module specifically includes the following: quantifying the interception performance by testing the expected value using the log-likelihood ratio of the intercepted signal; quantifying the recognition performance by using the amount of interactive information between the input and output signals of the intercepted receiver; and weighting and fusing the two to form a joint interception-recognition performance evaluation index.

5. The airborne radar low-observable waveform generation system for uncertain target scattering characteristics according to claim 2, characterized in that, In the solution module, specifically: under the constraint of transmit power, an optimization model is established with the objectives of maximizing the expected radar interaction information and minimizing the joint interception-identification index; by setting a radar detection performance threshold, the multi-objective problem is transformed into a single-objective constrained optimization problem; further, the model is transformed into a convex quadratic programming problem and solved using the effective set algorithm.

6. The airborne radar low-observable waveform generation system for uncertain target scattering characteristics according to claim 2, characterized in that, In the waveform implementation module, a random sequence step frequency modulation signal is used as the basis for time-domain waveform implementation. The pulse width is adjusted to maintain the pulse amplitude consistency, thereby maintaining the waveform resolution performance. The generated signal is called a random step frequency signal with uneven pulse width, which is used for final waveform synthesis and performance verification.

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