Inter-pulse waveform multi-parameter cognitive design anti-clutter method for airborne radar

Abstract

The application discloses a method for anti-clutter of airborne radar, which comprises the following steps: firstly, modeling the pulse-amplitude-phase time sequence hopping signal, establishing the airborne radar echo model, constructing the pulse-amplitude-phase agile waveform and the joint design of the anti-clutter optimization problem model of the receiving filter bank, and finally, quickly solving the pulse-amplitude-phase agile waveform and the receiving filter bank to realize the robust detection of multiple targets in the clutter background. The method can break through the technical bottleneck that the existing low PRF and medium-high PRF cannot simultaneously consider the range ambiguity and velocity ambiguity by modulating the pulse-amplitude-phase time sequence hopping signal, and based on the block coordinate descent and the efficient optimization method of quadratic transformation, the pulse-amplitude-phase agile waveform and the receiving filter bank are jointly designed to realize the robust detection of multiple targets in the clutter background. Compared with the existing pulse-amplitude-phase agile waveform technology, the method can realize the suppression of the range-velocity clutter and has the multiple target detection capability.

Description

Technical Field

[0001] This invention belongs to the field of signal processing technology, specifically relating to a method for anti-ambiguity clutter in airborne radar using multi-parameter cognitive design of inter-pulse waveforms. Background Technology

[0002] Pulse Doppler technology can suppress airborne radar clutter by utilizing the differences between airborne radar clutter and targets in space, time, and frequency. However, the pulse repetition frequency system of existing airborne radars has a technical bottleneck that makes it difficult to simultaneously address range ambiguity and velocity ambiguity between low and medium-high repetition frequencies. This results in weak targets being easily overwhelmed by ambiguous clutter, causing a sharp decline in the detection and early warning capabilities of airborne radar for distant targets.

[0003] With the development of arbitrary waveform generators and high-speed processing hardware, radar can utilize prior knowledge to adaptively adjust the transmitted waveform to improve radar detection performance in complex environments. Related research shows that airborne radar clutter spectrum and inter-pulse waveform parameters have a strong coupling relationship. By modulating the inter-pulse waveform parameters, the shape of airborne radar clutter spectrum can be reshaped, thereby suppressing fuzzy clutter. Existing technologies typically design parameters such as the initial phase and amplitude of the inter-pulse waveform to reduce the energy of range-fuzzy clutter folded into the target area and improve the signal-to-clutter ratio of the target. The literature "Knowledge-aided (potentiallycognitive) transmit signal and receive filter design in signal-dependent clutter, IEEE Transactions on Aerospace and Electronic Systems, 2013, 49(1): 93-117" improves the single-target detection capability under range-fuzzy clutter by jointly designing an inter-pulse amplitude-phase agile waveform and a receiving filter. However, relying solely on the amplitude and phase agility of the inter-pulse waveform is insufficient to suppress velocity-fuzzy clutter and is not suitable for multi-target detection scenarios. Furthermore, this method uses existing solvers such as the interior-point method to solve semidefinite programming problems, resulting in high computational complexity and limiting its practical application. The paper "Hidden convexity in robust waveform and receive filterbank optimization under range unambiguous clutter, IEEE Signal Processing Letters, 2020, 27(1): 885-889" developed a faster method for designing amplitude and phase parameters of inter-pulse waveforms, but it did not consider fuzzy clutter and also suffered from the problem of difficulty in suppressing velocity fuzzy clutter. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention proposes a multi-parameter cognitive design method for inter-pulse waveforms to combat airborne radar ambiguity clutter. Addressing the difficulty of simultaneously suppressing range and velocity ambiguity clutter in existing technologies, this method overcomes the technical bottleneck of simultaneously addressing range and velocity ambiguity in low and medium-high repetition frequencies by optimizing the configuration of parameters such as inter-pulse amplitude, phase, and timing of the waveform, as well as the receiving filter bank. This reduces the energy of ambiguity clutter folding to the target, providing performance assurance for robust multi-target detection in range and velocity ambiguity clutter environments.

[0005] The technical solution of this invention is: a method for anti-ambiguity clutter in airborne radar using multi-parameter cognitive design of inter-pulse waveforms, the specific steps of which are as follows:

[0006] S1, Modeling of inter-pulse amplitude-phase-timing jump signals;

[0007] S2, Airborne Radar Echo Modeling;

[0008] S3. Modeling of the anti-ambiguity clutter optimization problem in the joint design of pulse-to-pulse amplitude-phase agile waveforms and receiver filter banks;

[0009] S4, rapid solution of inter-pulse amplitude-phase agile waveform and receiving filter bank.

[0010] Furthermore, step S1 is specifically as follows:

[0011] Within a coherent processing time, the airborne radar transmission is set to be... An inter-pulse amplitude-phase-timing jump signal composed of pulses:

[0012] (1)

[0013] in, Indicates time, , They represent the first The amplitude-phase modulation codeword and transmission time of each pulse This indicates a pulse signal.

[0014] Furthermore, step S2 is specifically as follows:

[0015] S21. Modeling slow-time echoes from multiple targets;

[0016] Set with A point target flying at a constant speed, and the first... The amplitude and Doppler frequency of each target are respectively and Then the target slow time echo Written as:

[0017] (2)

[0018] in, This represents the amplitude-phase agile waveform. Indicates the first The slow-time steering vector of each target. This represents the Hadama product operator. This represents the transpose operator, the first... The power of a target can be expressed as , This represents the expectation operator.

[0019] S22. Modeling and statistical characteristic analysis of slow-time echoes from airborne radar clutter.

[0020] Clutter slow-time echo modeling at the target's distance loop for:

[0021] (3)

[0022] in, Indicates the number of clutter blurring events. Indicates the number of discrete azimuth sectors. Represents the displacement matrix. and They represent the first The second distance ambiguity The vector composed of the scattering coefficients and Doppler frequencies of each azimuth clutter element can be expressed as:

[0023] (4)

[0024] in, and Indicates delay The corresponding distance ring Scattering coefficients and Doppler frequencies of each azimuth clutter element. Indicates the time delay of the target.

[0025] set up They are uncorrelated random variables, and have as well as , It is a random variable that follows a uniform distribution, that is... , and These represent the clutter mean Doppler frequency and the Doppler frequency uncertainty component, respectively.

[0026] in, Indicates delay The corresponding distance ring Power of each azimuth clutter unit The mean is variance is The uniform distribution.

[0027] but It is a random vector with zero mean and variance:

[0028] (5)

[0029] in, , Indicates that the diagonal element is a diagonal square matrix, This represents the conjugate transpose operator.

[0030] S23, Airborne Radar Slow-Time Echo Modeling;

[0031] The airborne radar echo model is written as:

[0032] (6)

[0033] in, This indicates that the mean is zero and the covariance is... An additive complex Gaussian white noise random vector.

[0034] Furthermore, step S3 is specifically as follows:

[0035] S31, Average Signal-to-Noise Ratio (SNR) Criterion Design;

[0036] Definition of the first The target in the filter The signal-to-noise ratio at the output is:

[0037] (7)

[0038] in, This indicates that other targets have passed through the filter. The generated interference energy is expressed as the average signal-to-clutter-to-noise ratio (SNR) of multiple targets as:

[0039] (8)

[0040] in, Indicates the weighted value. ,and , .

[0041] S32, Optimization problem modeling;

[0042] Considering energy constraints and similarity constraints .

[0043] in, A real value representing the degree of similarity of a control waveform. This represents a reference signal with a constant envelope. Let L2 denote the vector norm. Based on the optimization criterion (8) and the actual constraints, the optimization model for the joint transmit and receive design is as follows:

[0044] (9)

[0045] Furthermore, step S4 is specifically as follows:

[0046] S41, Question Equivalent expression;

[0047] Based on scale invariance, the problem The equivalent representation is:

[0048] (10)

[0049] in, , This indicates the real part operator.

[0050] S42, Question Establishment of the algorithm framework;

[0051] The block coordinate descent method continuously maximizes the objective function by iteratively updating the waveform and filter alternately. Finally, the problem was obtained. An enhanced solution is as follows:

[0052] In the In the next iteration, a pulse-to-pulse amplitude-phase agile waveform is given. By maximizing Obtain the The optimal filter bank at the next iteration .exist After the update, maximize Get the first The waveform of the amplitude-phase agile change in the clock interval during the next iteration. A satisfactory solution. In the... In this iteration, the following two optimization problems are solved:

[0053] (11)

[0054] (12)

[0055] S43, Question Solve this problem;

[0056] based on In the objective function of the waveguide group Based on the separability of the filter bank, the closed-form solution of the filter bank can be obtained using the generalized Rayleigh entropy theorem.

[0057] S44, Question Solve this problem;

[0058] Based on the quadratic transformation paradigm, the problem The problem is transformed into an iterative solution of a quadratic constrained quadratic programming convex optimization problem, and the alternating iterative multiplier method is used to quickly find the solution. A satisfactory solution.

[0059] The beneficial effects of this invention are as follows: First, the method of this invention establishes an airborne radar echo model by modeling the inter-pulse amplitude-phase-time jump signal. Then, it constructs a joint design optimization model for anti-ambiguity clutter using the inter-pulse amplitude-phase agile waveform and the receiving filter bank. Finally, it rapidly solves for the inter-pulse amplitude-phase agile waveform and the receiving filter bank, achieving robust multi-target detection under ambiguous clutter backgrounds. This invention overcomes the technical bottleneck of existing methods that struggle to simultaneously address range and velocity ambiguity between low and medium-high repetition frequencies by modulating parameters such as amplitude, phase, and timing of the inter-pulse waveform. Based on efficient optimization methods such as block coordinate descent and quadratic transformation, it jointly designs the inter-pulse amplitude-phase agile waveform and the receiving filter bank, achieving robust multi-target detection under ambiguous clutter backgrounds. Compared to existing inter-pulse amplitude-phase agile waveform technology, it can suppress range and velocity ambiguity clutter while also possessing multi-target detection capabilities. Attached Figure Description

[0060] Figure 1 This is a flowchart illustrating a method for anti-airborne radar ambiguity clutter in inter-pulse waveform multi-parameter cognitive design according to the present invention.

[0061] Figure 2 This is a flowchart of the solution algorithm proposed in the embodiments of the present invention.

[0062] Figure 3 This is an iterative curve of the average signal-to-noise ratio as a function of the number of iterations and time in an embodiment of the present invention.

[0063] Figure 4 This is a comparison diagram of anti-ambiguity clutter between the embodiment of the present invention and the existing inter-pulse amplitude-phase agile waveform. Detailed Implementation

[0064] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0065] like Figure 1 The flowchart shown below illustrates a method for anti-ambiguity clutter design using multi-parameter inter-pulse waveforms according to the present invention. The specific steps are as follows:

[0066] S1, Modeling of inter-pulse amplitude-phase-timing jump signals;

[0067] S2, Airborne Radar Echo Modeling;

[0068] S3. Modeling of the anti-ambiguity clutter optimization problem in the joint design of pulse-to-pulse amplitude-phase agile waveforms and receiver filter banks;

[0069] S4, rapid solution of inter-pulse amplitude-phase agile waveform and receiving filter bank.

[0070] In this embodiment, step S1 is specifically as follows:

[0071] Within a coherent processing time, the airborne radar transmission is set to be... An inter-pulse amplitude-phase-timing jump signal composed of pulses:

[0072] (13)

[0073] in, Indicates time, , They represent the first The amplitude-phase modulation codeword and transmission time of each pulse This represents a pulse signal. To control the range of pulse emission timing without loss of generality, let... .

[0074] (14)

[0075] in, Indicates the coherent processing time. This represents the minimum repetition interval of the pulse, and has , Indicates the pulse width.

[0076] In this embodiment, step S2 is specifically as follows:

[0077] S21. Modeling slow-time echoes from multiple targets;

[0078] Set with A point target flying at a constant speed, and the first... The amplitude and Doppler frequency of each target are respectively and Then the target slow time echo Written as:

[0079] (15)

[0080] in, This represents the amplitude-phase agile waveform. Indicates the first The slow-time steering vector of each target. This represents the Hadama product operator. This represents the transpose operator, the first... The power of a target can be expressed as , This represents the expectation operator.

[0081] S22. Modeling and statistical characteristic analysis of slow-time echoes from airborne radar clutter.

[0082] Clutter slow-time echo modeling at the target's distance loop for:

[0083] (16)

[0084] in, Indicates the number of clutter blurring events. Indicates the number of discrete azimuth sectors. Represents the displacement matrix. and They represent the first The second distance ambiguity The vector composed of the scattering coefficients and Doppler frequencies of each azimuth clutter element can be expressed as:

[0085] (17)

[0086] in, and Indicates delay The corresponding distance ring (the distance ring to which the delay is mapped) Scattering coefficients and Doppler frequencies of each azimuth clutter element. Indicates the time delay of the target.

[0087] set up They are uncorrelated random variables, and have as well as , It is a random variable that follows a uniform distribution, that is... , and These represent the clutter mean Doppler frequency and the Doppler frequency uncertainty component, respectively.

[0088] in, Indicates delay The corresponding distance ring (the distance ring to which the delay is mapped) Power of each azimuth clutter unit The mean is variance is The uniform distribution.

[0089] but It is a random vector with zero mean and variance:

[0090] (18)

[0091] in, Indicates that the diagonal element is a diagonal square matrix, This represents the conjugate transpose operator. , its first Each element is defined as:

[0092] (19)

[0093] S23, Airborne Radar Slow-Time Echo Modeling;

[0094] The airborne radar echo model is written as:

[0095] (20)

[0096] in, This indicates that the mean is zero and the covariance is... An additive complex Gaussian white noise random vector.

[0097] In this embodiment, step S3 is specifically as follows:

[0098] S31, Average Signal-to-Noise Ratio (SNR) Criterion Design;

[0099] Passing through the filter in sequence After processing, the first The target in the filter Output It can be represented as:

[0100] (twenty one)

[0101] in, This indicates that other targets have passed through the filter. The generated interference energy is expressed as the average signal-to-clutter-to-noise ratio (SNR) of multiple targets as:

[0102] (twenty two)

[0103] in, Indicates the weighted value. ,and , .

[0104] S32, Optimization problem modeling;

[0105] Considering energy constraints and similarity constraints .

[0106] in, A real value representing the degree of similarity of a control waveform. This represents a reference signal with a constant envelope. Let L2 denote the vector norm. Based on the optimization criterion (22) and actual constraints, the optimization model for the joint transmit and receive design is as follows:

[0107] (twenty three)

[0108] like Figure 2 As shown, in this embodiment, step S4 is specifically as follows:

[0109] S41, Question Equivalent expression;

[0110] Similarity constraints can be equivalently represented as Based on scale invariance, the energy constraint can be relaxed to Then the problem The equivalent representation is:

[0111] (twenty four)

[0112] in, , This indicates the real part operator.

[0113] S42, Question Establishment of the algorithm framework;

[0114] The block coordinate descent method continuously maximizes the objective function by iteratively updating the waveform and filter alternately. Finally, the problem was obtained. An enhanced solution is as follows:

[0115] In the In the next iteration, given an inter-pulse amplitude-phase agile waveform... By maximizing Obtain the The optimal filter bank at the next iteration .exist After the update, maximize Get the first The waveform of the amplitude-phase agile change in the clock interval during the next iteration. A satisfactory solution. In the... In this iteration, the following two optimization problems are solved:

[0116] (25)

[0117] (26)

[0118] S43, Question Solve this problem;

[0119] Considering The objective function with respect to the waveguide group The separability of the filter bank can be leveraged by solving the following decoupling optimization problem to obtain an enhanced solution:

[0120] (27)

[0121] and:

[0122] (28)

[0123] in, Represents the identity matrix.

[0124] According to the generalized Rayleigh entropy theorem, the problem... The optimal solution is a matrix The normalized eigenvector corresponding to the largest eigenvalue.

[0125] S44, Question Solve this problem;

[0126] Introducing auxiliary variables ,question This can be transformed into solving the following quadratic programming problem:

[0127] (29)

[0128] in, This indicates the conjugate operator. This indicates the real part operator. This represents the modulo operator. yes The There are elements, and:

[0129] (30)

[0130] Through alternating iterative optimization Achieve The solution, the first In the next iteration The optimal solution can be written as:

[0131] (31)

[0132] Finally, the alternating multiplier method is used to quickly find a value that satisfies the Karush-Kuhn-Tucker conditions. .

[0133] In this embodiment, the following simulation verification and analysis are also provided:

[0134] First, set the simulation parameters: the airborne radar altitude and speed are set to 8 km and 80 m / s respectively, the carrier frequency is 10 GHz (X-band), and the number of transmitted pulses is set to... Coherent processing time The minimum pulse repetition interval is set to The average pulse repetition interval is The corresponding maximum unambiguous Doppler frequency is The noise power at the radar receiver end is set to 0 dB.

[0135] The airborne radar detection scenario is set to include three point targets with Doppler frequencies of 8.5 kHz, 9 kHz, and 9.5 kHz, respectively, and the power of each target is set to 10 dB.

[0136] Based on the flight altitude and speed of the airborne radar, the Doppler frequency range of the airborne radar clutter is calculated as follows: At pulse repetition intervals of There is velocity ambiguity; set the maximum distance ambiguity count for clutter. Each distance ring is divided according to the azimuth angle. Each clutter unit, and let , Doppler frequency uncertainty component .

[0137] like Figure 3 As shown, Figure 3 (a) Figure 3 (b) The curves showing the change of the average signal-to-noise ratio (SNR) obtained by the method of the present invention with the number of iterations and time are shown respectively. The fast solution method proposed in this invention is defined as BCD-QT-ADMM. For comparison, the method in step S44, which uses the CVX toolbox for direct solution, is defined as... The method used is BCD-QT-CVX, with the same algorithm exit conditions. As the number of iterations increases, the average signal-to-noise ratio obtained by the method of this invention continuously improves, eventually monotonically converging to a stable value, which is the same as the value obtained using the CVX solver. Meanwhile, The larger the value, the higher the signal-to-noise ratio (SNR) at final convergence. Furthermore, the convergence speed of the proposed algorithm BCD-QT-ADMM is significantly better than existing solvers.

[0138] like Figure 4 As shown, the suppression effects of range and velocity ambiguity clutter on airborne radar are compared. The same similarity constraints are considered. , Figure 4The curves showing the signal-to-noise ratio (SNR) as a function of iterations obtained by existing pulse-to-pulse amplitude-phase agile waveform techniques and the method of this invention are presented. Clearly, the method of this invention can effectively suppress range ambiguity and velocity ambiguity clutter, achieving an SNR improvement of nearly 10 dB compared to existing pulse-to-pulse amplitude-phase agile waveform techniques.

[0139] In summary, the method of this invention first establishes an airborne radar echo model under pulse-to-pulse waveform amplitude, phase, and timing parameter agility, analyzes the clutter statistical characteristics under such parameter agility, and overcomes the technical bottleneck of existing methods that struggle to simultaneously address range and velocity ambiguity between low and medium-high repetition frequencies by modulating parameters such as pulse-to-pulse waveform amplitude, phase, and timing. Furthermore, based on efficient optimization methods such as block coordinate descent and quadratic transformation, the method jointly designs pulse-to-pulse waveform parameters and receiving filter banks to achieve robust multi-target detection against ambiguous clutter backgrounds. Compared to existing pulse-to-pulse amplitude and phase agility waveform techniques, the method of this invention can suppress range and velocity ambiguity clutter while also possessing multi-target detection capabilities.

[0140] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A method for resisting airborne radar ambiguity clutter through multi-parameter cognitive design of inter-pulse waveforms, the specific steps of which are as follows: S1, Modeling of inter-pulse amplitude-phase-timing jump signals; The specific steps of S1 are as follows: Within one coherent processing time, the airborne radar transmission is set to be... An inter-pulse amplitude-phase-timing jump signal composed of pulses: （1）； in, Indicates time, , They represent the first The inter-pulse amplitude-phase agile waveform and transmission time of each pulse. Indicates a pulse signal; S2, Airborne Radar Echo Modeling; Step S2 is as follows: S21. Modeling slow-time echoes from multiple targets; Set with A point target flying at a constant speed, and the first... The amplitude and Doppler frequency of each target are respectively and Then the target slow time echo Written as: （2）； in, This represents the amplitude-phase agile waveform. Indicates the first The slow-time steering vector of each target. This represents the Hadama product operator. This represents the transpose operator, the first... The power of a target can be expressed as , Represents the expectation operator; S22. Modeling and statistical characteristic analysis of slow-time echoes from airborne radar clutter. Clutter slow-time echo modeling at the target's distance loop for: （3）； in, Indicates the number of clutter blurring events. Indicates the number of discrete azimuth sectors. Represents the displacement matrix. and They represent the first The second distance ambiguity The vector composed of the scattering coefficients and Doppler frequencies of each azimuth clutter element can be expressed as: （4）； in, and Indicates delay The corresponding distance ring Scattering coefficients and Doppler frequencies of each azimuth clutter element. Indicates the time delay of the target; Indicates the number of pulses. ; set up They are uncorrelated random variables, and have as well as , It is a random variable that follows a uniform distribution, that is... , and These represent the clutter mean Doppler frequency and the Doppler frequency uncertainty component, respectively. in, Indicates delay The corresponding distance ring Power of each azimuth clutter unit The mean is variance is Uniform distribution; but It is a random vector with zero mean and variance: （5）； in, , Indicates that the diagonal element is a diagonal square matrix, Represents the conjugate transpose operator; S23, Slow-time echo modeling of airborne radar; The airborne radar echo model is written as: （6）； in, This indicates that the mean is zero and the covariance is... An additive complex Gaussian white noise random vector; S3. Modeling of the anti-ambiguity clutter optimization problem in the joint design of pulse-to-pulse amplitude-phase agile waveforms and receiver filter banks; S4, rapid solution of inter-pulse amplitude-phase agile waveform and receiving filter bank.

2. The method for anti-airborne radar ambiguity clutter in multi-parameter cognitive design of inter-pulse waveforms according to claim 1, characterized in that, Step S3 is as follows: S31, Average Signal-to-Noise Ratio (SNR) Criterion Design; Definition of the first The target in the filter The signal-to-noise ratio at the output is: （7）； in, This indicates that other targets have passed through the filter. The generated interference energy is expressed as the average signal-to-clutter-to-noise ratio (SNR) of multiple targets as: （8）； in, Indicates the weighted value. ,and , ; S32, Optimization problem modeling; Considering energy constraints and similarity constraints ; in, A real value representing the degree of similarity of a control waveform. This represents a reference signal with a constant envelope. Let L2 be the vector norm; based on the optimization criterion (8) and the actual constraints, the optimization model for the joint design of transmit and receive is as follows: （9）。 3. The method for anti-airborne radar ambiguity clutter in multi-parameter cognitive design of inter-pulse waveforms according to claim 2, characterized in that, Step S4 is as follows: S41, Question Equivalent expression; Based on scale invariance, the problem The equivalent representation is: （10）； in, , This indicates the real part operator; S42, Question Establishment of the algorithm framework; The block coordinate descent method continuously maximizes the objective function by iteratively updating the waveform and filter alternately. Finally, the problem was obtained. An enhanced solution is as follows: In the In the next iteration, a pulse-to-pulse amplitude-phase agile waveform is given. By maximizing Obtain the The optimal filter bank at the next iteration ;exist After the update, maximize Get the first The waveform of the amplitude-phase agile change in the clock interval during the next iteration. A satisfactory solution; in the first In this iteration, the following two optimization problems are solved: （11）； （12）； S43, Question Solve this problem; based on In the objective function of the waveguide group Based on the separability of the filter bank, the closed-form solution of the filter bank can be obtained using the generalized Rayleigh entropy theorem. S44, Question Solve this problem; Based on the quadratic transformation paradigm, the problem The problem is transformed into an iterative solution of a quadratic constrained quadratic programming convex optimization problem, and the alternating iterative multiplier method is used to quickly find the solution. A satisfactory solution.

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