A Method for Suppressing Sidelobes of Pulse Compression Response of Linear Frequency Modulation Signals

Abstract

The present invention discloses a method for suppressing sidelobes of the pulse compression response of a chirp signal. The chirp signal is pulse-compressed to obtain a one-dimensional point target pulse compression response. The frequency-domain window function of a third-order spatial apodization filter is used to perform frequency-domain weighting on the real part and the imaginary part of the one-dimensional point target pulse compression response respectively. The constraint space of the filter coefficients is determined. The grey wolf optimization algorithm is used to perform a point-by-point operation on the ideal filtering results of the real part and the imaginary part of the one-dimensional point target pulse compression response respectively to complete the optimization process, and the maximum and minimum values that the filtering data can obtain are searched point by point within the constraint space. According to the optimization results, the final filtering result of the signal is determined, and the complex signal filtering processing result is calculated based on the filtering results of the real part and the imaginary part of the one-dimensional point target pulse compression response. The present invention improves the order of the filter, increases the dimension of the solution space, improves the flexibility of the filter, and can effectively suppress sidelobes. The present invention uses the grey wolf optimization algorithm to perform an effective point search, reducing the computational amount of people in analyzing the boundary points of the constraint space.

Description

Technical Field

[0001] The present invention belongs to the technical field of radar signal processing, and relates to a method for suppressing sidelobes of the pulse compression response of a chirp signal, in particular to a method for suppressing sidelobes of the pulse compression response of a chirp signal based on third-order apodization filtering. Background Art

[0002] Synthetic Aperture Radar (SAR) has the characteristics of high imaging resolution and all-weather operation, and is widely used in application requirements such as surface imaging and ground target detection. The echo signal of synthetic aperture radar has a very large dynamic range, up to more than 50 dB. After pulse compression, the peak sidelobe ratio of the chirp signal is -13.2 dB, which will cause the sidelobes of strong reflection targets to cover the main lobes of adjacent weak reflection targets, resulting in missed detection of targets or misjudging the sidelobes of strong reflection targets as the main lobes of weak reflection targets, increasing the false alarm probability of target detection.

[0003] The apodization algorithm is a non-linear frequency domain weighting method, which can effectively suppress sidelobes without any prior knowledge. The idea of apodization filtering is that for different sampling points, appropriate filtering parameters are adaptively selected according to the adjacent data to perform non-linear filtering operations on the echo signal, and mapping to the spatial domain is three-point convolution. Through this method, the sidelobes of the target can be suppressed without loss of image resolution. However, this method is only applicable to the scenario where the sampling rate of the receiving system is an integer multiple of the Nyquist sampling rate, and is not applicable to the data sampled at a non-Nyquist sampling rate.

[0004] "Generalization of spatially variant apodization to noninteger Nyquist sampling rates" published by Brian Hendee Smith in IEEE Transactions on Image Processing (Volume: 9, Issue: 6, June 2000) proposed a Generalized Spatially Variant Apodization (GSVA) algorithm for non-integer Nyquist sampling rates. This method can better suppress sidelobes while maintaining resolution, but there will still be some residual sidelobes. Ni Chong et al. published "An Improved SVA Algorithm for SAR Sidelobe Suppression" in Science China: Technological Sciences, which proposed an Improved Spatially Variant Apodization (MSVA) algorithm. By expanding the dimension of the finite impulse response (FIR) filter, the three-point convolution of the traditional spatially variant filter is extended to a five-point convolution, increasing the flexibility of the filter, and can effectively suppress sidelobes, but it is still affected by phase deviation, resulting in a reduction in the main lobe energy. Xu Zheng et al. published "Application of Constrained Optimization Spatially Variant Algorithm in Sidelobe Suppression" in Systems Engineering and Electronics, which strictly constrained the monotonicity of the constrained filter and the selection of effective points, but the sidelobe suppression effect is still not ideal enough. Summary of the Invention

[0005] In view of the above-mentioned prior art, the technical problem to be solved by the present invention is to provide a method for suppressing sidelobes of the pulse compression response of a chirp signal based on third-order spatially variant filtering, increasing the dimension of the solution space, improving the flexibility of the filter, and effectively suppressing sidelobes.

[0006] To solve the above technical problem, a method for suppressing sidelobes of the pulse compression response of a chirp signal according to the present invention includes the following steps:

[0007] Step 1: Pulse compress the chirp transmit signal to obtain a one-dimensional point target pulse compression response g(m), g(m) = g Re (m) + ig Im (m), where g Re (m) is the real part of g(m), and g Im (m) is the imaginary part of g(m);

[0008] Step 2: Use the frequency domain window function of the third-order spatially variant filter to perform frequency domain weighting on the real part g Re (m) and the imaginary part g Im (m) of the one-dimensional point target pulse compression response respectively, and obtain the real part ideal filtering result g Re ′(m) and the imaginary part ideal filtering result g Im ′(m) of the one-dimensional point target pulse compression response;

[0009] Step 3: Determine the filter coefficients a and w i constraint conditions, and form a constraint space from the constraint conditions;

[0010] Step 4: Use the Grey Wolf Optimization Algorithm to search for the maximum and minimum values that the filtering data can achieve point by point within the constraint space for the ideal filtering result of the real part of the one-dimensional point target pulse compression response. Obtain the filtering result of the real part of the one-dimensional point target pulse compression response according to the optimization result, and assign it to g Re ′(m);

[0011] Step 5: Repeat the operation of Step 4 for the ideal filtering result of the imaginary part of the one-dimensional point target pulse compression response. Obtain the filtering result of the imaginary part of the one-dimensional point target pulse compression response according to the optimization result, and assign it to g Im ′(m);

[0012] Step 6: Calculate the complex signal filtering processing result g′(m) according to the filtering results of the real part and the imaginary part of the one-dimensional point target pulse compression response obtained in Step 5

[0013] Furthermore, obtaining the one-dimensional point target pulse compression response by performing pulse compression on the chirp transmit signal includes:

[0014] Step 1.1: Sample the chirp transmit signal s(t) and the one-dimensional point target echo signal h(t) at a non-integer multiple of the Nyquist sampling rate f s to obtain the discrete signals s(m) and h(m);

[0015] The chirp transmit signal s(t) satisfies:

[0016]

[0017] where T is the pulse duration of s(t), K = f0 / T is the frequency modulation slope, and f0 is the bandwidth of s(t), The one-dimensional point target echo h(t) = s(t - τ), where τ is the time delay;

[0018] Step 1.2: Obtain the pulse compression response g(m) of the one-dimensional point target:

[0019] g(m) = ifft(fft(h(m)) × fft(conj(fliplr(s(m)))))

[0020] where ifft(·) represents performing the inverse fast Fourier transform on the discrete signal, fft(·) represents performing the fast Fourier transform on the discrete signal, fliplr(·) represents performing the anti-folding operation on the discrete signal, and conj(·) represents taking the conjugate of the signal;

[0021] Separate g(m) into its real and imaginary parts:

[0022] g(m) = g Re (m) + ig Im (m)

[0023] where g Re (m) is the real part of g(m), and g Im (m) is the imaginary part of g(m).

[0024] Furthermore, the frequency-domain window function of the third-order spatial apodization filter is specifically:

[0025]

[0026] where f0 is the bandwidth of the chirp transmit signal, and a and w i are filter coefficients.

[0027] Furthermore, the ideal filtering results g Re ′(m) of the real part and g Im ′(m) of the imaginary part of g(m) in step 2 are specifically:

[0028]

[0029]

[0030] where I(m) is the impulse response of W(f) and satisfies:

[0031]

[0032] where f s is a non-integer multiple of the Nyquist sampling rate, denotes rounding down the parameter.

[0033] Furthermore, the constraint space for determining the filter coefficients in step 3 is specifically:

[0034] Set the constraint terms for the filter coefficients a and w i as:

[0035]

[0036] where f s is a non-integer multiple of the Nyquist sampling rate, denotes rounding down the parameter.

[0037] Further, step 4 is specifically as follows:

[0038] Step 4.1: In the Grey Wolf Optimization Algorithm, w i is a decision variable, i = 1, 2, 3. Set the population size to num, and randomly generate num individuals within the constraint space of step 3 to complete the population initialization operation.

[0039] Step 4.2: Calculate the fitness values of all individuals in the population using the fitness function Fitness of the Grey Wolf Optimization Algorithm;

[0040] Step 4.3: Find the three individuals with the highest fitness values in the population, denoted as α, β, and γ respectively, and their fitness magnitudes are sorted as α > β > γ;

[0041] Step 4.4: Update the positions of all individuals in the population, and complete one update of the population positions according to the positions of individuals α, β, and γ. Specifically:

[0042]

[0043]

[0044]

[0045]

[0046] Among them, and are random variables, and their value ranges are [0, 1].[[]]END and are coefficient vectors, is the current individual position vector, L is the current iteration number, and are the position vectors of α, β, and γ respectively, is the updated individual position vector, and λ is the convergence factor, satisfying:

[0047] λ = 2 - 2(e L / iteration - 1) / (e - 1)

[0048] where iteration is the iteration number of the Grey Wolf Optimization Algorithm;

[0049] Step 4.5: According to the constraint conditions of step 3, determine whether there are individuals whose positions exceed the constraint space. If the position vector of individual q exceeds the constraint space after position update, then let individual q move along the vector at the step size towards the individual α with the optimal fitness until it meets the constraint conditions. M is a set positive integer. Update the fitness values of the population to complete one iteration process;​

[0050] Step 4.6: Repeat Steps 4.2 to 4.5 to search for the minimum value of g Re ′(m), denoted as g Re ′(m) min , complete iteration iterations. After each iteration, if there are two individuals with opposite fitness value signs or there is at least one individual with a fitness value of 0, then terminate the iterative optimization process at this point and set g Re ′(m) = g Re ′(m) min = 0; if the minimum value obtained after iteration iterations of optimization is not zero, then execute Step 4.7;

[0051] Step 4.7: Use Step 4.1 to generate a new population, repeat Steps 4.2 to 4.5 to search for the maximum value of g Re ′(m), denoted as g Re ′(m) max , complete iteration iterations. After each iteration, if there are two individuals with opposite fitness value signs or there is at least one individual with a fitness value of 0, then terminate the iterative optimization process at this point and set g Re ′(m) = g Re ′(m) max = 0. If the maximum value obtained after iteration iterations of optimization is not zero, then execute Step 4.8;

[0052] Step 4.8: If the signs of the obtained maximum and minimum values are opposite, then set g Re ′(m) = 0. If the signs are the same, then set g Re ′(m) = min(|g Re ′(m) min |, |g Re ′(m) max |), where min(a, b) is the function to calculate the minimum value of a and b.

[0053] Furthermore, the fitness function Fitness of the Grey Wolf Optimization Algorithm is specifically:

[0054]

[0055] where L is the current iteration number and q is the current individual number.

[0056] Advantages of the present invention: Aiming at the problems of the existing apodization filtering method with too low order of the frequency-domain window function and poor sidelobe suppression effect, the present invention proposes a new sidelobe suppression method based on a third-order apodization filter. This method expands the traditional filter from 5 points to 7 points, increases the dimension of the solution space, improves the flexibility of the filter, and can effectively suppress sidelobes. Aiming at the problem of difficult selection of effective points in three-dimensional and higher-dimensional constrained spaces, the present invention designs a solution approach for searching effective points using the grey wolf optimization algorithm. The grey wolf optimization algorithm reduces the computational amount of people in analyzing the boundary points of the constrained space. Especially for the case where the boundary effective points of the four-dimensional and higher-dimensional constrained spaces cannot be calculated using geometric relationships, it provides a solution idea, enabling the apodization filter to develop towards higher orders. Description of the Drawings

[0057] Figure 1 is the flowchart of the sidelobe suppression method based on the third-order apodization filtering algorithm.

[0058] Figure 2 is the flowchart of the grey wolf optimization algorithm.

[0059] Figure 3 is the flowchart of selecting the minimum value of the filtered data.

[0060] Figure 4 is the one-dimensional point target pulse compression response without frequency-domain weighting processing.

[0061] Figure 5 is the one-dimensional point target pulse compression response processed by MSVA.

[0062] Figure 6 is the one-dimensional point target pulse compression response processed by the third-order apodization filtering. Detailed Embodiments

[0063] The present invention will be further described below with reference to the drawings in the specification and embodiments.

[0064] Embodiment 1:

[0065] The purpose of the present invention is to design a sidelobe suppression method for third-order apodization filtering aiming at solving the problem of poor performance of the existing second-order apodization filtering algorithm in suppressing the range sidelobes of SAR images. The present invention improves the order of the filter, expands the filter from 5 points to 7 points, and increases the dimension of the solution space. Aiming at the problem of difficult selection of effective points in three-dimensional and higher-dimensional constrained spaces, the present invention designs a solution approach for searching effective points using the grey wolf optimization algorithm.

[0066] To achieve the above purpose, the technical solution of the present invention includes the following steps:

[0067] Step 1: Pulse compress the linear frequency modulation signal to obtain the one-dimensional point target pulse compression response to obtain the range profile of the point target SAR image.

[0068] Step 2: Use the frequency domain window function of the third-order spatial apodization filter to perform frequency domain weighting on the real and imaginary parts of the pulse compression response of the one-dimensional point target.

[0069] Step 3: Determine the constraint space of the filter coefficients.

[0070] Step 4: Use the Gray Wolf Optimization Algorithm to perform point-by-point operations on the ideal filtering results of the real part of the pulse compression response of the one-dimensional point target to complete the optimization process, and search point by point in the constraint space for the maximum and minimum values ​​that the filtering data can obtain. Determine the final filtering result of the signal based on the optimization result.

[0071] Step 5: Repeat step 4 to complete the filtering process of the imaginary part of the signal.

[0072] Step 6: Summarize the filtering results of the real and imaginary parts of the one-dimensional point target pulse compression response to calculate the complex signal filtering processing results.

[0073] In step 1, the one-dimensional point target pulse compression response is the one-dimensional range image of the point target obtained by pulse compression of the linear frequency modulation signal through the matched filtering method, which is equivalent to the range profile of the point target SAR image. The pulse compression response of the one-dimensional point target is expressed as g(m)=g Re (m)+ig Im (m), g Re (m) is the real part of g(m), g Im (m) is the imaginary part of g(m).

[0074] In step 2, the expression of the frequency domain window function of the third-order spatial apodization filter is as follows:

[0075]

[0076] in f0 is the bandwidth of the linear frequency modulation signal, f s is the sampling rate, a and w i (i=1,2,3) is the filter coefficient. After frequency domain weighting, the ideal filtered time domain signal g is obtained. Re ′(m) and g Im ′(m), its expression is:

[0077]

[0078]

[0079] Where I(m) is the impulse response of W(f), and its expression is as follows:

[0080]

[0081] wherein represents rounding down the parameter.

[0082] In step 3, set the filter coefficients a and w i (i = 1, 2, 3) constraint terms:

[0083]

[0084] In step 4, in the grey wolf optimization algorithm, w i (i = 1, 2, 3) are decision variables, set the population size to num, and randomly generate num individuals within the constraint space to complete the population initialization operation.

[0085] Furthermore, calculate the fitness values of all individuals in the population using the fitness function. The fitness function Fitness of the grey wolf optimization algorithm:

[0086]

[0087] where L is the current iteration number and q is the current individual number.

[0088] Furthermore, sort the fitness values Fitness of all individuals from high to low. If optimizing for the minimum value, the smaller the fitness value Fitness, the greater the fitness of the individual. If optimizing for the maximum value, the larger the fitness value Fitness, the greater the fitness of the individual.

[0089] Find the three individuals with the highest fitness in the population, denoted as α, β, and γ respectively. Their fitness magnitudes are sorted as α > β > γ.

[0090] Furthermore, update the positions of all individuals, and complete an update of the population positions based on the positions of α, β, and γ. The population update formula is as follows:

[0091]

[0092]

[0093]

[0094]

[0095] where and are random variables, and their value ranges are [0, 1], and is the coefficient vector, is the position vector of individual q, and are the position vectors of α, β, and γ respectively, is the updated position vector of individual q. λ is the convergence factor, and its expression is as follows:

[0096] λ = 2 - 2(e L / iteration - 1) / (e - 1)

[0097] where iteration is the number of iterations of the Grey Wolf Optimization algorithm.

[0098] Furthermore, after all individuals complete one update, it is judged whether the position of the individual exceeds the constraint space. If the position of individual q after update exceeds the constraint space, then let individual q move along the vector at a step size of towards the individual α with the best fitness until the constraint conditions are met. Update the fitness value of the population to complete one iteration process.

[0099] Furthermore, after completing iteration times of iteration, search for the minimum value g Re ′(m) as g Re ′(m) min . If there are two individuals with opposite fitness value signs or at least one individual has a fitness value of 0 at the end of each iteration process, then terminate the iterative optimization process at this point and let g Re ′(m) = g Re ′(m) min = 0.

[0100] Furthermore, if g Re ′(m) min ≠ 0, then generate a new population. Re - complete iteration times of iteration, search for the maximum value g Re ′(m) as g Re ′(m) max . If there are two individuals with opposite fitness value signs or at least one individual has a fitness value of 0 at the end of each iteration process, then terminate the iterative optimization process at this point and let g Re ′(m) = g Re ′(m) max = 0.

[0101] Furthermore, when g Re ′(m) max ≠ 0, if g Re ′(m) min ·g Re ′(m) max <0, then let gRe ′(m) = 0, if g Re ′(m) min ·g Re ′(m) max > 0, then let g Re ′(m) = min(|g Re ′(m) min |, |g Re ′(m) max |), where min(a, b) is to calculate the minimum value of a and b.

[0102] Step 6 includes: the result of complex signal filtering processing

[0103] Example 2:

[0104] Combined with Figure 1 , the present invention includes the following steps:

[0105] Step 1: Obtain the pulse compression response of a one-dimensional point target.

[0106] Step 1.1: The time-domain expression of the transmitted signal is as follows:

[0107]

[0108] where T is the pulse duration of the chirp signal, K = f0 / T is the chirp rate, and f0 is the bandwidth of the chirp signal. The echo of a one-dimensional point target h(t) = s(t - τ), where τ is the time delay.

[0109] Sampling the transmitted signal s(t) and the echo signal h(t) of the one-dimensional point target at a non-integer multiple of the Nyquist sampling rate f s to obtain discrete signals s(m) and h(m).

[0110] Step 1.2: Obtain the pulse compression response of the one-dimensional point target according to the following formula:

[0111] g(m) = ifft(fft(h(m)) × fft(conj(fliplr(s(m)))))

[0112] where ifft(·) represents the inverse fast Fourier transform of a discrete signal, fft(·) represents the fast Fourier transform of a discrete signal, fliplr(·) represents the anti-folding operation of a discrete signal, and conj(·) represents taking the conjugate of a signal.

[0113] Step 1.3: Divide the obtained pulse compression response of the one-dimensional point target into real and imaginary parts:

[0114] g(m) = gRe (m) + ig Im (m)

[0115] where g Re (m) is the real part of g(m), and g Im (m) is the imaginary part of g(m).

[0116] Step 2: Use the frequency-domain window function of the third-order apodization filter to perform frequency-domain weighting on the real and imaginary parts of the impulse compression response of the one-dimensional point target respectively.

[0117] Step 2.1: The expression of the frequency-domain window function of the third-order apodization filter is as follows:[[]]

[0118]

[0119] where a and w i (i = 1, 2, 3) are filter coefficients. After frequency-domain weighting, the ideal time-domain signals g Re ′(m) and g Im ′(m) are obtained, and their expressions are:[[]]

[0120]

[0121]

[0122] where I(m) is the impulse response of W(f), and its expression is as follows:[[]]

[0123]

[0124] where means rounding down the parameter.

[0125] Step 3: Determine the constraint space of the filter coefficients.

[0126] Step 3.1: Set the constraint terms of the filter coefficients a and w i (i = 1, 2, 3):

[0127]

[0128] Step 4: Use the grey wolf optimization algorithm to perform point-by-point operations on g Re ′(m) to complete the optimization process, and search point by point in the constraint space for the maximum and minimum values that the filtered g Re ′(m) can obtain. Determine the final filtering result of the signal according to the optimization result. Attached Figure 2 is the flow chart of the grey wolf optimization algorithm.

[0129] Step 4.1: In the Grey Wolf Optimization algorithm, w i (i = 1, 2, 3) are decision variables. Set the population size to num, and randomly generate num individuals within the constraint space in Step 3 to complete the population initialization operation.

[0130] Step 4.2: Calculate the fitness values of all individuals in the population using the fitness function. The fitness function Fitness of the Grey Wolf Optimization algorithm is:

[0131]

[0132] where L is the current iteration number and q is the current individual number.

[0133] Step 4.3: Sort the fitness values Fitness of all individuals from high to low. If optimizing for the minimum value, the smaller the fitness value Fitness, the greater the fitness of the individual. If optimizing for the maximum value, the larger the fitness value Fitness, the greater the fitness of the individual.

[0134] Find the three individuals with the highest fitness in the population, denoted as α, β, and γ respectively. Their fitness levels are sorted as α > β > γ.

[0135] Step 4.4: Update the positions of all individuals in the population, and complete one update of the population positions according to the positions of the three individuals α, β, and γ with the highest fitness in Step 4.3. The population update formula is as follows:

[0136]

[0137]

[0138]

[0139]

[0140] where and are random variables, and their value ranges are [0, 1]. and are coefficient vectors. is the current individual position vector. and are the position vectors of α and β respectively. is the updated individual position vector. λ is the convergence factor, and its expression is as follows:

[0141] λ = 2 - 2(e L / iteration -1) / (e - 1)

[0142] where iteration is the number of iterations of the Grey Wolf Optimization algorithm.

[0143] Step 4.5: After all individuals complete one update, determine whether the positions of all individuals exceed the constraint space according to the constraint conditions in Step 3.2. If the position vector of individual q exceeds the constraint space after the position update, then let individual q move along the vector at the current position with a step size of towards the individual α with the optimal fitness until the constraint conditions are met. Update the fitness value of the population to complete one iteration process.

[0144] Step 4.6: Repeat Steps 4.2 to 4.5 to search for the minimum value g Re ′(m) of g Re ′(m) min , and complete iteration times. If there are two individuals with opposite fitness value signs or at least one individual with a fitness value of 0 at the end of each iteration process, then terminate the iterative optimization process at this point, and let g Re ′(m) = g Re ′(m) min = 0. If the minimum value obtained after iteration times of iteration is not zero, then execute Step 4.7. Attached Figure 3 is the flowchart for selecting the minimum value of filtered data.

[0145] Step 4.7: Generate a new population using Step 4.1. Repeat Steps 4.2 to 4.5 to search for the maximum value g Re ′(m) of g Re ′(m) max , and complete iteration times. If there are two individuals with opposite fitness value signs or at least one individual with a fitness value of 0 at the end of each iteration process, then terminate the iterative optimization process at this point, and let g Re ′(m) = g Re ′(m) max = 0. If the maximum value obtained after iteration times of iteration is not zero, then execute Step 4.8.

[0146] Step 4.8: If the signs of the obtained maximum value and minimum value are opposite, then let g Re ′(m) = 0. If the signs are the same, then let g Re ′(m) = min(|g Re ′(m) min |, |g Re ′(m) max |), where min(a, b) is to calculate the minimum value of a and b.

[0147] ​Step 5: Repeat Step 4 to filter the imaginary part g Im (m) to obtain g Im ′(m).

[0148] Step 6: Calculate the result g′(m) of filtering the complex signal

[0149] The following gives an embodiment in combination with specific parameters:

[0150] Table 1 shows the exemplary sidelobe suppression simulation experiment parameters, including the chirp signal bandwidth f0, pulse duration T, sampling rate f s , echo signal delay τ, population number num, and number of iterations iteration. The peak sidelobe ratio (PSLR) and integrated sidelobe ratio (ISLR) are selected as the evaluation criteria for the sidelobe suppression effect. Table 2 compares the performance of the one-dimensional point target response without spectral weighting processing, applying improved spatial apodization filtering (MSVA), and applying the third-order spatial apodization filtering designed by the present invention.

[0151] Table 1

[0152]

[0153] Table 2

[0154]

[0155]

[0156] Testing the algorithm with a single one-dimensional point target, it can be seen from Table 2 that under the parameters in Table 1, the peak sidelobe ratio of the present invention is reduced by 10.65 dB, and the integrated sidelobe ratio is reduced by 6.77 dB. Attached Figure 4 is the pulse compression response of the one-dimensional point target without frequency domain weighting processing. Attached Figure 5 is the pulse compression response of the one-dimensional point target processed by MSVA. Attached Figure 6 is the pulse compression response of the one-dimensional point target processed by the third-order spatial apodization filtering.

[0157] In summary, the third-order spatial apodization filtering algorithm designed by the present invention has significantly improved performance compared with the second-order spatial apodization filtering algorithm (MSVA), and can effectively suppress the target sidelobe without losing the main lobe energy.

[0158] The present invention relates to the technical field of radar signal processing, and provides a new sidelobe suppression method based on third-order apodization filtering. This method expands the traditional filter from 5 points to 7 points, increases the dimension of the solution space, improves the flexibility of the filter, and can effectively suppress sidelobes without losing the main lobe energy. The present invention searches for the effective points on the boundary of the three-dimensional constraint space through the grey wolf optimization algorithm, and effectively reduces the manual calculation amount compared with the conventional method of analyzing geometric relationships. The present invention is also applicable to the selection of effective points on the boundary of the constraint space with more than three dimensions, enabling the apodization filter to develop towards higher orders.

[0159] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention can have various changes and modifications. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention. Each component not clearly defined in this embodiment can be implemented by the prior art.

Claims

1. A method for suppressing sidelobes of the pulse compression response of a chirp signal, characterized in that, Including the following steps: Step 1: Perform pulse compression on the chirp transmit signal to obtain the one-dimensional point target pulse compression response g(m), where g(m) = g Re (m) + ig Im (m), where g Re (m) is the real part of g(m), and g Im (m) is the imaginary part of g(m); Step 2: Use the frequency-domain window function of the third-order spatial apodization filter to perform frequency-domain weighting on the real part g Re (m) and the imaginary part g Im (m) of the one-dimensional point target pulse compression response respectively, and obtain the ideal filtering result g Re ′(m) of the real part and the ideal filtering result g Im ′(m) of the imaginary part of the one-dimensional point target pulse compression response g(m); Step 3: Determine the filter coefficients a and w i constraint conditions, and form a constraint space from the constraint conditions; Step 4: Use the Grey Wolf Optimization Algorithm to search for the maximum and minimum values that the filtering data can achieve point by point within the constraint space for the ideal filtering result of the real part of the impulse compression response of the one-dimensional point target. Obtain the filtering result of the real part of the impulse compression response of the one-dimensional point target according to the optimization result, and assign it to g Re ′(m); Step 5: Repeat the operation in Step 4 for the ideal filtering result of the imaginary part of the one-dimensional point target pulse compression response. Obtain the filtering result of the imaginary part of the one-dimensional point target pulse compression response according to the optimization result, and assign it to g Im ′(m); Step 6: Calculate the filtered result g′(m) of the complex signal filtering process based on the filtered results of the real and imaginary parts of the one-dimensional point target pulse compression response obtained in Step 5.

2. A method for suppressing sidelobes of a linear frequency modulation signal pulse compression response according to claim 1, characterized in that: The pulse compression of the chirp transmit signal to obtain the one-dimensional point target pulse compression response includes: Step 1.1: Sample the chirp transmit signal s(t) and the one-dimensional point target echo signal h(t) at a non-integer multiple of the Nyquist sampling rate f s to obtain the discrete signals s(m) and h(m); The chirp transmit signal s(t) satisfies: Among them, T is the pulse duration of s(t), K = f0 / T is the frequency modulation slope, and f0 is the bandwidth of s(t). The echo h(t) of a one-dimensional point target is h(t) = s(t - τ), where τ is the time delay. Step 1.2: Obtain the pulse compression response g(m) of the one-dimensional point target: g(m) = ifft(fft(h(m)) × fft(conj(fliplr(s(m))))) Where ifft(·) represents the inverse fast Fourier transform of the discrete signal, fft(·) represents the fast Fourier transform of the discrete signal, fliplr(·) represents the anti-folding operation of the discrete signal, and conj(·) represents the conjugate of the signal; Divide g(m) into real and imaginary parts: g(m) = g Re (m) + ig Im (m) Among them, g Re (m) is the real part of g(m), and g Im (m) is the imaginary part of g(m).

3. A method for suppressing sidelobes of the pulse compression response of a chirp signal, according to claim 1, characterized in that: The frequency domain window function of the third-order apodization filter is specifically: Among them, f0 is the bandwidth of the chirp transmit signal, and a and w i are filter coefficients.

4. A method for suppressing sidelobes of a linear frequency modulation signal pulse compression response according to claim 3, characterized in that: The real part ideal filtering result \(g_{Re}'(m)\) and the imaginary part ideal filtering result \(g_{Im}'(m)\) of \(g(m)\) described in step 2 are specifically as follows: Re ′(m) and the imaginary part ideal filtering result g Im ′(m) are specifically as follows: Where I(m) is the impulse response of W(f) and satisfies: Among them, f s is a non-integer multiple of the Nyquist sampling rate, represents rounding down the parameter.

5. A method for suppressing sidelobes of a pulse compression response of a chirp signal, according to claim 3, characterized in that: The constraint space for determining the filter coefficients in Step 3 is specifically: Set filter coefficients a and w i The constraint terms are as follows: Among them, f s is a non-integer multiple of the Nyquist sampling rate, represents rounding down the parameter.

6. A method for suppressing sidelobes of a pulse compression response of a chirp signal, according to claim 1, wherein: Step 4 is specifically: Step 4.1: In the Grey Wolf Optimization Algorithm, w i is the decision variable, i = 1, 2, 3. Set the population size to num, and randomly generate num individuals within the constraint space of Step 3 to complete the population initialization operation; Step 4.2: Calculate the fitness values of all individuals in the population using the fitness function Fitness of the Grey Wolf Optimization Algorithm; Step 4.3: Find the three individuals with the highest fitness values in the population, denoted as α, β, and γ respectively, and their fitness magnitudes are sorted as α > β > γ; Step 4.4: Update the positions of all individuals in the population, and complete an update of the population positions according to the positions of individuals α, β, and γ, specifically: Among them, and are random variables, and their value ranges are [0, 1]. and are coefficient vectors. is the current individual position vector, L is the current iteration number. and are the position vectors of α, β, and γ respectively. is the updated individual position vector, and λ is the convergence factor, satisfying: λ=2 - 2(e L / iteration - 1) / (e - 1) Where iteration is the number of iterations of the Grey Wolf Optimization Algorithm; Step 4.5: Determine whether there is an individual whose position exceeds the constraint space according to the constraint conditions in Step 3. If the position vector of individual q exceeds the constraint space after the position update then let individual q move along the vector at a step size of towards the individual α with the optimal fitness until the constraint conditions are met. M is a set positive integer, update the fitness value of the population, and complete one iteration process; Step 4.6: Repeat Steps 4.2 to 4.5 to search for the minimum value of g Re ′(m), i.e., g Re ′(m) min . Complete iteration iterations. At the end of each iteration, if there are two individuals with fitness values of opposite signs or at least one individual has a fitness value of 0, terminate the iterative optimization process at this point and set g Re ′(m) = g Re ′(m) min = 0; if the minimum value obtained after iteration iterations of optimization is not zero, then execute Step 4.7; Step 4.7: Generate a new population using Step 4.1, and repeat Steps 4.2 to 4.5 to search for the maximum value of g Re ′(m), denoted as g Re ′(m) max , complete iteration iterations. If there are two individuals with opposite fitness value signs or at least one individual with a fitness value of 0 at the end of each iteration process, terminate the iterative optimization process at this point, and set g Re (m) = g Re ′(m) max = 0. If the maximum value obtained after the iteration iterations is not zero, then execute Step 4.8; Step 4.8: If the signs of the maximum value and the minimum value obtained by optimization are opposite, then let g Re ′(m) = 0; if the signs are the same, then let g Re ′(m) = min(|g Re ′(m) min |, |g Re ′(m) max |), where min(a, b) is the minimum value of a and b.

7. A method for suppressing sidelobes of a linear frequency modulation signal pulse compression response according to claim 6, characterized in that: The fitness function Fitness of the Grey Wolf Optimization Algorithm is specifically: Where L is the current number of iterations and q is the current individual number.

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