Fast optimization method of weighted integrated sidelobe for MIMO radar spectrum compatible signals

Abstract

A method for fast optimization of weighted integrated sidelobe of MIMO radar spectrum compatible signal belongs to the field of radar waveform design. The purpose of the present invention is to solve the problem that the integrated sidelobe level is not considered when designing MIMO radar spectrum compatible signal. It includes: based on the coding vector of each array element of the MIMO radar array and the zero-padding vector of each array element coding vector, obtaining the spectrum and power spectrum corresponding to the coding vector; then obtaining the autocorrelation function and cross-correlation function of each array element coding vector; establishing the expression of the weighted integrated sidelobe level of the MIMO radar as the objective function; combining the stopband notch constraint and the constant modulus constraint to determine the optimization problem; using the BM algorithm to decompose the optimization problem into the optimization sub-problem of each array element, and then performing relaxation solution to obtain the simplified optimization sub-problem; combining the relationship between the autocorrelation function, cross-correlation function and the spectrum, transforming the simplified optimization sub-problem to obtain the final optimization problem. The present invention is used for the design of MIMO radar spectrum compatible signal.

Description

Technical Field

[0001] The invention relates to a method for fast optimizing weighted integral side lobes of MIMO radar spectrum compatible signals, and belongs to the field of radar waveform design. Background Art

[0002] Multiple Input Multiple Output (MIMO) radar is a new radar technology that offers flexible operation and a high degree of freedom on the transmitter side. The radar can transmit fully orthogonal waveforms to scan the entire airspace, or partially correlated waveforms to scan a wide airspace. Due to the high degree of freedom offered by MIMO radar transmit waveforms, designing them to detect target airspaces and achieve optimal signal performance has become a hot topic among researchers.

[0003] Furthermore, the number of radio systems has exploded in recent years. To improve signal and information transmission quality, the demand for operating bandwidth has also continued to grow. Radar is a common radio user. With the advancement and innovation of radar theory and technology, modern radars are widely used in various fields, resulting in an increasing demand for spectrum resources. However, spectrum resources are a limited natural resource. The growing demand for operating bandwidth from communication systems, radio stations, and other systems has made the spectrum coexistence issue between communication and radar increasingly acute and urgent. In addition to civilian radio equipment, modern radars also face various electronic interferences. Therefore, the electromagnetic environment in which modern high-frequency radars operate is subject to a large amount of co-channel interference, creating a complex and harsh electromagnetic environment. Therefore, improving the performance of radar systems in this complex electromagnetic spectrum environment has become a major challenge that needs to be addressed. Modern researchers have considered waveform design techniques, such as adding notches in unusable frequency bands to avoid other interference. However, the autocorrelation function is the inverse Fourier transform of the power spectral density. Therefore, adding notches in the interference band can affect the signal's autocorrelation function, specifically by increasing the signal's autocorrelation sidelobes, resulting in weak target masking. Therefore, it is necessary to optimize the autocorrelation sidelobe performance of discontinuous spectrum signals.

[0004] In a MIMO radar system, frequency domain interference can be jointly suppressed in the spatial and frequency domains. Existing research mostly focuses on optimizing the signal-to-interference-noise ratio, or performing joint shaping in the spatial and frequency domains to maximize / minimize the energy in a certain portion of the spatial and frequency domain to enhance signal echo strength / reduce interference effects, or to reduce the peak sidelobe performance between array element signals and design orthogonal signals. However, in the evaluation of autocorrelation sidelobes and cross-correlation performance, the integrated sidelobe level is also a very important indicator, which can characterize the comprehensive performance of the sidelobe area. Existing research has optimized the peak sidelobes of MIMO radar waveforms and designed weighted values ​​considering the importance of the sidelobe area. However, there is no research specifically optimizing the weighted integrated sidelobe level of MIMO radar spectrum-compatible waveforms. Therefore, there are still certain problems in optimizing the integrated sidelobe level of MIMO radar spectrum-compatible signals. Summary of the Invention

[0005] The purpose of the present invention is to solve the problem that the integrated sidelobe level is not considered when designing MIMO radar spectrum compatible signals. A fast optimization method for weighted integrated sidelobe of MIMO radar spectrum compatible signals is proposed.

[0006] The present invention provides a method for fast optimization of weighted integrated side lobes of MIMO radar spectrum compatible signals, comprising:

[0007] Based on the coding vector of each array element of the MIMO radar array and the zero-padding vector of each array element coding vector, the frequency spectrum and power spectrum corresponding to the coding vector are obtained; and then the autocorrelation function and cross-correlation function of each array element coding vector are obtained;

[0008] Based on the autocorrelation function and cross-correlation function, an expression for the weighted integrated sidelobe level of the MIMO radar is established as the objective function. Then, combined with the stopband notch constraint and the constant modulus constraint, the optimization problem is determined.

[0009] The BM algorithm is used to decompose the optimization problem into optimization subproblems for each array element, and then the optimization subproblems are relaxed and solved to obtain simplified optimization subproblems;

[0010] Combining the relationship between the autocorrelation function, cross-correlation function and spectrum, the simplified optimization sub-problem is transformed to obtain the final optimization problem; the final optimization problem is iteratively updated to obtain the final optimization result; and the MIMO radar spectrum compatible signal is designed based on the final optimization result.

[0011] According to the weighted integral sidelobe fast optimization method of the MIMO radar spectrum compatible signal of the present invention, the MIMO radar array is a uniform linear array with a half-wavelength array element spacing and a total of M array elements; assuming that the number of codes for each array element is N, the mth array element code vector s m for:

[0012] sm =[s m,1 ,...,s m,N ] T ,m=1,...,M(1),

[0013] Where s m,N is the encoding vector s m The Nth point of

[0014] make Then the mth array element encoding vector s m Zero-padding vector of for:

[0015]

[0016] According to the weighted integral sidelobe fast optimization method of the MIMO radar spectrum compatible signal of the present invention, the coding vector s m The spectrum f m and power spectrum p m for:

[0017]

[0018] Where f m,N-1 is the spectrum f m The N-1th point, p m,N-1 is the power spectrum p m The N-1th point; f m The conjugate of The DFT transformation matrix, ε represents the Hadamard product;

[0019]

[0020] Where l1 is the number of rows of the DFT transform matrix F, and l2 is the number of columns of the DFT transform matrix F.

[0021] According to the weighted integral sidelobe fast optimization method of MIMO radar spectrum compatible signal of the present invention, s m The autocorrelation function r m,m and the cross-correlation function r m,m' for:

[0022] r m,m =F H p m =[r m,m,1-N ,...,r m,m,N-1 ] T (4),

[0023]

[0024] Where F H is the conjugate transpose of F, r m,m,N-1 is the autocorrelation function r m,m The N-1th value of r m,m',N-1 is the cross-correlation function r m,m' The N-1th value of For r m,m' The conjugate of , m′=1,...,M, and m≠m′.

[0025] According to the fast optimization method of weighted integral sidelobe of MIMO radar spectrum compatible signal of the present invention, the expression of MIMO radar weighted integral sidelobe level WISL is:

[0026]

[0027] Where w m,m',k is the kth non-negative weighted value.

[0028] According to the weighted integral sidelobe fast optimization method of the MIMO radar spectrum compatible signal of the present invention, the stopband notch constraint is

[0029]

[0030] Where Ω u is the uth stopband position, Ω u ∈Ω=[Ω1,...,Ω U ] T , Ω is the stopband position set, u=1, 2, 3, …, U; is the stopband position Ω u The upper limit of the spectrum at

[0031] The constant modulus constraint is:

[0032]

[0033] In formula (6) is a constant and is ignored in the optimization, so the optimization problem is:

[0034]

[0035] According to the weighted integral sidelobe fast optimization method of the MIMO radar spectrum compatible signal of the present invention, the BM algorithm is used to decompose the optimization problem into the optimization sub-problem of each array element as follows:

[0036] Assume that in the t+1th iteration of the final optimization problem, the tth iteration value of the m′th array element code vector is fixed Solve the mth array element coding vector s m , we get the optimization sub-problem of the array element:

[0037]

[0038] Beneficial effects of the present invention: In order to optimize the weighted autocorrelation integral sidelobes and cross-correlation integrals of MIMO radar spectrum compatible signals, the present invention proposes a new spectrum compatible signal design optimization problem, which focuses on minimizing the weighted autocorrelation integral sidelobes and cross-correlation integrals of the signal. The present invention uses weighted integral sidelobes as the objective function, spectrum notch and constant modulus as constraints to establish an optimization problem, and proposes a BM algorithm. By decomposing the original problem into several sub-problems according to different array elements and finding alternative functions to iteratively solve them, the fast Fourier transform can be used in the solution process to speed up the calculation speed and improve the calculation efficiency. Simulation results show that the method of the present invention has a fast convergence speed and good convergence performance, and the waveform integral sidelobe performance of the final optimization result is greatly improved compared with the existing algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 It is a flow chart of the method for fast optimization of weighted integrated side lobes of MIMO radar spectrum compatible signals according to the present invention;

[0040] Figure 2 is the iterative convergence curve of the objective function of the method of the present invention;

[0041] Figure 3 To verify the normalized autocorrelation results of the first array element in the example;

[0042] Figure 4 To verify the normalized autocorrelation results of the second array element in the example;

[0043] Figure 5 To verify the cross-correlation results between the first and second array elements in the example;

[0044] Figure 6 It is a normalized autocorrelation comparison diagram of the method of the present invention, the ADMM algorithm and the BSUM algorithm;

[0045] Figure 7 It is a normalized cross-correlation comparison diagram of the method of the present invention, the ADMM algorithm and the BSUM algorithm;

[0046] Figure 8 It is a spectrum comparison diagram of the method of the present invention, the ADMM algorithm and the BSUM algorithm. DETAILED DESCRIPTION

[0047] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making any creative efforts shall fall within the scope of protection of the present invention.

[0048] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0049] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but they are not intended to limit the present invention.

[0050] Specific implementation method 1. Combination Figure 1 As shown, the present invention provides a method for fast optimization of weighted integrated side lobes of MIMO radar spectrum compatible signals, comprising:

[0051] Based on the coding vector of each array element of the MIMO radar array and the zero-padding vector of each array element coding vector, the frequency spectrum and power spectrum corresponding to the coding vector are obtained; and then the autocorrelation function and cross-correlation function of each array element coding vector are obtained;

[0052] Based on the autocorrelation function and cross-correlation function, an expression for the weighted integrated sidelobe level of the MIMO radar is established as the objective function. Then, combined with the stopband notch constraint and the constant modulus constraint, the optimization problem is determined.

[0053] The BM algorithm is used to decompose the optimization problem into optimization subproblems for each array element, and then the optimization subproblems are relaxed and solved to obtain simplified optimization subproblems;

[0054] Combining the relationship between the autocorrelation function, cross-correlation function and spectrum, the simplified optimization sub-problem is transformed to obtain the final optimization problem; the final optimization problem is iteratively updated to obtain the final optimization result; and the MIMO radar spectrum compatible signal is designed based on the final optimization result.

[0055] This embodiment describes the optimization problem based on the MIMO radar discontinuous spectrum signal model and then solves it using the BM method.

[0056] Let’s first establish a discontinuous spectrum signal model:

[0057] The MIMO radar array is a uniform linear array with a half-wavelength spacing between array elements and a total of M array elements. Assuming that the number of codes for each array element is N, the code vector s of the mth array element is m for:

[0058] s m =[s m,1 ,...,sm,N ] T ,m=1,...,M(1),

[0059] Where s m,N is the encoding vector s m The Nth point of

[0060] make Then the mth array element encoding vector s m Zero-padding vector of for:

[0061]

[0062] Encoded vector s m The spectrum f m and power spectrum p m for:

[0063]

[0064] Where f m,N-1 is the spectrum f m The N-1th point, p m,N-1 is the power spectrum p m The N-1th point; f m The conjugate of The DFT transformation matrix, ε represents the Hadamard product;

[0065]

[0066] Where l1 is the number of rows of the DFT transform matrix F, and l2 is the number of columns of the DFT transform matrix F.

[0067] s m The autocorrelation function r m,m and the cross-correlation function r m,m' for:

[0068] r m,m =F H p m =[r m,m,1-N ,...,r m,m,N-1 ] T (4),

[0069]

[0070] Where F H is the conjugate transpose of F, r m,m,N-1 is the autocorrelation function r m,m The N-1th value of r m,m',N-1 is the cross-correlation function rm,m' The N-1th value of For r m,m' The conjugate of , m′=1,...,M, and m≠m′.

[0071] Further, construct the optimization problem:

[0072] The optimization problem needs to consider the sidelobe performance of the autocorrelation function of each array element to reduce the shadowing effect of weak targets, consider the cross-correlation integral sidelobe between array elements to ensure the orthogonality between array elements to achieve omnidirectional scanning, and consider the different importance of the sidelobe area. Therefore, the weighted integral sidelobe level of the MIMO radar is considered. The expression of the weighted integral sidelobe level of the MIMO radar WISL is:

[0073]

[0074] Where w m,m',k is the kth non-negative weight value, representing the weight of the sidelobe area.

[0075] Formula (6) is the objective function considered in this embodiment. However, in the optimization of spectrum-compatible waveforms, some constraints need to be considered. The first is the stopband notch constraint. In order to achieve the anti-frequency domain interference effect of the spectrum-compatible waveform, it is necessary to impose a stopband notch constraint so that the waveform spectrum has a sufficiently deep notch in the unusable frequency band. The stopband notch constraint can be expressed as:

[0076]

[0077] Where Ω u is the uth stopband position, Ω u ∈Ω=[Ω1,...,Ω U ] T , Ω is the stopband position set, u=1, 2, 3, …, U; is the stopband position Ω u The upper limit of the spectrum at

[0078] In order to keep the transmitter power amplifier in the linear operating region to prevent waveform distortion, the waveform needs to satisfy the constant modulus constraint:

[0079]

[0080] In formula (6) is a constant and is ignored in the optimization, so the optimization problem is:

[0081]

[0082] Going further, we can solve the optimization problem:

[0083] This embodiment proposes the BSUM-MM (BM) algorithm for the optimization problem. The BSUM method can decompose the original problem into several subproblems by solving them in a block-by-block manner. It can be seen that the stopband constraint and constant modulus constraint in equation (9) are independent for each transmitting array element. Therefore, the original problem can be decomposed into M subproblems based on the antenna array elements, and then the MM method can be used to relax and transform the original problem for solution. Specifically:

[0084] Assume that in the t+1th iteration of the final optimization problem, the tth iteration value of the m′th array element code vector is fixed Solve the mth array element coding vector s m , we get the optimization sub-problem of the array element:

[0085]

[0086] In this embodiment, the method for obtaining the simplified optimization sub-problem is:

[0087] The MM method is used to optimize the subproblem for relaxation solution, and the objective function in formula (10) is defined as f1 m (s m ):

[0088]

[0089] Where diag(w m,m' ) is the diagonal element w m,m' The diagonal matrix of

[0090] For F1 m (s m ) for relaxation:

[0091] According to max(w m,m' )I 2N-1 ≥diag(w m,m' ) (12),

[0092] Where I 2N-1 represents the unit matrix of dimension 2N-1, then f1 m (s m ) for:

[0093]

[0094] In the formula

[0095]

[0096] Ignoring the constant c1, we can get the simplified optimization subproblem:

[0097]

[0098]

[0099] Combining the relationship between the autocorrelation function, cross-correlation function and spectrum, formula (14) can be rewritten as:

[0100]

[0101] In the formula

[0102] The first term in formula (15) is a quadratic term, which is easy to solve, while the second term is a quartic term, which is difficult to solve. Therefore, |f m | 2 Relaxation get:

[0103]

[0104]

[0105] The objective function in formula (16) is quadratic, let

[0106] Then in formula (16) Expands to:

[0107]

[0108] Where c2 is a constant, Then formula (16) can be rewritten as:

[0109]

[0110]

[0111] In the formula

[0112] Due to the existence of stopband constraints, formula (18) still cannot be solved directly.

[0113] Therefore, Ignoring the stopband notch constraint, define:

[0114]

[0115] In the formula And not satisfied

[0116] Further simplifying formula (18), we get:

[0117]

[0118] In the formula

[0119] Perform Fourier transform on formula (20) to obtain the final optimization problem:

[0120]

[0121] In the formula

[0122] The final optimization result is This completes the process of s in the t+1 iteration. m Update. Updating the signals of all array elements is one iteration. After multiple iterations, the final optimization result can be obtained.

[0123] Verification example:

[0124] The following examples are used to verify the beneficial effects of the present invention:

[0125] Set the simulation parameters, the number of array elements M = 2, the length of the single pulse intra-pulse coding code N = 128, the sidelobe weight value w m,m,1 =10 -10 , the rest are 1, the stopband depression depth The stopband position Ω∈[0.3,0.4], and the maximum number of iterations is 50000. First, a random phase is used as the initial value, and 100 simulation experiments are set to verify the convergence performance of the method of the present invention. Figure 2 The iterative convergence result of the objective function is given. Figure 3 The autocorrelation of the first array element of 100 simulation experiments is given. Figure 4 The autocorrelation of the second element is given by Figure 5 The cross-correlation between two array elements is given. It can be seen that good convergence results can be achieved for different initial values. The obtained autocorrelation and cross-correlation performance are good.

[0126] Next, the ADMM algorithm and the BSUM algorithm are used as comparison algorithms to verify the performance of the method of the present invention. Figure 6 The normalized autocorrelation results obtained by the three algorithms are given. Figure 7 The normalized cross-correlation results obtained by the three algorithms are given. Figure 8 The spectrum results obtained by the three algorithms are given. It can be seen that the three algorithms form a depression of similar depth at the stopband position, achieving similar frequency domain interference suppression effects. However, the autocorrelation sidelobe performance and cross-correlation performance of the method of the present invention are far superior to the comparison algorithm.

[0127] The present invention can also be applied to a variety of other data and scenarios. Without departing from the spirit and essence of the present invention, those skilled in the art can process different data in different scenarios according to the present invention, but these should all fall within the scope of protection of the claims attached to the present invention.

Claims

1. A method for fast optimization of weighted integrated sidelobes of MIMO radar spectrum compatible signals, characterized in that: include: Based on the coding vector of each array element of the MIMO radar array and the zero-padding vector of each array element coding vector, the frequency spectrum and power spectrum corresponding to the coding vector are obtained; Then the autocorrelation function and cross-correlation function of each array element coding vector are obtained; Based on the autocorrelation function and cross-correlation function, an expression for the weighted integrated sidelobe level of the MIMO radar is established as the objective function. Then, combined with the stopband notch constraint and the constant modulus constraint, the optimization problem is determined. The BM algorithm is used to decompose the optimization problem into optimization subproblems for each array element, and then the optimization subproblems are relaxed and solved to obtain simplified optimization subproblems; Combining the relationship between the autocorrelation function, cross-correlation function and spectrum, the simplified optimization sub-problem is transformed to obtain the final optimization problem; Iteratively update the final optimization problem to obtain the final optimization result; Then, based on the final optimization results, the MIMO radar spectrum compatible signal is designed; The MIMO radar array is a uniform linear array with a half-wavelength element spacing and a total of M elements. Assume that the number of codes for each element is N; m′=1,...,M, and m≠m′; The expression of the weighted integrated sidelobe level WISL of MIMO radar is: Where w m,m',k is the kth non-negative weighted value; The stopband notch constraint is: Where Ω u is the uth stopband position, Ω u ∈Ω=[Ω1,...,Ω U ] T , Ω is the stopband position set, u=1, 2, 3, …, U; is the stopband position Ω u The upper limit of the spectrum at The constant modulus constraint is: Where s m,n The encoding vector s for the mth array element m The nth value of ; In formula (6) is a constant and is ignored in the optimization, so the optimization problem is: Using the BM algorithm, the optimization problem is decomposed into the optimization sub-problems of each array element as follows: Assume that in the t+1th iteration of the final optimization problem, the tth iteration value of the m′th array element code vector is fixed Solve the mth array element coding vector s m , we get the optimization sub-problem of the array element:

2. The method for fast optimization of weighted integrated side lobes of MIMO radar spectrum compatible signals according to claim 1, characterized in that: The mth array element code vector s m for: s m =[s m,1 ,...,s m,N ] T ,m=1,...,M(1), Where s m,N is the encoding vector s m The Nth point of make Then the mth array element encoding vector s m Zero-padding vector of for:

3. The method for fast optimization of weighted integrated side lobes of MIMO radar spectrum compatible signals according to claim 2, characterized in that: Encoded vector s m The spectrum f m and power spectrum p m for: Where f m,N-1 is the spectrum f m The N-1th point, p m,N-1 is the power spectrum p m The N-1th point; f m The conjugate of The DFT transformation matrix, ε represents the Hadamard product; Where l1 is the number of rows of the DFT transform matrix F, and l2 is the number of columns of the DFT transform matrix F.

4. The method for fast optimization of weighted integrated side lobes of MIMO radar spectrum compatible signals according to claim 3, characterized in that: s m The autocorrelation function r m,m and the cross-correlation function r m,m' for: r m,m =F H p m =[r m,m,1-N ,...,r m,m,N-1 ] T (4), Where F H is the conjugate transpose of F, r m,m,N-1 is the autocorrelation function r m,m The N-1th value of r m,m',N-1 is the cross-correlation function r m,m' The N-1th value of For r m,m' The conjugation of .

5. The method for fast optimization of weighted integrated side lobes of MIMO radar spectrum compatible signals according to claim 4, characterized in that: The method to obtain the simplified optimization subproblem is: The MM method is used to optimize the subproblem for relaxation solution, and the objective function in formula (10) is defined as f1 m (s m ): Where diag(w m,m' ) is the diagonal element w m,m' The diagonal matrix, w m,m' =[w m,m',k , k=1-N:N-1] For F1 m (s m ) for relaxation: According to max(w m,m' )I 2N-1 ≥diag(w m,m' )(12), Where I 2N-1 represents the unit matrix of dimension 2N-1, then f1 m (s m ) for: In the formula Ignoring the constant c1, we can get the simplified optimization subproblem:

6. The method for fast optimization of weighted integrated side lobes of MIMO radar spectrum compatible signals according to claim 5, characterized in that: Combining the relationship between the autocorrelation function, cross-correlation function and spectrum, formula (14) can be rewritten as: In the formula In formula (15), |f m | 2 Relaxation get: make Then in formula (16) Expands to: Where c2 is a constant, Then formula (16) can be rewritten as: In the formula 7. The method for fast optimization of weighted integrated side lobes of MIMO radar spectrum compatible signals according to claim 6, characterized in that: make Ignoring the stopband notch constraint, define: In the formula And not satisfied Further simplifying formula (18), we get: In the formula Perform Fourier transform on formula (20) to obtain the final optimization problem: In the formula The final optimization result is

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