Weighted integral sidelobe rapid optimization method for MIMO radar spectrum compatible signal

Abstract

The invention discloses a weighted integral sidelobe rapid optimization method for MIMO radar spectrum compatible signals, and belongs to the field of radar waveform design. The objective of the invention is to solve the problem that the integral sidelobe level is not considered when MIMO radar spectrum compatible signals are designed in the prior art. Comprising the steps of obtaining a frequency spectrum and a power spectrum corresponding to a coding vector based on each array element coding vector of the MIMO radar array and a zero filling vector of each array element coding vector; further obtaining an autocorrelation function and a cross-correlation function of each array element coding vector; establishing an expression of the weighted integral sidelobe level of the MIMO radar as a target function; determining an optimization problem in combination with a stop band depression constraint and a constant modulus constraint; decomposing the optimization problem into optimization sub-problems of each array element by adopting a BM algorithm, and performing relaxation solution to obtain simplified optimization sub-problems; and transforming the simplified optimization sub-problem in combination with the relationship among the self-correlation function, the cross-correlation function and the frequency spectrum to obtain a final optimization problem. The method is used for designing MIMO radar frequency spectrum compatible signals.

Description

Technical Field

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

[0002] Multiple Input Multiple Output (MIMO) radar is a new radar technology that is flexible in operation and has a high degree of freedom at the transmitting end. The radar can transmit completely orthogonal waveforms at the transmitting end to achieve full airspace scanning, or transmit partially related waveforms to achieve wide airspace scanning. Since the MIMO radar transmit waveform has a high degree of freedom, designing the MIMO radar transmit waveform to detect the target airspace and obtain better signal performance has become a hot research topic among scholars.

[0003] In addition, the number of radio systems has exploded in recent years. In order to better improve the quality of signal and information transmission, the demand for working bandwidth of radio systems has continued to grow. Radar is one of the common radio users. With the improvement and innovation of radar theory and technology, modern radars have also been widely used in various fields, so the demand for spectrum resources is also increasing. However, spectrum resources are a limited natural resource. The growing demand for working bandwidth of communication systems, radio stations, etc. has made the problem of communication radar spectrum coexistence more acute and urgent. In addition to civil radio equipment, modern radars will also face a variety of electronic interference. Therefore, there are a lot of co-frequency interferences in the electromagnetic environment where modern high-frequency radars are located. The electromagnetic environment is complex and harsh. Therefore, how to improve the working performance of radar systems in complex electromagnetic spectrum environments has become a major problem that needs to be solved urgently. Modern scholars consider the means of waveform design and set notches in unusable frequency bands to avoid other interference. However, the autocorrelation function is the inverse Fourier transform of the power spectrum density. Therefore, setting a notch in the interference band will affect the autocorrelation function of the signal, which is specifically manifested as raising the autocorrelation sidelobe of the signal, resulting in a weak target shielding effect. Therefore, it is necessary to optimize the autocorrelation sidelobe performance of non-continuous spectrum signals.

[0004] In the MIMO radar system, the frequency domain interference can be jointly suppressed in the space-frequency domain. Existing research is mostly aimed at optimizing the signal-to-interference-noise ratio, or performing joint shaping in the space-frequency domain to maximize / minimize the energy of a certain part of the space-frequency domain to enhance the signal echo strength / reduce the impact of interference, 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 specific optimization of 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 weighted integrated sidelobe fast optimization method for MIMO radar spectrum compatible signals is proposed.

[0006] A method for fast optimization of weighted integrated side lobes of MIMO radar spectrum compatible signals of the present invention comprises:

[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, the expression of the weighted integrated sidelobe level of MIMO radar is established as the objective function; then combined with the stopband notch constraint and constant modulus constraint, the optimization problem is determined;

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

[0010] Combined with 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, the array element spacing is half a wavelength, and there are M array elements in total; assuming that the number of codes for each array element is N, then 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 The zero-padding vector 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 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 is: 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 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 weighted integral sidelobe fast optimization method of the MIMO radar spectrum compatible signal of the present invention, the expression of the weighted integral sidelobe level WISL of the MIMO radar 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 to obtain 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 encoding vector is fixed Solve the mth array element encoding 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 the optimization problem, and proposes a BM algorithm. The original problem is decomposed into several sub-problems according to different array elements, and an alternative function is found to iteratively solve the problem. In the solution process, fast Fourier transform can be used 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 weighted integral sidelobe fast optimization method of the MIMO radar spectrum compatible signal of 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 result of the first array element in the example;

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

[0043] Figure 5 To verify the cross-correlation results between the first array element and the second array element 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 be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. 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 creative work are 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 in conjunction with 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 integral 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, the expression of the weighted integrated sidelobe level of MIMO radar is established as the objective function; then combined with the stopband notch constraint and constant modulus constraint, the optimization problem is determined;

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

[0054] Combined with 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 implementation method describes the optimization problem based on the MIMO radar discontinuous spectrum signal model and then solves it through 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 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:

[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 The zero-padding vector for:

[0061]

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

[0063]

[0064] Where f m,N-1 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 is: 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 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 of the signal to reduce the shielding effect of weak targets, consider the cross-correlation integral sidelobe between the array elements to ensure the orthogonality between the 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 waveform, 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 apply the 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 make the transmitter power amplifier in the linear working area 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 solve the optimization problem:

[0083] This implementation method proposes a BSUM-MM (BM) algorithm for the optimization problem. The BSUM method can decompose the original problem into several sub-problems and solve them in sequence by solving them in blocks. 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 sub-problems based on the antenna array element, and then the MM method is 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 encoding vector is fixed Solve the mth array element encoding vector s m , we get the optimization sub-problem of the array element:

[0085]

[0086] In this implementation, 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] 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 obtain 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] Performing Fourier transform on formula (20) yields the final optimization problem:

[0120]

[0121] In the formula

[0122] The final optimization result is This completes the process of s in the t+1th iteration. m Update. Updating the signals of all array elements once is called 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. Firstly, the 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 gives the autocorrelation of the second element, Figure 5 The cross-correlation between two array elements is given. It can be found that for different initial values, good convergence performance results can be achieved. 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 depressions of similar depth at the stopband position and achieve similar frequency domain interference suppression effects. However, the autocorrelation sidelobe performance and cross-correlation performance of the method of the present invention are far better than those of the comparison algorithm.

[0127] The present invention can also be applied to various 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 side lobes 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, the expression of the weighted integrated sidelobe level of MIMO radar is established as the objective function; then combined with the stopband notch constraint and constant modulus constraint, the optimization problem is determined; The BM algorithm is used to decompose the optimization problem into optimization sub-problems for each array element, and then the optimization sub-problems are relaxed and solved to obtain simplified optimization sub-problems; Combining the relationship between the autocorrelation function, the cross-correlation function and the spectrum, the simplified optimization sub-problem is transformed to obtain the final optimization problem; Iterate and update the final optimization problem to obtain the final optimization result; Based on the final optimization results, the MIMO radar spectrum compatible signal is designed.

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 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: 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-filled vector s% m 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: Encoding vector s m The spectrum f m and power spectrum p m for: Where f m,N-1 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 is: 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 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′.

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 expression of weighted integrated sidelobe level WISL of MIMO radar is: Where w m,m',k is the kth non-negative weighted value.

6. The method for fast optimization of weighted integrated side lobes of MIMO radar spectrum compatible signals according to claim 5, characterized in that: 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: In formula (6) is a constant and is ignored in the optimization, so the optimization problem is:

7. The method for fast optimization of weighted integrated side lobes of MIMO radar spectrum compatible signals according to claim 6, characterized in that: Using the BM algorithm, the method of decomposing the optimization problem into the optimization sub-problem of each array element is as follows: Assume that in the t+1th iteration of the final optimization problem, the tth iteration value of the m′th array element encoding vector is fixed Solve the mth array element encoding vector s m , we get the optimization sub-problem of the array element:

8. The method for fast optimization of weighted integrated side lobes of MIMO radar spectrum compatible signals according to claim 7, 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] 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 obtain the simplified optimization subproblem:

9. The method for fast optimization of weighted integrated side lobes of MIMO radar spectrum compatible signals according to claim 8, 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 10. The method for fast optimization of weighted integrated side lobes of MIMO radar spectrum compatible signals according to claim 9, 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 Performing Fourier transform on formula (20) yields the final optimization problem: In the formula The final optimization result is

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