Radar waveform power spectrum processing method and device based on Cauchy-Schwarz divergence

Abstract

The present invention discloses a radar waveform power spectrum processing method and device based on Cauchy-Schwarz divergence. The method completes the initialization of radar parameters by setting initial parameters for the radar; estimates an N×N-dimensional clutter power spectrum and clutter frequency domain covariance based on radar echo data of a clutter signal; estimates an N×N-dimensional target power spectrum and target frequency domain covariance based on radar echo data of a target signal; determines a first matrix and a second matrix based on the power spectrum and noise frequency domain covariance of a set noise; and iteratively optimizes the initial reference waveform power spectrum based on the target frequency domain covariance, the clutter frequency domain covariance, the noise frequency domain covariance, the first matrix, and the second matrix to determine the radar waveform power spectrum under the Cauchy-Schwarz divergence criterion. The present invention can transform a complex non-convex optimization problem into a convex optimization problem that is easy to iteratively solve, further improving the target detection performance of the radar system.

Description

Technical Field

[0001] The present invention relates to the technical field of radar waveform power spectrum processing, and in particular to a radar waveform power spectrum processing method and device based on Cauchy-Schwarz divergence. Background Art

[0002] As electromagnetic environments become increasingly complex, relying solely on adaptive processing at the radar receiver end is reaching its performance bottleneck. Therefore, leveraging the capabilities of the radar system's transmitter to design transmit waveforms and improve the system's adaptability to the external environment has become a key topic in modern intelligent radar research. In traditional operating modes, radar systems typically maintain fixed transmit waveforms and transceiver modes, operating in an open-loop state. This lacks environmental awareness and prevents the effective use of the transmitter's degrees of freedom to optimize performance. Compared to traditional radars, cognitive radars possess closed-loop processing capabilities. They can adaptively design transmit waveforms based on target information, environmental conditions, and other factors to adapt to varying operating environments, thereby reducing negative environmental impacts and improving radar system performance. Appropriate transmit waveform design enables radar systems to maintain stable performance in complex environments, thereby improving detection capabilities and overall operational efficiency.

[0003] Currently, when designing radar transmit waveform energy spectra in clutter environments, waveform optimization design criteria are typically employed to adjust the transmitter waveform based on target and environmental information. Designing a transmit waveform that matches the environment, thereby improving radar target detection performance, has become a core issue in cognitive radar system detection waveform design. Traditional waveform optimization criteria primarily fall into two categories: maximizing the signal-to-noise ratio (SNR) criterion, which improves target detection performance by increasing the SNR of the system output; and maximizing the relative entropy criterion, which aims to enhance target detection in clutter environments by maximizing the relative entropy between probability density functions in binary hypothesis tests. However, these methods typically focus on improving target detection performance while failing to fully consider the system's false alarm suppression. From the perspective of radar system robustness, to prevent false alarms, the system must simultaneously improve target detection probability while ensuring low false alarm performance. In other words, when optimizing the radar waveform, it is crucial not only to enhance target signal detectability but also to control the false alarm rate to avoid excessive false alarms.

[0004] Therefore, in waveform design, how to balance the relationship between detection performance and false alarm suppression has become an important issue that needs to be solved urgently in cognitive radar waveform design. Summary of the Invention

[0005] To this end, the present invention provides a radar waveform power spectrum processing method and device based on Cauchy-Schwarz divergence. By using the Cauchy-Schwarz divergence between the probability density functions of two hypotheses to be tested as a criterion, a waveform optimization method that can balance the missed detection probability and the false alarm probability under energy constraints is constructed. This solves the problem that traditional single-criterion optimization methods are difficult to achieve the above-mentioned two probability trade-offs. In addition, by constructing a proxy function of the optimization criterion, the solution process can be simplified, and a complex non-convex optimization problem can be transformed into a convex optimization problem that is easy to solve iteratively, thereby further improving the target detection performance of the radar system.

[0006] To achieve the above object, the present invention provides the following technical solution: a radar waveform power spectrum processing method based on Cauchy-Schwarz divergence, comprising:

[0007] Set the initial parameters of the radar and complete the initialization of the radar parameters;

[0008] According to the radar echo data of the clutter signal, the N×N dimensional clutter power spectrum and the clutter frequency domain covariance are estimated; according to the radar echo data of the target signal, the N×N dimensional target power spectrum and the target frequency domain covariance are estimated;

[0009] Determine a first matrix and a second matrix according to a power spectrum of set noise and a noise frequency domain covariance;

[0010] An initial reference waveform power spectrum is iteratively optimized according to the target frequency domain covariance, the clutter frequency domain covariance, the noise frequency domain covariance, the first matrix, and the second matrix to determine the radar waveform power spectrum under the Cauchy-Schwarz divergence criterion.

[0011] As a preferred solution of the radar waveform power spectrum processing method based on Cauchy-Schwarz divergence, in the process of setting the initial parameters of the radar, the set initial parameters include: the total energy of the radar transmission waveform, the initial reference waveform power spectrum and the number of frequency points in the working frequency band.

[0012] As a preferred solution of the radar waveform power spectrum processing method based on Cauchy-Schwarz divergence, the expression of the first matrix is:

[0013] C1=R X +2R C

[0014] Where C1 is the first matrix; R X is the target frequency domain covariance; R C is the clutter frequency domain covariance;

[0015] The expression of the second matrix is:

[0016] C2=R X +RC

[0017] Where C2 is the second matrix.

[0018] As a preferred solution of the radar waveform power spectrum processing method based on Cauchy-Schwarz divergence, in the process of iteratively optimizing the initial reference waveform power spectrum, the first optimization objective function expression is:

[0019]

[0020] Where, I N is an N×N dimensional unit matrix; det(·) and tr(·) are the determinant operator and trace operator of the matrix respectively; log(·) represents the logarithm operator; (·) H is the conjugate transpose operator; E s is the total energy of the preset transmission waveform; R W is the noise frequency domain covariance; S = diag(s) is the Toeplitz matrix of the transmitted waveform power spectrum s, where diag(·) is the diagonal matrix construction operator.

[0021] As a preferred solution of the radar waveform power spectrum processing method based on Cauchy-Schwarz divergence, the steps of iteratively optimizing the initial reference waveform power spectrum are:

[0022] Set the initial number of iterations and the maximum number of iterations;

[0023] Calculate a first gradient auxiliary matrix according to the target frequency domain covariance, the clutter frequency domain covariance, the noise frequency domain covariance, and the first matrix, and divide the first gradient auxiliary matrix into four N×N dimensional block sub-matrices;

[0024] Obtaining a second gradient auxiliary matrix by calculation according to the target frequency domain covariance, the clutter frequency domain covariance, the noise frequency domain covariance, and the second matrix;

[0025] Calculating a third gradient auxiliary matrix according to the target frequency domain covariance, the clutter frequency domain covariance, and the noise frequency domain covariance;

[0026] Obtaining a third matrix and a first auxiliary vector of a k-th iteration by calculation according to the first gradient auxiliary matrix, the second gradient auxiliary matrix, the third gradient auxiliary matrix, the first matrix, and the noise frequency domain covariance;

[0027] Calculate the Lagrange multiplier and the radar transmit waveform power spectrum after the kth iteration according to the third matrix, the first auxiliary vector and the total energy of the radar transmit waveform;

[0028] Calculating an objective function residual value based on the radar transmit waveform power spectrum after the kth iteration and the radar transmit waveform power spectrum after the k-1th iteration;

[0029] The objective function residual value is judged. If the objective function residual value is less than a set threshold, the radar waveform power spectrum after the kth iteration is output, and the process ends. If the objective function residual value is not less than the set threshold, the first gradient auxiliary matrix is ​​recalculated.

[0030] The final radar waveform power spectrum is calculated based on the radar transmission waveform power spectrum after the kth iteration.

[0031] As a preferred solution of the radar waveform power spectrum processing method based on Cauchy-Schwarz divergence, in the process of calculating the residual value of the objective function, the second optimization objective function expression is:

[0032]

[0033] in,

[0034]

[0035] Where, represents the real part operator of a complex number; Λ (k) is the third matrix; ξ (k) is the first auxiliary vector; is the second gradient auxiliary matrix; is the third gradient auxiliary matrix; (·) -H is the conjugate transpose inverse operator; is the Kronecker product; vec(·) is the matrix vectorization operator; are all block sub-matrices of the first gradient auxiliary matrix;

[0036] The present invention also provides a radar waveform power spectrum processing device based on Cauchy-Schwarz divergence, based on the above radar waveform power spectrum processing method based on Cauchy-Schwarz divergence, comprising:

[0037] Radar parameter initialization module is used to set the initial parameters of the radar and complete the initialization of the radar parameters;

[0038] The power spectrum and frequency domain covariance acquisition module is used to estimate the N×N dimensional clutter power spectrum and clutter frequency domain covariance based on the radar echo data of the clutter signal; and to estimate the N×N dimensional target power spectrum and target frequency domain covariance based on the radar echo data of the target signal;

[0039] A first matrix and second matrix acquisition module, configured to determine the first matrix and the second matrix according to a power spectrum of set noise and a noise frequency domain covariance;

[0040] The waveform power spectrum iterative optimization module is used to iteratively optimize the initial reference waveform power spectrum based on the target frequency domain covariance, the clutter frequency domain covariance, the noise frequency domain covariance, the first matrix and the second matrix to determine the radar waveform power spectrum under the Cauchy-Schwarz divergence criterion.

[0041] As a preferred solution of the radar waveform power spectrum processing device based on Cauchy-Schwarz divergence, in the radar parameter initialization module, in the process of setting the initial parameters of the radar, the initial parameters include: the total energy of the radar transmission waveform, the initial reference waveform power spectrum and the number of frequency points in the working frequency band.

[0042] As a preferred solution of the radar waveform power spectrum processing device based on Cauchy-Schwarz divergence, in the first matrix and second matrix acquisition module, the expression of the first matrix is:

[0043] C1=R X +2R C

[0044] Where C1 is the first matrix; R X is the target frequency domain covariance; R C is the clutter frequency domain covariance;

[0045] The expression of the second matrix is:

[0046] C2=R X +R C

[0047] Where C2 is the second matrix.

[0048] As a preferred solution of the radar waveform power spectrum processing device based on Cauchy-Schwarz divergence, in the waveform power spectrum iterative optimization module, during the iterative optimization of the initial reference waveform power spectrum, the first optimization objective function expression is:

[0049]

[0050] Where, I N is an N×N dimensional unit matrix; det(·) and tr(·) are the determinant operator and trace operator of the matrix respectively; log(·) represents the logarithm operator; (·) H is the conjugate transpose operator; E s is the total energy of the preset transmission waveform; R W is the noise frequency domain covariance; S = diag(s) is the Toeplitz matrix of the transmitted waveform power spectrum s, where diag(·) is the diagonal matrix construction operator.

[0051] As a preferred solution of the radar waveform power spectrum processing device based on Cauchy-Schwarz divergence, in the waveform power spectrum iterative optimization module, the submodule for iteratively optimizing the initial reference waveform power spectrum includes:

[0052] The iteration number setting submodule is used to set the initial number of iterations and the maximum number of iterations;

[0053] A first gradient auxiliary matrix calculation submodule is configured to calculate a first gradient auxiliary matrix based on the target frequency domain covariance, the clutter frequency domain covariance, the noise frequency domain covariance, and the first matrix, and divide the first gradient auxiliary matrix into four N×N dimensional block sub-matrices;

[0054] A second gradient auxiliary matrix calculation submodule is configured to calculate a second gradient auxiliary matrix based on the target frequency domain covariance, the clutter frequency domain covariance, the noise frequency domain covariance, and the second matrix;

[0055] A third gradient auxiliary matrix calculation submodule is configured to calculate a third gradient auxiliary matrix based on the target frequency domain covariance, the clutter frequency domain covariance, and the noise frequency domain covariance;

[0056] A third matrix and first auxiliary vector calculation submodule, configured to calculate a third matrix and a first auxiliary vector of a k-th iteration based on the first gradient auxiliary matrix, the second gradient auxiliary matrix, the third gradient auxiliary matrix, the first matrix, and the noise frequency domain covariance;

[0057] a Lagrange multiplier and radar transmit waveform power spectrum calculation module, configured to calculate the Lagrange multiplier and the radar transmit waveform power spectrum after the kth iteration based on the third matrix, the first auxiliary vector, and the total energy of the radar transmit waveform;

[0058] An objective function residual value calculation submodule is used to calculate an objective function residual value based on the radar transmission waveform power spectrum after the kth iteration and the radar transmission waveform power spectrum after the k-1th iteration;

[0059] an objective function residual value judgment processing submodule, configured to judge the objective function residual value, and if the objective function residual value is less than a set threshold, output the radar waveform power spectrum after the kth iteration, and terminate; if the objective function residual value is not less than the set threshold, recalculate the first gradient auxiliary matrix;

[0060] The final radar waveform power spectrum calculation submodule is used to calculate and obtain the final radar waveform power spectrum based on the radar transmission waveform power spectrum after the kth iteration.

[0061] As a preferred solution of the radar waveform power spectrum processing device based on Cauchy-Schwarz divergence, in the objective function residual value calculation submodule of the waveform power spectrum iterative optimization module, in the process of calculating the objective function residual value, the second optimization objective function expression is:

[0062]

[0063] in,

[0064]

[0065] Where, represents the real part operator of a complex number; Λ (k) is the third matrix; ξ (k) is the first auxiliary vector; is the second gradient auxiliary matrix; is the third gradient auxiliary matrix; (·) -H is the conjugate transpose inverse operator; is the Kronecker product; vec(·) is the matrix vectorization operator; are all block sub-matrices of the first gradient auxiliary matrix.

[0066] The present invention has the following advantages: the present invention completes the initialization setting of radar parameters by setting initial parameters of the radar; estimates and obtains an N×N-dimensional clutter power spectrum and a clutter frequency domain covariance according to radar echo data of a clutter signal; estimates and obtains an N×N-dimensional target power spectrum and a target frequency domain covariance according to radar echo data of a target signal; determines a first matrix and a second matrix according to a power spectrum and a noise frequency domain covariance of a set noise; and iteratively optimizes an initial reference waveform power spectrum according to the target frequency domain covariance, the clutter frequency domain covariance, the noise frequency domain covariance, the first matrix, and the second matrix to determine a radar waveform power spectrum under a Cauchy-Schwarz divergence criterion. The steps of iteratively optimizing the power spectrum of the initial reference waveform are as follows: setting an initial number of iterations and a maximum number of iterations; calculating a first gradient auxiliary matrix according to the target frequency domain covariance, the clutter frequency domain covariance, the noise frequency domain covariance, and the first matrix, and dividing the first gradient auxiliary matrix into four N×N dimensional block sub-matrices; calculating a second gradient auxiliary matrix according to the target frequency domain covariance, the clutter frequency domain covariance, the noise frequency domain covariance, and the second matrix; calculating a third gradient auxiliary matrix according to the target frequency domain covariance, the clutter frequency domain covariance, and the noise frequency domain covariance; calculating a third gradient auxiliary matrix according to the first gradient auxiliary matrix, the second gradient auxiliary matrix, the third gradient auxiliary matrix, the first matrix, and the noise frequency domain covariance. The method comprises the following steps: calculating the frequency domain covariance, obtaining the third matrix and the first auxiliary vector of the k-th iteration; calculating the Lagrange multiplier and the radar transmit waveform power spectrum after the k-th iteration based on the third matrix, the first auxiliary vector and the total energy of the radar transmit waveform; calculating the objective function residual value based on the radar transmit waveform power spectrum after the k-th iteration and the radar transmit waveform power spectrum after the k-1-th iteration; judging the objective function residual value, and outputting the radar waveform power spectrum after the k-th iteration if the objective function residual value is less than a set threshold value, and terminating; recalculating the first gradient auxiliary matrix if the objective function residual value is not less than the set threshold value; and calculating the final radar waveform power spectrum based on the radar transmit waveform power spectrum after the k-th iteration. The present invention uses the Cauchy-Schwarz divergence between the probability density functions of two hypotheses to be tested as a criterion to construct a waveform optimization method that can balance the probability of missed detection and the probability of false alarm under energy constraints. This solves the problem that traditional single-criterion optimization methods are difficult to achieve the above-mentioned two probability trade-offs. In addition, by constructing a proxy function of the optimization criterion, the solution process can be simplified, and the complex non-convex optimization problem can be transformed into a convex optimization problem that is easy to solve iteratively, further achieving the improvement of the target detection performance of the radar system. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] To more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for the embodiments or the description of the prior art. Obviously, the drawings described below are merely exemplary, and those skilled in the art can, without inventive effort, derive other implementation drawings based on the provided drawings.

[0068] The structures, proportions, sizes, etc. illustrated in this specification are intended solely to complement the contents disclosed herein and to facilitate understanding and reading by persons skilled in the art. They are not intended to limit the conditions under which the present invention may be implemented and therefore have no substantive technical significance. Any structural modifications, changes in proportions, or adjustments in sizes, without affecting the efficacy and objectives of the present invention, shall remain within the scope of the technical contents disclosed herein.

[0069] Figure 1 This is a flow chart of a radar waveform power spectrum processing method based on Cauchy-Schwarz divergence provided in Example 1 of the present invention;

[0070] Figure 2 A schematic diagram of radar transmission and reception in which the extended target model is used in a possible embodiment provided in Example 1 of the present invention while taking into account signal-related clutter and signal-independent noise;

[0071] Figure 3 A schematic diagram comparing the energy spectra of the present invention with those of the traditional signal-to-noise ratio criterion, relative entropy criterion, and mutual information criterion in a possible embodiment provided in Example 1 of the present invention;

[0072] Figure 4 A schematic diagram of a receiver operating characteristic curve of an energy spectrum of the present invention in a possible embodiment provided in Embodiment 1 of the present invention;

[0073] Figure 5 This is a schematic diagram of how the target detection probability of the present invention varies with transmit power in a possible embodiment provided in Example 1 of the present invention;

[0074] Figure 6 Schematic diagram of the architecture of a radar waveform power spectrum processing device based on Cauchy-Schwarz divergence provided in Example 2 of the present invention. DETAILED DESCRIPTION

[0075] The following describes the implementation of the present invention using specific embodiments. Those skilled in the art will readily understand the other advantages and benefits of the present invention from the disclosure herein. Obviously, the embodiments described are only a portion of the present invention, not all of it. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without inventive effort are intended to fall within the scope of protection of the present invention.

[0076] Example 1

[0077] See also Figure 1 Embodiment 1 of the present invention provides a radar waveform power spectrum processing method based on Cauchy-Schwarz divergence, comprising the following steps:

[0078] S1. Set the initial parameters of the radar to complete the initialization of the radar parameters;

[0079] S2. Estimate and obtain an N×N-dimensional clutter power spectrum and clutter frequency domain covariance based on the radar echo data of the clutter signal; and estimate and obtain an N×N-dimensional target power spectrum and target frequency domain covariance based on the radar echo data of the target signal;

[0080] S3. Determine a first matrix and a second matrix according to a power spectrum of the set noise and a noise frequency domain covariance;

[0081] S4. Iteratively optimize the initial reference waveform power spectrum based on the target frequency domain covariance, the clutter frequency domain covariance, the noise frequency domain covariance, the first matrix, and the second matrix to determine the radar waveform power spectrum under the Cauchy-Schwarz divergence criterion.

[0082] In this embodiment, in step S1, initial parameters of the radar are set to complete the initialization of the radar parameters;

[0083] Specifically, the total energy of the radar transmission waveform, the initial reference waveform power spectrum, and the number of working frequency bands are set; the total energy of the radar transmission waveform is E s , should be set according to hardware conditions; the initial reference waveform power spectrum S0 can be set to a commonly used waveform power spectrum, which can be but not limited to a linear frequency modulation signal; the number of frequency points in the working frequency band is N.

[0084] In this embodiment, in step S2, based on the radar echo data of the clutter signal, an N×N-dimensional clutter power spectrum and a clutter frequency domain covariance are estimated; based on the radar echo data of the target signal, an N×N-dimensional target power spectrum and a target frequency domain covariance are estimated;

[0085] Specifically, according to the radar echo data of the clutter signal, the N×N dimensional clutter power spectrum and the clutter frequency domain covariance R are estimated. CAccording to the radar echo data of the target signal, the N×N-dimensional target power spectrum and target frequency domain covariance R are estimated. X ;

[0086] The radar echo data can be obtained by using previously collected observation data or by accessing the environmental database. The corresponding frequency domain covariance matrix is ​​calculated by the power spectrum estimation method.

[0087] In this embodiment, in step S3, the first matrix and the second matrix are determined according to the power spectrum and the noise frequency domain covariance of the set noise;

[0088] Specifically, the expression of the first matrix is:

[0089] C1=R X +2R C

[0090] Where C1 is the first matrix; R X is the target frequency domain covariance; R C is the clutter frequency domain covariance;

[0091] The expression of the second matrix is:

[0092] C2=R X +R C

[0093] Where C2 is the second matrix.

[0094] In this embodiment, in step S4, the initial reference waveform power spectrum is iteratively optimized based on the target frequency domain covariance, the clutter frequency domain covariance, the noise frequency domain covariance, the first matrix, and the second matrix to determine the radar waveform power spectrum under the Cauchy-Schwarz divergence criterion.

[0095] Specifically, in the process of iteratively optimizing the initial reference waveform power spectrum, the first optimization objective function expression is:

[0096]

[0097] Where, I N is an N×N dimensional unit matrix; det(·) and tr(·) are the determinant operator and trace operator of the matrix respectively; log(·) represents the logarithm operator; (·) H is the conjugate transpose operator; E s is the total energy of the preset transmission waveform; R W is the noise frequency domain covariance; S = diag(s) is the Toeplitz matrix of the transmitted waveform power spectrum s, where diag(·) is the diagonal matrix construction operator.

[0098] The steps of iteratively optimizing the power spectrum of the initial reference waveform are as follows:

[0099] S41, setting the initial number of iterations and the maximum number of iterations;

[0100] Specifically, set the number of iterations k = 1, and the maximum number of iterations K max ;

[0101] S42: Calculate a first gradient auxiliary matrix based on the target frequency domain covariance, the clutter frequency domain covariance, the noise frequency domain covariance, and the first matrix, and divide the first gradient auxiliary matrix into four N×N dimensional block sub-matrices;

[0102] Specifically, the first gradient auxiliary matrix is ​​calculated based on the target frequency domain covariance, the clutter frequency domain covariance, the noise frequency domain covariance, and the first matrix.

[0103]

[0104] Where, E=[I N ,O N ], and Π k for:

[0105]

[0106] The first gradient auxiliary matrix is ​​divided into four N×N dimensional block sub-matrices Right now:

[0107]

[0108] Where,

[0109] S43, calculating a second gradient auxiliary matrix according to the target frequency domain covariance, the clutter frequency domain covariance, the noise frequency domain covariance, and the second matrix;

[0110] Among them, the second gradient auxiliary matrix The calculation formula is:

[0111]

[0112] S44, calculating and obtaining a third gradient auxiliary matrix according to the target frequency domain covariance, the clutter frequency domain covariance, and the noise frequency domain covariance;

[0113] Among them, the third gradient auxiliary matrix The calculation formula is:

[0114]

[0115] S45. Calculate and obtain a third matrix and a first auxiliary vector of the kth iteration according to the first gradient auxiliary matrix, the second gradient auxiliary matrix, the third gradient auxiliary matrix, the first matrix, and the noise frequency domain covariance;

[0116] Among them, the third matrix Λ (k) The calculation formula is:

[0117]

[0118] Where, is the Kronecker product;

[0119] The first auxiliary vector ξ (k) The calculation formula is:

[0120]

[0121] Where vec(·) is the matrix vectorization operator.

[0122] S46. Calculate the Lagrange multiplier and the radar transmit waveform power spectrum after the kth iteration based on the third matrix, the first auxiliary vector, and the total energy of the radar transmit waveform;

[0123] Specifically, according to the third matrix Λ (k) , the first auxiliary vector ξ (k) and the total energy E of the radar emission waveform s , calculate the Lagrange multiplier λ after the kth iteration ( k ) and radar emission waveform power spectrum s( k ).

[0124] Among them, the second optimization objective function expression is:

[0125]

[0126] Where, Represents the complex real part operator.

[0127] The Lagrange multiplier method is used to obtain the radar waveform power spectrum s of the kth iteration ( k ):

[0128]

[0129] Where λ (k) It is an equation The solution of , and satisfy λ (k) >0.

[0130] S47. Calculate an objective function residual value based on the radar transmit waveform power spectrum after the kth iteration and the radar transmit waveform power spectrum after the k-1th iteration;

[0131] Specifically, according to the radar transmission waveform power spectrum s after the kth iteration (k) and the radar emission waveform power spectrum s after the k-1th iteration (k-1) , calculate and obtain the residual value of the objective function;

[0132] S48, judging the residual value of the objective function; if the residual value of the objective function is less than a set threshold, outputting the radar waveform power spectrum after the kth iteration, and terminating; if the residual value of the objective function is not less than the set threshold, recalculating the first gradient auxiliary matrix;

[0133] Specifically, the residual value of the objective function is judged. If the residual value of the objective function is less than the set threshold, the radar waveform power spectrum s after the kth iteration is output. (k) , end; if the residual value of the objective function is not less than the set threshold, proceed to step S42;

[0134] S49. Calculate and obtain a final radar waveform power spectrum based on the radar transmission waveform power spectrum after the kth iteration.

[0135] Specifically, according to the radar transmission waveform power spectrum s after the kth iteration (k) , calculate and obtain the final radar waveform power spectrum s opt .

[0136] In one possible embodiment, an example of radar waveform power spectrum processing for providing an extended target model is as follows:

[0137] The schematic diagram of radar transmission and reception in the extended target model considering signal-dependent clutter and signal-independent noise is as follows: Figure 2 As shown;

[0138] The comparison results of radar waveform power spectrum obtained by the present invention and the radar waveform power spectrum design method based on signal-to-noise ratio, mutual information and relative entropy under the same energy constraint conditions are as follows: Figure 3 Compared with the method based on signal-to-noise ratio, the waveform power spectrum obtained based on relative entropy and the design of the present invention can distribute the waveform energy to the frequencies where the target response is stronger than the clutter.

[0139] The receiver operating characteristic curves obtained by the present invention and the radar waveform power spectrum design methods based on signal-to-noise ratio, mutual information, and relative entropy under the same energy constraint conditions are as follows: Figure 4 As shown. Figure 4It can be seen that under the same false alarm probability condition, the waveform designed by the present invention has a higher detection probability than the waveforms obtained based on the signal-to-noise ratio and the relative entropy method, and can better detect the target.

[0140] The relationship curve between the total energy of the transmitted waveform and the target detection probability obtained by the radar waveform power spectrum design method based on the signal-to-noise ratio, mutual information and relative entropy under the same false alarm probability constraint condition is shown as follows: Figure 5 As shown. Figure 5 It can be seen that the waveform designed by the present invention has a higher detection probability than the waveforms obtained based on the signal-to-noise ratio and relative entropy methods under the same transmission energy conditions. That is, to achieve the same detection probability, the demand for transmission energy can be reduced.

[0141] In summary, the present invention completes the initialization setting of radar parameters by setting initial parameters of the radar; estimates and obtains an N×N-dimensional clutter power spectrum and a clutter frequency domain covariance based on radar echo data of a clutter signal; estimates and obtains an N×N-dimensional target power spectrum and a target frequency domain covariance based on radar echo data of a target signal; determines a first matrix and a second matrix based on a power spectrum and a noise frequency domain covariance of a set noise; and iteratively optimizes an initial reference waveform power spectrum based on the target frequency domain covariance, the clutter frequency domain covariance, the noise frequency domain covariance, the first matrix, and the second matrix to determine a radar waveform power spectrum under a Cauchy-Schwarz divergence criterion. The steps of iteratively optimizing the power spectrum of the initial reference waveform are as follows: setting an initial number of iterations and a maximum number of iterations; calculating a first gradient auxiliary matrix according to the target frequency domain covariance, the clutter frequency domain covariance, the noise frequency domain covariance, and the first matrix, and dividing the first gradient auxiliary matrix into four N×N dimensional block sub-matrices; calculating a second gradient auxiliary matrix according to the target frequency domain covariance, the clutter frequency domain covariance, the noise frequency domain covariance, and the second matrix; calculating a third gradient auxiliary matrix according to the target frequency domain covariance, the clutter frequency domain covariance, and the noise frequency domain covariance; calculating a third gradient auxiliary matrix according to the first gradient auxiliary matrix, the second gradient auxiliary matrix, the third gradient auxiliary matrix, the first matrix, and the noise frequency domain covariance. The method comprises the following steps: calculating the frequency domain covariance, obtaining the third matrix and the first auxiliary vector of the k-th iteration; calculating the Lagrange multiplier and the radar transmit waveform power spectrum after the k-th iteration based on the third matrix, the first auxiliary vector and the total energy of the radar transmit waveform; calculating the objective function residual value based on the radar transmit waveform power spectrum after the k-th iteration and the radar transmit waveform power spectrum after the k-1-th iteration; judging the objective function residual value, and outputting the radar waveform power spectrum after the k-th iteration if the objective function residual value is less than a set threshold value, and terminating; recalculating the first gradient auxiliary matrix if the objective function residual value is not less than the set threshold value; and calculating the final radar waveform power spectrum based on the radar transmit waveform power spectrum after the k-th iteration. The present invention uses the Cauchy-Schwarz divergence between the probability density functions of two hypotheses to be tested as a criterion to construct a waveform optimization method that can balance the probability of missed detection and the probability of false alarm under energy constraints. This solves the problem that traditional single-criterion optimization methods are difficult to achieve the above-mentioned two probability trade-offs. In addition, by constructing a proxy function of the optimization criterion, the solution process can be simplified, and the complex non-convex optimization problem can be transformed into a convex optimization problem that is easy to solve iteratively, further achieving the improvement of the target detection performance of the radar system.

[0142] It should be noted that the method of the embodiments of the present disclosure can be performed by a single device, such as a computer or server. The method of the embodiments of the present disclosure can also be applied in a distributed scenario, where multiple devices cooperate to perform the method. In such a distributed scenario, one of the multiple devices may only perform one or more steps of the method of the embodiments of the present disclosure, and the multiple devices will interact with each other to complete the method.

[0143] It should be noted that the above description is limited to some embodiments of the present disclosure. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recited in the claims may be performed in an order different from that described in the above embodiments and still achieve the desired results. Furthermore, the processes depicted in the accompanying drawings do not necessarily require the specific order or sequential order shown to achieve the desired results. In certain embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0144] Example 2

[0145] See also Figure 6 Embodiment 2 of the present invention further provides a radar waveform power spectrum processing device based on Cauchy-Schwarz divergence, comprising:

[0146] Radar parameter initialization module 001 is used to set the initial parameters of the radar and complete the initialization of the radar parameters;

[0147] The power spectrum and frequency domain covariance acquisition module 002 is used to estimate and obtain the N×N dimensional clutter power spectrum and clutter frequency domain covariance based on the radar echo data of the clutter signal; and estimate and obtain the N×N dimensional target power spectrum and target frequency domain covariance based on the radar echo data of the target signal;

[0148] A first matrix and second matrix acquisition module 003 is used to determine the first matrix and the second matrix according to the power spectrum and noise frequency domain covariance of the set noise;

[0149] The waveform power spectrum iterative optimization module 004 is used to iteratively optimize the initial reference waveform power spectrum based on the target frequency domain covariance, the clutter frequency domain covariance, the noise frequency domain covariance, the first matrix and the second matrix to determine the radar waveform power spectrum under the Cauchy-Schwarz divergence criterion.

[0150] In this embodiment, in the radar parameter initialization module 001, in the process of setting the initial parameters of the radar, the initial parameters include: the total energy of the radar transmission waveform, the initial reference waveform power spectrum and the number of frequency points in the working frequency band.

[0151] In this embodiment, in the first matrix and second matrix acquisition module 003, the expression of the first matrix is:

[0152] C1=R X +2R C

[0153] Where C1 is the first matrix; R X is the target frequency domain covariance; R C is the clutter frequency domain covariance;

[0154] The expression of the second matrix is:

[0155] C2=R X +R C

[0156] Where C2 is the second matrix.

[0157] In this embodiment, in the waveform power spectrum iterative optimization module 004, during the iterative optimization of the initial reference waveform power spectrum, the first optimization objective function expression is:

[0158]

[0159] Where, I N is an N×N dimensional unit matrix; det(·) and tr(·) are the determinant operator and trace operator of the matrix respectively; log(·) represents the logarithm operator; (·) H is the conjugate transpose operator; E s is the total energy of the preset transmission waveform; R W is the noise frequency domain covariance; S = diag(s) is the Toeplitz matrix of the transmitted waveform power spectrum s, where diag(·) is the diagonal matrix construction operator.

[0160] In this embodiment, in the waveform power spectrum iterative optimization module 004, the submodule for iteratively optimizing the initial reference waveform power spectrum includes:

[0161] Iteration number setting submodule 041 is used to set the initial number of iterations and the maximum number of iterations;

[0162] A first gradient auxiliary matrix calculation submodule 042 is configured to calculate a first gradient auxiliary matrix based on the target frequency domain covariance, the clutter frequency domain covariance, the noise frequency domain covariance, and the first matrix, and divide the first gradient auxiliary matrix into four N×N dimensional block sub-matrices;

[0163] A second gradient auxiliary matrix calculation submodule 043 is configured to calculate a second gradient auxiliary matrix based on the target frequency domain covariance, the clutter frequency domain covariance, the noise frequency domain covariance, and the second matrix;

[0164] A third gradient auxiliary matrix calculation submodule 044 is configured to calculate a third gradient auxiliary matrix based on the target frequency domain covariance, the clutter frequency domain covariance, and the noise frequency domain covariance;

[0165] A third matrix and first auxiliary vector calculation submodule 045 is configured to calculate a third matrix and a first auxiliary vector of the kth iteration based on the first gradient auxiliary matrix, the second gradient auxiliary matrix, the third gradient auxiliary matrix, the first matrix, and the noise frequency domain covariance;

[0166] a Lagrange multiplier and radar transmit waveform power spectrum calculation module 046, configured to calculate the Lagrange multiplier and the radar transmit waveform power spectrum after the kth iteration based on the third matrix, the first auxiliary vector, and the total energy of the radar transmit waveform;

[0167] The objective function residual value calculation submodule 047 is used to calculate the objective function residual value based on the radar transmission waveform power spectrum after the kth iteration and the radar transmission waveform power spectrum after the k-1th iteration;

[0168] The objective function residual value judgment processing submodule 048 is used to judge the objective function residual value. If the objective function residual value is less than a set threshold, the radar waveform power spectrum after the kth iteration is output and the process ends. If the objective function residual value is not less than the set threshold, the first gradient auxiliary matrix is ​​recalculated.

[0169] The final radar waveform power spectrum calculation submodule 049 is used to calculate and obtain the final radar waveform power spectrum according to the radar transmission waveform power spectrum after the kth iteration.

[0170] In this embodiment, in the objective function residual value calculation submodule 047 of the waveform power spectrum iterative optimization module 004, during the process of calculating the objective function residual value, the second optimization objective function expression is:

[0171]

[0172] in,

[0173]

[0174] Where, represents the real part operator of a complex number; Λ (k) is the third matrix; ξ (k)is the first auxiliary vector; is the second gradient auxiliary matrix; is the third gradient auxiliary matrix; (·) -H is the conjugate transpose inverse operator; is the Kronecker product; vec(·) is the matrix vectorization operator; are all block sub-matrices of the first gradient auxiliary matrix;

[0175] It should be noted that the information interaction, execution process, etc. between the modules of the above-mentioned system are based on the same concept as the method embodiment in Example 1 of the present application, and the technical effects they bring are the same as those of the method embodiment of the present application. For specific contents, please refer to the description in the method embodiment shown above in the present application, and no further details will be given here.

[0176] Example 3

[0177] Embodiment 3 of the present invention provides a non-transitory computer-readable storage medium, wherein the computer-readable storage medium stores program code for a radar waveform power spectrum processing method based on Cauchy-Schwarz divergence. The program code includes instructions for executing the radar waveform power spectrum processing method based on Cauchy-Schwarz divergence of embodiment 1 or any possible implementation thereof.

[0178] Computer-readable storage media can be any available medium that can be accessed by a computer or a data storage device such as a server or data center that includes one or more available media. The available media can be magnetic media (e.g., floppy disks, hard disks, magnetic tapes), optical media (e.g., DVDs), or semiconductor media (e.g., solid-state drives (SSDs)).

[0179] Example 4

[0180] Embodiment 4 of the present invention provides an electronic device, including: a memory and a processor;

[0181] The processor and the memory communicate with each other via a bus; the memory stores program instructions executable by the processor, and the processor calls the program instructions to execute the radar waveform power spectrum processing method based on Cauchy-Schwarz divergence of Example 1 or any possible implementation thereof.

[0182] Specifically, the processor can be implemented by hardware or by software. When implemented by hardware, the processor can be a logic circuit, an integrated circuit, etc.; when implemented by software, the processor can be a general-purpose processor, which is implemented by reading software code stored in a memory. The memory can be integrated into the processor or located outside the processor and exist independently.

[0183] In the above embodiments, it can be implemented in whole or in part by software, hardware, firmware or any combination thereof. When implemented using software, it can be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, the process or function described in the embodiment of the present invention is generated in whole or in part. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable systems. The computer instructions can be stored in a computer-readable storage medium, or transmitted from one computer-readable storage medium to another computer-readable storage medium. For example, the computer instructions can be transmitted from a website, computer, server or data center to another website, computer, server or data center via a wired (e.g., coaxial cable, optical fiber, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) mode.

[0184] Obviously, those skilled in the art will appreciate that the various modules or steps of the present invention described above can be implemented using a general-purpose computing system. They can be centralized on a single computing system or distributed across a network of multiple computing systems. Alternatively, they can be implemented using program code executable by a computing system, and thus, they can be stored in a storage system and executed by the computing system. In some cases, the steps shown or described herein can be performed in a different order than that shown, or they can be fabricated into separate integrated circuit modules, or multiple modules or steps can be fabricated into a single integrated circuit module. Thus, the present invention is not limited to any particular combination of hardware and software.

[0185] Although the present invention has been described in detail above using general descriptions and specific embodiments, it will be apparent to those skilled in the art that modifications and improvements may be made thereto. Therefore, such modifications and improvements, without departing from the spirit of the present invention, are intended to be within the scope of protection claimed herein.

Claims

1. A radar waveform power spectrum processing method based on Cauchy-Schwarz divergence, characterized in that: include: Set the initial parameters of the radar and complete the initialization of the radar parameters; According to the radar echo data of the clutter signal, the N×N dimensional clutter power spectrum and the clutter frequency domain covariance are estimated; according to the radar echo data of the target signal, the N×N dimensional target power spectrum and the target frequency domain covariance are estimated; Determine a first matrix and a second matrix according to a power spectrum of set noise and a noise frequency domain covariance; Iteratively optimize the initial reference waveform power spectrum according to the target frequency domain covariance, the clutter frequency domain covariance, the noise frequency domain covariance, the first matrix, and the second matrix to determine the radar waveform power spectrum under the Cauchy-Schwarz divergence criterion; In the process of setting the initial parameters of the radar, the initial parameters include: the total energy of the radar transmission waveform, the power spectrum of the initial reference waveform and the number of frequency points in the working frequency band; The expression of the first matrix is: C1=R X +2R C Where C1 is the first matrix; R X is the target frequency domain covariance; R C is the clutter frequency domain covariance; The expression of the second matrix is: C2=R X +R C Where C2 is the second matrix.

2. The radar waveform power spectrum processing method based on Cauchy-Schwarz divergence according to claim 1, characterized in that: In the process of iteratively optimizing the initial reference waveform power spectrum, the first optimization objective function expression is: Where, I N is an N×N dimensional unit matrix; det(·) and tr(·) are the determinant operator and trace operator of the matrix respectively; log(·) represents the logarithm operator; (·) H is the conjugate transpose operator; E s is the total energy of the preset transmission waveform; R W is the noise frequency domain covariance; S = diag(s) is the Toeplitz matrix of the transmitted waveform power spectrum s, where diag(·) is the diagonal matrix construction operator.

3. The radar waveform power spectrum processing method based on Cauchy-Schwarz divergence according to claim 2, characterized in that: The steps of iteratively optimizing the power spectrum of the initial reference waveform are: Set the initial number of iterations and the maximum number of iterations; Calculate a first gradient auxiliary matrix according to the target frequency domain covariance, the clutter frequency domain covariance, the noise frequency domain covariance, and the first matrix, and divide the first gradient auxiliary matrix into four N×N dimensional block sub-matrices; Obtaining a second gradient auxiliary matrix by calculation according to the target frequency domain covariance, the clutter frequency domain covariance, the noise frequency domain covariance, and the second matrix; Calculating a third gradient auxiliary matrix according to the target frequency domain covariance, the clutter frequency domain covariance, and the noise frequency domain covariance; Obtaining a third matrix and a first auxiliary vector of a k-th iteration by calculation according to the first gradient auxiliary matrix, the second gradient auxiliary matrix, the third gradient auxiliary matrix, the first matrix, and the noise frequency domain covariance; Calculate the Lagrange multiplier and the radar transmit waveform power spectrum after the kth iteration according to the third matrix, the first auxiliary vector and the total energy of the radar transmit waveform; Calculating an objective function residual value based on the radar transmit waveform power spectrum after the kth iteration and the radar transmit waveform power spectrum after the k-1th iteration; The objective function residual value is judged. If the objective function residual value is less than a set threshold, the radar waveform power spectrum after the kth iteration is output, and the process ends. If the objective function residual value is not less than the set threshold, the first gradient auxiliary matrix is ​​recalculated. The final radar waveform power spectrum is calculated based on the radar transmission waveform power spectrum after the kth iteration.

4. The radar waveform power spectrum processing method based on Cauchy-Schwarz divergence according to claim 3, characterized in that: In the process of calculating the residual value of the objective function, the second optimization objective function expression is: in, Where, represents the real part operator of a complex number; Λ (k) is the third matrix; ξ (k) is the first auxiliary vector; is the second gradient auxiliary matrix; is the third gradient auxiliary matrix; (·) -H is the conjugate transpose inverse operator; is the Kronecker product; vec(·) is the matrix vectorization operator; are all block sub-matrices of the first gradient auxiliary matrix.

5. A radar waveform power spectrum processing device based on Cauchy-Schwarz divergence, adopting the radar waveform power spectrum processing method based on Cauchy-Schwarz divergence according to any one of claims 1 to 4, characterized in that: include: Radar parameter initialization module is used to set the initial parameters of the radar and complete the initialization of the radar parameters; The power spectrum and frequency domain covariance acquisition module is used to estimate the N×N dimensional clutter power spectrum and clutter frequency domain covariance based on the radar echo data of the clutter signal; and to estimate the N×N dimensional target power spectrum and target frequency domain covariance based on the radar echo data of the target signal; A first matrix and second matrix acquisition module, configured to determine the first matrix and the second matrix according to a power spectrum of set noise and a noise frequency domain covariance; The waveform power spectrum iterative optimization module is used to iteratively optimize the initial reference waveform power spectrum based on the target frequency domain covariance, the clutter frequency domain covariance, the noise frequency domain covariance, the first matrix and the second matrix to determine the radar waveform power spectrum under the Cauchy-Schwarz divergence criterion.

6. The radar waveform power spectrum processing device based on Cauchy-Schwarz divergence according to claim 5, characterized in that: In the radar parameter initialization module, in the process of setting the initial parameters of the radar, the initial parameters include: total energy of the radar transmission waveform, initial reference waveform power spectrum and number of working frequency band frequencies.

7. The radar waveform power spectrum processing device based on Cauchy-Schwarz divergence according to claim 6, characterized in that: In the first matrix and second matrix acquisition module, the expression of the first matrix is: C1=R X +2R C Where C1 is the first matrix; R X is the target frequency domain covariance; R C is the clutter frequency domain covariance; The expression of the second matrix is: C2=R X +R C Where C2 is the second matrix.

8. The radar waveform power spectrum processing device based on Cauchy-Schwarz divergence according to claim 7, characterized in that: In the waveform power spectrum iterative optimization module, the submodule for iteratively optimizing the initial reference waveform power spectrum includes: The iteration number setting submodule is used to set the initial number of iterations and the maximum number of iterations; A first gradient auxiliary matrix calculation submodule is configured to calculate a first gradient auxiliary matrix based on the target frequency domain covariance, the clutter frequency domain covariance, the noise frequency domain covariance, and the first matrix, and divide the first gradient auxiliary matrix into four N×N dimensional block sub-matrices; A second gradient auxiliary matrix calculation submodule is configured to calculate a second gradient auxiliary matrix based on the target frequency domain covariance, the clutter frequency domain covariance, the noise frequency domain covariance, and the second matrix; A third gradient auxiliary matrix calculation submodule is configured to calculate a third gradient auxiliary matrix based on the target frequency domain covariance, the clutter frequency domain covariance, and the noise frequency domain covariance; A third matrix and first auxiliary vector calculation submodule, configured to calculate a third matrix and a first auxiliary vector of a k-th iteration based on the first gradient auxiliary matrix, the second gradient auxiliary matrix, the third gradient auxiliary matrix, the first matrix, and the noise frequency domain covariance; a Lagrange multiplier and radar transmit waveform power spectrum calculation module, configured to calculate the Lagrange multiplier and the radar transmit waveform power spectrum after the kth iteration based on the third matrix, the first auxiliary vector, and the total energy of the radar transmit waveform; An objective function residual value calculation submodule is used to calculate an objective function residual value based on the radar transmission waveform power spectrum after the kth iteration and the radar transmission waveform power spectrum after the k-1th iteration; an objective function residual value judgment processing submodule, configured to judge the objective function residual value, and if the objective function residual value is less than a set threshold, output the radar waveform power spectrum after the kth iteration, and terminate; if the objective function residual value is not less than the set threshold, recalculate the first gradient auxiliary matrix; The final radar waveform power spectrum calculation submodule is used to calculate and obtain the final radar waveform power spectrum based on the radar transmission waveform power spectrum after the kth iteration.

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