Non-contiguous spectrum signal spectrum shaping method with low sidelobes

Abstract

The application discloses a low-integral sidelobe non-continuous spectrum signal spectrum shaping method, and belongs to the field of radar waveform design.The present application aims at the problem that the existing spectrum shaping method does not comprehensively consider the WISL and SINR performance, and the obtained transmitting signal has defects.The application comprises the following steps: expressing the signal-to-interference-and-noise ratio SINR and the weighted integrated sidelobe level WISL of the transmitting signal through a power spectrum; setting a weighting value, weighting the signal-to-interference-and-noise ratio SINR and the weighted integrated sidelobe level WISL to obtain a target function; combining the power spectrum energy constraint and the stopband position constraint to establish a spectrum shaping optimization problem; solving the spectrum shaping optimization problem under different weighting values to obtain the optimal power spectrum under different weighting values; calculating the signal-to-interference-and-noise ratio SINR and the weighted integrated sidelobe level WISL corresponding to the optimal power spectrum under different weighting values to obtain a two-dimensional pareto curve of the SINR and the WISL; and selecting a target weighting value based on the two-dimensional pareto curve to design the transmitting signal according to the expected performance of the radar system.The application is used for designing a radar transmitting signal.

Description

TECHNICAL FIELD

[0001] The present application relates to a method for shaping the spectrum of a non-continuous spectrum signal with low integrated sidelobes, and belongs to the field of radar waveform design. BACKGROUND

[0002] Radar is a system that detects targets by transmitting and receiving electromagnetic waves. With the progress of science and technology, a large number of wireless communication services such as civilian radio stations, televisions, radios, mobile phones, and the like have exploded exponentially, and the supply and demand problem of frequency spectrum resources has become increasingly serious. In the face of a crowded electromagnetic environment, modern radar technology uses methods of receiving-end interference cancellation and transmitting-end waveform design to eliminate the influence of interference. However, receiving-end interference cancellation often causes a loss of signal to interference plus noise ratio (SINR), so the method of transmitting-end waveform design has received widespread attention and application. In order to eliminate the influence of co-channel interference, a notch can be designed at an unusable frequency band, and a plurality of silent frequency bands can be used to improve the SINR while ensuring the range resolution. However, setting a notch in the frequency spectrum will cause the sidelobe of the autocorrelation function of the transmitted signal to rise, resulting in the masking of nearby weak targets, so the sidelobe level and the SINR need to be considered simultaneously in signal waveform design.

[0003] There are two ways to measure the performance of the autocorrelation sidelobe: the weighted integral sidelobe level (WISL) and the weighted peak sidelobe level. In a cluttered environment, WISL is more suitable, so researchers have conducted a lot of research on the optimization of the WISL performance of non-continuous spectrum signals. Researchers have designed transmitted signals by taking the WISL and SINR as the objective function or constraint of the optimization problem, or by making the signal spectrum shape close to a certain template to make the signal have similar performance to the template. With the deepening of research, it is necessary and urgent to analyze the upper limit of the SINR and WISL performance and the trade-off relationship between the two performances in a co-channel interference dense environment.

[0004] In the prior art, the integral main lobe energy and the integral sidelobe energy of the autocorrelation function of a signal are weighted to comprehensively evaluate the range resolution and the range sidelobe level of the signal. Since the power spectrum and the autocorrelation function are Fourier transforms of each other, a relationship between the two can be established, so that the integral main lobe energy and the integral sidelobe energy of the autocorrelation function can be represented by the power spectrum, and an optimization problem can be established by weighting these two performances.

[0005] In actual radar transmitting system, the transmitting signal energy is constant, according to the Parseval theorem, the energy constraint needs to be imposed on the power spectrum, in addition to the amplitude constraint in the interference frequency band. Since the Fourier transform is a linear transform, it is easy to know that the objective function is a convex function, and the constraint is a linear constraint, which is a convex constraint, so the optimization problem is a convex problem. By solving the problem, the optimal power spectrum is obtained, and the trade-off relationship between the range resolution and the range sidelobe level is analyzed. However, the above-mentioned technology only considers WISL, and does not consider and weigh SINR level. At the same time, the spectrum template used in the existing signal optimization design method is a relatively simple 0 / 1 template, which cannot finely measure the autocorrelation performance of the signal. Therefore, the spectrum template used in the existing signal design method and the performance analysis of WISL and SINR have great defects and deficiencies, so that the existing spectrum shaping method is not perfect, WISL and SINR are not considered comprehensively, and the trade-off analysis of WISL and SINR cannot be performed. SUMMARY

[0006] In view of the problem that the existing spectrum shaping method does not comprehensively consider the performance of WISL and SINR, and the obtained transmitting signal has defects, the present application provides a low-integral sidelobe non-continuous spectrum signal spectrum shaping method.

[0007] The low-integral sidelobe non-continuous spectrum signal spectrum shaping method of the present application comprises,

[0008] Step one: express the signal-to-interference-and-noise ratio SINR and the weighted integral sidelobe level WISL of the transmitting signal through the power spectrum;

[0009] Step two: set the weighting value, weight the signal-to-interference-and-noise ratio SINR and the weighted integral sidelobe level WISL to obtain the objective function; combine the power spectrum energy constraint and the stop band position constraint to establish a spectrum shaping optimization problem;

[0010] Step three: solve the spectrum shaping optimization problem under different weighting values to obtain the optimal power spectrum under different weighting values;

[0011] Step four: calculate the signal-to-interference-and-noise ratio SINR and the weighted integral sidelobe level WISL corresponding to the optimal power spectrum under different weighting values to obtain a two-dimensional pareto curve of the signal-to-interference-and-noise ratio SINR and the weighted integral sidelobe level WISL; according to the expected performance of the radar system, select the target weighting value based on the two-dimensional pareto curve to design the transmitting signal.

[0012] According to the low-integral sidelobe non-continuous spectrum signal spectrum shaping method of the present application, in step one, the signal-to-interference-and-noise ratio SINR is expressed as:

[0013]

[0014] In the formula, R is the covariance matrix for the zero-padded form of the transmitted signal S;

[0015] The maxSINR problem is equivalently converted into According to Theorem, setting the dimension of the covariance matrix 2N greater than the setting dimension threshold, N is the number of signal points included in the transmitted signal S; then:

[0016] R≈F H ΛF,

[0017] Where Λ is a diagonal matrix with diagonal elements being the interference power spectral coefficients, F is the Fourier transform matrix; then Is expressed as:

[0018]

[0019] In the formula is the coefficient of the interference power spectral density at the kth frequency unit, Λ k,k is the diagonal element of the diagonal matrix Λ whose diagonal elements are the interference power spectral coefficients; p k is the power spectrum;

[0020] Therefore, the maxSINR problem is converted into the following optimization problem:

[0021] minf1(p), (3)

[0022] In the formula f1(p) is the signal-to-noise ratio optimization function;

[0023] Where

[0024] According to the low-integral sidelobe non-continuous spectrum signal spectrum shaping method of the present application, in step one, the weighted integral sidelobe level WISL is expressed as:

[0025]

[0026] In the formula γ n is the autocorrelation sidelobe weighting coefficient of the nth point signal, r n is the autocorrelation of the nth point signal;

[0027] The autocorrelation vector r of the transmitted signal S is represented by the inverse Fourier transform of the power spectrum:

[0028]

[0029] In the formula P is the power spectrum vector, P=[p1, p2,..., p 2N ];

[0030] The Fourier transform matrix F is:

[0031]

[0032] The weighted integrated sidelobe level WISL is further represented as:

[0033]

[0034] wherein:

[0035]

[0036] Diag(v) represents a diagonal matrix, diagonal elements of the diagonal matrix Diag(v) are elements in a vector v, the vector v is a vector composed of autocorrelation sidelobe weighting coefficients, and is defined as follows:

[0037]

[0038] According to formula (6), the weighted integrated sidelobe level WISL is further represented as:

[0039]

[0040] In the formula, R1 is an intermediate variable matrix:

[0041] R1=F H Diag(v)F.

[0042] According to the low-integrated-sidelobe non-continuous spectrum signal spectrum shaping method of the present application, in step two, the weighting value is set as λ, and a target function f2(p) is obtained:

[0043]

[0044] According to the low-integrated-sidelobe non-continuous spectrum signal spectrum shaping method of the present application, in step two, the power spectrum energy constraint is:

[0045] The total energy of the transmitted signal S is defined as 1, and according to the Parseval theorem, the following is obtained:

[0046]

[0047] At the same time, the power spectrum p k is a non-negative number;

[0048] The stopband position constraint is:

[0049]

[0050] In the formula, p represents the power spectrum at Ω u , and ε(Ω u ) represents that the stopband is located at Ω uThe upper limit of the power spectrum of the signal in the passband is Ω = [Ω1, Ω2, Ω3, …, Ω2N-1], and the upper limit of the power spectrum of the signal in the stopband is Ω = [Ω2N, Ω2N+1, Ω2N+2, …, Ω2N+2N-1]. U The stopband position set is u = 1, 2, 3, …, U, and U is the total number of stopband position points.

[0051] According to the low-integral sidelobe non-continuous spectrum signal spectrum shaping method of the application, in step two, the spectrum shaping optimization problem is established as follows:

[0052]

[0053] In the formula, E is energy, E = 2N; I is a 2N*1 vector, and the vector elements are all 1.

[0054] According to the low-integral sidelobe non-continuous spectrum signal spectrum shaping method of the application, in step three, the method for obtaining the optimal power spectrum under different weighting values comprises the following steps:

[0055] The intermediate variable matrix R1 is determined as a semi-positive definite matrix:

[0056] The intermediate variable matrix R1 is unfolded:

[0057]

[0058] Each element in the intermediate variable matrix R1 is expressed as:

[0059]

[0060] The element in the mth row and the qth column of the intermediate variable matrix R1 is expressed as m = 1, 2, 3, …, 2N, and q = 1, 2, 3, …, 2N;

[0061] According to formula (17), the diagonal elements of the intermediate variable matrix R1 are all positive real numbers, and:

[0062]

[0063] The intermediate variable matrix R1 is a Hermitian matrix, and the intermediate variable matrix R1 is expressed as:

[0064] R1 = F H Diag(v)F,

[0065] According to the property of the Hermitian matrix, the intermediate variable matrix R1 is determined as a semi-positive definite matrix.

[0066] According to the low-integral sidelobe non-continuous spectrum signal spectrum shaping method of the application, in step three, according to the fact that the intermediate variable matrix R1 is a semi-positive definite matrix, the spectrum shaping optimization problem expressed by formula (15) is determined as a convex problem, and the optimal power spectrum under different weighting values is solved by using the Lagrange dual function and the KKT condition.

[0067] According to the low-integral-side-lobe non-continuous spectrum signal spectrum shaping method of the present application, the Lagrange function L(P,μ,ω) of formula (15) is:

[0068]

[0069] In the formula, μ is the Lagrange multiplier one, a constant; ω is the Lagrange multiplier two, a vector;

[0070] is the in-band interference power spectral density,

[0071] ω = [ω1,...,ω 2N ] T ,

[0072] ω 2N is the element corresponding to p 2N in the vector ω;

[0073] According to the KKT condition, we have:

[0074]

[0075] Solving the first equation in formula (20), we obtain the optimal power spectrum P * of the power spectrum vector P:

[0076]

[0077] 0 < λ < 1;

[0078] Since the intermediate variable matrix R1 is a Hermitian matrix, if p k = 0, we need to make a full zero matrix; and the in-band interference power spectral density The coefficient at the available frequency band in a strong frequency domain interference environment is 0, and ω k is a non-negative number, so making a full zero matrix is not established, then p k = 0 is not established;

[0079] Therefore, making ω k = 0, k = 1,...,2N is established, then the expression of the optimal power spectrum P * is:

[0080]

[0081] Substituting P * into I T P = E, we obtain:

[0082]

[0083] Solving formula (22) obtains:

[0084]

[0085] Again, the mu is brought into formula (21) and the optimal power spectrum P * :

[0086]

[0087] According to the low-integration sidelobe non-continuous spectrum signal spectrum shaping method of the application, the optimal power spectrum P * Corresponding signal-to-interference-and-noise ratio SINR and weighted integration sidelobe level WISL are calculated, the weighting value is adjusted, and different optimal power spectrum P * Corresponding signal-to-interference-and-noise ratio SINR and weighted integration sidelobe level WISL are calculated, the weighting value is adjusted, and different optimal power spectrum P

[0088] The method of the application first establishes the relationship between signal-to-interference-and-noise ratio, weighted integration sidelobe and signal power spectrum, considers multi-criteria trade-off, adopts index weighting to construct objective function, and constructs multi-criteria multi-constraint optimization problem. Through matrix semi-positive proof, the convexity of the optimization problem is proved, and finally the problem is solved through convex optimization toolbox. Simulation experiments verify that the method of the application can comprehensively consider the signal-to-interference-and-noise ratio and weighted integration sidelobe performance, and by changing the weighting coefficient, the coupling relationship between the signal-to-interference-and-noise ratio and the weighted integration sidelobe can be analyzed.

[0089] The method of the application considers the WISL and SINR of the signal autocorrelation function, establishes a weighted objective function, and establishes a spectrum shaping optimization problem by adding constraints. By fixing the weighting value, the optimal power spectrum obtained by solving the optimization problem can be used as a template for subsequent signal design, and the upper limit of the WISL and SINR performance can be calculated. In addition, by adjusting the weighting value, different power spectrum templates and corresponding WISL and SINR performance can be obtained, and the constraint relationship between the two performances can be analyzed, so that the two performances can be better balanced in the design of the transmitted signal, and the problem that the prior art cannot simultaneously consider the WISL and SINR performance for spectrum shaping and balance the performance of the two is solved. BRIEF DESCRIPTION OF DRAWINGS

[0090] Figure 1 The flowchart of the low-integration sidelobe non-continuous spectrum signal spectrum shaping method of the application is shown in the figure;

[0091] Figure 2is a variation relationship output result graph of λ and SINR in the specific embodiment;

[0092] Figure 3 is a variation relationship output result graph of λ and WISL in the specific embodiment;

[0093] Figure 4 is a variation relationship output result graph of SINR and WISL with the variation of λ in the specific embodiment;

[0094] Figure 5 is an optimal power spectrum shape output result graph when λ = 0.25 in the specific embodiment;

[0095] Figure 6 is an optimal autocorrelation function shape output result graph when λ = 0.25 in the specific embodiment;

[0096] Figure 7 is a variation relationship output result graph of λ and WISL after changing the spectral notch depth in the specific embodiment;

[0097] Figure 8 is a variation relationship output result graph of λ and SINR after changing the spectral notch depth in the specific embodiment;

[0098] Figure 9 is a variation relationship output result graph of SINR and WISL with the variation of λ after changing the spectral notch depth in the specific embodiment. DETAILED DESCRIPTION

[0099] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative work fall within the protection scope of the present application.

[0100] It should be noted that the embodiments in the present application and the features in the embodiments can be combined with each other without conflict.

[0101] The present application will be further described below in combination with the drawings and specific embodiments, but is not limited to the present application.

[0102] Specific embodiment one, in combination Figure 1 As shown in the specific embodiment, the present application provides a low-integral sidelobe non-continuous spectrum signal spectrum shaping method, which comprises,

[0103] Step one: express the signal-to-interference-and-noise ratio SINR and the weighted integrated sidelobe level WISL of the transmitted signal through the power spectrum;

[0104] Step two: set the weighting value, weight the signal-to-interference-and-noise ratio SINR and the weighted integrated sidelobe level WISL to obtain a target function; combine the power spectrum energy constraint and the stopband position constraint to establish a spectrum shaping optimization problem;

[0105] Step three: solve the spectrum shaping optimization problem under different weighting values to obtain the optimal power spectrum under different weighting values;

[0106] Step four: calculate the signal-to-interference-and-noise ratio SINR and the weighted integrated sidelobe level WISL corresponding to the optimal power spectrum under different weighting values to obtain a two-dimensional pareto curve of the signal-to-interference-and-noise ratio SINR and the weighted integrated sidelobe level WISL; according to the expected performance of the radar system, select a target weighting value based on the two-dimensional pareto curve to design the transmitted signal.

[0107] The embodiment comprehensively considers the signal-to-interference-and-noise ratio SINR and the weighted integrated sidelobe level WISL, so that the obtained transmitted signal can adapt to the detection environment to the greatest extent and meet the design requirements. If only the WISL is considered and the SINR is not considered, the signal-to-noise ratio may be low and the detection probability may be seriously reduced; if only the SINR is considered and the WISL is not considered, the signal sidelobe may be high and the weak target may be seriously shielded, which will affect the detection of the weak target.

[0108] Further, in step one, the signal-to-interference-and-noise ratio SINR obtained by matching filtering the echo is expressed as:

[0109]

[0110] In the formula, is a zero-padded form of the transmitted signal S, and R is a covariance matrix;

[0111] For a radar system, the total energy of the transmitted signal is constant, that is, S H S=1, so the denominator of the SINR affects the size of the SINR is smaller, the SINR is larger. In the constant false alarm detection, the larger the SINR is, the larger the detection probability is, so the maxSINR problem can be equivalently converted into According to Theorem, when the dimension 2N of the covariance matrix is large enough, set the dimension 2N of the covariance matrix to be greater than the set dimension threshold, and N is the number of signal points included in the transmitted signal S; the covariance matrix R can be approximated as the following form:

[0112] R≈F H ΛF,

[0113] where Λ is a diagonal matrix with interference power spectrum coefficients as diagonal elements, F is a Fourier transform matrix; then is expressed as:

[0114]

[0115] where is the coefficient of the interference power spectrum density at the kth frequency unit, Λ k,k is the diagonal element of the diagonal matrix Λ whose diagonal elements are the coefficients of the interference power spectrum; p k is the power spectrum;

[0116] Obviously, formula (2) is a power spectrum density weighted form. Obviously, is non-zero in the set of stopband pointers, and the set of passband pointers is 0. is the weight of the signal leakage power penalty function in each stopband, which determines the depth of the power spectrum in each stopband. In detection, the greater the SINR, the greater the detection probability, so the maxSINR problem is converted into the following optimization problem:

[0117] minf1(p), (3)

[0118] where f1(p) is the signal-to-noise ratio optimization function;

[0119] where

[0120] In step one, the power spectrum representation weighted integral side lobe level WISL is based on:

[0121] In the spectrum setting, the notch will make the autocorrelation function of the transmitted signal side lobe lift, causing the weak target near the strong target to be shielded, so it is necessary to consider optimizing the autocorrelation side lobe level of the signal. WISL defines the weighted two norm of the autocorrelation function in the side lobe region, which represents the comprehensive performance of the autocorrelation function side lobe, so WISL is used to measure it. WISL is defined as:

[0122]

[0123] where γ n is the autocorrelation side lobe weighted coefficient of the nth point signal, r n is the autocorrelation of the nth point signal;

[0124] The autocorrelation vector r of the transmitted signal S is represented by the inverse Fourier transform of the power spectrum:

[0125]

[0126] where P is the power spectrum vector, P = [p1, p2,..., p 2N ];

[0127] The Fourier transform matrix F is:

[0128]

[0129] The weighted-integrated sidelobe level WISL is further represented as:

[0130]

[0131] wherein:

[0132]

[0133] Diag(v) represents a diagonal matrix, diagonal elements of the diagonal matrix Diag(v) are elements in a vector v, the vector v is a vector composed of autocorrelation sidelobe weighting coefficients, and is defined as follows:

[0134]

[0135] According to formula (6), the weighted-integrated sidelobe level WISL is further represented as:

[0136]

[0137] wherein R1 is an intermediate variable matrix:

[0138] R1 = F H Diag(v)F.

[0139] Further, in the design process of the radar waveform, multiple performance index requirements usually need to be met, and the multiple indexes are often coupled and contradictory. Therefore, the indexes need to be weighted to achieve trade-off. In order to enable the radar waveform to achieve good anti-interference ability and weak target detection performance, SINR and WISL need to be considered at the same time. In step two, the weighted form of SINR and WISL is defined, the weighting value is set as λ, and the objective function f2(p) is obtained:

[0140]

[0141] It can be seen that the objective function f2(p) is a function of the power spectrum. In addition to the objective function, the power spectrum should satisfy several constraint conditions. First, the energy constraint in step two is:

[0142] The total energy of the transmitted signal S is defined as 1, and then according to the Parseval theorem, the following is obtained:

[0143]

[0144] At the same time, the power spectrum p k is a non-negative number;

[0145] In order to prevent the power spectrum from being too high in some stopband positions in the optimization process, the upper limit of the power spectrum of the stopband position is set, and then the stopband position constraint is:

[0146]

[0147] where represents the power spectrum at Ω u , ε(Ω u ) represents the upper limit of the power spectrum where the stopband is located, Ω = [Ω1,..., Ω u ] is the set of stopband locations, u = 1, 2, 3,..., U, and U is the total number of stopband location points. U

[0148] In step two, the above objective function and constraints establish the spectrum shaping optimization problem as follows:

[0149]

[0150] where E is the energy, E = 2N; I is a 2Nx1 vector, and the vector elements are all 1.

[0151] Further, in order to solve the optimization problem defined by equation (15), first analyze the optimization problem. The constraints of the optimization problem are all linear constraints, which are convex constraints. Therefore, analyze the convexity of the objective function. The first term of the objective function is a linear term, which is a convex function. Therefore, analyze the convexity of the second term. It can be seen that the second term is a quadratic term. Therefore, as long as it is proved that the matrix R1 is a semi-definite matrix, the second term is a convex function, and the optimization problem represented by equation (15) is a convex problem. Next, solve R1.

[0152] In step three, the method for obtaining the optimal power spectrum under different weighting values includes:

[0153] Determine that the intermediate variable matrix R1 is a semi-definite matrix:

[0154] Expand the intermediate variable matrix R1:

[0155]

[0156] Each element in the intermediate variable matrix R1 is expressed as:

[0157]

[0158] R1(m, q) represents the element in the mth row and the qth column of the intermediate variable matrix R1, m = 1, 2, 3,..., 2N, and q = 1, 2, 3,..., 2N;

[0159] According to equation (17), it is determined that the diagonal elements of the intermediate variable matrix R1 are all positive real numbers, and:

[0160]

[0161] ​The intermediate variable matrix R1 is a Hermitian matrix, and the intermediate variable matrix R1 is expressed as:

[0162] R1 = F H Diag(v)F,

[0163] According to the properties of the Hermitian matrix, it is determined that the intermediate variable matrix R1 is a positive semi-definite matrix.

[0164] In step three of the embodiment, according to the fact that the intermediate variable matrix R1 is a positive semi-definite matrix, it is determined that the spectrum shaping optimization problem expressed by formula (15) is a convex problem, and the optimal power spectrum under different weighting values is solved by using the Lagrange dual function and the KKT condition.

[0165] The Lagrange function L(P, μ, ω) of formula (15) is:

[0166]

[0167] In the formula, μ is the Lagrange multiplier one, which is a constant; ω is the Lagrange multiplier two, which is a vector;

[0168] is the in-band interference power spectral density,

[0169] ω = [ω1,...,ω 2N ] T ,

[0170] ω 2N is the element corresponding to p 2N in the vector ω;

[0171] According to the KKT condition, the following is obtained:

[0172]

[0173] Solving the first equation in formula (20) obtains the optimal power spectrum P * of the power spectrum vector P:

[0174]

[0175] 0 < λ < 1;

[0176] In order for the three equations and inequalities in formula (20) to be satisfied, ω k p k = 0, k = 1,..., 2N, ω k ≥ 0, p k ≥ 0, it is necessary to satisfy ω k = 0, k = 1,..., 2N or p k = 0, k = 1,..., 2N. The following discusses the two cases respectively.

[0177] If p k =0, since the intermediate variable matrix R1 is a Hermitian matrix, it is necessary to make a full zero matrix, i.e. all elements are zero; and the in-band interference power spectral density In a strong frequency domain interference environment, its elements are large at the unusable frequency band, and the coefficients at the usable frequency band are 0, and ω k is a non-negative number, so that is not a full zero matrix, then p k =0 is not established;

[0178] Therefore, ω k =0, k = 1,..., 2N is established, then the expression of the optimal power spectrum P * is:

[0179]

[0180] Substitute P * into I T P = E, to obtain:

[0181]

[0182] Solving formula (22) obtains:

[0183]

[0184] Then, μ is brought into formula (21) to calculate the optimal power spectrum P * :

[0185]

[0186] In step three, the nature of the optimization problem is analyzed, and it is concluded that the optimization problem is a convex optimization problem, so the unique optimal power spectrum P * can be solved when the stopband position and the weighting value λ are known; in step four, the signal-to-interference-and-noise ratio SINR and the weighted integrated sidelobe level WISL corresponding to the optimal power spectrum P * are calculated, and the weighting value is adjusted to obtain the performance upper limit of the signal-to-interference-and-noise ratio SINR and the weighted integrated sidelobe level WISL corresponding to different optimal power spectra P * ; then the two-dimensional pareto curve of SINR and WISL with the change of the weighting value is obtained; based on the two-dimensional pareto curve, the trade-off relationship between SINR and WISL is analyzed, and then the target weighting value is selected according to the expected performance of the radar system to design the transmitted signal. Specific embodiments:

[0188] The simulation conditions are set as follows: N is 256, the frequency stopband dip position is Ω=[0.0988,0.1469]∪[0.2593,0.2840]∪[0.6074,0.6938]∪[0.8185,0.8556], the weighting value λ of SINR and WISL varies from 0.1 to 0.9, and the autocorrelation sidelobe weighting coefficient γ n =1, n=2,...2N; Interference intensity at the passband The interference intensity at the stopband is 0. Given a set of Gaussian distributed random numbers with a mean of 10 and a variance of 0.1, ε(Ω) u ),Ω u ∈Ω is set to -20dB. Simulation results show the SINR variation with λ as follows: Figure 2 As shown, WISL varies with λ as follows Figure 3 As shown, the relationship between SINR and WISL is as follows: Figure 4 As shown, it can be seen that as λ increases, the weight of the SINR term increases, while the weight of the WISL term decreases. Ultimately, the SINR corresponding to the optimal spectrum obtained through spectral shaping increases, while the WISL decreases. This indicates that the larger the weight in the shaping process, the more importance is placed on this performance, resulting in a better performance after optimization. Furthermore, it can be seen that as λ changes... As the value changes from 0 to 10, SINR changes from 0.1 to +∞, while WISL changes from 0.247 to 0.252. It can be seen that due to the influence of the spectral dip on the signal autocorrelation, there is a design upper limit for WISL after determining the location of the spectral dip, and the performance of WISL is contradictory to SINR.

[0189] The optimization results for λ = 0.25 are given below. The optimal power spectrum shape is as follows: Figure 5 As shown, the corresponding autocorrelation function is as follows: Figure 6 As shown, by Figure 5 It can be seen that there are deep spectral dips in the set unusable frequency bands, resulting in good SINR performance, with a SINR of 11.29 dB.

[0190] Finally, set ε(Ω) u ),Ω u With ∈Ω set to -40dB and other conditions remaining constant, the simulation results show that WISL varies with λ as follows: Figure 7 As shown, the SINR varies with λ as follows: Figure 8 As shown, the relationship between SINR and WISL is as follows: Figure 9 As shown, it can be observed that as the spectral dip deepens, the damage to the autocorrelation function becomes more severe, resulting in poorer WISL performance, while the SINR trend remains basically unchanged.

[0191] The present application can also be used for other various data and scenes, and those skilled in the art can process different data in different scenes according to the present application without departing from the spirit and essence of the present application, which should all belong to the protection scope of the appended claims of the present application.

Claims

1. A method of spectral shaping of a non-contiguous spectrum signal with low-integral sidelobes, characterized by Comprising, Step one: express the signal-to-interference-and-noise ratio SINR and the weighted integrated sidelobe level WISL of the transmit signal through the power spectrum; Step two: set the weighting value, weight the signal-to-interference-and-noise ratio SINR and the weighted integrated sidelobe level WISL to obtain the objective function; combine the power spectrum energy constraint and the stopband position constraint to establish the spectrum shaping optimization problem; Step three: solve the spectrum shaping optimization problem under different weighting values to obtain the optimal power spectrum under different weighting values; Step four: calculate the signal-to-interference-and-noise ratio SINR and the weighted integrated sidelobe level WISL corresponding to the optimal power spectrum under different weighting values to obtain the two-dimensional pareto curve of the signal-to-interference-and-noise ratio SINR and the weighted integrated sidelobe level WISL; select the target weighting value based on the two-dimensional pareto curve to design the transmit signal according to the expected performance of the radar system.

2. The low-integrated sidelobe non-continuous spectrum signal spectrum shaping method according to claim 1, wherein in step one, the signal-to-interference-and-noise ratio SINR is expressed as: Therefore, the maxSINR problem is converted into the following optimization problem: wherein R is the covariance matrix for the zero-padded form of the transmit signal S. The max SINR problem is equivalently transformed into According to Theorem, setting the covariance matrix dimension 2N greater than the set dimension threshold, N is the number of signal points included in the transmitted signal S; then: R≈F H ΛF, where Λ is a diagonal matrix with the diagonal elements being the interference power spectrum coefficients, F is a Fourier transform matrix; then is represented as: wherein is the coefficient of the interference power spectral density in the kth frequency cell, Λ k,k is the diagonal element of the diagonal matrix Λ whose diagonal elements are the coefficients of the interference power spectrum; p k is the power spectrum; minf1(p), (3) where f1(p) is the signal-to-interference-and-noise ratio optimization function; 3. The low-integrated sidelobe non-continuous spectrum signal spectrum shaping method according to claim 2, wherein in step one, the weighted integrated sidelobe level WISL is expressed as: wherein The autocorrelation vector r of the transmit signal S is expressed by the inverse Fourier transform of the power spectrum: The Fourier transform matrix F is: where γ n is the autocorrelation sidelobe weighting coefficient of the signal at the nth point, r n is the autocorrelation of the signal at the nth point; Then the weighted integrated sidelobe level WISL is further expressed as: where P is the power spectrum vector, P = [p1, p2,..., pN] ; and 2N ] ; where: Diag(v) represents a diagonal matrix, the diagonal elements of the diagonal matrix Diag(v) are the elements in the vector v, and the vector v is a vector composed of autocorrelation sidelobe weighting coefficients, which is defined as follows: Then according to formula (6), the weighted integrated sidelobe level WISL is further expressed as: where R1 is an intermediate variable matrix:

4. The low-integrated sidelobe non-continuous spectrum signal spectrum shaping method according to claim 3, wherein in step two, the weighting value is set as λ to obtain the objective function f2(p):

5. The low-integrated sidelobe non-continuous spectrum signal spectrum shaping method according to claim 4, wherein in step two, the power spectrum energy constraint is: R1= F H Diag(v) F. Define the total energy of the transmit signal S as 1, then according to the Parseval theorem, we have: The stopband position constraint is:

6. The low-integrated sidelobe non-continuous spectrum signal spectrum shaping method according to claim 5, wherein in step two, the spectrum shaping optimization problem is established as follows: where E is the energy, E = 2N; I is a 2Nx1 vector, and the vector elements are all 1.

7. The low-integrated sidelobe non-continuous spectrum signal spectrum shaping method according to claim 6, wherein in step three, the method for obtaining the optimal power spectrum under different weighting values comprises: At the same time, the power spectrum p k is non-negative; determining that the intermediate variable matrix R1 is a positive semi-definite matrix: In the formula represents the power spectrum at Ω u u represents the upper limit of the power spectrum at Ω u Ω = [Ω1,..., Ω U ] is a set of stopband positions, u = 1, 2, 3,..., U, and U is the total number of stopband position points.​ expanding the intermediate variable matrix R1: each element in the intermediate variable matrix R1 is expressed as: According to formula (17), it is determined that the diagonal elements of the intermediate variable matrix R1 are all positive real numbers, and: Therefore, the intermediate variable matrix R1 is a Hermitian matrix, and the intermediate variable matrix R1 is expressed as: ​ ​ ​ ​ R1(m,q) denotes the element in the mth row and qth column of the intermediate variable matrix R1, m = 1, 2, 3,..., 2N, q = 1, 2, 3,..., 2N; ​ ​ R1= F H Diag(v) F, According to the property of the Hermitian matrix, the intermediate variable matrix R1 is determined as a semi-positive definite matrix.

8. The low-integration sidelobe non-contiguous spectrum signal spectrum shaping method according to claim 7, characterized in that, In step three, according to the intermediate variable matrix R1 being a semi-positive definite matrix, the spectrum shaping optimization problem expressed by formula (15) is determined as a convex problem, and the optimal power spectrum under different weighting values is solved by using the Lagrange dual function and the KKT condition.

9. The low-integration sidelobe non-contiguous spectrum signal spectrum shaping method according to claim 8, characterized in that, The Lagrange function L(P, μ, ω) of formula (15) is: In the formula, μ is the Lagrange multiplier one, which is a constant; ω is the Lagrange multiplier two, which is a vector; for the in-band interference power spectral density, ω = [ω1,..., ωN]T 2N ] T , ω 2N is the element of the vector ω corresponding to p 2N ; According to the KKT condition, the following formula (22) is obtained: Solving the first equation in equation (20) gives the optimal power spectrum P of the power spectrum vector P * : 0 < λ < 1; Since the intermediate variable matrix R1 is a Hermitian matrix, if p k = 0, it is required that is a full 0 matrix; and the in-band interference power spectral density The coefficients at the available frequency bands in the strong frequency domain interference environment are 0, and ω k is a non-negative number, thus making a full 0 matrix is not established, p k = 0 is not established; Thus, ω k = 0, k = 1,..., 2N holds, then the expression of the optimal power spectrum P * is: Substitute P * into I T P = E, we get: Solving formula (22) obtains: Again, plug in μ into equation (21) to calculate the optimal power spectrum P * :

10. The low-integration sidelobe non-contiguous spectrum signal spectrum shaping method according to claim 9, characterized in that, According to the optimal power spectrum P * The signal-to-interference-and-noise ratio SINR and the weighted integrated sidelobe level WISL corresponding to the transmitted signal are calculated, the weighting value is adjusted, and different optimal power spectra P * The performance upper limit of the corresponding signal-to-interference-and-noise ratio SINR and the weighted integrated sidelobe level WISL; and then a two-dimensional pareto curve of SINR and WISL changing with the weighting value is obtained; based on the two-dimensional pareto curve, the trade-off relationship between SINR and WISL is analyzed, and then according to the expected performance of the radar system, a target weighting value is selected to design the transmitted signal.

Images