An inter-pulse waveform amplitude and phase agile design method against range folding clutter

Abstract

The application discloses a method for designing inter-pulse waveform amplitude and phase agility against range folding clutter, which comprises the following steps: firstly, under the amplitude and phase agility airborne radar system, a slow-time echo model of a target, clutter and noise is established, and mathematical expressions of target sidelobe and clutter energy are derived; then, considering the constraints of transmitting power and peak-to-average power ratio (PAR), an inter-pulse amplitude and phase agility waveform optimization design problem based on minimizing target sidelobe and clutter energy is established; finally, the accelerated power method of least squares iteration (PMLI) algorithm is used to optimize the inter-pulse amplitude and phase parameters, adjust the clutter energy distribution of the airborne radar, improve the signal-to-clutter-and-noise ratio of a long-distance target under the near-distance folding clutter of the airborne radar, and complete the solution of the optimization problem. The method can suppress the clutter base in the region of interest, realize the target detection against the range folding clutter, and has good robustness and strong realizability without relying on the clutter prior knowledge such as the clutter covariance matrix, and has certain generalization for the clutter suppression of different terrains.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of signal processing, and particularly relates to an inter-pulse waveform amplitude and phase agile design method for resisting range folded clutter. BACKGROUND

[0002] In the process of target detection, airborne radar has the problems of wide distribution range of clutter and high echo intensity, and when working at high repetition frequency, there is serious range ambiguity, which causes the target to be easily submerged by near distance strong folded clutter, so that the target is missed, and the working performance of the airborne radar is seriously affected.

[0003] Research shows that the airborne radar clutter spectrum and the inter-pulse parameters of the signal are closely related, and the distribution of the radar clutter spectrum can be adjusted by designing the inter-pulse parameters, so as to realize the suppression of the clutter in a specific area. Although the initial phase agile signal is sensitive to Doppler shift, and high sidelobes are easily generated in the non-zero frequency area, the design of the initial phase agile signal is a typical combinatorial optimization problem, and the objective function generally has a large number of local extreme points, which is very beneficial to the design of the inter-pulse waveform parameters. Therefore, the initial phase agile signal is considered as a technical approach to solve such problems, which suppresses the sidelobes and clutter energy by changing the inter-pulse initial phase and performing matching and mismatching processing at the receiving end. The document "Optimizing Radar Waveform and Doppler Filter Bank via Generalized Fractional Programming, IEEE Journal of Selected Topics in Signal Processing, vol. 9, no. 8, pp. 1387-1399, Dec. 2015." maximizes the signal-to-clutter-and-noise ratio by jointly designing the inter-pulse amplitude and phase code words of the transmitted waveform and the Doppler filter, so as to realize the suppression of the range folded clutter, but this research needs to rely on the known clutter prior information, and can only suppress the clutter in a specific scene, which has limitations. SUMMARY

[0004] To solve the above technical problems, the application provides an inter-pulse waveform amplitude and phase agile design method for resisting range folded clutter. Under the amplitude and phase agile airborne radar system, a slow-time echo model of the target, the clutter and the noise is established, so as to deduce the mathematical expressions of the target sidelobe and the clutter energy, and an energy minimization model is constructed under the peak-to-average-power ratio (PAR) constraint, and the optimization problem is solved by combining the power method-like iterations (PMLI) algorithm and the convergence acceleration algorithm.

[0005] The technical scheme of the present application is: a method for designing inter-pulse waveform amplitude and phase agility against range folding clutter, and the specific steps are as follows:

[0006] S1, a slow-time total echo model of an airborne radar under a clutter environment is established for amplitude and phase agility;

[0007] S2, echo signals are processed to construct a sidelobe and clutter suppression optimization problem;

[0008] S3, the optimization problem is solved.

[0009] Further, the step S1 is specifically as follows:

[0010] S11, an inter-pulse amplitude and phase agility signal model is established;

[0011] It is assumed that the airborne radar transmits P pulses within a CPI, and the amplitude and initial phase of the pulse train both exist inter-pulse agility, and the model s(t) of the transmitted signal is expressed as:

[0012]

[0013] Wherein, t represents the signal observation time, c i represents the amplitude and phase information of the i-th pulse, i.e., the amplitude and phase code word, T represents the pulse repetition period, and u(t) represents the pulse signal.

[0014] The adjacent pulse transmission time is ensured to be T≥2T p , T p represents the pulse width.

[0015] S12, an amplitude and phase agility single-target slow-time echo model is established;

[0016] In the detection range of the airborne radar, the Doppler shift of the target is f d , the two-way propagation delay is τ, and the echo signal model r(t) of the target is expressed as:

[0017]

[0018] Wherein, f0 represents the carrier frequency, and α represents the target complex amplitude.

[0019] Let be the updated target complex amplitude, and the echo signal r T (t) after the down-conversion processing is expressed as:

[0020]

[0021] S13, the target echo signal is matched filtered and sampled;

[0022] It is assumed that the impulse response of the matched filter is h(t)=u *(-t), (·) * represents the conjugate operator, the processed echo signal v T (t) is expressed as:

[0023]

[0024] wherein, represents the ambiguity function of the intra-pulse waveform.

[0025] The echo signal model of formula (4) is sampled at time , represents the slow time moment, the slow time echo model of the target is expressed as:

[0026]

[0027] The intra-pulse waveform ambiguity function is irrelevant to the amplitude and phase code word c i , and the ambiguity function is expressed as χ p (0, f d ) = 1.

[0028] Set i = 1, 2,..., P, and let c = [c1, c2,..., c P ] T , (·) T represents the transpose operator, and represents the Hadamard product operator, and the vector form of the slow time echo model of the single target v T is expressed as:

[0029] v T = α T c⊙p(f d ) (6)

[0030] S14, divide the clutter cells in the radar detection range;

[0031] The clutter cells are divided by equidistant and equi-Doppler rings, and the Doppler shift value range of the clutter cells is set as [-f r / 2, f r / 2], f r represents the pulse repetition frequency, and the Doppler shift corresponding to the i-th Doppler ring is f Di .

[0032] S15, establish a slow time clutter model corresponding to the ambiguity distance ring;

[0033] The matched filtering and sampling processing mode of the clutter signal is the same as that of the target echo, and the processed slow time clutter model is essentially the echo of the clutter cell overlapping with the target echo in different ambiguity intervals, and is expressed as:

[0034]

[0035] wherein r = 1, 2,..., n represents the ambiguity number of the clutter cell, corresponding to a specific ambiguity range; J r represents the displacement matrix under r ambiguity; σ ri represents the echo power of the clutter cell; represents the Doppler vector function of the clutter cell, f ri represents the Doppler shift of the clutter cell.

[0036] S16, establishing a slow-time total echo model;

[0037] Considering the noise signal contained in the echo, the slow-time echo model of the airborne radar amplitude-phase agile signal target detection under the clutter environment is represented as:

[0038]

[0039] wherein n represents the noise in the slow-time echo model, that is, a complex Gaussian white noise.

[0040] Further, the step S2 is specifically as follows:

[0041] S21, processing the slow-time echo signal by using a Doppler matrix;

[0042] Supposing that the Doppler vector of the i th slow-time cell is p(-f Di ), the i th slow-time echo processed by the Doppler matrix is represented as: i

[0043]

[0044] wherein q(f ri -f Di ) represents the Doppler processed vector of the clutter echo under r ambiguity, and q(f) = J -r p(f); let the frequency domain range be [-f r / 2, f r / 2], and the Doppler division region of the clutter cell be consistent with the frequency domain, then f Di in formula (9) represents the frequency domain sampling point; represents the clutter echo noise processed by the Doppler vector.

[0045] Supposing that the Doppler shift range of the target and the clutter cell is [-f r / 2, f r / 2], for the convenience of the construction of the energy model, let f i = f d -f Di , f j = f ri ​-f Di , and f i ,f j ∈[-f r / 2,f r / 2].

[0046] When the sampling interval is small enough, there exists f i =0,f j When f = 0, the echoes from the target and clutter elements produce peak values ​​at that frequency, thus achieving coherent accumulation of the echo signals. i =0 corresponds to the target main lobe, f i When ≠0, it corresponds to the target sidelobe.

[0047] S22. Perform amplitude and phase compensation processing on the echo signal;

[0048] The amplitude-phase compensation filter vector is the conjugate transpose of the amplitude-phase modulation codeword sequence c, ξ i The output y after amplitude and phase compensation processing i Represented as:

[0049]

[0050] in,(·) H The conjugate transpose operator, y Ti y c , These represent the slow-time target echo, clutter, and noise after processing by the i-th Doppler vector and the amplitude-phase compensation filter, respectively.

[0051] When the sampling interval is small enough, there exists f i =0 and f j The condition = 0 indicates that the echoes from both the target and clutter elements reach a peak at that frequency, i.e., the main lobe location. The mathematical model for the sum of the processed target echo sidelobes and clutter element echo energy is equivalent to the sum of the echo power at each slow-time sampling point, specifically expressed as:

[0052]

[0053] Consider ε as the objective function of the optimization problem.

[0054] Furthermore, step S3 is specifically as follows:

[0055] S31. Simplify and optimize the problem;

[0056] Based on step S2, ε is optimized using PAR constraints with c as the independent variable. The optimization problem is expressed as:

[0057]

[0058] where J0denotes the displacement matrix under the r = 0th blur, i.e., the identity matrix, σ rl denotes the complex amplitude of the echo signal of the clutter cell, c(i) denotes the i th element of the amplitude-phase code word sequence, and γ denotes the maximum modulus of the PAR constraint.

[0059] The optimization problem is preliminarily simplified, and the fourth-order optimization problem is converted into a second-order optimization problem:

[0060]

[0061] where C = cc H denotes a Hermite matrix,

[0062] S32, an accelerated PMLI algorithm is used to solve the optimization problem;

[0063] The iterative update expression of the PMLI combined with the convergence acceleration algorithm is:

[0064]

[0065] where c (k) denotes the amplitude-phase code word sequence after the k th iteration; denotes y (k) and the function transformation relationship between c (k) , λ T and λ C respectively denote the maximum eigenvalues of the matrices Θ(c (k) ) and , I P denotes a P × P identity matrix, and Θ(c (k) ) = R - 2λ max (Λ T ) c (k) c (k)H , λ max (Λ T ), λ max (Λ c ) respectively denote the maximum eigenvalues of the matrices Λ T and Λ c ; R and respectively are R = Φ + Φ H , Φ and both denote Hermite matrices, and

[0066]

[0067] where l i= (J0diag(p(f i ))c (k) ) H c (k) , l r,i = [J r diag(q(f j ))c (k) ] H c (k) ; vector function formula of vector L R≥0 and L R≤0 is as follows: A , mathematical expression u m and definition of δ are as follows:

[0068]

[0069]

[0070]

[0071] Wherein, x represents the xth element of vector function L A , A represents a set of all variables x that can be taken, and L is a unit vector when the vector function is abbreviated as L; m represents the number of non-zero elements in y (k) ; represents the ith element of vector y (k) .

[0072] Based on the objective function and iteration formula of the optimization problem derived from steps S1-S3, an acceleration algorithm is introduced to solve the optimization problem:

[0073] Definition , Γ = c1-c (k) , Λ = c2-c1-Γ, λ =-||Γ|| / ||Λ||; then the amplitude-phase code sequence updated each time by the acceleration algorithm is c2 is updated by twice PMLI iteration from c (k) The algorithm determines the step size λ by backtracking λ <- (λ-1) / 2 to update the sequence phase, and the backtracking range is from λ to-1. After multiple iterations, the enhanced solution is obtained, and the solution of the optimization problem is completed.

[0074] The beneficial effects of the present application: the method of the present application firstly establishes the slow-time echo model of the target, clutter and noise under the amplitude-phase agile airborne radar system, deduces the mathematical expressions of the target sidelobe and clutter energy, then comprehensively considers the constraints of the transmitting power and the peak-to-average power ratio (PAR), establishes the inter-pulse amplitude-phase agile waveform optimization design problem based on the minimization of the target sidelobe and clutter energy, finally optimizes the inter-pulse amplitude-phase parameters by using the accelerated power method of iterative (PMLI) algorithm, adjusts the clutter energy distribution of the airborne radar, improves the signal-to-clutter-and-noise ratio of the long-distance target under the near-distance folded clutter of the airborne radar, and completes the solution of the optimization problem. The method of the present application suppresses the clutter base in the region of interest, realizes the anti-distance folded clutter target detection, and does not depend on the clutter priori knowledge such as the clutter covariance matrix, has good robustness and strong realizability, and has certain generalization for the clutter suppression of different terrains. BRIEF DESCRIPTION OF DRAWINGS

[0075] Figure 1 The flow chart of the inter-pulse waveform amplitude-phase agile design method against the distance folded clutter of the present application.

[0076] Figure 2 The ambiguity function graph after the sidelobe and clutter suppression in the embodiment of the present application.

[0077] Figure 3 The curve graph of the total energy of the target sidelobe and clutter changing with the iteration number in the algorithm optimization process in the embodiment of the present application.

[0078] Figure 4 The target detection RD plane comparison graph of the algorithm optimization in the embodiment of the present application.

[0079] Figure 5 The distance direction section graph of the region target detection RD plane of the algorithm optimization in the embodiment of the present application. DETAILED DESCRIPTION

[0080] The present application will be further described below in combination with the drawings and embodiments.

[0081] As shown in the flow chart of the inter-pulse waveform amplitude-phase agile design method against the distance folded clutter of the present application, the specific steps are as follows: Figure 1

[0082] S1, establishing the slow-time total echo model of the amplitude-phase agile airborne radar under the clutter environment;

[0083] S2, processing the echo signal and constructing the sidelobe and clutter suppression optimization problem;

[0084] S3, solving the optimization problem.

[0085] In the embodiment, the step S1 is specifically as follows: ​

[0086] S11, a pulse-to-pulse amplitude and phase chirp signal model is established;

[0087] Suppose that the airborne radar transmits P pulses in a CPI, and the amplitude and initial phase of the pulse train are both pulse-to-pulse chirped, the model s(t) of the transmitted signal is expressed as:

[0088]

[0089] where t represents the signal observation time, c i represents the amplitude and phase information of the i-th pulse, i.e., the amplitude and phase code word, T represents the pulse repetition period, and u(t) represents the pulse signal.

[0090] The transmission time of adjacent pulses is ensured to satisfy T≥2T p , T p represents the pulse width, which prevents the pulse of the echo signal from being mixed with the pulse of the original signal or the sidelobe caused by autocorrelation.

[0091] S12, a single-target slow-time echo signal model with amplitude and phase chirp is established;

[0092] In the detection range of the airborne radar, the Doppler shift of the target is f d , the two-way propagation delay is τ, and the echo signal model r(t) of the target is expressed as:

[0093]

[0094] where f0represents the carrier frequency, and α represents the complex amplitude of the target.

[0095] Let be the updated complex amplitude of the target, and the echo signal r T (t) after the down-conversion processing is expressed as:

[0096]

[0097] S13, the target echo signal is matched filtered and sampled;

[0098] Suppose that the impulse response of the matched filter is h(t) = u * (-t), (·) * represents the conjugate operator, and the processed echo signal v T (t) is expressed as:

[0099]

[0100] where, represents the ambiguity function of the intra-pulse waveform.

[0101] The echo signal model of equation (4) at time sampling, denotes the slow-time echo model of the target is expressed as:

[0102]

[0103] the intrapulse waveform ambiguity function (fast-time dimension) and the amplitude-phase code word c i independent of f, the ambiguity function is expressed as χ p (0, f d ) = 1.

[0104] Let i = 1, 2,..., P, and let c = [c1, c2,..., c P ] T , (·) T denotes the transpose operator, and denotes the Hadamard product operator, then the vector form v T of the slow-time echo model of the single target is expressed as:

[0105] v T = α T c⊙p(f d ) (23)

[0106] S14, divide the clutter cells in the radar detection range;

[0107] The clutter cells are divided by equidistant and equi-Doppler rings, and the Doppler shift value range of the clutter cells is set as [-f r / 2, f r / 2], f r denotes the pulse repetition frequency, and the Doppler shift corresponding to the i-th Doppler ring is f Di .

[0108] S15, establish the slow-time clutter model corresponding to the ambiguity distance ring;

[0109] The matched filtering and sampling processing of the clutter signal is the same as that of the target echo, and the processed slow-time clutter model is essentially the echo of the clutter cell that overlaps with the target echo in different ambiguity intervals, which is expressed as:

[0110]

[0111] wherein r = 1, 2,..., n denotes the ambiguity number of the clutter cell, corresponding to a specific ambiguity distance ring; J r denotes the displacement matrix under r times ambiguity; σ ri denotes the echo power of the clutter cell; denotes the Doppler vector function of the clutter cell, f ri denotes the Doppler shift of the clutter cell.

[0112] S16, a slow-time total echo model is established;

[0113] Considering the noise signal contained in the echo, the slow-time echo model of the airborne radar amplitude-phase agile signal target detection in the clutter environment is expressed as:

[0114]

[0115] Wherein, n represents the noise in the slow-time echo model, that is, a complex Gaussian white noise.

[0116] In the embodiment, the step S2 is specifically as follows:

[0117] S21, a Doppler matrix is used to process the slow-time echo signal;

[0118] The Doppler vector of the i-th slow-time unit is set as p(-f Di ), and the i-th slow-time echo processed by the Doppler vector is expressed as: i

[0119]

[0120] Wherein, q(f ri -f Di ) represents the Doppler processed vector of the clutter echo under r times of blurring, and q(f) = J -r p(f); the frequency domain range is set as [-f r / 2, f r / 2], and the Doppler division region of the clutter unit is consistent with the frequency domain, f Di in formula (9) represents the frequency domain sampling point. represents the clutter echo noise after the Doppler vector processing.

[0121] The Doppler frequency shift range of the target and the clutter unit is set as [-f r / 2, f r / 2], in order to facilitate the construction of the energy model, f i = f d -f Di , f j = f ri -f Di , and f i , f j ∈ [-f r / 2, f r / 2].

[0122] In the case that the sampling interval is small enough, f i = 0, f j ​= 0 holds, so that the echoes of the target and the clutter unit produce a peak at this frequency point, thereby realizing coherent accumulation of the echo signal. i = 0 corresponds to the main lobe of the target, and f i ≠ 0 corresponds to the side lobe of the target.

[0123] S22, amplitude and phase compensation processing is performed on the echo signal.

[0124] The amplitude and phase compensation filter vector is the conjugate transpose of the amplitude and phase modulation code word sequence c, that is, ξ i The output y i after amplitude and phase compensation processing is represented as:

[0125]

[0126] Where (·) H represents the conjugate transpose operator, y Ti , y c , respectively represent the slow-time target echo, clutter and noise after the i th Doppler vector and amplitude and phase compensation filter processing.

[0127] In the case where the sampling interval is small enough, there exist f i = 0 and f j = 0 holds, so that the echoes of the target and the clutter unit produce a peak at this frequency point, that is, the main lobe position. The mathematical model of the sum of the processed target echo side lobe and the clutter unit echo energy is equivalent to the sum of the echo powers at each slow-time sampling point, which is specifically represented as:

[0128]

[0129] In order to make the target in the echo easier to be detected, it is necessary to reduce the target side lobe and the clutter energy in the processed echo. Therefore, the optimization process of the airborne radar under the initial phase agile signal system for target detection in the clutter can be equivalent to minimizing the value of ε, that is, taking ε as the objective function of the optimization problem.

[0130] In this embodiment, the step S3 is specifically as follows:

[0131] S31, simplifying the optimization problem;

[0132] Based on step S2, the PAR constraint is adopted to optimize ε with c as the independent variable, and the optimization problem is represented as:

[0133]

[0134] Where J0 represents the displacement matrix under the r = 0 th blur, that is, the unit matrix, and σ rlrepresents the echo signal complex amplitude of the clutter cell, c(i) represents the i th element of the amplitude-phase code sequence, and γ represents the maximum modulus value of the PAR constraint.

[0135] The optimization problem is preliminarily simplified, and the fourth-order optimization problem is converted into a second-order optimization problem:

[0136]

[0137] wherein C = cc H represents a Hermite matrix,

[0138] S32, the accelerated PMLI algorithm is used to solve the optimization problem;

[0139] The iterative update expression of the PMLI combined with the convergence acceleration algorithm is:

[0140]

[0141] wherein c (k) represents the amplitude-phase code sequence after the k th iteration; represents y (k) and the function transformation relationship between c (k) , λ T and λ C respectively represent the maximum eigenvalues of the matrices Θ(c (k) ) and , I P represents a unit matrix with a size of P × P, and Θ(c (k) ) = R - 2λ max (Λ T ) c (k) c (k)H , λ max (Λ T ), λ max (Λ c ) respectively represent the maximum eigenvalues of the matrices Λ T and Λ c ; R and respectively are R = Φ + Φ H , Φ and both represent Hermite matrices, and

[0142] wherein l i = (J0diag(p(f i )) c (k) ) H c (k) , l r,i= [J r diag(q(f j ))c (k) ] H c (k) ; vector L R≥0 and L R≤0 vector function L A , mathematical expression u m and the definition of delta are as follows:

[0143]

[0144]

[0145]

[0146] where x represents the xth element of the vector function L A , A represents the set of all possible independent variables x, and L is the unit vector when the vector function is abbreviated as L; m represents the number of non-zero elements in y (k) ; represents the ith element of the vector y (k) .

[0147] Based on the objective function and iterative formula of the optimization problem derived from steps S1-S3, an acceleration algorithm is introduced to solve the optimization problem:

[0148] Definition c1-c (k) , Λ = c2-c1-Γ, λ =-||Γ|| / ||Λ||; then the amplitude-phase code sequence updated by the acceleration algorithm each time is c2 is obtained by twice PMLI iterative update of c (k) , so as to ensure the monotonicity of the objective function ε, thereby ensuring the effectiveness of the algorithm; and the algorithm is a two fixed point iterative problem, which determines the step length λ by backtracking λ←(λ-1) / 2 to update the sequence phase, and the backtracking range is from λ to-1, and the enhanced solution is obtained after multiple iterations, thereby completing the solution of the optimization problem.

[0149] In this embodiment, the amplitude-phase agile signal airborne radar transmitting antenna in the simulation scenario is set as a planar phased array and the working mode is a positive side array, P = 64 pulses are transmitted, the pulse width is T p = 50 μs, the pulse repetition period is T = 500 μs, the carrier frequency is f0= 500 MHz, and the maximum unambiguous distance is R m = 75 km. The height of the aircraft is h = 8 km, and the speed is V = 120 m / s.

[0150] The Morchin model of hilly terrain is used to model the range-doppler energy of the clutter by using the clutter backscattering rate. The target is at a distance of R = 385 km from the airborne radar, and the radial velocity of the target is v = 80 m / s, and the target scattering cross section is σ T = 10 m 2 .

[0151] Regarding the optimization model, the initial phase is randomly generated in a uniform distribution between [0, 2π], and the optimization weight vector is w C = [1, 0, 0, 0, 0, 100] T , and the target complex amplitude is α T = 1, the echo power of all clutter units in the rth ambiguity interval is σ ri = w C (r+1), i = 1, 2,..., P.

[0152] In this embodiment, the simulation is performed based on the convergence acceleration algorithm of the PML, and the optimization iteration is performed under the setting of the optimization weight w C = [1, 0, 0, 0, 0, 100] T , and the optimized ambiguity function diagram and the sidelobe and clutter energy curve with the number of iterations are plotted. As shown in Figure 2 , it can be seen that the sidelobe and total clutter energy of the 5th ambiguity region after optimization are extremely low, that is, the optimized region of interest is effectively suppressed in theory; as shown in Figure 3 , it can be seen that the convergence speed of the optimization algorithm of the method is fast, and the overall optimization process is efficient, and the theoretical average of the energy suppression of all regions is 25 dB.

[0153] As shown in Figure 4 , when there is a target in the region of interest, the algorithm of the method is evaluated. The target detection is performed under the airborne clutter background in the Gaussian white noise and hilly terrain environment. Figure 4 (a) is the constant initial phase signal target detection RD plane; Figure 4 (b) is the target detection RD plane of the optimized amplitude and phase agile signal, Figure 4 (c) is the local diagram of the target detection RD plane of the optimized amplitude and phase agile signal, and the signal-to-clutter-and-noise ratio in the region of interest is improved by 33.02 dB, and the results show that the optimization algorithm of the method can effectively suppress the target sidelobe and clutter of the initial phase agile signal airborne radar, thereby improving the target detection performance of the airborne radar in the clutter environment.

[0154] As shown in Figure 5As shown, under the contrast of the target and clutter energy of the constant initial phase signal and the optimized target and clutter energy distance, the contrast section view. Compared with the constant initial phase signal, the clutter energy of the initial phase agile signal is obviously higher as a whole, and the target is completely covered; after optimization, the clutter energy of the amplitude and phase agile signal in the region of interest is suppressed by more than 30dB, and the high linear clutter in the fifth fuzzy region is completely suppressed, and target detection can be realized.

[0155] In summary, the above simulation proves that the algorithm can effectively suppress the target sidelobe and clutter energy in the region of interest, thereby realizing anti-range folding clutter target detection. The method of the present application constructs the energy equivalent mathematical model of the target sidelobe and clutter by the amplitude and phase agile airborne radar slow-time echo model, and uses the model as the objective function and the PAR constraint to establish an optimization problem. Solving this optimization problem can realize the suppression of the target echo sidelobe energy and the range folding fuzzy clutter, and for the clutter energy, the method of the present application can suppress the clutter base in the region of interest, thereby realizing anti-range folding clutter target detection; on the other hand, the method of the present application does not need to rely on prior knowledge such as clutter covariance matrix, and the optimization object is not only for a specific type of clutter, and has realizability and generalizability.

[0156] Those skilled in the art will appreciate that the embodiments described herein are presented for purposes of illustration and should be understood not to be limiting the scope of the present application. The present application can be modified and varied in various ways, and it is therefore to be understood that, within the scope of the present application, any modifications, equivalent replacements, improvements, etc. made without departing from the spirit and principles of the present application should be included in the scope of the claims of the present application.

Claims

1. A method for designing inter-pulse waveform amplitude-phase agile against range folding clutter, comprising the following steps: S1, establishing a slow-time total echo model of airborne radar amplitude-phase agile in clutter environment; S2, processing echo signals and constructing a sidelobe and clutter suppression optimization problem; S3, solving the optimization problem; The step S2 is specifically as follows: S21, processing slow-time echo signals by using Doppler matrix; The Doppler vector of the first slow time unit is set as , and the first slow time echo processed therefrom is represented as: （1） wherein represents the updated target complex amplitude, represents the amplitude and phase modulated code sequence, and the target Doppler shift is , represents the total ambiguity number of the clutter cell, and the airborne radar transmits pulses in one CPI, represents the displacement matrix under the ambiguity; represents the echo power of the clutter cell, represents the Doppler shift of the clutter cell; represents the Doppler processing vector of the clutter echo under the ambiguity, and has , represents the displacement matrix under the ambiguity; represents the pulse repetition frequency, and let the frequency domain range be , and the Doppler division area of the clutter cell is consistent with the frequency domain, then in formula (1) represents the frequency domain sampling point; represents the noise in the slow-time echo model, which is a complex Gaussian white noise; represents the noise of the clutter echo after Doppler vector processing; The Doppler frequency shift range of the target and the clutter cell are both set as , for the construction of the energy model, let , , and ; In the case of a sufficiently small sampling interval, there exists , , which is established, so that the echoes of the target and clutter cells produce peaks at the frequency point, thereby realizing coherent accumulation of the echo signals; when , it corresponds to the target main lobe, , it corresponds to the target side lobe; S22, performing amplitude-phase compensation processing on echo signals; The amplitude and phase compensation filter vector is the amplitude and phase modulation code word sequence the conjugate transpose of The output after the amplitude and phase compensation processing is represented as （2） wherein, denotes the conjugate transpose operator, , , denote the slow-time target echo, clutter and noise after the first and second Doppler vector and amplitude and phase compensation filter processing, respectively. In the case of sufficiently small sampling intervals, there exists and holds, so that the echoes of the target and the clutter cell produce a peak at this frequency, i.e. at the main lobe position; the mathematical model of the sum of the processed target echo side lobes and the clutter cell echo energy is equivalent to the sum of the echo powers at each slow-time sampling point, which is expressed as: （3） Consider as the objective function of the optimization problem.

2. The method of claim 1, wherein the method is characterized by: The step S1 is specifically as follows: S11, establishing an inter-pulse amplitude-phase agile signal model; Suppose that the airborne radar transmits a number of pulses within a CPI and the amplitude and initial phase of the pulses are both interpulse variant, the model of the transmitted signal is represented as （4） wherein, denotes the signal observation time, denotes the amplitude and phase information of the denotes the pulse repetition period, denotes the pulse signal;​ to ensure that adjacent pulse transmission times are guaranteed , denotes the pulse width; S12, establishing a slow-time echo model of amplitude-phase agile single target; In the detection range of the airborne radar, the Doppler shift of the target is , the two-way propagation delay is , and the echo signal model of the target is represented as ​ （5） wherein represents a carrier frequency, represents a target complex amplitude; Let The echo signal after down-conversion processing as the target complex amplitude of update is represented as: （6） S13, performing matched filtering and sampling processing on target echo signals; The impulse response of the matched filter is set to , denotes the conjugate operator, the processed echo signal is represented as: （7） wherein denotes the ambiguity function of the intravascular waveform; The echo signal model of equation (7) is sampled at time t = t0+ ntΔt, where t0is the slow time instant, the slow time echo model of the target is represented as: （8） In-pulse waveform ambiguity function and amplitude-phase code word Irrespective, the ambiguity function is expressed as ; Set , let , , denotes the transpose operator, denotes the amplitude and phase information of the th pulse, denotes the Hadamard product operator, then the vector form of the single objective slow time echo model is given by: （9） S14, dividing clutter units in radar detection range; The Doppler frequency shift value range of the clutter cell is set as , The pulse repetition frequency is represented as fpr, and the Doppler frequency shift corresponding to the first Doppler ring is represented as fdoppler1. ;​ S15, establishing a slow-time clutter model corresponding to a fuzzy distance ring; The matched filtering and sampling processing mode of clutter signals is the same as that of target echoes, and the processed slow-time clutter model is essentially the echo of clutter units overlapping with target echoes in different fuzzy intervals, and is expressed as: （10） in, This indicates the number of ambiguities in the clutter cell, corresponding to a specific ambiguity range ring; This represents the total number of ambiguities in the clutter cell. express Displacement matrix under sub-fuzziness; This indicates the echo power of the clutter element; The Doppler vector function representing the clutter element. Indicates the Doppler frequency shift of clutter units; S16, establishing a slow-time total echo model; Considering noise signals contained in echoes, a slow-time echo model of airborne radar amplitude-phase agile signal target detection in clutter environment is expressed as: （11） wherein represents the noise in the slow-time echo model, i.e. complex Gaussian white noise.

3. The method of claim 1, wherein the method is characterized by: The step S3 is specifically as follows: S31, simplifying the optimization problem; Based on step S2, with Taking the PAR constraint as the independent variable, the optimization is performed, and the optimization problem is represented as: Optimization, the optimization problem is represented as: （12） wherein denotes the amplitude-phase modulation code word sequence, denotes the displacement matrix under the th ambiguity, i.e. the identity matrix, denotes the displacement matrix under the th range ambiguity and the th azimuth ambiguity, denotes the th element of the amplitude-phase code word sequence, denotes the maximum modulus of the PAR constraint; The optimization problem is preliminarily simplified, and a fourth-order optimization problem is converted into a second-order optimization problem: （13） wherein denotes a Hermite matrix, , ; S32, solving the optimization problem by using an accelerated PMLI algorithm; The iterative update expression of PMLI combined with a convergence acceleration algorithm is: （14） wherein, denotes the amplitude-phase code word sequence after the th iteration; , denotes the function transformation relationship between , and denote the maximum eigenvalues of the matrices and , denotes the identity matrix of size , and , , , denote the maximum eigenvalues of the matrices and ; and are , ; and both denote Hermite matrices, and , ; wherein , ; vector and vector function formula , mathematical expression and definition formula respectively as follows: （15） （16） （17） in, Representing vector functions The One element, Represents all possible independent variables The set of vector functions, when the vector function is abbreviated as hour, That is, a unit vector; express The number of non-zero elements in the array; Representing vectors The One element; Based on the optimization problem objective function and iterative formula derived from steps S1-S3, an acceleration algorithm is introduced to solve the optimization problem: Definition , , get , , ; then the amplitude-phase code sequence updated by the acceleration algorithm each time is ; by two PMLI iteration updates get the algorithm to determine the step size by backtracking to update the sequence phase, the backtracking range is -1, after multiple iterations, the enhanced solution is obtained, and the solution of the optimization problem is completed.

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