Full polarization radar transmit waveform optimization method, computer device and storage medium

Abstract

The application discloses a full polarization radar transmitting waveform optimization method, a computer device and a storage medium, and aims at the deficiency of an anti-ISRJ joint design method, fully considers the modulation condition of an extended target characteristic on a transmitting signal, further modifies a'signal-to-interference-and-noise ratio' expression in an original target function, simultaneously combines polarization information of a jammer, and designs two-way polarization waveforms and filters on horizontal-vertical channels, so as to design a joint optimization problem of a wideband full polarization radar anti-ISRJ transmitting waveform and a receiving filter, so as to improve anti-interference performance while keeping signal processing simple. Under the condition of wideband full polarization detection, compared with a traditional method, the full polarization radar transmitting waveform optimization method improves the suppression ability of an interference signal and the detection ability of a target, and keeps excellent robust performance on a target characteristic. The application is widely applied to the field of radar technology.

Description

Technical Field

[0001] This invention relates to the field of radar technology, and in particular to a method for optimizing the transmitted waveform of a fully polarized radar, a computer device, and a storage medium. Background Technology

[0002] In recent years, with the continuous development of electronic technology, the adversarial environment faced by radar has become increasingly intense. In particular, the continuous improvement of Digital Radio Frequency Memory (DRFM) has brought enormous challenges to the anti-jamming performance of radar systems. As a new type of coherent jamming derived from DRFM, Interrupted Sampling Repeater Jamming (ISRJ) effectively solves the problems of high-speed sampling and isolation between transmitting and receiving antennas by partially sampling and retransmitting intercepted radar signals. After pulse compression processing by the radar receiver, this jamming method creates a series of coherent false targets, simultaneously deceiving and suppressing friendly radar, significantly weakening the target detection capability of radar systems on the modern battlefield. Due to its fast response speed and simple engineering implementation, ISRJ has become a hot issue that urgently needs to be addressed in the field of radar countermeasures in modern electronic warfare. Summary of the Invention

[0003] To address the radar interference problem caused by intermittent sample-and-retransmit jamming (ISRJ), the present invention aims to provide a method for optimizing the transmitted waveform of a fully polarized radar, a computer device, and a storage medium.

[0004] On one hand, embodiments of the present invention include a method for optimizing the transmitted waveform of a fully polarized radar, the method comprising the following steps:

[0005] Through formula

[0006]

[0007] Establish a joint optimization problem; where s is the transmitted waveform sequence of a broadband fully polarimetric radar under energy constraints, h is the received filter sequence of a broadband fully polarimetric radar under energy constraints, Γ() is the gamma function, ε is the Pareto weight, f1() and f2() are the cost functions, the superscript H indicates finding the Hermite matrix, T indicates finding the transpose matrix, M is the number of echo points after the fully polarimetric radar transmitted pulse is reflected by the target, |s n |=|(s H,n ,s V,n )| TThis is the mathematical expression for the phase-coded pulse signal transmitted by a fully polarimetric radar system in a fast time, where n represents the ordinal number of the pulse in the phase-coded pulse signal, N represents the total number of pulses in the phase-coded pulse signal, and s H,n For the phase-coded pulse signal of the horizontal transmission channel of the fully polarimetric radar, s V,n This refers to the phase-coded pulse signal for the vertical transmission channel of a fully polarimetric radar.

[0008] The joint optimization problem is solved to determine the optimal transmit waveform and the optimal receive filter.

[0009] Furthermore, solving the joint optimization problem to determine the optimal transmit waveform and the optimal receive filter includes:

[0010] The first iteration and the second iteration are executed alternately until the stopping iteration condition is met; in the first iteration, the latest obtained optimal transmission waveform is fixed, and the latest optimal receiving filter is obtained by solving; in the second iteration, the latest obtained optimal receiving filter is fixed, and the latest optimal transmission waveform is obtained by solving.

[0011] When the stopping iteration condition is met, the optimal receiving filter obtained in the last iteration of the first process is obtained as the final optimal receiving filter. The optimal transmission waveform obtained in the last second iteration is taken as the final optimal transmission waveform.

[0012] Further, the alternating execution of the first iteration process and the second iteration process includes:

[0013] After completing the second iteration of the i-th round, the latest optimal transmission waveform s is obtained. (i) Then, the first iteration process in the (i+1)th round is executed;

[0014] In the first iteration of the (i+1)th round, the optimal transmission waveform s is fixed. (i) Through formula

[0015] h (i+1) =arg minΓ(s (i) ,h) (38)

[0016] Calculations are performed to obtain the optimal receiving filter h generated by the first iteration process in the (i+1)th round. (i+1) .

[0017] Furthermore, the optimal receiving filter h generated by the first iteration process in the (i+1)th round is obtained. (i +1) ,include:

[0018] Through formula

[0019]

[0020] u(h (i) )=(P-tr(P)I 2M )h (i) -p (51)

[0021]

[0022]

[0023] Determine the optimal receiving filter h (i+1) Among them, M h = 2M, where M represents a diagonal matrix of dimension 2M-1, X T Let X be the target echo matrix. J Let γ1 be the peak constraint weight, γ2 be a constant, Q be the number of peak mismatches between the interference signal and the receiving filter during the unmatched filtering process, and a be the peak constraint weight. max Let a be a constant representing the maximum value. min Let be a constant representing the minimum value.

[0024] Further, the alternating execution of the first iteration process and the second iteration process includes:

[0025] After completing the first iteration process in the (i+1)th round, the latest optimal receiving filter h is obtained. (i+1) Then, the second iteration process is executed in the (i+1)th round;

[0026] In the (i+1)th round of the second iteration, the optimal receiving filter h is fixed. (i+1) Through formula

[0027] s (i+1) =arg minΓ(s,h (i+1) (39)

[0028] Calculations are performed to obtain the optimal transmission waveform s generated by the second iteration process in the (i+1)th round. (i+1) .

[0029] Furthermore, the optimal transmission waveform s generated by the (i+1)th iteration process is obtained. (i+1) ,include:

[0030] Through formula

[0031] s (i+1) =-exp(j.arg(v(s) (i)))) (60)

[0032] v(s (i) )=(Q-tr(Q)I 2N )s (i) -q (61)

[0033]

[0034]

[0035] Determine the optimal transmission waveform s (i+1) Where T(θ) is the target impulse response matrix, M is the characteristic matrix of the fully polarized jammer. h = 2M, where M represents a diagonal matrix of dimension 2M-1, I 2n Let γ1 be the peak constraint weight, γ2 be a constant, Q be the number of peak mismatches between the interference signal and the receiving filter during the unmatched filtering process, and a be the identity matrix of size 2n. max Let a be a constant representing the maximum value. min Let be a constant representing the minimum value.

[0036] Furthermore, the stopping iteration condition is given by formula |Γ (i+1) (s,h)-Γ (i) (s,h)| / |Γ (i) (s,h)|≤η Γ The convergence condition represented by the expression;

[0037] Among them, Γ (i) (s,h) represents the optimal transmission waveform s (i) With the optimal receiving filter h (i) Substituting the result into the gamma function, Γ (i+1) (s,h) represents the optimal transmission waveform s (i+1) With the optimal receiving filter h (i+1) Substituting the result into the gamma function, η Γ It is a constant.

[0038] Furthermore, the stopping iteration condition is that the sum of the number of execution rounds of the first iteration process and the second iteration process reaches a certain threshold.

[0039] On the other hand, embodiments of the present invention also include a computer device, including a memory and a processor, the memory for storing at least one program, and the processor for loading at least one program to execute a fully polarized radar transmission waveform optimization method according to the embodiments.

[0040] On the other hand, embodiments of the present invention also include a storage medium storing a processor-executable program, which, when executed by a processor, is used to perform a fully polarized radar transmission waveform optimization method in the embodiments.

[0041] The beneficial effects of this invention are as follows: The fully polarimetric radar transmit waveform optimization method in the embodiments addresses the shortcomings of the joint design method for ISRJ anti-interference, fully considers the modulation of the transmitted signal by the extended target characteristics, further modulates the "signal-to-interference-plus-noise ratio" expression in the original objective function, and, in conjunction with the polarization information of the jammer, designs two-way polarimetric waveforms and filters in the horizontal-vertical channels. This leads to the design of a joint optimization problem for the transmit waveform and receive filter of a broadband fully polarimetric radar against ISRJ, aiming to improve anti-jamming performance while maintaining signal processing simplicity. Under broadband fully polarimetric detection conditions, compared with traditional methods, the fully polarimetric radar transmit waveform optimization method in the embodiments significantly improves the ability to suppress jamming signals and detect targets while maintaining excellent robustness against target characteristics. Attached Figure Description

[0042] Figure 1 This is a schematic diagram illustrating the principle of direct intermittent sampling and forwarding interference.

[0043] Figure 2 This is a schematic diagram of the signal processing flow for a broadband fully polarized radar system in the embodiment.

[0044] Figure 3 This is a schematic diagram illustrating the steps of the fully polarized radar transmit waveform optimization method in the embodiment;

[0045] Figure 4 This is a flowchart illustrating the fully polarized radar transmit waveform optimization method in this embodiment. Detailed Implementation

[0046] Currently, anti-interference methods for ISRJ can be broadly classified into three categories. The first category employs the idea of ​​transmitting waveform design, transmitting waveforms with orthogonal LFM-phase coding or sparse Doppler characteristics, and then using methods such as segmented pulse compression or sliding window decimation at the receiver to identify and filter out ISRJ signals. The second category focuses on receiver signal processing, suppressing interference by analyzing the time-frequency characteristics or inter-class variance characteristics of the interference signal and the normal echo signal. However, most of these methods rely on estimating ISRJ-related parameters, and the processing flow is complex. The third category combines the first two categories, employing a joint design system of transmitting waveform and receiving filter. By solving a non-convex optimization problem, it obtains waveforms and unmatched filter sequences with good anti-interference characteristics, achieving significantly higher degrees of freedom in anti-interference compared to the first two categories, thus improving anti-interference performance.

[0047] It should be noted that the third type of method mentioned above, when considering the signal-to-interference-plus-noise ratio (SINR) modeling for waveform optimization, only considers the point target case under low-resolution detection. Under broadband detection conditions, the target echo is a one-dimensional high-resolution range profile with multiple scattering centers. Furthermore, this work only focuses on the joint design of a single polarization channel and does not fully utilize the polarization domain information of the jammer. In terms of anti-jamming, some techniques design two-path polarization waveforms by using target scattering characteristics and the jammer's equivalent scattering matrix, and comprehensively consider the isolation problem of the main and auxiliary channels, thereby significantly improving ISRJ suppression performance. This fully demonstrates the importance of expanding the joint design in the polarization domain for improving the anti-jamming performance of radar systems.

[0048] If, based on the third type of method mentioned above, we introduce constant mode constraints to construct an objective function and effectively solve it by combining the two indicators of weighted pulse compression sidelobe and signal-to-interference-plus-noise ratio loss, then we can expect to achieve an effective joint design method that can achieve significant anti-interference performance.

[0049] Based on the above principles, this embodiment presents a method for optimizing the transmitted waveform of a fully polarized radar. To illustrate the principle of this method, a problem model to be solved is first established, followed by a problem-solving process. The results of this problem-solving process constitute the core steps of the fully polarized radar transmitted waveform optimization method.

[0050] 1. Problem Model

[0051] This section first presents a mathematical model of the ISRJ (Inter-Independent Radio Jupiter) problem for broadband fully polarimetric radar, and then presents the mathematical expression for the optimization problem of the joint design of the transmit waveform and the receive filter.

[0052] 1.1 System Model

[0053] Without loss of generality, the mathematical expression for the phase-coded pulse signal transmitted by a fully polarimetric radar system in a fast time can be written as:

[0054]

[0055] Where H and V represent the horizontal and vertical transmission channels of the fully polarized radar, respectively, and N represents the code length of the transmitted pulse signal. T This indicates a transpose operation on the matrix. Simultaneously, to ensure the radar system's transmitter operates in power saturation mode, the transmitted phase-coded signal must satisfy the constant modulus constraint, i.e.

[0056]

[0057] Where X∈{H,V}, n=0,1,...,N-1. For ease of study, the mathematical expression for the transmitted pulse in equation (1) can be rewritten as follows after overlapping and merging:

[0058]

[0059] Among them are |(s) H,n ,s V,n ) T |=2. Correspondingly, considering the unmatched filtering scheme, the filter sequence of the receiver in a fully polarimetric radar system can be written as:

[0060]

[0061] Where M is the number of echo points after the fully polarized radar transmit pulse is reflected by the target, and the filter sequence satisfies the energy constraint h. H h = M h =2M.

[0062] In a broadband fully polarimetric radar detection system, the detected target can no longer be considered a point target located within a single radar range cell, but rather an extended target with multiple scattering centers in the range dimension. In this case, the modulation effect of the target on the transmitted pulse signal can be characterized by the Target Impulse Response (TIR). Considering the polarimetric scattering characteristics of the detected target, and assuming the length of the TIR sequence is Q = M - N + 1, then the nth range cell of the sequence can be represented as...

[0063]

[0064] Where θ represents the target azimuth angle (TAA) relative to the radar line of sight, T XY,n (θ) represents the target scattering coefficient in the nth range cell, where the transmitted pulse polarization channel is X and the received echo polarization channel is Y, XY∈{HH,HV,VH,VV}. To more intuitively characterize the vector relationship between the transmitted pulse and the received target echo of a broadband fully polarized radar, a target impulse response matrix (TIRM)T(θ) is introduced for description, as follows:

[0065]

[0066] This represents the Kronecker product operation, where C in equation (6) n The expression can be written as

[0067]

[0068] Compared to TIRM, which characterizes the scattering properties of a single polarization, TIRM, which represents the scattering properties of a target across all polarizations, changes each range unit of the TIR sequence from a scalar form to a 2×2 vector form. Its expansion is a block-Toeplitz matrix, mathematically expressed as follows:

[0069]

[0070] Because TIRM is quite sensitive to slight perturbations in TAA, it is often averaged over the interval θ∈[θ1,θ2] to enhance the robustness of the system.

[0071]

[0072] Therefore, the echo signal after a fully polarimetric radar transmits a pulse signal and is reflected by the target can be expressed as:

[0073]

[0074] Reference Figure 1 Regarding the ISRJ signal directly relayed by the jammer, its time-domain sampled rectangular envelope pulse train signal in the horizontal or vertical channel is as follows:

[0075]

[0076] Where X∈{H,V}, in any polarization channel, N X,J T represents the number of slices in the jammer. X,I T represents the slice width of the interference signal. X,J Let T represent the forwarding period of the interference signal, and let the two satisfy the relationship T. X,I =D X,J T X,J D X,J The symbol represents the duty cycle of the interference signal, and "*" indicates the convolution operation.

[0077] Discretizing equation (11) allows us to determine the time-domain sampling characteristics of the jammer in both the horizontal and vertical channels using J. H J V To indicate that there is

[0078]

[0079] in and Let M represent the discrete sequences of intermittent sampling for channels H and V, respectively, which can be obtained through an auxiliary measurement system. Let M be the length of the interference echo received by the unified fully polarized radar receiver. And satisfy

[0080]

[0081] Where p = 1, 2, ..., M, q = 1, 2, ..., N, then the broadband fully polarized radar horizontal and vertical signals intercepted by the jammer are respectively

[0082]

[0083] Let the equivalent scattering matrix of the fully polarized jammer be...

[0084]

[0085] The ISRJ signals relayed by the fully polarized jammer in the horizontal and vertical channels can be expressed as follows:

[0086]

[0087] Without loss of generality, the time-domain sampling parameters of the fully polarized jammer remain consistent in both the horizontal and vertical channels, therefore J H =J V Furthermore, by overlapping the horizontal and vertical polarization components, the relay signal of a fully polarized jammer can be written in matrix form as follows:

[0088]

[0089] in

[0090]

[0091]

[0092] Ultimately, the echo signal received by the fully polarimetric radar can be modeled as follows:

[0093]

[0094] Where, α T To account for complex parameters such as radar range and atmospheric loss, This indicates that the mean is 0 and the variance is . And independent of the additive white Gaussian noise of the transmitted signal s, i.e.

[0095]

[0096] In summary, the peak pulse compression output of a fully polarized radar system can be written as:

[0097]

[0098] 1.2 Optimization Problem Modeling

[0099] This section continues the analysis of the mathematical model for the joint optimization problem of the transmitted waveform and the received filter, aiming to suppress ISRJ from multiple perspectives. Among these factors, the echo x reflected from the target... T The mathematical expression for the aperiodic cross-correlation function of the receiving filter h of the fully polarimetric radar is:

[0100]

[0101] When the target echo sequence x T The receive filter sequence h satisfies the following relationship

[0102]

[0103] Where a max The peak value of the cross-correlation function is represented by the mathematical expression for the impulse function δ(n):

[0104]

[0105] Then at this point, x can be called T h and are complementary sequences, and their cross-correlation function has pulse compression output performance in the form of an "impulse function". Furthermore, the echo x of the ISRJ interference signal can also be obtained according to equation (23). J Mathematical expression for the non-periodic cross-correlation function of the receiving filter h of a fully polarimetric radar

[0106]

[0107] The purpose of jointly designing the transmitted waveform s and the receiving filter h is twofold: firstly, to maximize the match between the target echo and target characteristics, i.e., to minimize the sidelobe energy of the cross-correlation function between the target echo and the receiving filter; and secondly, to keep the cross-correlation function energy between the interference signal and the receiving filter as close to zero as possible, thereby effectively suppressing ISRJ. Based on the above requirements for both the target echo and the interference signal in a fully polarimetric radar, the corresponding mathematical expression for the cross-correlation function energy can be written as follows:

[0108]

[0109] Furthermore, due to the use of unmatched filtering, the target echo x T During receive filtering, the pulse compression peak will experience peak loss, i.e., signal-to-noise ratio loss (SNRL). Due to matrix compatibility, we have...

[0110] ||h H x T ||=||h HT(θ)s||≤||h||||T(θ)||||s|| (28)

[0111] Where · represents the 2-norm of a vector or matrix. Therefore, the expression for SNRL can be defined as follows:

[0112]

[0113] Therefore, the target echo x can be given T The following peak value constraint condition is applied to ensure that the pulse pressure peak value has a certain stability, namely

[0114]

[0115] Since the transmitted signal satisfies the constant modulus constraint condition, that is Meanwhile, the receiving filter of the fully polarimetric radar satisfies the energy constraint h. H h = M h =2M, the target echo x can be obtained by inverse calculation using equation (30). T peak pulse pressure

[0116]

[0117] Therefore, based on the penalty function method, the target echo x is suppressed. T The cost function for sidelobe energy is:

[0118] f1(s,h)=ζ1(s,h)+γ1g1(s,h) (32)

[0119] Here, γ1 represents the corresponding peak constraint weight. It should be noted that in order to ensure the penalty strength of the constraint, γ1 is usually taken as a large value so as to effectively control the filter output of the waveform.

[0120] Based on this, in order to further suppress the interference signal, it is necessary to apply peak constraint to the interference echo to reduce the pulse compression peak value of the interference signal as much as possible. Since the ISRJ signal relayed by the fully polarized jammer and the receiving filter length of the fully polarized radar are not equal (N and M respectively), in order to ensure that there is a Q-order peak mismatch between the interference signal and the receiving filter h during the unmatched filtering process, the following definition is made based on equation (13).

[0121]

[0122] Then there is

[0123]

[0124] Therefore, a peak constraint function in the weighted average form of equation (35) can be constructed.

[0125]

[0126] Among them, a min via a max The proportional relationship determines the value, and the smaller value is taken. Therefore, based on the idea of ​​the penalty function, the cost function for suppressing the total energy of the interference echo is:

[0127] f2(s,h)=ζ2(s,h)+γ2g2(s,h) (36)

[0128] Here, γ2 also needs to be taken as a large value to ensure effective suppression of interference signals. In summary, combining the Pareto equalization framework, the joint optimization problem of the transmitted waveform sequence s and the received filter sequence h of a broadband fully polarimetric radar under energy constraints can be expressed as:

[0129]

[0130] Where ε∈[0,1] is the Pareto weight.

[0131] This concludes the mathematical modeling of the ISRJ problem for broadband fully polarimetric radar.

[0132] At the same time, such as Figure 2 As shown in the block diagram, the working principle of the broadband fully polarimetric radar system in this embodiment is explained. The waveform generator first generates waveform sequences for the horizontal and vertical channels by solving a convex optimization problem. These waveforms are then radiated through the horizontal and vertical channel transmitting antennas via a power amplifier at the radar front end. At the radar receiver, two main signals are received: a broadband target echo reflected from an extended target, and an intermittently sampled jamming signal intercepted and relayed by a jammer. These signals first enter the horizontal and vertical channel receiving antennas of the radar, respectively. After frequency modulation to an intermediate frequency via mixing, they undergo unmatched filtering using the designed horizontal and vertical receiving filter sequences. The pulse compression signals from the two main channels are then superimposed to obtain the final pulse compression result processed by the method in this embodiment, which is used for subsequent signal detection.

[0133] 2. Problem Solving

[0134] In equation (37), both the objective function and the constraints of the optimization problem are non-convex, making them difficult to solve directly. Therefore, this embodiment will use an alternating iterative method to solve the above optimization problem. Specifically, given an initial transmit phase encoded waveform sequence s( 0 Based on this, first fix s (i) Solve for h (i+1) Then fix h (i+1) Solve for s (i+1)Repeat the above process until the set convergence condition is met, thereby obtaining the optimal transmission waveform of the broadband fully polarimetric radar. Receiver filter In summary, the mathematical form of the above iterative process can be expressed as follows:

[0135] h (i+1) =arg minΓ(s (i) ,h) (38)

[0136] s (i+1) =arg minΓ(s,h (i+1) (39)

[0137] Where s (i+1) h represents the optimal transmit waveform weight vector obtained after the i-th iteration of the algorithm. (i+1) This represents the optimal receiver filter weight vector obtained after the i-th iteration of the algorithm.

[0138] Furthermore, regarding the stopping iteration condition, it can be set as in formula |Γ (i+1) (s,h)-Γ (i) (s,h)| / |Γ (i) (s,h)|≤η Γ The convergence conditions shown are used to control the algorithm to reach convergence. It is easy to see that the advantage of the above solution method is that it transforms the multivariate non-convex optimization problem under multiple constraints into multiple subproblems that solve a single unknown, thereby reducing the difficulty of solving the problem. The following will solve the unknown receiver filter h in the iteration process separately. (i+1) Transmitted waveform s (i+1) The corresponding sub-problems.

[0139] In this embodiment, a count can be performed after each of the first or second iterations. When the count reaches a threshold, the iteration stop condition is considered met, and thus the formula |Γ (i+1) (s,h)-Γ (i) (s,h)| / |Γ (i) (s,h)|≤η Γ Even if the convergence condition shown is never met, the iterative process can still be stopped.

[0140] 2.1 Fixed Transmit Waveform s (i) Solve for the optimal receiving filter h (i+1)

[0141] According to equations (37) and (38), the transmitted waveform s is fixed when the algorithm goes through the i-th iteration. (i) Solve for the optimal receiving filter h (i+1) The optimization problem can be written as

[0142]

[0143] For the convenience of solving the above optimization problem, the target echo matrix X is defined respectively. T and ISRJ matrix X J for

[0144]

[0145]

[0146] Where n = 1, 2, ..., M, p = 1, 2, ..., M, q = 1, 2, ..., 2M-1. X T and X J The block-Toeplitz matrix has the following matrix expansion:

[0147]

[0148]

[0149] At this point, the optimization problem described in equation (40) can be equivalently written as

[0150]

[0151] in

[0152]

[0153]

[0154] Re(·) represents the operation of extracting the real part, and M represents a diagonal matrix of dimension 2M-1 (except for the Mth diagonal element which is equal to 0, all other diagonal elements are 1, and all elements other than the diagonal elements are 0).

[0155] For the optimization problem (45), according to the MM principle, assume z (i) Given the optimal solution obtained in the i-th iteration, find the principal component function u(z,z) of the objective function. (i) ), such that for any z∈Ω, u(z,z) satisfies (i) Let Ω represent the domain of the independent variable z. By optimizing the principal component function, the optimal solution for the (i+1)th iteration can be obtained as follows: Therefore, we can obtain g(z) (i+1) )≤g(z (i) Since matrix P satisfies the positive semi-definite property, the principal component function of the i-th iteration can be obtained.

[0156] tr(P (i) )h H h+(h (i) )H (tr(P (i) )I 2M -p (i) )h (i) +2Re(h H (p (i) -tr(P (i) )I 2M )h (i) (48)

[0157] Where P (i) and p (i) Let represent the values ​​assigned to matrices P and p respectively in the i-th iteration, and tr(·) denotes the trace operation on the matrix. Thus, the optimization problem (45) can be simplified to

[0158]

[0159] The optimal solution to the quadratic constrained linear programming problem in equation (45) is:

[0160]

[0161] in

[0162] u(h (i) )=(P-tr(P)I 2M )h (i) -p (51)

[0163] Thus, the i-th iteration has been completed, and the optimal receiving filter h for the fully polarimetric radar has been determined. (i+1) Solve for it.

[0164] 2.2 Fixed receiving filter h (i+1) Solve for the optimal transmission waveform s (i+1)

[0165] Based on equations (37) and (39), it can be similarly concluded that in the i-th iteration, the receiving filter h is fixed. (i+1) Solve for the optimal transmission waveform s (i) The optimization problem can be written as

[0166]

[0167] Similarly, the receiving filter matrix H is defined as follows:

[0168]

[0169] Where n = 1, 2, ..., M, p = 1, 2, ..., M, q = 1, 2, ..., 2M-1. And X T and X J Consistent, H is also a block-Toeplitz matrix, and its matrix expansion is:

[0170]

[0171] At this point, the function optimization problem in equation (52) is equivalent to:

[0172]

[0173] in

[0174]

[0175]

[0176] As can be seen, the optimization problem (55) is a constant modulus constrained linear programming problem. Since matrix Q satisfies the positive semi-definite property, its principal component function can be obtained as follows:

[0177] tr(Q (i) )s H s+(s (i+1) ) H (tr(Q (i) )I 2N -Q (i) )s (i+1) +2Re((s (i+1) ) H (Q (i) -tr(Q (i) )I 2N )s) (58)

[0178] Problem (55) can then be simplified to

[0179]

[0180] Q (i) and q (i) Let Q and q represent the values ​​assigned to matrices Q and q respectively during the i-th iteration. Therefore, the optimization problem (55) has an optimal solution.

[0181] s (i+1) =-exp(j.arg(v(s) (i) ))) (60)

[0182] in

[0183] v(s (i) )=(Q-tr(Q)I 2N )s (i) -q (61)

[0184] Thus, the optimal transmission waveform s of the fully polarized radar in the i-th iteration has been completed. (i+1) Solve for it.

[0185] 2.3 Complete Process of Iterative Optimization Method

[0186] By combining the above iterative solution method of alternating between the transmitted waveform sequence s and the received filter sequence h, the optimal design of the constant-mode complementary waveform against ISRJ can be completed. To further shorten the convergence time of the algorithm, the Squared Iterative Method (SQUAREM) framework can be introduced without sacrificing algorithm performance to significantly improve the convergence speed. This optimization framework meets the requirements of accelerating the computation of traditional complex high-dimensional problems with low storage requirements, and since the accelerator itself only adjusts the parameters of the update step, it can be migrated to the algorithm in this embodiment. The flowchart of the constant-mode complementary waveform design algorithm for broadband fully polarimetric radar after using the Squared Iterative Method framework is as follows: Figure 3 As shown.

[0187] As can be seen from the figure, before using the algorithm in this embodiment to design the transmit waveform and receive filter, it is necessary to first obtain the weighted average target impulse response matrix from the auxiliary knowledge base. and the characteristic matrix of the fully polarized jammer For the i-th iteration, the principal component minimization method is used. First, the transmitted waveform sequence s is fixed, and the received filter sequence h is solved; then, the received filter sequence h is fixed, and the transmitted waveform sequence s is solved. Based on this, to ensure monotonically convergent algorithm in alternating iterations, the SQUAREM framework is introduced in the steps of solving sequences s and h, respectively. That is, the step size factor α is continuously reduced in each step of the solution process, ensuring that the objective function monotonically decreases in each principal component solution step. Finally, after satisfying the convergence condition of adjacent SINRs, the outer loop is terminated, and the optimal transmitted waveform sequence of the response is output. and receive filter sequence

[0188] based on Figure 1 and Figure 2 Based on the principle, this embodiment designs a method for optimizing the transmitted waveform of a fully polarized radar. (Refer to...) Figure 3 The method for optimizing the transmitted waveform of a fully polarized radar includes the following steps:

[0189] S1. Through the formula Establish a joint optimization problem;

[0190] S2. Solve the joint optimization problem to determine the optimal transmission waveform. and optimal receiving filter

[0191] Where s is the transmitted waveform sequence of a broadband fully polarimetric radar under energy constraints, h is the received filter sequence of a broadband fully polarimetric radar under energy constraints, Γ() is the gamma function, ε is the Pareto weight, f1() and f2() are cost functions, the superscript H indicates calculating the Hermite matrix, T indicates calculating the transpose matrix, M is the number of echo points after the fully polarimetric radar transmitted pulse is reflected by the target, |s n |=|(s H,n ,s V,n )| T This is the mathematical expression for the phase-coded pulse signal transmitted by a fully polarimetric radar system in a fast time, where n represents the ordinal number of the pulse in the phase-coded pulse signal, N represents the total number of pulses in the phase-coded pulse signal, and s H,n For the phase-coded pulse signal of the horizontal transmission channel of the fully polarimetric radar, s V,n This is the phase-coded pulse signal for the vertical transmission channel of a fully polarized radar.

[0192] Based on the principles of Section 2, "Problem Solving," we can follow... Figure 4 The process shown involves executing steps S1-S2 to obtain the optimal transmission waveform. and optimal receiving filter

[0193] In summary, addressing the shortcomings of the existing ISRJ anti-interference joint design method, this embodiment fully considers the modulation of the transmitted signal by extended target characteristics, further revising the "signal-to-interference-plus-noise ratio" expression in the original objective function. Simultaneously, combining the polarization information of the jammer, two-path polarization waveforms and filters are designed in the horizontal-vertical channels, thus tackling the joint optimization problem of the transmitted waveform and received filter for broadband fully polarimetric radar anti-ISRJ, aiming to improve anti-jamming performance while maintaining signal processing simplicity. Under broadband fully polarimetric detection conditions, compared to traditional methods, the method proposed in this embodiment significantly improves the suppression capability of jamming signals and the target detection capability while maintaining excellent robustness against target characteristics.

[0194] According to the principles in Section 2, "Problem Solving," by executing steps S1-S2, the "signal-to-interference-plus-noise ratio" modeling method of the joint design method of the transmitter and receiver in the existing technology is corrected. Under the detection conditions of broadband fully polarized radar, the modulation effect of target characteristics on the radar's transmitted waveform is expanded, so that the transmitted waveform can further match the target characteristics. In view of the significant azimuth angle disturbance error of the radar due to ISRJ, based on the robustness of the weighted average of the preset azimuth angle interval, the joint optimization problem in step S1 is designed. The optimal transmitted waveform and optimal receiver filter obtained by solving the joint optimization problem are more robust to the target characteristics. The joint optimization problem extends the single-polarized channel waveform design to the fully polarized waveform design, thereby increasing the degree of freedom of the transmitted waveform in terms of anti-interference and adaptation to target characteristics, and significantly improving the radar detection performance.

[0195] A computer program that executes the fully polarized radar transmission waveform optimization method in this embodiment can be written into a computer device or storage medium. When the computer program is read out and run, the fully polarized radar transmission waveform optimization method in this embodiment is executed, thereby achieving the same technical effect as the fully polarized radar transmission waveform optimization method in the embodiment.

[0196] It should be noted that, unless otherwise specified, when a feature is referred to as "fixed" or "connected" to another feature, it can be directly fixed or connected to the other feature, or indirectly fixed or connected to the other feature. Furthermore, the descriptions of "upper," "lower," "left," and "right" used in this disclosure are only relative to the relative positional relationships of the components of this disclosure in the accompanying drawings. The singular forms "a," "an," and "the" used in this disclosure are also intended to include the plural forms, unless the context clearly indicates otherwise. Moreover, unless otherwise defined, all technical and scientific terms used in this embodiment have the same meaning as commonly understood by one of ordinary skill in the art. The terminology used in this embodiment specification is only for describing particular embodiments and is not intended to limit the invention. The term "and / or" as used in this embodiment includes any combination of one or more of the associated listed items.

[0197] It should be understood that although the terms first, second, third, etc., may be used to describe various elements in this disclosure, these elements should not be limited to these terms. These terms are only used to distinguish elements of the same type from each other. For example, a first element may also be referred to as a second element without departing from the scope of this disclosure, and similarly, a second element may also be referred to as a first element. The use of any and all instances or exemplary language (“e.g.,” “such as,” etc.) provided in this embodiment is intended only to better illustrate embodiments of the invention and, unless otherwise required, does not impose a limitation on the scope of the invention.

[0198] It should be recognized that embodiments of the present invention can be implemented or carried out by computer hardware, a combination of hardware and software, or by computer instructions stored in a non-transitory computer-readable storage medium. The method can be implemented using standard programming techniques—including a non-transitory computer-readable storage medium configured with a computer program, wherein such a storage medium causes the computer to operate in a specific and predefined manner—according to the methods and drawings described in the specific embodiments. Each program can be implemented in a high-level procedural or object-oriented programming language to communicate with the computer system. However, if desired, the program can be implemented in assembly or machine language. In any case, the language can be a compiled or interpreted language. Furthermore, for this purpose, the program can run on a programmed application-specific integrated circuit (ASIC).

[0199] Furthermore, the procedures described in this embodiment can be performed in any suitable order unless otherwise indicated by this embodiment or clearly contradicted by the context. The procedures (or variations and / or combinations thereof) described in this embodiment can be executed under the control of one or more computer systems configured with executable instructions, and can be implemented by hardware or a combination thereof as code (e.g., executable instructions, one or more computer programs, or one or more applications) that commonly executes on one or more processors. A computer program includes multiple instructions executable by one or more processors.

[0200] Furthermore, the method can be implemented in any suitable type of computing platform, including but not limited to personal computers, minicomputers, mainframes, workstations, networked or distributed computing environments, standalone or integrated computer platforms, or in communication with charged particle tools or other imaging devices, etc. Aspects of the invention can be implemented as machine-readable code stored on a non-transitory storage medium or device, whether removable or integrated into a computing platform, such as a hard disk, optical read and / or write storage medium, RAM, ROM, etc., such that it is readable by a programmable computer, and when the storage medium or device is read by the computer, it can be used to configure and operate the computer to perform the processes described herein. Furthermore, the machine-readable code, or portions thereof, can be transmitted via wired or wireless networks. The invention of this embodiment includes these and other different types of non-transitory computer-readable storage media when such media comprises instructions or programs that implement the steps above in conjunction with a microprocessor or other data processor. When programmed according to the methods and techniques of the invention, the invention also includes the computer itself.

[0201] A computer program can be applied to input data to perform the functions of this embodiment, thereby transforming the input data to generate output data stored in non-volatile memory. The output information can also be applied to one or more output devices, such as a display. In a preferred embodiment of the invention, the transformed data represents physical and tangible objects, including a specific visual depiction of physical and tangible objects generated on the display.

[0202] The above are merely preferred embodiments of the present invention. The present invention is not limited to the above-described embodiments. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention, as long as they achieve the technical effects of the present invention by the same means, should be included within the scope of protection of the present invention. Within the scope of protection of the present invention, the technical solutions and / or implementation methods can have various modifications and variations.

Claims

1. A method for optimizing the transmitted waveform of a fully polarized radar, characterized in that, The fully polarimetric radar transmit waveform optimization method includes: Through formula （37） Establish a joint optimization problem; among which, This is the transmitted waveform sequence of a broadband fully polarimetric radar under energy constraints. This is the receiver filter sequence for a broadband fully polarimetric radar under energy constraints. For gamma function, For Pareto weights, The cost function for suppressing the sidelobe energy of the target echo, The cost function for suppressing the total energy of interference echoes, with superscript... This indicates the search for the Hermite matrix. This indicates finding the transpose of the matrix. This represents the number of echo points after the transmitted pulse from a fully polarized radar is reflected by the target. Here is the mathematical expression for the phase-coded pulse signal transmitted by a fully polarized radar system in a fast time, where Indicates the ordinal number of the pulse in the phase-coded pulse signal. This indicates the total number of pulses in the phase-coded pulse signal. This refers to the phase-coded pulse signal of the horizontal transmission channel of a fully polarimetric radar. This refers to the phase-coded pulse signal for the vertical transmission channel of a fully polarimetric radar. Solve the joint optimization problem to determine the optimal transmit waveform and the optimal receive filter; Solving the joint optimization problem to determine the optimal transmit waveform and the optimal receive filter includes: The first iteration and the second iteration are executed alternately until the stopping iteration condition is met; in the first iteration, the latest obtained optimal transmission waveform is fixed, and the latest optimal receiving filter is obtained by solving; in the second iteration, the latest obtained optimal receiving filter is fixed, and the latest optimal transmission waveform is obtained by solving. When the stopping iteration condition is met, the optimal receiving filter obtained in the last iteration of the first process is obtained as the final optimal receiving filter. The optimal transmission waveform obtained in the last second iteration is taken as the final optimal transmission waveform. .

2. The method for optimizing the transmitted waveform of a fully polarized radar according to claim 1, characterized in that, The alternating execution of the first iteration process and the second iteration process includes: After executing the first In the second iteration, the latest optimal transmission waveform is obtained. Then, execute the first The first iteration process is repeated; For the first The optimal transmission waveform generated by the second iteration process; In the During the first iteration, the optimal transmission waveform is fixed. Through formula （38） Perform calculations to obtain the first... The optimal receiving filter generated in the first iteration process .

3. The method for optimizing the transmitted waveform of a fully polarized radar according to claim 2, characterized in that, The acquisition of the first The optimal receiving filter generated in the first iteration process ,include: Through formula （50） （51） （46） （47） Determine the optimal receiving filter ;in, , The dimension is A diagonal matrix of -1, Indicates size is The identity matrix, This represents the trace operation on a matrix. For the first The optimal receiving filter generated in the first iteration process. For the target echo matrix, For the ISRJ matrix, For the target echo sequence, This is an echo of the ISRJ interference signal. For peak constraint weights, It is a constant. This represents the number of peak mismatches between the interference signal and the receiving filter during the unmatched filtering process. A constant representing the maximum value. Let be a constant representing the minimum value.

4. The method for optimizing the transmitted waveform of a fully polarized radar according to claim 2, characterized in that, The alternating execution of the first iteration process and the second iteration process includes: After executing the first In the first iteration process, the latest optimal receiving filter is obtained. Then, execute the first The second iteration process continues; In the During the second iteration, the optimal receiving filter is fixed. Through formula （39） Perform calculations to obtain the first... The optimal transmission waveform generated in the second iteration process .

5. The method for optimizing the transmitted waveform of a fully polarized radar according to claim 4, characterized in that, The acquisition of the first The optimal transmission waveform generated in the second iteration process ,include: Through formula （60） （61） （56） （57） Determine the optimal transmission waveform ;in, The target impulse response matrix, The characteristic matrix of the fully polarized jammer. , The dimension is A diagonal matrix of -1, Indicates size is The identity matrix, This represents the trace operation on a matrix. For peak constraint weights, It is a constant. This represents the number of peak mismatches between the interference signal and the receiving filter during the unmatched filtering process. A constant representing the maximum value. Let be a constant representing the minimum value.

6. The method for optimizing the transmitted waveform of a fully polarized radar according to any one of claims 1-5, characterized in that, The stopping iteration condition is the formula. The convergence condition represented by the expression; in, To achieve the optimal transmission waveform With the optimal receiving filter The result obtained by substituting into the gamma function, To achieve the optimal transmission waveform With the optimal receiving filter The result obtained by substituting into the gamma function, It is a constant.

7. The method for optimizing the transmitted waveform of a fully polarized radar according to any one of claims 1-5, characterized in that, The stopping iteration condition is when the sum of the number of execution rounds of the first iteration process and the second iteration process reaches a certain threshold.

8. A computer device, characterized in that, It includes a memory and a processor, the memory being used to store at least one program, and the processor being used to load at least one program to execute the fully polarized radar transmit waveform optimization method according to any one of claims 1-7.

9. A computer-readable storage medium storing a processor-executable program, characterized in that, The processor-executable program, when executed by the processor, is used to perform the fully polarized radar transmit waveform optimization method according to any one of claims 1-7.

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