A space-time two-dimensional processing method for airborne radar based on linear frequency modulation signal

Abstract

The present invention discloses a space-time two-dimensional processing method for airborne radar based on linear frequency modulation (LFM) signals, which relates to the field of signal processing technology. A space-time clutter ring data model of the LFM signal is obtained based on the LFM echo signal. A space-time two-dimensional processing model based on the LFM signal is established based on a narrowband space-time two-dimensional processing (STAP) model. A space-time two-dimensional processing method based on the LFM signal is obtained through phase information compensation. The performance of the space-time two-dimensional clutter suppression improvement factor based on the LFM signal is analyzed, and an mDT processing method for LFM signals for practical engineering applications is provided. The present invention uses the above method to perform range phase compensation on the space-time two-dimensional processing model of the LFM signal and compensate for the coupled phase errors of platform motion and array element spacing to obtain a STAP processing method for the LFM signal. The implementation of the LFM signal under the fixed dimensionality reduction method (mDT) for space-time two-dimensional processing is derived and analyzed from the perspective of engineering application.

Description

Technical Field

[0001] The present invention relates to the technical field of signal processing, and in particular to a space-time two-dimensional processing method of an airborne radar based on a linear frequency modulation signal. Background Art

[0002] Compared to ground-based radar, airborne radar has a wider field of view and greater maneuverability, enabling it to detect smaller targets at greater distances. Generally, airborne radar operates in downward-looking mode. The received echo signals contain not only possible moving targets but also a large amount of strong ground clutter. Airborne clutter exhibits strong space-time two-dimensional coupling characteristics, and Space-Time Adaptive Processing (STAP) technology is typically used to suppress airborne clutter.

[0003] As airborne radars demand ever-higher resolution, broadband signals such as linear frequency modulation (LFM) signals are becoming widely used. However, airborne radar models for LFM signals are rarely explored, and research on their space-time processing is also limited. Furthermore, most studies fail to consider the impact of phase errors associated with the distance from the clutter scattering point to the radar platform on STAP performance, focusing solely on the accuracy of clutter ring data modeling. The distance between the airborne platform and the scattering point results in a significant amount of range-phase coupling in the echo signal. Furthermore, factors such as platform motion and array element spacing contribute to some coupled phase errors, leading to significant errors using traditional STAP (space-time adaptive processing). Without compensation for these coupling terms, accurate target information cannot be acquired.

[0004] Therefore, a space-time two-dimensional processing method for airborne radar based on linear frequency modulation signal is provided. Summary of the Invention

[0005] The purpose of the present invention is to provide an airborne radar space-time two-dimensional processing method based on linear frequency modulation signals. On the basis of linear frequency modulation signals and airborne space-time two-dimensional processing, a space-time two-dimensional processing model based on linear frequency modulation signals is established, and the distance phase error and the coupled phase error caused by platform motion and array element spacing are analyzed and compensated to obtain a space-time two-dimensional processing method for linear frequency modulation signals. Based on the perspective of actual engineering applications, the simulation results of 3DT dimensionality reduction processing are given.

[0006] To achieve the above object, the present invention provides an airborne radar space-time two-dimensional processing method based on linear frequency modulation signals, comprising the following steps:

[0007] Step 1: Based on the airborne clutter model, derive and establish the echo signal data model of the linear frequency modulation signal. Substitute the echo delay formula into the down-converted echo signal to obtain the complete echo signal data model. The formula is as follows:

[0008]

[0009] In the above formula, j is an imaginary unit, R is the distance from the scattering point to the airborne platform, V r is the relative radial velocity between the airborne platform and the clutter block or target on the clutter ring, t = mT r is the echo pulse sampling time, m=0,1,…,M-1 represents the mth pulse processed, n=0,1,…,N-1 represents the antenna array element number, T r is the pulse repetition interval, f0 is the carrier frequency of the linear FM signal, μ is the modulation rate of the linear FM signal, C is the amplitude of the echo signal, f(ξ)=dcosξ / c, d is the antenna element spacing, ξ is the angle between the line connecting the phase center of the array antenna to the clutter block and the array axis, and c is the speed of light;

[0010] Step 2: Classify the phase terms in the complete echo data signal model. The classification result is the linear frequency modulation signal clutter ring data formula, which is as follows:

[0011]

[0012] In the above formula, l refers to a certain clutter ring, N c Refers to the number of clutter blocks in a clutter ring, Φ R (m) refers to the range phase error caused by the distance from the scattering point to the airborne platform; Φ μi (m,n) refers to the phase error caused by the coupling of distance, speed and array element spacing, Φ 0i (m,n) refers to the phase factor in the basic narrowband pulse space-time two-dimensional processing model, C i It refers to the scattered echo amplitude in each azimuth direction on the clutter ring, where i = 1,…,N c ;

[0013] Step 3: Use the formula in step 2 to establish different linear frequency modulation signals based on the narrowband pulse space-time two-dimensional steering vector model. The formula is as follows:

[0014]

[0015] In the above formula, S(f s ,f d ) is the space-time two-dimensional steering vector of the narrowband pulse, S'(f s ,f d ) is regarded as the space-time two-dimensional steering vector under the linear frequency modulation signal, ° is the Hadamard product (dot product);

[0016] Step 4: Perform phase compensation on the error in the newly established space-time processing model of the linear frequency modulation signal. The space-time two-dimensional processing model formula of the linear frequency modulation signal after phase compensation is as follows:

[0017]

[0018] In the above formula, Φ R '(m) is the phase error compensation caused by the distance from the scattering point to the airborne platform, S V (f st ,f dt ) is the phase error compensation caused by platform motion and array element spacing coupling, is the Kronecker product;

[0019] Step 5: Use the dimensionality reduction method based on mDT under linear frequency modulation signal to process the signal.

[0020] Preferably, in step 1, the formula for echo delay is as follows:

[0021]

[0022] In the above formula, R represents the initial distance from the clutter block to the airborne platform. All clutter blocks on the same distance clutter ring have the same distance from the airborne platform. V r The formula for the down-converted echo signal is as follows:

[0023] y(t)=C*exp[j2π(-f0τ n (t)-μtτ n (t)+μτ n (t) 2 / 2)]

[0024] Substituting the echo delay formula into the down-converted echo signal formula, a complete echo data model is obtained.

[0025] Preferably, in step 2, the phase terms in the complete echo data signal model in step 1 are classified and analyzed, and the specific classification process is as follows:

[0026] The complete echo signal data model is decomposed into four parts: phase error, phase coupling error, basic phase factor, and constant term:

[0027]

[0028] The above formula is the phase error caused by the distance R between the clutter ring scattering point and the airborne platform. When the distance R is fixed, this term is a fixed value.

[0029]

[0030] The above formula is the distance R, the relative radial velocity V between the platform and the scattering point r Phase coupling error caused by the array element spacing d, where f(ξ) = dcosξ / c;

[0031]

[0032] The above formula is the basic phase factor in the STAP processing model;

[0033]

[0034] The above formula is a fixed constant phase term;

[0035] When there are N c clutter blocks, N c The linear frequency modulation signal clutter ring data formula is obtained by superimposing the clutter block data.

[0036] Preferably, in step 3, the specific method of establishing the space-time two-dimensional steering vectors of different linear frequency modulation signals is as follows:

[0037] First calculate the basic phase factor, the formula is as follows:

[0038]

[0039] Φ0(m,n) is the basic phase factor in the STAP processing model, let f s =f0f(ξ) is the spatial frequency,

[0040] is the Doppler frequency;

[0041] The formula for the spatial steering vector is as follows:

[0042]

[0043] The time domain steering vector formula is as follows:

[0044]

[0045] In the above formula, S is the space-time two-dimensional steering vector Where R = E[x l x l H ] is the NK×KN dimensional clutter covariance matrix, represents the Kronecker product. Based on the above, the formula of the space-time two-dimensional steering vector under the linear frequency modulation signal is derived.

[0046] Preferably, in step 4, the specific method of phase compensation is as follows:

[0047] By Φ R (n) is determined by the phase, when When , the phase error compensation formula caused by the distance from the scattering point to the airborne platform is as follows:

[0048]

[0049] The space-time snapshot data after distance compensation is as follows:

[0050]

[0051] After distance compensation, coupling phase compensation is performed. The coupling phase compensation formula is as follows:

[0052]

[0053] In the above formula, S V (f st ,f dt ) is the coupling phase compensation, and the specific formula is as follows:

[0054] S V (f st ,f dt )=vec(Φ V (n,m))

[0055] In the above formula, vec(Φ V (n,m)) is to convert the matrix into a column vector, Φ V The formula for (n,m) is as follows:

[0056]

[0057] In the above formula, R is the distance from the scattering point to the airborne platform, V r is the relative radial velocity between the airborne platform and the clutter block or target on the clutter ring, m=0,1,…,M-1 represents the mth pulse processed, n=0,1,…,N-1 represents the antenna array element number, T r is the pulse repetition interval, μ is the frequency of the linear frequency modulation signal, f(ξ)=dcosξ / c, d is the antenna element spacing, ξ is the angle between the line connecting the phase center of the array antenna to the clutter block and the array axis, and c is the speed of light

[0058] Through distance compensation and coupling phase compensation, the formula for the compensated snapshot data over the fixed-distance clutter ring is as follows:

[0059]

[0060] According to the above formula, the space-time two-dimensional processing model of the linear frequency modulation signal after phase compensation is obtained.

[0061] Preferably, in step 5, the mDT dimensionality reduction method is specifically a 3DT dimensionality reduction method, and the specific process is as follows:

[0062] The formula of the dimensionality reduction transformation matrix is ​​as follows

[0063]

[0064] In the above formula, T s is the spatial transformation matrix, T t is the time domain transformation matrix, and the clutter covariance matrix becomes

[0065] R 3DT =T H RT

[0066] The formula for the space-time two-dimensional steering vector is as follows

[0067] S 3DT =T H S

[0068] At this time, the formula for the improvement factor IF of the 3DT processor is as follows

[0069] IF 3DT =S 3DT H R 3DT -1 S 3DT (1+CNR)σ n 2

[0070] In the above formula, R 3DT is the clutter covariance matrix under 3DT dimensionality reduction processing, S 3DT is the space-time two-dimensional steering vector under 3DT dimension reduction processing, CNR is the noise-clutter ratio, σ n 2 is the noise variance.

[0071] Therefore, the present invention adopts a method for space-time two-dimensional processing of airborne radar based on linear frequency modulation signals according to the above method, which has the following advantages:

[0072] (1) When establishing the basic signal processing model, the phase error caused by the distance between the scattering point and the airborne platform, as well as the platform motion and array element spacing, is fully considered, which is more in line with the actual situation during airborne detection.

[0073] (2) A space-time two-dimensional processing method suitable for linear frequency modulation signals is obtained through distance phase compensation, platform motion phase compensation, and array element spacing phase compensation. By compensating for errors, the results are more accurate.

[0074] (3) Considering that the full space-time STAP technology has a large amount of computation and cannot be used in practice, a 3DT dimensionality reduction method is proposed. Through the 3DT processing flow and simulation result diagram, the performance close to that of the STAP technology is obtained while reducing the usage requirements.

[0075] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] Figure 1 The present invention provides an airborne radar clutter ring model in a space-time two-dimensional processing method of an airborne radar based on a linear frequency modulation signal;

[0077] Figure 2 This is a structural diagram of STAP adaptive processing in a space-time two-dimensional processing method for airborne radar based on linear frequency modulation signals of the present invention;

[0078] Figure 3 This is a schematic diagram of the 3DT principle structure in a space-time two-dimensional processing method for airborne radar based on linear frequency modulation signals of the present invention;

[0079] Figure 4 A space-time two-dimensional response plane diagram without phase compensation in a space-time two-dimensional processing method for an airborne radar based on a linear frequency modulation signal according to the present invention;

[0080] Figure 5 It is a space-time two-dimensional response plane diagram after phase compensation in a space-time two-dimensional processing method of an airborne radar based on a linear frequency modulation signal of the present invention;

[0081] Figure 6 A 3DT processing response plane diagram of a linear frequency modulation signal in a space-time two-dimensional processing method of an airborne radar based on a linear frequency modulation signal according to the present invention;

[0082] Figure 7 It is the linear frequency modulation signal STAP and 3DT processing improvement factor in the linear frequency modulation signal-based airborne radar space-time two-dimensional processing method of the present invention. DETAILED DESCRIPTION

[0083] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention as claimed, but rather merely represents selected embodiments of the present invention. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without creative effort shall fall within the scope of protection of the present invention.

[0084] The present invention provides an airborne radar space-time two-dimensional processing method based on a linear frequency modulation signal, comprising the following steps:

[0085] Step 1: Establish the echo signal data model of the linear frequency modulation signal based on the airborne clutter model.

[0086] The echo delay formula is as follows:

[0087]

[0088] The formula for the down-converted echo signal is as follows

[0089] y(t)=C*exp[j2π(-f0τ n (t)-μtτ n (t)+μτ n (t) 2 / 2)]

[0090] Substituting the echo delay formula into the down-converted echo signal, we can obtain the complete echo signal data model, which is as follows:

[0091]

[0092] In the above formula, R is the distance from the scattering point to the airborne platform, V r is the relative radial velocity between the airborne platform and the clutter block or target on the clutter ring, t = mT r is the echo pulse sampling time, m=0,1,…,M-1 represents the mth pulse processed, n=0,1,…,N-1 represents the antenna array element number, T r is the pulse repetition interval, f0 is the carrier frequency of the linear FM signal, μ is the modulation rate of the linear FM signal, C is the amplitude of the echo signal, f(ξ)=dcosξ / c, d is the antenna element spacing, ξ is the angle between the line connecting the phase center of the array antenna to the clutter block and the array axis, and c is the speed of light;

[0093] Step 2: Classify the phase terms in the complete echo data signal model. First, decompose the complete echo signal data model into four parts: phase error, phase coupling error, basic phase factor, and constant term:

[0094]

[0095] The above formula is the phase error caused by the distance R between the clutter ring scattering point and the airborne platform. When the distance R is fixed, this term is a fixed value.

[0096]

[0097] The above formula is the distance R, the relative radial velocity V between the platform and the scattering point r Phase coupling error caused by the array element spacing d, where f(ξ) = dcosξ / c;

[0098]

[0099] The above formula is the basic phase factor in the STAP processing model;

[0100] It is a fixed constant phase term and does not affect the space-time processing modeling results and can be ignored.

[0101] When there are N c clutter blocks, N c After the clutter block data are superimposed and classified, the linear frequency modulation signal clutter ring data formula is obtained, which is as follows:

[0102]

[0103] In the above formula, l refers to a certain clutter ring, N c Refers to the number of clutter blocks in a clutter ring, Φ R (m) refers to the range phase error caused by the distance from the scattering point to the airborne platform; Φ μi (m,n) refers to the phase error caused by the coupling of distance, speed and array element spacing, Φ 0i (m,n) refers to the phase factor in the basic narrowband pulse space-time two-dimensional processing model, C i It refers to the scattered echo amplitude in each azimuth direction on the clutter ring, where i = 1,…,N c ;

[0104] Step 3: Use the formula in step 2 to establish different linear frequency modulation signals based on the narrowband pulse space-time two-dimensional steering vector model. The derivation process is as follows:

[0105] In the linear frequency modulation signal clutter ring data formula in step 2, the formula for calculating the basic phase factor is as follows:

[0106]

[0107] Φ0(m,n) is the basic phase factor in the STAP processing model, let f s =f0f(ξ) is the spatial frequency, is the Doppler frequency,

[0108] The spatial steering vector formula is as follows:

[0109]

[0110] The time domain steering vector formula is as follows:

[0111]

[0112] S is a two-dimensional steering vector when space Where R = E[x l x l H ] is the NK×KN dimensional clutter covariance matrix, represents the Kronecker product. Based on the above, the formula for the space-time two-dimensional steering vector under the linear frequency modulation signal can be derived. The formula for the space-time two-dimensional steering vector under the linear frequency modulation signal is as follows:

[0113]

[0114] In the above formula, S(f s ,f d ) is the space-time two-dimensional steering vector of the narrowband pulse, S'(f s ,f d ) can be regarded as a two-dimensional space-time steering vector under the linear frequency modulation signal, is the Hadamard product (dot product);

[0115] Step 4: Perform phase compensation on the error in the newly established linear frequency modulation signal space-time processing model. The specific compensation process is as follows:

[0116] when When , the phase error compensation formula caused by the distance from the scattering point to the airborne platform is as follows:

[0117]

[0118] The space-time snapshot data after distance compensation is as follows:

[0119]

[0120] After distance compensation, coupling phase compensation is also required. The formula for coupling phase compensation is as follows:

[0121]

[0122] In the above formula, S V (f st ,f dt ) is the coupling phase compensation, and the specific formula is as follows:

[0123] S V (f st ,f dt )=vec(Φ V (n,m))

[0124] In the above formula,

[0125]

[0126] In the above formula,

[0127] Through distance compensation and coupling phase compensation, the formula for the compensated snapshot data over the fixed-distance clutter ring is as follows:

[0128]

[0129] According to the above formula, the space-time two-dimensional processing model of the linear frequency modulation signal after phase compensation can be obtained, and the formula is as follows:

[0130]

[0131] Step 5: Based on the perspective of engineering application, use the mDT dimensionality reduction method based on the linear frequency modulation signal, specifically the 3DT dimensionality reduction method. The specific process is as follows:

[0132] The formula of the dimensionality reduction transformation matrix is ​​as follows

[0133]

[0134] In the above formula, T s is the spatial transformation matrix, T t is the time domain transformation matrix, and the clutter covariance matrix becomes

[0135] R 3DT =T H RT

[0136] The formula for the space-time two-dimensional steering vector is as follows

[0137]

[0138] At this time, the formula for the improvement factor IF of the 3DT processor is as follows

[0139] IF 3DT =S 3DT H R 3DT -1 S 3DT (1+CNR)σ n 2

[0140] In the above formula, R 3DT is the clutter covariance matrix under 3DT dimensionality reduction processing, S 3DT is the space-time two-dimensional steering vector under 3DT dimension reduction processing, CNR is the noise-clutter ratio, σ n 2 is the noise variance.

[0141] Example

[0142] like Figure 1 The figure shows the geometric diagram of the clutter ring model of airborne radar. When airborne radar is working, it is inevitable to be adversely affected by ground clutter. The received signal contains a strong ground clutter component. The ground clutter it receives can be divided into many equidistant rings according to the distance. The same range ring is divided into N according to the same azimuth interval. cclutter blocks, assuming that the radar antenna is an equidistant linear array with N elements, the element spacing is d, and the platform height is H. For a clutter block P on the clutter ring, its azimuth is The pitch angle is θ, the slant range from the clutter block P to the platform is R, β is the angle between the carrier speed and the array axis, the angle between the line connecting the phase center of the array antenna to the clutter block and the array axis is the spatial cone angle ξ, and ψ is the angle between the carrier speed and the line connecting the phase center of the array antenna to the clutter block.

[0143] Step 1: Get a complete echo signal data model. First, analyze the echo signal model of the linear frequency modulation signal. For the convenience of description, LFM is used to represent the linear frequency modulation signal. The basic expression of the LFM signal is as follows:

[0144]

[0145] In the above formula, A is the signal amplitude value, f0 is the signal carrier frequency, μ is the linear FM signal modulation frequency and μ = B / T, B is the FM signal bandwidth, T is the FM signal single pulse width, The value range of is as follows:

[0146]

[0147] Assume that the target echo delay received by the nth array element is τ n (t), the LFM echo signal can be expressed as:

[0148]

[0149] In the above formula, C is the amplitude of the echo signal. Expanding y(t) yields the following formula:

[0150]

[0151] Analyze y(t), specifically, This is the known part. The echo data received by each array element contains this item. We can multiply the signal by The down-converted signal is obtained by filtering. The formula of the down-converted signal after filtering is as follows:

[0152] y(t)=C*exp[j2π(-f0τ n (t)-μtτ n (t)+μτ n (t) 2 / 2)]

[0153] In the down-converted signal, only the phase change term and the echo envelope term with the target delay need to be considered. For the echo data delay, Figure 1The geometric relationship diagram can be used to derive the echo delay formula:

[0154]

[0155] In the above formula, R represents the initial distance from the clutter block to the airborne platform. All clutter blocks on the same distance clutter ring have the same distance from the airborne platform. V r represents the relative radial velocity between the scattering point and the airborne platform, and ndcosξ / c is the spatial phase error caused by the array element spacing. We set f(ξ) = dcosξ / c, so Where n=0,1,2,…,N-1. n Substituting (t) into y(t), we can get the following formula:

[0156]

[0157] Assume that the number of pulses processed in one CPI (coherent processing time) is M and the pulse repetition interval is T r , take t = mT r , where m=0,1,…,M-1 represents the mth pulse processed, and τ n (t) and t=mT r Substituting y(t) into the equation, we can get the complete echo signal data model:

[0158]

[0159] In the above formula, j is an imaginary unit, R is the distance from the scattering point to the airborne platform, V r is the relative radial velocity between the airborne platform and the clutter block or target on the clutter ring, t = mT r is the echo pulse sampling time, m=0,1,…,M-1 represents the mth pulse processed, n=0,1,…,N-1 represents the antenna array element number, T r is the pulse repetition interval, f0 is the carrier frequency of the linear FM signal, μ is the modulation rate of the linear FM signal, C is the amplitude of the echo signal, f(ξ)=dcosξ / c, d is the antenna element spacing, ξ is the angle between the line connecting the phase center of the array antenna to the clutter block and the array axis, and c is the speed of light;

[0160] Step 2: Analyze the phase of each part of y(t) and classify the phase terms into four categories: phase error, phase coupling error, basic phase factor and constant term:

[0161]

[0162] The above formula is a fixed constant term, which does not affect our modeling results. Here we will not consider the impact of this term on the space-time two-dimensional processing results;

[0163]

[0164] The above formula is the phase error caused by the distance R from the scattering point to the airborne platform, recorded as Φ R (m), Φ R (m) is the part that needs phase compensation. This value is large and has a great impact on the results of space-time adaptive processing;

[0165] The phase coupling error caused by the coupling of distance, speed and array element spacing is denoted as Φ μ (m,n), the resulting formula is as follows:

[0166]

[0167] Φ μ (m,n) compared to Φ R (m), the phase value of this part is small, but it will not be ignored when the frequency modulation bandwidth of the linear frequency modulation signal is large. This part of the coupling phase will have a greater impact on the target information detection. For the applicability and effectiveness of the solution, we still consider the impact of this part on space-time processing;

[0168]

[0169] The above formula is the basic phase factor in the space-time two-dimensional processing model, recorded as Φ0(m,n), where the Doppler frequency is Spatial frequency f s =f0f(ξ);

[0170] Arranging the above formula, we get the following formula:

[0171] y(t)=C*Φ R (m)·Φ μ (m,n)·Φ0(m,n)

[0172] Let it be x c , there are N on a clutter ring l c clutter blocks, Φ R (m) is a fixed item on a fixed clutter loop. The classification result is the linear frequency modulation signal clutter loop data formula, which is as follows:

[0173]

[0174] In the above formula, l refers to a certain clutter ring, N c Refers to the number of clutter blocks in a clutter ring, Φ R (m) refers to the range phase error caused by the distance from the scattering point to the airborne platform; Φ μi(m,n) refers to the phase error caused by the coupling of distance, speed and array element spacing, Φ 0i (m,n) refers to the phase factor in the basic narrowband pulse space-time two-dimensional processing model, C i It refers to the scattered echo amplitude in each azimuth direction on the clutter ring, where i = 1,…,N c ;

[0175] Step 3: Establish two-dimensional space-time steering vectors for different linear frequency modulation signals. Assume that the airborne radar antenna array has N elements, and all elements receive K echo data delayed by the pulse period within one CPI (coherent processing time). Then the space-time snapshot data received by the lth range gate can be represented by an N×K dimensional matrix as follows:

[0176]

[0177] x l Rearrange into a column vector of NK×1 dimension

[0178] x l =[x 1,1 … x 1,K x 2,1 … x 2,K … x N,1 … x N,K ] T

[0179] STAP space-time two-dimensional processing weight vector w∈C NK×1 Expressed as a vector:

[0180] w=[w 1,1 … w 1,K W 2,1 … w 2,K … w N,1 … w N,K ] T

[0181] The adaptive output after weighted processing of the received data is y=w H x l .

[0182] like Figure 2 , is the architecture diagram of the full-dimensional STAP adaptive processing. Assuming that the clutter follows a Gaussian distribution, under the maximum output signal-to-noise ratio criterion, the processor allows the signal of interest to pass through without distortion while minimizing the output power of clutter and noise, achieving the goal of clutter and noise suppression. According to the linearly constrained minimum variance (LCMV) criterion, the STAP processor is described as the following optimization problem:

[0183]

[0184] In the above formula, R=E[x l x l H ] is the NK×KN-dimensional clutter covariance matrix, S is the space-time two-dimensional steering vector, and the formula is as follows:

[0185]

[0186] In the above formula, the spatial steering vector f s =f0f(ξ) is the spatial frequency, the time domain steering vector f d = is the Doppler frequency, where represents the Kronecker product, then the final vector formula is as follows:

[0187]

[0188] In the above formula, S(f s ,f d ) is the space-time two-dimensional steering vector of the narrowband pulse, S'(f s ,f d ) can be regarded as a two-dimensional space-time steering vector under the linear frequency modulation signal, is the Hadamard product (dot product);

[0189] Step 4: Perform phase compensation for the error. According to the established linear frequency modulation signal clutter data model, the model formula is as follows:

[0190]

[0191] In the above formula, S'(f s ,f d ) can be regarded as a new space-time steering vector based on the linear frequency modulation signal, where Φ R (m) has a greater impact on target detection, so we need to perform corresponding distance phase compensation, φ R By Φ R (m) is determined by the phase, so and Correspondingly, Φ R (m) and Φ R '(m) corresponds to, by R '(m) and diagonal matrix I N×1 The phase error Φ caused by distance is converted into R (m) Compensation. Shillings Thus we get The space-time snapshot data after distance compensation is as follows:

[0192]

[0193] After distance compensation, the coupling of the airborne platform motion, array element spacing, and the distance from the scattering point to the platform will simultaneously introduce a certain phase error. The coupled phase compensation is as follows:

[0194]

[0195] In the above formula, S V (f st ,f dt ) is the coupling phase compensation, and the specific formula is as follows:

[0196] S V (f st ,f dt )=vec(Φ V (n,m))

[0197] In the above formula, vec(Φ V (n,m)) is to convert the matrix into a column vector, Φ V The formula for (n,m) is as follows:

[0198]

[0199] In summary, the snapshot data after compensation when the fixed distance is above the clutter ring l is as follows:

[0200]

[0201] The optimal solution weight vector for the STAP optimization problem is as follows

[0202] w opt =μR -1 S',

[0203] μ=1 / (S' H R -1 S') is a constant, R=E[x cl x cl H ] is the NK×KN dimensional clutter covariance matrix. Here, the clutter covariance matrix of a clutter ring at a fixed position is studied. S' is the space-time steering vector under the linear frequency modulation signal model. When the statistical characteristics of the clutter are known, the STAP processor can zero the clutter in two dimensions in the angle domain and the Doppler domain, thereby extracting the moving target of interest.

[0204] Step 5: Using the 3DT dimensionality reduction method, the formula for the clutter improvement factor is as follows:

[0205] IF=(S' H R -1 S')(CNR+1)σ n2

[0206] In the above formula, IF is the clutter improvement factor, CNR is the clutter-to-noise ratio, σ n 2 is the noise variance, where the noise is assumed to be Gaussian white noise

[0207] However, STAP technology requires a large amount of computation and a high demand for training samples, including a large number of independent and identically distributed samples, making it difficult to apply in practice. The mDT method is a Doppler adaptive processing method currently widely used in engineering implementations. Among them, the 3DT method can simultaneously create notches that match the clutter spectrum in both the angle and Doppler domains, effectively improving clutter suppression performance in both the sidelobe and mainlobe regions.

[0208] like Figure 3 , which is the principle structure diagram of the 3DT dimensionality reduction method, where N represents the number of radar receiving elements and K represents the number of time-domain Doppler channels. Fast Fourier transform (FFT) is first used to convert the received space-time snapshot data from the element-pulse domain to the element-Doppler domain. Local adaptive filtering is then performed on the Doppler element domain and its two adjacent Doppler channels. The 3DT method filters only in the time domain, reducing the temporal degrees of freedom of the signal subspace while maintaining the spatial degrees of freedom.

[0209] Assuming that the unit to be detected is located in the kth channel, the two adjacent Doppler channels on both sides are numbered k-1 and k+1 respectively. The time domain dimension reduction matrix of 3DT can be represented by a transformation matrix T t express:

[0210]

[0211] Where f d,k-1 、f d,k 、f d,k+1 are the Doppler frequencies of the k-1th, kth, and k+1th Doppler channels respectively. Since the 3DT method does not reduce the dimension in the spatial domain, the spatial transformation matrix T s It is represented by an N×N identity matrix, that is, T s =I N , so the dimensionality reduction transformation matrix T of 3DT can be expressed as

[0212]

[0213] According to the linear constrained minimum variance (LCMV) criterion, the STAP constraint equation is transformed into

[0214]

[0215] In the above formula, R3DT =T H RT, S 3DT =T H S, the processor weight of 3DT becomes

[0216]

[0217] Correspondingly, the improvement factor IF of the 3DT processor becomes

[0218] IF 3DT =S 3DT H R 3DT -1 S 3DT (1+CNR)σ n 2

[0219] where R 3DT is the clutter covariance matrix under 3DT dimensionality reduction processing, S 3DT is the space-time two-dimensional steering vector under 3DT dimension reduction processing, CNR is the noise-clutter ratio, σ n 2 is the noise variance.

[0220] The specific simulation process is as follows: The effectiveness of the airborne STAP technology based on linear frequency modulation signals in this method is verified through simulation parameters. The simulation parameters are shown in Table 1:

[0221] Table 1 Simulation parameters

[0222]

[0223] When the radar is looking sideways, Figure 4 It is the space-time two-dimensional response plane diagram of the linear frequency modulation signal without phase compensation. From the simulation results, it can be seen that the target information obtained without phase compensation does not match the actual situation and there is a large error. Figure 5 It represents the target response result obtained after phase compensation, that is, under the compensation model provided by the solution of the present invention. From the simulation results, it can be seen that this method can obtain more accurate target information, even in the case of large linear frequency modulation bandwidth.

[0224] The traditional STAP processing method cannot be applied in practice due to the large amount of computation. The processing results of the dimensionality reduction method 3DT are given below. Under the same parameters in Table 1, Figure 6 This is a response result diagram of 3DT space-time two-dimensional processing based on linear frequency modulation signal after phase compensation. It can be seen from the result diagram that the dimensionality reduction method of the present invention can also obtain relatively accurate target information.

[0225] At the same time, the clutter suppression performance improvement factor of STAP and 3DT methods is simulated and obtained Figure 7 ,From the simulation results, it can be seen that the 3DT method ,can achieve performance close to that of STAP, but at the same time ,the computational complexity of the 3DT space-time ,two-dimensional processing is greatly reduced.

[0226] Therefore, the present invention provides a two-dimensional space-time processing method for airborne radar based on linear frequency modulation signals. Regarding the STAP technology of airborne radar based on linear frequency modulation signals, the present invention analyzes the two-dimensional space-time clutter data model of the linear frequency modulation signal and establishes a STAP processing method based on the traditional STAP processing model. Accurate target spatial frequency and Doppler frequency information is obtained by compensating for the phase error caused by the coupling between the range phase and platform motion, array element spacing, and the distance from the clutter scattering point to the airborne platform. To facilitate practical application, the present invention also proposes a 3DT method based on existing fixed dimensionality reduction processing of linear frequency modulation signals. Simulation results show that it can also obtain relatively accurate target information, and the clutter suppression performance is similar to that of STAP under this model.

[0227] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit the same. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solutions of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for space-time two-dimensional processing of airborne radar based on linear frequency modulation signals, characterized by: The following steps are involved: Step 1: Based on the airborne clutter model, derive and establish the echo signal data model of the linear frequency modulation signal. Substitute the echo delay formula into the down-converted echo signal to obtain the complete echo signal data model. The formula is as follows: ； In the above formula, is an imaginary unit, is the distance from the scattering point to the airborne platform, is the relative radial velocity between the airborne platform and the clutter block or target on the clutter ring, is the echo pulse sampling time, represents the mth pulse processed, Indicates the antenna element number, is the pulse repetition interval, is the carrier frequency of the linear frequency modulation signal, is the frequency modulation of the linear frequency modulation signal, is the echo signal amplitude, , is the antenna element spacing, is the angle between the line from the phase center of the array antenna to the clutter block and the array axis, is the speed of light; Step 2: Classify the phase terms in the complete echo data signal model. The classification result is the linear frequency modulation signal clutter ring data formula, which is as follows: ； In the above formula, refers to a certain clutter ring, Refers to the number of clutter blocks in a clutter ring, It refers to the range phase error caused by the distance from the scattering point to the airborne platform; It refers to the phase error caused by the coupling of distance, speed and array element spacing. Refers to the phase factor in the basic narrowband pulse space-time two-dimensional processing model, It refers to the scattered echo amplitude in each azimuth direction on the clutter ring, where ; Step 3: Use the formula in step 2 to establish different linear frequency modulation signals based on the narrowband pulse space-time two-dimensional steering vector model. The formula is as follows: ； In the above formula, is the space-time two-dimensional steering vector of the narrowband pulse, is regarded as a two-dimensional space-time steering vector under a linear frequency modulation signal, for product; Step 4: Perform phase compensation on the error in the newly established space-time processing model of the linear frequency modulation signal. The space-time two-dimensional processing model formula of the linear frequency modulation signal after phase compensation is as follows: ； In the above formula, To compensate for the phase error caused by the distance from the scattering point to the airborne platform, Compensate for the phase error caused by platform motion and array element spacing coupling. is the Kronecker product; Step 5: Use the dimensionality reduction method based on mDT under linear frequency modulation signal to process the signal.

2. The method for space-time two-dimensional processing of airborne radar based on linear frequency modulation signals according to claim 1, characterized in that: In step 1, the formula for echo delay is as follows: ； In the above formula, Indicates the initial distance from the clutter block to the airborne platform. All clutter blocks on the same distance clutter ring have the same distance from the airborne platform. The formula for the down-converted echo signal is as follows: ； Substituting the echo delay formula into the down-converted echo signal formula, a complete echo data model is obtained.

3. The method for space-time two-dimensional processing of airborne radar based on linear frequency modulation signals according to claim 1, characterized in that: In step 2, the phase terms in the complete echo data signal model in step 1 are classified and analyzed. The specific classification process is as follows: The complete echo signal data model is decomposed into four parts: phase error, phase coupling error, basic phase factor, and constant term: ； The above formula is the distance from the clutter ring scattering point to the airborne platform The phase error caused by the distance When fixed, this item is a fixed value; ； The above formula is the distance , the relative radial velocity between the platform and the scattering point Distance between array elements The phase coupling error caused by ; ； In the above formula, is the basic phase factor in the STAP processing model; ； The above formula is a fixed constant phase term; When a fixed distance clutter ring There is clutter blocks, The linear frequency modulation signal clutter ring data formula is obtained by superimposing the clutter block data.

4. The method for space-time two-dimensional processing of airborne radar based on linear frequency modulation signals according to claim 1, characterized in that: In step 3, the specific method of establishing the space-time two-dimensional steering vectors of different linear frequency modulation signals is as follows: First calculate the basic phase factor, the formula is as follows: ； is the basic phase factor in the STAP processing model, let is the spatial frequency, is the Doppler frequency; The formula for the spatial steering vector is as follows: ； The time domain steering vector formula is as follows: ； In the above formula, Two-dimensional steering vector when empty ,in for dimensional clutter covariance matrix, represents the Kronecker product. Based on the above, the formula of the space-time two-dimensional steering vector under the linear frequency modulation signal is derived.

5. The method for space-time two-dimensional processing of airborne radar based on linear frequency modulation signals according to claim 1, characterized in that: In step 4, the specific method of phase compensation is as follows: Depend on The middle phase is determined when When , the phase error compensation formula caused by the distance from the scattering point to the airborne platform is as follows: ； The space-time snapshot data after distance compensation is as follows: ； After distance compensation, coupling phase compensation is performed. The coupling phase compensation formula is as follows: ； In the above formula, is the coupling phase compensation, and the specific formula is as follows: ； In the above formula, is to convert the matrix into a column vector, The formula is as follows: ； In the above formula, is the distance from the scattering point to the airborne platform, is the relative radial velocity between the airborne platform and the clutter block or target on the clutter ring, represents the mth pulse processed, Indicates the antenna element number, is the pulse repetition interval, is the frequency modulation of the linear frequency modulation signal, , is the antenna element spacing, is the angle between the line from the phase center of the array antenna to the clutter block and the array axis, is the speed of light; Through distance compensation and coupling phase compensation, the formula for the compensated snapshot data over the fixed-distance clutter ring is as follows: ； According to the above formula, the space-time two-dimensional processing model of the linear frequency modulation signal after phase compensation is obtained.

6. The method for space-time two-dimensional processing of airborne radar based on linear frequency modulation signals according to claim 1, characterized in that: In step 5, the mDT dimensionality reduction method is specifically a 3DT dimensionality reduction method, and the specific process is as follows: The formula of the dimensionality reduction transformation matrix is ​​as follows: ； In the above formula, is the spatial transformation matrix, is the time domain transformation matrix, and the clutter covariance matrix becomes ； The space-time two-dimensional steering vector formula is as follows: ； At this time, the formula of the improvement factor IF of the 3DT processor is as follows: ； In the above formula, is the clutter covariance matrix after 3DT dimensionality reduction processing, is the space-time two-dimensional steering vector under 3DT dimensionality reduction processing, is the noise ratio, is the noise variance.

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