Frequency division MIMO radar fast moving target detection method

Abstract

The invention discloses a frequency division MIMO radar fast moving target detection method, and relates to the technical field of radars. The method comprises the following steps of: performing frequency mixing and matched filtering decomposition processing on an obtained echo signal, converting the echo signal into a frequency domain for pulse compression, and correcting linear range deviation and a speed fuzzy index of a pulse compression frequency domain signal; obtaining an estimated target speed fuzzy index and an estimated radial speed of the moving target by using the first correction frequency domain signal; and after the pulse compression frequency domain signal is compensated, the baseline transformation and the estimated target speed fuzzy index are used for correction to obtain a second correction frequency domain signal, and the second correction frequency domain signal is used for obtaining enhanced angle estimation of the moving target in a transmitting-receiving domain. According to the method, the linear range offset and the velocity fuzzy index are corrected, so that the coupling term is corrected, and the angle and velocity parameters of the moving target can be accurately detected and obtained.

Description

Technical Field

[0001] The invention belongs to the technical field of radars, and in particular relates to a method for detecting fast-moving targets by a frequency-division MIMO radar. Background Art

[0002] Pulse Doppler radar (PD) faces a trade-off between range ambiguity and Doppler ambiguity when dealing with Doppler ambiguity of high-speed moving targets. Specifically, to avoid range ambiguity, a lower pulse repetition frequency (PRF) needs to be selected, while to achieve unambiguous velocity measurement, a higher PRF is required. Typically, dealing with range ambiguity is more difficult, so a lower PRF is usually selected, which results in Doppler ambiguity.

[0003] In recent years, a new array structure called frequency diversity array (FDA) has attracted extensive research interest. By applying a small frequency offset on the transmitting array elements, a transmit beam pattern related to range, angle, and time is formed. However, the transmit beam pattern of coherent FDA presents an "S" shape and contains multiple peaks, which leads to ambiguity problems in the range-angle pair, thus affecting the accuracy of target positioning. In addition, the change of beam pattern over time brings complex processing challenges. Therefore, by combining MIMO technology and transmitting orthogonal waveforms and then separating these waveforms after matched filtering, the degree of freedom (DOF) can be achieved in the range domain. In this context, FDA-MIMO radar has been widely used in the fields of suppressing mainlobe deceptive interference, unambiguous parameter estimation, range ambiguity clutter suppression, and high-resolution synthetic aperture radar (SAR) imaging due to its flexible signal processing capabilities.

[0004] The frequency diversity array solves the range ambiguity by introducing a small frequency offset between array elements, but for high-speed moving targets, Doppler ambiguity will occur, and the power spectrum in the transmit space frequency domain will become expanded, affecting the target detection and positioning performance. The frequency offset in the echo signal introduces different degrees of coupling between parameters such as angle and velocity, making it challenging to directly estimate these parameters from the echo signal. Summary of the invention

[0005] In order to solve the above problems existing in the prior art, the present invention provides a method for detecting fast moving targets using a frequency division MIMO radar. The technical problem to be solved by the present invention is achieved through the following technical solutions:

[0006] The present invention provides a method for detecting fast-moving targets using a frequency-division MIMO radar, comprising:

[0007] Step 1: Use the receiving array element of the frequency division MIMO radar to obtain the echo signal;

[0008] Step 2: After mixing and matched filtering decomposition processing of the echo signal, a matched filtering output signal is obtained;

[0009] Step 3: transform the matched filter output signal into the frequency domain and then perform pulse compression to obtain a corresponding pulse compression frequency domain signal, and correct the linear range offset and speed fuzzy index of the pulse compression frequency domain signal to obtain a first corrected frequency domain signal;

[0010] Step 4: transforming the first corrected frequency domain signal into the time domain to obtain a corresponding corrected time domain signal, obtaining an estimated target speed fuzzy index according to the corrected time domain signal, and obtaining an estimated radial speed of the moving target according to the estimated target speed fuzzy index;

[0011] Step 5: compensating the pulse compression frequency domain signal to obtain a compensation signal, and correcting the coupling term of the compensation signal using baseline transformation and the estimated target speed fuzzy index to obtain a second corrected frequency domain signal;

[0012] Step 6: Obtain an enhanced angle estimate of the moving target in the transmit-receive domain based on the second corrected frequency domain signal.

[0013] Compared with the prior art, the present invention has the following beneficial effects:

[0014] The method for detecting fast moving targets of a frequency division MIMO radar of the present invention comprises the following steps: obtaining an echo signal by using a receiving array element of a frequency division MIMO radar; performing mixing and matched filtering decomposition processing on the echo signal to obtain a matched filtering output signal; transforming the matched filtering output signal into a frequency domain and then performing pulse compression to obtain a corresponding pulse compression frequency domain signal, correcting a linear range offset and a speed fuzziness index of the pulse compression frequency domain signal to obtain a first corrected frequency domain signal; transforming the first corrected frequency domain signal into a time domain to obtain a corresponding corrected time domain signal, obtaining an estimated target speed fuzziness index according to the corrected time domain signal, and obtaining an estimated radial speed of the moving target according to the estimated target speed fuzziness index; compensating the pulse compression frequency domain signal to obtain a compensation signal, correcting a coupling term of the compensation signal by using a baseline transformation and an estimated target speed fuzziness index to obtain a second corrected frequency domain signal; and obtaining an enhanced angle estimation of the moving target in a transmitting-receiving domain according to the second corrected frequency domain signal. The present invention aims at the problem that the frequency offset in the echo signal introduces different degrees of coupling between the angle and speed parameters. By correcting the linear range offset and the speed fuzzy index, the coupling term is corrected, and the angle and speed parameters of the moving target can be accurately detected.

[0015] The above description is only an overview of the technical solution of the present invention. In order to more clearly understand the technical means of the present invention, it can be implemented in accordance with the contents of the specification. In order to make the above and other purposes, features and advantages of the present invention more obvious and easy to understand, the following specifically cites a preferred embodiment and describes it in detail with the accompanying drawings as follows. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 It is a schematic diagram of a method for detecting fast-moving targets using a frequency-division MIMO radar provided by an embodiment of the present invention;

[0017] Figure 2 is the estimation result of the target speed fuzzy index provided by the embodiment of the present invention;

[0018] Figure 3 is the result of enhanced angle estimation of a moving target provided by an embodiment of the present invention;

[0019] Figure 4 It is a comparison diagram of focusing results before and after beamforming provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0020] In order to further explain the technical means and effects adopted by the present invention to achieve the predetermined invention purpose, a frequency division MIMO radar fast moving target detection method proposed in the present invention is described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0021] The above and other technical contents, features and effects of the present invention are clearly presented in the following detailed description of the specific implementation modes in conjunction with the accompanying drawings. Through the description of the specific implementation modes, the technical means and effects adopted by the present invention to achieve the predetermined purpose can be more deeply and specifically understood. However, the attached drawings are only for reference and explanation purposes and are not used to limit the technical solutions of the present invention.

[0022] The present invention provides a method for detecting fast moving targets by frequency division MIMO radar. Figure 1 , Figure 1 FIG. 1 is a schematic diagram of a method for detecting fast moving targets using a frequency division MIMO radar according to an embodiment of the present invention. Figure 1 As shown, the frequency division MIMO radar fast moving target detection method of this embodiment includes:

[0023] Step 1: Use the receiving array element of the frequency division MIMO radar to obtain the echo signal.

[0024] In this embodiment, the frequency division MIMO radar includes M transmitting array elements and N receiving array elements, and both the transmitting and receiving array elements are uniform linear arrays (ULA), wherein the spacing between the transmitting array elements is d T , the receiving array element spacing is dR Frequency division MIMO radar is based on MIMO radar, adding frequency offset Δf between transmitting array elements, that is, there is a frequency offset between the transmitting carrier frequencies of M transmitting array elements. Taking the transmitting carrier frequency of the first transmitting array element as the reference, the transmitting carrier frequency of the mth transmitting array element is:

[0025] f m =f0+Δf m ,m=1,2,...,M;

[0026] Where f0 is the carrier frequency of the first transmitting array element; Δf m =(m-1)Δf represents the frequency offset associated with the mth transmitting array element. Then, the vector form of the transmitting carrier frequency of the M transmitting array elements can be expressed as f=[f1,f2,…,f M ] T ∈C M , the vector form of the frequency offset of the M transmitting array elements can be expressed as Δf = [Δf1, Δf2, …, Δf M ] T ∈C M .

[0027] Assuming that a linear frequency modulation (LFM) signal is used as the transmission signal, the baseband waveform transmitted by the mth transmitting array element can be expressed as:

[0028]

[0029] in, is the waveform representation of the linear frequency modulation signal LFM, t is the fast time variable, Indicates T p As the pulse duration, is the frequency modulation slope, and B is the signal bandwidth.

[0030] When a moving target in the far field is located at angle θ, range R, and enters the radar at radial velocity V, consider the case of two-way propagation and select the first transmitting array element as the reference. Therefore, the echo signal of the kth pulse received by the nth receiving array element is expressed as:

[0031]

[0032] In the formula, s n (t,t k ) is the echo signal of the kth pulse received by the nth receiving element, t is the fast time variable, t k is a slow time variable, M is the number of transmitting array elements, ξ t is the complex echo amplitude, R m,n (t k) is the round-trip distance between the mth transmitting element and the nth receiving element, c is the speed of light, j is the imaginary unit, and f m is the transmitting carrier frequency of the mth transmitting array element.

[0033] In this embodiment, ξ t The complex echo amplitude considering the transmission amplitude-phase, target scattering and propagation effects is expressed as Among them, P t , G t , G r ,λ0,δ t They represent the target’s peak transmission power, element transmission gain, element receiving gain, signal wavelength, and radar cross section (RCS) coefficient. m,n (t k )=2R-2Vt k -(m-1)d T sinθ-(n-1)d R sinθ, where t k =kT r represents the slow time variable; T r is the pulse repetition time (PRT).

[0034] Step 2: After mixing and matched filtering the echo signal, a matched filtering output signal is obtained.

[0035] In an optional embodiment, step 2 includes:

[0036] Step 2.1: Perform mixing processing on the echo signal to obtain a mixed echo signal.

[0037] Step 2.2: Decompose the mixed echo signal using a matched filter to obtain M independent matched filter output signals, where M is the number of transmitting array elements.

[0038] In this embodiment, after the echo signal is multiplied by exp{-j2πf0t} for mixing processing, the mixed echo signal is decomposed by a matched filter to obtain M independent matched filter output signals, wherein the mth matched filter output signal is expressed as:

[0039]

[0040] in, is the pulse compression coefficient after the mth matched filter is modulated, which can simultaneously complete the pulse compression and waveform separation of the signal. ss [Δt,(m'-m)Δf] is the correlation function between different transmission waveforms, expressed as:

[0041] χ ss[Δt,(m'-m)Δf]=Asinc[((m'-m)Δf+μΔt)(T p -|Δt|)];

[0042] Where A is the amplitude of the correlation function, expressed as m' represents a matched filter different from m.

[0043] Since the cross-correlation between different frequency-divided waveforms is small, the output signal after the mth matched filter can be approximated as:

[0044]

[0045] Step 3: transform the matched filter output signal into the frequency domain and perform pulse compression to obtain the corresponding pulse compression frequency domain signal, correct the linear range offset and speed fuzzy index of the pulse compression frequency domain signal to obtain the first corrected frequency domain signal.

[0046] In an optional embodiment, step 3 includes:

[0047] Step 3.1: Transform the matched filter output signal into the frequency domain to obtain the corresponding frequency domain signal.

[0048] In this embodiment, the frequency domain signal obtained by transforming the matched filtering output signal into the frequency domain can be expressed as:

[0049]

[0050] In the formula, f r is the frequency variable corresponding to the fast time variable, is the intermediate parameter, c is the speed of light, j is the imaginary unit, θ is the angle of the moving target, B is the signal bandwidth, v0 is the main velocity of the moving target, and l0 is the target velocity ambiguity index.

[0051] Step 3.2: According to the fixed phase principle, the frequency domain signal is pulse compressed to obtain a pulse compressed frequency domain signal.

[0052] In this embodiment, according to the fixed phase principle, the frequency domain signal is pulse compressed to obtain a pulse compressed frequency domain signal, which can be expressed as:

[0053]

[0054] Where V is the radial velocity of the moving target.

[0055] From the above formula, we can see that the linear distance traveled is determined by the variable f r and the slow time variable t kThe coupling is caused and becomes more obvious when fast-moving targets are detected.

[0056] For fast moving targets, velocity ambiguity is very likely to occur due to the limited radar pulse repetition frequency (PRF). In this case, the radial velocity of the moving target can be written as:

[0057] V=v0+l0V u ;

[0058] Where v0 represents the main velocity of the moving target, l0V u represents the fuzzy speed of the moving target, l0 is the target speed fuzzy index, V u is the maximum unambiguous speed, expressed as

[0059] Substituting the expression of the radial velocity of the moving target into the pulse compression frequency domain signal, we can obtain:

[0060]

[0061] From the above formula, we can see that the variable f r and the slow time variable t k The coupling term between t and t is related to the main velocity v0 of the moving target and the target velocity ambiguity index l0. In addition, due to the frequency difference between the transmitting array elements, t k and Δf m There is a coupling term between them, which causes the echoes output by different matched filters to be incoherent.

[0062] Step 3.3: Use baseline transformation to correct the first channel data of the pulse compression frequency domain signal, eliminate the linear range offset caused by the main speed of the moving target, and obtain the first channel data after the linear range offset correction.

[0063] Since the baseline transformation (KT) has excellent performance in a low signal-to-noise ratio environment, the influence of linear range migration is eliminated by baseline transformation in this embodiment. The original baseline transformation can be expressed as:

[0064]

[0065] Among them, τ k Represents the new slow time variable.

[0066] Taking into account the incoherence between different matched filter output signals, the original baseline transformation is used to correct the first channel data of the pulse compression frequency domain signal. The obtained first channel data after linear range offset correction can be expressed as:

[0067]

[0068] At this time, the linear range deviation caused by the main velocity v0 of the moving target is corrected.

[0069] Step 3.4: According to the first channel data corrected by the linear range offset, all velocity fuzzy indexes are corrected iteratively to obtain a first corrected frequency domain signal.

[0070] In this embodiment, the first modified frequency domain signal obtained by iteratively modifying all possible velocity ambiguity indices can be expressed as:

[0071]

[0072] Step 4: transform the first corrected frequency domain signal into the time domain to obtain a corresponding corrected time domain signal, obtain an estimated target speed ambiguity index based on the corrected time domain signal, and obtain an estimated radial speed of the moving target based on the estimated target speed ambiguity index.

[0073] In an optional embodiment, step 4 includes:

[0074] Step 4.1: Use range IFFT (Inverse Fast Fourier Transform) and azimuth FFT (Fast Fourier Transform) to perform time domain transformation on the first modified frequency domain signal to obtain a modified time domain signal.

[0075] In this embodiment, the modified time domain signal obtained by performing time domain transformation on the first modified frequency domain signal using range IFFT and azimuth FFT can be expressed as:

[0076]

[0077] Among them, A d is the compression gain of the slow time variable, f d is τ k The corresponding Doppler frequency variable.

[0078] In this embodiment, the moving target can be focused in the range time and azimuth Doppler domains through the corrected time domain signal.

[0079] Step 4.2: Focus the moving target in the range time and azimuth Doppler domains based on the corrected time domain signal. Get the estimated target velocity ambiguity index, where f d is τ k The corresponding Doppler frequency variable, τ k is the new slow time variable, f0 is the transmitting carrier frequency of the first transmitting array element, v0 is the main velocity of the moving target, and c is the speed of light.

[0080] In this embodiment, the velocity fuzzy index is matched by using the modified time domain signal to focus the target on At this time, the estimated target speed ambiguity index can be obtained It can be expressed as:

[0081]

[0082] in, represents the fast Fourier transform along slow time, represents the inverse fast Fourier transform along the range frequencies.

[0083] Step 4.3: The estimated radial velocity of the moving target is calculated based on the estimated target velocity ambiguity index.

[0084] In this embodiment, the calculation formula for the estimated radial velocity of the moving target is:

[0085]

[0086] In the formula, is the estimated radial velocity of the moving target, is the estimated target velocity ambiguity index, V u is the maximum unambiguous speed.

[0087] Step 5: Compensate the pulse compression frequency domain signal to obtain a compensation signal, and use the baseline transformation and the estimated target speed ambiguity index to correct the coupling term of the compensation signal to obtain a second corrected frequency domain signal.

[0088] In an optional embodiment, step 5 includes:

[0089] Step 5.1: Construct a speed-related compensation function, and use the compensation function to compensate the pulse compression frequency domain signal to obtain a compensated signal.

[0090] Due to t k and Δf m There is incoherence caused by a coupling term, which can be compensated by applying a velocity-dependent compensation function to the echo signal.

[0091] In this embodiment, the compensation function of the mth matched filter output signal of the kth pulse is expressed as:

[0092]

[0093] In the formula, is the compensation function of the mth matched filter output signal of the kth pulse, is the estimated target velocity ambiguity index, t k is a slow time variable, j is an imaginary unit, is the estimated main velocity of the moving target, Δfm The frequency offset of the transmitting carrier frequency of the mth transmitting array element, c is the speed of light, f0 is the transmitting carrier frequency of the first transmitting array element, T r is the pulse repetition time.

[0094] The compensated signal obtained by compensating the pulse compression frequency domain signal using the compensation function can be expressed as:

[0095] Step 5.2: Use the baseline transformation and the estimated target velocity ambiguity index to correct the coupling term of the compensation signal to obtain a second corrected frequency domain signal.

[0096] In this embodiment, after the coupling term is corrected using the baseline transformation and the estimated target speed ambiguity index based on the compensation signal, the obtained second corrected frequency domain signal can be expressed as:

[0097] Step 6: Based on the second corrected frequency domain signal, an enhanced angle estimation of the moving target is obtained in the transmit-receive domain.

[0098] In an optional embodiment, step 6 includes:

[0099] Step 6.1: According to the second corrected frequency domain signal, obtain the MN×1 dimensional vector after the k-th pulse is superimposed.

[0100] In this embodiment, first, the second modified frequency domain signal is processed using IFFF, and Substituting the second corrected signal after IFFF processing, we get:

[0101]

[0102] in,

[0103] Secondly, the kth pulse in the second corrected signal after IFFF processing is superimposed to obtain a MN×1-dimensional vector, which can be expressed as:

[0104]

[0105] Step 6.2: Obtain the enhanced angle estimation of the moving target in the transmit-receive domain according to the MN×1 dimensional vector. The enhanced angle estimation of the moving target is expressed as:

[0106]

[0107] In the formula, is the enhanced angle estimation of the moving target, w H (θ) is the transmit-receive domain weight vector, K is the number of pulses, y kis a MN×1 dimensional vector, c is the speed of light, R is the distance of the moving target, θ is the angle, τ k is the new slow time variable, and H is the conjugate transpose of the matrix.

[0108] In this embodiment, the transmit-receive domain weight vector w H (θ) is used to estimate the enhanced angle of the moving target, which can be expressed as: Where b(θ) represents the receiving steering vector, d(θ) represents the launch steering vector associated with the angle.

[0109]

[0110] In an optional embodiment, the frequency division MIMO radar fast moving target detection method of this embodiment further includes: performing two-dimensional beamforming in the transmit-receive domain according to the transmit-receive domain weight vector and the MN×1 dimensional vector to improve the range resolution of the frequency division MIMO radar.

[0111] In this embodiment, two-dimensional beamforming is performed in the transmit-receive domain using the transmit-receive domain weight vector and the MN×1-dimensional vector, and bandwidth splicing is performed at the same time. The spliced ​​signal can be expressed as:

[0112]

[0113] When the frequency offset Δf = B, the above formula can be expressed as:

[0114]

[0115] Compared with the second corrected signal after IFFF processing, it can be seen that the bandwidth of the spliced ​​signal has increased by M times, which means that the range resolution performance has been improved by M times and the target detection performance has been improved.

[0116] The frequency division MIMO radar fast moving target detection method of the present invention aims at the problem that the frequency offset in the echo signal introduces different degrees of coupling between the angle and speed parameters, and corrects the coupling term by correcting the linear range offset and the speed fuzzy index, so as to accurately detect the angle and speed parameters of the moving target. Through beam forming (bandwidth splicing), the range resolution performance can be improved by M times, and the position parameters of the target can be accurately derived.

[0117] Furthermore, the effect of the frequency division MIMO radar fast moving target detection method of this embodiment is explained through simulation experiments.

[0118] Basic parameters: Consider a fast-moving target with a signal-to-noise ratio of -30 dB before matched filtering. The actual distance, radial velocity and angle of the target are 3.6 km, 1604 m / s and 30° respectively, the main velocity is 104 m / s, and the target velocity ambiguity index is 2.

[0119] Apply KT to the output signal corresponding to the first channel of the matched filter to obtain the estimated target speed ambiguity index, as Figure 2 As shown, Figure 2 This is the estimation result of the target speed fuzzy index provided by the embodiment of the present invention. It can be seen from the figure that the estimated target speed fuzzy index is consistent with the real target speed fuzzy index, which illustrates the effectiveness of the method of the present invention.

[0120] Enhanced angle estimates for moving targets. Combining both transmit and receive array degrees of freedom results in lower side lobes and more accurate estimates. Figure 3 , Figure 3 is the result of the enhanced angle estimation of the moving target provided by the embodiment of the present invention, such as Figure 3 As shown, the enhanced angle estimation of the moving target is consistent with the real target angle, which illustrates the effectiveness of the method of the present invention.

[0121] Beamforming is performed based on the parameter estimation results. The focusing results before and after beamforming are compared. Figure 4 As shown, Figure 4 This is a comparison diagram of focusing results before and after beamforming provided by an embodiment of the present invention. Through numerical comparison, it can be found that the target amplitude is increased by 30dB. It can be observed that compared with the accumulation result of a single channel, beamforming not only increases the amplitude of the target, but also realizes the synthesis of a large bandwidth.

[0122] It should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply that there is any such actual relationship or order between these entities or operations. Moreover, the term "include", "comprise" or any other variant is intended to cover non-exclusive inclusion, so that the article or device including a series of elements includes not only those elements, but also other elements that are not explicitly listed. In the absence of more restrictions, the elements defined by the sentence "including one..." do not exclude the existence of other identical elements in the article or device including the elements. "Connect" or "connected" and similar words are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. The orientation or position relationship indicated by "up", "down", "left", "right", etc. is based on the orientation or position relationship shown in the accompanying drawings, which is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation of the present invention.

[0123] The above contents are further detailed descriptions of the present invention in combination with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is limited to these descriptions. For ordinary technicians in the technical field to which the present invention belongs, several simple deductions or substitutions can be made without departing from the concept of the present invention, which should be regarded as falling within the protection scope of the present invention.

Claims

1. A method for fast moving target detection using frequency division MIMO radar. It is characterized in that include: Step 1: Use the receiving array element of the frequency division MIMO radar to obtain the echo signal; Step 2: After mixing and matched filtering decomposition processing of the echo signal, a matched filtering output signal is obtained; Step 3: transform the matched filter output signal into the frequency domain and then perform pulse compression to obtain a corresponding pulse compression frequency domain signal, and correct the linear range offset and speed fuzzy index of the pulse compression frequency domain signal to obtain a first corrected frequency domain signal; Step 4: transforming the first corrected frequency domain signal into the time domain to obtain a corresponding corrected time domain signal, obtaining an estimated target speed fuzzy index according to the corrected time domain signal, and obtaining an estimated radial speed of the moving target according to the estimated target speed fuzzy index; Step 5: compensating the pulse compression frequency domain signal to obtain a compensation signal, and correcting the coupling term of the compensation signal using baseline transformation and the estimated target speed fuzzy index to obtain a second corrected frequency domain signal; Step 6: Obtain an enhanced angle estimate of the mobile target in the transmit-receive domain based on the second corrected frequency domain signal.

2. The method for detecting fast moving targets by frequency division MIMO radar according to claim 1, It is characterized in that The frequency division MIMO radar includes M transmitting array elements and N receiving array elements, and there is a frequency offset between the transmitting carrier frequencies of the M transmitting array elements; Among them, the echo signal of the kth pulse received by the nth receiving array element is expressed as: In the formula, s n (t,t k ) is the echo signal of the kth pulse received by the nth receiving element, t is the fast time variable, t k is a slow time variable, M is the number of transmitting array elements, ξ t is the complex echo amplitude, R m,n (t k ) is the round-trip distance between the mth transmitting element and the nth receiving element, c is the speed of light, j is the imaginary unit, and f m is the transmitting carrier frequency of the mth transmitting array element.

3. The method for detecting fast moving targets by frequency division MIMO radar according to claim 1, It is characterized in that The step 2 comprises: Step 2.1: performing frequency mixing processing on the echo signal to obtain a mixed echo signal; Step 2.2: Decompose the mixed echo signal using a matched filter to obtain M independent matched filter output signals, where M is the number of transmitting array elements.

4. The method for detecting fast moving targets by frequency division MIMO radar according to claim 1, It is characterized in that The step 3 comprises: Step 3.1: transform the matched filtering output signal into the frequency domain to obtain a corresponding frequency domain signal; Step 3.2: According to the fixed phase principle, pulse compressing the frequency domain signal to obtain the pulse compressed frequency domain signal; Step 3.3: Correcting the first channel data of the pulse compression frequency domain signal by using baseline transformation to eliminate the linear range offset caused by the main speed of the moving target, and obtaining the first channel data after the linear range offset correction; Step 3.4: According to the first channel data after the linear range offset correction, all speed fuzzy indexes are corrected iteratively to obtain the first corrected frequency domain signal.

5. The method for detecting fast moving targets by frequency division MIMO radar according to claim 1, It is characterized in that The step 4 comprises: Step 4.1: Performing a time domain transformation on the first modified frequency domain signal by using a range IFFT and an azimuth FFT to obtain the modified time domain signal; Step 4.2: Focus the moving target in the range, time and azimuth Doppler domains according to the modified time domain signal. The estimated target speed ambiguity index is obtained, where f d is τ k The corresponding Doppler frequency variable, τ k is the new slow time variable, f 0 is the transmitting carrier frequency of the first transmitting array element, v 0 is the main velocity of the moving target, c is the speed of light; Step 4.3: Calculate the estimated radial velocity of the moving target according to the estimated target velocity ambiguity index.

6. The method for detecting fast moving targets using frequency division MIMO radar according to claim 5, It is characterized in that The calculation formula of the estimated radial velocity of the moving target is: In the formula, is the estimated radial velocity of the moving target, is the estimated target velocity ambiguity index, V u is the maximum unambiguous speed.

7. The method for detecting fast moving targets using frequency division MIMO radar according to claim 1, It is characterized in that The step 5 comprises: Step 5.1: Construct a speed-related compensation function, and use the compensation function to compensate the pulse compression frequency domain signal to obtain the compensated signal, wherein the compensation function of the mth matched filter output signal of the kth pulse is expressed as: In the formula, is the compensation function of the mth matched filter output signal of the kth pulse, is the estimated target velocity ambiguity index, t k is a slow time variable, j is an imaginary unit, is the estimated main velocity of the moving target, Δf m The frequency offset of the transmitting carrier frequency of the mth transmitting array element, c is the speed of light, f 0 is the transmitting carrier frequency of the first transmitting array element, T r is the pulse repetition time; Step 5.2: Use the baseline transformation and the estimated target speed ambiguity index to correct the coupling term of the compensation signal to obtain the second corrected frequency domain signal.

8. The method for detecting fast moving targets using frequency division MIMO radar according to claim 1, It is characterized in that The step 6 comprises: Step 6.1: Obtaining an MN×1-dimensional vector after the k-th pulse is superimposed according to the second corrected frequency domain signal; Step 6.2: Obtain an enhanced angle estimate of the mobile target in the transmit-receive domain according to the MN×1 dimensional vector. The enhanced angle estimate of the mobile target is expressed as: In the formula, is the enhanced angle estimation of the moving target, w H (θ) is the transmit-receive domain weight vector, K is the number of pulses, y k is a MN×1 dimensional vector, c is the speed of light, R is the distance of the moving target, θ is the angle, τ k is the new slow time variable, and H is the conjugate transpose of the matrix.

9. The method for detecting fast moving targets using frequency division MIMO radar according to claim 8, It is characterized in that The method further includes: performing two-dimensional beamforming in the transmit-receive domain according to the transmit-receive domain weight vector and the MN×1 dimensional vector to improve the range resolution of the frequency division MIMO radar.

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