Transmit-receive joint multi-beam design method based on coherent frequency diversity array

Abstract

This invention discloses a coherent frequency diversity array-based transceiver joint multibeam design method, primarily addressing the shortcomings of existing technologies that cannot simultaneously achieve transmit beamforming and pulse compression, and cannot cover wide-angle regions, resulting in insufficient spatial coverage. The implementation scheme involves: establishing the LFM baseband signal envelope of a coherent FDA radar; acquiring the received echo signal from the coherent FDA radar, and designing an angle-dependent matched filter as the time-reversed conjugate of the baseband signal; calculating the filtered transmit domain echo data based on the radar's received echo signal; extracting the transmit steering vector from the transmit domain echo data, and calculating the transceiver joint beam steering vector based on the receive steering vector under a phased array architecture; constructing constraints for the transceiver joint weight vector, and calculating the transceiver joint weight vector. This invention can simultaneously achieve receive, transmit beamforming, and pulse compression without splitting the transmit and receive channels, improving multibeam wide-area wide-angle coverage, and can be used for transmit beamforming and pulse compression.

Description

Technical Field

[0001] This invention belongs to the field of radar technology, and specifically relates to a transceiver joint multi-beam design method, which can be used for transmit beamforming and pulse compression. Background Technology

[0002] The transmit pattern of a frequency diversity array (FDA) radar differs from that of a traditional phased array (PA) radar. PA radar transmit patterns depend only on angle, while FDA radar obtains a range / time-angle three-dimensional transmit pattern by introducing frequency step sizes between array elements. By combining with multiple-input multiple-output (MIMO) technology, FDA-MIMO radar can extract target range information in the transmit dimension, thus achieving joint target range-angle estimation. Traditional matched filtering methods cannot simultaneously achieve transmit DBF and pulse compression processing to obtain coverage over a wider angular region.

[0003] To overcome the aforementioned shortcomings, researchers have proposed a sub-pulse range-angle matched filtering receiving and processing method. By rationally arranging system parameters, the full-area coverage capability of the coherent frequency diversity array (FDA) radar is improved. By designing a low-peak-sidelobe level mismatch filter, wide-area coverage and high-resolution observation of the coherent frequency diversity array (FDA) are achieved. Since the carrier frequency of the frequency diversity array (FDA) is linearly related to time, and the frequency increment is proportional to the frequency gradient relative to time, a linear frequency modulation (LFM) waveform can be used, and frequency step modulation in the frequency diversity array (FDA) radar can be equivalently achieved through a time-delay microwave circuit.

[0004] Patent document with application number 201610948592.9 discloses a "coherent frequency diversity array radar segmented matched filtering method", which mainly solves the problem of range-angle two-dimensional matched filtering under wide-area coverage conditions that is difficult to achieve in existing radar systems. The implementation steps are as follows: First step: Obtain the echo signal of the coherent frequency diversity array receiver and construct the expression of the corresponding transmission pattern; Second step: According to the corresponding transmission pattern, obtain the illumination time period of the main lobe of the beam at a specific angle in the pointing space, and design the time width of the matched sub-pulse; Third step: According to the time width of the matched sub-pulse, divide the transmission pulse time evenly and construct the angle-time two-dimensional segmented matched filtering function corresponding to each matched sub-pulse.

[0005] Patent application number 201910948592.9 discloses a "segmented matched filtering method for coherent frequency diversity array radar," which combines two-dimensional space-time coding technology with the coherent frequency diversity array (FDA) based on the angle-frequency dependence characteristics of the FDA. To meet practical needs, a waveform receiving and processing procedure is designed, including receiving beamforming, time-angle matched filtering, and Doppler compensation. By performing two-dimensional space-time coding on the transmitted signal of the FDA, the problem of reduced range resolution in the FDA is solved.

[0006] The two methods mentioned above cannot simultaneously achieve transmit digital beamforming (DBF) and pulse compression processing, thus they cannot achieve beam coverage over a wide angle area, resulting in insufficient spatial coverage capability. Summary of the Invention

[0007] The purpose of this invention is to address the shortcomings of the prior art by proposing a coherent frequency diversity array-based transceiver multibeam design method. This method simultaneously achieves coherent frequency diversity array (FDA) transceiver multibeamforming and signal pulse compression, enabling wide-area, wide-angle coverage of the frequency diversity array radar and improving its spatial coverage capability.

[0008] The technical approach to achieving the objective of this invention is as follows: Under the coherent frequency diversity array (FDA) radar system, based on the baseband envelope of the received signal that simultaneously depends on the transmitted signal waveform and the transmitted radiation pattern, an angle-dependent matched filter is designed. Multiple digital receiving channels, typical of traditional phased array systems, are used for receiving beamforming (DBF), achieving combined transmit and receive multi-beamforming, including both transmit and receive DBFs. The received signal is processed using angle-dependent matched filtering (ADMF), and equivalent transmit beamforming and signal pulse compression are simultaneously achieved through ADMF processing, thereby forming wide-area, wide-angle coverage for the frequency diversity array (FDA) radar.

[0009] Based on the above approach, the technical solution is as follows:

[0010] 1. A method for designing a coherent frequency diversity array-based transceiver multibeam, comprising a steering vector for the transceiver multibeam and a transmit-receive weighting vector for the transceiver multibeam, characterized by comprising the following steps:

[0011] (1) Obtain the received echo signal x(t,θ0) of the coherent frequency diversity array FDA radar based on the envelope of the linear frequency modulated (LFM) baseband signal of the coherent frequency diversity array FDA radar.

[0012] (2) Design an angle-dependent matched filter (ADMF) based on the echo signal x(t,θ0):

[0013] (2a) The angle-dependent matched filter ADMF is designed as the time-reversed conjugate of the baseband envelope signal of the coherent frequency diversity array (FDA) radar, and is expressed as:

[0014]

[0015] Where h(t|θ) represents the angle-dependent matched filter, and the superscript * indicates the conjugate operator. It is a rectangular pulse envelope, Ψ represents the envelope of the coherent frequency diversity array FDA radar signal, exp{-jπγt} 2} represents a linear frequency modulated (LFM) signal, γ represents the frequency modulation slope, θ represents a specified angle, and T p The pulse width;

[0016] (2b) Based on the number of transmit array elements M under the phased array system, calculate the matched filter h(t|θ) for each orthogonal ADMF. m ) angle θ m m = 1, 2, ..., M, where M is the number of array elements;

[0017] (3) Based on multiple orthogonal ADMF matched filters, design a joint transmit and receive multibeam:

[0018] (3a) The received echo data x(t,θ0) is passed through ADMF matched filters h(t|θ) at different angles. m The data is processed to obtain the echo data z(τ) in the transmitted beam domain:

[0019]

[0020] in, Let y(t, θ0|θ) represent convolution, T represent transpose, ξ represent the complex coefficients of the target signal, and ξ represent the complex coefficients of the target signal. m ) represents angle θ m Echo data in the lower transmit beam domain;

[0021] (3b) Based on the transmitted beam domain echo data z(τ), calculate the frequency domain value X(f,θ0) of the echo data and the frequency domain value H(f|θ) of the ADMF filter, respectively:

[0022] X(f,θ0)=∫x(t,θ0)e -j2πft dt, H(f|θ)=∫h(tθ)e -j2πft dt

[0023] (3c) Calculate the frequency domain value Y(f,θ0|θ) of the echo data based on the frequency domain value X(f,θ0) of the echo data and the frequency domain value H(f|θ) of the ADMF filter:

[0024]

[0025] in, λ0 is the signal complex coefficient, d is the carrier wavelength, and d is the array element spacing.

[0026] (3d) Based on the frequency domain value Y(f,θ0|θ) of the transmitted beam domain echo data, extract the angle-dependent part of the result to obtain the transmitted beam domain steering vector.

[0027]

[0028] (3e) Based on the transmit beam domain steering vector Given the receive beam steering vector a(θ) in phased array mode, calculate the transmit / receive joint beam steering vector C(θ) for each receiver / transmitter configuration:

[0029]

[0030] (3f) Based on the transmit-receive joint beam steering vector in the phased array system, construct its corresponding transmit-receive weighting vector w. TX-RX The constraints under the Minimum Variance Distortionless Response (MVDR) criterion are substituted into the MVDR criterion to calculate the transmit-receive weight vector w. TX-RX :

[0031]

[0032] in, This represents the echo data in the combined transmit and receive beam domain, where H represents the conjugate transpose. It is a combined beam domain echo data transmission and reception system. The covariance matrix.

[0033] Compared with the prior art, the present invention has the following advantages:

[0034] First, the present invention utilizes the ADMF matched filtering method to achieve transmit beamforming and matched filtering. Unlike traditional matched filtering, ADMF can simultaneously achieve transmit beamforming (DBF) and pulse compression.

[0035] Second, this invention designs a transmit-receive joint multibeamforming for coherent frequency diversity array (FDA) radar and constructs constraints for transmit-receive joint beamforming under the minimum variance distortionless response (MVDR) criterion. Compared with traditional beamforming, the coherent frequency diversity array (FDA) can process echo signals from different spatial angles in parallel, achieving simultaneous multibeam wide-area wide-angle coverage.

[0036] The embodiments of the present invention will be further described in detail below with reference to the accompanying drawings. Attached Figure Description

[0037] Figure 1 This is a flowchart illustrating the implementation of the present invention;

[0038] Figure 2 The coherent frequency diversity array FDA transceiver joint nine-beam diagram simulated using this invention;

[0039] Figure 3 The coherent frequency diversity array FDA transceiver joint eighteen beam diagram simulated using this invention. Detailed Implementation

[0040] This example demonstrates a combined transmit and receive multi-beam design, including the steering vector and transmit-receive weight vector of the combined transmit and receive multi-beam. Specifically: calculating the steering vector of the combined transmit and receive beam involves first calculating the beam pointing angle, and then calculating the corresponding steering vector; calculating the transmit-receive weight vector involves first constructing the combined transmit and receive echo data, and then constructing the constraints for the corresponding weight vector based on the Minimum Variance Distortionless Response (MVDR) criterion, before calculating the transmit-receive weight vector of the combined transmit and receive beam.

[0041] Reference Figure 1 The implementation steps for this example are as follows:

[0042] Step 1: Construct a linear frequency modulated (LFM) target signal model for a coherent frequency diversity array (FDA) radar.

[0043] 1.1) Using a linear frequency modulated (LFM) waveform, construct the transmitted signal s of the m-th antenna. m (t):

[0044]

[0045] Where Tp is the pulse width. It is a rectangular pulse function.

[0046] B is the modulation frequency of a linear frequency modulated (LFM) signal. w It is the signal bandwidth, f m f0 is the modulation carrier frequency of the m-th transmitting antenna, f0 is the reference carrier frequency, and Δf is the frequency step between array elements, which is much smaller than the reference carrier frequency f0.

[0047] 1.2) Based on the transmitted signal s m (t), construct a far-field target signal model x(t-τ0,θ0) with target angle θ0 and distance r0:

[0048]

[0049] Where ξ0 is the complex scattering coefficient of the target, c is the speed of light, and d is the element spacing. It is the target delay, fd0 It is the Doppler frequency offset of the target echo, f PRF It is the pulse repetition frequency.

[0050] Step 2: Design a coherent frequency diversity array (FDA) to transmit multiple beams.

[0051] 2.1) Based on the far-field target signal model x(t-τ0,θ0) and the receiving pattern F under the phased array system R (θ0), construct the received echo model y(t,θ0) with a pointing angle θ0:

[0052]

[0053] Among them, w R =[ω1,ω2,…,ω N ] T It is the receiving weight vector. It is the receive steering vector, H is the conjugate transpose, and T is the transpose. The envelope of the far-field target signal, where n(t) is the signal noise;

[0054] 2.2) Design an angle-dependent matched filter ADMF, i.e., the time-reversed conjugate of the coherent FDA radar baseband envelope signal, which is expressed as:

[0055]

[0056] The superscript * indicates the conjugate operator;

[0057] 2.3) Calculate the different angles θ of multiple orthogonal ADMF matched filters. m :

[0058]

[0059] 2.4) Perform ADMF matched filtering on the far-field echo signal at different angles to obtain the transmitted beam domain echo data z(τ):

[0060]

[0061] Where ξ represents the complex coefficients of the target signal, Let y(t,θ0|θ) represent the target steering vector corresponding to the transmitted beam domain, and T represent the transpose operation. m ) represents angle θ m Echo data in the lower transmit beam domain;

[0062] 2.5) Calculate the frequency domain value X(f,θ0) of the echo data:

[0063]

[0064] Where Δf is the frequency offset, B w It is the signal bandwidth, f d0 It is the Doppler frequency offset of the target echo, f PRF γ is the pulse repetition frequency, and γ is the frequency modulation slope;

[0065] 2.6) Calculate the frequency domain value H(f|θ) of the ADMF filter:

[0066]

[0067] 2.7) Calculate the frequency domain value Y(f,θ0|θ) of the transmitted beam domain echo data based on the frequency domain value X(f,θ0) of the echo data and the frequency domain value H(f|θ) of the ADMF filter:

[0068]

[0069] 2.8) Based on the frequency domain value Y(f,θ0|θ) of the transmitted beam domain echo data, extract the angle-dependent portion of the result to obtain the transmitted beam domain steering vector.

[0070]

[0071] 2.5) Based on the transmit beam domain echo data z(τ), construct the constraints for the transmit beam domain under the minimum variance distortionless response (MVDR) criterion:

[0072]

[0073] Step 3: Design a coherent frequency diversity array FDA transceiver joint multibeam.

[0074] 3.1) Based on the transmitted beam domain steering vector Given the receive beam steering vector a(θ) in phased array mode, calculate the transmit / receive joint beam steering vector C(θ) for each receiver / transmitter configuration:

[0075]

[0076] 3.2) Based on the receive steering vector a(θ) in the receive echo model, construct the corresponding transmit / receive joint domain echo data.

[0077]

[0078] 3.3) Based on the combined transmit and receive domain echo data Constructing constraints for the transmit-receive joint beam domain under the minimum variance distortionless response (MVDR) criterion:

[0079]

[0080] 3.4) Based on the constraints of the transmit / receive joint beam domain under the minimum variance distortionless response (MVDR) criterion, calculate the transmit / receive weight vector w. TX-RX :

[0081] 3.4.1) Solve the minimum variance-free MVDR criterion under constraints using the Lagrange operator method, and construct the Lagrange operator L(W,λ):

[0082]

[0083] 3.4.2) Calculate L for each pair of w TX-RX Partial derivative and the partial derivative with respect to λ

[0084]

[0085] 3.4.3) According to Obtain w containing the unknown λ TX-RX expression:

[0086]

[0087] 3.4.4) Multiply both sides of the equation by C(θ0) to obtain the intermediate variable λ:

[0088]

[0089] 3.4.5) Substitute the expression for λ into w TX-RX The transmit and receive weight vector w is obtained. TX-RX :

[0090]

[0091] in, Echo data representing the combined transmit and receive beam domain, This represents the covariance matrix.

[0092] The following section, using algorithm simulation, further illustrates the effectiveness of this invention:

[0093] 1. Simulation experimental conditions:

[0094] The software platform for the simulation experiment of this invention is: Windows 10 operating system and MATLAB R2021a.

[0095] The simulation parameters for the coherent frequency diversity array FDA radar of this invention are set as follows:

[0096] It has 8 transceiver elements, a reference carrier frequency of 3GHz, a frequency step of 100kHz, a signal bandwidth of 20MHz, a sampling rate of 40MHz, a pulse repetition frequency (PRF) of 10KHz, and 64 pulses.

[0097] 2. Simulation content and result analysis:

[0098] Simulation 1: Under the above conditions, the present invention is used to design M+1=9 beams, and their corresponding angles are calculated as follows. Calculate its corresponding transmit / receive joint beam diagram, the result is as follows Figure 2 The horizontal axis represents spatial angles in radians (rad), and the vertical axis represents amplitude in dB. sin(θ) = -1

[0099] Depend on Figure 2 It is evident that the coherent frequency diversity array FDA radar can effectively form a combined transmit and receive pattern. The first sidelobe of the two-way pattern is approximately -25dB, and the second sidelobe is approximately -33dB, which can meet the requirements for moving target detection. The nine beams can cover the entire observation space, but there is gain loss at different beam intervals.

[0100] Simulation 2: Under the above conditions, 2*(M+1) = 18 beams were designed using this invention, and their corresponding angles were calculated. Calculate its corresponding transmit / receive joint beam diagram, the result is as follows Figure 3 , Figure 3 The horizontal axis represents spatial angles in radians (rad), and the vertical axis represents amplitude in dB.

[0101] Depend on Figure 3 It is evident that in the coherent frequency diversity array FDA radar receiver processing, parallel beams can be flexibly added without beam scanning loss, effectively improving detection performance by approximately 3–5 dB.

[0102] The above description is merely a specific example of the present invention and does not constitute any limitation on the present invention. Obviously, those skilled in the art, after understanding the content and principles of the present invention, may make various modifications and changes in form and details without departing from the principles and structure of the present invention. However, these modifications and changes based on the ideas of the present invention are still within the scope of protection of the claims of the present invention.

[0103] It should be noted that the step numbers in the specification and claims of this invention are only for the purpose of clearly describing the embodiments of this invention and facilitating understanding, and their order is not limited.

Claims

1. A transceiver joint multibeam design method based on a coherent frequency diversity array, characterized in that, Includes the following steps: (1) Obtain the received echo signal of the coherent FDA radar based on the LFM baseband signal envelope of the coherent FDA radar. ; (2) Based on the echo signal Design angle-dependent matched filter ADMF: (2a) The angle-dependent matched filter ADMF is designed as the time-reversed conjugate of the coherent FDA radar baseband envelope signal, and is expressed as: ； in This represents an angle-dependent matched filter, with the superscript * indicating the conjugate operator. It is a rectangular pulse envelope. Represented as the coherent FDA radar signal envelope, This represents a linear frequency modulated (LFM) signal. Indicates the frequency modulation slope. To represent a specified angle, The pulse width; (2b) Calculate the matched filter for each orthogonal ADMF based on the number of transmit array elements M under the phased array system. Angle m = 1, 2, ..., M, where M is the number of array elements; (3) Based on multiple orthogonal ADMF matched filters, design a joint transmit and receive multibeam: (3a) Receive echo data ADMF matched filters at different angles The data is processed to obtain the echo data in the transmitted beam domain. : ； in, Let T denote convolution, and T denote transpose. Indicates angle Echo data in the lower transmit beam domain; (3b) Based on the transmitted beam domain echo data Calculate the frequency domain values ​​of the echo data respectively. and the frequency domain value of the ADMF filter : ， ； (3c) Based on the frequency domain value of the echo data and the frequency domain value of the ADMF filter Calculate the frequency domain value of the transmitted beam domain echo data. : ； in, These are the complex coefficients of the signal. It is the carrier wavelength. It is the spacing between array elements; (3d) Based on the frequency domain values ​​of the transmitted beam domain echo data Extract the dependent angle from the results The part that obtains the transmit beam domain steering vector : ; (3e) Based on the transmitted beam domain steering vector and the receiving beam steering vector under phased array system Calculate the steering vector for each transmit / receive joint beam. : ； (3f) Based on the transmit-receive joint beam steering vector under the phased array system, construct its corresponding transmit-receive weighting vector. The constraints under the minimum variance-free MVDR criterion are substituted into the minimum variance-free MVDR criterion to calculate the transmit-receive weight vector. : ， ； in, This represents the echo data in the combined transmit and receive beam domain, where H represents the conjugate transpose. It is a combined beam domain echo data transmission and reception system. The covariance matrix.

2. The method according to claim 1, characterized in that, The received echo signal of the coherent FDA radar obtained in step (1) , means as follows: ， in, Represents the complex scattering coefficients of the target. It is the target latency. The reference carrier frequency is represented by m = 1, 2, ..., M, where M represents the number of array elements and d represents the spacing between antenna elements. Indicates the target angle. The carrier wavelength; It is frequency offset. It is the frequency modulation slope.

3. The method according to claim 1, characterized in that, In step (2b), the number of transmitter array elements M under the phased array system is used to calculate the matched filter for each orthogonal ADMF. Angle The formula is as follows: ， Where m = 1, 2, ..., M, and M is the number of array elements.

4. The method according to claim 1, characterized in that, In step (3b), the echo data from the transmitted beam domain is used as a basis. Calculate the frequency domain value of the echo data The formula is expressed as follows: ， in, It is frequency offset. It is the signal bandwidth. It is the Doppler frequency offset of the target echo. It is the pulse repetition frequency. It is the frequency modulation slope.

5. The method according to claim 4, characterized in that, In step (3b), the echo data from the transmitted beam domain is used as a basis. Calculate the frequency domain value of the ADMF filter. The formula is expressed as follows: ， in, It is frequency offset. It is the signal bandwidth. It is the pulse repetition frequency. It is the frequency modulation slope.

6. The method according to claim 5, characterized in that, In step (3c), the frequency domain value of the echo data is used as a basis. and the frequency domain value of the ADMF filter Calculate the frequency domain value of the transmitted beam domain echo data. The formula is expressed as follows: ， in, It is frequency offset. It is the signal bandwidth. It is the Doppler frequency offset of the target echo. It is the pulse repetition frequency.

7. The method according to claim 1, characterized in that, Step (3e) involves receiving the beam steering vector in a phased array configuration. , means as follows: ， Where N is the number of receiver array elements.

8. The method according to claim 1, characterized in that, Echo data in the transmit and receive joint beam domain in step (3f) and its covariance matrix They are represented as follows: ， 。 9. The method according to claim 1, characterized in that, Step (3f) substitutes the constraints into the minimum variance-free MVDR criterion to calculate the transmit-receive weight vector. The implementation is as follows: (3f1) Solve the minimum variance-free MVDR criterion under constraints using the Lagrange operator method, and construct the Lagrange operator. : ； (3f2) Calculate separately right Partial derivative and to partial derivatives : ， ， (3f3) According to To obtain unknown quantities of expression: ， (3f4) Multiply both sides of the equation Find the intermediate variables : ； (3f5) will Expression Substitution ,get: ； in, Echo data representing the combined transmit and receive beam domain, This represents the covariance matrix.

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