A time-domain waveform response conversion method based on sweep data

Abstract

A time-domain waveform response conversion method based on swept-frequency data is proposed. First, the selected time-domain signal waveform is analyzed. Corresponding swept-frequency parameters are designed based on bandwidth and target geometry. Broadband scattering characteristic data of the target are obtained through frequency-domain electromagnetic scattering modeling or testing. Fourier transform is used to convert the frequency-domain scattering field data into the target's time-domain impulse response. The time-domain response of the target to arbitrary waveforms is obtained by convolving the incident time-domain waveform with the target's impulse response. This is an effective method for generating time-domain waveform responses for complex targets. By obtaining the time-domain waveform response through signal processing of the swept-frequency data, the limitations of time-domain electromagnetic scattering modeling algorithms and arbitrary time-domain waveform measurement systems are avoided. It enables rapid generation of target responses under arbitrary incident waveforms based on traditional frequency-domain electromagnetic scattering modeling algorithms or stepped-frequency electromagnetic scattering measurement systems, greatly expanding its applicability.

Description

Technical Field

[0001] This invention relates to the field of electromagnetic scattering modeling, and in particular to a time-domain waveform response conversion method based on swept frequency data. Background Technology

[0002] Target electromagnetic scattering modeling algorithms are broadly categorized into frequency domain and time domain algorithms. Traditionally, for acquiring the target's time-domain waveform response, a model of the incident time-domain waveform signal is first established, and then this model is substituted into the time-domain electromagnetic scattering modeling algorithm to model the target's time-domain response samples under various observation angles. While this method can directly obtain the target's time-domain waveform response through simulation, it significantly increases the computational load for complex incident waveforms. Furthermore, when the incident waveform needs to be changed for the same target, a new simulation is required, making it difficult to meet the need for real-time comparison and analysis of a large number of incident waveform response characteristics. In addition, during the process of acquiring the target's time-domain waveform response through testing, limitations in equipment conditions generally make it difficult to generate arbitrary time-domain waveforms. Although many domestic and international institutions have conducted research on acquiring target time-domain waveform responses, covering areas such as electromagnetic scattering modeling and microwave anechoic chamber simulation testing, the production of large-scale and arbitrary waveform response data remains lacking.

[0003] The statements herein provide only background information in relation to this invention and do not necessarily constitute prior art. Summary of the Invention

[0004] The purpose of this invention is to provide a time-domain waveform response conversion method based on frequency sweep data, which can realize the rapid generation of target response characteristics under arbitrary time-domain waveform input.

[0005] To achieve the above objectives, the present invention provides a time-domain waveform response conversion method based on frequency sweep data, comprising the following steps:

[0006] Step S1: Solve for the one-dimensional range profile of the target that matches the incident time-domain waveform parameters;

[0007] Based on the sweep frequency parameters corresponding to the incident time-domain waveform signal, broadband scattering characteristic data of the target are obtained through frequency-domain electromagnetic scattering modeling or microwave anechoic chamber step-frequency electromagnetic scattering test, and then converted into one-dimensional range image information of the target through Fourier transform.

[0008] Step S2: Solve for the target time-domain impulse response;

[0009] The one-dimensional distance image of the target is changed from radial distance to time on the horizontal axis to obtain the target's impact response. Interpolation is then used to ensure that the target's impact response has a consistent time sampling interval with the incident narrow pulse.

[0010] Step S3: Solve for the target response under time-domain waveform incidence;

[0011] The response characteristics of the target to the incident time-domain signal are obtained by convolving the incident time-domain waveform signal with the target impact response.

[0012] In step S1, the frequency sweep parameters include the center frequency, the frequency sweep step size, and the frequency sweep bandwidth.

[0013] The center frequency is equal to the center frequency f of the time-domain waveform. c ;

[0014] The sweep bandwidth satisfies:

[0015] B = 1 / T c (1)

[0016] In the formula, T c The pulse width of the time-domain waveform;

[0017] The frequency sweep step size is determined by the Narquist sampling rate, and the radial width of the radar image window is:

[0018]

[0019] In the formula, Δf is the sweep step size, and c is the speed of light;

[0020] If the maximum size of the target is D, the frequency sweep step size must satisfy:

[0021]

[0022] Using the frequency sweep parameters that match the incident time-domain waveform as input, simulations are carried out using frequency-domain electromagnetic scattering modeling algorithms, or simulation tests are carried out in a microwave anechoic chamber using a step-frequency electromagnetic scattering measurement system to obtain the frequency sweep scattering field data of complex targets.

[0023] Assuming a complex extended target's one-dimensional range profile contains M sampling points radially, and the swept-frequency echo signal contains information from N frequency points, the target's one-dimensional range profile, i.e., the distribution characteristic A(r) of the target's scattering center along the radial distance, is... k ) is represented as:

[0024]

[0025] In the formula, r k X is the distance at the radial position numbered k relative to the center of the reference distance; M (f vi f represents the target swept-frequency scattering field; vi is the sweep frequency sequence; j is the imaginary unit; c is the speed of light.

[0026] In step S2, the time sampling step size of the incident time-domain waveform signal is:

[0027] t p =1 / f p (5)

[0028] In the formula, f p The sampling rate of the incident time-domain waveform signal;

[0029] Without zero-padding during the Fourier transform, the sampling interval of the radial distance coordinate axis in a one-dimensional image after conversion to time is:

[0030] t b =1 / (2B) (6)

[0031] In the formula, B is the sweep bandwidth;

[0032] The peak values ​​in the one-dimensional range image are extracted and loaded into the corresponding positions in the new impact response array, thereby solving the impact response of complex targets.

[0033] In step S3, the response of the transmitted time-domain waveform signal is expressed as follows:

[0034] PRX(t)=PTX(t)*HRP(t) (7)

[0035] In the formula, PTX(t) is the transmitted time-domain waveform signal; HRP(t) is the target's impact response; PRX(t) is the response of the transmitted signal; and t is time.

[0036] This invention enables the rapid generation of target response characteristics under arbitrary time-domain waveform input. First, the invention analyzes the selected time-domain signal waveform, designs corresponding frequency sweep parameters based on bandwidth and target geometry, obtains broadband scattering characteristic data of the target through frequency-domain electromagnetic scattering modeling or testing, and converts the frequency-domain scattering field data into the target's time-domain impulse response using Fourier transform. The time-domain response of the target to arbitrary waveforms is obtained by convolving the incident time-domain waveform with the target's impulse response. This is an effective method for generating time-domain waveform responses for complex targets. By obtaining the time-domain waveform response through signal processing of the frequency sweep data, this invention avoids the limitations of time-domain electromagnetic scattering modeling algorithms and arbitrary time-domain waveform measurement systems. It can rapidly generate target responses under arbitrary incident waveforms based on traditional frequency-domain electromagnetic scattering modeling algorithms or stepped-frequency electromagnetic scattering measurement systems, greatly expanding its applicability. Attached Figure Description

[0037] Figure 1 This is a flowchart of a time-domain waveform response conversion method based on swept frequency data provided by the present invention.

[0038] Figure 2It is the incident time-domain waveform signal.

[0039] Figure 3 It is a one-dimensional distance image of a point target.

[0040] Figure 4 It is the impact response of a point target.

[0041] Figure 5 It is the target's response to the time-domain waveform. Detailed Implementation

[0042] The following is based on Figures 1-5 The preferred embodiments of the present invention will be described in detail below.

[0043] Currently, most mainstream electromagnetic scattering characteristic measurement systems are stepped frequency scanning measurement systems, which can conveniently acquire the swept frequency scattering characteristics of targets. Therefore, by processing and analyzing the swept frequency scattering characteristic data of targets, a time-domain waveform response transformation method based on swept frequency data is established. On the one hand, this method can solve the problem of the difficulty in modeling the response characteristics of complex incident waveforms; on the other hand, it can generate response characteristics under arbitrary incident waveforms based on the swept frequency data obtained from tests. This will greatly expand and simplify the method of acquiring the time-domain waveform response of complex targets, and has significant research value.

[0044] This invention provides a time-domain waveform response conversion method based on swept-frequency data. The overall idea of ​​this method is to obtain the target's impulse response through analysis of frequency domain data, and then solve for the response characteristics by convolving the impulse response with the time-domain waveform. Therefore, the primary problem of this method is solving for the target's time-domain impulse response. The target's impulse response is closely related to the detection parameters. It is necessary to analyze the swept-frequency parameters contained within the incident time-domain signal based on its form, obtain frequency-domain scattering field data using parameters consistent with the time-domain signal, and then solve for the impulse response based on the frequency-domain data through transformations such as Fourier transform. Figure 1 As shown, the time-domain waveform response conversion method based on frequency sweep data specifically includes the following steps:

[0045] Step S1: Solve for the one-dimensional range profile of the target that matches the incident time-domain waveform parameters;

[0046] By analyzing the incident time-domain waveform signal, corresponding sweep frequency parameters are designed based on its corresponding carrier frequency, bandwidth and other information. Broadband scattering characteristic data of the target are obtained through frequency domain electromagnetic scattering modeling or microwave anechoic chamber step-frequency electromagnetic scattering test, and then converted into one-dimensional range image information of the target through Fourier transform.

[0047] The main parameters of the incident time-domain waveform include the center frequency f. c Pulse width T c Signal sampling rate fp To ensure the matching between the frequency-domain scattered field data and the incident time-domain waveform, the parameters used in frequency-domain electromagnetic scattering simulations or tests must match the parameters of the incident time-domain waveform. The sweep parameters mainly include the center frequency, sweep step size, and bandwidth. The center frequency of the sweep is the same as the time-domain waveform, both being f0. c The frequency sweep bandwidth satisfies:

[0048] B = 1 / T c (1)

[0049] In the formula, T c The pulse width is the time-domain waveform.

[0050] The sweep step size is determined by the Narquist sampling rate, which defines the range of the radar image window in the slant range direction (radial). Generally, the radial width of the radar image window is:

[0051]

[0052] In the formula, Δf is the sweep step size; c is the speed of light. If the maximum size of the target is D, then L ≥ D is obviously required to ensure that the target is completely within the radar window in the radial direction, thus preventing aliasing of the one-dimensional range image. In this case, the sweep step size should satisfy:

[0053]

[0054] Only when equation (3) is satisfied can it be guaranteed that the target is completely within the radar window in the slant range direction without aliasing.

[0055] Using frequency sweep parameters that match the incident time-domain waveform as input, simulations are conducted using frequency-domain electromagnetic scattering modeling algorithms, or simulation tests are conducted in a microwave anechoic chamber using a stepped-frequency electromagnetic scattering measurement system to obtain frequency sweep scattering field data of complex targets.

[0056] According to radar signal processing theory, the target echo, which varies with the step frequency, and the target's one-dimensional range profile form a Discrete Fourier Transform (DFT) relationship. Therefore, given the target's swept-frequency scattering field data, the target's one-dimensional range profile, i.e., the distribution of the target's scattering centers in each range cell, can be obtained through the one-dimensional inverse discrete Fourier transform (IDFT). Assuming that the complex extended target's one-dimensional range profile contains M sampling points radially, and the swept-frequency echo signal contains information from N frequency points, the target's one-dimensional range profile, i.e., the distribution characteristic A(r) of the target's scattering centers along the radial distance, is... k This can be represented as:

[0057]

[0058] In the formula, r kX is the distance at the radial position numbered k relative to the center of the reference distance; M (f vi f represents the target swept-frequency scattering field; vi is the sweep frequency sequence; j is the imaginary unit; c is the speed of light.

[0059] Step S2: Solve for the target time-domain impulse response;

[0060] The target's one-dimensional distance image horizontal axis is changed from radial distance to time to obtain the target's impact response, and interpolation processing is used to ensure that the target's impact response has a consistent time sampling interval with the incident narrow pulse.

[0061] In the one-dimensional range profile of the target, the horizontal axis represents distance. Based on the electromagnetic wave propagation relationship, the horizontal axis of the target's one-dimensional range profile is changed from distance to time; this is the target's impact response. To facilitate subsequent processing operations such as convolution of the incident signal and the target's impact response, it is necessary to ensure that the sampling interval of the target's impact response is consistent with the waveform of the incident time-domain signal. The time sampling step size of the incident time-domain waveform signal is:

[0062] t p =1 / f p (5)

[0063] In the formula, f p The sampling rate is the incident time-domain waveform signal.

[0064] Without zero-padding during the Fourier transform, the sampling interval of the radial distance coordinate axis in a one-dimensional image after conversion to time is:

[0065] t b =1 / (2B) (6)

[0066] In the formula, B is the sweep bandwidth.

[0067] Generally speaking, the sampling rate of the incident time-domain waveform is relatively high, i.e., t b It must be greater than t p Therefore, interpolation is required on the one-dimensional range image results. To prevent the expansion of the impact response peaks during the interpolation process, the peaks in the one-dimensional range image can be extracted and loaded into the corresponding positions in the new impact response array, thereby enabling the solution of the impact response of complex targets.

[0068] Step S3: Solve for the target response under time-domain waveform incidence;

[0069] The response characteristics of the target to the incident time-domain signal are obtained by convolving the incident time-domain waveform signal with the target impact response.

[0070] According to signal and system theory, a target's response to an incident signal is the convolution of the incident signal and the target's own impact response. Furthermore, there is a correspondence between the target's impact response and the distribution of scattering centers in its one-dimensional range profile. Therefore, the echo response of the transmitted signal can be obtained by convolving the transmitted time-domain waveform signal with the target's impact response.

[0071] The response of the transmitted time-domain waveform signal can be expressed as:

[0072] PRX(t)=PTX(t)*HRP(t) (7)

[0073] In the formula, PTX(t) is the transmitted time-domain waveform signal; HRP(t) is the target's impact response; PRX(t) is the response of the transmitted signal; and t is time.

[0074] Through the above processing, the response characteristics of complex targets under arbitrary incident time-domain waveform input can be obtained based on frequency sweep data. These response characteristics are a function of time; by performing a Fourier transform on them, their spectral features can be obtained, thereby enabling the analysis of the detection effect of the incident time-domain waveform.

[0075] In one embodiment of the present invention, taking the solution of the time-domain waveform response of a point target under Gaussian narrow pulse detection as an example, firstly, the incident time-domain waveform signal to be selected is analyzed, such as... Figure 2 As shown, the time-domain waveform and spectral form of a modulated Gaussian narrow pulse signal, used as a typical incident time-domain waveform signal example, are presented. This narrow pulse incident signal has a center frequency of 1 GHz, a pulse width of 1 ns, a corresponding bandwidth of 1 GHz, a signal sampling rate of 10 GHz, and a corresponding time sampling interval of 0.1 ns. It is assumed that there exists an ideal point target located at the origin, whose backscattering at all frequencies is 1. Based on its corresponding carrier frequency, bandwidth, and other information, corresponding sweep frequency parameters are designed. By performing a Fourier transform on the sweep frequency scattering field data of the point target, the one-dimensional range profile information of the target is obtained. The results are shown below. Figure 3 As shown, the scattering field data center frequency used in the one-dimensional range image imaging is 1 GHz, the bandwidth is 1 GHz, and the sweep step size is 0.02 GHz. Then, based on the electromagnetic wave propagation relationship, the horizontal axis of the one-dimensional range image of the point target is changed from distance to time to obtain the target's impact response. Interpolation is used to ensure that the sampling interval of the target's impact response is consistent with the incident narrow pulse signal. The obtained results are shown below. Figure 4 As shown. Finally, the time-domain response of the target is obtained by convolving the incident signal with the target's own impact response. The time-domain response waveform and spectral form of the point target to the Gaussian narrow pulse signal are shown in the figure. Figure 5 As shown.

[0076] This invention enables the rapid generation of target response characteristics under arbitrary time-domain waveform input. First, the invention analyzes the selected time-domain signal waveform, designs corresponding frequency sweep parameters based on bandwidth and target geometry, obtains broadband scattering characteristic data of the target through frequency-domain electromagnetic scattering modeling or testing, and converts the frequency-domain scattering field data into the target's time-domain impulse response using Fourier transform. The time-domain response of the target to arbitrary waveforms is obtained by convolving the incident time-domain waveform with the target's impulse response. This is an effective method for generating time-domain waveform responses for complex targets. By obtaining the time-domain waveform response through signal processing of the frequency sweep data, this invention avoids the limitations of time-domain electromagnetic scattering modeling algorithms and arbitrary time-domain waveform measurement systems. It can rapidly generate target responses under arbitrary incident waveforms based on traditional frequency-domain electromagnetic scattering modeling algorithms or stepped-frequency electromagnetic scattering measurement systems, greatly expanding its applicability.

[0077] It should be noted that, in the embodiments of the present invention, the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," "counterclockwise," "axial," "radial," and "circumferential," etc., indicating the orientation or positional relationship, are based on the orientation or positional relationship shown in the accompanying drawings and are only for the convenience of describing the embodiments. They do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the present invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0078] In this invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," "linking," and "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0079] Although the present invention has been described in detail through the preferred embodiments above, it should be understood that the above description should not be considered as a limitation of the present invention. Various modifications and substitutions to the present invention will be apparent to those skilled in the art after reading the above description. Therefore, the scope of protection of the present invention should be defined by the appended claims.

Claims

1. A time-domain waveform response conversion method based on swept-frequency data, characterized by, Includes the following steps: Step S1: Solve for the one-dimensional range profile of the target that matches the incident time-domain waveform parameters; Based on the sweep frequency parameters corresponding to the incident time-domain waveform signal, broadband scattering characteristic data of the target are obtained through frequency-domain electromagnetic scattering modeling or microwave anechoic chamber step-frequency electromagnetic scattering test, and then converted into one-dimensional range image information of the target through Fourier transform. The sweep parameters include the center frequency, sweep step size, and sweep bandwidth; The center frequency is equal to the center frequency of the time domain waveform ; The sweep bandwidth satisfies: （1） In the formula, is the time-domain waveform pulse width; The frequency sweep step size is determined by the Narquist sampling rate, and the radial width of the radar image window is: （2） wherein is the frequency sweep step size, is the speed of light; If the maximum dimension of the target is The sweep step must satisfy: （3） Using the frequency sweep parameters that match the incident time-domain waveform as input, simulations are carried out using frequency-domain electromagnetic scattering modeling algorithms, or simulation tests are carried out in a microwave anechoic chamber using a step-frequency electromagnetic scattering measurement system to obtain the frequency sweep scattering field data of complex targets. Suppose that the complex extended target one-dimensional range profile contains M sampling points in the radial direction, and the sweep echo signal contains N frequency point information, and the one-dimensional range profile of the target is the distribution characteristics of the scattering center of the target along the radial distance is represented as: （4） In the formula, For the number The distance at the radial position relative to the center of the reference distance; For the target frequency sweep scattering field; It is a swept frequency sequence; The imaginary unit; The speed of light; Step S2: Solve for the target time-domain impulse response; The one-dimensional distance image of the target is changed from radial distance to time on the horizontal axis to obtain the target's impact response. Interpolation is then used to ensure that the target's impact response has a consistent time sampling interval with the incident narrow pulse. Step S3: Solve for the target response under time-domain waveform incidence; The response characteristics of the target to the incident time-domain signal are obtained by convolving the incident time-domain waveform signal with the target impact response.

2. The method of converting a time domain waveform response based on swept frequency data as recited in claim 1, wherein, In step S2, the time sampling step size of the incident time-domain waveform signal is: （5） In the formula, The sampling rate of the incident time-domain waveform signal; Without zero-padding during the Fourier transform, the sampling interval of the radial distance coordinate axis in a one-dimensional image after conversion to time is: （6） In the formula, is the swept bandwidth; The peak values ​​in the one-dimensional range image are extracted and loaded into the corresponding positions in the new impact response array, thereby solving the impact response of complex targets.

3. The method of converting a time domain waveform response based on swept frequency data as recited in claim 2, wherein, In step S3, the response of the transmitted time-domain waveform signal is expressed as follows: （7） wherein is a transmitted time domain waveform signal; is a target impulse response; is a response to the transmitted signal; is time.

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