CN114545353A - Pulse Doppler signal undersampling and parameter estimation method based on FRI sampling and Chinese remainder theorem - Google Patents

Pulse Doppler signal undersampling and parameter estimation method based on FRI sampling and Chinese remainder theorem Download PDF

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CN114545353A
CN114545353A CN202210150859.5A CN202210150859A CN114545353A CN 114545353 A CN114545353 A CN 114545353A CN 202210150859 A CN202210150859 A CN 202210150859A CN 114545353 A CN114545353 A CN 114545353A
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付宁
尉志良
姜思仪
乔立岩
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Harbin Institute of Technology
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Abstract

The invention discloses a pulse Doppler signal undersampling and parameter estimation method based on FRI sampling and Chinese remainder theorem. Step 1: transmitting two sets of pulse sequences having the same baseband signal but mutually orthogonal frequency spectra and having a mutually prime PRI; step 2: respectively acquiring Fourier coefficients of the two groups of PRI pulse sequences in the step 1 by using a designed FRI sampling structure; and step 3: estimating a time delay parameter of a signal by combining the sampling data of a plurality of PRI pulse sequences by utilizing a subspace method; and 4, step 4: separating the Doppler parameters of each target by using the time delay parameters of the estimated signals in the step (3); and 5: and respectively estimating the separated aliasing-free Doppler parameters by utilizing a subspace method and the CRT. The method aims at the problem of delay Doppler parameter estimation under the undersampling condition of fast time and slow time of the pulse Doppler signal.

Description

Pulse Doppler signal undersampling and parameter estimation method based on FRI sampling and Chinese remainder theorem
Technical Field
The invention relates to the field of signal processing, in particular to a pulse Doppler signal undersampling and parameter estimation method based on FRI sampling and Chinese remainder theorem.
Background
The pulse Doppler signal is widely applied to detection systems such as radars, sonars and ultrasound, and the distance and the speed of a target can be detected by estimating the time delay and the Doppler parameter. To achieve higher range resolution, large bandwidth signals are typically sampled, requiring higher sampling rates according to the nyquist sampling theorem. Slow time undersampling refers to reducing the number of transmitted pulses by increasing the Pulse Repetition Interval (PRI), but this results in folding of the doppler parameters. Slow time undersampling has a number of advantages. For example, in ultrasound imaging, idle time may be used to make other modes of measurement; reducing the number of transmit pulses increases the power of the individual pulses, thereby increasing the detection range; in electronic intelligence reconnaissance, non-uniformity of the pulse emission provides some protection for PRI analysis.
In recent years, Finite new Rate of Innovation (FRI) sampling theory has been proposed. The theory states that for FRI signals determined by finite parameters, sampling and parameter estimation of the signal can be done at a rate equal to or greater than the signal's new information rate. A pulsed doppler signal is a signal that can be characterized by delay, doppler and amplitude parameters, and belongs to the FRI signal. Bajwa et al propose a delay-Doppler parameter joint estimation method based on FRI theory, however, the method has poor noise immunity. Bar-Ilan et al propose a Doppler focusing method with good noise immunity, however the algorithm requires the setting of a Doppler grid and the accuracy of parameter estimation for off-grid drops off rapidly.
The Chinese Remainder Theorem (CRT) is commonly used to solve the frequency folding problem, but these methods are all performed under the Nyquist sampling Theorem. Cohen proposes a non-uniform slow-time transmit doppler estimation scheme based on sparse arrays. This method does not make a distance estimate, however, and when using a relatively prime array, it requires that the pulse be transmitted at a time outside the observation window. Li proposes a sequential estimation method based on spatial and slow time domain co-prime sampling that can extend the freedom of parameter estimation but still requires Nyquist sampling.
A pulsed doppler signal consists of a series of pulses with doppler shift, whose mathematical expression is:
Figure BDA0003510445310000011
where P is the number of transmit pulses, L is the target number, T is the PRI of the signal, h (T) is the pulse basis function for which the waveform is known
Figure BDA0003510445310000012
An unknown amplitude parameter representing the ith target echo of the signal,
Figure BDA0003510445310000013
respectively, unknown time delay and Doppler parameters of the ith target echo of the signal. In this patent, it is assumed that the parameters of all targets are different from each other, i.e. that
Figure BDA0003510445310000014
When v islBelow 1/T, a Doppler parameter fold will occur. In this case, the Doppler parameter of the target echo can be expressed as
Figure BDA0003510445310000021
Wherein
Figure BDA0003510445310000022
And
Figure BDA0003510445310000023
are unknown.
Figure BDA0003510445310000024
Is the folded doppler shift of the signal. At this time, the received signal may be expressed as:
Figure BDA0003510445310000025
the invention aims to design a pulse transmitting mechanism and an FRI sampling structure, which realize the time delay of a pulse Doppler signal and the undersampling estimation of Doppler parameters by using fewer transmitting pulse numbers and fewer sampling points than the existing method.
Disclosure of Invention
The invention provides a pulse Doppler signal undersampling and parameter estimation method based on FRI sampling and Chinese remainder theorem, aiming at the problem of delay Doppler parameter estimation under the condition of pulse Doppler signal undersampling in fast time and slow time, the delay and Doppler parameter undersampling estimation of the pulse Doppler signal is realized by using fewer transmitting pulse numbers and fewer sampling points than the existing method.
The invention is realized by the following technical scheme:
a pulse Doppler signal undersampling and parameter estimation method based on FRI sampling and Chinese remainder theorem specifically comprises the following steps:
step 1: transmitting two sets of pulse sequences having the same baseband signal but mutually orthogonal frequency spectra and having a mutually prime PRI;
step 2: respectively acquiring Fourier coefficients of the two groups of PRI pulse sequences in the step 1 by using a designed FRI sampling structure;
and step 3: estimating a time delay parameter of a signal by combining the sampling data of a plurality of PRI pulse sequences by utilizing a subspace method;
and 4, step 4: separating the Doppler parameters of each target by using the time delay parameters of the estimated signals in the step (3);
and 5: and respectively estimating the separated aliasing-free Doppler parameters by utilizing a subspace method and the CRT.
Further, in step 1, specifically, it is assumed that the pulse doppler signal x (t) to be sampled is composed of 2 groups of pulse sequences with different PRIs, each PRI includes L target echoes, and may be represented as:
Figure BDA0003510445310000026
where i ═ 1,2 are the indices of the two groups of pulses, PiIs the number of transmitted pulses, h (t) is the pulse basis function with known waveform,
Figure BDA0003510445310000031
unknown amplitude parameter, t, representing the ith target echo of the signall＜T1＜T2Is an unknown time delay parameter of the ith target echo of the signal,
Figure BDA0003510445310000032
is the folded Doppler shift of the signal, fiIs the carrier frequency of the signal, TiIs the PRI of the ith set of pulse signals; the PRI of the two sets of signal pulses satisfy coprime, that is:
T1＝n1T',T2＝n2T' (5)
wherein
Figure BDA0003510445310000033
And n1,n2And } are relatively prime.
Further, the step 2 is specifically that the pulse doppler signal is sampled by a baseband signal Fourier coefficient FRI sampling scheme as shown in fig. 1, x (t) is divided, and then is respectively mixed with modulation signals of different frequencies, and then is subjected to low-pass filtering and low-speed sampling, and finally Fourier coefficients of two groups of pulse signals are obtained by Discrete Fourier Transform (DFT); limiting the effective processing time within the p-th PRI of a pulse-echo signal to T1Then the fourier coefficients of the p-th PRI inner sample of the ith group of pulses are expressed as:
Figure BDA0003510445310000034
wherein H (k) is the Fourier coefficients of the basis function h (t); because the basis functions are known, the fourier coefficients are simplified to:
Figure BDA0003510445310000035
wherein
Figure BDA0003510445310000036
And is
Figure BDA0003510445310000037
K-1 for Y, let K be 0,11 p[k]P is 0,11-1, for
Figure BDA00035104453100000311
P is 0,12-1。
Further, the step 3 is to construct a vector by using the sampling values
Figure BDA0003510445310000038
Constructing autocorrelation matrices
Figure BDA0003510445310000039
Where K' is the vector x that each of the samples in the PRI can make upp,k'The number of (2); when p is 0 or n1n2When there is
Figure BDA00035104453100000310
So that the total effective transmission pulse number P < P1+P2(ii) a Within each PRI if none of the parameters are the same
Figure BDA0003510445310000041
The Fourier coefficient can ensure that the rank of the autocorrelation matrix R is L, and the requirement of an ESPRIT algorithm on an input matrix is met; determining unknown delay parameters
Figure BDA0003510445310000042
Further, in step 4, a time delay parameter is obtained
Figure BDA0003510445310000043
Then, the complex amplitude shown in equation (8)
Figure BDA0003510445310000044
Solving by using the formula (7), and further obtaining the amplitude of the signal:
Figure BDA0003510445310000045
further, in step 5, for L targets with different parameters, P ≧ 3 valid transmission pulses and each PRI
Figure BDA0003510445310000046
The sampled fourier coefficients ensure accurate estimation of the time delay and aliasing free doppler parameters.
Further, the complex amplitude shown in formula (8) is used
Figure BDA0003510445310000047
Respectively finishing independent estimation of each folded Doppler parameter;
when P is1Not less than 2 and P2When the Doppler is more than or equal to 2, folding Doppler parameter
Figure BDA0003510445310000048
Solving by an ESPRIT method to obtain;
since when p is 0, there is
Figure BDA0003510445310000049
The minimum number of active transmit pulses required to estimate the folded Doppler parameter is P ≧ 3.
Further, using the estimated folded Doppler parameters
Figure BDA00035104453100000410
The following problem of the chinese remainder theorem is established,
Figure BDA00035104453100000411
when v isl≤1/T'，n1,n2Relatively prime, 1/T' is an integer, and folded Doppler shift
Figure BDA00035104453100000412
Is less than
Figure BDA00035104453100000413
Then, the parameters are solved by using the Chinese remainder theorem
Figure BDA00035104453100000414
And further obtaining aliasing-free Doppler parameters of the signal:
Figure BDA00035104453100000415
a pulse Doppler signal undersampling and parameter estimation device comprises a signal transmitting device, a sampling device, a processor, a communication interface, a memory and a communication bus, wherein the processor, the communication interface and the memory finish mutual communication through the communication bus;
the signal transmitting device is used for transmitting signals to the sampling device;
the sampling device is used for collecting the signals transmitted by the signal transmitting device;
a memory for storing a computer program;
and the processor is used for realizing the steps of the method when executing the program stored in the memory.
A computer-readable storage medium, in which a computer program is stored which, when being executed by a processor, carries out the above-mentioned method steps.
The invention has the beneficial effects that:
the pulse transmitting mode and the FRI sampling structure designed by the invention can realize the time delay of the pulse Doppler signal and the undersampling estimation of the Doppler parameter by using fewer transmitting pulse numbers and sampling points than the existing method, and can simultaneously realize the undersampling of two dimensions of fast time and slow time. The proposed sequential parameter estimation method can process each Doppler parameter respectively, and reduces the algorithm freedom requirement. Meanwhile, the Doppler parameter estimation problem is converted into a robust Chinese remainder theorem problem, and the robustness of parameter estimation is greatly improved.
Drawings
FIG. 1 is a schematic of the present invention.
FIG. 2 is a diagram illustrating the result of parameter estimation in the case of no noise according to the present invention.
Fig. 3 is a graph of parameter estimation NMSE in the noisy case of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
A pulse Doppler signal undersampling and parameter estimation method based on FRI sampling and Chinese remainder theorem specifically comprises the following steps:
step 1: transmitting two sets of pulse sequences having the same baseband signal but mutually orthogonal frequency spectra and having a mutually prime PRI;
step 2: respectively acquiring Fourier coefficients of the two groups of PRI pulse sequences in the step 1 by utilizing a designed FRI sampling structure shown in the figure 1;
and step 3: estimating a time delay parameter of a signal by combining the sampling data of a plurality of PRI pulse sequences by utilizing a subspace method;
and 4, step 4: separating the Doppler parameters of each target by using the time delay parameters of the estimated signals in the step (3);
and 5: and respectively estimating the separated aliasing-free Doppler parameters by utilizing a subspace method and a CRT.
Further, in step 1, specifically, it is assumed that the pulse doppler signal x (t) to be sampled is composed of 2 groups of pulse sequences with different PRIs, each PRI includes L target echoes, and may be represented as:
Figure BDA0003510445310000061
where i ═ 1,2 are the indices of the two groups of pulses, PiIs the number of transmitted pulses, h (t) is the pulse basis function with known waveform,
Figure BDA0003510445310000062
unknown amplitude parameter, t, representing the ith target echo of the signall＜T1＜T2Is an unknown time delay parameter of the ith target echo of the signal,
Figure BDA0003510445310000063
is the folded Doppler shift of the signal, fiIs the carrier frequency of the signal, TiIs the PRI of the ith set of pulse signals; the PRI of the two sets of signal pulses satisfy coprime, that is:
T1＝n1T',T2＝n2T' (5)
wherein
Figure BDA0003510445310000064
And n1,n2And } are relatively prime.
Further, the step 2 specifically includes sampling the pulse doppler signal by a baseband signal fourier coefficient FRI sampling scheme as shown in fig. 1, splitting x (t), mixing the split pulse doppler signal with modulation signals of different frequencies, low-pass filtering, low-speed sampling, and finally using Discrete fourier transform (Discrete)Fourier Transform, DFT) to obtain Fourier coefficients of two groups of pulse signals; limiting the effective processing time within the p-th PRI of a pulse-echo signal to T1Then the fourier coefficients of the p-th PRI inner sample of the ith group of pulses are expressed as:
Figure BDA0003510445310000065
wherein H (k) is the Fourier coefficients of the basis function h (t); because the basis functions are known, the fourier coefficients are simplified to:
Figure BDA0003510445310000066
wherein
Figure BDA0003510445310000067
And is
Figure BDA0003510445310000071
K-1 for Y, let K be 0,11 p[k]P is 0,11-1, for
Figure BDA0003510445310000072
P is 0,12-1。
Further, the step 3 is to construct a vector by using the sampling values
Figure BDA0003510445310000073
Constructing autocorrelation matrices
Figure BDA0003510445310000074
Where K' is the vector x that each of the samples in the PRI can make upp,k'Number of (2)(ii) a When p is 0 or n1n2When it comes to
Figure BDA0003510445310000075
So that the total effective transmission pulse number P < P1+P2(ii) a Within each PRI if none of the parameters are the same
Figure BDA0003510445310000076
The Fourier coefficient can ensure that the rank of the autocorrelation matrix R is L, and the requirement of an ESPRIT algorithm on an input matrix is met; determining unknown delay parameters
Figure BDA0003510445310000077
Further, in step 4, a time delay parameter is obtained
Figure BDA0003510445310000078
Then, the complex amplitude shown in equation (8)
Figure BDA0003510445310000079
Solving by using the formula (7), and further obtaining the amplitude of the signal:
Figure BDA00035104453100000710
further, in step 5, for L targets with different parameters, P ≧ 3 valid transmission pulses and each PRI
Figure BDA00035104453100000711
The sampled fourier coefficients ensure accurate estimation of the time delay and aliasing free doppler parameters.
Further, the complex amplitude shown in formula (8) is used
Figure BDA00035104453100000712
Respectively finishing independent estimation of each folded Doppler parameter;
when P is present1Not less than 2 and P2When the pressure is more than or equal to 2, the pressure is reducedFolded Doppler parameter
Figure BDA00035104453100000713
Solving by using an ESPRIT method to obtain;
since when p is 0, there is
Figure BDA00035104453100000714
The minimum number of active transmit pulses required to estimate the folded Doppler parameter is P ≧ 3.
Further, using the estimated folded Doppler parameters
Figure BDA00035104453100000715
The following problem of the chinese remainder theorem is established,
Figure BDA0003510445310000081
when v isl≤1/T'，n1,n2Relatively prime, 1/T' is an integer, and folded Doppler shift
Figure BDA0003510445310000082
Is less than
Figure BDA0003510445310000083
Then, the parameters are solved by using the Chinese remainder theorem
Figure BDA0003510445310000084
And further obtaining aliasing-free Doppler parameters of the signal:
Figure BDA0003510445310000085
first two sets of pulse sequences with co-prime PRI are transmitted, the two sets of pulse signals having the same baseband signal but mutually orthogonal spectra.
And respectively acquiring Fourier coefficients of the two groups of pulses by using a designed FRI sampling structure.
And estimating the time delay parameter of the signal by combining the sampling data of a plurality of PRIs by utilizing a subspace method.
The Doppler parameters of each target can be separated by using the estimated time delay parameters, and then each aliasing-free Doppler parameter is respectively estimated by using a subspace method and a CRT.
For L targets with different parameters, P ≧ 3 valid transmit pulses and within each PRI
Figure BDA0003510445310000086
The sampling Fourier coefficients can ensure accurate estimation of time delay and aliasing-free Doppler parameters.
Noiseless experiment
Setting the number L of each PRI echo of a signal to be detected to be 4, setting the pulse basis function to be a sinc function with the bandwidth of 100MHz, and setting the PRI of two groups of pulse sequences to be T respectively130 μ s and T 240 mus. The number of effective transmission pulses is set to P-3, and the number of fourier coefficients per PRI sample is set to K-6. Fig. 3 shows the signal delay parameter tlAnd Doppler parameter vlThe reconstruction effect of (1). It can be seen that, in the absence of noise, the sampling structure and method reconstruct the delay parameter and the doppler parameter of the signal without error under the condition of the minimum number of pulses and the minimum number of sampling points.
Noise experiment
Setting the number L of each PRI echo of a signal to be detected as 4, setting the pulse basis function as a sinc function with the bandwidth of 100MHz, and setting the PRI of two groups of pulse sequences as T 130 μ s and T 240 mus. The signal-to-noise ratio of the received signal is set to be-28 dB-0dB, the number of the transmitted pulses is set to be P-20, and the number of Fourier coefficients of each PRI sample is K-20. Fig. 3 shows the signal delay parameter tlAnd Doppler parameter vlAnd (3) reconstructing a normalized mean-squared error (NMSE) curve. The experimental result shows that the effect of estimating the signal parameter by the sampling structure and the method is better and better along with the improvement of the signal-to-noise ratio.
A pulse Doppler signal undersampling and parameter estimation device comprises a signal transmitting device, a sampling device, a processor, a communication interface, a memory and a communication bus, wherein the processor, the communication interface and the memory finish mutual communication through the communication bus;
the signal transmitting device is used for transmitting signals to the sampling device;
the sampling device is used for collecting the signals transmitted by the signal transmitting device;
a memory for storing a computer program;
and the processor is used for realizing the steps of the method when executing the program stored in the memory.
A computer-readable storage medium, in which a computer program is stored which, when being executed by a processor, carries out the above-mentioned method steps.

Claims (10)

1. A pulse Doppler signal undersampling and parameter estimation method based on FRI sampling and Chinese remainder theorem is characterized by comprising the following steps:
step 1: transmitting two sets of pulse sequences having the same baseband signal but mutually orthogonal frequency spectra and having a mutually prime PRI;
step 2: respectively acquiring Fourier coefficients of the two groups of PRI pulse sequences in the step 1 by using a designed FRI sampling structure;
and step 3: estimating a time delay parameter of a signal by combining the sampling data of a plurality of PRI pulse sequences by utilizing a subspace method;
and 4, step 4: separating the Doppler parameters of each target by using the time delay parameters of the estimated signals in the step (3);
and 5: and respectively estimating the separated aliasing-free Doppler parameters by utilizing a subspace method and the CRT.
2. The pulse doppler signal undersampling and parameter estimation method based on FRI sampling and chinese remainder theorem according to claim 1, wherein the step 1 is specifically to assume that the pulse doppler signal x (t) to be sampled is composed of 2 groups of pulse sequences of different PRIs, each PRI includes L target echoes, which can be expressed as:
Figure FDA0003510445300000011
where i ═ 1,2 are the indices of the two groups of pulses, PiIs the number of transmitted pulses, h (t) is the pulse basis function with known waveform,
Figure FDA0003510445300000012
unknown amplitude parameter, t, representing the ith target echo of the signall＜T1＜T2Is an unknown time delay parameter of the ith target echo of the signal,
Figure FDA0003510445300000013
is the folded Doppler shift of the signal, fiIs the carrier frequency of the signal, TiIs the PRI of the ith set of pulse signals; the PRI of the two sets of signal pulses satisfy coprime, that is:
T1＝n1T',T2＝n2T' (5)
wherein
Figure FDA0003510445300000014
And n1,n2And } are relatively prime.
3. The method according to claim 1, wherein the step 2 is specifically that the pulse doppler signal is sampled by a baseband signal Fourier coefficient FRI sampling scheme as shown in fig. 1, x (t) is divided and then respectively mixed with modulation signals of different frequencies, and then low-pass filtered and low-speed sampled, and finally Fourier coefficients of two groups of pulse signals are obtained by Discrete Fourier Transform (DFT); limiting the effective processing time in the p-th PRI of the pulse echo signal to T1Then, the i-th group of pulsesThe fourier coefficients of the p-th PRI inner sample of the burst are expressed as:
Figure FDA0003510445300000021
wherein H (k) is the Fourier coefficients of the basis function h (t); because the basis functions are known, the fourier coefficients are simplified to:
Figure FDA0003510445300000022
wherein
Figure FDA0003510445300000023
And is
Figure FDA0003510445300000024
K-1 for Y, let K be 0,11 p[k]P is 0,11-1, for
Figure FDA0003510445300000025
P is 0,12-1。
4. The method of claim 1, wherein the step 3 is to construct a vector by using the sampled values
Figure FDA0003510445300000026
Constructing autocorrelation matrices
Figure FDA0003510445300000027
Where K' ═ K-L can be made up of the values sampled in each PRIVector xp,k'The number of (2); when p is 0 or n1n2When there is
Figure FDA0003510445300000028
So that the total effective transmission pulse number P < P1+P2(ii) a Within each PRI if none of the parameters are the same
Figure FDA0003510445300000029
The Fourier coefficient can ensure that the rank of the autocorrelation matrix R is L, and the requirement of an ESPRIT algorithm on an input matrix is met; determining unknown delay parameters
Figure FDA00035104453000000210
5. The method of claim 1, wherein the step 4 is to find the delay parameter in the step of calculating the pulse doppler signal undersampling and parameter estimation based on FRI sampling and the chinese remainder theorem
Figure FDA00035104453000000211
Then, the complex amplitude shown in equation (8)
Figure FDA00035104453000000212
Solving by using the formula (7), and further obtaining the amplitude of the signal:
Figure FDA00035104453000000213
6. the pulse Doppler signal undersampling and parameter estimation method based on FRI sampling and Chinese remainder theorem according to claim 1, wherein in step 5, for L targets with different parameters, P ≧ 3 valid transmission pulses and each PRI
Figure FDA0003510445300000031
The sampled fourier coefficients ensure accurate estimation of the time delay and aliasing free doppler parameters.
7. The method of claim 3, wherein the complex magnitude shown in formula (8) is used for undersampling and parameter estimation of pulse Doppler signal based on FRI sampling and the Chinese remainder theorem
Figure FDA0003510445300000032
Respectively finishing independent estimation of each folded Doppler parameter;
when P is present1Not less than 2 and P2When the Doppler is more than or equal to 2, folding Doppler parameter
Figure FDA0003510445300000033
Solving by an ESPRIT method to obtain;
since when p is 0, there is
Figure FDA0003510445300000034
The minimum number of active transmit pulses required to estimate the folded Doppler parameter is P ≧ 3.
8. The method of claim 7 wherein the method of undersampling and parameter estimation of pulsed Doppler signals based on FRI sampling and the Chinese remainder theorem utilizes estimated folded Doppler parameters
Figure FDA0003510445300000035
The following problem of the chinese remainder theorem is established,
Figure FDA0003510445300000036
when v isl≤1/T'，n1,n2Relatively prime, 1/T' is an integer, and folded Doppler shift
Figure FDA0003510445300000037
Is less than
Figure FDA0003510445300000038
Then, the parameters are solved by using the Chinese remainder theorem
Figure FDA0003510445300000039
And further obtaining aliasing-free Doppler parameters of the signal:
Figure FDA00035104453000000310
9. a pulse Doppler signal undersampling and parameter estimation device comprises a signal transmitting device, a sampling device, a processor, a communication interface, a memory and a communication bus, wherein the processor, the communication interface and the memory finish mutual communication through the communication bus;
the signal transmitting device is used for transmitting signals to the sampling device;
the sampling device is used for collecting the signals transmitted by the signal transmitting device;
a memory for storing a computer program;
and the processor is used for realizing the steps of the method when executing the program stored in the memory.
10. A computer-readable storage medium, characterized in that a computer program is stored in the computer-readable storage medium, which computer program, when being executed by a processor, carries out the method steps of any one of the claims 1-8.
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CN115201776A (en) * 2022-07-04 2022-10-18 哈尔滨工业大学 Multichannel random modulation undersampling structure for frequency agile radar and parameter estimation method thereof

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115201776A (en) * 2022-07-04 2022-10-18 哈尔滨工业大学 Multichannel random modulation undersampling structure for frequency agile radar and parameter estimation method thereof

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