CN112731306A - UWB-LFM signal parameter estimation method based on CS and simplified FrFT - Google Patents

UWB-LFM signal parameter estimation method based on CS and simplified FrFT Download PDF

Info

Publication number
CN112731306A
CN112731306A CN202011509981.4A CN202011509981A CN112731306A CN 112731306 A CN112731306 A CN 112731306A CN 202011509981 A CN202011509981 A CN 202011509981A CN 112731306 A CN112731306 A CN 112731306A
Authority
CN
China
Prior art keywords
signal
simplified
ultra
fourier transform
sampling
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN202011509981.4A
Other languages
Chinese (zh)
Other versions
CN112731306B (en
Inventor
李如玮
孙兴武
杨登才
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Beijing University of Technology
Original Assignee
Beijing University of Technology
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Beijing University of Technology filed Critical Beijing University of Technology
Priority to CN202011509981.4A priority Critical patent/CN112731306B/en
Publication of CN112731306A publication Critical patent/CN112731306A/en
Application granted granted Critical
Publication of CN112731306B publication Critical patent/CN112731306B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/36—Means for anti-jamming, e.g. ECCM, i.e. electronic counter-counter measures
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/14—Fourier, Walsh or analogous domain transformations, e.g. Laplace, Hilbert, Karhunen-Loeve, transforms
    • G06F17/141—Discrete Fourier transforms
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

Landscapes

  • Physics & Mathematics (AREA)
  • Engineering & Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Mathematical Physics (AREA)
  • Mathematical Optimization (AREA)
  • Theoretical Computer Science (AREA)
  • Data Mining & Analysis (AREA)
  • Pure & Applied Mathematics (AREA)
  • Computational Mathematics (AREA)
  • Mathematical Analysis (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Discrete Mathematics (AREA)
  • Algebra (AREA)
  • Remote Sensing (AREA)
  • Databases & Information Systems (AREA)
  • Software Systems (AREA)
  • General Engineering & Computer Science (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Radar Systems Or Details Thereof (AREA)

Abstract

The invention discloses a UWB-LFM signal parameter estimation method based on CS and simplified FrFT, which introduces a compressive sensing method, and firstly carries out sparse representation and AIC sampling on an ultra wide band linear frequency modulation signal; secondly, a discrete simplified fractional Fourier transform dictionary is established to be used as a base dictionary matrix for observation, and the algorithm complexity is reduced; and finally, an improved CoSaMP reconstruction algorithm is used for reconstructing the observation vector, regularization in the traditional ROMP reconstruction algorithm is combined with a self-adaptive idea in an SAMP reconstruction algorithm, the defects of lack of prior signal information and huge calculation amount in practical application are overcome, the reconstruction precision and the anti-interference capability of the signal are improved, and the method has good precision and real-time performance.

Description

UWB-LFM signal parameter estimation method based on CS and simplified FrFT
Technical Field
The invention relates to the fields of ultra wide band linear frequency modulation signal technology, microwave photon technology and signal processing, in particular to a parameter estimation method of an ultra wide band linear frequency modulation signal based on compressed sensing and simplified fractional Fourier transform.
Background
For the ultra-wideband chirp signal, in view of the detection characteristics of ultra-high bandwidth and low signal-to-noise ratio, the traditional nyquist sampling law is used for sampling, the sampling rate needs to be two times or more than the maximum bandwidth to realize accurate reconstruction of the signal, but huge sampling data brings great pressure to a signal acquisition and processing mechanism. The development of Compressed Sensing (CS) theory has effectively alleviated the problem, and has become the subject of research in recent years.
The compressed sensing theory utilizes the sparse characteristic of the signal, projects the signal to a given domain to obtain a group of compressed sampling data, processes the compressed sampling data by utilizing an optimization algorithm, estimates important information of the original signal and removes the limitation of the Nyquist sampling theorem. And the Ultra Wide Band Linear Frequency Modulation (UWB-LFM) just meets the characteristics of the impulse signal in the Transform domain of the simplified Fractional Fourier Transform (CFrFT), so that the realization of parameter estimation for the UWB-LFM signal under the compressed sensing framework becomes possible.
The existing research based on ultra-wideband chirp signal parameter estimation has the following two defects: firstly, the calculation amount of the algorithm is huge under the condition of lacking prior LFM information, in the scene of unknown actual signal environment, the sparsity of the signal to be estimated in the CFrFT transform domain is unknown, and blind optimization and peak value search bring considerable calculation complexity; secondly, the method has the defects of no excellent detection efficiency and estimation accuracy under the condition of low signal to noise ratio, and aims at how to avoid the influence of noise interference under the condition of low signal to noise ratio in the actual environment of microwave photon broadband radar electronic warfare, so that the important problem to be solved urgently is solved.
Disclosure of Invention
In view of the above, the present invention provides a method for estimating parameters of an ultra-wideband chirp signal based on compressed sensing and simplified fractional fourier transform.
In order to achieve the purpose, the invention provides the following technical scheme:
the invention provides a parameter estimation method of an ultra wide band linear frequency modulation signal based on compressed sensing and simplified fractional order Fourier transform, which comprises the following steps:
acquiring an ultra-wideband linear frequency modulation signal containing Gaussian white noise;
constructing a discrete simplified fractional Fourier transform dictionary matrix to carry out sparse representation on the ultra-wideband linear frequency modulation signal;
carrying out compression sampling on the ultra-wideband linear frequency modulation signal;
reconstructing the coefficient vector by using an improved compression sampling matching tracking algorithm;
and estimating the starting frequency and the frequency modulation slope of the ultra-wideband chirp signal according to the distribution characteristics of the signal in the discrete fractional Fourier transform domain.
Further, acquiring an ultra-wideband chirp signal containing white gaussian noise, wherein a model x expression of the signal is as follows:
x＝s+n；
wherein s is an ultra-wideband chirp signal and n is additive white gaussian noise.
Further, constructing a discrete CFrFT dictionary matrix ultra-wideband chirp signal for sparse representation to perform compression sampling, selecting an optimal transformation order and subsequent signal detection and parameter estimation, and constructing a discrete CFrFT matrix expression as follows:
Figure BDA0002846108070000021
wherein Ψ represents a discrete simplified fractional Fourier transform dictionary matrix, j is an imaginary part of an exponential function, n is the number of sampling points of a discretized continuous signal x, m is the number of discrete points of the discretized continuous signal x after CFrFT, α represents a coordinate axis rotation angle of the simplified fractional Fourier transform,
Figure BDA0002846108070000022
ΔT＝N/fsn is the number of sampling points, fsIs the sampling frequency;
taking the dictionary matrix as an observation matrix, and performing sparse representation according to the following formula:
Figure BDA0002846108070000023
wherein x isInput signal, thetaiIs a coefficient vector of psi ═ psi1，ψ2，...，ψiIs a sparse base.
Further, the ultra-wideband chirp signal is compressed and sampled, and the method is realized according to the following steps:
by using an observation matrix phi e R that is not related to the sparse basis psiM×NTo observe an input signal x to obtain M observations y, where M < N. For wideband signals, the specific compressive sampling is typically accomplished by an Analog-to-Information Converter (AIC).
Further, reconstructing the coefficient vector after compression sampling by using an improved compression sampling matching tracking algorithm according to the following steps:
firstly, calculating a fuzzy threshold value of a selected index in the operation process of a reconstruction algorithm according to the following formula:
Figure BDA0002846108070000024
wherein, aprAnd bprAs fuzzy threshold parameter, thrFor selecting condition parameters of indexes, rand (1) is a random number within 0-1, F is a support set, r is a residual error, k is an iteration number, A is a sensing matrix, and A isTThe method comprises the following steps that (1) for transposition of a sensing matrix, i is an index stored in a supporting set and selected, and j is a maximum index meeting a selection condition;
forming a measurement matrix by using atoms corresponding to the support set indexes;
calculating a correlation coefficient, and extracting indexes corresponding to the size maximum values for secondary screening;
selecting a group of indexes corresponding to the largest energy value to be merged into a support set by utilizing a regularization thought;
reconstructing the signal by using a least square method, and solving a new residual error;
and determining a signal reconstruction mode according to the relation between the energy of the residual norm and the clipping threshold.
Further, the starting frequency and the chirp rate of the ultra-wideband chirp signal are estimated according to the distribution characteristics of the signal in the discrete fractional Fourier transform domain, and the method is realized according to the following steps:
firstly, calculating the simplified fractional Fourier transform distribution of the ultra-wideband chirp signal according to the following formula:
Figure BDA0002846108070000031
CFp(u) represents the frequency domain distribution after CFrFT transformation, t is time, j is an exponential function imaginary part, u is frequency, and alpha is the coordinate axis rotation angle of CFrFT;
secondly, performing peak value search on the simplified fractional Fourier transform distribution, and estimating the initial frequency and the frequency modulation slope of the signal according to the following formula:
Figure BDA0002846108070000032
Figure BDA0002846108070000033
wherein,
Figure BDA0002846108070000034
is an estimate of the chirp rate and is,
Figure BDA0002846108070000035
is an estimate of the starting frequency of the frequency,
Figure BDA0002846108070000036
in order to optimize the rotation angle of the rotary shaft,
Figure BDA0002846108070000037
is the peak frequency location, S is the normalization factor, calculated according to the following equation:
Figure BDA0002846108070000038
wherein, Δ T is N/fsN is the number of sampling points, fsIs the sampling frequency.
The invention has the beneficial effects that:
the UWB-LFM parameter estimation method based on CS and CFrFT provided by the invention comprises the steps of firstly carrying out sparse representation and AIC compression sampling on UWB-LFM signals in Gaussian white noise to obtain coefficient vectors after compression sampling of the signals; constructing a discrete CFrFT dictionary matrix in the range of the order [0, 2) with the precision of 0.01 to perform rough search; solving coefficient vectors of UWB-LFM signals in each-order discrete CFrFT matrix in rough estimation by using an improved CoSaMP algorithm to obtain a primary peak position; carrying out fine search by using an energy gravity center principle to obtain the position of the maximum peak value; and finishing the final frequency modulation slope and the initial frequency according to the position of the maximum value and the relation between the rotation angle and the order.
The invention relieves the pressure of Nyquist sampling theorem through a compressed sensing framework, uses discrete simplified fractional Fourier transform to establish a dictionary matrix, reduces the complexity of algorithm calculation, improves the traditional CoSaMP signal reconstruction algorithm, introduces the regularization thought of the traditional ROMP algorithm and the self-adaption thought of the SAMP algorithm, improves the defects of large data redundancy and large calculation amount caused by the lack of prior UWB-LFM signal information in practical application, and finally improves the reconstruction precision and the anti-interference capability of the signal.
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention. The objectives and other advantages of the invention may be realized and attained by the means of the instrumentalities and combinations particularly pointed out hereinafter.
Drawings
In order to make the object, technical scheme and beneficial effect of the invention more clear, the invention provides the following drawings for explanation:
FIG. 1 is a flow chart of UWB-LFM signal parameter estimation based on CS and CFrFT.
FIG. 2 is a diagram of a UWB-LFM time domain signal.
FIG. 3 is a schematic diagram of the distribution of UWB-LFM signals in the discrete CFrFT domain.
Fig. 4 is a schematic diagram of the structure of AIC compressed sampling.
Fig. 5 is a diagram showing comparison of UWB-LFM signals before and after reconstruction.
FIG. 6 is a diagram illustrating the optimal transform order distribution of the UWB-LFM signal in the discrete CFrFT domain.
Detailed Description
The present invention is further described with reference to the accompanying drawings and detailed description so that one skilled in the art can better understand the present invention and can implement it, but the present invention is not limited by the examples.
As shown in fig. 1, the present embodiment provides a UWB-LFM parameter estimation method based on CS, CFrFT and improved CoSaMP reconstruction algorithm, first acquiring an ultra wide band chirp signal including white gaussian noise; constructing a discrete simplified fractional Fourier transform dictionary matrix ultra-wideband linear frequency modulation signal for sparse representation; carrying out compression sampling on the ultra-wideband linear frequency modulation signal; reconstructing the coefficient vector by using an improved compression sampling matching tracking algorithm; and estimating the starting frequency and the frequency modulation slope of the ultra-wideband chirp signal according to the distribution characteristics of the signal in the discrete fractional Fourier transform domain.
As shown in fig. 1, the method specifically comprises the following steps:
the mathematical representation of a single component LFM signal is:
Figure BDA0002846108070000041
Figure BDA0002846108070000042
if the signal contains white gaussian noise, the signal model can be expressed as: x is s + n (2)
Where t is time, A is amplitude, f0Is the starting frequency，k0Is the chirp rate, Δ T is the duration of the signal, and j is the imaginary part of the exponential function.
The study of ultra-wideband signals commonly uses the definition rules specified by the Federal Communications Commission (FCC) in the united states: signals with the working frequency band of 3.1-10.6GHz and the bandwidth of more than 500MHz are called UWB signals, and the time domain diagram thereof is shown in FIG. 2.
The goal of the technique is to estimate the starting frequency f of the UWB-LFM signal0And chirp slope k0。
CS is introduced to process the single-component UWB-LFM signals, a CS framework can be divided into three parts of sparse representation, compression sampling and reconstruction algorithm, and the specific steps are as follows:
suppose for a discrete signal x ∈ RN×1In other words, l satisfying that the number of non-zero elements is at most K (K < N)0-norm condition: | x | non-conducting phosphor0K is ≦ K, i.e., K-sparse signal, set expressed as: sigmaK＝{x：||x||0≤K} (3)
Assuming the presence of sparse groups Ψ ∈ RN×NThe sparsity that makes the K-sparse signal available under the sparse basis is represented as:
Figure BDA0002846108070000051
Figure BDA0002846108070000052
where x is the input signal, θiIs a coefficient vector of psi ═ psi1，ψ2，...，ψiIs a sparse base.
Since the chirp signal exhibits the characteristics of an impulse signal in the fractional Fourier transform domain, as shown in FIG. 3, the UWB-LFM signal satisfies the above-mentioned l of the K-sparse signal in this domain0-norm condition, thus constructing a discrete simplified fractional fourier transform dictionary matrix ultra wide band chirp signal for the UWB-LFM signal for sparse representation, the specific steps are as follows:
1. the discrete sampling is carried out on the input continuous signal (2), and dimension normalization is carried out to obtain a resampling sequence expression of the signal, wherein the resampling sequence expression is as follows:
Figure BDA0002846108070000053
wherein f issFor the sampling frequency, Δ T is the duration of the signal, Δ x is the sampling interval, and n is the number of x (T) samples of the discretized continuous signal.
2. Performing discrete Chirp multiplication on the resampled sequence x (n/delta x) to obtain a new sequence expression as follows:
Figure BDA0002846108070000054
wherein n is the number of sampling points, j is an imaginary part of an exponential function, and alpha is a coordinate axis rotation angle of CFrFT;
3. and (3) performing fast Fourier transform on the sequence s (n) to obtain a discrete CFrFT expression:
Figure BDA0002846108070000055
wherein m is the discrete point number after the fast Fourier transform,
Figure BDA0002846108070000056
as a dispersion
Kernel function of CFrFT transform, Xα(m) can be regarded as
Figure BDA0002846108070000057
At KαProjection on the (m, n) set of bases, the kernel function
Can be used as a base dictionary of the discrete CFrFT, and the expression is as follows:
Figure BDA0002846108070000061
at this stage, make provision for performing a coarse search stepConstructing a DCFrFT matrix in the range of order p ∈ [0, 2) with an accuracy of 0.01
Figure BDA0002846108070000062
Compressive sampling is performed by using an observation matrix phi epsilon R that is not related to the sparse basis psiM×NObserving an input signal x to obtain M observation data y, wherein M < N, and the expression of the matrix is as follows: y phi x phi psi theta (9)
Where y is an M × 1-dimensional column vector, x is an N × 1-dimensional column vector, and θ is an observation vector.
For wideband signals, the compressive sampling process is performed by an analog-to-digital converter, and a typical AIC structure is shown in fig. 4, in which a continuous signal x (t) passes through a perceptual function ΘiM is modulated to provide the necessary randomness to the signal, which is then passed through a window function to TWThe Analog low-pass filter performs filtering processing to ensure that the signal is not distorted, and finally, the signal is sampled by an Analog-to-Digital Converter (ADC) to obtain compressed and sampled data
Figure BDA0002846108070000063
Reconstructing the UWB-LFM signal after coefficient representation and compression sampling through an improved CoSaMP algorithm, wherein the specific flow steps of the reconstruction algorithm are as follows:
1. inputting a sensing matrix A, an observation vector y and a fuzzy threshold parameter aptAnd bprLarge step size clipping threshold and stop threshold epsilon1
And ε2；
2. Initializing the sparsity K equal to 1, estimating the step size of the sparsity, supporting the set F, residual t equal to y, observing the vector y, initial stage equal to 1, iteration number K equal to 1, supporting the set length size equal to K, and indexing the set
Figure BDA0002846108070000065
Candidate set
Figure BDA0002846108070000066
An empty set C;
3. atom pre-selection operation: selecting an index by using a fuzzy threshold value, and storing the index into a support set F, wherein the expression of the fuzzy threshold value is as follows:
Figure BDA0002846108070000064
wherein the fuzzy threshold parameter aprAnd bprSelecting too small reduces reconstruction accuracy and increases computation time, but large step clipping thresholds and stopping thresholds ε1And ε2The selection principle of (A) is just the opposite, it must obey ∈1＞＞ε2The actual parameter selection depends on the situation-specific deviations.
4. Forming a measurement matrix meeting constraint Isometry Property (RIP) by using atoms corresponding to the support set index, if the measurement matrix does not meet the RIP, making K equal to K +1, and returning to the step 3;
5. calculating the atomic correlation coefficient | ATrk-1Extracting the indexes corresponding to the size maximum values and storing the indexes into a set C for secondary screening;
6. dividing the size correlation coefficients into a plurality of groups by taking half of the maximum sparse value as a threshold value by utilizing a regularization thought in ROMP, and selecting a group of indexes corresponding to the group with the maximum energy value to be combined into a support set F;
7. and (3) reconstructing the signal by using a least square method, and solving a new residual error, wherein the expression is as follows:
Figure BDA0002846108070000071
wherein,
Figure BDA0002846108070000072
to reconstruct the signal, rnewFor new residual errors, AFFor supporting the combined sensor matrix, AF +Is the inverse of the sensing matrix, and y is the observation vector;
8. when norm of residual errorWhen the energy is less than the clipping threshold, i.e.
Figure BDA0002846108070000073
Then, proceed to step 9, when
Figure BDA0002846108070000074
Figure BDA0002846108070000075
If yes, executing step 10;
9. step 5 is executed until reconstruction is completed, wherein the stage is required to be stage +1, the step size step is unchanged, the size of the support set is size + step, and the iteration number k is k + 1;
10. and (3) requiring stage +1, step + 2, support set size + step, and iteration number k +1 until the reconstruction is completed.
The steps (1) to (2) complete the estimation of the initial value of the sparsity, the steps (3) to (4) introduce the idea of regularization to select matching atoms, the steps (6) to (8) control the sizes of a support set and an iteration step by introducing two thresholds to improve the recovery accuracy, and a comparison graph of the UWB-LFM signals before and after reconstruction is shown in FIG. 5.
Solving each-order DCFrFT matrix psi in rough estimation of UWB-LFM signal by utilizing improved CoSaMP reconstruction algorithmDCFrFT-pCoefficient vector of (1)
Figure BDA0002846108070000076
Obtaining the preliminary peak position
Figure BDA0002846108070000077
Performing fine search according to the energy center of gravity principle: constructing an order p ∈ [ p ] with an accuracy of 0.001coarse-0.015，pcoarse+0.015) DCFrFT matrix
Figure BDA0002846108070000078
Solving UWB-LFM signals in fine search by utilizing improved CoSaMP reconstruction algorithmRespective order DCFrFT matrix ΨDCFrFT-pCoefficient vector of (1)
Figure BDA0002846108070000079
The position of the maximum peak is obtained
Figure BDA00028461080700000710
At the position, the frequency modulation slope and the initial frequency are carried out through a formula after dimension normalization and the relation between the rotation angle and the order
Figure BDA00028461080700000711
The expression is as follows:
Figure BDA00028461080700000712
α＝pπ/2 (14)
wherein,
Figure BDA00028461080700000713
the method is characterized in that the optimal rotation angle is p, the order corresponding to the optimal rotation angle is p, S is a dimensional normalization factor and is used for reducing the frequency modulation slope of a signal and reducing the angle search range of CFrFT during signal detection so as to improve the efficiency and reduce the complexity in the CFrFT calculation process, and the expression is as follows:
Figure BDA0002846108070000081
where Δ T is the duration of the signal, fsIs the sampling frequency.
The above-mentioned embodiments are merely preferred embodiments for fully illustrating the present invention, and the scope of the present invention is not limited thereto. The equivalent substitution or the change made by the technical personnel in the technical field on the basis of the invention are all within the protection scope of the invention. The protection scope of the invention is subject to the claims.

Claims (6)

1. The UWB-LFM signal parameter estimation method based on CS and simplified FrFT is characterized in that: the method comprises the following steps:
acquiring an ultra-wideband linear frequency modulation signal containing Gaussian white noise;
constructing a discrete simplified fractional Fourier transform dictionary matrix ultra-wideband linear frequency modulation signal for sparse representation;
carrying out compression sampling on the ultra-wideband linear frequency modulation signal;
reconstructing the coefficient vector by using an improved compression sampling matching tracking algorithm;
the initial frequency and the chirp rate of the ultra-wideband chirp signal are estimated according to the distribution characteristics of the signal in the discrete fractional Fourier transform domain.
2. The CS-based and simplified FrFT-based UWB-LFM signal parameter estimation method of claim 1, wherein: acquiring an ultra-wideband linear frequency modulation signal containing Gaussian white noise, wherein a model x expression of the signal is as follows:
x＝s+n；
wherein s is an ultra-wideband chirp signal and n is additive white gaussian noise.
3. The CS-based and simplified FrFT-based UWB-LFM signal parameter estimation method of claim 1, wherein: constructing a discrete simplified fractional Fourier transform dictionary matrix to perform sparse representation on the sparsely represented ultra-wideband linear frequency modulation signal so as to perform compression sampling, selection of an optimal transform order, subsequent signal detection and subsequent parameter estimation;
calculating a discrete simplified fractional Fourier transform dictionary matrix according to the following formula:
Figure FDA0002846108060000011
where Ψ represents a discrete reduced fractional Fourier transform dictionary matrix,
alpha denotes the rotation angle of the coordinate axis of the reduced fractional fourier transform,
Figure FDA0002846108060000012
ΔT＝N/fsn is the number of sampling points, fsIn order to be able to sample the frequency,
taking the dictionary matrix as an observation matrix, and performing sparse representation according to the following formula:
Figure FDA0002846108060000013
where x is the input signal, θiIs a coefficient vector of psi ═ psi1，ψ2，...，ψiIs a sparse base.
4. The CS-based and simplified FrFT-based UWB-LFM signal parameter estimation method of claim 1, wherein: carrying out compression sampling on the ultra-wideband linear frequency modulation signal, and realizing the compression sampling according to the following steps:
the essence of the compressive sampling is to use an observation matrix Φ ∈ R that is not correlated with the sparse basis ΨM×NObserving an input signal x to obtain M observation data y, wherein M < N; for wideband signals, specific compressive sampling is typically accomplished through an analog to digital converter AIC.
5. The CS-based and simplified FrFT-based UWB-LFM signal parameter estimation method of claim 1, wherein: in the improved compression sampling matching tracking algorithm, a fuzzy threshold value of an index selected in the algorithm operation process is calculated according to the following formula:
Figure FDA0002846108060000021
wherein, aprAnd bprThe fuzzy threshold parameter is F, the support set is F, the residual error is r, and the sensing matrix is A;
forming a measurement matrix by using atoms corresponding to the support set indexes;
calculating a correlation coefficient, and extracting indexes corresponding to the size maximum values for secondary screening;
selecting a group of indexes corresponding to the largest energy value to be merged into a support set by utilizing a regularization thought;
reconstructing the signal by using a least square method, and solving a new residual error;
and determining a signal reconstruction mode according to the relation between the energy of the residual norm and the clipping threshold.
6. The CS-based and simplified FrFT-based UWB-LFM signal parameter estimation method of claim 1, wherein: the parameter estimation of the ultra-wideband linear frequency modulation signal in the discrete fractional Fourier transform domain is carried out according to the following steps:
calculating the simplified fractional Fourier transform distribution of the ultra-wideband chirp signal according to the following formula:
Figure FDA0002846108060000022
alpha represents the rotation angle of the coordinate axis of the simplified fractional Fourier transform;
estimating the initial frequency and the chirp rate of the signal according to the following formula by performing peak search on the reduced fractional Fourier transform distribution:
Figure FDA0002846108060000023
Figure FDA0002846108060000024
wherein,
Figure FDA0002846108060000025
is an estimate of the chirp rate and is,
Figure FDA0002846108060000026
is an estimate of the initial frequency of the frequency,
Figure FDA0002846108060000027
for the optimal rotation angle, S is a normalization factor, calculated according to the following formula:
Figure FDA0002846108060000028
wherein, Δ T is N/fsN is the number of sampling points, fsIs the sampling frequency.
CN202011509981.4A 2020-12-19 2020-12-19 UWB-LFM signal parameter estimation method based on CS and simplified FrFT Active CN112731306B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202011509981.4A CN112731306B (en) 2020-12-19 2020-12-19 UWB-LFM signal parameter estimation method based on CS and simplified FrFT

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202011509981.4A CN112731306B (en) 2020-12-19 2020-12-19 UWB-LFM signal parameter estimation method based on CS and simplified FrFT

Publications (2)

Publication Number Publication Date
CN112731306A true CN112731306A (en) 2021-04-30
CN112731306B CN112731306B (en) 2024-03-15

Family

ID=75603289

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202011509981.4A Active CN112731306B (en) 2020-12-19 2020-12-19 UWB-LFM signal parameter estimation method based on CS and simplified FrFT

Country Status (1)

Country Link
CN (1) CN112731306B (en)

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113537062A (en) * 2021-07-16 2021-10-22 浙江大学 Anomaly detection method based on FrFT (fractional Fourier transform) and total variation regularization
CN113670435A (en) * 2021-08-20 2021-11-19 西安石油大学 Underground vibration measuring device based on compressed sensing technology and measuring method thereof
CN114499601A (en) * 2021-12-23 2022-05-13 西安电子科技大学 Large-scale MIMO signal detection method based on deep learning

Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105783974A (en) * 2014-12-25 2016-07-20 中国科学院声学研究所 Chirp signal detection, parameter estimation method, and system thereof
CN110098882A (en) * 2019-05-14 2019-08-06 大连大学 Multiple antennas broadband frequency spectrum detection method based on compressed sensing and entropy
CN110133628A (en) * 2019-06-13 2019-08-16 哈尔滨工业大学 A kind of restoration methods of LFM Signal Embeded in Strong Interference in short-term
CN111600821A (en) * 2020-04-30 2020-08-28 哈尔滨工业大学 Linear frequency modulation signal sparse sampling and reconstruction method based on fractional Fourier transform domain

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105783974A (en) * 2014-12-25 2016-07-20 中国科学院声学研究所 Chirp signal detection, parameter estimation method, and system thereof
CN110098882A (en) * 2019-05-14 2019-08-06 大连大学 Multiple antennas broadband frequency spectrum detection method based on compressed sensing and entropy
CN110133628A (en) * 2019-06-13 2019-08-16 哈尔滨工业大学 A kind of restoration methods of LFM Signal Embeded in Strong Interference in short-term
CN111600821A (en) * 2020-04-30 2020-08-28 哈尔滨工业大学 Linear frequency modulation signal sparse sampling and reconstruction method based on fractional Fourier transform domain

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
陈旗;曹汉强;左炜;: "正切形非线性调频信号压缩感知", 太赫兹科学与电子信息学报, no. 06 *

Cited By (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113537062A (en) * 2021-07-16 2021-10-22 浙江大学 Anomaly detection method based on FrFT (fractional Fourier transform) and total variation regularization
CN113537062B (en) * 2021-07-16 2024-01-09 浙江大学 Anomaly detection method based on FrFT transformation and total variation regularization
CN113670435A (en) * 2021-08-20 2021-11-19 西安石油大学 Underground vibration measuring device based on compressed sensing technology and measuring method thereof
CN113670435B (en) * 2021-08-20 2023-06-23 西安石油大学 Underground vibration measuring device and method based on compressed sensing technology
CN114499601A (en) * 2021-12-23 2022-05-13 西安电子科技大学 Large-scale MIMO signal detection method based on deep learning
CN114499601B (en) * 2021-12-23 2023-04-28 西安电子科技大学 Large-scale MIMO signal detection method based on deep learning

Also Published As

Publication number Publication date
CN112731306B (en) 2024-03-15

Similar Documents

Publication Publication Date Title
CN112731306B (en) UWB-LFM signal parameter estimation method based on CS and simplified FrFT
CN111273238B (en) SAR (synthetic aperture radar) wide-band and narrow-band interference simultaneous inhibition method based on low-rank recovery
CN110865357A (en) Laser radar echo signal noise reduction method based on parameter optimization VMD
CN107527371B (en) Approximating smoothness L in compressed sensing0Design and construction method of norm image reconstruction algorithm
Duan et al. Relevant modes selection method based on Spearman correlation coefficient for laser signal denoising using empirical mode decomposition
CN111046791A (en) Current signal filtering and denoising method based on generalized S transform containing variable factors
CN109586728B (en) Signal blind reconstruction method under modulation broadband converter framework based on sparse Bayes
CN115616518A (en) Method for estimating weak target motion parameters and reconstructing high-resolution range profile of broadband radar
CN109165432B (en) Magnetic resonance spectrum reconstruction method based on partial singular value sum
CN113589253A (en) Method for detecting weak echo signal based on wavelet transform algorithm of pseudo time domain
CN116449369B (en) Inverse synthetic aperture radar imaging method based on multi-norm constraint
CN111582205B (en) Noise reduction method based on multi-resolution singular value decomposition model
CN113238193A (en) Multi-component combined reconstruction SAR echo broadband interference suppression method
CN116389198A (en) Multi-target time delay sparse reconstruction estimation method based on exponential filter
CN110441749B (en) Frequency stepping radar target motion parameter estimation method
CN116660883A (en) Single-bit compressed sensing radar target delay Doppler DOA estimation method
CN107977943B (en) Spatial target spectrum unmixing method based on purification optimization
CN112965066B (en) Single-bit bandpass sampling synthetic aperture radar imaging method
CN113705335B (en) Time-frequency super-resolution extraction method for low-frequency sparse line spectrum signal
CN115795272A (en) Spectral line denoising method based on fractional order iterative discrete wavelet transform
Zhang et al. Compressed Sensing Reconstruction of Radar Echo Signal Based on Fractional Fourier Transform and Improved Fast Iterative Shrinkage‐Thresholding Algorithm
CN113655443A (en) Low-frequency band SAR radio frequency interference suppression method for broadband digital television signal
CN114217286A (en) Radar unintentional modulation signal extraction method based on form component
CN108337205B (en) BPSK signal undersampling parameter estimation method based on multi-channel feedback structure
CN110927678B (en) Adaptive sparse fractional order fuzzy function clutter suppression and moving target detection method

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant