CN114448762A - Linear frequency modulation signal parameter estimation method based on nonlinear transformation under impact noise environment - Google Patents
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Abstract
The invention discloses a linear frequency modulation signal parameter estimation method based on nonlinear transformation in an impulse noise environment, which comprises the following steps: obtaining fractional Fourier transform from the angle of linear integral transform; obtaining fractional order Fourier transform of the LFM signal; analyzing the performance of fractional Fourier transform in an impulse noise environment; obtaining fractional order Fourier transform based on Tunable-Sigmoid transform; and carrying out linear frequency modulation signal parameter estimation according to the fractional Fourier transform of the adjustable Sigmoid function. The invention utilizes a new method of fractional Fourier transform and adjustable Sigmoid transform to realize the detection and estimation of the multi-component LFM signal parameters in the impulse noise environment (such as the Internet of vehicles). For multi-component signals, based on a signal separation technology of a TS-FRFT fractional Fourier domain, interference of strong components on weak component detection is effectively inhibited through peak searching, and therefore LFM signal parameter estimation is achieved. The method does not need prior knowledge of noise and has higher estimation precision under the environment of alpha stable distributed noise.
Description
Technical Field
The invention relates to the technical field of communication and information systems, in particular to a linear frequency modulation signal parameter estimation method based on nonlinear transformation in an impulse noise environment.
Background
Early Linear Frequency Modulated (LFM) signals were widely used in radar and communication systems. In a radar system, a target is extracted using a pulse compression characteristic of an LFM signal while being modulated as a spread spectrum waveform to suppress interference in communication. In recent years, wireless sensor networks, military ad hoc networks and the like have required integration of self-positioning, sensing and communication functions, and are also dedicated to target estimation and positioning using LFM signals.
In other fields, broadband wireless communication in high-speed vehicles (such as airplanes and high-speed trains) is in great demand. Conventional phase-based transceivers cannot meet the need for large doppler shifts caused by mobile speeds in excess of 200km/h unless they employ complex frequency shift estimation and compensation. The LFM signal is a time-frequency signal with a constant modulus, and does not require phase detection, so that it is widely paid attention and researched.
The LFM signal is insensitive to Doppler frequency shift, has large time-width bandwidth product, can effectively increase the detection distance under the condition of ensuring high resolution, and is widely applied to the fields of communication, radar, sonar, seismic survey and the like. Therefore, the parameter estimation of LFM signals has been a hot problem in the field of signal processing. A great deal of research has been carried out by many scholars, and a general sequential estimation framework has been proposed to realize the joint estimation of the delay and the doppler shift. Some provide a Doppler frequency shift and multipath delay joint estimation method for LFM pulse radar echo signals based on maximum likelihood parameter estimation. Some proposals have been made to use cyclic correlation transformation of echoes to achieve joint estimation of doppler shift and delay in echo signals based on cyclic correlation properties. A pulse radar parameter extraction and estimation method based on a compressed sensing theory is proposed. The methods can solve the estimation problem of related parameters, but the methods are all established on the basis of taking LFM pulse radar echo signals as general non-stationary signals, and the characteristics of the LFM signals are not fully utilized.
Fractional fourier transform (FRFT) is a new time-frequency analysis tool, which is of great interest for LFM signals because it has the best energy accumulation characteristics, and is widely used for parameter estimation of LFM signals. The parameter estimation of the linear frequency modulation signal is realized by utilizing fractional Fourier transform, short-time fractional Fourier transform, fractional correlation and fractional power spectrum respectively. The above modes all assume that the noise mixed in the echo signal is white gaussian noise, and theoretical research and actual measurement results find that actual noise of radar, sonar and wireless communication systems often contains a large amount of pulse components, and such noise is more suitable to be described by an Alpha stable distribution model. For a stable distribution of 0 < α < 2, only the statistics below the α -th order are present, and the high order statistics, both second and above, are absent. The performance of the conventional second-order statistic-based approach to estimate performance in impulse noise environments will be severely degraded.
In order to reduce the interference of Alpha stable distributed noise and improve the performance of the algorithm, researchers provide a plurality of FRFT parameter estimation methods based on a fraction low order statistic theory. Although the method obtains a good estimation effect, the method has certain limitations: (1) the fractional low-order moment p must satisfy 1 ≦ p < alpha or 0 < p < alpha/2; (2) if the prior knowledge of the noise characteristic index alpha is not available, or a correct estimated value of the alpha cannot be obtained, or the improper value of the order can cause the performance of the algorithm to be seriously reduced or even fail, so the estimation result of the characteristic index alpha and the value of the fraction low-order moment p can influence the performance of the algorithm.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a new time-frequency distribution, based on fractional Fourier transform (TS-FRFT) of an adjustable Sigmoid function, and the time-frequency distribution method is applied to parameter detection and estimation of LFM signals.
In order to achieve the above object, the present application provides a linear frequency modulation signal parameter estimation method based on nonlinear transformation in an impulse noise environment, including:
obtaining fractional Fourier transform from the angle of linear integral transform;
obtaining fractional order Fourier transform of the LFM signal;
analyzing the performance of fractional Fourier transform in an impulse noise environment;
obtaining fractional order Fourier transform based on Tunable-Sigmoid transform;
and performing linear frequency modulation signal parameter estimation according to the fractional Fourier transform of the adjustable Sigmoid function.
Further, a fractional fourier transform is obtained from a linear integral transform angle, specifically: the fractional fourier transform of order b, defined as the function x (t) in the t domain, is a linear integral operation:
wherein FbRepresenting the FRFT operator, Kb(t, m) is a kernel function of the fractional Fourier transform, expressed as:
wherein
b (0 < b ≦ 2) is the order of the fractional Fourier transform, β is the rotation angle of the fractional Fourier transform, β ≡ b π/2, n is an integer.
Further, obtaining fractional order fourier transform of the LFM signal specifically includes: let the expression for the chirp signal x (t) be as follows:
x(t)＝exp(j2π(f0t+μ0t2/2)) (3)
wherein f is0As initial frequency, mu0For adjusting the frequency;
the fractional fourier transform of the LFM signal x (t) is obtained from the fractional fourier transform, defined by equation (1):
when f is0Mcsc beta and u0X (β, m) has an energy-concentrating property when it is-cot β, exhibiting a sharp peak in the fractional fourier transform domain, i.e. a sharp peak
Wherein beta is0And m0Represents the coordinates of the peak point of the signal x (t) in the fractional fourier transform domain.
Further, analyzing the performance of fractional order fourier transform in an impulse noise environment specifically includes: let the chirp signal y (t) mixed with the alpha stationary distributed noise be:
y(t)＝x(t)+n(t) (6)
wherein n (t) is SaS noise; the characteristic function of the S.alpha.S distribution has the form of
ρ(ω)＝exp(-γ|ω|α) (7)
Where α is the noise figure. The smaller the value of α, the thicker the tail of the corresponding distribution, and therefore the more pronounced the pulse characteristic. Conversely, the larger the α value is, the thinner the tail of the distribution function thereof, i.e., the weaker the pulse characteristic. Gamma > 0 is a dispersion coefficient used to control the degree of deviation of the variables from the mean.
Further, the fractional order power spectrum based on fractional order fourier transform is defined as follows:
where X (ρ, m) is the fractional fourier transform of the signal X (t), equation (8) is further written as:
wherein x (t)1) And x (t)2) Are two sample values of the signal x (t).
Further, obtaining fractional order fourier transform based on Tuneable-Sigmoid transform specifically comprises:
firstly, obtaining an adjustable Sigmoid transformation, as shown in formula (10):
wherein λ is a scale factor;
then obtaining fractional order Fourier transform based on Tuenable-Sigmoid transform, and defining formula XTS(ρ, m) is represented by the following formula:
further, the linear frequency modulation signal parameter estimation is performed according to the fractional order fourier transform of the adjustable Sigmoid function, which specifically comprises the following steps: let the chirp signal y (t) mixed with Alpha stable distribution noise be:
y(t)＝x(t)+n(t) (12)
wherein n (t) is SaS noise;
obtaining the fractional order Fourier transform Y of the adjustable Sigmoid function of the signal Y (t) according to the definition of TS-FRFTTS(ρ, m), the expression of which is shown below:
wherein N isTS(ρ, m) represents TS-FRFT of impulse noise;
by making a pair of YTS(rho, m) to obtain the peak point position (rho)0,m0) Thereby obtaining the LFM signal parameter f0And mu0The estimated value of (c) is shown as follows:
compared with the prior art, the technical scheme adopted by the invention has the advantages that: the invention provides a novel method for realizing detection and estimation of multi-component LFM signal parameters in an impulse noise environment (such as Internet of vehicles) by utilizing fractional Fourier transform and adjustable Sigmoid transform. For multi-component signals, based on a signal separation technology of a TS-FRFT fractional Fourier domain, interference of strong components on weak component detection is effectively inhibited through peak searching, and therefore LFM signal parameter estimation is achieved. The method does not need prior knowledge of noise and has higher estimation precision under the environment of alpha stable distributed noise.
Drawings
FIG. 1 is a graph comparing the suppression capability of the TS-FRFT algorithm and the FRFT algorithm on impulse noise;
FIG. 2 is a comparison result diagram of single estimation spectral peaks of a FRFT algorithm and a TS-FRFT algorithm of a multi-path LFM signal;
FIG. 3 is a graph of the relationship between the estimation accuracy of each method parameter and the generalized signal-to-noise ratio GSNR;
FIG. 4 is a graph of performance versus noise figure for each method estimation.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application more apparent, the present application is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the application, i.e., the embodiments described are only a subset of, and not all embodiments of the application. The components of the embodiments of the present application, generally described and illustrated in the figures herein, can be arranged and designed in a wide variety of different configurations.
Thus, the following detailed description of the embodiments of the present application, presented in the accompanying drawings, is not intended to limit the scope of the claimed application, but is merely representative of selected embodiments of the application. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present application without making any creative effort, shall fall within the protection scope of the present application.
Example 1
The embodiment provides a linear frequency modulation signal parameter estimation method based on nonlinear transformation in an impulse noise environment, which comprises the following steps:
s1, obtaining fractional order Fourier transform from the angle of linear integral transform;
specifically, the b-order fractional fourier transform defined as the function x (t) in the t domain is a linear integration operation:
wherein FbRepresenting the FRFT operator, Kb(t,m)Is a kernel function of fractional Fourier transform, and has an expression of
Wherein
b (0 < b ≦ 2) is the order of the fractional Fourier transform, β is the rotation angle of the fractional Fourier transform, β ≡ b π/2, n is an integer. It can be found that when b is 1, i.e. β is pi/2, the fractional Fourier transform becomes Fourier transform, and it can be seen that the conventional Fourier transform is a special case of fractional Fourier transform.
S2, obtaining fractional order Fourier transform of the LFM signal;
specifically, the expression of the chirp signal x (t) is as follows:
x(t)＝exp(j2π(f0t+μ0t2/2)) (3)
wherein f is0As initial frequency, mu0For adjusting the frequency;
the fractional fourier transform of the LFM signal x (t) is obtained from the fractional fourier transform, defined by equation (1):
when f is0Mcsc beta and u0X (β, m) has an energy-concentrating property when it is-cot β, exhibiting a sharp peak in the fractional fourier transform domain, i.e. a sharp peak
Wherein beta is0And m0Represents the coordinates of the peak point of the signal x (t) in the fractional fourier transform domain. As can be seen from equation (5), the rotation angle β of the fractional Fourier transform of the signal is only modulated with the frequency of the LFM signalRate u0It is related.
When α -stationary distributed noise is mixed in the signal x (t), peak point positioning based on the fractional fourier transform algorithm fails. Because alpha stationary distributed noise exists only for statistics below the alpha order, high order statistics, both second order and above, do not exist. And the fractional order fourier transform is based on the second order statistics, the performance of the method based on the fractional order fourier transform is significantly reduced in an impulse noise environment. Therefore, the invention proposes to utilize a nonlinear transformation-adjustable Sigmoid transformation to inhibit the interference of alpha stable distribution noise.
S3, analyzing the performance of fractional Fourier transform in an impulse noise environment;
specifically, let the chirp signal y (t) mixed with the alpha stable distribution noise be:
y(t)＝x(t)+n(t) (6)
wherein n (t) is SaS noise; the characteristic function of the S.alpha.S distribution has the form of
ρ(ω)＝exp(-γ|ω|α) (7)
Where α is the noise figure. The smaller the value of α, the thicker the tail of the corresponding distribution, and therefore the more pronounced the pulse characteristic. Conversely, the larger the α value is, the thinner the tail of the distribution function thereof, i.e., the weaker the pulse characteristic. γ > 0 is a dispersion coefficient used to control the degree of deviation of a variable from a mean, which acts like a variance in a Gaussian distribution.
The fractional order power spectrum based on fractional order fourier transform is defined as follows:
where X (ρ, m) is the fractional fourier transform of the signal X (t), equation (8) is further written as:
wherein x (t)1) And x (t)2) Are two sample values of the signal x (t).
FRFT-based fractional order power spectra are not present for the steady distribution process, since Alpha steady distributions have finite second order moments. Therefore, in a stable distributed noise environment, the FRFT-based parameter estimation algorithm fails. Therefore, the present invention proposes a nonlinear transformation to suppress the interference of impulse noise.
S4, obtaining a fractional order Fourier transform based on Tunable-Sigmoid transform;
specifically, an adjustable Sigmoid transform is obtained first, as shown in formula (10):
wherein λ is a scale factor;
in order to solve the problem of performance degradation of a fractional order Fourier transform method under an impulse noise environment and the problem of dependence of a fractional order statistic method on noise prior knowledge, the fractional order Fourier transform based on the Tuenable-Sigmoid transform is defined by an X formulaTS(ρ, m) is represented by the following formula:
the linear frequency modulation signal has energy aggregation characteristics in a fractional Fourier transform domain, and the fractional Fourier transform based on the Tuneable-Sigmoid still has good energy aggregation characteristics in the fractional Fourier transform domain according to the property of the adjustable Sigmoid transform.
As shown in fig. 1, the suppression capability of the TS-FRFT algorithm and the FRFT algorithm for impulse noise is compared under impulse noise environment (the generalized signal-to-noise ratio GSNR is 5dB, and α is 1.2), where fig. 1(a) is the time-frequency distribution of FRFT of the LFM signal, and fig. 1(c) is the time-frequency distribution of TS-FRFT of the standard S α S stable distribution noise. Fig. 1(b) and (d) are time-frequency distributions of FRFT and Sigmoid-FRFT of LFM signal mixed with standard S α S stationary distributed noise. It can be seen from the figure that, due to the influence of the stable distribution noise of the S alpha S, the FRFT peak of the LFM signal in the fractional Fourier transform domain is submerged, the performance of the parameter estimation algorithm is degraded or even fails, after the tuning-Sigmoid transform, the impulse noise is obviously inhibited, and the TS-FRFT peak point of the LFM signal in the fractional Fourier transform domain is very obvious.
And S5, estimating parameters of the linear frequency modulation signals according to the fractional Fourier transform of the adjustable Sigmoid function.
Specifically, the linear frequency modulation signal parameter estimation is performed according to the fractional order fourier transform of the adjustable Sigmoid function, and specifically comprises the following steps: let the chirp signal y (t) mixed with Alpha stable distribution noise be:
y(t)＝x(t)+n(t) (12)
wherein n (t) is SaS noise;
obtaining the fractional order Fourier transform Y of the adjustable Sigmoid function of the signal Y (t) according to the definition of TS-FRFTTS(ρ, m), the expression of which is shown below:
wherein N isTS(ρ, m) represents TS-FRFT of impulse noise;
by making a pair of YTS(rho, m) to obtain the peak point position (rho)0,m0) Thereby obtaining LFM signal parameters f0And mu0The estimated value of (c) is shown as follows:
in order to discuss the estimation performance and effectiveness of the method provided by the invention, different algorithms are respectively used in the following three aspects of spectral peak analysis, generalized signal-to-noise ratio and noise characteristic index of a single estimation result: the parameter estimation performances of the FRFT method, the FLOS-FPSD method and the TS-FRFT method are compared under the impulse noise environment. In the following simulation experiment, 3 linear frequency modulation signal parameters are setStarting frequencies are respectively f10＝0.25fs，f20＝0.5fs，f30＝0.75fsFrequency modulation rate of mu10＝0.1fs 2/N，μ20＝0.2fs 2/N，μ30＝0.4fs 2N, sampling frequency fsThe number of sampling points N is 1000 at 1 MHz. Since Alpha stationary distributed noise does not have finite second moments, the signal-to-noise ratio (GSNR) is used to measure the signal-to-noise strength, and is defined as follows:
wherein
Represents the variance of the signal, gamma is the dispersion coefficient of S alpha S noise; the Monte Carlo count L is 200.
Simulation experiment 1: spectral peak contrast of single estimation of three algorithms under impulse noise environment
In this experiment, the comparison results of single-time estimated spectral peaks of the FRFT method and the TS-FRFT method of multiple LFM signals in an impulse noise environment are discussed, as shown in fig. 2, showing the estimation results of FRFT and Tunable-signature-FRFT on three LFM signals under impulse noise with GSNR being 5dB and α being 1.2. As can be seen from fig. 2(a) - (b), the FRFT algorithm fails when impulse noise is involved. In contrast to the FRFT spectrum of a pure LFM signal, in the FRFT spectrum of an LFM signal containing impulse noise, the FRFT spectrum peak is buried by the noise and cannot be identified. Therefore, in an impulse noise environment, the FRFT-based method cannot obtain a correct peak value, and the estimation performance is seriously degraded. As shown in fig. 2(c), the TS-FRFT of the LFM signal containing impulse noise forms three distinct spectral peaks because the Tuneable-Sigmoid can suppress impulse noise interference. Therefore, the TS-FRFT-based method provided by the invention can effectively inhibit pulse noise interference, generate three accurate peak values and have better estimation performance.
In this experiment, to discuss the estimated performance of the three algorithms, the corresponding parameters were set to: the characteristic index α of noise is 1.2, and in the flo-FPSD algorithm, the fractional lower-order moments are p 1.2, respectively, and fig. 3 shows the RMSE versus GSNR curve of parameter estimation.
As can be seen from fig. 3, both the FRFT method and the flo-FPSD method have poor estimation performance in the case of noise interference. And the TS-FRFT method can inhibit noise interference through adjustable Sigmoid transformation, and the estimation performance of the TS-FRFT is not influenced by fractional low-order moments. Therefore, the TS-FRFT method outperforms the other two methods.
In this experiment, the generalized signal-to-noise ratio GSNR is 5dB, and when discussing the estimated performance of the flo-FPSD method, the fractional lower-order moments are p 1.1, respectively. Fig. 4 shows the variation of the parameter estimation performance with the characteristic index α.
As can be seen from fig. 4, the flo-FPSD method has better estimated performance when the characteristic index is close to 2. The FLOS-FPSD method can inhibit-stably distribute noise interference by utilizing a fractional low-order statistical theory. The performance of the FLOS-FPSD method proved superior to the FRFT method.
The TS-FRFT method is obviously superior to the FLOS-FPSD method in performance through the experiment. This is because, although both Sigmoid transformation and fractional low order statistics theory have the ability to suppress impulse noise, flo's ability to suppress impulse noise is weaker than tuneable-Sigmoid transformation. FLOS noise suppression increases with decreasing order p, but when | x2(t)|＞|x1If (t) > 1, still | x2(t)|p＞|x1(t)|pAnd 1, the reason is that when the impulse is strong, the outliers far away from the mean value of the signal are not sufficiently suppressed, and the estimation is easy to generate errors. Compared to FLOS, for the Tunable-Sigmoid transform, there is always | TS [ x (t)]The equation of | < 1 holds. For | x (t) | > 1, there is | x2(t)|p＞|x1(t)|p＞1＞|Sigmoid[x(t)]The | inequality holds, so it is known that the Tuneable-Sigmoid transform can suppress impulse noiseThe force is slightly stronger than the fractional low order statistics (flo) theory. Therefore, under the impulse noise environment, the estimation performance of the TS-FRFT method is superior to that of the FLOS-FPSD method.
The foregoing descriptions of specific exemplary embodiments of the present invention have been presented for purposes of illustration and description. It is not intended to limit the invention to the precise form disclosed, and obviously many modifications and variations are possible in light of the above teaching. The exemplary embodiments were chosen and described in order to explain certain principles of the invention and its practical application to enable one skilled in the art to make and use various exemplary embodiments of the invention and various alternatives and modifications as are suited to the particular use contemplated. It is intended that the scope of the invention be defined by the claims and their equivalents.
Claims (7)
1. The linear frequency modulation signal parameter estimation method based on nonlinear transformation in the impact noise environment is characterized by comprising the following steps:
obtaining fractional Fourier transform from the angle of linear integral transform;
obtaining fractional order Fourier transform of the LFM signal;
analyzing the performance of fractional Fourier transform in an impulse noise environment;
obtaining fractional order Fourier transform based on Tunable-Sigmoid transform;
and carrying out linear frequency modulation signal parameter estimation according to the fractional Fourier transform of the adjustable Sigmoid function.
2. The method for estimating parameters of a chirp signal based on nonlinear transformation as claimed in claim 1, wherein the fractional fourier transform is obtained from a linear integral transform, specifically: the fractional fourier transform of order b, defined as a function x (t) in the t domain, is a linear integration operation:
wherein FbRepresenting the FRFT operator, Kb(t, m) is the kernel function of the fractional Fourier transform, expressed as:
wherein
b (0 < b ≦ 2) is the order of the fractional Fourier transform, β is the rotation angle of the fractional Fourier transform, β ≡ b π/2, n is an integer.
3. The method for estimating parameters of a chirp signal based on nonlinear transformation as claimed in claim 1, wherein the fractional fourier transform of the LFM signal is obtained by: let the expression for the chirp signal x (t) be as follows:
x(t)＝exp(j2π(f0t+μ0t2/2)) (3)
wherein f is0As initial frequency, mu0For adjusting the frequency;
the fractional fourier transform of the LFM signal x (t) is obtained from the fractional fourier transform, defined by equation (1):
when f is0Mcsc beta and u0X (β, m) has an energy-concentrating property when it is-cot β, exhibiting a sharp peak in the fractional fourier transform domain, i.e. a sharp peak
Wherein beta is0And m0Represents the coordinates of the peak point of the signal x (t) in the fractional fourier transform domain.
4. The method for estimating parameters of a chirp signal based on nonlinear transformation according to claim 1, wherein the performance of fractional fourier transform in impulse noise environment is analyzed, specifically: let the chirp signal y (t) mixed with alpha stable distributed noise be:
y(t)＝x(t)+n(t) (6)
wherein n (t) is SaS noise; the characteristic function of the S.alpha.S distribution has the form of
ρ(ω)＝exp(-γ|ω|α) (7)
Wherein α is a noise characteristic index; the smaller the alpha value is, the thicker the tail of the corresponding distribution is, so that the pulse characteristic is more remarkable; conversely, the larger the α value is, the thinner the tail of the distribution function thereof, i.e., the weaker the pulse characteristic. Gamma > 0 is a dispersion coefficient used to control the degree of deviation of the variables from the mean.
5. The method for estimating parameters of a chirp signal based on nonlinear transformation as claimed in claim 1, wherein the fractional power spectrum based on fractional fourier transform is defined as follows:
where X (ρ, m) is the fractional fourier transform of the signal, equation (8) is further written as:
wherein x (t)1) And x (t)2) Are two sample values of the signal x (t).
6. The method for estimating parameters of linear frequency modulated signals based on nonlinear transformation according to claim 1, wherein fractional fourier transform based on Tuneable-Sigmoid transform is obtained, specifically:
firstly, obtaining an adjustable Sigmoid transformation, as shown in formula (10):
wherein λ is a scale factor;
then obtaining fractional order Fourier transform based on Tuenable-Sigmoid transform, and defining formula XTS(ρ, m) is represented by the following formula:
7. the method for linear frequency modulation signal parameter estimation based on nonlinear transformation according to claim 1, wherein the linear frequency modulation signal parameter estimation is performed according to fractional order fourier transform of an adjustable Sigmoid function, specifically: let the chirp signal y (t) mixed with Alpha stable distribution noise be:
y(t)＝x(t)+n(t) (12)
wherein n (t) is SaS noise;
obtaining the fractional order Fourier transform Y of the adjustable Sigmoid function of the signal Y (t) according to the definition of TS-FRFTTS(ρ, m), the expression of which is shown below:
wherein N isTS(ρ, m) represents TS-FRFT of impulse noise;
by making a pair of YTS(rho, m) to obtain the peak point position (rho)0,m0) Thereby obtaining the LFM signal parameter f0And mu0The estimated value of (c) is shown as follows:
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Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| EP2993849A1 (en) * | 2014-09-04 | 2016-03-09 | Alcatel Lucent | Preprocessing and detection for nonlinear Fourier transform based optical receiver |
| CN106326633A (en) * | 2016-08-02 | 2017-01-11 | 电子科技大学 | Multi-component three-order phase signal parameter estimation method of product nonlinear transformation |
| CN108333568A (en) * | 2018-01-05 | 2018-07-27 | 大连大学 | Wideband echoes Doppler and delay time estimation method based on Sigmoid transformation under impulsive noise environment |
| CN108957416A (en) * | 2018-04-17 | 2018-12-07 | 大连大学 | Linear frequency-modulated parameter estimating method based on fractional order power spectral density under impulse noise environment |
-
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- 2022-01-28 CN CN202210108937.5A patent/CN114448762A/en active Pending
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| EP2993849A1 (en) * | 2014-09-04 | 2016-03-09 | Alcatel Lucent | Preprocessing and detection for nonlinear Fourier transform based optical receiver |
| CN106326633A (en) * | 2016-08-02 | 2017-01-11 | 电子科技大学 | Multi-component three-order phase signal parameter estimation method of product nonlinear transformation |
| CN108333568A (en) * | 2018-01-05 | 2018-07-27 | 大连大学 | Wideband echoes Doppler and delay time estimation method based on Sigmoid transformation under impulsive noise environment |
| CN108957416A (en) * | 2018-04-17 | 2018-12-07 | 大连大学 | Linear frequency-modulated parameter estimating method based on fractional order power spectral density under impulse noise environment |
Non-Patent Citations (1)
| Title |
|---|
| LI LI ETAL: "A Novel Parameter Estimation Method Based on a Tuneable Sigmoid in Alpha-Stable Distribution Noise Environments", 《SENSORS》, pages 5 * |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN115426235A (en) * | 2022-09-02 | 2022-12-02 | 西安电子科技大学 | Communication interference integrated signal design and processing method based on FRFT |
| CN115426235B (en) * | 2022-09-02 | 2024-04-16 | 西安电子科技大学 | FRFT-based communication interference integrated signal design and processing method |
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