CN106249208B - Signal detecting method under amplitude modulated jamming based on Fourier Transform of Fractional Order - Google Patents
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- 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
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- G01S7/292—Extracting wanted echo-signals
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- 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
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- G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
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Abstract
The present invention proposes signal detecting method under a kind of amplitude modulated jamming based on Fourier Transform of Fractional Order, the technical problem relatively narrow for solving detection process complexity present in signal detecting method and application range under existing amplitude modulated jamming, the present invention handles the reception signal of radar receiver two neighboring pulse repetition period using Fourier Transform of Fractional Order, and determine fractional order optimal value, keep the aggregation of linear frequency modulation echo signal after relevant treatment optimal, to realize that the detection of signal, specific steps include：1, acquisition receives signal and establishes signal model；2, Fourier Transform of Fractional Order is carried out to receipt signal model；3, related operation is carried out to Fourier Transform of Fractional Order model；4, the aggregation of linear frequency modulation echo signal correlation function is optimized.Detection process of the present invention is simple, and need not carry out parameter Estimation, can be used for realizing the detection under amplitude modulated jamming background to linear FM signal.
Description
Technical Field
The invention belongs to the technical field of communication, relates to a technology of combining fractional Fourier transform and related operation, and particularly relates to a signal detection method under noise amplitude modulation interference based on the fractional Fourier transform, which can be used for realizing detection of linear frequency modulation signals (LFM).
Background
The radar interference is of various types, and is generally divided into active interference and passive interference, wherein the active interference includes press type interference and deceptive interference. The suppression type interference mainly submerges radar echo signals through random signals, so that the radar cannot effectively acquire target echo information. In radar countermeasure, in order to effectively suppress the radar, a noise modulation mode is generally adopted to generate interference signals, including the modulation of parameters such as amplitude, phase, frequency and pulse width of the signals by the noise. Typical compression type interference can be classified into noise amplitude modulation interference, noise phase modulation interference, noise frequency modulation interference and radio frequency noise interference according to different noise modulation modes.
The noise amplitude modulation interference is an important interference mode in radar compression type interference, has the characteristics of simple signal generation, variable bandwidth, obvious compression effect and the like, and is widely applied to aiming type or composite type interference on radar at present. With the development of interference technology, the energy of an interference signal entering a radar receiver can exceed that of a radar echo signal by more than tens of decibels, the radar echo signal is completely submerged in the interference signal, and the detection of the echo signal under a strong interference background is an important problem faced by a radar.
In the disclosed data, under the condition of strong noise amplitude modulation interference, the signal detection performance mainly depends on the interference suppression effect, and usually a method of performing parameter estimation on the interference, performing filtering processing on the interference, and then suppressing the interference is adopted to detect a target echo signal, but the signal detection process is complicated because the interference is subjected to parameter estimation and filtering, and particularly, when the requirements of gaussian hypothesis, stationary hypothesis or certain prior information and the like are not met, and when the signal-to-interference ratio is too low, the signal processing capability is poor, a certain information loss is introduced, and the application range of detection is limited.
An LFM signal detection method is provided in an article 'LFM signal detection under noise amplitude modulation interference based on phase matching' published in electronic and information newspaper by Du Dong Hei et al in 2008, carrier frequency estimation is carried out on the noise amplitude modulation interference signal, then LFM signal detection is realized based on a least square phase matching method, the signal detection realization steps are complex, meanwhile, the method is influenced by factors such as interference frequency agility caused by non-stationary characteristics of interference emission parameters and radar frequency agility, the carrier frequency in the noise amplitude modulation interference is generally a time-varying function, the method needs the interference signal to have extremely stable carrier frequency and phase, and the use range of the method is limited.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, provides a signal detection method under noise amplitude modulation interference based on fractional order Fourier transform, and is used for solving the technical problems of complex detection process and narrow application range in the existing signal detection method under noise amplitude modulation interference.
The technical idea of the invention is as follows: and performing fractional Fourier transform on the received signals of two adjacent pulse repetition periods of the radar receiver through different fractional orders, and performing correlation operation on the transformed signals, so that the linear frequency modulation target signal is positioned at the peak value of a correlation function, two fractional orders with the best effect are determined, and the detection of the LFM signal is realized.
According to the technical thought, the technical scheme adopted for achieving the purpose of the invention is as follows:
a signal detection method under noise amplitude modulation interference based on fractional order Fourier transform comprises the following steps:
(1) the signal acquisition system acquires a received signal containing a linear frequency modulation target signal and noise amplitude modulation interference at any section in a radar antenna through receiver equipment of a continuous wave radar, and establishes a received signal model of any two adjacent pulse repetition periods, and the implementation steps are as follows:
(1a) establishing a signal model of the acquired receiving signals:
wherein A (t) is a linear frequency modulationSignal amplitude of the target signal, f0Is the initial frequency of the target signal; u shape0(t) is the carrier voltage of the noise amplitude modulation interference, Un(t) modulation noise of interference, ωjIs the carrier frequency and is,is the initial phase; n (t) is white noise;
(1b) selecting a received signal of any two adjacent pulse repetition periods from the established signal model x (t), and establishing a received signal model of two pulse repetition periods by using the selected received signal of any two adjacent pulse repetition periods:
x(t1)＝S(t1)+N(t1)+M(t1)
x(t2)＝S(t2)+N(t2)+M(t2)
wherein, x (t)1)、S(t1)、N(t1) And M (t)1) A received signal model, a linear frequency modulation target signal model, a noise amplitude modulation interference signal model and a white noise signal model of the first pulse repetition period, x (t)2)、S(t2)、N(t2) And M (t)2) A received signal model, a linear frequency modulation target signal model, a noise amplitude modulation interference signal model and a white noise signal model of a second pulse repetition period are respectively;
(2) received signal model x (t) for the first pulse repetition period1) And a received signal pattern x (t) of a second pulse repetition period2) Respectively carrying out fractional Fourier transform to obtain fractional Fourier transform models of two pulse repetition periods:
wherein,XS(u1)、XN(u1) And XM(u1) Fractional order Fourier transform models of a first pulse repetition period received signal, a linear frequency modulation target signal, noise amplitude modulation interference and white noise respectively,XS(u2)、XN(u2) And XM(u2) Fractional Fourier transform models for the second pulse repetition period received signal, the chirp target signal, the noise amplitude modulation interference and the white noise, respectively α1＝p1π/2，α2＝p2π/2；
(3) Fractional Fourier transform model for two pulse repetition periodsAndperforming correlation operation to obtain correlation function X of linear frequency modulation target signalS(u1,u2)；
(4) For the obtained linear frequency modulation target signal correlation function XS(u1,u2) When the aggregation of the two adjacent pulse repetition periods is optimized, the optimal value group of the fractional order Fourier transform of the received signal in the two adjacent pulse repetition periodsIs composed ofOrAnd then, obtaining the correlation function of the linear frequency modulation target signal with the optimal aggregation.
Compared with the prior art, the invention has the following advantages:
in the process of signal detection under noise amplitude modulation interference, the method processes the received signals of two adjacent pulse repetition periods of the radar receiver through fractional order Fourier transform, and determines the optimal value group of the fractional orderThe method has the advantages that the aggregative property of the linear frequency modulation target signals after the correlation processing is optimized, the detection process adopts relatively simple operation methods such as fractional Fourier transform and correlation processing, parameter estimation is not needed, compared with the method for detecting the signals by performing parameter estimation and filtering on noise amplitude modulation interference in the prior art, the detection process is effectively simplified, meanwhile, the method is not limited by requirements of Gaussian hypothesis, stability hypothesis or certain prior information, and the like, and the application range is expanded.
Drawings
FIG. 1 is a block diagram of an implementation flow of the present invention;
FIG. 2 is a time-frequency transform schematic of the fractional Fourier transform of the present invention;
FIG. 3 is an analysis diagram of the present invention for determining fractional order values of received signals of two adjacent pulse repetition periods;
FIG. 4 is a diagram showing simulation results of a received signal and a chirp target signal after fractional order Fourier transform of two adjacent pulse repetition periods in a fractional order of 0.5 and 1.5 according to the present invention;
FIG. 5 is a simulation result diagram of a correlation function between a received signal and a chirp target signal after fractional order Fourier transform when fractional orders of two adjacent pulse repetition periods are 0.5 and 1.5 in the present invention;
fig. 6 is a simulation result diagram of correlation functions of a received signal and a chirp target signal after fractional order fourier transform when fractional orders of two adjacent pulse repetition periods are 0.8, 1.2, 0.3 and 1.2 in the invention.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings.
Referring to fig. 1, the present invention includes the steps of:
step 1, collecting a received signal and establishing a signal model.
The signal acquisition system acquires any section of received signals in a radar antenna through receiver equipment of a continuous wave radar, wherein the received signals comprise linear frequency modulation target signals, noise amplitude modulation interference and white noise carried by the radar receiver equipment, and establishes a received signal model of any two adjacent pulse repetition periods, and the implementation steps are as follows:
step 1a, establishing a signal model of the acquired received signal:
where A (t) is the signal amplitude of the chirp target signal, f0Is the initial frequency of the target signal; u shape0(t) is the carrier voltage of the noise amplitude modulation interference, Un(t) modulation noise of interference, ωjIs the carrier frequency and is,is the initial phase; n (t) is white noise;
step 1b, selecting received signals of any two adjacent pulse repetition periods from the established signal model x (t), and establishing a received signal model of two pulse repetition periods by using the selected received signals of any two adjacent pulse repetition periods:
x(t1)＝S(t1)+N(t1)+M(t1)
x(t2)＝S(t2)+N(t2)+M(t2)
wherein, x (t)1)、S(t1)、N(t1) And M (t)1) A received signal model, a linear frequency modulation target signal model, a noise amplitude modulation interference signal model and a white noise signal model of the first pulse repetition period, x (t)2)、S(t2)、N(t2) And M (t)2) A received signal model, a linear frequency modulation target signal model, a noise amplitude modulation interference signal model and a white noise signal model of a second pulse repetition period are respectively;
and 2, performing fractional Fourier transform on the received signal model.
Received signal model x (t) for the first pulse repetition period1) And a received signal pattern x (t) of a second pulse repetition period2) Respectively carrying out fractional Fourier transform:
wherein, Fp[·]Representing a fractional Fourier transform operation, Kα(t, u) is the kernel function of the fractional Fourier transform, which is defined as:
obtaining fractional order Fourier transform models of two pulse repetition periods:
wherein,XS(u1)、XN(u1) And XM(u1) Fractional order Fourier transform models of a first pulse repetition period received signal, a linear frequency modulation target signal, noise amplitude modulation interference and white noise respectively,XS(u2)、XN(u2) And XM(u2) Fractional order Fourier transform models of a second pulse repetition period received signal, a linear frequency modulation target signal, noise amplitude modulation interference and white noise respectively;
and 3, performing correlation operation on the fractional Fourier transform model.
Fractional Fourier transform model for two pulse repetition periodsAndperforming correlation operation to obtain correlation function X of linear frequency modulation target signalS(u1,u2) The realization process is as follows:
whereinIs a sign of the correlation operation.
Since N is noise-amplitude-modulated interference and M is white noise, then XS(ui) And XN(ui) Uncorrelated, XS(ui) And XM(ui) Not related, XN(ui) And XM(ui) Uncorrelated, XN(u1) And XN(u2) Uncorrelated, XM(u1) And XM(u2) Is not relevant. And the chirp target signal is correlated in two adjacent pulse repetition periods, then XS(u1) And XS(u2) Are relevant. If a chirp target signal is present in the two adjacent pulse repetition periodsAndhas a maximum value.
Therefore, in a noise amplitude modulation interference environment, only the fractional Fourier transform correlation function of the LFM signal has a peak value, so that the signal detection analysis can be carried out. However, for two adjacent pulse repetition periods, fractional order p is used1And p2The aggregation of LFM signals after correlation processing is affected, and the fractional order p should be determined for better signal detection and analysis1And p2The value of (2) is chosen to maximize the aggregation of LFM signals.
And 4, optimizing the aggregation of correlation functions of the linear frequency modulation target signals.
In the time-frequency two-dimensional plane, the time axis and the frequency axis are generally represented by two mutually orthogonal straight lines. If X (t), which is an argument of time, represents the representation of the signal along the time axis t and its corresponding conventional fourier transform X (ω) represents the representation of the signal along the frequency axis f, the conventional fourier transform of the signal can be regarded as a rotation operator on a two-dimensional time-frequency plane and it is rotated counterclockwise by π/2 from the time axis t to the frequency axis. The time-frequency transformation principle of the fractional fourier transform is shown in fig. 2.
Since α p · pi/2 only occurs at the parameter position of the trigonometric function, the definition of the fractional fourier transform with p (or α) as the parameter is periodic by 4 (or 2 pi.) only the interval p e (-2,2] (or α e (-pi, pi ]). for the interference context of the present invention, the processing results of p e (-2,0] and p e (0, 2) are the same with the fractional fourier transform and correlation operations, and therefore the present invention only discusses the case of p e (0, 2).
If p is divided into two intervals of (0.5,1.5) and (0,0.5) ∪ (1.5,2), then the two intervals are compared for discussion1And p2All lie within the interval (0.5,1.5) or all lie within the interval (0,0.5) ∪ (1.5,2), e.g. 0.8 and 1.2Andthe frequency domain correlation of (a) becomes larger at the relatively front and relatively rear positions of time, and the aggregation of linear frequency modulation target signals becomes worse; if p is1And p2Within the intervals (0.5,1.5) and (0,0.5) ∪ (1.5,2), such as 0.3 and 1.2, respectively, p within the interval (0.5,1.5) will make the correlation of the frequency domain in the corresponding pulse repetition period time large, and the chirp target signal aggregation will be poorSet of optimal valuesOrThen, the correlation function X of the linear frequency modulation target signal with the optimal aggregation is obtainedS(u1,u2) The purpose of signal detection is achieved. The analysis of the fractional order value of the received signal of two adjacent pulse repetition periods is shown in fig. 3.
Referring to fig. 2, the fractional fourier transform can be interpreted as an operator rotated in a counterclockwise direction by α degrees on a two-dimensional time-frequency plane from a time axis t to a frequency axis f, where the time axis t and the frequency axis f are respectively rotated to a u-axis and a v-axis of a fractional fourier transform domain, and the fractional fourier transform fuses information of a signal in both time and frequency domains.
Referring to FIG. 3, if p1And p2Within the interval (0,0.5) ∪ (0.5,1.5) ∪ (1.5,2), such as 0.8 and 1.2, or 0.3 and 1.2, the correlation function of the chirp target signal is less concentrated, and when the fractional order of the fractional Fourier transform of the received signal is two adjacent pulse repetition periodsSet of optimal valuesOrAnd the correlation function aggregation of the linear frequency modulation target signal is optimal.
The technical effects of the present invention will be further described below with reference to simulation experiments.
1. And (5) simulating conditions.
The running system of the simulation experiment is an Intel (R) core (TM) i5CPU 650@3.20GHz 32-bit Windows operating system, simulation software adopts MATLAB R (2010a), and simulation parameters are set as follows.
Suppose a noise amplitude modulation jammer interferes with a radar of an L wave band, the radar wavelength is 0.15m, and the pulse repetition period is 500 mu s. ThunderThe transmitting signal is an LFM signal, the time width of the signal is 20 mus, the bandwidth is 10MHz, the central frequency of the signal is 0MHz, and the sampling frequency is 40 MHz. The basic frequency of the jammer is equal to the working frequency of the radar, the pulse repetition period is 500 mus, and the initial phase isThe modulation factor is 1000. When a linear frequency modulation target signal exists in the radar signal, the target signal is supposed to be submerged by noise, the power signal-to-interference ratio is set to be-15 dB, and the signal-to-noise ratio is set to be 6 dB.
2. And (5) simulating content and result analysis.
2.1, simulating the received signal and the linear frequency modulation target signal after the time division fractional order Fourier transform of two adjacent pulse repetition periods with the fractional order of 0.5 and 1.5, wherein the simulation result is shown in FIG. 4;
2.2, simulating a correlation function of the received signal and the linear frequency modulation target signal after fractional order Fourier transform when the fractional order of two adjacent pulse repetition periods is 0.5 and 1.5, wherein the simulation result is shown in FIG. 5;
2.3, simulating the correlation function of the received signal and the chirp target signal after fractional order Fourier transform when the fractional order of two adjacent pulse repetition periods is 0.8, 1.2, 0.3 and 1.2, wherein the simulation result is shown in fig. 6.
Referring to fig. 4, fig. 4(a) is a three-dimensional diagram of a received signal after fractional fourier transform, without correlation processing; fig. 4(b) is a three-dimensional diagram in the case of only a chirp target signal. Wherein the fractional order is respectively 0.5 and 1.5. As can be seen from fig. 4(a) and 4(b), only fractional fourier transform is performed without correlation processing, and it is difficult to identify a target signal from a received signal, and the purpose of signal detection cannot be achieved.
Referring to fig. 5, fig. 5(a) is a three-dimensional graph of a correlation function after a fractional fourier transform of a received signal; fig. 5(b) is a three-dimensional diagram of the same process in the case of only a chirp target signal. Wherein the fractional order is respectively 0.5 and 1.5. As is clear from fig. 5(a) and 5(b), the higher the correlation function aggregability of the target signal, the easier it is to detect the target signal from the received signal.
Referring to fig. 6, fig. 6 is a three-dimensional diagram of correlation functions under values of different fractional orders. Fig. 6(a) is a three-dimensional graph of correlation functions of received signals when fractional order values of the received signals of two adjacent pulse repetition periods are 0.8 and 1.2, respectively; fig. 6(b) is a three-dimensional graph of correlation functions of the chirp target signal when fractional order values of the received signals of two adjacent pulse repetition periods are 0.8 and 1.2, respectively; fig. 6(c) is a three-dimensional graph of correlation functions of received signals when fractional orders of the received signals of two adjacent pulse repetition periods are respectively 0.3 and 1.2; fig. 6(d) is a three-dimensional graph of correlation functions of the chirp target signal when the fractional order values of the received signal of two adjacent pulse repetition periods are 0.3 and 1.2, respectively. Compared with fig. 5, if the fractional order is 0.8 and 1.2, or 0.3 and 1.2, respectively, the aggregation of the correlation function of the target signal is poor, and it is difficult to detect the correlation function from the received signal. If the fractional order is respectively 0.5 and 1.5, the correlation function of the target signal has good aggregation, and the purpose of detecting the linear frequency modulation target signal can be achieved. Theoretical analysis and simulation experiments can determine the optimal value group of the fractional order of the received signals of two adjacent pulse repetition periodsIs composed ofOrAt the moment, the correlation function X of the linear frequency modulation target signalS(u1,u2) The aggregation performance is optimal, and the aim of signal detection is fulfilled.
In conclusion, three results obtained by three simulation experiments show that the linear frequency modulation target signal can be effectively detected by adopting the method, the complexity of the detection process is reduced, and the application range is expanded.
Claims (4)
1. A signal detection method under noise amplitude modulation interference based on fractional order Fourier transform comprises the following steps:
(1) the signal acquisition system acquires a received signal containing a linear frequency modulation target signal and noise amplitude modulation interference at any section in a radar antenna through receiver equipment of a continuous wave radar, and establishes a received signal model of any two adjacent pulse repetition periods, and the implementation steps are as follows:
(1a) establishing a signal model of the acquired receiving signals:
where A (t) is the signal amplitude of the chirp target signal, f0Is the initial frequency of the target signal; u shape0(t) is the carrier voltage of the noise amplitude modulation interference, Un(t) modulation noise of interference, ωjIs the carrier frequency and is,is the initial phase; n (t) is white noise;
(1b) selecting a received signal of any two adjacent pulse repetition periods from the established signal model x (t), and establishing a received signal model of two pulse repetition periods by using the selected received signal of any two adjacent pulse repetition periods:
x(t1)＝S(t1)+N(t1)+M(t1)
x(t2)＝S(t2)+N(t2)+M(t2)
wherein, x (t)1)、S(t1)、N(t1) And M (t)1) A received signal model, a linear frequency modulation target signal model, a noise amplitude modulation interference signal model and a white noise signal model of the first pulse repetition period, x (t)2)、S(t2)、N(t2) And M (t)2) A received signal model, a linear frequency modulation target signal model, a noise amplitude modulation interference signal model and a white noise signal model of a second pulse repetition period are respectively;
(2) received signal model x (t) for the first pulse repetition period1) And a received signal pattern x (t) of a second pulse repetition period2) Respectively carrying out fractional Fourier transform to obtain fractional Fourier transform models of two pulse repetition periods:
wherein,XS(u1)、XN(u1) And XM(u1) Fractional order Fourier transform models of a first pulse repetition period received signal, a linear frequency modulation target signal, noise amplitude modulation interference and white noise respectively,XS(u2)、XN(u2) And XM(u2) Fractional Fourier transform models for the second pulse repetition period received signal, the chirp target signal, the noise amplitude modulation interference and the white noise, respectively α1＝p1π/2，α2＝p2π/2；
(3) Fractional Fourier transform model for two pulse repetition periodsAndperforming correlation operation to obtain correlation function X of linear frequency modulation target signalS(u1,u2)；
(4) For the obtained linear frequency modulation target signal correlation function XS(u1,u2) When the aggregation of the two adjacent pulse repetition periods is optimized, the optimal value group of the fractional order Fourier transform of the received signal in the two adjacent pulse repetition periodsIs composed ofOrAnd then, obtaining the correlation function of the linear frequency modulation target signal with the optimal aggregation.
2. The method according to claim 1, wherein the received signal model x (t) for the first pulse repetition period in step (2) is1) And a received signal pattern x (t) of a second pulse repetition period2) Respectively carrying out fractional Fourier transform, and realizing the following formula:
wherein, Fp[·]Representing a fractional Fourier transform operation, Kα(t, u) is the kernel function of the fractional Fourier transform, which is defined as:
3. the method according to claim 1, wherein the fractional Fourier transform is used as a model of the fractional Fourier transform for two pulse repetition periods in step (3)Andperforming correlation operation, wherein the implementation process comprises the following steps:
whereinIs a sign of the correlation operation.
4. The method according to claim 1, wherein the correlation function X of the linear frequency modulation target signal in the step (4) is related to the linear frequency modulation target signalS(u1,u2) The aggregation performance is optimized, and the method is realized by the following steps:
(4a) determining the value interval of the fractional order p as (0, 2) according to the principle of fractional order Fourier transform;
(4b) by taking the interval (0, 2) of the fractional order p]The discussion of different values in the two groups obtains the optimal value group of the fractional order Fourier transform of the received signals of two adjacent pulse repetition periods
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