CN112346022A - Dense false target interference suppression method based on two-dimensional reduced fractional Fourier transform - Google Patents

Dense false target interference suppression method based on two-dimensional reduced fractional Fourier transform Download PDF

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CN112346022A
CN112346022A CN202011212099.3A CN202011212099A CN112346022A CN 112346022 A CN112346022 A CN 112346022A CN 202011212099 A CN202011212099 A CN 202011212099A CN 112346022 A CN112346022 A CN 112346022A
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王国宏
张亮
张翔宇
于洪波
杨志国
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Naval Aeronautical University
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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
    • 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
    • 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
    • G01S7/41—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 invention belongs to the field of radar anti-interference, and provides a dense false target interference suppression method based on two-dimensional reduced fractional order Fourier transform (FRFT) aiming at the problem of low probability of detecting a real target of linear frequency modulation Pulse Doppler (PD) caused by self-defense dense false target interference and target instantaneous maneuver. Determining an optimal transformation order according to a radar transmitting signal frequency modulation slope, and calculating an echo fast time optimal order and simplifying FRFT; aiming at the characteristic that the interference forwarding delay is slow and the time is messy, the median absolute deviation is introduced to identify and remove the interference outliers; and finally, estimating the target acceleration by using the maximum high-order moment criterion, determining the optimal transformation order of the slow time, and calculating the two-dimensional reduced FRFT of the echo after interference elimination. The PD radar loses the accumulation advantage due to the dense false target interference and the target instantaneous maneuver under the condition of high interference-to-signal ratio, and the real target detection probability can be greatly improved by compensating the Doppler frequency and eliminating the interference outlier.

Description

Dense false target interference suppression method based on two-dimensional reduced fractional Fourier transform
Technical Field
The invention belongs to the field of radar anti-interference, and is suitable for solving the problem of low true target detection probability of a linear frequency modulation pulse Doppler radar under the condition of high interference-to-signal ratio dense false target interference.
Background
The pulse Doppler radar is widely applied to the fields of space monitoring, weapon control, missile warning and the like, is defined as a 'next generation threat radar' due to the inherent electronic protection characteristic, and is one of the common signal forms of the pulse Doppler radar by using a linear frequency modulation signal. The dense false target interference based on the digital radio frequency storage device is an effective interference pattern against a pulse Doppler radar, interference signals are generated by intercepting full-pulse radar signals, prior information of radar pulse repetition frequency is not needed, the energy domain is effectively suppressed by absolute quantity and power advantages, and the digital radio frequency storage device is applicable to various interference scenes. The coherent accumulation function of the pulse Doppler radar can inhibit interference signals to a certain degree, but because the interference signals are matched with a radar matched filter and distributed in a messy manner, the interference quantity increase and the power increase can also counteract the interference inhibition effect of the interference signals, and particularly when the interference signals are more in quantity and the interference power is larger, the interference signals after coherent accumulation can completely submerge a real target. Meanwhile, under the self-defense interference condition, the jammer usually has instantaneous maneuver, which causes the doppler spread of the target, and will further affect the detection efficiency of the radar on the real target.
At present, the signal layer interference suppression algorithm for dense false targets mainly utilizes the characteristic that the slow time of the peak position after the target pulse pressure is linear, and the interference suppression problem is equivalent to a linear detection problem. The method comprises the following steps of taking an echo matrix envelope after pulse pressure in a radar intensive forwarding interference suppression algorithm [ J ] based on Hough transformation, a system engineering and an electronic technology, 2019,41(12) 2371 and 2376, setting a real echo and an interference signal to be 1, setting noise data to be 0 and reconstructing a real target through Hough forward and reverse transformation. The radar dense forwarding interference suppression algorithm based on Hough transformation has the following two defects: (1) when the real echo peak value after pulse pressure is equal to or lower than the average power of noise, the binary voting is easy to set the real echo data to 0, and the real target detection efficiency is influenced; (2) the binary voting is essentially interference amplitude limiting, and when the interference-signal ratio is high, the energy of interference main lobes and side lobes after amplitude limiting can also influence real target detection.
Disclosure of Invention
The invention aims to provide a dense false target interference suppression method based on two-dimensional reduced fractional order Fourier transform, and aims to solve the problem that a radar dense forwarding interference suppression algorithm based on Hough transform is low in real target detection probability under the conditions of low signal-to-noise ratio and high interference-to-signal ratio. The technical scheme comprises the following steps:
step (I): and simplifying the fractional Fourier transform, designing and simplifying the fractional Fourier transform, expanding the fractional Fourier transform to two dimensions, and obtaining the two-dimensional simplified fractional Fourier transform. The method comprises the following specific steps:
(1) the fractional fourier transform of signal x (t) is decomposed into a 4-step cascade:
Figure BDA0002759111300000021
h(u)＝exp(-iπu2tanα/2)
g(u)＝exp(iπcscαu2)
wherein u corresponds to the u domain of the fractional Fourier transform, and alpha is the rotation angle.
(2) Omitting the first two terms, a one-dimensional reduced fractional Fourier transform (RFRFT) expression is obtained as:
Figure BDA0002759111300000022
(3) expanding to two dimensions, obtaining (p) of the signal x (s, t)1,p2) The order two-dimensional reduced fractional Fourier transform (2D-RFT) is:
Figure BDA0002759111300000023
wherein the content of the first and second substances,
Figure BDA0002759111300000024
is a kernel function, α1＝p1π/2、α2＝p2And pi/2 is a two-dimensional rotation angle.
Step (II): determining the optimal order p according to the frequency modulation slope k of the radar transmission signalkCalculate the echo (p) as acot (-k)/(pi/2)k0) order 2D-RFT is:
Figure BDA0002759111300000025
Figure BDA0002759111300000026
Figure BDA0002759111300000027
wherein the content of the first and second substances,
Figure BDA0002759111300000028
respectively a real echo, a first interference signal and a noise transformation result; u and v represent the u domain and the v domain of the echo 2D-RFRFT respectively; alpha is alphak＝πpk/2；TpTransmitting the pulse width of an LFM signal for a radar, wherein lambda is the wavelength; sigma, t0Respectively true echo reflection coefficient and time delay, R (t)m) As a function of slow time distance; l is the number of interference signals, Aj、τl(tm) Respectively the amplitude and the time delay function of the ith interference signal.
Step (three): sequentially taking echoes (p)kAnd 0) distinguishing a real part and an imaginary part of each u-domain unit of the 2D-FRFT, respectively carrying out interference outlier detection to obtain two groups of outlier labels, carrying out OR operation, and carrying out outlier detection to 0 according to the labels. Wherein, the detection principle of 1 u-domain unit outlier is as follows:
(1) let echo (p)k0) order 2D-FRFT1 u-domain units are sample set X, and the absolute deviation MAD of the number of bits is calculated as:
MAD＝b·med[|xi-med(X)|]
where b is a correction factor, typically 1.4826, med [. cndot.)]Representing the median, xiAre sample values.
(2) According to the sample valueThe distance between the sample set and the digit number is judged to be xiWhether it is an interference outlier:
Figure BDA0002759111300000031
wherein th is an identification threshold, and 3 is taken as a very conservative value, 2.5 is taken as a general conservative value, and 2 is taken as a non-conservative value.
Step (IV): setting order step length, and estimating to obtain target acceleration a by maximum high-order moment criteriontAccording to atDetermining the echo slow time optimal transformation order pa ═ acot (2 a)tThe/lambda)/(pi/2) and the echo (p) after interference rejection is calculatedk,pa) 2D-FRFT order, peak search to obtain target corresponding coordinate (u)max,vmax) Further obtain the target radial distance RtAnd velocity vt：
Rt＝cumax/2/cos(pkπ/2)
vt＝vmaxλ/2/sin(paπ/2)
Where c is the speed of light.
The beneficial effects of the invention are illustrated as follows:
(1) the design provides simplified fractional order Fourier transform, and compared with sampling type discrete fractional order Fourier transform, the calculation amount is lower; the simplified fractional Fourier transform is expanded to two dimensions, the method is suitable for one coherent processing interval echo, and the calculated amount is equivalent to the radar moving target detection processing.
(2) The median absolute deviation robust statistic is introduced, enough samples are not required, the maximum ratio of the outliers is allowed to be 50%, and the influence of the outliers on the variance and standard deviation is small; compared with a binary voting method, the outlier detection method based on the median absolute deviation is more thorough in interference rejection.
Drawings
FIG. 1 is a flow chart of the method steps of the present invention;
FIG. 2 shows the disturbed echo (p)k0) order two-dimensional reduced fractional order Fourier transform results;
FIG. 3 is an interference outlier detection tag;
FIG. 4 is a comparison of interference rejection effects;
FIG. 5 is a result of order estimation corresponding to target acceleration;
FIG. 6 shows the interference-rejected echo (p)k,pa) Order two-dimensional simplified fractional order Fourier transform results;
FIG. 7 is a graph of true target detection rate versus signal-to-noise ratio before interference;
FIG. 8 is a graph showing the variation of the true target detection rate with the interference-to-signal ratio after interference;
FIG. 9 is a graph of the true target detection rate after interference suppression by the algorithm herein as a function of the interference-to-signal ratio;
FIG. 10 is a graph of the true target detection rate after interference suppression by the contrast algorithm as a function of the interference-to-signal ratio.
Detailed description of the invention
The following describes the dense decoy interference suppression method based on two-dimensional reduced fractional order fourier transform in detail with reference to the accompanying drawings. Referring to the attached figure 1, the specific implementation steps are as follows:
(1) according to the frequency modulation slope of the radar emission signal, the optimal transformation order p of the echo fast time is ensuredkCalculating the disturbed echo (p)k0) order 2D-FRFT;
(2) taking the real part and the imaginary part of the transformed echo, respectively carrying out interference outlier detection, carrying out OR operation on the detected outlier position label to obtain a final detection label, and setting the interference data to be 0;
(3) searching the maximum higher-order moment criterion to obtain a target acceleration atAccording to atDetermining an echo slow time optimal transformation order paCalculating the echo (p) after eliminating the interferencek,pa) 2D-FRFT order;
(4) and searching the peak value to obtain the corresponding coordinates of the real target, and estimating to obtain the initial distance and the radial speed of the target.
The implementation conditions are as follows: the simulation experiment was performed under the following parameter conditions:
TABLE 1 Radar, target and interference parameters
Figure BDA0002759111300000041
The radar has the carrier frequency of 400MHz, the pulse repetition frequency of 2000Hz and the coherent accumulation number of 128, and transmits an LFM pulse signal with the pulse width of 50us, the bandwidth of 4MHz and the sampling frequency of 16 MHz. Under self-defense interference, the interference machine is a point target, the initial distance is 31km, the radial speed is 120m/s, the radial acceleration is 600m/s2, and the real echo amplitude is 1V. The amplitude of 1 coherent processing interval of the dense false target interference signals is the same, 5 interference signals are released in each pulse repetition period, 640 interference signals are counted, and the false targets (after pulse pressure) are randomly distributed within the range of 27km to 42 km. The signal-to-noise ratio is set to be-15 dB and the interference-to-signal ratio is set to be 30dB, and the echo fast time conversion order p is obtained according to the frequency modulation slope of the transmitting signalkIs-0.5, disturbed echo (p)kAnd, 0) order 2D-FRFT results are shown in FIG. 2. Setting the outlier detection threshold as 2.5, performing outlier detection on the echo transformation result and the imaginary part respectively, as shown in fig. 3(a) and 3(b), and performing or operation to obtain an outlier final detection label as shown in fig. 3 (c). Zeroing outliers according to a final detection label, enabling interference elimination effect to be shown in figure 4, performing Fourier transform on echo slow time after interference elimination, searching a peak value to obtain a 1601 th u-domain unit signal, setting the order step length to be 0.02, estimating target acceleration by using a high-order moment criterion, and enabling interference elimination echo (p) to be shown in figure 5 as a resultk,pa) The two-dimensional reduced fractional order fourier transform results are shown in fig. 6. In order to evaluate the performance of the algorithm, the signal-to-noise ratio is set to be-20 dB to 0dB, Monte Carlo simulation is run for 500 times, and a curve of the true target detection rate before the radar is interfered along with the change of the signal-to-noise ratio is shown in FIG. 7. The SNR takes-20 dB, -15dB, -10dB and-5 dB, the interference-to-signal ratio takes 0-60 dB, and the change curve of the real target detection rate along with the interference-to-signal ratio after the radar is interfered is shown in figure 8. Fig. 9 and fig. 10 are graphs showing the change of the real target detection rate with the interference-to-signal ratio after the interference suppression of the present algorithm and the contrast algorithm, respectively. As can be seen from the attached figure 2, the interference signals are distributed in 1400-2400 u-domain units in a messy manner, and the u-domain units where the real targets are located are covered due to overlarge interference power; as can be seen from FIG. 3, most of the componentsThe interference outliers are effectively detected, and partial noise is detected; as can be seen from fig. 4, the interference component is significantly less; as can be seen from fig. 5 and 6, the real target is effectively detected. As can be seen from the attached drawings 7, 8, 9 and 10, the radar loses the accumulation advantage due to the dense false target interference and the target instantaneous maneuver under the condition of high interference-signal ratio, the target Doppler is compensated, the interference outlier is removed, the detection probability of the real target can be obviously improved, the tolerance of the algorithm to the interference-signal ratio is higher, and the critical interference-signal ratio of the real target detection rate close to 0 after the interference suppression is higher than about 15dB of the contrast algorithm.

Claims (4)

1. The dense false target interference suppression method based on two-dimensional reduced fractional Fourier transform is characterized by comprising the following steps of:
step one, determining the optimal transformation order p of the echo fast time according to the frequency modulation slope of the radar emission signalkCalculating the disturbed echo (p)k0) order two-dimensional reduced fractional order Fourier transform;
step (two) of sequentially taking echoes (p)k0) carrying out order two-dimensional reduced fractional order Fourier transform on each u-domain unit, distinguishing a real part and an imaginary part by using median absolute deviation robust statistics, respectively carrying out interference outlier detection to obtain two groups of outlier position labels, carrying out OR operation, and carrying out 0-degree outlier data according to the label positions;
step three, searching and obtaining the target acceleration a according to the maximum high-order moment criteriontThen according to atDetermining an echo slow time optimal transformation order paCalculating the echo (p) after eliminating the interferencek,pa) Order two-dimensional simplified fractional order Fourier transform;
and step four, obtaining the corresponding coordinates of the real target through peak value searching, and then estimating to obtain the initial distance and the radial speed of the target.
2. The dense decoy interference suppression method based on two-dimensional reduced fractional Fourier transform of claim 1, wherein the two-dimensional reduced fractional Fourier transform in the step (I) is specifically:
(1) fractional Fourier transform X of signal X (t)p(u) decomposition into a 4-step cascade:
Figure FDA0002759111290000011
wherein u corresponds to the u domain of fractional Fourier transform, alpha is a rotation angle, and h (u) exp (-i pi u)2tanα/2)，
Figure FDA0002759111290000012
For convolution symbols, g (u) exp (i π csc α u)2)。
(2) Omitting the first two terms, obtaining a one-dimensional reduced fractional Fourier transform expression of the signal x (t) as:
Figure FDA0002759111290000013
(3) expanding the one-dimensional reduced fractional Fourier transform of the signal x (t) into (p) of the two-dimensional signal x (s, t)1,p2) Order two-dimensional reduced fractional order fourier transform:
Figure FDA0002759111290000014
Figure FDA0002759111290000015
wherein the content of the first and second substances,
Figure FDA0002759111290000016
is a kernel function, u and v respectively correspond to a u domain and a v domain of two-dimensional reduced fractional order Fourier transform, alpha1＝p1π/2、α2＝p2And pi/2 is a two-dimensional rotation angle.
3. The method for suppressing interference of dense decoys based on two-dimensional reduced fractional fourier transform as recited in claim 1, wherein the method for detecting interference outliers in step (ii) specifically comprises:
(1) let echo (p)k0) taking 1 u-domain unit of the order two-dimensional reduced fractional Fourier transform as a sample set X, and calculating the absolute deviation MAD of the number of bits:
MAD＝b·med[|xi-med(X)|]
wherein b is correction factor, 1.4826 med [. cndot]Representing the median, xiAre sample values.
(2) Judging x according to the distance between the sample value and the sample concentration digitiWhether it is an interference outlier:
Figure FDA0002759111290000021
wherein th is the discrimination threshold.
4. The dense decoy interference suppression method based on two-dimensional reduced fractional Fourier transform according to claim 3, wherein the discrimination threshold specifically takes the following values: when the conservation is very conservative, 3 is taken, 2.5 is generally conservative, and 2 is not conservative.
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