CN116106836B - Anti-interference method for inverse synthetic aperture radar based on phase coding frequency modulation waveform - Google Patents
Anti-interference method for inverse synthetic aperture radar based on phase coding frequency modulation waveform Download PDFInfo
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- G—PHYSICS
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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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- 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
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/88—Radar or analogous systems specially adapted for specific applications
- G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
- G01S13/90—Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
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- G01S13/88—Radar or analogous systems specially adapted for specific applications
- G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
- G01S13/90—Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
- G01S13/9004—SAR image acquisition techniques
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- G—PHYSICS
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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
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/88—Radar or analogous systems specially adapted for specific applications
- G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
- G01S13/90—Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
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- G01S13/9064—Inverse SAR [ISAR]
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- 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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Abstract
The invention relates to a radar anti-interference signal processing technology, in particular to an anti-interference method of an inverse synthetic aperture radar based on a phase coding frequency modulation waveform; the invention provides a new ISAR anti-interference waveform design method based on the basic principle of an alternate projection algorithm, wherein the adopted waveform is a phase coding frequency modulation waveform, and the problems of high operation complexity and inconvenient physical realization of the designed waveform in the existing method are solved; the method is based on an AP algorithm in principle, has low operation complexity and is designed efficiently; the PCFM waveform reserves the design freedom of the random phase coding signal, has continuous phase characteristics and is convenient for actual physical realization; the designed waveform and filter have good ISRJ resistance.
Description
Technical Field
The invention relates to a radar anti-interference signal processing technology, in particular to an anti-interference method of an inverse synthetic aperture radar (Inverse Synthetic Aperture Radar, ISAR) based on a phase-Coded FM (frequency modulation) waveform.
Background
Radar plays a vital role in the military field as an all-day, all-weather detector. Along with the development of radar technology and radar signal processing theory, the radar has multiple functions such as ranging, speed measurement and imaging. The broadband radar can acquire high-resolution images of targets, and has important application value in the fields of space target monitoring, air defense, reverse conduction and the like. Inverse synthetic aperture radar (Inverse Synthetic Aperture Radar, ISAR) is a typical broadband radar that achieves radial high resolution by transmitting broadband signals, and azimuth high resolution by using the relative rotation of the target and radar.
However, there is a spear that must be shielded. Interference techniques for ISAR have also evolved rapidly. Intermittent sampling and forwarding Interference (ISRJ) is used as a novel coherent interference pattern, and a plurality of false targets can be formed in one pulse by alternately storing and forwarding intercepted radar signals in one radar pulse, so that the novel coherent interference pattern has the effects of suppressing and spoofing interference. And ISRJ is easy to engineer, and has high response speed and high interference efficiency, thereby bringing great challenges to ISAR work. At present, the method for resisting ISRJ mainly comprises a receiving end signal processing method and a transmitting end signal design method, and the two methods are not separated from further processing of signals at the receiving end in the later period, so that the complexity of the receiving end of the radar system is greatly increased. In addition, studies on waveform design for ISAR anti-forwarding interference are rarely found in publicly published literature and reports.
Based on the background, it is necessary to jointly use waveform resources and signal processing means, a more suitable waveform and more efficient implementation method is sought, a novel ISAR anti-interference waveform design method is provided, and the novel ISAR anti-interference waveform design method is popularized and applied to an ISAR practical system application, so that the development of ISAR anti-forwarding interference technology is promoted.
Disclosure of Invention
Aiming at the problems existing in the prior art, the invention provides a novel ISAR anti-interference waveform design method based on the basic principle of an alternating projection (Alternating Projections, AP) algorithm, wherein the adopted waveform is a phase-Coded frequency modulation (PCFM) waveform, and the problems of high operation complexity and inconvenient physical realization of the designed waveform in the existing method are solved; the method is based on an AP algorithm in principle, has low operation complexity and is designed efficiently; the PCFM waveform reserves the design freedom of the random phase coding signal, has continuous phase characteristics and is convenient for actual physical realization; the designed waveform and filter have good ISRJ resistance.
The invention adopts the technical scheme that: an anti-interference method for an inverse synthetic aperture radar based on a phase coding frequency modulation waveform comprises the following steps:
s1: building a model
The model comprises a PCFM waveform model, an ISRJ model and an optimization model, and is specifically as follows:
s1.1 construction of PCFM waveform model
Phi-shaped N×1 ＝[φ 1 ，φ 2 ，...，φ N ] T Representing the phase vector, [] T Represent the transpose, phi n ∈[-π，π]N=1, 2,. -%, N; then by the phase jump coefficient alpha n The set of components alpha N×1 ＝[α 1 ，α 2 ，…，α N ] T The elements in (a) are
Wherein, delta phi n ＝φ n -φ n-1 Indicating the phase difference phi 0 Representing the initial phase of the PCFM signal, ψ (·) represents the phase difference Δφ n To the phase jump coefficient alpha n Is that sgn (·) represents a sign function.
Thus, the PCFM signal s (t) may be expressed as
Wherein "×" denotes a convolution operation, g (τ) is a rectangular shaping filter; delta (τ) is an impulse function; t (T) c The duration of one phase jump coefficient is called chip. Where g (τ) requires: (1) at [0, T c ]Time support is provided to prevent overlap between different chips; (2) integration over a single chip as 1, i.e
The expression of the rectangular shaping filter g (τ) is generally
anti-ISRJ design based on PCFM waveform is to search proper phase jump coefficient alpha N×1 Achieving the final purpose.
In radar systems, the PCFM waveform may be generated by an arbitrary digital waveform generator, sampling frequency f s The higher the PCFM waveform that is generated, the more accurate. The total number of samples L can be expressed as NT c f s When f s ＝1/T c I.e. when only one point is sampled per chip, the PCFM signal becomes a phase encoded signal (PC), so f is generally taken for the PCFM signal s ＞1/T c The PCFM signal s (t) after being discretized can be expressed as
s＝[s 1 ，s 2 ，...，s l ，...，s L ] T ，L＝NT c f s (5)
Taking f for facilitating later processing s ＝k/T c ，k∈N + ，N + Represents a positive integer; then
Wherein each row shows k sampling points in one chip; phi (phi) n For each chip end phase value, since s is a discrete value for the PCFM signal, φ n Satisfy phi n -φ n-1 Pi, delta phi n And pi.ltoreq.then alpha is obtainable from formula (1) n ＝Ψ(Δφ n )＝Δφ n ＝φ n -φ n-1 。
Taking a normal matrix Q (N+1)×kN ：
ThenWherein (1)>
To this end, design alpha N×1 The problem of (2) is converted into design phi (N+1)×1 Is a problem of (a).
S1.2 construction of ISRJ model
When the radar transmits PCFM signal s (t), the jammer sampling signal is
s j (t)＝s(t)p(t) (8)
Where p (t) is a square wave pulse train.
The discrete form of the intermittent sample-and-repeat interference signal can be expressed as
s j ＝s⊙p (9)
Wherein s= [ s ] 1 ，s 2 ，...，s L ] T In discrete form, the PCFM signal s (t), simply referred to as the radar transmit signal; p= [ p ] 1 ，p 2 ，...，p L ] T Representing the discrete form of a square wave pulse train p (t), s j Sampling signal s for jammer j In discrete form of (t), by Hadamard product; p can be expressed as a vector containing only "1 (sample)", "0 (forward)", regardless of the jammer added gain and propagation loss.
S1.3 constructing an optimization model
Let the existing echo filtering result be r, according to the nature of Fourier transform
r＝F -1 (S e ⊙H) (10)
Wherein S is e H is respectively the echo s e 2L-1 point Fourier transform of non-matched filter h, F -1 Is an inverse fourier transform matrix.
From the viewpoint of ISRJ resistance, the amplitude of the current echo filtering result r is larger at the real target position, and the rest positions are very small, namely no obvious false target peak exists; from the viewpoint of effective detection of target signals, the aim is toThe filtering result at the target location should be as large as possible while the rest is as small as possible. Then, the filtering result of the echo is expectedIs that
Wherein, gamma (·) represents the filtering result from the existing echo filtering result r to the desired echo filtering resultIs the position of the target, r l Representing the filtering result at position l, w l Is a weighting coefficient, w is more than or equal to 0 l ＜1。
Then, the optimization model can be built as
Wherein, kappa is a tolerance value, generally taken as-10 dB; LPG is a gain loss of non-matched filtering process, and its expression is
The expected echo filtering result is projected to s and h based on the principle of an alternate projection algorithm, so that the optimization model is solved.
S2: a non-matched filter h is fixed, and radar emission signals s are optimized
S2.1, initializing a radar transmitting signal S and a non-matched filter h by using a random phase encoding signal;
s2.2 calculating echo filtering result under interference-free condition
In the absence of interference, the echo contains only the target signal, S e =s, S is the 2L-1 point fourier transform of the radar transmit signal S. Set its echo filter junctionFruit is r (1) From formula (10), r can be obtained (1) ＝F -1 (S⊙H)。
S2.3 calculating echo filtering result under interference condition
For intermittent sampling-forwarding interference, since the alternating of "sampling" and "forwarding" will cause the interference signal to always lag the target echo by one intermittent sampling time, the interference signal s is actually received jr Is that
Wherein T is jp For intermittent sampling pulse width.
The echo filtering result r in the presence of interference (2) Should be as follows
r (2) ＝F -1 ((S+S jr )⊙H) (15)
Wherein S is jr As interference signal s jr 2L-1 point fourier transform of (c).
S2.4 calculating the total echo filtering result r=r (1) +r (2) ；
S2.5 setting w l Value (e.g., w at target position Ω l =1, rest w l =0.5), the filtering result of the desired echo is calculated according to equation (11)
S2.6 calculationWherein F is a Fourier transform matrix, X e Means that the result of the desired echo filtering given a non-matched filter +.>The obtained echo signal frequency domain form;
s2.7 calculating x e ＝F -1 X e Wherein x is e Is X e The result of the inverse Fourier transform, namely the echo signal time domain form;
s2.8 is represented by x e X is obtained, x representing the obtained transmit signal.
According to the intermittent sampling-forwarding interference principle, the total echo contains the transmitted signal and the interference signal, but the interference signal is only the sampling (s j Time delay of =s++p)The transmit signal is easily separated therefrom. The specific implementation flow is as follows:
s2.8.1 obtaining intermittent sampling forwarding interference signal x j ：x e ⊙p＝2x j ；
S2.8.2 intermittently samples and forwards the interference signal x j Delay is carried out to obtain a forwarded interference signal x jr ：
S2.8.3 from echo x e Removing interference signal x jr Obtaining a zero-filled emission signal x': (x) e -x jr )＝2x’；
S2.8.4 the zero-padded transmit signal x' is restored to the original transmit signal x: x '(1:L) =x, i.e., x is the front L point of x'. The resulting transmit signal is denoted here by x and the radar transmit signal s is not used, since x is not constrained by the PCFM signal model and requires further processing.
S2.9 obtaining phi from x (N+1)×1 The method is characterized by comprising the following steps:
s2.9.1 take phi 0 ＝0；
S2.9.2 the phase value phi at the end of each chip is obtained in the case that each chip corresponds to k sampling points according to equation (6) n Thus, φ (2:N+1) =arg (x (k: k: end)), where φ (2:N+1) represents φ (N+1)×1 From the 2 nd value to the n+1th value; arg (x (k: k: end)) means that from the kth point, the phase value of x is taken every k points until the end of x. Note that at this time phi (N+1)×1 Is not fully satisfied with|φ n -φ n-1 Pi is less than or equal to pi, and needs to be converted into alpha first N×1 Then obtain phi satisfying phase constraint (N+1)×1 ；
S2.9.3 according to formula (1), from phi (N+1)×1 Obtaining alpha N×1 ；
S2.9.4 according to alpha n ＝Ψ(Δφ n )＝Δφ n ＝φ n -φ n-1 From alpha N×1 Obtain phi satisfying phase constraint (N+1)×1 。
S2.10 according toBy phi (N+1)×1 Generating s;
s2.11 updating S, and repeating S2.2-S2.10 for a plurality of times; the number of iterations Iter1 is typically taken as 20.
s3: optimizing a non-matched filter h according to the radar emission signal s obtained in s2
S3.1 calculating echo filtering result r under interference-free condition (1) ＝F -1 (S.sup.H), let r=r (1) ；
S3.2 setting w l Value (example target position Ω position w l =1, rest w l =0.5), the expectation is calculated according to equation (11)
S3.3 calculation
S3.4 calculation h=f -1 H, note that the length of the time domain form H of the non-matched filter is 2L-1, and the length actually required by us is L, so we only cut out the front L point;
s3.5, carrying out 2L-1 point Fourier transform on the front L point of the H to obtain updated H, and calculating an echo filtering result r under the condition of interference 2 )＝F -1 ((S+S jr ) H), let r=r (2) ；
S3.6 repeating S3.2-S3.4, namely further optimizing the unmatched filter h under the condition of interference;
s3.7 updating h, repeating S3.1-S3.6 for a plurality of times; the iteration number Iter2 is generally taken as 20.
S4: repeating S2.2-S2.11 and S3 for a plurality of times, namely repeatedly iterating Iter times, and respectively optimizing the radar emission signal S and the non-matched filter h until the termination condition is met.
The termination condition is
Wherein Iter represents the total iteration number, iter max Representing the maximum total iteration number, typically 10; a is that j For decoy amplitude, C is the maximum decoy amplitude tolerance value (relative to the true target amplitude), typically taking 0.25.
The invention has the following beneficial effects: based on the principle of an alternate projection algorithm and combining with the property of Fourier transformation, the method does not involve complex matrix operation, matrix inversion and the like in the whole iterative optimization process, and has low algorithm complexity and high operation efficiency; in addition, the (inverse) fourier transform can be further accelerated by means of an FFT algorithm; the designed PCFM waveform has continuous phase characteristics, and adjacent phase jumps are within +/-pi/2, so that the generation of a radar transmitter is facilitated; the designed waveform and filter can approximate to the expected filtering result, and a better ISRJ inhibition effect is achieved.
Drawings
FIG. 1 is a process flow diagram of the present invention;
fig. 2 is a graph of the real part of the signal: (a) designing a PCFM waveform; (b) designing a non-matched filter;
fig. 3 is a phase backward differential plot of signals: (a) transmitting a PCFM waveform; (b) a random phase encoded waveform;
fig. 4 is an echo filtering result: (a) non-matched filtering without interference; (b) non-matched filtering in the presence of interference; (c) matched filtering in the presence of interference;
FIG. 5 is a diagram of a radar transmit signal versus an jammer sample forwarding jammer signal;
fig. 6 is the result of echo processing of different transmit signals using different filters: (a) The transmitting signal is linear frequency modulation waveform, and echo processing is carried out by using a matched filter; (b) The transmitting signal is designed into PCFM waveform, and echo processing is carried out by using a non-matched filter;
fig. 7 is a graph showing the ratio of the target amplitude to peak sidelobes of the echo filtering results at various interference gains, and statistics of the signal-to-noise loss.
Detailed Description
The invention is further described below with reference to the accompanying drawings:
FIG. 1 is a general process flow of the present invention.
The invention relates to an anti-interference method for an inverse synthetic aperture radar based on a phase coding frequency modulation waveform, which comprises the following steps:
s1: models (PCFM waveform model, ISRJ model, optimization model) were constructed.
S2: the non-matched filter is fixed to optimize the radar transmit signal.
S3: the radar emission signal is fixed, and the non-matched filter is optimized.
S4: repeating S2.2-S2.10 and S3 until the termination condition is met.
The following experiments were conducted to examine the advantages of the present invention.
Fig. 2 (a) (b) shows a real plot of the designed PCFM waveform and the unmatched filter, respectively, both of which can be seen to satisfy the constant modulus constraint. Fig. 3 shows a phase backward differential plot of the designed PCFM waveform and the random phase encoded waveform. In comparison, most of the phase differences in fig. 3 (a) are distributed within ±pi/2, and few phase jumps are larger than pi, which is reasonable and correct, because the PCFM signal causes the signal phase change to take the "shortest" path, where the phase has already entered another 2 pi period, and the phase change remains essentially within pi/2. The phase transitions of the random phase encoded waveform of fig. 3 (b) are extremely sharp and irregular, with most phase transitions being greater than pi. Thus, the PCFM waveform is more convenient to physically implement. Fig. 4 shows the filtering results of the echoes in various cases. As can be seen from fig. 4 (a) (b), the PCFM waveform and the non-matched filter are designed to suppress ISRJ well while the target is detected. Fig. 4 (c) shows that under matched filtering, the addition of ISRJ makes a distinct decoy appear on the right side of the real target, which affects the detection of the real target.
Fig. 5 shows waveforms of the ISRJ signal and the target signal when the interference gain is 4. Fig. 6 (a) and (b) show the results of detection of the target using "lfm+matched filtering" and "pcfm+unmatched filtering", respectively, for the same scene setting. It can be seen that ISRJ brings great influence on the target detection of the former, and it is difficult to distinguish the real target; in the latter case, the amplitude of the decoys is effectively suppressed and the real targets are highlighted. It can be seen that the designed waveform and filter can effectively suppress ISRJ.
Figure 7 shows the performance of echo filtering at different interference gains. It can be seen that as the gain of the jammer increases, the overall trend of each performance index is reduced, the gain loss change of the non-matched filtering processing is slower, and the side lobe ratio of the echo peak is reduced faster, but the peak value can still be kept above 10dB when the interference gain is 10, so that the algorithm is quite stable.
Based on the principle of an alternate projection algorithm and combining with the property of Fourier transformation, the method does not involve complex matrix operation, matrix inversion and the like in the whole iterative optimization process, and has low algorithm complexity and high operation efficiency; the designed PCFM waveform has continuous phase characteristics, and is more convenient for a radar transmitter to generate; the designed waveform and filter can approximate to the expected filtering result, and a better ISRJ inhibition effect is achieved.
Claims (7)
1. An anti-interference method for an inverse synthetic aperture radar based on a phase coding frequency modulation waveform is characterized by comprising the following steps:
s1: building a model
The model comprises a PCFM waveform model, an ISRJ model and an optimization model, and is specifically as follows:
s1.1 construction of PCFM waveform model
Phi-shaped N×1 ＝[φ 1 ，φ 2 ，...，φ N ] T Representing the phase vector, [] T Represent the transpose, phi n ∈[-π，π]N=1, 2,. -%, N; then by the phase jump coefficient alpha n The set of components alpha N×1 ＝[α 1 ，α 2 ，…，α N ] T The elements in (a) are
Wherein, delta phi n ＝φ n -φ n-1 Indicating the phase difference phi 0 Representing the initial phase of the PCFM signal, ψ (·) represents the phase difference Δφ n To the phase jump coefficient alpha n Sgn (·) represents a sign function;
thus, the PCFM signal s (t) may be expressed as
Wherein "×" denotes a convolution operation, g (τ) is a rectangular shaping filter; delta (τ) is an impulse function; t (T) c The duration of one phase jump coefficient, called chip; where g (τ) requires: (1) at [0, T c ]Time support is provided to prevent overlap between different chips; (2) integration over a single chip as 1, i.e
anti-ISRJ design based on PCFM waveform is to search proper phase jump coefficient alpha N×1 Achieving the final purpose;
in radar systems, the PCFM waveform may be generated by an arbitrary digital waveform generator, sampling frequency f s The higher the PCFM waveform generated, the more accurate; the total number of samples L can be expressed as NT c f s When f s ＝1/T c I.e. only one sample per chipAt a single point, the PCFM signal becomes a phase encoded signal, so f is taken for the PCFM signal s ＞1/T c The PCFM signal s (t) is expressed as after being discretized
s＝[s 1 ，s 2 ，...，s l ，...，s L ] T ，L＝NT c f s (4)
Taking f for facilitating later processing s ＝k/T c ，k∈N + ，N + Represents a positive integer; then
Wherein each row shows k sampling points in one chip; phi (phi) n For each chip end phase value, since s is a discrete value for the PCFM signal, φ n Satisfy phi n -φ n-1 Pi, delta phi n And pi.ltoreq.then alpha is obtainable from formula (1) n ＝Ψ(Δφ n )＝Δφ n ＝φ n -φ n-1 ；
Taking a normal matrix Q (N+1)×kN ：
ThenWherein (1)>
To this end, design alpha N×1 The problem of (2) is converted into design phi (N+1)×1 Is a problem of (2);
s1.2 construction of ISRJ model
When the radar transmits PCFM signal s (t), the jammer sampling signal is
s j (t)＝s(t)p(t) (7)
Wherein p (t) is a square wave pulse train;
the discrete form of the intermittent sample-and-repeat interference signal can be expressed as
s j ＝s⊙p (8)
Wherein s= [ s ] 1 ，s 2 ，...，s L ] T In discrete form, the PCFM signal s (t), simply referred to as the radar transmit signal; p= [ p ] 1 ，p 2 ，...，p L ] T Representing the discrete form of a square wave pulse train p (t), s j Sampling signal s for jammer j In discrete form of (t), by Hadamard product; p can be expressed as a vector containing only "1", "0", without considering the jammer added gain and propagation loss;
s1.3 constructing an optimization model
Let the existing echo filtering result be r, according to the nature of Fourier transform
r＝F -1 (S e ⊙H) (9)
Wherein S is e H is respectively the echo s e 2L-1 point Fourier transform of non-matched filter h, F -1 Is an inverse fourier transform matrix;
filtering results of desired echoIs that
Wherein, gamma (·) represents the filtering result from the existing echo filtering result r to the desired echo filtering resultIs the position of the target, r l Representing the filtering result at position l, w l Is a weighting coefficient;
then, the optimization model can be built as
Wherein, κ is a tolerance value; LPG is a gain loss of non-matched filtering process, and its expression is
The expected echo filtering result is projected to s and h based on the principle of an alternate projection algorithm, so that the solution of an optimization model is realized;
s2: a non-matched filter h is fixed, and radar emission signals s are optimized
S2.1, initializing a radar transmitting signal S and a non-matched filter h by using a random phase encoding signal;
s2.2 calculating echo filtering result under interference-free condition
In the absence of interference, the echo contains only the target signal, S e S, S is the 2L-1 point fourier transform of the radar transmit signal S; let the echo filtering result be r (1) From formula (9), r can be obtained (1) ＝F -1 (S⊙H)；
S2.3 calculating echo filtering result under interference condition
For intermittent sampling-forwarding interference, since the alternating of "sampling" and "forwarding" will cause the interference signal to always lag the target echo by one intermittent sampling time, the interference signal s is actually received jr Is that
Wherein T is jp The pulse width is intermittently sampled;
the echo filtering result r in the presence of interference (2) Should be r (2) ＝F -1 ((S+S jr )⊙H) (14)
Wherein S is jr As interference signal s jr 2L-1 point fourier transform of (b);
s2.4 calculating the total echo filtering result r=r (1) +r (2) ；
S2.5 setting w l A value obtained by calculating a filtering result of the desired echo according to the formula (10)
S2.6 calculationWherein F is a Fourier transform matrix, X e Means that the result of the desired echo filtering given a non-matched filter +.>The obtained echo signal frequency domain form;
s2.7 calculating x e ＝F -1 X e Wherein x is e Is X e The result of the inverse Fourier transform, namely the echo signal time domain form;
s2.8 is represented by x e Obtaining x, wherein x represents the obtained transmission signal;
according to the intermittent sampling forwarding interference principle, the total echo contains a transmitting signal and an interference signal, but the interference signal is only the time delay added to the sampling of the transmitting signal, so that the transmitting signal is easy to separate from the interference signal; the specific implementation flow is as follows:
s2.8.1 obtaining intermittent sampling forwarding interference signal x j ：x e ⊙p＝2x j ；
S2.8.2 intermittently samples and forwards the interference signal x j Delay is carried out to obtain a forwarded interference signal x jr ：
S2.8.3 from echo x e Removing interference signal x jr Obtaining the complementThe transmitted signal x' after zero: (x) e -x jr )＝2x’；
S2.8.4 the zero-padded transmit signal x' is restored to the original transmit signal x: x '(1:L) =x, i.e., x is the front L point of x'; the resulting transmit signal is denoted here by x and the radar transmit signal s is not used, since x is not constrained by the PCFM signal model and requires further processing;
s2.9 obtaining phi from x (N+1)×1 The method is characterized by comprising the following steps:
s2.9.1 take phi 0 ＝0；
S2.9.2 the phase value phi at the end of each chip is obtained in the case of k sampling points per chip according to equation (5) n Thus, φ (2:N+1) =arg (x (k: k: end)), where φ (2:N+1) represents φ (N+1)×1 From the 2 nd value to the n+1th value; arg (x (k: k: end)) means that from the kth point, the phase value of x is taken every k points until the end of x; phi at this time (N+1)×1 Is not fully satisfied with |phi n -φ n-1 Pi is less than or equal to pi, and needs to be converted into alpha first N×1 Then obtain phi satisfying phase constraint (N+1)×1 ；
S2.9.3 according to formula (1), from phi (N+1)×1 Obtaining alpha N×1 ；
S2.9.4 according to alpha n ＝Ψ(Δφ n )＝Δφ n ＝φ n -φ n-1 From alpha N×1 Obtain phi satisfying phase constraint (N+1)×1 ；
S2.10 according toBy phi (N+1)×1 Generating s;
s2.11 updating S, and repeating S2.2-S2.10 for a plurality of times;
s3: optimizing a non-matched filter h according to the radar emission signal S obtained in S2
S3.1 calculating echo filtering result r under interference-free condition (1) ＝F -1 (S.sup.H), let r=r (1) ；
S3.2 setting w l Calculating a desired value according to formula (10)
S3.3 calculation
S3.4 calculation h=f -1 H, note that the length of the time domain form H of the non-matched filter is 2L-1, and the length actually required by us is L, so we only cut out the front L point;
s3.5, carrying out 2L-1 point Fourier transform on the front L point of the H to obtain updated H, and calculating an echo filtering result r under the condition of interference (2) ＝F -1 ((S+S jr ) H), let r=r (2) ；
S3.6 repeating S3.2-S3.4, namely further optimizing the unmatched filter h under the condition of interference;
s3.7 updating h, repeating S3.1-S3.6 for a plurality of times;
s4: repeating S2.2-S2.11 and S3 for a plurality of times, namely repeatedly iterating Iter times, respectively optimizing the radar emission signal S and the non-matched filter h until the termination condition is met;
the termination condition is
Wherein Iter represents the total iteration number, iter max Representing the maximum total iteration number; a is that j And C is the maximum false target amplitude tolerance value.
2. A method of reverse synthetic aperture radar anti-interference based on phase encoded frequency modulated waveforms according to claim 1, wherein: in S1.1, the rectangular shaping filter g (τ) has the expression of
3. A method of reverse synthetic aperture radar anti-interference based on phase encoded frequency modulated waveforms according to claim 1, wherein: in S1.3, the weight coefficient is 0.ltoreq.w l ＜1。
4. A method of reverse synthetic aperture radar anti-interference based on phase encoded frequency modulated waveforms according to claim 1, wherein: in S1.3, the tolerance value takes 10dB.
5. A method of reverse synthetic aperture radar anti-interference based on phase encoded frequency modulated waveforms according to claim 1, wherein: in S2.11, the number of iterations is taken to be 20.
6. A method of reverse synthetic aperture radar anti-interference based on phase encoded frequency modulated waveforms according to claim 1, wherein: in S3.7, the number of iterations is taken to be 20.
7. A method of reverse synthetic aperture radar anti-interference based on phase encoded frequency modulated waveforms according to claim 1, wherein: s4, taking 10 maximum total iteration times; the maximum spurious target amplitude tolerance value takes 0.25.
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