CN107526074B - Distance and speed two-dimensional high-resolution processing method for sparse frequency hopping signal - Google Patents
Distance and speed two-dimensional high-resolution processing method for sparse frequency hopping signal Download PDFInfo
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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
- 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
- G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
- G01S13/06—Systems determining position data of a target
- G01S13/42—Simultaneous measurement of distance and other co-ordinates
- G01S13/422—Simultaneous measurement of distance and other co-ordinates sequential lobing, e.g. conical scan
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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
- 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
- G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
- G01S13/50—Systems of measurement based on relative movement of target
- G01S13/58—Velocity or trajectory determination systems; Sense-of-movement determination systems
Abstract
The invention discloses a distance and speed two-dimensional high-resolution processing method of sparse frequency hopping signals, which comprises the following processes of: randomly extracting frequency hopping codes from the frequency set to form a transmitting waveform of a sparse frequency hopping signal; performing initial speed compensation on the echo sampling baseband signal; aligning the speed dimension; cross term compensation; performing distance dimension iterative interpolation sidelobe suppression high-resolution processing; carrying out inverse Fourier transform processing on the velocity dimension; doppler iterative interpolation high resolution processing. The invention has the advantages of being suitable for the problem of distance sidelobe suppression caused by random frequency hopping or discontinuous frequency spectrum in the two-dimensional processing of the distance and the speed of the radar signal and improving the speed resolution.
Description
Technical Field
The invention relates to the technical field of radar signal processing, in particular to a distance and speed two-dimensional high-resolution processing method of a sparse frequency hopping signal.
Background
The classic synthesis broadband technology waveform form such as a step frequency pulse signal or a Costas coding signal has the problems of speed blurring and the like under high relative speed. In long distance, in order to improve the energy of the echo signal, the pulse width of the transmitted signal is required to be wide, the pulse interval time between sub-pulses is required to be long, the step frequency interval of the signal is low at the moment, the speed processing performed by sampling at the same frequency point is seriously blurred, and the requirement of high data rate is not met.
The sparse frequency hopping signal has the advantages of a frequency stepping signal, has an ideal pin-shaped fuzzy function, and has the characteristics of excellent low interception probability, electromagnetic compatibility, radio frequency interference resistance and the like. Meanwhile, the sparse frequency hopping signal forms a transmitting signal by extracting part of frequency points in available frequency points, so that the number of synthesized pulses is reduced on the premise of ensuring the bandwidth, the non-fuzzy speed range is enlarged when multi-frame joint speed processing is adopted, and Doppler aliasing on each scattering point of a target is eliminated; and the problem of high resolution is solved in the speed dimension, so that the imaging resolution and the signal data rate are greatly improved.
However, the sparse step frequency signal has a non-continuous and randomly hopped signal frequency point, so that the resolution of general matched filtering processing is not high, and the distance side lobe is high; in addition, a reduction in waveform cycle time results in a reduction in coherent processing intervals, and thus a reduction in velocity resolution. Therefore, for the problem of overhigh distance side lobe caused by frequency point randomness, the design of low side lobe waveform can be carried out at the source through a waveform design method (for details, the design and the processing of full-random frequency hopping pulse signals, Zhao De Hua and the like, system engineering and electronic technology, 2014, 3 rd); a self-Adaptive matching Compression method for distance side lobes (see the literature, Adaptive pulse Compression for stepped frequency dependent-wave Radar, b.zhao et. al. ieee CIE International Conference on Radar, 2011); a compressed sensing method (see in detail: research on application of sparse signal processing in radar detection and imaging, jinying hui, doctor paper of the university of sienna electronics, 2012) can also be utilized. However, these methods have inherent disadvantages, such as limited sidelobe suppression performance, lattice mismatch, etc., and also limit the application of these methods in two-dimensional processing.
Disclosure of Invention
The sparse frequency hopping signal is that a part of frequency points are randomly extracted on the basis of a step frequency signal to serve as a transmitting signal, broadband synthesis is realized by fewer pulses, the period time of a high-resolution waveform can be reduced, the number of transmitting pulses is reduced, the number of the synthesized pulses is reduced on the premise of ensuring the bandwidth, the unambiguous speed range is enlarged when multi-frame joint speed processing is adopted, Doppler aliasing on each scattering point of a target is eliminated, and meanwhile the problem of short-distance rapid high-resolution detection is solved.
However, the sparse step frequency signal has the problems of high distance side lobe due to discontinuous and random jump of signal frequency points, and meanwhile, the speed resolution is reduced under the condition of the same waveform period number due to the reduction of the waveform period time.
The invention aims to provide a distance and speed two-dimensional high-resolution processing method of a sparse frequency hopping signal, which carries out iterative interpolation on the distance and speed dimensional resolution of the sparse frequency hopping signal and carries out distance and speed two-dimensional low-sidelobe high-resolution processing, thereby achieving the purpose of solving the problems.
In order to achieve the above purpose, the invention is realized by the following technical scheme:
a distance and speed two-dimensional high-resolution processing method of sparse frequency hopping signals comprises the following processes:
and step S1, randomly extracting frequency hopping codes from the frequency set to form a transmitting waveform of the sparse frequency hopping signal.
And step S2, performing initial speed compensation on the echo sampling baseband signal.
And step S3, aligning the speed dimension.
And step S4, cross term compensation.
And step S5, distance dimension iterative interpolation sidelobe suppression high-resolution processing.
Step S6, a velocity dimension inverse fourier transform process.
And step S7, Doppler iterative interpolation high-resolution processing.
Preferably, the step S1 includes the following processes:
randomly extracting H (N > H) frequency points from a frequency set {0, delta f, …, (N-1) delta f } to be used as the step quantity of the transmitted signal; when the echo signal is sampled once in each sub-pulse after being mixed, the normalized dispersion of the H (0, 1, …, H-1) th pulse sample of the M (M is 0,1, …, M-1) th waveform period of the target echo signal with the distance R and the velocity v is expressed as
In the formula (f)cIs the carrier frequency, fh=chΔf,chE {0,1, …, (N-1) } is frequency hopping coding; j is defined as2-1; c is the speed of light; t isrIs the pulse repetition interval.
Preferably, said stepS2 includes the following processes: assume an initial velocity v0Then the velocity compensation term is
After the initial velocity compensation is
Wherein Δ v ═ v0-v represents the point target velocity compensation residual.
Preferably, the step S3 includes the following processes:
at carrier frequency fcThe corresponding Doppler range is used as a reference for alignment, the velocity dimension scale alignment is realized through velocity dimension discrete Fourier transform processing,
in the formula of gammah=chΔf/fc(ii) a l (l ═ 0,1, …, M-1) is a doppler dimensional sequence.
Preferably, the step S4 includes the following processes:
after the speed dimension is aligned, the corresponding speed dimension resolution of each distance unit is the same, and the compensation is expressed as the compensation of the cross term through direct phase compensation
s2(l,h)=s1(l,h)exp(j2π(1+γh)lh/(MH))。
Preferably, the step S5 includes the following processes: constructing a regularization function according to the target distance spectrum model, and obtaining a high-resolution range profile with low side lobes by adopting an iterative interpolation method;
for the two-dimensional data after cross term compensation, the sampling sequence vector of each waveform period is s ═ s1,s2,…,sH]TThe corresponding synthesized low side lobe range image is x ═ x1,x2,…,xN]TSubject to variance ofIs expressed as the influence of white Gaussian noise n
s=Ax+n
Wherein the associated DFT matrix A is represented as
Wherein Δ r ═ c/(2N Δ f) is the distance resolution; fh=[fc+c0Δf,fc+c1Δf,…,fc+cM-1Δf]T;
Regularizing an objective function of
Where ln represents a logarithmic function based on e, H represents a conjugate transpose,representing the signal magnitude spectral variance; x is the number ofnAn nth point representing the sought range image, subject to a cauchy distribution with trailing properties;
the regularization solution is obtained by minimizing a cost function, denoted as
In the formula, regularization parameterQ is a diagonal matrix of NxN, and the elements on the diagonal are
Preferably, said solving for x by an iterative method comprises the following process:
step S5.1, initialize x(0)=AHs, wherein x(0)The matching receiving result is obtained;
Step S5.3, solving x by using the following formula(k):
b(k-1)=(λIN+AQ(k-1)AH)-1s
x(k)=Q(k-1)AHb(k-1)
In the formula INAn identity matrix of NxN is represented, and k represents the number of iterations;
s5.4, judging that iteration is terminated, and if the following criterion is met, turning to the step S5.2 if the iteration is terminated;
|J(x(k))-J(x(k-1))|<
in the formula, the value is a constant close to 0.
Preferably, the step S6 includes the following processes:
in the process of aligning the speed dimension, the slow time dimension is converted into a frequency domain, and the frequency domain is subjected to inverse Fourier transform to a time domain and then subjected to Doppler high-resolution processing.
Preferably, the step S7 includes the following processes:
the speed dimension inhibits sinc sidelobes caused by finite time sampling through iterative interpolation processing, so that high speed resolution is obtained;
doppler high resolution processing is achieved by using the same iterative interpolation method as the range high resolution processing, where it matches the matrix AvThe element in (A) is
In the formula, K is the number of units subjected to interpolation processing, namely the speed resolution is improved by K/M times;
will matrix AvAnd (4) performing iterative processing on the matching matrix A instead of the distance high-resolution iterative interpolation processing to finish the Doppler high-resolution processing.
Compared with the prior art, the invention has the following advantages:
the invention discloses a technology for realizing broadband processing by using less pulses through distance and speed two-dimensional high-resolution processing of sparse frequency hopping signals, and low-side-lobe distance and speed two-dimensional high-resolution distribution is obtained through the same iterative interpolation processing process in the distance and speed dimensions. The invention can solve the contradiction between the long-time property of broadband synthesis and Doppler ambiguity in the high-resolution detection process, and eliminates Doppler aliasing on each scattering point. Meanwhile, the processing problem of the short waveform period with large bandwidth for high-resolution detection of a high-speed target by a short distance can be solved.
Drawings
FIG. 1 is a flow chart of a distance and speed two-dimensional high resolution processing method of sparse frequency hopping signals according to the present invention;
FIG. 2 is a distance and velocity two-dimensional distribution of conventional matching correlation processing of a distance and velocity two-dimensional high resolution processing method of a sparse frequency hopping signal of the present invention;
FIG. 3 is a two-dimensional distribution of distance dimension high resolution processing of a distance and speed two-dimensional high resolution processing method of a sparse frequency hopping signal of the present invention;
fig. 4 is a two-dimensional distribution of distance and speed two-dimensional high-resolution processing of a distance and speed two-dimensional high-resolution processing method of a sparse frequency hopping signal according to the present invention.
Detailed Description
The present invention will now be further described by way of the following detailed description of a preferred embodiment thereof, taken in conjunction with the accompanying drawings.
As shown in fig. 1, the distance and speed two-dimensional high resolution processing method of sparse frequency hopping signal of the present invention comprises the following processes:
Assuming that a waveform period of the sparse frequency hopping signal is composed of H pulses, the step size of each pulse is selected from the frequency set {0, Δ f, …, (N-1) Δ f } (N>H) In (H) th (H is 0,1, …, H-1) pulse frequency is Fh=fc+fhWherein f iscIs the carrier frequency, fh=chΔf,chE {0,1, …, (N-1) } is the frequency hopping code. And the sparse frequency hopping code is the same for each waveform period.
When the echo signal is sampled once for each sub-pulse after mixing, the normalized dispersion of the h-th pulse sample of the M-th (M is 0,1, …, M-1) waveform period of the target echo signal with the distance R and the velocity v is expressed as
Wherein j is defined as j2-1; c is the speed of light; t isrIs the pulse repetition interval.
And 2, compensating the initial speed.
Assume an initial velocity v0Then the velocity compensation term is
After the initial velocity compensation is
Wherein Δ v ═ v0-v represents the point target velocity compensation residual. The 1 st exponential term is a constant term, the 2 nd exponential term is a distance term in a frame, the 3 rd exponential term is a cross term caused by compensation errors, and the 4 th exponential term is a Doppler term of compensation errors between frames.
And 3, aligning the speed dimension.
In order to effectively perform two-dimensional joint processing, the doppler term needs to be processed first, because of different frequency pointsThe upper carrier frequency is different, and the corresponding speed dimension is different. At carrier frequency fcThe corresponding Doppler range is used as a reference for alignment, and the invention realizes the speed dimension scale alignment through the speed dimension Discrete Fourier Transform (DFT) processing, which is expressed as
In the formula of gammah=chΔf/fc(ii) a l (l ═ 0,1, …, M-1) is a doppler dimensional sequence.
And 4, cross term compensation.
After the speed dimension is aligned, the corresponding speed dimension resolution of each distance unit is the same, and the 3 rd cross term is compensated through direct phase compensation, namely
s2(l,h)=s1(l,h)exp(j2π(1+γh)lh/(MH)) (5)
And 5, distance dimension high-resolution processing.
And constructing a regularization function according to the target distance spectrum model, and obtaining a high-resolution range image with low side lobe by adopting an iterative interpolation method.
For the two-dimensional data after cross term compensation, the sampling sequence vector of each waveform period is s ═ s1,s2,…,sH]TThe corresponding synthetic distance image is x ═ x1,x2,…,xN]TSubject to variance ofCan be expressed as the influence of white Gaussian noise n
s=Ax+n (6)
In the formula, the correlation matrix A is expressed as
Wherein Δ r ═ c/(2N Δ f) is the distance resolution; fh=[fc+c0Δf,fc+c1Δf,…,fc+cH-1Δf]T。
To obtain a low side lobe range profile x, xnAn nth point representing the sought range image, subject to a cauchy distribution with trailing properties; simultaneously, under the influence of Gaussian white noise, a regularized target function is obtained and expressed as
Where ln represents a logarithmic function based on e, H represents the conjugate transpose,representing the signal magnitude spectral variance. The regularization solution is obtained by minimizing a cost function, denoted as
x=(λQ-1+AHA)-1AHs (9)
In the formula, the regularization parameter Q is a diagonal matrix of NxN, and the elements on the diagonal are
Due to the non-linearity of the diagonal matrix Q and xnRegarding, therefore, x needs to be solved by an iterative method, which includes the following steps:
(ii) constructing and initializing a correlation discrete Fourier transform matrix, i.e. x(0)=AHs, wherein x(0)The matching receiving result is obtained;
Solving for x by using the following formula(k+1):
b(k-1)=(λIN+AQ(k-1)AH)-1s (10)
x(k)=Q(k-1)AHb(k-1) (11)
In the formula INAn identity matrix of N × N is represented, and k represents the number of iterations.
Judging iteration termination, when the following criterion is met, if not, turning to the second step.
|J(x(k))-J(x(k-1))|< (12)
Wherein the value is a constant close to 0.
In the solving, regularizing parametersIs the ratio of the noise variance to the signal amplitude spectral variance, the noise varianceThe singular value decomposition can be performed through a covariance matrix of the observation data. WhileSince unknown, this embodiment, at initialization, causesThen, in each iteration process, the variance of the amplitude spectrumReplaced by the results from the previous iteration.
The Iterative Interpolation (II) process to obtain the distance dimension high resolution process is expressed as follows:
and step 6, carrying out IFFT processing on the speed dimension.
In the process of aligning the speed dimension, the slow time dimension is converted into the frequency domain, and the frequency domain is subjected to inverse Fourier transform (IFFT) to the time domain and then subjected to Doppler high resolution processing, namely
s3(m,n)=IFFT{sII(l,n)} (14)
And 7, Doppler high-resolution processing.
And the velocity dimension suppresses sinc side lobes caused by finite time sampling through iterative interpolation processing, so that high-resolution velocity is obtained.
In this embodiment, the doppler high resolution processing uses the same iterative interpolation method as the range high resolution processing, and the doppler high resolution processing is different in the matching correlation matrix, and the matching matrix avThe element in (A) is
Where K is the number of units subjected to interpolation processing, that is, the speed resolution is improved by K/M times, and in the present invention, K is 4M.
Will matrix AvThe matching matrix A for replacing the distance high-resolution iterative interpolation processing is subjected to iterative processing, and the Doppler high-resolution processing can be realized. The distance in the embodiment is the same as the doppler high resolution processing process, namely only the relevant discrete fourier transform moment needs to be transformed, but the distance is different in nature, and the distance iterative interpolation high resolution processing is estimation recovery of missing frequency points, so that low side lobe distance high resolution processing is obtained; and the Doppler high-resolution processing is to suppress sinc side lobes caused by finite time sampling and simultaneously carry out frequency spectrum refinement, thereby obtaining speed high-resolution processing.
In this embodiment, the parameters of the simulated radar echo signal are set as follows: the carrier frequency is 35GHz, the unit step amount Δ f is 5MHz, the number of selectable hopping points in the frequency set is 512, that is, {0, Δ f, …,511 Δ f }, and the frequency set randomly extracts H, which is 64 frequency points, to form a sparse frequency hopping transmission signal. The number of waveform cycles M in the slow time dimension is 64, the number of points after speed iterative interpolation is 256, the pulse width is 0.1 μ s, and the pulse repetition period is 2 μ s. Then 64 pulse transmitting signals are realized through distance high resolution processing to obtain a synthetic broadband of equivalent 512 pulses, namely, the distance resolution is that Δ r is c/(2 × 512 × Δ f) is 0.0586 m; and the speed resolution is improved by 4 times.
Setting 3 point targets, wherein the parameters are as follows: t is1(100m,1010m/s),T2(110m,1010mS) and T3(110m,1020m/s), and the scattering cross-sectional areas of the targets are all 1.
Fig. 2 shows a distance and speed two-dimensional result obtained by conventional processing after cross term compensation, i.e., matching correlation processing, and it can be seen that under the radar parameter, the correlation processing result has a higher distance side lobe and a lower speed resolution. Fig. 3 shows the distance dimension iterative interpolation high resolution processing result of the present invention, and it can be seen that the distance sidelobe suppression is significant. The distance and speed two-dimensional high-resolution processing result is shown in fig. 4, and the result shows that the distance and speed side lobe is reduced after distance and speed two-dimensional iterative interpolation processing, and the resolution of the speed dimension is improved.
While the present invention has been described in detail with reference to the preferred embodiments, it should be understood that the above description should not be taken as limiting the invention. Various modifications and alterations to this invention will become apparent to those skilled in the art upon reading the foregoing description. Accordingly, the scope of the invention should be determined from the following claims.
Claims (8)
1. A distance and speed two-dimensional high-resolution processing method of sparse frequency hopping signals is characterized by comprising the following processes:
step S1, randomly extracting frequency hopping codes from the frequency set to form a transmitting waveform of a sparse frequency hopping signal;
step S2, performing initial speed compensation on the echo sampling baseband signal;
step S3, aligning the speed dimension;
the step S3 includes the following processes:
at carrier frequency fcThe corresponding Doppler range is used as a reference for alignment, the velocity dimension scale alignment is realized through velocity dimension discrete Fourier transform processing,
in the formula of gammah=chΔf/fc;l(l=0,1, …, M-1) is a doppler dimension sequence;
step S4, cross term compensation;
step S5, distance dimension iteration interpolation sidelobe suppression high resolution processing;
step S6, speed dimension inverse Fourier transform processing;
and step S7, Doppler iterative interpolation high-resolution processing.
2. The distance and speed two-dimensional high resolution processing method of sparse frequency hopping signal according to claim 1, wherein said step S1 comprises the following procedures:
randomly extracting H (N > H) frequency points from a frequency set {0, delta f, …, (N-1) delta f } to be used as the step quantity of the transmitted signal; when the echo signal is sampled once in each sub-pulse after being mixed, the normalized dispersion of the H (0, 1, …, H-1) th pulse sample of the M (M is 0,1, …, M-1) th waveform period of the target echo signal with the distance R and the velocity v is expressed as
In the formula (f)cIs the carrier frequency, fh=chΔf,chE {0,1, …, (N-1) } is frequency hopping coding; j is defined as2-1; c is the speed of light; t isrIs the pulse repetition interval.
3. The distance and speed two-dimensional high resolution processing method of sparse frequency hopping signal according to claim 2, wherein said step S2 comprises the following procedures:
assume an initial velocity v0Then the velocity compensation term is
After the initial velocity compensation is
Wherein Δ v ═ v0-v represents the point target velocity compensation residual.
4. The distance and speed two-dimensional high resolution processing method of sparse frequency hopping signal according to claim 3, wherein said step S4 comprises the following procedures:
after the speed dimension is aligned, the corresponding speed dimension resolution of each distance unit is the same, and the compensation is expressed as the compensation of the cross term through direct phase compensation
s2(l,h)=s1(l,h)exp(j2π(1+γh)lh/(MH))。
5. The method for distance and speed two-dimensional high resolution processing of sparse frequency hopping signal according to claim 4, wherein said step S5 comprises the following procedures:
constructing a regularization function according to the target distance spectrum model, and obtaining a high-resolution range profile with low side lobes by adopting an iterative interpolation method;
for the two-dimensional data after cross term compensation, the sampling sequence vector of each waveform period is s ═ s1,s2,…,sH]TThe corresponding synthesized low side lobe range image is x ═ x1,x2,…,xN]TSubject to variance ofIs expressed as the influence of white Gaussian noise n
s=Ax+n
Wherein the associated DFT matrix A is represented as
Wherein Δ r ═ c/(2N Δ f) is the distance resolution; fh=[fc+c0Δf,fc+c1Δf,…,fc+cM-1Δf]T;
Regularizing an objective function of
Where ln represents a logarithmic function based on e, H represents a conjugate transpose,representing the signal magnitude spectral variance; x is the number ofnAn nth point representing the sought range image, subject to a cauchy distribution with trailing properties;
the regularization solution is obtained by minimizing a cost function, denoted as
6. The method according to claim 5, wherein said solving for x by an iterative method comprises the following steps:
step S5.1, initialize x(0)=AHs, wherein x(0)The matching receiving result is obtained;
Step S5.3, solving x by using the following formula(k):
b(k-1)=(λIN+AQ(k-1)AH)-1s
x(k)=Q(k-1)AHb(k-1)
In the formula INAn identity matrix of NxN is represented, and k represents the number of iterations;
s5.4, judging that iteration is terminated, and if the following criterion is met, turning to the step S5.2 if the iteration is terminated;
|J(x(k))-J(x(k-1))|<
in the formula, the value is a constant close to 0.
7. The method of claim 6, wherein the step S6 comprises the following steps:
in the process of aligning the speed dimension, the slow time dimension is converted into a frequency domain, and the frequency domain is subjected to inverse Fourier transform to a time domain and then subjected to Doppler high-resolution processing.
8. The method of claim 7, wherein the step S7 comprises the following steps:
the velocity dimension suppresses the sine side lobe caused by finite time sampling through iterative interpolation processing, thereby obtaining high-resolution velocity;
doppler high resolution processing is achieved by using the same iterative interpolation method as the range high resolution processing, where it matches the matrix AvThe element in (A) is
In the formula, K is the number of units subjected to interpolation processing, namely the speed resolution is improved by K/M times;
will be described inMatrix AvAnd (4) performing iterative processing on the matching matrix A instead of the distance high-resolution iterative interpolation processing to finish the Doppler high-resolution processing.
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