CN114594425B - Short-time pulse train waveform design method for resisting clutter interference - Google Patents

Short-time pulse train waveform design method for resisting clutter interference Download PDF

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CN114594425B
CN114594425B CN202210246873.5A CN202210246873A CN114594425B CN 114594425 B CN114594425 B CN 114594425B CN 202210246873 A CN202210246873 A CN 202210246873A CN 114594425 B CN114594425 B CN 114594425B
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short
pulse train
time pulse
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CN114594425A (en
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易青颖
张翠
黄钰林
张寅�
裴季方
霍伟博
杨建宇
张永超
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Sichuan Jianweizhishu Technology Co ltd
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University of Electronic Science and Technology of China
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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
    • G01S7/023—Interference mitigation, e.g. reducing or avoiding non-intentional interference with other HF-transmitters, base station transmitters for mobile communication or other radar systems, e.g. using electro-magnetic interference [EMI] reduction techniques
    • 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
    • G01S7/40—Means for monitoring or calibrating
    • G01S7/4052—Means for monitoring or calibrating by simulation of echoes
    • 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
    • G01S7/414—Discriminating targets with respect to background clutter
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02A—TECHNOLOGIES FOR ADAPTATION TO CLIMATE CHANGE
    • Y02A90/00—Technologies having an indirect contribution to adaptation to climate change
    • Y02A90/10—Information and communication technologies [ICT] supporting adaptation to climate change, e.g. for weather forecasting or climate simulation

Abstract

The invention discloses a method for designing a short-time pulse train waveform with clutter interference resistance, which utilizes target priori information to construct a maximized signal-to-noise ratio objective function, and solves an optimal emission waveform and an optimal matched filter based on a Lagrange multiplier method; combining the waveform emission rule of the short-time pulse train to construct a combined objective function of waveform power spectrum approximation and autocorrelation integral sidelobe level suppression; and iterating in a mode searching mode to obtain the optimal short-time pulse train waveform. The short-time pulse train waveform designed by the invention has the capability of resisting interception of an jammer, can inhibit interference of environmental clutter on target detection, can avoid interference forwarded after interception by an adversary jammer, realizes simultaneous inhibition of the environmental clutter and the jammer interference, and improves the target detection capability under clutter environment.

Description

Short-time pulse train waveform design method for resisting clutter interference
Technical Field
The invention belongs to the technical field of radar detection, and particularly relates to target detection suitable for radar in a clutter environment.
Background
The radar transmit waveform controls the range resolution, doppler resolution, peak-to-side lobe ratio, and energy distribution of the system, which determines how the transmit waveform plays a critical role in the radar system. Therefore, radar transmit waveform design is an effective way to improve performance. The short-time pulse train signal has the characteristics of narrow pulse width and high peak power, has anti-interception capability, can effectively inhibit relevant interference forwarded by enemy, and has great potential for detecting high-probability targets of the airborne radar. Therefore, in a complex electromagnetic environment, in order to reduce the influence of environmental clutter on target detection, the target detection probability can be improved by designing a short-time pulse train waveform emitted by the radar.
Signal related clutter in different detection environments always exists, and the signal related clutter has extremely strong correlation with a transmitting waveform, so that weak target detection is easily influenced. In order to improve the Gaussian point target detection performance under the signal correlation clutter, literature (Kay, S.Optimal Signal Design for Detection of Gaussian Point Targets in Stationary Gaussian Clutter/reconstruction [ J ]. IEEE Journal of Selected Topics in Signal Processing,2007,1 (1): 31-41) derives an optimal waveform frequency domain water injection method expression under the energy constraint according to the NP criterion, and concentrates the energy spectrum density at a frequency band with smaller interference and noise energy, so that the interference of the clutter on target detection is inhibited, however, the method only solves the optimal waveform frequency domain form and cannot directly obtain the optimal emission waveform. In order to ensure that waveforms have good fuzzy function characteristics and spectrum coexistence capability at the same time, in the literature (Aubry A, maio A D, piezzo M, et al, cognitive radar waveform design for spectral coexistence in Signal-dependent interference [ C ].2014IEEE Radar Conference (RadarCon). IEEE, 2014), august Aubry et al propose a method for designing a transmission and reception joint under the constraint of similarity, energy and spectrum by maximizing a Signal-to-Noise Ratio (SCNR) objective function, and propose an algorithm for solving the problem through iterative optimization of sequences, and the obtained transmission waveform can inhibit corresponding Clutter and Noise interference, but the Signal of the method does not have anti-interception capability and is easy to be interfered by related signals forwarded by an jammer.
Disclosure of Invention
Aiming at the problem that the conventional waveform design in the prior art cannot be realized and simultaneously the environment clutter and the jammer interference are restrained, the invention provides a method for designing a short-time pulse train waveform for resisting clutter interference.
For convenience in describing the present invention, the following terms will be explained.
Terminology 1: autocorrelation integral sidelobe levels (integrated side lobe, ISL)
The autocorrelation ISL is the sum of squares of all autocorrelation sidelobe levels of a signal, and because the autocorrelation function of the signal is the same as a matched filtering result obtained by a pulse compression technique, the autocorrelation ISL is used to represent an integral sidelobe level of a matched filtering output result of the signal.
The specific technical scheme of the invention is as follows: a method for designing short-time pulse train waveform of anti-clutter interference features that the short-time pulse train waveform is a signal model composed of multiple sub-pulses with same duty ratio, each sub-pulse is composed of M chips, and T is set up 1 Is held by pulse trainLength τ 2 For pulse repetition interval of sub-pulses τ 3 Is the sub-pulse width. Let T be 1 The short pulse emission waveform in the time period is s (t), s (t) can be expressed as:
Figure BDA0003545111370000021
wherein N is the number of sub-pulses, x ij (t) is the ith chip at the jth sub-pulse, chip width τ 1 . Let m=τ 3 /τ 1 ＝Bτ 3 The transmit waveform discrete vector may be expressed as:
Figure BDA0003545111370000022
wherein ,
Figure BDA0003545111370000023
representing a vector of complex domain dimensions Kx1, 0 1×P The size of P is determined by the duty cycle of the burst sequence, and k=n (m+p) represents the total number of chips of the burst sequence.
The short-time pulse train waveform adopts a relatively complex modulation mode, has a special waveform structure system with sub-pulses as pulse trains, and has two advantages different from other emission waveforms: 1) The pulse duration is short, and the pulse is not easy to intercept by a radar; 2) The peak power is high and the radar action distance is long.
The method specifically comprises the following steps:
step one: the spectrum of the optimal waveform is solved,
under the strong clutter interference environment, clutter and noise information in the environment are firstly acquired through an environment sensing technology before the radar works, and the prior information can be utilized to design a transmitting waveform on the premise that the clutter in the detection environment is stable clutter.
Let the echo signal y (t) be:
y(t)＝s(t)*g(t)+s(t)*c(t)+n(t) (3)
where g (t) is the target parameter, c (t) is the clutter impulse response, and n (t) is the noise.
From the definition, t 0 The SCNR at time is:
Figure BDA0003545111370000024
wherein ,Pc (f) Is the power spectral density, P, of the clutter n (f) Is the power spectral density of the noise, S (f) is the transmit signal spectrum, G (f) is the target parameter spectrum, and H (f) is the receive filter spectrum.
In order to make the energy of the optimized waveform constant, it is necessary to limit the energy of the optimized waveform to be constant. From the pasmodic theorem, it is known that energy constraint can be performed on the spectrum of the optimized waveform, and the energy E of the optimized waveform s Can be expressed as
Figure BDA0003545111370000031
To sum up, a problem model is constructed that maximizes Signal-to-Noise-Ratio (SCNR) criteria:
Figure BDA0003545111370000032
order the
Figure BDA0003545111370000033
The echo signal-to-noise ratio can be expressed as: />
Figure BDA0003545111370000039
wherein ,L-1 (f) Is the inverse of L (f);
shrinking the above by using Schvalz inequality to obtain
Figure BDA0003545111370000034
If and only if
Figure BDA0003545111370000035
When the equal sign is true, the receiving filter expression is:
Figure BDA0003545111370000036
wherein ,α1 Is a constant. Here a constant alpha 1 Is a constant coefficient derived from a formula, and is represented by a symbol because it does not affect the solution.
At this time, the SCNR can be expressed as:
Figure BDA0003545111370000037
the problem model of equation (6) may be converted into:
Figure BDA0003545111370000038
constructing a function by using a Lagrangian multiplier method, and converting the constrained optimization problem into an unconstrained optimization problem, wherein the constructed function is as follows:
Figure BDA0003545111370000041
wherein ,α2 Is a constant in the Lagrangian multiplier method. J [ |S (f) | 2 ]Is dependent on S (f) 2 Is a generalized function of (1). According to the principle of the variational method, when the generalized function takes the extreme value, the optimization parameter is in the optimal state. Therefore, the square of the frequency domain amplitude of the optimal transmitting waveform is obtained when the extremum of the above formula is satisfied. The above pair |S (f) | 2 Deriving and setting the derivative to 0, and solving the most significant of the transmitted waveform based on the maximum signal-to-noise ratio criterionOptimal frequency spectrum S o (f)：
Figure BDA0003545111370000042
wherein ,α2 The value of (2) is determined by the energy of the transmitted signal, if:
Figure BDA0003545111370000043
the maximum signal-to-noise ratio is:
Figure BDA0003545111370000044
step two: burst waveform design
According to the time domain form of the short-time pulse string which cannot be obtained by the optimal waveform spectrum based on the maximized SCNR criterion, combining the short-time pulse string signal model, and minimizing the square error of the optimal waveform spectrum and the short-time pulse string waveform spectrum, the short-time pulse string signal waveform similar to the optimal emission waveform spectrum can be obtained.
The short-time pulse string signal model is shown as (1) and has a frequency spectrum S t (f) And (3) representing. The optimal emission waveform frequency spectrum obtained based on the maximum signal-to-noise ratio criterion is S o (f) The objective function may be expressed as a Square Error (SE) of both
SE＝|S t (f)-S o (f)| 2 (16)
However, the autocorrelation sidelobes of the burst waveform obtained by considering only the spectrum similarity also affect the detection probability of the target. Thus, a cost function is constructed that optimizes both the spectrum and the integrated sidelobe levels of the short bursts, the cost function being expressed as:
C＝λSE+(1-λ)ISL (17)
where λ represents the weight of the square error function, ISL is the integral sidelobe of the short-time pulse train, and by definition, ISL can be written as:
Figure BDA0003545111370000051
wherein, R is the autocorrelation function of the short-time pulse train sequence s, R (k) is the kth side lobe of the autocorrelation function, expressed as:
Figure BDA0003545111370000052
wherein ,sn An nth element representing a burst sequence,
Figure BDA0003545111370000053
is the conjugate of the (n-k) th element of the burst sequence.
The discrete phase parameter corresponding to the short pulse sequence of equation (2) can be expressed as:
Figure BDA0003545111370000054
by changing the phase parameters of the transmit waveform to minimize the square error between the transmit waveform spectrum and the optimal transmit waveform spectrum, the short-time pulse train integral sidelobes are as low as possible, and then the problem model based on the minimized square error criterion can be expressed as:
Figure BDA0003545111370000055
since the objective function is a nonlinear function, the optimization problem cannot be directly solved by using a convex optimization tool, so that a Pattern Search (PS) algorithm is selected to solve the problem, namely, the phase parameters of the waveform are subjected to traversal Search, the multidimensional optimization Search problem is converted into a plurality of one-dimensional optimization Search problems in each iteration process by means of an iteration mode, and the optimal phase parameters phi are obtained through a plurality of iterations.
Further, the specific steps of the pattern search algorithm are as follows:
(1) The initialization phase parameter phi can be random phase, or the initial phase of the short-time pulse string waveform can be formed by using the phase of common phase code waveforms such as P3 code or P4 code according to a short-time pulse string signal model.
(2) N-th phase parameter phi for transmit waveform n The objective function SE can be expressed as a unitary function SE [ phi ] of the phase parameter n ]. At this time, the multi-dimensional optimization problem of equation (21) is converted into a one-dimensional optimization problem:
Figure BDA0003545111370000056
the phase parameter Φ is updated using the one-dimensional optimized search result of equation (22) until all phase parameters of all waveforms are updated once.
(3) And (3) repeating the step (2) until the set stopping condition (such as the number of iterations, the phase parameter vector variation of the vector for two iterations, the cost function variation and the like) is reached.
The PS algorithm converts the multidimensional optimization problem into a plurality of one-dimensional optimization problems, and searches phase parameters which enable the objective function to be minimum when one-dimensional optimization is carried out each time, so that the objective function can be further reduced, a lower objective function value can be obtained after each iteration, and the minimum value is approximated.
The invention has the beneficial effects that: the method utilizes target priori information to construct a maximized signal-to-noise ratio target function, and solves the optimal emission waveform and the optimal matched filter based on the Lagrangian multiplier method; combining the waveform emission rule of the short-time pulse train to construct a combined objective function of waveform power spectrum approximation and autocorrelation integral sidelobe level suppression; and iterating in a mode searching mode to obtain the optimal short-time pulse train waveform. The short-time pulse train waveform designed by the invention has the capability of resisting interception of an jammer, can inhibit interference of environmental clutter on target detection, can avoid interference forwarded after interception by an adversary jammer, realizes simultaneous inhibition of the environmental clutter and the jammer interference, and improves the target detection capability under clutter environment.
Drawings
FIG. 1 is a schematic diagram of a burst signal model according to an embodiment of the present invention;
FIG. 2 is a flow chart of a method for designing a short-time pulse train waveform for anti-clutter interference according to an embodiment of the present invention;
FIG. 3 is a graph showing the comparison between the clutter power spectrum and the optimal waveform spectrum according to the embodiment of the present invention;
FIG. 4 is a graph showing the comparison of an optimized burst spectrum and an optimized waveform spectrum according to an embodiment of the present invention;
FIG. 5 is a graph of the output result of the point-target matched filtering of an unoptimized waveform according to an embodiment of the present invention;
FIG. 6 is a plot of the output of the point-target matched filter of the optimized burst waveform provided by the embodiments of the present invention;
fig. 7 is a graph of SCNR improvement comparison results before and after optimizing signals with different lengths according to an embodiment of the present invention.
Detailed Description
The invention mainly adopts a simulation experiment method to verify the effectiveness of the proposed short-time pulse train waveform design method for resisting clutter interference. All steps and conclusions are verified to be correct through the MATLAB 2018a platform on the Windows10 operating system. The present invention will be further described with reference to the accompanying drawings, in order to facilitate understanding of the technical content of the present invention by those skilled in the art.
FIG. 1 is a schematic diagram of an anti-interception burst emission signal, the signal emission rule of which can be summarized as a pulse repetition interval T 3 A pulse train consisting of a plurality of sub-pulses, each sub-pulse being a phase encoded signal consisting of a plurality of sub-chips, is internally transmitted.
The waveform design flow of the short-time pulse string is shown in figure 2. Firstly, obtaining an optimal frequency spectrum of a transmitting waveform and an optimal receiver based on a maximized SCNR criterion; secondly, combining the characteristic of short-time pulse train signal transmission, constructing a cost function of minimizing the square error of the weighted pulse train frequency spectrum and the optimal waveform frequency spectrum and waveform autocorrelation sidelobes; finally, the mode searching algorithm is utilized to obtain the optimized time domain form of the short-time pulse train, and the design of the anti-interference waveform of the short-time pulse train is completed. The method comprises the following specific steps:
step one: solving for optimal transmit waveform spectrum
Clutter and noise information in the environment can be quickly acquired by using an environment sensing technology, and a transmitting waveform can be designed by using priori information on the premise that the clutter in the detection environment is stable clutter. Let the echo signal y (t) be
y(t)＝s(t)*g(t)+s(t)*c(t)+n(t) (23)
Where "×" denotes the convolution operation, s (t) is the transmitted signal, g (t) is the target parameter, c (t) is the clutter impulse response, and n (t) is the noise.
The echo signal-to-noise ratio definition is available:
Figure BDA0003545111370000071
wherein ,Pc (f) Is the power spectral density, P, of the clutter n (f) Is the power spectral density of the noise, S (f) is the transmit signal spectrum, G (f) is the target parameter spectrum, and H (f) is the receive filter spectrum.
The transmitted waveform is often limited by the constant energy, energy E, of the transmitted waveform according to the Pasteur theorem s Can be expressed as
Figure BDA0003545111370000072
To sum up, constructing a problem model maximizing signal-to-noise ratio criteria
Figure BDA0003545111370000073
Order the
Figure BDA0003545111370000074
The echo signal-to-noise ratio can be expressed as:
Figure BDA0003545111370000075
shrinking the above by using Schvalz inequality to obtain
Figure BDA0003545111370000076
If and only if
Figure BDA0003545111370000077
When the equal sign is true. Wherein ( * Representing the conjugate, the receive filter expression is:
Figure BDA0003545111370000081
the signal-to-noise ratio at this time can be expressed as:
Figure BDA0003545111370000082
the optimization problem model is converted into:
Figure BDA0003545111370000083
constructing a function by using a Lagrangian multiplier method, and converting the constrained optimization problem into an unconstrained optimization problem, wherein the constructed function is as follows:
Figure BDA0003545111370000084
wherein ,α2 Is a constant in the Lagrangian multiplier method. J [ |S (f) | 2 ]Is dependent on S (f) 2 Is a generalized function of (1). According to the principle of the variational method, when the generalized function takes the extreme value, the optimized parameter is in the optimal stateStatus of the device. Therefore, the square of the frequency domain amplitude of the optimal transmitting waveform is obtained when the extremum of the above formula is satisfied. The above pair |S (f) | 2 Deriving and setting the derivative to 0, and solving to obtain the optimal frequency spectrum S of the transmitted waveform based on the maximum signal-to-noise ratio criterion o (f)：
Figure BDA0003545111370000085
wherein ,α2 The value of (2) is determined by the energy of the transmitted signal.
If the conditions are satisfied:
Figure BDA0003545111370000086
the maximum signal-to-noise ratio is:
Figure BDA0003545111370000087
step two: burst waveform design
According to the optimal waveform spectrum obtained based on the maximized SCNR criterion, the time domain form of the short-time pulse string cannot be obtained, and the short-time pulse string signal waveform meeting the spectrum requirement is obtained by minimizing the square error of the optimal waveform spectrum and the short-time pulse string waveform spectrum.
The short-time pulse string signal model is shown as (1) and has a frequency spectrum S t (f) And (3) representing. The optimal emission waveform frequency spectrum obtained based on the maximum signal-to-noise ratio criterion is S o (f) The objective function may be expressed as a Square Error (SE) of both
SE＝|S t (f)-S o (f)| 2 (36)
However, the autocorrelation sidelobes of the burst waveform obtained by considering only the spectrum similarity also affect the detection probability of the target. Thus, a cost function is constructed that optimizes both the spectrum and the integrated sidelobe levels of the short bursts. The cost function may be expressed as
C＝λSE+(1-λ)ISL (37)
Where λ represents the weight of the square error function, ISL is the integral sidelobe of the short-time pulse train, and, according to its definition, ISL is expressed as:
Figure BDA0003545111370000091
wherein R (k) is an autocorrelation function of the burst sequence s, expressed as:
Figure BDA0003545111370000092
wherein, the phase parameter of the transmit waveform discrete vector can be expressed as:
Figure BDA0003545111370000093
by changing the phase parameters of the transmit waveform to minimize the square error between the transmit waveform spectrum and the optimal transmit waveform spectrum, the short-time pulse train integral sidelobes are as low as possible, and then the problem model based on the minimized square error criterion can be expressed as:
Figure BDA0003545111370000094
since the objective function is a nonlinear function, the optimization problem cannot be directly solved by using a convex optimization tool, so that a Pattern Search (PS) algorithm is selected to solve the problem, namely, the phase parameters of the waveform are subjected to traversal Search, the multidimensional optimization Search problem is converted into a plurality of one-dimensional optimization Search problems in each iteration process by means of an iteration mode, and the optimal phase parameters phi are obtained through a plurality of iterations.
The specific steps of the pattern search algorithm are as follows:
(1) The initialization phase parameter phi can be random phase, or the initial phase of the short-time pulse string waveform can be formed by using the phase of common phase code waveforms such as P3 code or P4 code according to a short-time pulse string signal model.
(2) N-th phase parameter phi for transmit waveform n The objective function SE can be expressed as a unitary function SE [ phi ] of the phase parameter n ]. At this time, the multidimensional optimization problem of equation (41) is converted into a one-dimensional optimization problem:
Figure BDA0003545111370000101
the phase parameter Φ is updated using the one-dimensional optimized search result of equation (42) until all phase parameters of all waveforms are updated once.
(3) And (3) repeating the step (2) until the set stopping condition (such as the number of iterations, the phase parameter vector variation of the vector for two iterations, the cost function variation and the like) is reached.
The PS algorithm converts the multidimensional optimization problem into a plurality of one-dimensional optimization problems, and searches phase parameters which enable the objective function to be minimum when one-dimensional optimization is carried out each time, so that the objective function can be further reduced, a lower objective function value can be obtained after each iteration, and the minimum value is approximated.
In the design of the short-time pulse train waveform, the short-time pulse train is composed of 5 pulses, the pulse width of one pulse train is 5 mu s, the signal length N is 500, the pulse duty ratio is 80%, and the initial phase of the pulse train is a random sequence.
FIG. 3 is a comparison of clutter power spectrum and an optimal spectrum obtained according to step two in the practice of the present invention. It can be seen that the energy of the optimal waveform spectrum is concentrated at the position with very low clutter power spectrum, and the lower signal energy is distributed at the position with higher clutter power spectrum energy, so that the optimal transmission waveform can inhibit the interference of the clutter in the frequency domain. However, the above steps can only obtain the frequency spectrum of the transmitted waveform, and in order to obtain the time domain transmitted waveform of the short-time pulse train, the invention combines the short-time pulse train transmission form, and according to the step three in the specific implementation of the invention, the optimal short-time pulse train transmitted waveform is obtained.
Fig. 4 is a comparison of the optimized burst spectrum with the optimum waveform spectrum. It can be seen that the designed short-time pulse train spectrum is consistent with the energy distribution rule of the optimal waveform spectrum. In order to verify that the designed short-time pulse train waveform has clutter rejection capability, the invention respectively provides a point target matched filtering output of an unoptimized waveform and a point target matched filtering output of an optimized short-time pulse train waveform under the same clutter environment, as shown in fig. 5 and 6. Compared with the non-optimized waveform, the matched filtering result obtained by transmitting the optimized short-time pulse train waveform has lower side lobe level, so that the short-time pulse train waveform designed by the invention is beneficial to improving the target detection probability. To analyze the effect of signal length on target detection, the present invention gives a comparison of SCNR of matched filtered outputs for signal lengths of 100, 500 and 900, respectively, as shown in FIG. 7. It can be seen that, as the signal length increases, the SCNR is improved, but the SCNR obtained by the short-time pulse train waveform designed by the invention is better than the emission waveform when not optimized, and when the signal length is 500, the performance of the short-time pulse train waveform is obviously improved. The specific SCNR results are shown in table 1:
TABLE 1
Figure BDA0003545111370000111
In summary, the method of the invention considers the optimization design of the short-time pulse train waveform with narrow pulse width, high peak power and anti-interception capability, reduces the energy distribution of the short-time pulse train signal at the clutter energy concentration frequency band by using the priori information of the environmental clutter, suppresses the interference of the clutter power to the target echo power while ensuring that the clutter power is not interfered by the sidelobe level, improves the target detection capability in the clutter environment, and has important application value in complex detection scenes.

Claims (2)

1. A method for designing short-time pulse train waveform with clutter interference resistance includes using multiple sub-with same duty ratio as short-time pulse train waveformSignal model composed of pulses, each sub-pulse is composed of M chips, T is set 1 For burst duration, τ 2 For pulse repetition interval of sub-pulses τ 3 For sub-pulse width, the signal bandwidth is B, assuming T 1 The short pulse emission waveform in the time period is s (t), s (t) is expressed as:
Figure FDA0003545111360000011
wherein N is the number of sub-pulses, x ij (t) is the ith chip at the jth sub-pulse, chip width τ 1 Let m=τ 3 /τ 1 ＝Bτ 3 The transmit burst discrete vector is expressed as:
Figure FDA0003545111360000012
wherein ,
Figure FDA0003545111360000013
representing a vector of complex domain dimensions Kx1, 0 1×P Representing an all-zero matrix of dimension 1×p, k=n (m+p) representing the total number of chips of the burst sequence;
the method specifically comprises the following steps:
step one: the spectrum of the optimal waveform is solved,
let the echo signal y (t) be:
y(t)＝s(t)*g(t)+s(t)*c(t)+n(t) (3)
wherein g (t) is a target parameter, c (t) is clutter impulse response, and n (t) is noise;
t 0 the SCNR at time is:
Figure FDA0003545111360000014
wherein ,Pc (f) Work being clutterSpectral density, P n (f) Is the power spectral density of the noise, S (f) is the transmit signal spectrum, G (f) is the target parameter spectrum, and H (f) is the receive filter spectrum;
energy constraint is carried out on the frequency spectrum of the optimized waveform, and the energy E of the optimized waveform s Expressed as:
Figure FDA0003545111360000015
constructing a problem model maximizing SCNR criteria:
Figure FDA0003545111360000021
order the
Figure FDA0003545111360000022
The echo signal-to-noise ratio is expressed as:
Figure FDA0003545111360000023
wherein ,L-1 (f) Is the inverse of L (f);
shrinking equation (7) using the schwaltz inequality gives:
Figure FDA0003545111360000024
if and only if
Figure FDA0003545111360000025
When the equal sign is true, the receiving filter expression is:
Figure FDA0003545111360000026
wherein ,α1 Is a constant, at which time SCNR is expressed as:
Figure FDA0003545111360000027
the problem model of equation (6) may be converted into:
Figure FDA0003545111360000028
constructing a function by using a Lagrangian multiplier method, and converting the constrained optimization problem into an unconstrained optimization problem, wherein the constructed function is as follows:
Figure FDA0003545111360000029
wherein ,α2 J [ |S (f) |being a constant in Lagrangian multiplier method 2 ]Is dependent on S (f) 2 Is a generalized function of (1); the pair of formula (12) S (f) I 2 Deriving and setting the derivative to 0, and solving to obtain the optimal frequency spectrum S of the transmitted waveform based on the maximum signal-to-noise ratio criterion o (f)：
Figure FDA0003545111360000031
wherein ,α2 The value of (2) is determined by the energy of the transmitted signal, if:
Figure FDA0003545111360000032
the maximum signal-to-noise ratio is:
Figure FDA0003545111360000033
step two: the waveform design of the short-time pulse train,
s for spectrum of short-time pulse train signal t (f) Representing that the optimal emission waveform frequency spectrum obtained based on the maximum signal-to-noise ratio criterion is S o (f) The objective function can be expressed as the square error of both:
SE＝|S t (f)-S o (f)| 2 (16)
constructing a cost function, and simultaneously optimizing the frequency spectrum and the integral sidelobe level of the short-time pulse train, wherein the cost function is expressed as follows:
C＝λSE+(1-λ)ISL (17)
where λ represents the weight of the square error function, ISL is the integral sidelobe of the short-time pulse train, ISL is:
Figure FDA0003545111360000034
wherein, R is the autocorrelation function of the short-time pulse train sequence s, R (k) is the kth side lobe of the autocorrelation function, expressed as:
Figure FDA0003545111360000035
wherein ,sn An nth element representing a burst sequence,
Figure FDA0003545111360000036
is the conjugate of the (n-k) th element of the burst sequence, and the discrete phase parameter corresponding to the burst sequence of equation (2) is expressed as:
Figure FDA0003545111360000037
wherein the problem model based on the minimized square error criterion can be expressed as:
Figure FDA0003545111360000041
solving a solution formula (21) by using a mode search algorithm, namely performing traversal search on the phase parameters of the waveform, converting a multi-dimensional optimization search problem into a plurality of one-dimensional optimization search problems in each iteration process by using an iteration mode, and obtaining the optimal phase parameters phi through a plurality of iterations, namely completing the design of the short-time pulse string waveform.
2. The method for designing a short-time pulse train waveform for resisting clutter interference according to claim 1, wherein the specific steps of the pattern search algorithm are as follows:
(1) Initializing a phase parameter phi;
(2) N-th phase parameter phi for transmit waveform n The objective function SE is expressed as a unitary function SE [ phi ] of the phase parameter n ]The multi-dimensional optimization problem of equation (21) translates into a one-dimensional optimization problem:
Figure FDA0003545111360000042
updating the phase parameters Φ using the one-dimensional optimized search result of equation (22) until all phase parameters of all waveforms are updated once;
(3) Repeating the step (2) until the set stop condition is reached.
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