CN116047425A - Anti-intra-pulse forwarding interference method based on orthogonal transmission sequence and multi-sub carrier frequency transmission scheme - Google Patents

Abstract

The invention discloses an anti-intra-pulse forwarding interference method based on an orthogonal transmission sequence and a multi-sub-carrier frequency transmission scheme, which is used for establishing an array receiving mathematical model with intra-pulse forwarding interference based on the multi-sub-carrier frequency transmission scheme of a MIMO radar platform; deducing a space-frequency domain two-dimensional intra-pulse forwarding interference suppression filter by using a minimum undistorted response principle on the basis of intra-pulse forwarding interference so as to suppress forwarding interference; considering that the multi-sub carrier frequency transmitting scheme needs the orthogonality of transmitting waveforms of different channels to realize the separation of receiving signals, adopting an ADMM algorithm to optimize the orthogonal transmitting sequences, and obtaining the orthogonal spread spectrum coding LFM waveform after optimization has the characteristics of low cross-correlation energy and low autocorrelation sidelobe level. The interference suppression processing process of the invention does not increase complexity, and can be used for supporting accurate estimation of the distance and the azimuth of the real target while the radar does not interrupt work.

Description

Anti-intra-pulse forwarding interference method based on orthogonal transmission sequence and multi-sub carrier frequency transmission scheme

Technical Field

The invention belongs to the technical field of radar anti-intra-pulse forwarding interference, and particularly relates to an anti-intra-pulse forwarding interference method based on an orthogonal transmission sequence and a multi-carrier frequency transmission scheme.

Background

The advent of MIMO radar gives higher degrees of freedom to digital array radar, but with the rapid development of digital chips and high-speed a/D chips, high-performance DRFM jammers are emerging gradually, and jammers with faster response speeds and rapid forwarding capabilities seriously affect the detection performance of radar.

The existing method utilizes the difference of true and false target information to resist interference in different domains of distance, doppler, polarization and the like. MIMO radar systems are still limited by the available degrees of freedom (Degree of Freedom, DOF), so higher degrees of freedom radar system resistance to main lobe interference is an important research direction and research hotspot.

FDA-MIMO can generate transmit beams that are independent of distance and angle by adding a small frequency increment. FDA-MIMO can distinguish echoes at different ambiguous distances, depending on the advantage of distance angle dependence. FDA-MIMO is also applied to main lobe interference cancellation, and nulling is generated in a range direction corresponding to main lobe interference by using accurate transmit-receive beam forming to suppress interference, however, these methods generally require a priori information such as the range and covariance of the main lobe interference.

An Element-pulse Coding (EPC) method can form an equivalent transmission beam in a three-dimensional space of transmission, reception and time to suppress false target interference, but such a method can only suppress false target interference with a delay greater than one PRI.

The existing method capable of resisting the intra-pulse forwarding interference can be mainly classified into two methods, namely a parameterization method and a semi-parameterization method, wherein the parameterization method estimates interference parameters in a one-dimensional frequency domain, accurate information of the interference is obtained by modeling the interference and estimating the parameters, and the parameterization method is generally applicable to a single interference type.

The existing method establishes a series of signal models aiming at narrowband interference and broadband interference, and Miller et al recover real signals by using a least squares method based on narrowband radio frequency interference prior information. I.e. approximating the received signal with a sinusoidal signal, the parameters of which are estimated to minimize the difference between the two. In general, the parameterized model can only be used for an isolated single interference model, parameter estimation must be performed on each pulse echo, the calculation complexity is high, the parameterized interference model does not consider the signal characteristics of the real echo, and protection is lacking. Along with the development of information theory, the complex signal separation problem can be converted into an optimization problem of super parameters for reasonable solution. In some specific cases, these methods can achieve better interference suppression effect, but the super-parameterized method relies on accurate estimation of model parameters, so that the method does not have robust characteristics.

Disclosure of Invention

The invention aims to solve the technical problems of the prior art, provides an anti-intra-pulse forwarding interference method based on an orthogonal transmission sequence and a multi-sub carrier frequency transmission scheme, and designs an orthogonal spread spectrum coding (LFM) waveform which has low autocorrelation peak sidelobe level and cross correlation energy.

In order to achieve the technical purpose, the invention adopts the following technical scheme:

an anti-intra-pulse forwarding interference method based on orthogonal transmission sequences and a multi-sub carrier frequency transmission scheme comprises the following steps:

s1, establishing an array receiving mathematical model with intra-pulse forwarding interference based on a multi-sub carrier frequency transmitting scheme of a MIMO radar platform;

s2, deducing a space-frequency domain two-dimensional intra-pulse forwarding interference suppression filter by utilizing a minimum undistorted response principle on the basis of intra-pulse forwarding interference so as to suppress forwarding interference;

s3, considering that the multi-sub carrier frequency transmission scheme needs the orthogonality of the transmission waveforms of different channels to realize the separation of the received signals, adopting an ADMM algorithm to optimize the orthogonal transmission sequences, and obtaining the orthogonal spread spectrum coding LFM waveform after optimization has the characteristics of low cross-correlation energy and low autocorrelation sidelobe level.

In order to optimize the technical scheme, the specific measures adopted further comprise:

the transmission scheme of the multi-sub carrier frequency in the step S1 is as follows:

assuming that there are one-dimensional linear arrays of P transmitting array elements and Q receiving array elements, the transmitting signal of the P-th transmitting channel is expressed as

wherein ,

for baseband signals generated using orthogonal transmit sequences, f _p A carrier frequency for the p-th transmit signal;

under the narrowband assumption, the target position of the far field is represented as (θ, R), where θ is the beam dip angle, and R is the true distance between the target and the radar, and then the echo of the q-th receiving channel is represented as:

wherein ,τ_p,q ＝[2R-d(p-1)sin(θ)-d(q-1)sinθ]And/c is the double-pass time delay from the p-th transmitting array element to the q-th receiving array element;

in addition, τ=2r/c

Wherein, gamma is the receiving scattering coefficient of the target, which is determined by the RCS of the target, the propagation response of the channel and the like, d is the array element interval, lambda ₁ ＝c/f ₁ Representing the wavelength of the radiated signal;

the Q receiving channel echo output results are written into a matrix form, and the receiving echo after fast time matching filtering processing is expressed as

Wherein ω (t) = [ ω ] _1,1 (t),ω _1,2 (t),…,ω _q,p (t),…,ω _Q,P (t)] ^T Matching and filtering output results for each receiving channel, wherein a (R, theta) is a transmitting guide vector; b (θ) represents a received steering vector:

let the spatial position of the real object be (θ) _T ,R _T ) While the repeater jammer position is (θ _J ,R _J ) The mixed received echo is expressed as

Where ΔR/c is expressed as the fast time delay generated by the jammer DRFM, which is less than one PRI.

Carrier frequency f of p-th transmission signal _p The method comprises the following steps:

f _p ＝f ₁ +(p-1)Δf,p＝1,2,…,P

wherein ,f₁ For the carrier frequency of the first transmit channel, Δf is the minimum frequency step interval of the subcarrier frequency;

the emission steering vector a (R, θ) is:

the received steering vector b (θ) is:

in the step S2, the design scheme of the spatial domain-frequency domain two-dimensional intra-pulse forwarding interference suppression filter is as follows:

firstly, preprocessing a received mixed echo, namely, blocking each range gate receiving the echo by utilizing a two-dimensional blocking matrix;

defining the sub-carrier frequency of the target as f _T ＝2Δf·R _T The carrier frequency domain blocking matrix is expressed as

The airspace blocking matrix is expressed as

The q-th receive channel echo after two-dimensional blocking preprocessing is expressed as

The space-frequency two-dimensional blocking processing is carried out on each range gate to inhibit the real target echo signal, so that the data after the blocking processing only contains the forwarding interference signal, the covariance matrix of the signal after the space-frequency two-dimensional blocking processing is equivalent to the covariance matrix of the interference signal, and the interference covariance matrix is expressed as

Wherein L is the snapshot number;

thereby establishing a space-frequency filter equation for suppressing interference, expressed as

min w ^H (f _T ,θ _T )R _q (t)w(f _T ,θ _T )

s.t. w ^H (f _T ,θ _T )s(f _T ,θ _T )＝1

Wherein s (f _T ,θ _T )＝s _f (f _T )⊙s _s (θ _T ) The steering vector corresponding to the carrier frequency domain is expressed as

The steering vector corresponding to the transmit spatial domain is represented as

The optimal weight vector of the adaptive spatial-frequency domain two-dimensional intra-pulse transfer interference suppression filter based on the minimum undistorted response principle is given by:

and (3) performing space-frequency two-dimensional filtering processing on the received signal of each range gate after space-frequency two-dimensional blocking processing to inhibit the interference signal so as to obtain an echo corresponding to the real target:

wherein there is->

Because the subcarrier frequencies of the real targets have a one-to-one correspondence with DOA, the false targets are distributed on the diagonal of the space domain-carrier frequency domain, and the false targets have an offset of 2 delta f (R _J -R _T ) And/c, the true target will remain unchanged after the above filtering process, and the false target is filtered out due to the offset.

The above S2 further includes a scheme of transmitting different sub-carrier frequencies to four array elements in a pitching manner: firstly, echo signals of different channels are obtained through orthogonal transmitting sequence decoding, secondly, blocking preprocessing is adopted to inhibit real target signals so as to obtain accurate covariance matrixes of intra-pulse transfer main lobe interference signals, the obtained interference covariance matrixes are utilized to filter the interference signals through space domain-frequency domain two-dimensional filtering, and finally, distance Doppler processing is carried out to obtain final real target results.

In the step S3, the optimization processing of the orthogonal transmitting sequence by adopting the ADMM algorithm is to optimize the continuous phase spread spectrum coding sequence, and the process includes:

and establishing a mathematical model of the spread spectrum coding LFM signal, deducing a specific processing process of a spread spectrum technology in coding and decoding, and optimizing a continuous phase spread spectrum coding sequence by using an ADMM method.

The mathematical model building process of the spread spectrum coding LFM signal comprises the following steps:

assuming that the signal to be transferred is represented as a standard LFM signal, there is

Wherein T is the pulse width of the LFM signal, alpha is the frequency modulation slope of the LFM signal, and the spread spectrum coding signal is expressed as

wherein ,C_n For discrete spread-spectrum coding sequences, T _C For the encoded sub-pulse width, P (t) is a rectangular window function;

multiplying the LFM signal with the spread spectrum coded signal to obtain a spread spectrum coded LFM signal, expressed as

B(t)＝A(t)·C(t)

After up-conversion treatment, the radio frequency end transmitting signal is expressed as

T _x (t)＝B(t)·cos(2πf _c t)

The receiver receives the echo signal, and performs the down-conversion processing and the spread spectrum coding and decoding process, which is expressed as

D(t)＝R _x (t)·[C(t)] ^*

To verify orthogonality between spread spectrum coded LFM signals, a cross-correlation ambiguity function of different spread spectrum coded LFM signals is given, assuming a set of spread spectrum coded LFM signals exist, respectively satisfying

wherein ,C_m ，D _m Respectively correspond to different spread spectrum sequences, T _C For sub-pulse width, P (t) is a rectangular pulsePunching, alpha ₁ And alpha is ₂ Frequency modulation slopes corresponding to different LFM signals respectively;

the cross-correlation function of the spread spectrum encoded LFM signal is written as

When alpha is ₁ ＝α ₂ When the above conditions are satisfied

Order the

Then the above is rewritten as

The above-mentioned optimization process of the continuous phase spread spectrum coding sequence by using the ADMM method includes:

assuming that the discrete spread spectrum code sequence contains M pulse signals, wherein each pulse contains N sub-pulses, the mth spread spectrum code signal is expressed as

x _m ＝[x _m (0),x _m (1),…,x _m (N-1)] ^T

The cross-correlation function of the spread spectrum coded signal is expressed as

i,j＝1,…,M,k＝1-N,…,N-1

Peak sidelobe level is commonly used as an evaluation criterion for waveform cross-correlation optimization, and is as follows

/>

i,j＝1,…,M,k＝1-N,…,N-1

Wherein k+.0 when i=j;

the expected waveform sequence has lower autocorrelation peak sidelobe level and simultaneously lower cross correlation peak level, so that an optimization problem shown in the following formula is established, the side level of the autocorrelation peak of the waveform sequence is restrained at the level epsilon, and the cross correlation peak level of the waveform sequence is restrained within the level range delta;

x _i (n)＝1,i,j＝1,...,M,n＝1,...,N,k＝1-N,…,N-1

first, the objective function is simplified and then

Written in matrix form expressed as

i,j＝1,...,M,k＝1-N,...,N-1

Wherein there are

H _k For an N Toeplitz matrix, the transmitted signal is written in vector form, expressed as

In addition Q _m A matrix is selected for the N-dimension partitions, expressed as

Q _m ＝[0 _N×(m-1)N ,I _N ,0 _N×(M-m)N ]

Introducing an auxiliary variable r _i,j (k) Rewriting optimization problems to

s.t. |r _i,j (k)| ² ≤ε,k≠0,i＝j,

|r _i,j (k)| ² ≤δ,i≠j

x(n ₁ )|＝1,i,j＝1,...,M,n ₁ ＝1,...,NM,k＝1-N,...,N-1

The above is a non-convex optimization problem under multiple constraints, which is solved by the ADMM algorithm, and the augmented Lagrangian function of the problem is expressed as

The output optimization sequence x is solved by an ADMM algorithm.

The specific iterative steps of solving using ADMM described above include:

(1) Fixed variables x and λ _i,j (k) Updating

δ ^(t+1) />

By introducing auxiliary variables

and />

Re-representing the optimization problem as

s.t. |r _i,i (k) ² ≤ε,k≠0

|ri，j(k)|2 ²

r _i,j (k)|2≤δ,i≠j

Obtaining

In the above formula, because delta is equal to

Coupling, so that the above formula is re-substituted into the objective function to obtain

Wherein there are

The optimization problem is approximately expressed as

wherein ,

(2) Fixed variable

and δ^(t) Update x ^(t+1)

The optimization problem is expressed as

s.t.|x(n ₁ )|＝1,n ₁ ＝1,…,NM

Wherein there are

Converting the above optimization problem into the following form, the corresponding objective function is simplified into

/>

s.t.|x(n ₁ )|＝1,n ₁ ＝1,...,NM

Ignoring the constant term, the above equation is re-expressed as

s.t.|x(n ₁ )|＝1,n ₁ ＝1,...,NM

Wherein there are

and

U ₁ Is a real symmetric matrix, then Diag (U) -U ₁ Is a semi-positive definite matrix, wherein

Corresponding attestation procedure in appendix D, definition l ₁ For the number of iterations

s.t.|x(n ₁ )|＝1,n ₁ ＝1,...,NM

At the position of

The maximum value is obtained

Because of the constant modulus of x, the first term of the above equation is constant and the relaxation of the optimization problem is re-expressed as

s.t.|x(n ₁ )|＝1,n ₁ ＝1,...,NM

U is set to ₁ Substituting the target function to obtain

s.t.|x(n ₁ )|＝1,n ₁ ＝1,…,NM

Wherein there are

Order the

The optimized objective function is converted into

Ignoring the constant term, the corresponding optimization problem is re-expressed as

s.t.|x(n ₁ )|＝1,n ₁ ＝1,…,NM

Wherein there are

The corresponding solution is

(3) Fixing other variables and updating

The invention has the following beneficial effects:

the method can accurately estimate the distance and the azimuth information of the real target while the radar does not interrupt the work, and compared with the traditional interference suppression method, the method provided by the invention requires the freedom degree of the carrier frequency domain of the transmitting end, and the complexity is not increased in the interference suppression processing process. And finally, verifying the effectiveness of the method by using point target and surface target simulation results, performing actual measurement data verification on a complex waveform generation platform, and giving out the processing results of orthogonal waveform separation and interference suppression actual measurement data.

Drawings

FIG. 1 is a comparison of different intra-pulse transfer main lobe interference suppression methods;

FIG. 2 is a schematic diagram of intra-pulse forwarding-main-lobe interference;

FIG. 3 is a distribution of real and false targets in carrier frequency domain and space domain, respectively;

FIG. 4 is a process flow of the intra-pulse forwarding main lobe interference suppression method;

fig. 5 shows the autocorrelation optimization result (constraint cross correlation peak level epsilon= -24 dB) of the orthogonal spread spectrum coding sequence;

fig. 6 is a cross-correlation optimization result of an orthogonal spread spectrum coded sequence (constraint cross-correlation peak level epsilon= -24 dB);

fig. 7 shows the cross-correlation optimization result of the orthogonal spread spectrum coding sequence (constraint autocorrelation sidelobe peak level epsilon= -24 dB);

fig. 8 is an autocorrelation optimization result (constraint autocorrelation sidelobe peak level epsilon= -24 dB) of an orthogonal spread spectrum coding sequence;

FIG. 9 is a point target simulation result;

FIG. 10 is a spatial-frequency domain beam pattern;

FIG. 11 is a distributed object simulation result;

FIG. 12 is a measured environment;

FIG. 13 is a diagram showing the data collected by the receiving channel 1, and the upper computer interface;

FIG. 14 is a channel 1 receive echo;

FIG. 15 is a time domain result after receiving echo separation processing;

FIG. 16 is a frequency domain result after receiving echo separation processing;

FIG. 17 is a graph showing the pulse compression result after the received echo separation process;

FIG. 18 is a schematic diagram of radar and interference transmit pulses;

FIG. 19 is a measured environment;

FIG. 20 is a acquired echo time domain;

FIG. 21 is an echo matrix;

figure 22 is a range-doppler processing result;

FIG. 23 is a flow chart of the method of the present invention.

Detailed Description

The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.

Although the steps of the present invention are arranged by reference numerals, the order of the steps is not limited, and the relative order of the steps may be adjusted unless the order of the steps is explicitly stated or the execution of a step requires other steps as a basis. It is to be understood that the term "and/or" as used herein relates to and encompasses any and all possible combinations of one or more of the associated listed items.

The multi-sub carrier frequency transmitting scheme based on the MIMO radar platform effectively suppresses the forwarding interference by designing a space domain-frequency domain two-dimensional filter aiming at the array receiving problem of the intra-pulse forwarding main lobe interference. Because the multi-sub carrier frequency transmitting scheme needs the orthogonality of transmitting waveforms of different channels to realize the separation of receiving signals, an orthogonal spread spectrum coding LFM waveform is designed to have lower autocorrelation peak sidelobe level and cross correlation energy. 1-23, the method provided by the invention can accurately estimate the distance and azimuth information of a real target while the radar does not interrupt work, and compared with the traditional interference suppression method, the anti-intra-pulse forwarding interference method based on the orthogonal transmission sequence and the multi-sub-carrier frequency transmission scheme provided by the invention requires the freedom degree of the carrier frequency domain of the transmission end, and the interference suppression processing process does not increase the complexity, and comprises the following steps:

s1: based on a multi-sub carrier frequency transmitting scheme of the MIMO radar platform, establishing an array receiving mathematical model with intra-pulse main lobe interference;

in specific implementation, a MIMO echo mathematical model based on a multi-sub carrier frequency transmission scheme is provided, and the method is as follows:

assuming that there are one-dimensional linear arrays of P transmitting array elements and Q receiving array elements, the transmitting signal of the P-th transmitting channel can be expressed as

wherein ,

for baseband signals generated using orthogonal transmit sequences, f _p Is the carrier frequency of the p-th transmitted signal, which can be expressed as

f _p ＝f ₁ +(p-1)Δf,p＝1,2,…,P

wherein ,f₁ For the carrier frequency of the first transmit channel, Δf is the minimum frequency step interval of the subcarrier frequency.

Under narrowband assumption, the target position in the far field may be represented as (θ, R), where θ is the beam dip angle and R is the true distance between the target and the radar. The echo of the q-th receive channel can be expressed as

wherein ,τ_p,q ＝[2R-d(p-1)sin(θ)-d(q-1)sinθ]And/c is the double-pass time delay from the p-th transmitting array element to the q-th receiving array element. In addition there are

τ＝2R/c

Gamma is the received scattering coefficient of the target and is determined by the target RCS, channel propagation response, etc. d is array element interval lambda ₁ ＝c/f ₁ Indicating the radiated signal wavelength.

The Q receiving channel echo output results are written into a matrix form, and the receiving echo after fast time matching filtering processing can be expressed as

Wherein ω (t) = [ ω ] _1,1 (t),ω _1,2 (t),…,ω _q,p (t),…,ω _Q,P (t)] ^T The result of the matched filtering output for each receiving channel, a (R, θ) is the transmission steering vector expressed as

b (θ) is expressed as a received steering vector

Let the spatial position of the real object be (θ) _T ,R _T ) While the repeater jammer position is (θ _J ,R _J ) The mixed received echo can be expressed as

Where ΔR/c is expressed as the fast time delay generated by the jammer DRFM, which is less than one PRI. The jammer can store and immediately forward the radar transmitting signal in each PRI moment, so that the traditional method of inter-pulse waveform agility is invalid, and the prior information of the interference cannot be accurately obtained.

In fig. 2, a schematic diagram of intra-pulse transmission main lobe interference is given, and an jammer can store and immediately transmit a radar transmitting signal in each PRI moment, so that a traditional inter-pulse waveform agility method is invalid, and prior information of interference cannot be accurately obtained.

S2: deducing a space-frequency domain two-dimensional intra-pulse forwarding interference suppression filter by using a minimum undistorted response principle on the basis of intra-pulse forwarding interference so as to suppress forwarding interference;

when the method is implemented, the weighting coefficient of the space-frequency domain two-dimensional intra-pulse forwarding interference suppression filter is deduced by utilizing the minimum undistorted response principle on the basis of intra-pulse forwarding interference; comprising the following steps:

the received hybrid echoes are first preprocessed, i.e. blocking processing is performed at each range gate of the received echoes using a two-dimensional blocking matrix. Defining the sub-carrier frequency of the target as f _T ＝2Δf·R _T The carrier frequency domain blocking matrix can be expressed as/c

The airspace blocking matrix is expressed as

The qth receive channel echo after two-dimensional blocking preprocessing can be expressed as

The space-frequency two-dimensional blocking processing can be performed on each range gate to inhibit the real target echo signal, so that the data after the blocking processing only contains the forwarding interference signal, and the covariance matrix of the signal after the space-frequency two-dimensional blocking processing can be approximately equivalent to the covariance matrix of the interference signal, wherein the approximate equivalent is because the influence factors of partial noise are also considered. The interference covariance matrix can be expressed as

Wherein L is the snapshot number.

A space-frequency filter equation for suppressing interference can thus be established, expressed as

min w ^H (f _T ,θ _T )R _q (t)w(f _T ,θ _T )

s.t. w ^H (f _T ,θ _T )s(f _T ,θ _T )＝1

Wherein s (f _T ,θ _T )＝s _f (f _T )⊙s _s (θ _T ) The steering vector corresponding to the carrier frequency domain is expressed as

The steering vector corresponding to the transmit spatial domain is represented as

The optimal weight vector of the adaptive space-frequency two-dimensional filter based on the principle of minimum undistorted response (Minimum Variance Distortionless Response, MVDR) can be given by

The receiving signal of each range gate after the space-frequency two-dimensional blocking treatment is subjected to space-frequency two-dimensional filtering treatment, so that the interference signal can be restrained to obtain the echo corresponding to the real target

Wherein there is->

As shown in fig. 3, due toThe subcarrier frequencies of the real targets have a one-to-one correspondence with DOA and are therefore distributed on the spatial-carrier frequency domain diagonal, and unlike conventional MIMO radars, the false targets have an offset of 2Δf (R _J -R _T ) And/c, which means that after the above filtering process, the real target will remain unchanged, while the false target is filtered out because of this offset.

As shown in fig. 4, a scheme of transmitting different sub-carrier frequencies from pitching to four array elements is provided, firstly, echo signals of different channels are obtained through orthogonal transmission sequence decoding, secondly, a blocking preprocessing is adopted to inhibit real target signals so as to obtain an accurate covariance matrix of intra-pulse transfer main lobe interference signals, the obtained interference covariance matrix is utilized to filter interference signals through space domain-frequency domain two-dimensional filtering, and finally, distance doppler processing is carried out so as to obtain a final real target result.

S3: considering that the multi-sub carrier frequency transmitting scheme needs the orthogonality of transmitting waveforms of different channels to realize the separation of receiving signals, adopting an ADMM algorithm to optimize the orthogonal transmitting sequences, and obtaining the orthogonal spread spectrum coding LFM waveform after optimization has the characteristics of low cross-correlation energy and low autocorrelation sidelobe level.

In a specific embodiment, the process of optimizing the continuous phase spread code sequence includes: giving a mathematical model of spread spectrum coding LFM signals, deducing specific processing procedures in coding and decoding by a spread spectrum technology, and optimizing a continuous phase spread spectrum coding sequence by using an ADMM method.

Wherein the mathematical model of the spread spectrum coded LFM signal comprises:

assuming that the signal to be transferred can be represented as a standard LFM signal, there is

Wherein T is the pulse width of the LFM signal, alpha is the frequency modulation slope of the LFM signal, and the spread spectrum coded signal can be expressed as

wherein ,C_n For discrete spread-spectrum coding sequences, T _C To encode the sub-pulse width, P (t) is a rectangular window function. Multiplying the LFM signal with the spread spectrum coded signal to obtain a spread spectrum coded LFM signal, expressed as

B(t)＝A(t)·C(t)

B(t)＝A(t)·C(t)

After up-conversion, the radio frequency end transmitting signal can be expressed as

T _x (t)＝B(t)·cos(2πf _c t)

The receiver receives the echo signal, and performs the down-conversion processing and the spread spectrum coding and decoding process, which is expressed as

D(t)＝R _x (t)·[C(t)] ^*

To verify orthogonality between spread spectrum coded LFM signals, a cross-correlation ambiguity function of different spread spectrum coded LFM signals is given, assuming a set of spread spectrum coded LFM signals exist, respectively satisfying

wherein ,C_m ，D _m Respectively correspond to different spread spectrum sequences, T _C For sub-pulse width, P (t) is a rectangular pulse, alpha ₁ And alpha is ₂ Respectively correspond to the frequency modulation slopes of the different LFM signals. The cross-correlation function of the spread spectrum encoded LFM signal can be written as

When alpha is ₁ ＝α ₂ When the above is satisfied->

Order the

The above can be rewritten as

From the above equation, it can be found that the orthogonality of the spread spectrum encoded LFM signals depends on the cross-correlation between the spread spectrum encoded signals, the lower the cross-correlation function peak level of the spread spectrum LFM signals when the spread spectrum encoded signals are orthogonal, and the higher the cross-correlation function peak level of the spread spectrum LFM signals when the spread spectrum encoded signals are identical. The spread spectrum coding LFM waveform with better orthogonality can be obtained only by optimizing the spread spectrum coding signal, and the spread spectrum coding sequence optimizing method based on ADMM is provided below.

The optimization process of the continuous phase spread spectrum coding sequence by using the ADMM method comprises the following steps:

assuming that the discrete spread spectrum code sequence contains M pulse signals, wherein each pulse contains N sub-pulses, the mth spread spectrum code signal can be expressed as

x _m ＝[x _m (0),x _m (1),…,x _m (N-1)] ^T

The cross-correlation function of the spread spectrum coded signal can be expressed as

i,j＝1,…,M,k＝1-N…,…,N-1

Peak sidelobe level is commonly used as an evaluation criterion for waveform cross-correlation optimization, and is as follows

i,j＝1,…,M,k＝1-N,…,N-1

Where k+.0 when i=j.

The desired waveform sequence has a low level of autocorrelation peak sidelobes and a low level of cross correlation peak at the same time, so an optimization problem is created as shown in the following equation, which constrains the level beside the autocorrelation peak of the waveform sequence to the level of epsilon, while constrains the cross correlation peak level of the waveform sequence to the level of delta.

x _i (N) =1, i, j=1, …, M, n=1, …, N, k=1-N, …, N-1 first performs a simplification process on the objective function to be

Written in matrix form can be expressed as

/>

i,j＝1,…,M,k＝1-N,…,N-1

Wherein there are

H _k For an N Toeplitz matrix, the transmitted signal is written in vector form, which can be expressed as

In addition Q _m A matrix is selected for the N-dimension partitions, expressed as

Q _m ＝[0 _N×(m-1)N ,I _N ,0 _N×(M-m)N ]

Introducing an auxiliary variable r _i,j (k) The optimization problem can be rewritten as

s.t. |r _i,j (k)| ² ≤ε,k≠0,i＝j,

|r _i,j (k)| ² ≤δ,i≠j

x(n ₁ )|＝1,i,j＝1,…,M,n ₁ =1..the NM, k=1-N, …, N-1, obviously, the above formula is a non-convex optimization problem under multiple constraints, whereas ADMM algorithm can effectively solve this type of problem, the augmented Lagrangian function of this optimization problem can be expressed as

The optimized sequence x can be output by the above function.

Based on the above scheme, the following simulation experiment is completed:

the performance of the orthogonal transmitting sequence and the space-frequency two-dimensional filter in inhibiting the interference of the main lobe of the intra-pulse transmission is verified through a simulation experiment.

Firstly, an optimized comparison result of an orthogonal spread spectrum coding sequence is given, and then simulation experiment results of a point target and a surface target for inhibiting the intra-pulse forwarding interference are respectively given to illustrate the effectiveness of the method provided by the invention.

In an orthogonal spread spectrum coding sequence optimization simulation experiment, assuming that the transmitted pulse number M=4, the sub-pulse coding number N=128 of each pulse is divided into two cases:

the first test condition is to restrict the cross-correlation peak level epsilon= -24dB first, the obtained optimized results of the cross-correlation and the autocorrelation of the orthogonal spread spectrum coding sequence are shown in fig. 5 and 6 respectively, and in order to embody the optimization effect of the algorithm of the invention, two latest waveform optimization algorithms are adopted for comparison, CAN and MM. As can be seen from fig. 5, the peak value levels of the autocorrelation sidelobes of the sequences optimized by the method of the present invention are at a lower level, and the autocorrelation sidelobes levels of the 4 code sequences are also nearly equal. As shown in fig. 6, since the given cross-correlation peak level constraint epsilon= -24dB, the cross-correlation average between the code sequences is controlled to be-24 dB, and compared with the CAN and MM algorithm, the code sequences optimized by the method of the present invention have lower auto-correlation side lobe level and cross-correlation level at the same time. In the comparison result of the side lobe level of the self-correlation peak value, the method provided by the invention has about 5.7dB and about 5.3dB of improvement compared with the CAN and the MM algorithm, and in the cross-correlation peak level result, the method has about 7.1dB and about 8.1dB of improvement compared with the CAN and the MM algorithm.

The second experimental case constrains the peak level epsilon= -24dB of the autocorrelation sidelobe, and the specific result is shown in fig. 7 and 8, and the cross correlation between the code sequences CAN be kept at a lower level after optimization, and the peak level of the autocorrelation is better than the result of the CAN and MM algorithm.

The method provided by the invention has about 6.4dB and 7.8dB of improvement compared with the CAN and MM algorithm in the cross-correlation peak level result, and about 5.4dB and 5.0dB of improvement compared with the CAN and MM algorithm in the self-correlation peak side lobe level comparison result.

In a point target simulation experiment, a point target simulation result of performing intra-pulse transfer main lobe interference suppression by using a space domain-frequency domain two-dimensional filter is given, an actual target input SNR is assumed to be 5dB, an artificial target interference input JSR is set to be 10dB, as shown in fig. 9 (a), the actual target is output by a red circular virtual coil, the actual target is submerged in the false target, the actual target and the false target cannot be distinguished, as shown in fig. 3, the actual target is positioned on a diagonal line of a carrier frequency domain and a space domain, at the moment, the actual target in echo can be removed by using a blocking matrix process, and the false target is reserved, so that an accurate covariance matrix of an interference signal is obtained, and as shown in fig. 9 (b), the point target simulation result after the space domain-frequency domain two-dimensional process is given, the false target is completely removed after the processing, and the actual target is reserved.

Fig. 10 shows the beam pattern at the real object range gate and the beam pattern at the false object range gate, and it can be found from the results in the figure that the corresponding nulls are generated at the range gates corresponding to the false objects, so that the false objects can be effectively suppressed.

In the face target simulation experiment, it should be noted that, for the face target scene, it is not feasible to decode and reprocess the received signal, because the decoding is a time domain processing method, alignment must be performed at each distance gate receiving the echo, and the imaging process is a frequency domain processing method. In this part of the experiment, imaging processing was directly performed using orthogonal transmit sequences without decoding.

In order to verify the effectiveness of the method provided by the invention, fig. 11 shows the results of an intra-pulse transfer main lobe interference suppression simulation experiment of a distributed scene. The radar transmitting array elements are distributed in the pitching direction and have different subcarrier frequencies, and the separation of receiving channels is realized by transmitting orthogonal coded signals.

Assuming that the forwarding jammer performs time delay forwarding within the receiving time of each transmitting pulse, an original scene is shown in fig. 11 (a), as shown in fig. 11 (b), forwarding jammer energy is gathered in an image, the imaging quality of the image is poor, after preprocessing by a two-dimensional blocking matrix, as shown in fig. 11 (c), interference is separated from a real target echo, and the imaging scene of an interference signal can be obviously seen. The method provided by the invention can obviously reduce the energy of interference and has better imaging quality as shown in fig. 11 (d), and finally the suppression processing of the main lobe interference of the intra-pulse transfer is completed by constructing a space domain-frequency domain two-dimensional filter through the covariance matrix of the interference signal obtained after the blocking pretreatment.

In the actual measurement interference data verification experiment of any complex waveform generation system, the actual measurement data verification is carried out by utilizing a Stream6400 broadband signal acquisition, playback and recording system, and the system provides A/D, D/A with the maximum of 6.4GHz and can be accessed to the radio frequency signal with the maximum of 8.1GHz.

First, a set of orthogonal spread spectrum coded LFM waveforms is generated, and the measured environment is shown in fig. 12, where transmit channels 1 and 2 transmit orthogonal spread spectrum coded LFM waveforms 1 and 2, respectively. And two signal echoes are received at the receiving end at the same time and respectively subjected to waveform separation processing so as to verify the orthogonality of the transmitted waveforms, and the radar works in an L-band.

As shown in fig. 13 to 17, it can be seen that the receiving channel 1 cannot directly separate two waveforms from the time domain and the frequency domain, but can effectively separate two orthogonal waveforms through orthogonal waveform separation processing, and specific distance information of the target can be obtained through pulse compression.

The algorithm verification is carried out by utilizing actually measured interference data, 4 alternate transmitting signals with different sub carrier frequencies are generated by utilizing one transmitting channel due to the limit of the number of transmitting channels in the experiment, and the other channel is used as an interference transmitting channel, and the corresponding carrier frequency of the transmitting waveform 1 is f due to the pulse receiving time delay at the receiving A/D sampling end, so that the waveform separation is convenient ₁ The initial phase of the signal of (1) is 0 and the initial phase of the transmitted waveform of (1) at the 5 th PRI moment is pi, so that the signals alternately reciprocate, and the corresponding carrier frequency f can be found through FFT processing at slow time ₁ Pulse echo. The transmitted baseband signal is in the form of LFM, bandwidth 150MHz, pulse width 10us, PRI 30us and frequency interval 0.1MHz. Because of the distance limitation in the experimental environment, a time delay smaller than PRI needs to be added to the interference emission channel, the frequency of each interference pulse is ensured to be consistent with the frequency of the emission pulse at the current moment of the radar, the specific radar and the interference emission pulse are shown in fig. 18, the actual measurement environment is shown in fig. 19, and the radar works in the x-band.

First, fig. 20 (a) shows the echo time domain result acquired by the radar receiving channel 1, where each received pulse corresponds to a different subcarrier frequency, and the corresponding frequency is shown in the figure. Fig. 20 (b) shows the first received pulse time domain result, and fig. 21 shows the echo matrix of the acquired data. The 4 peak values can be obtained in the range-doppler plane through pulse compression and doppler processing and respectively correspond to 1 real target and 3 false targets, the result is shown in fig. 22 (a), interference signals can be suppressed by performing carrier frequency domain filtering processing on received pulse separation, the real targets are reserved, and the result after interference suppression processing is shown in fig. 22 (b). From the results, the interference suppression algorithm provided by the invention can effectively suppress the pulse-transmitted main lobe interference signal, and the real target is reserved.

It will be evident to those skilled in the art that the invention is not limited to the details of the foregoing illustrative embodiments, and that the present invention may be embodied in other specific forms without departing from the spirit or essential characteristics thereof. The present embodiments are, therefore, to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. Any reference sign in a claim should not be construed as limiting the claim concerned.

Furthermore, it should be understood that although the present disclosure describes embodiments, not every embodiment is provided with a separate embodiment, and that this description is provided for clarity only, and that the disclosure is not limited to the embodiments described in detail below, and that the embodiments described in the examples may be combined as appropriate to form other embodiments that will be apparent to those skilled in the art.

Claims (9)

1. An anti-intra-pulse forwarding interference method based on an orthogonal transmission sequence and a multi-sub carrier frequency transmission scheme is characterized by comprising the following steps:

s1, establishing an array receiving mathematical model with intra-pulse forwarding interference based on a multi-sub carrier frequency transmitting scheme of a MIMO radar platform;

s2, deducing a space-frequency domain two-dimensional intra-pulse forwarding interference suppression filter by utilizing a minimum undistorted response principle on the basis of intra-pulse forwarding interference so as to suppress forwarding interference;

s3, considering that the multi-sub carrier frequency transmission scheme needs the orthogonality of the transmission waveforms of different channels to realize the separation of the received signals, adopting an ADMM algorithm to optimize the orthogonal transmission sequences, and obtaining the orthogonal spread spectrum coding LFM waveform after optimization, which has the characteristics of low cross-correlation energy and low autocorrelation sidelobe level.

2. The method for anti-intra-pulse forwarding interference based on orthogonal transmission sequences and multi-carrier frequency transmission scheme according to claim 1, wherein the multi-carrier frequency transmission scheme in step S1 is as follows:

assuming that there are one-dimensional linear arrays of P transmitting array elements and Q receiving array elements, the transmitting signal of the P-th transmitting channel is expressed as

wherein ,

for baseband signals generated using orthogonal transmit sequences, f _p A carrier frequency for the p-th transmit signal;

under the narrowband assumption, the target position of the far field is represented as (θ, R), where θ is the beam dip angle, and R is the true distance between the target and the radar, and then the echo of the q-th receiving channel is represented as:

wherein ,τ_p,q ＝[2R-d(p-1)sin(θ)-d(q-1)sinθ]And/c is the double-pass time delay from the p-th transmitting array element to the q-th receiving array element;

in addition, τ=2r/c

Wherein, gamma is the receiving scattering coefficient of the target, which is determined by the RCS of the target, the propagation response of the channel and the like, d is the array element interval, lambda ₁ ＝c/f ₁ Representing the wavelength of the radiated signal;

the Q receiving channel echo output results are written into a matrix form, and the receiving echo after fast time matching filtering processing is expressed as

Wherein ω (t) = [ ω ] _1,1 (t),ω _1,2 (t),…,ω _q,p (t),…,ω _Q,P (t)] ^T Matching and filtering output results for each receiving channel, wherein a (R, theta) is a transmitting guide vector; b (θ) represents a received steering vector:

let the spatial position of the real object be (θ) _T ,R _T ) While the repeater jammer position is (θ _J ,R _J ) The mixed received echo is expressed as

Where ΔR/c is expressed as the fast time delay generated by the jammer DRFM, which is less than one PRI.

3. The method for anti-intra-pulse transmission interference based on orthogonal transmission sequence and multi-carrier frequency transmission scheme as claimed in claim 2, wherein the carrier frequency f of the p-th transmission signal _p The method comprises the following steps:

f _p ＝f ₁ +(p-1)Δf,p＝1,2,…,P

wherein ,f₁ For the carrier frequency of the first transmit channel, Δf is the minimum frequency step interval of the subcarrier frequency;

the emission steering vector a (R, θ) is:

the received steering vector b (θ) is:

4. the method for anti-intra-pulse transmission interference based on the orthogonal transmission sequence and the multi-carrier frequency transmission scheme according to claim 1, wherein in the step S2, the design scheme of the spatial-frequency domain two-dimensional intra-pulse transmission interference suppression filter is as follows:

firstly, preprocessing a received mixed echo, namely, blocking each range gate receiving the echo by utilizing a two-dimensional blocking matrix;

defining the sub-carrier frequency of the target as f _T ＝2Δf·R _T The carrier frequency domain blocking matrix is expressed as

The airspace blocking matrix is expressed as

The q-th receive channel echo after two-dimensional blocking preprocessing is expressed as

The space-frequency two-dimensional blocking processing is carried out on each range gate to inhibit the real target echo signal, so that the data after the blocking processing only contains the forwarding interference signal, the covariance matrix of the signal after the space-frequency two-dimensional blocking processing is equivalent to the covariance matrix of the interference signal, and the interference covariance matrix is expressed as

Wherein L is the snapshot number;

thereby establishing a space-frequency filter equation for suppressing interference, expressed as

min w ^H (f _T ,θ _T )R _q (t)w(f _T ,θ _T )

s.t.w ^H (f _T ,θ _T )s(f _T ,θ _T )＝1

Wherein s (f _T ,θ _T )＝s _f (f _T )⊙s _s (θ _T ) The steering vector corresponding to the carrier frequency domain is expressed as

The steering vector corresponding to the transmit spatial domain is represented as

The optimal weight vector of the adaptive spatial-frequency domain two-dimensional intra-pulse transfer interference suppression filter based on the minimum undistorted response principle is given by:

and (3) performing space-frequency two-dimensional filtering processing on the received signal of each range gate after space-frequency two-dimensional blocking processing to inhibit the interference signal so as to obtain an echo corresponding to the real target:

wherein there is->

Because the subcarrier frequencies of the real targets have a one-to-one correspondence with DOA, the false targets are distributed on the diagonal of the space domain-carrier frequency domain, and the false targets have an offset of 2 delta f (R _J -R _T ) And/c representsAfter the above filtering process, the real target will remain unchanged, while the false target is filtered out due to this offset.

5. The method for anti-intra-pulse transmission interference based on orthogonal transmission sequence and multi-carrier frequency transmission scheme according to claim 1, wherein said S2 further comprises a scheme of transmitting different sub-carrier frequencies to four array elements in a pitching manner: firstly, echo signals of different channels are obtained through orthogonal transmitting sequence decoding, secondly, blocking preprocessing is adopted to inhibit real target signals so as to obtain accurate covariance matrixes of intra-pulse transfer main lobe interference signals, the obtained interference covariance matrixes are utilized to filter the interference signals through space domain-frequency domain two-dimensional filtering, and finally, distance Doppler processing is carried out to obtain final real target results.

6. The method for anti-intra-pulse forwarding interference based on orthogonal transmission sequences and multi-carrier frequency transmission scheme according to claim 1, wherein in the step S3, the optimization of the orthogonal transmission sequences by adopting an ADMM algorithm is to optimize the continuous phase spread spectrum coding sequences, and the process includes:

and establishing a mathematical model of the spread spectrum coding LFM signal, deducing a specific processing process of a spread spectrum technology in coding and decoding, and optimizing a continuous phase spread spectrum coding sequence by using an ADMM method.

7. The method for anti-intra-pulse transmission interference based on orthogonal transmission sequences and multi-carrier frequency transmission scheme according to claim 6, wherein the mathematical model building process of the spread spectrum coding LFM signal comprises:

assuming that the signal to be transferred is represented as a standard LFM signal, there is

Wherein T is the pulse width of the LFM signal, alpha is the frequency modulation slope of the LFM signal, and the spread spectrum coding signal is expressed as

wherein ,C_n For discrete spread-spectrum coding sequences, T _C For the encoded sub-pulse width, P (t) is a rectangular window function;

multiplying the LFM signal with the spread spectrum coded signal to obtain a spread spectrum coded LFM signal, expressed as

B(t)＝A(t)·C(t)

After up-conversion treatment, the radio frequency end transmitting signal is expressed as

T _x (t)＝B(t)·cos(2πf _c t)

The receiver receives the echo signal, and performs the down-conversion processing and the spread spectrum coding and decoding process, which is expressed as

D(t)＝R _x (t)·[C(t)] ^*

To verify orthogonality between spread spectrum coded LFM signals, a cross-correlation ambiguity function of different spread spectrum coded LFM signals is given, assuming a set of spread spectrum coded LFM signals exist, respectively satisfying

wherein ,C_m ，D _m Respectively correspond to different spread spectrum sequences, T _C For sub-pulse width, P (t) is a rectangular pulse, alpha ₁ And alpha is ₂ Frequency modulation slopes corresponding to different LFM signals respectively;

the cross-correlation function of the spread spectrum encoded LFM signal is written as

When alpha is ₁ ＝α ₂ When the above conditions are satisfied

Order the

Then the above is rewritten as

8. The method for anti-intra-pulse transmission interference based on orthogonal transmission sequences and multi-carrier frequency transmission scheme according to claim 6, wherein said optimizing the continuous phase spread spectrum coding sequence by using ADMM method comprises:

assuming that the discrete spread spectrum code sequence contains M pulse signals, wherein each pulse contains N sub-pulses, the mth spread spectrum code signal is expressed as

x _m ＝[x _m (0),x _m (1),…,x _m (N-1)] ^T

The cross-correlation function of the spread spectrum coded signal is expressed as

/>

i,j＝1,…,M,k＝1-N,…,N-1

Peak sidelobe level is commonly used as an evaluation criterion for waveform cross-correlation optimization, and is as follows

i,j＝1,…,M,k＝1-N,…,N-1

Wherein k+.0 when i=j;

the expected waveform sequence has lower autocorrelation peak sidelobe level and simultaneously lower cross correlation peak level, so that an optimization problem shown in the following formula is established, the side level of the autocorrelation peak of the waveform sequence is restrained at the level epsilon, and the cross correlation peak level of the waveform sequence is restrained within the level range delta;

|x _i (n)|＝1,i,j＝1,...,M,n＝1,...,N,k＝1-N,…,N-1

first, the objective function is simplified and then

Written in matrix form expressed as

i,j＝1,...,M,k＝1-N,...,N-1

Wherein there are

H _k For an N Toeplitz matrix, the transmitted signal is written in vector form, expressed as

In addition Q _m A matrix is selected for the N-dimension partitions, expressed as

Q _m ＝[0 _N×(m-1)N ,I _N ,0 _N×(M-m)N ]

Introducing an auxiliary variable r _i,j (k) Rewriting optimization problems to

s.t.|r _i,j (k)| ² ≤ε,k≠0,i＝j,

|r _i,j (k)| ² ≤δ,i≠j

|x(n ₁ )|＝1,i,j＝1,...,M,n ₁ ＝1,...,NM,k＝1-N,…,N-1

The above is a non-convex optimization problem under multiple constraints, which is solved by the ADMM algorithm, and the augmented Lagrangian function of the problem is expressed as

The output optimization sequence x is solved by an ADMM algorithm.

9. The method for anti-intra-pulse transmission interference based on orthogonal transmission sequences and multi-carrier frequency transmission scheme according to claim 8, wherein said specific iterative step of solving by means of ADMM comprises:

(1) Fixed variables x and λ _i,j (k) Updating

δ ^(t+1)

By introducing auxiliary variables

and />

Re-representing the optimization problem as

s.t.|r _i,i (k)| ² ≤ε,k≠0

|r _i,j (k)| ² ≤δ,i≠j

Obtaining

In the above formula, because delta is equal to

Coupling, so that the above formula is re-substituted into the objective function to obtain

Wherein there are

The optimization problem is approximately expressed as

wherein ,

(2) Fixed variable

and δ^(t) Update x ^(t+1)

The optimization problem is expressed as

/>

s.t.|x(n ₁ )|＝1,n ₁ ＝1,...,NM

Wherein there are

Converting the above optimization problem into the following form, the corresponding objective function is simplified into

s.t.|x(n ₁ )|＝1,n ₁ ＝1,…,NM

Ignoring the constant term, the above equation is re-expressed as

s.t.|x(n ₁ )|＝1,n ₁ ＝1,…,NM

Wherein there are

and

U ₁ Is a real symmetric matrix, then Diag (U) -U ₁ Is half ofA positive definite matrix, wherein

Corresponding attestation procedure in appendix D, definition l ₁ For the number of iterations

s.t.|x(n ₁ )|＝1,n ₁ ＝1,...,NM

At the position of

The maximum value is obtained

Because of the constant modulus of x, the first term of the above equation is constant and the relaxation of the optimization problem is re-expressed as

s.t.|x(n ₁ )|＝1,n ₁ ＝1,...,NM

U is set to ₁ Substituting the target function to obtain

s.t.|x(n ₁ )|＝1,n ₁ ＝1,...,NM

Wherein there are

/>

Order the

The optimized objective function is converted into

Ignoring the constant term, the corresponding optimization problem is re-expressed as

s.t.|x(n ₁ )|＝1，n1＝1，...，NM

Wherein there are

The corresponding solution is

(3) Fixing other variables and updating

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