CN114696788B - Wave form and filter combined cognition design method for resisting multi-main lobe interference - Google Patents
Wave form and filter combined cognition design method for resisting multi-main lobe interference Download PDFInfo
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Abstract
The invention discloses a wave form and filter joint cognition design method for resisting multi-main lobe interference, which comprises the following steps: s1, constructing a C & I, direct intermittent sampling and repeated intermittent sampling interference signal model and a mismatch filter model based on a constant-mode phase coded signal; s2, under the condition that interference parameters are completely known or deviation exists, establishing a wave form correlation function peak value level, a correlation function main lobe template matching error and an interference energy weighting and minimizing criterion transmitting-receiving joint optimization problem under the constraint of signal to noise ratio; s3, converting the optimization problem into a minimization problem related to the independent variable function, and solving by using an iterative L-BFGS algorithm. The optimized signal designed by the invention has good Doppler tolerance, multi-main-lobe interference resistance and lower peak sidelobes after mismatch filtering.
Description
Technical Field
The invention belongs to the field of radar anti-interference surgery, and particularly relates to a wave form and filter combined cognition design method for resisting multi-main-lobe interference.
Background
In recent years, with the high-speed development of modern electronic technology, electronic countermeasure is increasingly strong, various interference patterns are layered, and the normal operation of a radar system is seriously hindered. For main lobe interference, the interference energy has absolute advantages, the main lobe interference is highly overlapped with a target in dimensions such as space time frequency, and the like, the effect of the existing interference suppression means is poor, and the main lobe interference is still one of the problems to be solved in the radar industry. The general main lobe interference resistance method comprises the following steps: signal processing and waveform design.
In terms of a signal processing main lobe interference resisting method, a common signal processing method includes: blind source separation and filtering. The blind source separation can separate the mixed signals without priori knowledge, and if the blind source separation main lobe interference resisting algorithm based on matrix combined diagonalization feature vectors is provided in the document [ G.Huang, L.Yang, G.Su.Blind source separation used for radar anti-jamming [ C ].2003International Conference on Neural Networks and Signal Processing,Nanjing,China,2003:1382-1385 ], the target signals and the interference signals are separated, so that interference suppression is realized, and the influence of main lobe interference on radar detection performance can be effectively reduced. However, after the mixed signal is separated, there is often a small amount of interference residual, and a single type of interference is aimed at. The filtering process mainly utilizes the difference of interference signals and target echoes in time, frequency, space, polarization and other domains, and designs filter parameters in different dimensions to achieve the effect of interference suppression, such as document [ S.Zhang, Y.Yang, G.Cui, et al range-velocity jamming suppression algorithm based on adaptive iterative filtering [ C ] 2016IEEE Radar Conference,Philadelphia,PA,USA,2016:1-6 ], and the distance-speed joint spoofing interference suppression is achieved by designing a mismatch filter for each distance-Doppler unit. However, this method requires that the waveform of the interfering signal be precisely known and is only applicable to a certain interference type.
The method for resisting main lobe interference by waveform design is characterized in that the difference of target echo and interference signals in time, frequency, space, polarization and other domains is amplified by designing the information of the phase, frequency and the like of intra-pulse and inter-pulse waveforms, so that the purpose of resisting interference is achieved, such as document [ Xu Leilei ], radar waveform design and a plurality of technical researches on resisting main lobe active interference [ D ]. Siemens, siemens electronic technology university, 2019 ] ], the interference signals are compressed by utilizing a waveform optimization method based on the amplitude difference between angular domain waveforms and the interference signals, and DRFM forward interference is effectively resisted. However, this method can only resist a single type of interference, and cannot effectively resist the composite interference where multiple interference types are superimposed.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a waveform and filter combined cognition design method for resisting multi-main-lobe interference.
The aim of the invention is realized by the following technical scheme: a wave form and filter joint cognition design method for resisting multi-main lobe interference comprises the following steps:
s1, constructing a C & I, direct intermittent sampling and repeated intermittent sampling interference signal model and a mismatch filter model based on a constant-mode phase coded signal;
s2, under the condition that interference parameters are completely known or deviation exists, establishing a wave form correlation function peak value level, a correlation function main lobe template matching error and an interference energy weighting and minimizing criterion transmitting-receiving joint optimization problem under the constraint of signal to noise ratio;
s3, converting the optimization problem into a minimization problem related to the independent variable function, and solving by using an iterative L-BFGS algorithm.
Further, the step S1 specifically includes the following sub-steps:
s11, the constant-mode phase coding signal is expressed as:
in the formula [ (] T Representing the transpose s n For transmitting codewords of the waveform, n=1, 2, …, N s ，N s The number of codewords for the phase encoded waveform; the nth element s n Expressed as:
in the method, in the process of the invention,
representation->
Phase of the nth codeword, +.>
Encoding the phase of the signal s for a constant mode phase;
s12, establishing C&I interference signal model: for C&I interference, suppose that the DRFM jammer intercepts radar signals, from s i Starting, m code words are taken as one section, each section is forwarded for l times, k sections are intercepted in total, and the whole C&I interference signal codeword length N s ＝klm；C&The I interference signal is:
wherein H is t T is more than or equal to 1 and less than or equal to k in the t section intercepted by the jammer; h t The represented codeword is expressed as:
Η t ＝[s (t-1)ml+i ,s (t-1)ml+i+1 ,…,s (t-1)ml+i+m-1 ]；
s13, directly intermittently sampling an interference signal model: for direct intermittent sampling interference, suppose that a DRFM (digital radio frequency modulation) jammer intercepts radar signals, and s is a reference number i Firstly, m code words are taken as a section, and are intercepted and forwarded once every ml code words, k sections are intercepted in total, and interference is directly and intermittently sampledThe signals are as follows:
J 2 ＝[Η′ 1 ,Η′ 0 ,Η′ 2 ,Η′ 0 ,…,Η′ k ,Η′ 0 ] T
in the formula, H' 0 ＝0 1×m(l-1) ，0 1×m(l-1) A 0 vector representing 1×m (l-1); h' t For the t-th segment intercepted by the jammer, the represented codeword is expressed as:
Η′ t ＝[s (t-1)ml+i ,s (t-1)ml+i+1 ,…s (t-1)ml+i+m-1 ]；
s14, repeating the intermittent sampling interference signal model: for repeated intermittent sampling interference, assume that a DRFM (digital radio frequency modulation) jammer intercepts radar signals, and then s i Firstly, m code words are taken as a section, the code words are intercepted once every ml, the code words are repeated q times and then forwarded, k sections are intercepted in total, and the repeated intermittent sampling interference signals are as follows:
in the formula, H 0 ＝0 1×m(l-q) ，Η″ t For the t-th segment intercepted by the jammer, the represented codeword is expressed as:
Η″ t ＝[s (t-1)ml+i ,s (t-1)ml+i+1 ,…s (t-1)ml+i+m-1 ]；
s15, a mismatch filter signal model: assume that the length of a corresponding mismatch filter h of a radar receiving end is N h ，N h ≥N s The mismatch filter h is denoted as:
the nth element h n Expressed as:
where a is the magnitude vector of the mismatch filter h, a n Is the nth element in a; θ is the phase vector of the mismatch filter h, θ n Is the n element in theta; h=a.exp (j θ), and a indicates the Hadamard product.
Further, the step S2 specifically includes:
s21, designing optimization criteria:
(1) Distance sidelobe: the output of the phase encoded signal s through the mismatch filter h is represented at a distance displacement j as:
wherein, represents conjugation, Γ 1 Represents a value interval, Γ 1 ＝[-(N s +N h )/2+1,(N s +N h )/2-1]；
Let ω be j For the widened main lobe region, j=0, ±1, …, ±m, M is a main lobe width control parameter;
all the distance main lobe levels are stacked in vector omega main Expressed as:
ω main ＝[ω -M ,…,ω -1 ,ω 0 ,ω 1 ,…,ω M ] T
all range side lobe levels are stacked in vector ω side Expressed as:
let the sidelobe region be denoted as Γ 2 ，Γ 2 Expressed as:
Γ 2 ＝[-(N s +N h )/2+1,-M+1]∪[M-1,(N s +N h )/2-1]
the range side lobe is reduced by minimizing the peak side lobe, namely:
(2) Loss of signal-to-noise ratio:
|h H h-N s |≤η 1
|ω 0 -N s |≤η 2
in the formula, the constant eta 1 ≥0，η 2 More than or equal to 0, and the superscript H represents conjugate transposition;
(3) Main lobe control: assume that
Is the desired main lobe, i.e. q is a vector of dimension 2m+1; vector e is the error vector of the desired main lobe and the designed main lobe, expressed as:
e＝ω main -q
the nth element e (n) of the error vector e is expressed as:
e(n)＝ω n-M-1 -q(n)，1≤n≤2M+1
the main lobe shape is maintained with a method that minimizes the maximum main lobe matching error, namely:
(4) Multi-main lobe interference resistance: interference signal J m The output result via the mismatch filter h is represented at a distance displacement j as:
J m (n) represents J m In (2) the n-th element, all distance levels in the above formula are stacked in vector ω' m Expressed as:
when the interference parameters are completely known: cognitive radar senses multi-main-lobe interference and generates interference parametersUnder completely known conditions, different interference signals J m Distance level stack vector ω 'generated by mismatch filter h' m ，m＝1,2,…,N J All stacked on vector omega J ，ω J Expressed as:
N J indicating the number of interferences;
when the interference parameter has deviation: let it be assumed that actual C&The number of interception segments of the interference I is k, the forwarding frequency is l, the number of interception segments of the perceived parameter is k ', and the forwarding frequency is l'. Assuming that the error is small, there is k=k '+l, l=l' -L, L being a natural number greater than 0. In the presence of errors, C&I interference distance level stack vector
Expressed as:
in the formula omega' 1 C is generated by intercepting segment number k' and forwarding frequency l&Stacking vectors of all distance levels after filtering processing of the I interference and mismatch filter;
c is generated by intercepting segment number k '+i and forwarding frequency l' -i&Stacking vectors of all distance levels after filtering processing of the I interference and mismatch filter; />
C is generated by intercepting segment number k '-i and forwarding frequency l' +i&Stacking vectors of all distance levels after filtering processing of the I interference and mismatch filter, i=1, 2, …, L;
the actual direct intermittent sampling interference generation mode is assumed to be: taking m code words as a section, and every mIntercepting and forwarding l code words once, intercepting k sections altogether, wherein the perceived generation mode of direct intermittent sampling interference is as follows; taking m code words as a section, intercepting and forwarding every ml 'code words, intercepting k' sections altogether, and assuming that the error is smaller, k=k '+L, and l=l' -L are included; direct intermittent sampling of interference distance level stacking vectors in the presence of deviations
Expressed as:
ω′ 2 taking m code words as a section, intercepting and forwarding every ml code words, and intercepting the stacking vectors of direct intermittent sampling interference generated by the k section and all distance levels after filtering treatment of a mismatch filter;
taking m code words as a section, intercepting and forwarding every m (l '-i) code words, and intercepting direct intermittent sampling interference generated by k' +i sections and stacking vectors of all distance levels after filtering treatment of a mismatch filter; />
Taking m code words as a section, intercepting and forwarding every m (l '+i) code words, and intercepting the stacking vectors of direct intermittent sampling interference generated by the section k' -i and all distance levels after filtering treatment of a mismatch filter;
the actual repeated intermittent sampling interference generation mode is assumed to be: taking m code words as a section, intercepting and forwarding q times every ml code words, and intercepting k sections altogether; the perceived repeated intermittent sampling interference generation mode is as follows; taking m code words as a section, intercepting and forwarding q times every ml 'code words, intercepting k' sections altogether, and assuming that the error is smaller, k=k '+L, and l=l' -L are included; repeated intermittent sampling of interference distance level stacking vectors in the presence of deviations
Expressed as: />
ω′ 3 Taking m code words as a section, intercepting and forwarding q times every ml 'code words, and intercepting the stacking vectors of the repeated intermittent sampling interference generated by the k' section and all distance levels after filtering treatment of a mismatch filter altogether;
taking m code words as a section, intercepting and forwarding q times every m (l '-i) code words, and intercepting repeated intermittent sampling interference generated by k' +i sections and stacking vectors of all distance levels after filtering treatment of a mismatch filter; />
Taking m code words as a section, intercepting and forwarding q times every m (l '+i) code words, and intercepting the repeated intermittent sampling interference generated by the k' -i section and the stacking vectors of all distance levels after the filtering treatment of a mismatch filter;
all distance levels ω of all interference output via mismatched filters J The method comprises the following steps: if there is no deviation in several disturbance parameters, all distance levels omega J Is that
If there is a deviation in one or more of the interference parameters, then +.>
The corresponding vector in (a) is replaced by a distance level stack vector when errors exist;
all distance levels of all interference output via the mismatch filter are compressed using a min-max optimization criterion, namely:
s22, establishing an optimization problem: according to the optimization criterion of the S21 design, the optimization problem of the phase coding signal S and the mismatch filter h resisting the multi-main lobe interference is expressed as follows:
s.t.|h H h-N s |≤γ 1
wherein lambda is 1 ，λ 2 Is a preset weight coefficient.
Further, the specific implementation method of the S3 is as follows:
s31, optimizing problem conversion: converting the optimization problem into a minimization problem with respect to the independent variable function, namely:
wherein lambda is 3 For the weight coefficient to be set in advance, I ∞ Represents an infinite norm;
defining an objective function as:
f(x)＝||ω side || p +λ 1 ||ω J || p +λ 2 ||e|| p +λ 3 ||h H h-N s || p
in the method, in the process of the invention, I p Represents the p-norm; vector quantity
Is composed of vector->
a and θ are sequentially formed column vectors expressed as:
s32, solving an optimization problem: and solving the problem by using an L-BFGS algorithm based on iteration, solving the minimum value of the objective function by using the L-BFGS algorithm, continuously iterating until the objective function f (x) reaches the minimum descent epsilon, stopping iterating, and outputting x.
The beneficial effects of the invention are as follows: firstly, constructing a C & I, direct intermittent sampling and repeated intermittent sampling interference signal model based on a constant-mode phase coding signal; then under the condition that the interference parameters are completely known or deviation exists, the problem of transmitting-receiving joint optimization of waveform correlation function peak level, correlation function main lobe template matching error and interference energy weighted sum minimization criterion under the constraint of signal to noise ratio is established; finally, the optimization problem of non-convex, non-smooth and constraint is converted into the minimization problem of the function of independent variables (composed of signal phase, filter amplitude and phase) by using methods such as penalty function method, norm conversion and the like, and the iterative L-BFGS algorithm is used for solving. The optimized signal designed by the invention has good Doppler tolerance, multi-main-lobe interference resistance and lower peak sidelobes after mismatch filtering.
Drawings
FIG. 1 is a flow chart of a method for joint cognitive design of waveforms and filters for multi-lobe interference resistance in accordance with the present invention;
FIG. 2 is a schematic diagram of C & I interference generation;
FIG. 3 is a schematic diagram of direct intermittent sampling interference generation;
FIG. 4 is a schematic diagram of a repeated intermittent sampling disturbance generation;
FIG. 5 is a flowchart of an iteration-based L-BFGS algorithm;
FIG. 6 is an optimized signal Doppler tolerance designed when the interference parameters are fully known and there is a deviation in the interference parameters;
FIG. 7 is a graph showing the result of the matched filtering of the LFM signal and its corresponding C & I interference, direct intermittent sampling interference and repeated intermittent sampling interference;
FIG. 8 is a result of mismatch filtering the optimized signal and its corresponding multi-lobe interference when the interference parameter is completely known and has a deviation from the interference parameter;
fig. 9 is a comparison diagram of detection results of an optimized signal designed when LFM signals and interference parameters are completely known and have deviations from the interference parameters.
Detailed Description
The technical scheme of the invention is further described below with reference to the accompanying drawings.
As shown in fig. 1, the method for designing the waveform and filter joint cognition for resisting multi-main lobe interference comprises the following steps:
s1, constructing a C & I, direct intermittent sampling and repeated intermittent sampling interference signal model and a mismatch filter model based on a constant-mode phase coded signal; the method specifically comprises the following sub-steps:
s11, the constant-mode phase coding signal is expressed as:
in the formula [ (] T Representing the transpose s n For transmitting codewords of the waveform, n=1, 2, …, N s ，N s The number of codewords for the phase encoded waveform; the nth element s n Expressed as:
in the method, in the process of the invention,
representation->
Phase of the nth codeword, +.>
Encoding the phase of the signal s for a constant mode phase;
s12, establishing C&I interference signal model: for C&I trunkScrambling, suppose that the DRFM jammer intercepts radar signals, from s i Starting, m code words are taken as one section, each section is forwarded for l times, k sections are intercepted in total, and the whole C&I interference signal codeword length N s =klm; as shown in FIG. 2, C&The I interference signal is:
wherein H is t T is more than or equal to 1 and less than or equal to k in the t section intercepted by the jammer; h t The represented codeword is expressed as:
Η t ＝[s (t-1)ml+i ,s (t-1)ml+i+1 ,…,s (t-1)ml+i+m-1 ]
A 1 as a matrix, it can be expressed as:
1. 1 represents that the elements at positions i to i+m-1 are all 1;
s13, directly intermittently sampling an interference signal model: for direct intermittent sampling interference, suppose that a DRFM (digital radio frequency modulation) jammer intercepts radar signals, and s is a reference number i Firstly, m code words are taken as a section, and are intercepted and forwarded once every ml code words, k sections are intercepted in total, as shown in fig. 3, and the direct intermittent sampling interference signals are as follows:
J 2 ＝[Η′ 1 ,Η′ 0 ,Η′ 2 ,Η′ 0 ,…,Η′ k ,Η′ 0 ] T
＝A 2 s
in the formula, H' 0 ＝0 1×m(l-1) ，0 1×m(l-1) A 0 vector representing 1×m (l-1); h' t For the t-th segment intercepted by the jammer, the represented codeword is expressed as:
Η′ t ＝[s (t-1)ml+i ,s (t-1)ml+i+1 ,…s (t-1)ml+i+m-1 ]
A 2 as a matrix, it can be expressed as:
s14, repeating the intermittent sampling interference signal model: for repeated intermittent sampling interference, assume that a DRFM (digital radio frequency modulation) jammer intercepts radar signals, and then s i Firstly, m code words are taken as a section, the code words are intercepted once every ml, the code words are repeated q times and then forwarded, k sections are intercepted in total, and as shown in fig. 4, the repeated intermittent sampling interference signals are as follows:
in the formula, H 0 ＝0 1×m(l-q) ，Η″ t For the t-th segment intercepted by the jammer, the represented codeword is expressed as:
Η″ t ＝[s (t-1)ml+i ,s (t-1)ml+i+1 ,…s (t-1)ml+i+m-1 ]
A 3 as a matrix, it can be expressed as:
s15, a mismatch filter signal model: assume that the length of a corresponding mismatch filter h of a radar receiving end is N h ，N h ≥N s The mismatch filter h is denoted as:
the nth element h n Expressed as:
where a is the magnitude vector of the mismatch filter h, a n Is the nth element in a; θ is the phase vector of the mismatch filter h, θ n Is the n element in theta; h=a.exp (j θ), and a indicates the Hadamard product.
S2, under the condition that interference parameters are completely known or deviation exists, establishing a wave form correlation function peak value level, a correlation function main lobe template matching error and an interference energy weighting and minimizing criterion transmitting-receiving joint optimization problem under the constraint of signal to noise ratio;
the step S2 specifically comprises the following steps:
s21, designing optimization criteria:
(1) Distance sidelobe: in practical application, the distance sidelobe level output by the mismatch filter should be as low as possible, so as to ensure that a weak target is not submerged by a high sidelobe of a strong target echo signal;
the output of the phase encoded signal s through the mismatch filter h is represented at a distance displacement j as:
wherein, represents conjugation, Γ 1 Represents a value interval, Γ 1 ＝[-(N s +N h )/2+1,(N s +N h )/2-1]；
Let ω be j For the widened main lobe region, j=0, ±1, …, ±m, M is a main lobe width control parameter;
all the distance main lobe levels are stacked in vector omega main Expressed as:
ω main ＝[ω -M ,…,ω -1 ,ω 0 ,ω 1 ,…,ω M ] T
all range side lobe levels are stacked in vector ω side Expressed as:
let the sidelobe region be denoted as Γ 2 ，Γ 2 Represented as：
Γ 2 ＝[-(N s +N h )/2+1,-M+1]∪[M-1,(N s +N h )/2-1]
The range side lobe is reduced by minimizing the peak side lobe, namely:
(2) Loss of signal-to-noise ratio, which can cause a certain loss in the process of designing a mismatch filter. There is therefore a need to control the signal-to-noise loss, namely:
|h H h-N s |≤η 1
|ω 0 -N s |≤η 2
in the formula, the constant eta 1 ≥0，η 2 More than or equal to 0, wherein the specific value can be defined by a user, and the superscript H represents conjugate transposition;
(3) Main lobe control: assume that
Is the desired main lobe, i.e. q is a vector of dimension 2m+1; vector e is the error vector of the desired main lobe and the designed main lobe, expressed as:
e＝ω main -q
the nth element e (n) of the error vector e is expressed as:
e(n)＝ω n-M-1 -q(n)，1≤n≤2M+1
the main lobe shape is maintained with a method that minimizes the maximum main lobe matching error, namely:
(4) Multi-main lobe interference resistance: in practical applications, the distance level between the mismatched filter and the multi-main lobe interference output should be as low as possible, so as to reduce the influence of the interference signal on the real target detection. Interference signal J m Output result through mismatch filter hExpressed at distance displacement j as:
J m (n) represents J m In (2) the n-th element, all distance levels in the above formula are stacked in vector ω' m Expressed as:
when the interference parameters are completely known: the cognitive radar senses multi-main-lobe interference, and different interference signals J are transmitted under the condition that interference parameters are completely known m Distance level stack vector ω 'generated by mismatch filter h' m ，m＝1,2,…,N J All stacked on vector omega J ，ω J Expressed as:
N J indicating the number of disturbances, in this example 3;
when the interference parameter has deviation: the cognitive radar senses multi-main-lobe interference, and under the condition that other types of interference signal parameters are known, C&The interference parameters of I have deviations. Let it be assumed that actual C&The number of interception segments of the interference I is k, the forwarding frequency is l, the number of interception segments of the perceived parameter is k ', and the forwarding frequency is l'. Assuming that the error is small, there is k=k '+l, l=l' -L, L being a natural number greater than 0. In the presence of errors, C&I interference distance level stack vector
Expressed as: />
Wherein omega is 1 'is C generated by intercepting segment number k' and forwarding frequency l&Stacking vectors of all distance levels after filtering processing of the I interference and mismatch filter;
c is generated by intercepting segment number k '+i and forwarding frequency l' -i&Stacking vectors of all distance levels after filtering processing of the I interference and mismatch filter; />
C is generated by intercepting segment number k '-i and forwarding frequency l' +i&Stacking vectors of all distance levels after filtering processing of the I interference and mismatch filter, i=1, 2, …, L;
similarly, under the condition that other types of interference signal parameters are known, the estimation of the direct intermittent sampling interference parameters has a certain error. The actual direct intermittent sampling interference generation mode is assumed to be: taking m code words as a section, intercepting and forwarding every ml code words, intercepting k sections altogether, and the perceived generation mode of direct intermittent sampling interference is as follows; taking m code words as a section, intercepting and forwarding every ml 'code words, intercepting k' sections altogether, and assuming that the error is smaller, k=k '+L, and l=l' -L are included; direct intermittent sampling of interference distance level stacking vectors in the presence of deviations
Expressed as:
ω′ 2 taking m code words as a section, intercepting and forwarding every ml code words, and intercepting the stacking vectors of direct intermittent sampling interference generated by the k section and all distance levels after filtering treatment of a mismatch filter;
m code words are used as a section, every otherm (l '-i) code words are intercepted once and forwarded, and stacking vectors of direct intermittent sampling interference generated by k' +i sections and all distance levels after filtering treatment of a mismatch filter are intercepted altogether; />
Taking m code words as a section, intercepting and forwarding every m (l '+i) code words, and intercepting the stacking vectors of direct intermittent sampling interference generated by the section k' -i and all distance levels after filtering treatment of a mismatch filter;
under the condition that other types of interference signal parameters are known, the estimation of the repeated intermittent sampling interference parameters has a certain error. The actual repeated intermittent sampling interference generation mode is assumed to be: taking m code words as a section, intercepting and forwarding q times every ml code words, and intercepting k sections altogether; the perceived repeated intermittent sampling interference generation mode is as follows; taking m code words as a section, intercepting and forwarding q times every ml 'code words, intercepting k' sections altogether, and assuming that the error is smaller, k=k '+L, and l=l' -L are included; repeated intermittent sampling of interference distance level stacking vectors in the presence of deviations
Expressed as:
ω′ 3 taking m code words as a section, intercepting and forwarding q times every ml 'code words, and intercepting the stacking vectors of the repeated intermittent sampling interference generated by the k' section and all distance levels after filtering treatment of a mismatch filter altogether;
taking m code words as a section, intercepting and forwarding q times every m (l '-i) code words, and intercepting repeated intermittent sampling interference generated by k' +i sections and stacking vectors of all distance levels after filtering treatment of a mismatch filter; />
Taking m code words as a section, intercepting and forwarding q times every m (l '+i) code words, and intercepting the repeated intermittent sampling interference generated by the k' -i section and the stacking vectors of all distance levels after the filtering treatment of a mismatch filter;
all distance levels ω of all interference output via mismatched filters J The method comprises the following steps: no deviation exists in a plurality of interference parameters (whether the deviation exists in the interference parameters or not is obtained by the interference sensing of the cognitive radar), and the total distance level omega J Is that
If there is a deviation in one or more of the interference parameters, then +.>
The corresponding vector in (a) is replaced by a distance level stack vector when errors exist; for example, when C&When the I interference parameter has errors, the obtained total distance level omega J The method comprises the following steps: />
All distance levels of all interference output via the mismatch filter are compressed using a min-max optimization criterion, namely:
s22, establishing an optimization problem: according to the optimization criterion of the S21 design, the optimization problem of the phase coding signal S and the mismatch filter h resisting the multi-main lobe interference is expressed as follows:
s.t.|h H h-N s |≤γ 1
wherein lambda is 1 ，λ 2 Is a preset weight coefficient.
S3, converting the optimization problem which is non-convex, non-smooth and provided with constraint into the minimization problem of the function of the independent variable (composed of signal phase, filter amplitude and phase) by using a penalty function method, a norm conversion method and the like, and solving by using an iterative L-BFGS algorithm.
The specific implementation method of S3 is as follows:
s31, optimizing problem conversion: the optimization problem of non-convex, non-smooth and constraint is converted into the minimization problem of the function of the independent variables (composed of signal phase, filter amplitude and phase) by using the methods of penalty function, norm conversion and the like, namely:
wherein lambda is 3 For the weight coefficient to be set in advance, I ∞ Represents an infinite norm;
defining an objective function as:
f(x)＝||ω side || p +λ 1 ||ω J || p +λ 2 ||e|| p +λ 3 ||h H h-N s || p
in the method, in the process of the invention, I p Represents the p-norm; vector quantity
Is composed of vector->
a and θ are sequentially formed column vectors expressed as:
s32, solving an optimization problem: based on the analysis, the problem is solved by using an L-BFGS algorithm based on iteration, and the main idea is to solve the minimum value of the objective function by using the L-BFGS algorithm, iterate continuously until the objective function f (x) reaches the minimum descent epsilon, stop iterating, and output x. As shown in fig. 5, the specific steps are as follows:
step I: initializing variable x 0 Epsilon, p, mu: set x 0 As a starting value, epsilon is the minimum descent of the objective function, let iteration number w=1, parameter p=2, μ=2;
step II: calculate the current function value f (x w ): will x w-1 As an initial value, the minimization function f (x) is used to find x by using the L-BFGS algorithm w Let f w ＝f(x w )；
Step III: if |f w-1 -f w If the I is less than or equal to epsilon, obtaining x w And stopping the iteration; if not, p=μp, w=w+1, and step II is skipped.
The step II, where the minimization of the function f (x) is required, can be implemented using the L-BFGS algorithm. Compared with the quasi-Newton method, the L-BFGS algorithm utilizes a small quantity of vectors to estimate the Hessian matrix, so that the calculated amount is greatly reduced, and the method is easy to realize. The L-BFGS algorithm flow is as follows:
first, an initial iteration number w=1 is set, and an initial vector x 0 And calculate the objective function value f 1 Sum of derivative values
To derive the sign and select the starting direction +.>
And the algorithm updates the variable n. The specific circulation process is as follows:
step 1: for the w-th iteration, calculate f w ，
And g w And obtaining the step length lambda by using a backtracking line searching algorithm w ；
Step 2: calculate q w ＝λ w g w ，x w+1 ＝x w +λ w g w ；
Step 3: calculation of
And->
Step 4: order the
Step 5: fori=w, w-1, …, w-n+ 1
end
Step 6:
step 7: fori=w, w-1, …, w-n+ 1
end
Step 8: g w+1 ＝-z；
Step 9: w=w+1;
and finally, when the termination condition is met, obtaining an optimization result.
It should be explained that, in the step 5-7, the product of the Hessian matrix and the gradient p is mainly constructed by using the gradient information of the adjacent n iterative functions, and the search direction of the next step is obtained according to the obtained vector z. Step 1 requires obtaining a step length lambda by using a backtracking line search algorithm w The specific process of the backtracking search algorithm is as follows:
step a: selecting a lambda w ＞0，ρ,c 1 ∈(0,1)；
Step b: if it is
Let lambda get w ＝ρλ w ；
Step c: repeating step b until the relation is satisfied
Output lambda w 。
Simulation verification and analysis
Simulation parameters:
the phase coded signal has a time width of 60 mu s, a bandwidth of 5MHz, an LFM signal has a time width of 60 mu s, a bandwidth of 5MHz, a mismatch filter has a time width of 120 mu s, a radar system carrier frequency of 2GHz, a number of transmitted pulses of 100, a pulse repetition period of 480 mu s, a signal to noise ratio of 0dB, a signal to interference ratio of 20dB, a target distance of 45km, a C & I interference distance of 46km, a direct intermittent sampling interference distance of 44km, a repeated intermittent sampling interference distance of 48km, a target speed of 30m/s, a C & I interference speed of 32m/s, a direct intermittent sampling speed of 28m/s, and a repeated intermittent sampling interference speed of 26m/s.
The interference parameters are completely known:
c & I interference generation mode: 10 segments are intercepted, each segment is forwarded 5 times, and each segment has 12 sampling points.
Direct intermittent sampling interference generation mode: 10 segments are intercepted, each segment is forwarded 1 time, and 8 sampling points are adopted in each segment.
Repeating intermittent sampling interference generation modes: 10 segments are intercepted, each segment is forwarded for 4 times, and each segment has 4 sampling points.
The interference parameters have deviation:
c & I interference generation mode: 9 segments are intercepted, each segment is forwarded 6 times, and each segment has 12 sampling points.
Direct intermittent sampling interference generation mode: 10 segments are intercepted, each segment is forwarded 1 time, and 8 sampling points are adopted in each segment.
Repeating intermittent sampling interference generation modes: 10 segments are intercepted, each segment is forwarded for 4 times, and each segment has 4 sampling points.
Weight coefficient lambda 1 ＝1，λ 2 ＝1，λ 3 Main lobe width control parameter m=3, iterate 100 times.
Simulation analysis: fig. 6 shows the doppler tolerance of an optimized signal designed under the condition that the interference parameters are completely known (fig. 6 (a)) and the interference parameters deviate (fig. 6 (b)). When the speed offset is 150m/s, the main lobe of the optimized waveform designed under the condition that the interference parameters are completely known is about 23dB higher than the peak side lobe level, and the main lobe of the optimized waveform designed under the condition that the interference parameters have deviation is about 20dB higher than the peak side lobe level. It can be seen that the cognitive waveform generated by the method has better Doppler tolerance, and the interference parameter is completely known to be better than the Doppler tolerance of the optimized waveform designed under the condition that the interference parameter has deviation. Fig. 7 shows the result of the matched filtering processing of the LFM signal and its corresponding C & I interference, direct intermittent sampling interference and repeated intermittent sampling interference. Fig. 8 shows the result of mismatch filtering processing of the optimized signal and the corresponding multi-main lobe interference under the conditions that the interference parameters are completely known and the interference parameters have deviation, wherein (a) is that the interference parameters are completely known, and (b) is that the interference parameters have deviation. As can be seen from fig. 7 and 8, the peak sidelobe level of the optimized signal after the mismatch processing designed by the method is at least 12dB lower than the peak sidelobe level of the LFM signal after pulse compression, and the designed optimized signal detection performance is superior to that of the LFM signal; the multi-main-lobe interference resistance of the optimized signal is also superior to that of the LFM signal, but a certain signal-to-noise ratio loss exists in the design process, and the interference parameter is completely known to have superior detection performance and multi-main-lobe interference resistance compared with the interference parameter under the deviation condition. Fig. 9 is a comparison chart of detection results of the designed optimized signal when the LFM signal and the interference parameter are completely known and have deviation from the interference parameter, as shown in fig. 9 (a), (b), and (c), respectively. As can be seen from fig. 9, under the simulation parameters, the LFM cannot effectively detect the target, and the optimized signal can effectively detect the distance and speed of the target, and the detection performance of the optimized signal designed under the condition that the interference parameters are completely known is slightly better than that of the optimized signal designed under the condition that the interference parameters have deviation.
Those of ordinary skill in the art will recognize that the embodiments described herein are for the purpose of aiding the reader in understanding the principles of the present invention and should be understood that the scope of the invention is not limited to such specific statements and embodiments. Those of ordinary skill in the art can make various other specific modifications and combinations from the teachings of the present disclosure without departing from the spirit thereof, and such modifications and combinations remain within the scope of the present disclosure.
Claims (2)
1. A wave form and filter joint cognition design method for resisting multi-main lobe interference is characterized by comprising the following steps:
s1, constructing a C & I, direct intermittent sampling and repeated intermittent sampling interference signal model and a mismatch filter model based on a constant-mode phase coded signal; the method specifically comprises the following sub-steps:
s11, the constant-mode phase coding signal is expressed as:
in the formula [ (] T Representing the transpose s n For transmitting codewords of the waveform, n=1, 2, …, N s ，N s The number of codewords for the phase encoded waveform;
the nth element s n Expressed as:
in the method, in the process of the invention,
representation->
Phase of the nth codeword, +.>
Encoding the phase of the signal s for a constant mode phase;
s12, establishing C&I interference signal model: for C&I interference, suppose DRFM jammer pairIntercepting radar signals from s i Starting, m code words are taken as one section, each section is forwarded for l times, k sections are intercepted in total, and the whole C&I interference signal codeword length N s ＝klm；C&The I interference signal is:
wherein H is t T is more than or equal to 1 and less than or equal to k in the t section intercepted by the jammer; h t The represented codeword is expressed as:
Η t ＝[s (t-1)ml+i ,s (t-1)ml+i+1 ,…,s (t-1)ml+i+m-1 ]；
s13, directly intermittently sampling an interference signal model: for direct intermittent sampling interference, suppose that a DRFM (digital radio frequency modulation) jammer intercepts radar signals, and s is a reference number i Firstly, m code words are taken as a section, and are intercepted and forwarded once every ml code words, k sections are intercepted in total, and the direct intermittent sampling interference signal is as follows:
J 2 ＝[Η′ 1 ,Η′ 0 ,Η′ 2 ,Η′ 0 ,…,Η′ k ,Η′ 0 ] T
in the formula, H' 0 ＝0 1×m(l-1) ，0 1×m(l-1) A 0 vector representing 1×m (l-1); h' t For the t-th segment intercepted by the jammer, the represented codeword is expressed as:
Η′ t ＝[s (t-1)ml+i ,s (t-1)ml+i+1 ,…s (t-1)ml+i+m-1 ]；
s14, repeating the intermittent sampling interference signal model: for repeated intermittent sampling interference, assume that a DRFM (digital radio frequency modulation) jammer intercepts radar signals, and then s i Firstly, m code words are taken as a section, the code words are intercepted once every ml, the code words are repeated q times and then forwarded, k sections are intercepted in total, and the repeated intermittent sampling interference signals are as follows:
in the formula, H 0 ＝0 1×m(l-q) ，Η″ t For the t-th segment intercepted by the jammer, the represented codeword is expressed as:
Η″ t ＝[s (t-1)ml+i ,s (t-1)ml+i+1 ,…s (t-1)ml+i+m-1 ]；
s15, a mismatch filter signal model: assume that the length of a corresponding mismatch filter h of a radar receiving end is N h ，N h ≥N s The mismatch filter h is denoted as:
the nth element h n Expressed as:
where a is the magnitude vector of the mismatch filter h, a n Is the nth element in a; θ is the phase vector of the mismatch filter h, θ n Is the n element in theta; h=a.exp (j θ), where a represents the Hadamard product;
s2, under the condition that interference parameters are completely known or deviation exists, establishing a wave form correlation function peak value level, a correlation function main lobe template matching error and an interference energy weighting and minimizing criterion transmitting-receiving joint optimization problem under the constraint of signal to noise ratio; the method comprises the following steps:
s21, designing optimization criteria:
(1) Distance sidelobe: the output of the phase encoded signal s through the mismatch filter h is represented at a distance displacement j as:
wherein, represents conjugation, Γ 1 Represents a value interval, Γ 1 ＝[-(N s +N h )/2+1,(N s +N h )/2-1]；
Let ω be j For the widened main lobe region, j=0, ±1, …, ±m, M is a main lobe width control parameter;
all the distance main lobe levels are stacked in vector omega main Expressed as:
ω main ＝[ω -M ,…,ω -1 ,ω 0 ,ω 1 ,…,ω M ] T
all range side lobe levels are stacked in vector ω side Expressed as:
let the sidelobe region be denoted as Γ 2 ，Γ 2 Expressed as:
Γ 2 ＝[-(N s +N h )/2+1,-M+1]∪[M-1,(N s +N h )/2-1]
the range side lobe is reduced by minimizing the peak side lobe, namely:
(2) Loss of signal-to-noise ratio:
|h H h-N s |≤η 1
|ω 0 -N s |≤η 2
in the formula, the constant eta 1 ≥0，η 2 More than or equal to 0, and the superscript H represents conjugate transposition;
(3) Main lobe control: assume that
Is the desired main lobe, i.e. q is a vector of dimension 2m+1; vector e is the error vector of the desired main lobe and the designed main lobe, expressed as:
e＝ω main -q
the nth element e (n) of the error vector e is expressed as:
e(n)＝ω n-M-1 -q(n)，1≤n≤2M+1
the main lobe shape is maintained with a method that minimizes the maximum main lobe matching error, namely:
(4) Multi-main lobe interference resistance: interference signal J m The output result via the mismatch filter h is represented at a distance displacement j as:
J m (n) represents J m In (2) the n-th element, all distance levels in the above formula are stacked in vector ω' m Expressed as:
when the interference parameters are completely known: the cognitive radar senses multi-main-lobe interference, and different interference signals J are transmitted under the condition that interference parameters are completely known m Distance level stack vector ω 'generated by mismatch filter h' m ，m＝1,2,…,N J All stacked on vector omega J ，ω J Expressed as:
N J indicating the number of interferences;
when the interference parameter has deviation: actual C&The number of interception segments of the interference I is k, the forwarding frequency is l, the number of interception segments of the perceived parameter is k ', and the forwarding frequency is l'; with k=k '+l, l=l' -L, L being a natural number greater than 0; in the presence of errors, C&I interference distance level stack vector
Expressed as:
in the formula omega' 1 C is generated by intercepting segment number k' and forwarding frequency l&Stacking vectors of all distance levels after filtering processing of the I interference and mismatch filter;
c is generated by intercepting segment number k '+i and forwarding frequency l' -i&Stacking vectors of all distance levels after filtering processing of the I interference and mismatch filter; omega' 1-i C is generated by intercepting segment number k '-i and forwarding frequency l' +i&Stacking vectors of all distance levels after filtering processing of the I interference and mismatch filter, i=1, 2, …, L;
the actual direct intermittent sampling interference generation mode is as follows: taking m code words as a section, intercepting and forwarding every ml code words, intercepting k sections altogether, and the perceived generation mode of direct intermittent sampling interference is as follows; taking m code words as a section, intercepting and forwarding every ml code words, and intercepting k sections altogether; direct intermittent sampling of interference distance level stacking vectors in the presence of deviations
Expressed as:
ω′ 2 taking m code words as a section, intercepting and forwarding every ml code words, and intercepting direct intermittent sampling interference generated by k section and stacking all distance levels after filtering treatment of a mismatch filterAn amount of;
taking m code words as a section, intercepting and forwarding every m (l '-i) code words, and intercepting direct intermittent sampling interference generated by k' +i sections and stacking vectors of all distance levels after filtering treatment of a mismatch filter; />
Taking m code words as a section, intercepting and forwarding every m (l '+i) code words, and intercepting the stacking vectors of direct intermittent sampling interference generated by the section k' -i and all distance levels after filtering treatment of a mismatch filter;
the actual repeated intermittent sampling interference generation mode is as follows: taking m code words as a section, intercepting and forwarding q times every ml code words, and intercepting k sections altogether; the perceived repeated intermittent sampling interference generation mode is as follows; taking m code words as a section, intercepting and forwarding q times every ml 'code words, and intercepting k' sections altogether; repeated intermittent sampling of interference distance level stacking vectors in the presence of deviations
Expressed as:
ω′ 3 taking m code words as a section, intercepting and forwarding q times every ml 'code words, and intercepting the stacking vectors of the repeated intermittent sampling interference generated by the k' section and all distance levels after filtering treatment of a mismatch filter altogether;
taking m code words as a section, intercepting and forwarding q times every m (l '-i) code words, and intercepting repeated intermittent sampling interference generated by k' +i sections and stacking vectors of all distance levels after filtering treatment of a mismatch filter;/>
taking m code words as a section, intercepting and forwarding q times every m (l '+i) code words, and intercepting the repeated intermittent sampling interference generated by the k' -i section and the stacking vectors of all distance levels after the filtering treatment of a mismatch filter;
all distance levels ω of all interference output via mismatched filters J The method comprises the following steps: if there is no deviation in several disturbance parameters, all distance levels omega J Is that
If there is a deviation in one or more interference parameters, then
The corresponding vector in (a) is replaced by a distance level stack vector when errors exist;
all distance levels of all interference output via the mismatch filter are compressed using a min-max optimization criterion, namely:
s22, establishing an optimization problem: according to the optimization criterion of the S21 design, the optimization problem of the phase coding signal S and the mismatch filter h resisting the multi-main lobe interference is expressed as follows:
s.t.|h H h-N s |≤γ 1
wherein lambda is 1 ，λ 2 The weight coefficient is preset;
s3, converting the optimization problem into a minimization problem related to the independent variable function, and solving by using an iterative L-BFGS algorithm.
2. The method for combined cognitive design of a waveform and a filter for resisting multi-main lobe interference according to claim 1, wherein the specific implementation method of S3 is as follows:
s31, optimizing problem conversion: converting the optimization problem into a minimization problem with respect to the independent variable function, namely:
wherein lambda is 3 For the weight coefficient to be set in advance, I ∞ Represents an infinite norm;
defining an objective function as:
f(x)＝||ω side || p +λ 1 ||ω J || p +λ 2 ||e|| p +λ 3 ||h H h-N s || p
in the method, in the process of the invention, I p Represents the p-norm; vector quantity
Is composed of vector->
a and θ are sequentially formed column vectors expressed as:
s32, solving an optimization problem: and solving the problem by using an L-BFGS algorithm based on iteration, solving the minimum value of the objective function by using the L-BFGS algorithm, continuously iterating until the objective function f (x) reaches the minimum descent epsilon, stopping iterating, and outputting x.
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