CN114696788A - Multi-main-lobe interference resistant waveform and filter joint cognitive design method - Google Patents

Multi-main-lobe interference resistant waveform and filter joint cognitive design method Download PDF

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CN114696788A
CN114696788A CN202210379049.7A CN202210379049A CN114696788A CN 114696788 A CN114696788 A CN 114696788A CN 202210379049 A CN202210379049 A CN 202210379049A CN 114696788 A CN114696788 A CN 114696788A
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崔国龙
林瑜
卜祎
樊涛
余显祥
方学立
张立东
吴尚
孔令讲
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Abstract

The invention discloses a multi-main lobe interference resistant waveform and filter joint cognitive design method, 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 the constant modulus phase coding signal; s2, under the condition that interference parameters are completely known or have deviation, establishing a transmitting-receiving combined optimization problem of waveform correlation function peak level, correlation function main lobe template matching error and interference energy weighting and minimizing criterion under the constraint of signal-to-noise ratio; and S3, converting the optimization problem into a minimization problem about an independent variable function, and solving by using an iterative L-BFGS algorithm. The optimized signal designed by the invention has good Doppler tolerance and multi-main lobe interference resistance, and has lower peak side lobe after mismatch filtering.

Description

Multi-main-lobe interference resistant waveform and filter joint cognitive design method
Technical Field
The invention belongs to the field of radar anti-interference technology, and particularly relates to a multi-main lobe interference resistant waveform and filter joint cognitive design method.
Background
In recent years, with the high-speed development of modern electronic technology, electronic countermeasures are increasingly violent, various interference patterns are infinite, and the normal operation of a radar system is seriously hindered. For the main lobe interference, the interference energy has absolute advantage, and the main lobe interference is highly overlapped with the target in the dimensions of space-time frequency and the like, the effect of the existing interference suppression means is poor, and one of the difficult problems to be solved is still needed in the radar field. The general anti-mainlobe interference method includes: signal processing and waveform design.
In terms of a method for processing a signal to resist main lobe interference, a common method for processing a signal includes: blind source separation and filtering process. The blind source separation can separate the mixed signals without prior knowledge, for example, a blind source separation main lobe interference resisting algorithm based on a matrix joint diagonalization characteristic vector is proposed in documents G.Huang, L.Yang, G.Su.B. source separation used for radar anti-interference [ C ].2003International Conference on Neural Networks and Signal Processing, Nanjing, China,2003: 1382-. However, after the mixed signal is separated, there is often a small amount of interference residue, and a single type of interference is targeted. The filtering process mainly utilizes the difference between the interference signal and the target echo in time, frequency, space, polarization and other domains to design filter parameters in different dimensions, so as to achieve the effect of interference suppression, for example, in documents [ s.zhang, y.yang, g.cui, et al.range-robust sampling suppression [ C ]. IEEE Radar Conference, philidelphia, PA, USA,2016:1-6 ], by designing a mismatch filter for each range-doppler cell, the range-speed joint deception interference suppression is achieved. However, this method requires that the waveform of the interfering signal is known accurately and is only suitable for a certain interference type.
A waveform design main lobe interference resisting method amplifies differences of target echoes and interference signals in time, frequency, space, polarization and other domains by designing phase, frequency and other information of waveforms in pulses and between pulses so as to achieve the purpose of resisting interference, for example, documents [ creep epitaxy, radar waveform design and main lobe active interference resisting technical researches [ D ]. Sian: Sian electronics technology university, 2019 ], based on amplitude difference between angular domain waveforms and interference signals, the interference signals are compressed by a waveform optimization method, and DRFM forwarding interference is effectively resisted. However, this method can only resist a single type of interference, and cannot effectively resist the composite interference superimposed by multiple interference types.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a multi-main-lobe interference resistant waveform and filter joint cognitive design method.
The purpose of the invention is realized by the following technical scheme: a multi-main lobe interference resistant waveform and filter joint cognitive design method 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 the constant modulus phase coding signal;
s2, under the condition that interference parameters are completely known or have deviation, establishing a transmitting-receiving combined optimization problem of waveform correlation function peak level, correlation function main lobe template matching error and interference energy weighting and minimizing criterion under the constraint of signal-to-noise ratio;
and S3, converting the optimization problem into a minimization problem about an 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 modulus phase encoded signal is represented as:
Figure BDA0003591934730000021
in the formula [ ·]TDenotes transposition, snFor transmitting code words of the waveform, N is 1,2, …, Ns，NsThe number of code words of the phase encoded waveform; n element snExpressed as:
Figure BDA0003591934730000022
in the formula (I), the compound is shown in the specification,
Figure BDA0003591934730000023
to represent
Figure BDA0003591934730000024
The phase of the nth code word of (a),
Figure BDA0003591934730000025
encoding the phase of the signal s for a constant modulus phase;
s12, establishing C&I interference signal model: for C&I interference, assuming that the DRFM jammer intercepts the radar signal, from siBeginning, taking m code words as one segment, forwarding each segment for one time, and intercepting k segments and the whole C&I interference signal codeword length Ns＝klm；C&The I interference signal is:
Figure BDA0003591934730000026
in the formula, HtT is a t section intercepted by the jammer, and is more than or equal to 1 and less than or equal to k; htThe represented codeword is represented as:
Ηt＝[s(t-1)ml+i,s(t-1)ml+i+1,…,s(t-1)ml+i+m-1]；
s13, directly and intermittently sampling an interference signal model: for the direct intermittent sampling interference, the DRFM jammer is assumed to intercept the radar signal, from siBeginning, taking m code words as a section, intercepting and forwarding every ml code words, and intercepting k sections in total, wherein the interference signals are directly and intermittently sampled as follows:
J2＝[Η′1,Η′0,Η′2,Η′0,…,Η′k,Η′0]T
h in formula (II)'0＝01×m(l-1)，01×m(l-1)Represents a 0 vector of 1 xm (l-1); h'tAnd the t-th section intercepted by the jammer represents a code word represented by:
Η′t＝[s(t-1)ml+i,s(t-1)ml+i+1,…s(t-1)ml+i+m-1]；
s14, repeatedly and intermittently sampling an interference signal model: for repeated intermittent sampling interference, assuming that a DRFM jammer intercepts radar signals, from siBeginning, taking m code words as a section, intercepting every ml code words once, copying q times and then forwarding, intercepting k sections altogether, and repeatedly and intermittently sampling interference signals as follows:
Figure BDA0003591934730000031
in the formula, H0＝01×m(l-q)，Η″tAnd the t-th section intercepted by the jammer represents a code word represented by:
Η″t＝[s(t-1)ml+i,s(t-1)ml+i+1,…s(t-1)ml+i+m-1]；
s15, mismatch filter signal model: suppose that the length h of the corresponding mismatch filter at the receiving end of the radar is Nh，Nh≥NsThe mismatched filter h is expressed as:
Figure BDA0003591934730000032
n element hnExpressed as:
Figure BDA0003591934730000033
where a is the magnitude vector of the mismatched filter h, anIs the nth element in a; theta is the phase vector of the mismatched filter h, thetanIs the nth element in theta; h ═ a ∑ exp (j θ), which indicates a Hadamard product.
Further, the step S2 is specifically:
s21, designing an optimization criterion:
(1) range side lobe: the output result of the phase-encoded signal s through the mismatched filter h at the distance displacement j is represented as:
Figure BDA0003591934730000034
wherein R represents a conjugate1Denotes a value range, Γ1＝[-(Ns+Nh)/2+1,(Ns+Nh)/2-1]；
Let omega bejJ is 0, ± 1, …, ± M, M is a main lobe width control parameter;
all distance mainlobe levels are stacked at vector ωmainExpressed as:
ωmain＝[ω-M,…,ω-1,ω0,ω1,…,ωM]T
all range sidelobe levels are stacked at vector ωsideExpressed as:
Figure BDA0003591934730000041
the sidelobe regions are denoted as Γ2，Γ2Expressed as:
Γ2＝[-(Ns+Nh)/2+1,-M+1]∪[M-1,(Ns+Nh)/2-1]
range sidelobes are reduced by minimizing peak sidelobes, namely:
Figure BDA0003591934730000042
(2) loss of signal-to-noise ratio:
|hHh-Ns|≤η1
|ω0-Ns|≤η2
in the formula, constant eta1≥0，η2The superscript H is more than or equal to 0 and represents conjugate transposition;
(3) main lobe control: suppose that
Figure BDA0003591934730000043
Is the desired main lobe, i.e. q is a vector with dimension 2M + 1; vector e is the error vector of the desired main lobe and the designed main lobe, and is expressed as:
e＝ωmain-q
the nth element e (n) of the error vector e is represented as:
e(n)＝ωn-M-1-q(n)，1≤n≤2M+1
the main lobe shape is maintained by a method of minimizing the maximum main lobe matching error, namely:
Figure BDA0003591934730000044
(4) the multi-main lobe interference resistance performance is as follows: interference signal JmThe output result of the mismatched filter h at distance shift j is represented as:
Figure BDA0003591934730000045
Jm(n) represents JmThe nth element in the above formulaLevel is stacked at vector ω'mExpressed as:
Figure BDA0003591934730000046
when the interference parameters are fully known: the cognitive radar senses the interference of multiple main lobes and transmits different interference signals J under the condition that the interference parameters are completely knownmDistance level stack vector ω 'generated by mismatched filter h'm，m＝1,2,…,NJAll stacked on the vector omegaJ，ωJExpressed as:
Figure BDA0003591934730000047
NJrepresenting the number of interferers;
when the interference parameters have deviation: suppose actual C&The number of the intercepting segments of the I interference is k, the forwarding times is l, the number of the perceived intercepting segments of the parameters is k ', and the forwarding times is l'. Assuming that the error is small, k ═ k '+ L, L ═ L' -L, and L is a natural number greater than 0. In the presence of errors, C&I interference distance level stacking vector
Figure BDA0003591934730000051
Expressed as:
Figure BDA0003591934730000052
in formula (II), omega'1Is C generated by the number of the intercepted segments being k' and the number of forwarding times being l&I, stacking vectors of all distance levels after filtering processing of the interference and mismatch filter;
Figure BDA0003591934730000053
is C generated by the interception segment number of k '+ i and the forwarding times of l' -i&I, stacking vectors of all distance levels after filtering processing of the interference and mismatch filter;
Figure BDA0003591934730000054
is C generated by the number of interception segments k '-i and the forwarding times l' + i&Stacking vectors of all distance levels after filtering processing of the I interference and mismatched filter, wherein I is 1,2, …, L;
the method for generating the interference by the actual direct intermittent sampling is assumed as follows: taking m code words as one section, intercepting once every ml code words and forwarding, and intercepting k sections in total, wherein the perceived direct intermittent sampling interference generation mode is; taking m code words as a section, intercepting every ml code words once and forwarding, and intercepting k ' sections altogether, wherein the assumed error is small, and k is k ' + L, and L is L ' -L; then in case of deviation, directly and intermittently sampling the interference distance level stacking vector
Figure BDA0003591934730000055
Expressed as:
Figure BDA0003591934730000056
ω′2taking m code words as a section, intercepting once every ml code words and forwarding, and intercepting all stacking vectors of distance levels generated by k' section after direct intermittent sampling interference and filter processing of a mismatch filter;
Figure BDA0003591934730000057
taking m code words as a section, intercepting and forwarding every m (l '-i) code words, and intercepting all stacking vectors of distance levels after filtering processing of direct intermittent sampling interference and mismatched filters generated by a k' + i section;
Figure BDA0003591934730000058
taking m code words as one section, intercepting and forwarding every m (l '+ i) code words, and intercepting all stacking vectors of distance levels after filtering processing of direct intermittent sampling interference and mismatched filters generated by a k' -i section;
the method for generating the interference by the actual repeated intermittent sampling is assumed as follows: taking m code words as one segment and every other mlIntercepting the code word once and forwarding the code word for q times, and intercepting k sections in total; the perceived interference generation mode of repeated intermittent sampling is as follows; taking m code words as a section, intercepting every ml 'code words and forwarding the code words q times, and intercepting k' sections altogether, wherein the assumed error is small, k is k '+ L, and L is L' -L; repeatedly and intermittently sampling the interference distance level stacking vector in the presence of the deviation
Figure BDA0003591934730000059
Expressed as:
Figure BDA00035919347300000510
ω′3taking m code words as a section, intercepting once every ml code words and forwarding for q times, and intercepting all stacking vectors of distance levels after repeated intermittent sampling interference generated by the k' section and filtering processing of a mismatched filter;
Figure BDA00035919347300000511
taking m code words as a section, intercepting once every m (l '-i) code words and forwarding for q times, and intercepting all stacking vectors of distance levels after repeated intermittent sampling interference generated by a k' + i section and filtering processing of a mismatched filter;
Figure BDA00035919347300000512
taking m code words as a section, intercepting once every m (l '+ i) code words and forwarding for q times, and intercepting all stacking vectors of distance levels after repeated intermittent sampling interference generated by a k' -i section and filtering processing of a mismatched filter;
all interference is output via the mismatch filter at all distance levels omegaJComprises the following steps: if there is no deviation in the interference parameters, all the distance levels omegaJIs composed of
Figure BDA0003591934730000061
If one or more interference parameters have deviation, the interference parameters will be
Figure BDA0003591934730000062
Replacing the corresponding vector in the distance level stack vector with a distance level stack vector when an error exists;
all distance levels of all interference output by the mismatched filter are compressed using a min-max optimization criterion, namely:
Figure BDA0003591934730000063
s22, establishing an optimization problem: according to the optimization criterion designed by S21, the optimization problem of the phase coding signal S and the mismatched filter h for resisting the multi-main lobe interference is expressed as follows:
Figure BDA0003591934730000064
s.t.|hHh-Ns|≤γ1
in the formula, λ1，λ2Is a preset weight coefficient.
Further, the specific implementation method of S3 is as follows:
s31, optimizing problem transformation: the optimization problem is converted into a minimization problem with respect to the argument function, namely:
Figure BDA0003591934730000065
wherein λ is3To a predetermined weight coefficient, | | | | | non-calculation∞Represents an infinite norm;
the objective function is defined as:
f(x)＝||ωside||p+λ1||ωJ||p+λ2||e||p+λ3||hHh-Ns||p
in the formula, | | | non-conducting phosphorpRepresents a p-norm; vector quantity
Figure BDA0003591934730000066
Is composed of a vector
Figure BDA0003591934730000067
a and θ are sequentially constructed as a column vector, represented as:
Figure BDA0003591934730000068
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 drop epsilon, stopping iteration, and outputting x.
The invention has the beneficial effects that: firstly, constructing a C & I, direct intermittent sampling and repeated intermittent sampling interference signal model based on a constant modulus phase coding signal; then, under the condition that interference parameters are completely known or have deviation, establishing a transmitting-receiving combined optimization problem of waveform correlation function peak level, correlation function main lobe template matching error and interference energy weighting and minimizing criteria under the constraint of signal-to-noise ratio; and finally, converting the non-convex, non-smooth and constrained optimization problem into a minimization problem about an independent variable (consisting of signal phase, filter amplitude and phase) function by using a penalty function method, norm conversion and other methods, and solving by using an iterative L-BFGS algorithm. The optimized signal designed by the invention has good Doppler tolerance and multi-main lobe interference resistance, and has lower peak side lobe after mismatch filtering.
Drawings
FIG. 1 is a flow chart of a multi-mainlobe interference resistant waveform and filter joint cognitive design method of 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 the interference generation by repeated intermittent sampling;
FIG. 5 is a flowchart of an iteration-based L-BFGS algorithm;
FIG. 6 shows the optimized signal Doppler tolerance for a design with fully known interference parameters and a deviation in the interference parameters;
fig. 7 shows the results of the LFM signal and its corresponding C & I interference, direct intermittent sampling interference, and repeated intermittent sampling interference after matched filtering;
fig. 8 is a result of mismatch filtering processing performed on the optimized signal and the multi-main lobe interference corresponding to the optimized signal when the interference parameter is completely known to have a deviation from the interference parameter;
fig. 9 is a comparison graph of detection results of the designed optimized signal when the LFM signal and the interference parameter are completely known and have a deviation from the interference parameter.
Detailed Description
The technical scheme of the invention is further explained by combining the attached drawings.
As shown in fig. 1, the method for cognitive design of a waveform and filter combination for resisting multi-main lobe interference of the present invention includes 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 the constant modulus phase coding signal; the method specifically comprises the following steps:
s11, the constant modulus phase encoded signal is represented as:
Figure BDA0003591934730000071
in the formula [ ·]TDenotes transposition, snFor transmitting code words of the waveform, N is 1,2, …, Ns，NsThe number of code words of the phase encoded waveform; n element snExpressed as:
Figure BDA0003591934730000072
in the formula (I), the compound is shown in the specification,
Figure BDA0003591934730000073
to represent
Figure BDA0003591934730000074
The phase of the nth code word of (a),
Figure BDA0003591934730000075
encoding the phase of the signal s for a constant modulus phase;
s12, establishing C&I interference signal model: for C&I jammer, assuming DRFM jammer intercepts radar signal, from siStarting, taking m code words as one segment, forwarding each segment for l times, and intercepting k segments in total, wherein the whole C&I interference signal codeword length NsKlm; as shown in FIG. 2, C&The I interference signal is:
Figure BDA0003591934730000081
in the formula, HtT is a t section intercepted by the jammer, and is more than or equal to 1 and less than or equal to k; htThe represented codeword is represented as:
Ηt＝[s(t-1)ml+i,s(t-1)ml+i+1,…,s(t-1)ml+i+m-1]
A1is a matrix, which can be expressed as:
Figure BDA0003591934730000082
1. 1 represents that the elements at positions i to i + m-1 are all 1;
s13, directly and intermittently sampling an interference signal model: for the direct intermittent sampling interference, the DRFM jammer is assumed to intercept the radar signal, from siStarting, taking m code words as a segment, intercepting and forwarding every ml code words, and intercepting k segments in total, as shown in fig. 3, directly and intermittently sampling an interference signal is:
J2＝[Η′1,Η′0,Η′2,Η′0,…,Η′k,Η′0]T
＝A2s
h in formula (II)'0＝01×m(l-1)，01×m(l-1)Represents a 0 vector of 1 xm (l-1); h'tAnd the t-th section intercepted by the jammer represents a code word represented by:
Η′t＝[s(t-1)ml+i,s(t-1)ml+i+1,…s(t-1)ml+i+m-1]
A2is a matrix, which can be expressed as:
Figure BDA0003591934730000091
s14, repeatedly and intermittently sampling the interference signal model: for repeated intermittent sampling interference, assuming that a DRFM jammer intercepts radar signals, from siStarting, taking m code words as a segment, intercepting every ml code words, copying q times and then forwarding, and intercepting k segments in total, as shown in fig. 4, repeatedly and intermittently sampling an interference signal:
Figure BDA0003591934730000092
in the formula, H0＝01×m(l-q)，Η″tAnd the t-th section intercepted by the jammer represents a code word represented by:
Η″t＝[s(t-1)ml+i,s(t-1)ml+i+1,…s(t-1)ml+i+m-1]
A3is a matrix, which can be expressed as:
Figure BDA0003591934730000093
s15, mismatch filter signal model: suppose that the length h of the corresponding mismatch filter at the receiving end of the radar is Nh，Nh≥NsThe mismatched filter h is expressed as:
Figure BDA0003591934730000094
n element hnExpressed as:
Figure BDA0003591934730000095
where a is the magnitude vector of the mismatched filter h, anIs the nth element in a; theta is the phase vector of the mismatched filter h, thetanIs the nth element in theta; h ═ a ∑ exp (j θ), which indicates a Hadamard product.
S2, under the condition that interference parameters are completely known or have deviation, establishing a transmitting-receiving combined optimization problem of waveform correlation function peak level, correlation function main lobe template matching error and interference energy weighting and minimizing criterion under the constraint of signal-to-noise ratio;
step S2 specifically includes:
s21, designing an optimization criterion:
(1) range side lobe: in practical application, the range sidelobe level output by the mismatched filter should be as low as possible, so as to ensure that a weak target is not submerged by the high sidelobe of a strong target echo signal;
the output result of the phase-encoded signal s through the mismatched filter h at the distance displacement j is represented as:
Figure BDA0003591934730000101
wherein R represents a conjugate1Denotes a value range, Γ1＝[-(Ns+Nh)/2+1,(Ns+Nh)/2-1]；
Suppose ω isjJ is 0, ± 1, …, ± M, M is a main lobe width control parameter;
all distance mainlobe levels are stacked at vector ωmainExpressed as:
ωmain＝[ω-M,…,ω-1,ω0,ω1,…,ωM]T
all range sidelobe level stackingIn the vector omegasideExpressed as:
Figure BDA0003591934730000102
the sidelobe regions are denoted as Γ2，Γ2Expressed as:
Γ2＝[-(Ns+Nh)/2+1,-M+1]∪[M-1,(Ns+Nh)/2-1]
range sidelobes are reduced by minimizing peak sidelobes, namely:
Figure BDA0003591934730000103
(2) the signal-to-noise ratio is lost, and a certain loss is caused by the signal-to-noise ratio in the process of designing the mismatched filter. There is therefore a need to control the loss of signal to noise ratio, namely:
|hHh-Ns|≤η1
|ω0-Ns|≤η2
in the formula, constant eta1≥0，η2The specific value can be defined by a user, and the superscript H represents the conjugate transpose;
(3) main lobe control: suppose that
Figure BDA0003591934730000104
Is the desired main lobe, i.e. q is a vector with dimension 2M + 1; vector e is the error vector of the desired main lobe and the designed main lobe, and is expressed as:
e＝ωmain-q
the nth element e (n) of the error vector e is represented as:
e(n)＝ωn-M-1-q(n)，1≤n≤2M+1
the main lobe shape is maintained by a method of minimizing the maximum main lobe matching error, namely:
Figure BDA0003591934730000111
(4) multi-main lobe interference resistance: in practical application, 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 detection of the real target. Interference signal JmThe output result of the mismatched filter h at distance shift j is represented as:
Figure BDA0003591934730000112
Jm(n) represents JmThe nth element of (n), all distance levels in the above formula are stacked at vector ω'mExpressed as:
Figure BDA0003591934730000113
when the interference parameters are fully known: the cognitive radar senses the interference of multiple main lobes and transmits different interference signals J under the condition that the interference parameters are completely knownmDistance level stack vector ω 'generated by mismatched filter h'm，m＝1,2,…,NJAll stacked on the vector omegaJ，ωJExpressed as:
Figure BDA0003591934730000114
NJthe number of interferers is 3in this embodiment;
when the interference parameters have deviation: the cognitive radar senses the multi-main-lobe interference, and C is carried out under the condition that other types of interference signal parameters are known&The interference parameter is biased. Suppose actual C&The number of the intercepting segments of the I interference is k, the forwarding times is l, the number of the perceived intercepting segments of the parameters is k ', and the forwarding times is l'. Assuming that the error is small, k ═ k '+ L, L ═ L' -L, and L is a natural number greater than 0. In the presence of errors, C&I interference distance level stacking vector
Figure BDA0003591934730000115
Expressed as:
Figure BDA0003591934730000116
in the formula, ω1'is C generated by the number of intercepted segments k' and the number of forwarding times l&Stacking vectors of all distance levels after filtering processing of the I interference and mismatch filter;
Figure BDA0003591934730000117
is C generated by the interception segment number of k '+ i and the forwarding times of l' -i&I, stacking vectors of all distance levels after filtering processing of the interference and mismatch filter;
Figure BDA0003591934730000118
is C generated by the number of interception segments k '-i and the forwarding times l' + i&Stacking vectors of all distance levels after the filtering processing of the I interference and mismatched filter, I is 1,2, …, L;
similarly, under the condition that parameters of other types of interference signals are known, the estimation of the interference parameters by directly and intermittently sampling has certain errors. The method for generating the interference by the actual direct intermittent sampling is assumed as follows: taking m code words as one section, intercepting once every ml code words and forwarding, and intercepting k sections in total, wherein the perceived direct intermittent sampling interference generation mode is; taking m code words as a section, intercepting every ml code words once and forwarding, and intercepting k ' sections altogether, wherein the assumed error is small, and k is k ' + L, and L is L ' -L; then in the case of deviation, directly and intermittently sampling the interference distance level stacking vector
Figure BDA0003591934730000121
Expressed as:
Figure BDA0003591934730000122
ω′2is m code words as one segment, every ml'Intercepting and forwarding the code words once, and intercepting all stacking vectors of distance levels generated by the k' section and subjected to filtering processing by the mismatched filter;
Figure BDA0003591934730000123
taking m code words as a section, intercepting and forwarding every m (l '-i) code words, and intercepting all stacking vectors of distance levels after filtering processing of direct intermittent sampling interference and mismatched filters generated by a k' + i section;
Figure BDA0003591934730000124
taking m code words as one section, intercepting and forwarding every m (l '+ i) code words, and intercepting all stacking vectors of distance levels after filtering processing of direct intermittent sampling interference and mismatched filters generated by a k' -i section;
under the condition that parameters of other types of interference signals are known, the estimation of the interference parameters by repeated intermittent sampling has certain errors. The method for generating the interference by the actual repeated intermittent sampling is assumed as follows: taking m code words as a section, intercepting once every ml code words and forwarding for q times, and intercepting k sections in total; the perceived interference generation mode of repeated and intermittent sampling is as follows; taking m code words as a section, intercepting every ml 'code words and forwarding the code words q times, and intercepting k' sections altogether, wherein the assumed error is small, k is k '+ L, and L is L' -L; repeatedly and intermittently sampling the interference distance level stacking vector in the presence of the deviation
Figure BDA0003591934730000125
Expressed as:
Figure BDA0003591934730000126
ω′3taking m code words as a section, intercepting once every ml code words and forwarding for q times, and intercepting all stacking vectors of distance levels after repeated intermittent sampling interference generated by the k' section and filtering processing of a mismatched filter;
Figure BDA0003591934730000127
taking m code words as a section, intercepting once every m (l '-i) code words and forwarding for q times, and intercepting all stacking vectors of distance levels after repeated intermittent sampling interference generated by a k' + i section and filtering processing of a mismatched filter;
Figure BDA0003591934730000128
taking m code words as a section, intercepting once every m (l '+ i) code words and forwarding for q times, and intercepting all stacking vectors of distance levels after repeated intermittent sampling interference generated by a k' -i section and filtering processing of a mismatched filter;
all interference is output via the mismatched filter at all range levels omegaJComprises the following steps: if the interference parameters are not deviated (whether the interference parameters are deviated or not is obtained by interference perception of a cognitive radar), all distance levels omegaJIs composed of
Figure BDA0003591934730000129
If one or more interference parameters have deviation, the interference parameters will be
Figure BDA00035919347300001210
Replacing the corresponding vector in the distance level stack vector with a distance level stack vector when an error exists; for example, when C&When I interference parameters have errors, all the obtained distance levels omegaJComprises the following steps:
Figure BDA00035919347300001211
all distance levels of all interference output by the mismatched filter are compressed using a min-max optimization criterion, namely:
Figure BDA0003591934730000131
s22, establishing an optimization problem: according to the optimization criterion designed by S21, the optimization problem of the phase coding signal S and the mismatched filter h for resisting the multi-main lobe interference is expressed as follows:
Figure BDA0003591934730000132
s.t.|hHh-Ns|≤γ1
in the formula of lambda1，λ2Is a preset weight coefficient.
S3, converting the non-convex, non-smooth and constrained optimization problem into a minimization problem about an independent variable (composed of signal phase, filter amplitude and phase) function by using a penalty function method, norm conversion and other methods, and solving by using an iterative L-BFGS algorithm.
The specific implementation method of S3 is as follows:
s31, optimizing problem transformation: the non-convex, non-smooth and constrained optimization problem is converted into a minimization problem with respect to the function of the independent variables (composed of signal phase, filter amplitude and phase) by using a method such as a penalty function method, norm conversion and the like, that is:
Figure BDA0003591934730000133
wherein λ is3To a predetermined weight coefficient, | | | | | non-calculation∞Represents an infinite norm;
the objective function is defined as:
f(x)＝||ωside||p+λ1||ωJ||p+λ2||e||p+λ3||hHh-Ns||p
in the formula, | | | non-conducting phosphorpRepresents a p-norm; vector quantity
Figure BDA0003591934730000134
Is composed of a vector
Figure BDA0003591934730000135
a and θ are sequentially constructed column vectors, represented as:
Figure BDA0003591934730000136
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 use the L-BFGS algorithm to solve the minimum value of the objective function, and continuously iterate until the objective function f (x) reaches the minimum drop epsilon, and then the iteration is stopped, and x is output. As shown in fig. 5, the specific steps are as follows:
step I: initializing variable x0ε, p, μ: setting x0As an initial value, epsilon is the minimum reduction of the objective function, the iteration number w is 1, the parameter p is 2, and mu is 2;
step II: calculating the current function value f (x)w): x is to bew-1As an initial value, using L-BFGS algorithm, the minimization function f (x) is used to find xwLet fw＝f(xw)；
Step III: if fw-1-fwIf | < epsilon, then x is obtainedwAnd stopping the iteration; otherwise, let p ═ μ p and w ═ w +1, jump to step II.
And step II, a minimization function f (x) is required and can be realized by adopting an L-BFGS algorithm. Compared with a quasi-Newton method, the L-BFGS algorithm estimates the Hessian matrix by using a small amount of vectors, greatly reduces the calculated amount and is easy to realize. The L-BFGS algorithm flow is as follows:
first, an initial iteration number w is set to 1, and an initial vector x is set0And calculating the objective function value f1Sum of derivative value
Figure BDA0003591934730000141
To derive symbols and to select a starting direction
Figure BDA0003591934730000142
And an algorithm update variable n. The specific cycle process is as follows:
step 1: for the w-th iteration, f is calculatedw，
Figure BDA0003591934730000143
And gwAnd obtaining the step length lambda by using a backtracking search algorithmw；
Step 2: calculating qw＝λwgw，xw+1＝xw+λwgw；
And step 3: computing
Figure BDA0003591934730000144
And with
Figure BDA0003591934730000145
And 4, step 4: order to
Figure BDA0003591934730000146
And 5: fori ═ w, w-1, …, w-n +1
Figure BDA0003591934730000147
p＝p-tiyi
end
Step 6:
Figure BDA0003591934730000148
and 7: fori ═ w, w-1, …, w-n +1
Figure BDA0003591934730000149
z＝z+(ti-β)qi
end
And 8: gw+1＝-z；
And step 9: w is w + 1;
and finally, when the termination condition is met, obtaining an optimization result.
It should be explained that, in step 5-7, the product of the Hessian matrix and the gradient p is constructed mainly by using the first-order gradient information of the adjacent n-times iteration function, and the search direction of the next step is obtained according to the obtained vector z. Step 1, obtaining step length lambda by utilizing backtracking search algorithmwThe specific process of the backtracking search algorithm is as follows:
step a: selecting a lambdaw＞0，ρ,c1∈(0,1)；
Step b: if it is not
Figure BDA00035919347300001410
Let lambdaw＝ρλw；
Step c: repeating the step b until the relational expression is satisfied
Figure BDA00035919347300001411
Output lambdaw。
Simulation verification and analysis
Simulation parameters:
the time width of a phase coding signal is 60 mu s, the bandwidth is 5MHz, the time width of an LFM signal is 60 mu s, the bandwidth is 5MHz, the time width of a mismatch filter is 120 mu s, the carrier frequency of a radar system is 2GHz, the number of transmitted pulses is 100, the pulse repetition period is 480 mu s, the signal-to-noise ratio is 0dB, the interference-to-signal ratio is 20dB, the target distance is 45km, the C & I interference distance is 46km, the direct intermittent sampling interference distance is 44km, the repeated intermittent sampling interference distance is 48km, the target speed is 30m/s, the C & I interference speed is 32m/s, the direct intermittent sampling speed is 28m/s, and the repeated intermittent sampling interference speed is 26 m/s.
The interference parameters are fully known:
c & I interference generation mode: 10 segments are intercepted, each segment is forwarded 5 times, and each segment has 12 sampling points.
The interference generation mode of direct intermittent sampling: and intercepting 10 sections, forwarding each section for 1 time, and each section has 8 sampling points.
The repeated intermittent sampling interference generation mode comprises the following steps: and intercepting 10 sections, forwarding each section 4 times, and each section has 4 sampling points.
The interference parameters have deviation:
c & I interference generation manner: and 9 sections are intercepted, each section is forwarded 6 times, and each section has 12 sampling points.
The interference generation mode of direct intermittent sampling: and (4) intercepting 10 sections, forwarding for 1 time each section, and obtaining 8 sampling points each section.
Repeated intermittent sampling interference generation mode: and intercepting 10 sections, forwarding each section 4 times, and each section has 4 sampling points.
Weight coefficient lambda1＝1，λ2＝1，λ3The main lobe width control parameter M is 3 for 1 and iterates 100 times.
Simulation analysis: fig. 6 shows the doppler tolerance of the designed optimized signal under the condition that the interference parameters are completely known (fig. 6(a)) and the interference parameters are deviated (fig. 6 (b)). When the speed deviates 150m/s, the optimized waveform main lobe designed under the completely known interference parameter condition is about 23dB higher than the peak side lobe level, and the optimized waveform main lobe designed under the condition of the deviation of the interference parameter 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 Doppler tolerance of the interference parameter is completely known to be better than that of the optimized waveform designed under the condition that the interference parameter has deviation. Fig. 7 shows the results of the LFM signal and its corresponding C & I interference, direct intermittent sampling interference, and repeated intermittent sampling interference after matched filtering. Fig. 8 shows the results of the mismatch filtering process between the optimized signal and the multi-main-lobe interference corresponding to the optimized signal under the condition that the interference parameters are completely known and there is a deviation in the interference parameters, where (a) is that the interference parameters are completely known, and (b) is that the interference parameters are deviated. As can be seen from fig. 7 and 8, the peak side lobe level after the optimized signal mismatch processing designed by the method is at least 12dB lower than the peak side lobe level after the LFM signal pulse compression, and the designed optimized signal detection performance is superior to the LFM signal; the multi-main-lobe interference resistance of the optimized signal is also superior to that of an LFM signal, but a certain signal-to-noise ratio loss exists in the design process, and the interference parameter is completely known to have the detection performance and the multi-main-lobe interference resistance under the deviation condition. Fig. 9 is a comparison graph of detection results of the designed optimized signal when the LFM signal and the interference parameter are completely known and have a 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, but the optimization signal can effectively detect the distance and the speed of the target, and the detection performance of the optimization signal designed under the condition that the disturbance parameters are completely known is slightly better than that of the optimization signal designed under the condition that the disturbance parameters have deviations.
It will be appreciated by those of ordinary skill in the art that the embodiments described herein are intended to assist the reader in understanding the principles of the invention and are to be construed as being without limitation to such specifically recited embodiments and examples. Those skilled in the art can make various other specific changes and combinations based on the teachings of the present invention without departing from the spirit of the invention, and these changes and combinations are within the scope of the invention.

Claims (4)

1. A multi-main lobe interference resistant waveform and filter joint cognitive design method 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 the constant modulus phase coding signal;
s2, under the condition that interference parameters are completely known or have deviation, establishing a transmitting-receiving combined optimization problem of waveform correlation function peak level, correlation function main lobe template matching error and interference energy weighting and minimizing criterion under the constraint of signal-to-noise ratio;
and S3, converting the optimization problem into a minimization problem about an independent variable function, and solving by using an iterative L-BFGS algorithm.
2. The method for cognitive design of a multi-mainlobe interference resistant waveform and filter combination according to claim 1, wherein the step S1 specifically includes the following substeps:
s11, the constant modulus phase encoded signal is represented as:
Figure FDA0003591934720000011
in the formula [ ·]TDenotes transposition, snFor transmitting code words of the waveform, N is 1,2, …, Ns，NsThe number of code words of the phase encoded waveform;
n element snExpressed as:
Figure FDA0003591934720000012
in the formula (I), the compound is shown in the specification,
Figure FDA0003591934720000013
to represent
Figure FDA0003591934720000014
The phase of the nth code word of (a),
Figure FDA0003591934720000015
encoding the phase of the signal s for a constant modulus phase;
s12, establishing C&I interference signal model: for C&I jammer, assuming DRFM jammer intercepts radar signal, from siStarting, taking m code words as one segment, forwarding each segment for l times, and intercepting k segments in total, wherein the whole C&I interference signal codeword length Ns＝klm；C&The I interference signal is:
Figure FDA0003591934720000016
in the formula, HtT is a t section intercepted by the jammer, and is more than or equal to 1 and less than or equal to k; htThe represented codeword is represented as:
Ηt＝[s(t-1)ml+i,s(t-1)ml+i+1,…,s(t-1)ml+i+m-1]；
s13, directly and intermittently sampling an interference signal model: for the direct intermittent sampling interference, the DRFM jammer is assumed to intercept the radar signal, from siBeginning, taking m code words as a section, intercepting and forwarding every other ml code words, and intercepting k sections in total, wherein interference signals are directly and intermittently sampled as follows:
J2＝[Η′1,Η′0,Η′2,Η′0,…,Η′k,Η′0]T
h in formula (II)'0＝01×m(l-1)，01×m(l-1)Represents a 0 vector of 1 xm (l-1); h (H)t' t-th section 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, repeatedly and intermittently sampling an interference signal model: for repeated intermittent sampling interference, assuming that a DRFM jammer intercepts radar signals, from siBeginning, taking m code words as a section, intercepting every ml code words once, copying q times and then forwarding, intercepting k sections altogether, and repeatedly and intermittently sampling interference signals as follows:
Figure FDA0003591934720000021
in the formula, H0＝01×m(l-q)，Η″tAnd the t-th section intercepted by the jammer represents a code word represented by:
Η″t＝[s(t-1)ml+i,s(t-1)ml+i+1,…s(t-1)ml+i+m-1]；
s15, mismatch filter signal model: suppose that the length h of the corresponding mismatch filter at the receiving end of the radar is Nh，Nh≥NsThe mismatched filter h is expressed as:
Figure FDA0003591934720000022
n element hnExpressed as:
Figure FDA0003591934720000023
where a is the magnitude vector of the mismatched filter h, anIs the nth element in a; theta is the phase vector of the mismatched filter h, thetanIs the nth element in theta; h ═ a ∑ exp (j θ), which indicates a Hadamard product.
3. The method for cognitive design of a multi-mainlobe interference resistant waveform and filter combination according to claim 1, wherein the step S2 specifically comprises:
s21, designing an optimization criterion:
(1) range side lobe: the output result of the phase-encoded signal s through the mismatched filter h at the distance displacement j is represented as:
Figure FDA0003591934720000024
wherein R represents a conjugate1Denotes a value range, Γ1＝[-(Ns+Nh)/2+1,(Ns+Nh)/2-1]；
Let omega bejJ is 0, ± 1, …, ± M, M is a main lobe width control parameter;
all distance mainlobe levels are stacked at vector ωmainExpressed as:
ωmain＝[ω-M,…,ω-1,ω0,ω1,…,ωM]T
all range sidelobe levels are stacked at vector ωsideExpressed as:
Figure FDA0003591934720000031
the side lobe region is denoted as F2，Γ2Expressed as:
Γ2＝[-(Ns+Nh)/2+1,-M+1]∪[M-1,(Ns+Nh)/2-1]
range sidelobes are reduced by minimizing peak sidelobes, namely:
Figure FDA0003591934720000032
(2) loss of signal-to-noise ratio:
|hHh-Ns|≤η1
|ω0-Ns|≤η2
in the formula, constant eta1≥0，η2The superscript H is more than or equal to 0 and represents conjugate transposition;
(3) main lobe control: suppose that
Figure FDA0003591934720000033
Is the desired main lobe, i.e. q is a vector with dimension 2M + 1; vector e is the error vector of the desired main lobe and the designed main lobe, and is expressed as:
e＝ωmain-q
the nth element e (n) of the error vector e is represented as:
e(n)＝ωn-M-1-q(n)，1≤n≤2M+1
the main lobe shape is maintained by a method of minimizing the maximum main lobe matching error, namely:
Figure FDA0003591934720000034
(4) the multi-main lobe interference resistance performance is as follows: interference signal JmThe output result of the mismatched filter h at distance shift j is represented as:
Figure FDA0003591934720000035
Jm(n) represents JmThe nth element of (n), all distance levels in the above formula are stacked at vector ω'mExpressed as:
Figure FDA0003591934720000036
when the interference parameters are fully known: the cognitive radar senses the interference of multiple main lobes and transmits different interference signals J under the condition that the interference parameters are completely knownmDistance level stack vector ω 'generated by mismatched filter h'm，m＝1,2,…,NJAll stacked on the vector ωJ，ωJExpressed as:
Figure FDA0003591934720000037
NJrepresenting the number of interferers;
when the interference parameters have deviation: actual C&The number of the interception segments of the interference I is k, the forwarding times are l, the number of the perceived parameter interception segments is k ', and the forwarding times are l'; k ═ k '+ L, L ═ L' -L, L is a natural number greater than 0; in the presence of errors, C&I interference distance level stacking vector
Figure FDA0003591934720000041
Expressed as:
Figure FDA0003591934720000042
in formula (II), omega'1C generated by the interception segment number of k' and the forwarding times of l&I, stacking vectors of all distance levels after filtering processing of the interference and mismatch filter;
Figure FDA00035919347200000410
is C generated by the interception segment number of k '+ i and the forwarding times of l' -i&I, stacking vectors of all distance levels after filtering processing of the interference and mismatch filter;
Figure FDA00035919347200000411
is C generated by the number of interception segments k '-i and the forwarding times l' + i&Stacked vector of all distance levels after filtering processing of I interference and mismatched filter，i＝1,2,…,L；
Similarly, the actual direct intermittent sampling interference generation mode is as follows: taking m code words as one section, intercepting once every ml code words and forwarding, and intercepting k sections in total, wherein the perceived direct intermittent sampling interference generation mode is; taking m code words as a section, intercepting and forwarding every ml code words, and intercepting k sections; then in case of deviation, directly and intermittently sampling the interference distance level stacking vector
Figure FDA0003591934720000043
Expressed as:
Figure FDA0003591934720000044
ω′2taking m code words as a section, intercepting once every ml code words and forwarding, and intercepting all stacking vectors of distance levels generated by k' section after direct intermittent sampling interference and filter processing of mismatched filter;
Figure FDA0003591934720000045
taking m code words as a section, intercepting and forwarding every m (l '-i) code words, and intercepting all stacking vectors of distance levels after filtering processing of direct intermittent sampling interference and mismatched filters generated by a k' + i section;
Figure FDA0003591934720000046
taking m code words as one section, intercepting and forwarding every m (l '+ i) code words, and intercepting all stacking vectors of distance levels after filtering processing of direct intermittent sampling interference and mismatched filters generated by a k' -i section;
the actual repeated intermittent sampling interference generation mode is as follows: taking m code words as a section, intercepting once every ml code words and forwarding for q times, and intercepting k sections in total; the perceived interference generation mode of repeated intermittent sampling is as follows; taking m code words as a section, intercepting once every ml code words and forwarding for q times, and intercepting k' sections altogether; in case of deviation, it is heavyComplex intermittent sampling interference distance level stacking vector
Figure FDA0003591934720000047
Expressed as:
Figure FDA0003591934720000048
ω′3taking m code words as a section, intercepting once every ml code words and forwarding for q times, and intercepting all stacking vectors of distance levels after repeated intermittent sampling interference generated by the k' section and filtering processing of a mismatched filter;
Figure FDA0003591934720000049
taking m code words as a section, intercepting once every m (l '-i) code words and forwarding for q times, and intercepting all stacking vectors of distance levels after repeated intermittent sampling interference generated by a k' + i section and filtering processing of a mismatched filter;
Figure FDA0003591934720000051
taking m code words as a section, intercepting once every m (l '+ i) code words and forwarding for q times, and intercepting all stacking vectors of distance levels after repeated intermittent sampling interference generated by a k' -i section and filtering processing of a mismatched filter;
all interference is output via the mismatched filter at all range levels omegaJComprises the following steps: if there is no deviation in the interference parameters, all the distance levels omegaJIs composed of
Figure FDA0003591934720000052
If one or more interference parameters have deviation, the interference parameters will be
Figure FDA0003591934720000053
Replacing the corresponding vector in the distance level stack vector with a distance level stack vector when an error exists;
all distance levels of all interference output by the mismatched filter are compressed using a min-max optimization criterion, namely:
Figure FDA0003591934720000054
s22, establishing an optimization problem: according to the optimization criterion designed by S21, the optimization problem of the phase coding signal S and the mismatched filter h for resisting the multi-main lobe interference is expressed as follows:
Figure FDA0003591934720000055
s.t.|hHh-Ns|≤γ1
in the formula, λ1，λ2Is a preset weight coefficient.
4. The method for cognitive design of a multi-mainlobe interference resistant waveform and filter combination according to claim 1, wherein the S3 is specifically implemented by:
s31, optimizing problem transformation: the optimization problem is converted into a minimization problem with respect to the argument function, namely:
Figure FDA0003591934720000056
wherein λ is3To a predetermined weight coefficient, | | | | | non-calculation∞Represents an infinite norm;
the objective function is defined as:
Figure FDA0003591934720000057
in the formula, | | | non-conducting phosphorpRepresents a p-norm; vector quantity
Figure FDA0003591934720000058
Is composed of a vector
Figure FDA0003591934720000059
a and θ are sequentially constructed column vectors, represented as:
Figure FDA00035919347200000510
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 drop epsilon, stopping iteration, and outputting x.
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CN116224246B (en) * 2022-12-14 2023-11-17 南京航空航天大学 Suppression interference suppression method for joint design of transmitting waveform and receiving filter

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