CN112630732A - Anti-radio frequency interference design method based on ISL constraint - Google Patents
Anti-radio frequency interference design method based on ISL constraint Download PDFInfo
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- CN112630732A CN112630732A CN202011466896.4A CN202011466896A CN112630732A CN 112630732 A CN112630732 A CN 112630732A CN 202011466896 A CN202011466896 A CN 202011466896A CN 112630732 A CN112630732 A CN 112630732A
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
- G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
- G01S7/36—Means for anti-jamming, e.g. ECCM, i.e. electronic counter-counter measures
Abstract
The invention discloses an anti-radio frequency interference design method based on ISL constraint, wherein in the method, in order to control the distance side lobe level of an echo signal after passing through a matched filter, the self-correlation ISL of a design waveform is not higher than a specified threshold value for constraint when the waveform optimization problem is modeled. Meanwhile, aiming at the problem model provided by the invention, an iterative solution algorithm based on ADMM and MM methods is provided. Compared with a similarity constraint method adopted in the current anti-interference waveform design, the ISL constraint is more direct in controlling the side lobe, more meets the actual engineering requirements, and avoids the problem of similarity threshold setting in the similarity constraint.
Description
Technical Field
The invention relates to the technical field of anti-interference communication, in particular to an anti-radio frequency interference design method based on ISL constraint.
Background
High frequency radars generally need to share a frequency band with devices such as short wave communication, broadcasting stations and the like, so that radio frequency interference is inevitably existed in echoes of the high frequency radars. After Range-Doppler (RD) processing, the broadband radio frequency interference will appear as irregular stripes over a large area or throughout the entire RD pattern, while the narrowband radio frequency interference appears as elongated straight lines parallel to the Range axis at a fixed Doppler frequency. Due to the strong energy of the radio frequency interference, the presence of the radio frequency interference can easily cover the target, so that the target cannot be detected or identified by the radar.
An Environmental Sensing Based Waveform (ESBW) design is a technology capable of effectively suppressing radio frequency interference. As shown in fig. 1, a flow chart of interference suppression by ESBW design is that a radar monitors an environment first, and acquires interference characteristics (such as a covariance matrix of interference) in the environment as prior knowledge by using monitoring data. And then establishing a corresponding anti-interference waveform design problem according to the prior information and the specific engineering requirement and solving the problem. The radar transmits the waveform with anti-interference capability by utilizing an ESBW design technology, so that interference suppression is not required when a receiving end processes signals.
Generally, in a current anti-interference waveform design method, a Signal to interference plus noise ratio (SINR) of a maximized receiving filter (most common matched filter) is generally adopted as an object function of waveform design, and a similarity constraint is adopted to control a side lobe level of a waveform, so that a distance side lobe generated after an echo Signal passes through the filter is low, and therefore, the influence of a strong clutter/target in an adjacent distance unit on target detection in a current distance unit is reduced.
The modeling of the classical anti-interference waveform design problem based on similarity constraint is as follows:
where s is the waveform to be designed, RIA covariance matrix representing interference plus noise. The control of the side lobe levels in this method employs a similarity constraint. I.e. given a reference waveform s with a low level of autocorrelation sidelobes0By limiting the design waveform s and the reference waveform s0Norm distance between to ensure s also has a lower valueThe autocorrelation sidelobe level of. In general, the smaller β, the lower the autocorrelation sidelobe level of the design waveform s.
In engineering, the output range sidelobe level of the echo signal after passing through the filter is also very interesting. The range sidelobe level represents the degree of influence of echo signals in adjacent range units on target detection of the current range unit. If the range sidelobe is too high, strong clutter and the like in an adjacent range unit can influence the detection of the radar on the target in the current detection unit through sidelobe leakage, and the problems of difficult target separation or too high false alarm rate and the like are caused. In general, when using matched filters for reception, the range sidelobes requirements can translate into waveform autocorrelation sidelobes. In engineering, it is generally required that the autocorrelation ISL/PSL of a waveform is below a given threshold, i.e.:
where epsilon and epsilon' are the corresponding threshold values,is a displacement matrix whose elements consist of 0 and 1:
in order to avoid non-linear distortion and wasted performance of the amplifier, it is also generally desirable to design the waveform to have a constant modulus characteristic, namely:
where N is the number of design points for the transmit waveform.
In practical engineering, the requirements for the side lobes of the filter are usually provided for two indexes, i.e., Integrated Sidelobe Level (ISL) and Peak Sidelobe Level (PSL). For example, if the receiving end employs a matched filter, the autocorrelation ISL/PSL of the waveform is required to be lower than a given threshold. However, because of the lack of direct and unambiguous correspondence between the similarity and the ISL/PSL of the design waveform, it is difficult to translate a given ISL/PSL specification requirement into a requirement for similarity, and thus difficult to determine an appropriate threshold for the similarity constraint. In conclusion, the similarity constraint is an indirect method for controlling the side lobe, and is inconvenient to use in practical engineering.
Disclosure of Invention
The invention aims to solve the technical problem of ensuring the anti-interference performance of the designed waveform and realizing the direct control of the output sidelobe level of the matched filter by utilizing the autocorrelation ISL constraint. ISL constraint directly corresponds to index requirements in actual engineering, so that the method is more in line with actual requirements.
The technical scheme adopted by the invention is as follows:
an anti-radio frequency interference design method based on ISL constraint comprises the following steps:
(1) monitoring the environment by a radar, and acquiring interference characteristics in the environment by using monitoring data;
(2) setting an autocorrelation ISL constraint and a constant modulus constraint;
(3) the method comprises the steps of establishing an anti-interference waveform design model by taking the output SINR of a maximum matched filter as a target and combining autocorrelation ISL constraint and constant modulus constraint;
(4) and iterating the established anti-interference waveform design model by using an ADMM-MM algorithm to finally obtain the required anti-interference waveform.
Wherein, the autocorrelation ISL constraint and the constant modulus constraint in the step (2) are specifically as follows:
ISL constraint:
wherein s is the waveform to be designed, epsilon is the corresponding threshold value,is a displacement matrix whose elements are composed of 0 and 1;
constant modulus constraint:
wherein N is the number of design points of the transmitted waveform.
Wherein, the design model of the anti-interference waveform in the step (3) specifically comprises:
with the output SINR of the maximum matched filter as a target and the autocorrelation ISL constraint and the constant modulus constraint, an anti-interference waveform design model is as follows:
wherein R isIA covariance matrix representing interference plus noise.
Wherein the step (4) is specifically as follows:
the anti-interference waveform design model is equivalent to:
wherein the content of the first and second substances,will be provided withCalled ISL constraint term and willReferred to as ISL constraint threshold;
introduction of auxiliary variable kappa ═ kappa1,...,κ2N]TFurther equivalently converting the problem into:
and consider the following augmented lagrange function:
wherein v ═ v [ v ]1,...,ν2N]TFor dual variables, rho is a penalty factor, and under the framework of an ADMM method, the variables s, kappa and v are updated in sequence in each iteration; the method comprises the following specific steps:
firstly, initializing the iteration number l to be 0, the iteration index q of each iteration to be 0, and initializing s(0),v(0)=02N;
② the l +1 th iteration value s(l+1)Update as the optimal solution to the problem:
wherein, κ(l),ν(l)Respectively the values of the first iteration;
thirdly, iterative searching of suboptimal solution by MM method, and recording the optimization result with iterative index as q-th time as s(q)Wherein s is(0)=s(l)Then, the generation index is the optimization problem to be solved in the q +1 th iteration as follows:
wherein the content of the first and second substances,
λmax(RI) Is a matrix RIMaximum eigenvalue of U (s; s)(q)) Is L (s, κ)(l),ν(l)) At s(q)A tight upper bound function of (c); the optimal solution to the problem is:
calculate | L(s)(q+1),κ(l),ν(l))-L(s(q),κ(l),ν(l))|/L(s(q),κ(l),ν(l)) If the value is greater than the set threshold value delta0If q is q +1, then calculate s again(q+1)Until the value is greater than a set threshold delta0To obtain s(l+1)=s(q+1)(ii) a If the value is less than the set threshold value delta0Then directly obtain s(l+1)=s(q+1);
(l +1 st iteration value kappa)(l+1)Update as the optimal solution to the problem:
wherein mup (l+1)=s(l+1)HAps(l+1);
the l +1 th iteration value v(l+1)The update is as follows:
ν(l+1)=ν(l)+ρ(μ(l+1)-κ(l+1)) (13)
the convergence condition for the ADMM iteration is:
whereinWhich represents the original residual error, is shown,representing dual residual errors, δ1And delta2Then the residual error tolerance value is the corresponding residual error tolerance value; judging s(l+1),κ(l+1),v(l+1)Judging whether the current time is less than the preset time, if not; if yes, obtaining a waveform optimization result s(l+1)。
Drawings
FIG. 1 is a flow chart of an embodiment of the present invention.
Detailed Description
The technical solution in the embodiments of the present invention is clearly and completely described below with reference to the drawings and formulas. The invention relates to an anti-radio frequency interference design method based on ISL constraint, which comprises the following specific implementation modes:
(1) the radar firstly monitors the environment and acquires the interference characteristic in the environment by using monitoring data;
(2) setting an autocorrelation ISL constraint and a constant modulus constraint;
wherein the ISL constraint and the constant modulus constraint are:
(2.1) ISL constraint:
where s is the waveform to be designed, epsilon is the corresponding threshold,is a displacement matrix whose elements consist of 0 and 1:
(2.2) constant modulus constraint:
where N is the number of design points for the transmit waveform.
(3) The method comprises the following steps of establishing an anti-interference waveform design problem model by taking the output SINR of a maximized matched filter as a target and considering autocorrelation ISL constraint and constant modulus constraint:
(4) and iterating the established anti-interference waveform design model by using an ADMM-MM algorithm to finally obtain the required anti-interference waveform.
whereinHereinafter, will beCalled ISL constraint term and willReferred to as the ISL-constrained threshold. Since the ISL constraint is fourth order with respect to s, problem (4) is non-convex.
First, an auxiliary variable k ═ k is introduced1,...,κ2N]TAnd further equivalently converting the problem (12) into:
for the problem, consider the following augmented Lagrangian function:
wherein v ═ v [ v ]1,...,ν2N]TFor dual variables, ρ is a penalty factor. In the framework of the ADMM method, the variables s, κ, v are updated in turn for each iteration. The method comprises the following specific steps:
firstly, initializing the iteration number l to be 0, the iteration index q of each iteration to be 0, and initializing s(0),v(0)=02N;
② the l +1 th iteration value s(l+1)Update as the optimal solution to the problem:
wherein, κ(l),ν(l)Respectively for the first iterationA value;
thirdly, iterative searching of suboptimal solution by MM method, and recording the optimization result with iterative index as q-th time as s(q)Wherein s is(0)=s(l)Then, the generation index is the optimization problem to be solved in the q +1 th iteration as follows:
wherein the content of the first and second substances,
λmax(RI) Is a matrix RIMaximum eigenvalue of U (s; s)(q)) Is L (s, κ)(l),ν(l)) At s(q)A tight upper bound function of (c); the optimal solution to the problem is:
calculate | L(s)(q+1),κ(l),ν(l))-L(s(q),κ(l),ν(l))|/L(s(q),κ(l),ν(l)) If the value is greater than the set threshold value delta0If q is q +1, then calculate s again(q+1)Until the value is greater than a set threshold delta0To obtain s(l+1)=s(q+1)(ii) a If the value is less than the set threshold value delta0Then directly obtain s(l+1)=s(q+1);
(l +1 st iteration value kappa)(l+1)Update as the optimal solution to the problem:
the l +1 th iteration value v(l+1)The update is as follows:
ν(l+1)=ν(l)+ρ(μ(l+1)-κ(l+1)) (13)
the convergence condition for the ADMM iteration is:
whereinWhich represents the original residual error, is shown,representing dual residual errors, δ1And delta2Then the residual error tolerance value is the corresponding residual error tolerance value; judging s(l+1),κ(l+1),v(l+1)Judging whether the current time is less than the preset time, if not; if yes, obtaining a waveform optimization result s(l+1)。
Claims (4)
1. An anti-radio frequency interference design method based on ISL constraint is characterized by comprising the following steps:
(1) monitoring the environment by a radar, and acquiring interference characteristics in the environment by using monitoring data;
(2) setting an autocorrelation ISL constraint and a constant modulus constraint;
(3) the method comprises the steps of establishing an anti-interference waveform design model by taking the output SINR of a maximum matched filter as a target and combining autocorrelation ISL constraint and constant modulus constraint;
(4) and iterating the established anti-interference waveform design model by using an ADMM-MM algorithm to finally obtain the required anti-interference waveform.
2. The ISL constraint-based radio frequency interference rejection design method according to claim 1, wherein the autocorrelation ISL constraint and the constant modulus constraint in step (2) are specifically:
ISL constraint:
wherein s is the waveform to be designed, epsilon is the corresponding threshold value,is a displacement matrix whose elements are composed of 0 and 1;
constant modulus constraint:
wherein N is the number of design points of the transmitted waveform.
3. The ISL constraint-based anti-radio frequency interference design method according to claim 2, wherein the anti-interference waveform design model in step (3) is specifically:
with the output SINR of the maximum matched filter as a target and the autocorrelation ISL constraint and the constant modulus constraint, an anti-interference waveform design model is as follows:
wherein R isIA covariance matrix representing interference plus noise.
4. The ISL constraint-based anti-radio frequency interference design method according to claim 1, wherein the step (4) is specifically:
the anti-interference waveform design model is equivalent to:
wherein the content of the first and second substances,will be provided withCalled ISL constraint term and willReferred to as ISL constraint threshold;
introduction of auxiliary variable kappa ═ kappa1,...,κ2N]TFurther equivalently converting the problem into:
and consider the following augmented lagrange function:
wherein v ═ v [ v ]1,...,ν2N]TFor dual variables, rho is a penalty factor, and under the framework of an ADMM method, the variables s, kappa and v are updated in sequence in each iteration; the method comprises the following specific steps:
firstly, initializing the iteration number l to be 0, the iteration index q of each iteration to be 0, and initializing s(0),v(0)=02N;
② the l +1 th iteration value s(l+1)Update as the optimal solution to the problem:
wherein, κ(l),ν(l)Respectively the values of the first iteration;
thirdly, iterative searching of suboptimal solution by MM method, and recording the optimization result with iterative index as q-th time as s(q)Wherein s is(0)=s(l)Then, the generation index is the optimization problem to be solved in the q +1 th iteration as follows:
wherein the content of the first and second substances,
λmax(RI) Is a matrix RIMaximum eigenvalue of U (s; s)(q)) Is L (s, κ)(l),ν(l)) At s(q)A tight upper bound function of (c); the optimal solution to the problem is:
calculate | L(s)(q+1),κ(l),ν(l))-L(s(q),κ(l),ν(l))|/L(s(q),κ(l),ν(l)) If the value is greater than the set threshold value delta0If q is q +1, then calculate s again(q+1)Until the value is greater than a set threshold delta0To obtain s(l+1)=s(q+1)(ii) a If the value is less than the set threshold value delta0Then directly obtain s(l+1)=s(q+1);
(l +1 st iteration value kappa)(l+1)Update as the optimal solution to the problem:
the l +1 th iteration value v(l+1)The update is as follows:
ν(l+1)=ν(l)+ρ(μ(l+1)-κ(l+1)) (13)
the convergence condition for the ADMM iteration is:
whereinWhich represents the original residual error, is shown,representing dual residual errors, δ1And delta2Then the residual error tolerance value is the corresponding residual error tolerance value; judging s(l +1),κ(l+1),v(l+1)Judging whether the current time is less than the preset time, if not; if yes, obtaining a waveform optimization result s(l+1)。
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