CN116224246A - Suppression interference suppression method for joint design of transmitting waveform and receiving filter - Google Patents

Suppression interference suppression method for joint design of transmitting waveform and receiving filter Download PDF

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CN116224246A
CN116224246A CN202211605536.7A CN202211605536A CN116224246A CN 116224246 A CN116224246 A CN 116224246A CN 202211605536 A CN202211605536 A CN 202211605536A CN 116224246 A CN116224246 A CN 116224246A
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filter
optimization
signal
interference
mismatch
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CN116224246B (en
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张劲东
吕树肜
张瑞
刘思琪
徐婧
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Nanjing University of Aeronautics and Astronautics
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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
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Abstract

The invention discloses a suppression interference suppression method for joint design of a transmitting waveform and a receiving filter, which comprises the steps of establishing a transmitting signal sequence, a receiving signal sequence model and an ASL-based receiving mismatch filter model; constructing a transmit waveform and receive filter joint optimization model considering the dynamic range of the receiver; and solving a joint optimization model by adopting a joint optimization algorithm of the transmitting waveform and the receiving filter to obtain an optimal solution of the transmitting signal and the mismatched filter parameters so as to guide the design of the transmitting signal sequence and the receiving filter. The dynamic range of the combined and optimized transmitting signal and receiving filter can be improved, and the optimized dynamic range can be obtained under different input interference signal ratios.

Description

Suppression interference suppression method for joint design of transmitting waveform and receiving filter
Technical Field
The invention belongs to the technical field of radar interference, and particularly relates to a suppression interference suppression method for joint design of a transmitting waveform and a receiving filter.
Background
In modern radar systems, pulse compression techniques may utilize specially designed transmit and receive filters to achieve better target detection capability and higher range resolution. The dynamic range of a radar receiver is generally defined as a ratio of the maximum received signal amplitude to the minimum received signal amplitude as an important system design index, which directly affects the performance of multi-target detection. Increasing the dynamic range of the receiver may be achieved by designing a reasonable transmit signal sequence and receive filter.
The problem of jointly optimizing the transmit signal and the receive filter with a priori knowledge of the interference or clutter has been widely studied. Previous studies have focused on optimization of the cross-correlation and cross-ambiguity functions for transmit and receive filters under different doppler conditions. And meanwhile, the SINR/SCNR output by the optimizing filter is used as a measurement criterion, and the receiving filter is optimized. In the convergence process of these algorithms, each iteration needs to solve a convex optimization problem and a hidden convex optimization problem, which increases the complexity of the optimization algorithm. Meanwhile, the radar dynamic receiving range is improved to have an important influence on the target detection performance, and if the radar dynamic receiving range is not considered in the system design, targets are possibly submerged in side lobes of interference or side lobes of the targets are higher than other weak targets, so that the detection capability of the radar is reduced.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a suppression interference suppression method for joint design of a transmitting waveform and a receiving filter aiming at the defects of the prior art.
In order to achieve the technical purpose, the invention adopts the following technical scheme:
a suppression interference suppression method for joint design of a transmitting waveform and a receiving filter comprises the following steps:
s1: establishing a transmitting signal sequence model, a receiving signal sequence model and an ASL-based receiving mismatch filter model;
s2: aiming at the model established in the step S1, constructing a transmitting waveform and receiving filter joint optimization model considering the dynamic range of a receiver;
s3: and solving a joint optimization model by adopting a joint optimization algorithm of the transmitting waveform and the receiving filter to obtain an optimal solution of the transmitting signal and the mismatched filter parameters so as to guide the design of the transmitting signal sequence and the receiving filter.
In order to optimize the technical scheme, the specific measures adopted further comprise:
the above S1 describes a process for establishing a model of a signal sequence to be transmitted and a model of a signal sequence to be received, that is, a model of a signal sequence to be received by superimposing and suppressing discrete point target signals, wherein the process comprises:
the transmitted signal sequence is expressed as s= [ s ] 1 ,s 2 ,...,s N ] T The method comprises the steps of carrying out a first treatment on the surface of the I.e. the transmitted signal is in the form of a phase-keyed signal
The received baseband signal contains a point target signal and a suppressed interference signal, which satisfies the following equation
r＝Sx+w
wherein ,
Figure BDA0003997658590000021
representing the transmitted sequence at different distance units, x= [ x ] 0 ,x 1 ,…,x N-1 ,x -(N-1) ,…,x -1 ] T ，x k The scattering coefficients representing different distance units, w, are defined as the interference independent of the target signal, assuming w and { x } k -independent of each other;
the electromagnetic scattering amplitude of the point target is x 0 Average clutter power E [ |x 0 | 2 ]＝α 2 ；
The characteristics of the suppression interference use an interference covariance matrix W (1) Represented as
Figure BDA0003997658590000022
wherein ,/>
Figure BDA0003997658590000023
Defined as the average power of the interference, W (1) Is a diagonal element in the interference covariance matrix.
The process for establishing the receiving mismatch filter model based on the minimum mean square error characteristic of ASL in the above step S1 is as follows:
the receive filter employs a mismatch filter with minimum mean square error MSE at the desired distance bin x0The mismatch filter h satisfies h H s=1, then at distance x 0 The mean square error MSE at this point can be expressed as
Figure BDA0003997658590000024
wherein ,hH Q (s)h and sH Q (h) s represents the average sidelobe level, h H W (1) h represents the interference level after the mismatch filtering process,
Figure BDA0003997658590000025
J k representing a shift matrix with the expression +.>
Figure BDA0003997658590000026
Delta is the unit dirac function;
average sidelobe level ASL and h H s=1 can be expressed as h respectively H Q (s)h and sH Q (h) s, the ASL-based reception mismatch filter can be expressed as:
Figure BDA0003997658590000031
wherein ,
Figure BDA0003997658590000032
signal-to-interference Ratio (SIR);
when h H When s is constant, kappa h H Q (s)h and hH W (1) The maximum of both h may be used to determine the dynamic range of the receive mismatch filter.
The above-mentioned construction process of the joint optimization model of the transmitting waveform and the receiving filter based on the JTRD algorithm in S2 is as follows:
to obtain a larger receiver dynamic range, it is desirable to minimize the average sidelobe level kh H Q (s) h and mismatch filter interference levelh H W (1) And h, enabling the interference level processed by the mismatch filter to be equal to the side lobe level as far as possible, and simultaneously designing the transmitting signal and the mismatch filter to maximally promote the receiving degree of freedom.
JTRD algorithm minimizes the average sidelobe level kh of the mismatch filtered signal H Q (s) h is used as an objective function, and the interference level h of a mismatch filter under a certain signal-to-interference ratio kappa is used H W (1) h. Maximizing the mismatched filtering output of the target signal as a constraint condition, and constructing an optimization model in the following form:
Figure BDA0003997658590000033
s.t.h H s＝1
h H W (1) h＝c (κ)
|s n |＝1,n＝1,2,...,N
wherein ,c(κ) The interference level defined as the mismatch filtering output is related to the preset signal-to-interference ratio kappa; h is a H The s=1 constraint can maximize the mismatch filtered output of the target signal, h H W (1) h suppresses the interference level to a given c (κ) Range at the same time of |s n I=1, n=1, 2.
The above-mentioned S3 combined optimization algorithm of the transmit waveform and the receive filter uses an alternate iterative direction optimization method to decompose the optimization model of the original problem into two sub-problems for alternate iterative optimization, where the two sub-problems are respectively: optimization sub-problem of optimizing filter coefficients when fixing transmit waveforms
Figure BDA0003997658590000034
And sub-problem of optimizing the transmit signal when fixing the mismatch filter coefficients +.>
Figure BDA0003997658590000035
The optimization sub-problem when optimizing the filter coefficients in the fixed transmit waveform is described as
Figure BDA0003997658590000036
Figure BDA0003997658590000041
s.t.s H h＝1
h H W (1) h＝c (κ)
Figure BDA00039976585900000427
Is a convex optimization problem, because the objective function and the constraint term are both convex problems, the eigenvalue decomposition of the interference covariance matrix can be carried out to obtain +.>
Figure BDA0003997658590000043
wherein ,V(1) Is a feature vector matrix;
order the
Figure BDA0003997658590000044
The optimization problem can be rewritten->
Figure BDA0003997658590000045
Described as optimization problem->
Figure BDA0003997658590000046
Figure BDA0003997658590000047
Figure BDA0003997658590000048
v H v＝c (κ)
wherein ,
Figure BDA0003997658590000049
problem pairing using Lagrangian dual method
Figure BDA00039976585900000428
Solving the problem->
Figure BDA00039976585900000411
Can be expressed as +.>
Figure BDA00039976585900000412
Wherein a and b correspond to the problems +.>
Figure BDA00039976585900000413
Real and complex variables in the constraint, +.>
Figure BDA00039976585900000414
Equivalent to
Figure BDA00039976585900000415
For a given parameter a and b, one can obtain
Figure BDA00039976585900000416
Minimum solution, denoted->
Figure BDA00039976585900000417
The method is equivalent to solving unconstrained minimisation +.>
Figure BDA00039976585900000418
Lagrangian equation by letting +.>
Figure BDA00039976585900000419
Gradient equal to 0, i.e
Figure BDA00039976585900000420
I.e. by letting +.>
Figure BDA00039976585900000421
Gradient equal to 0, can be obtained +.>
Figure BDA00039976585900000422
Minimum solution, denoted->
Figure BDA00039976585900000423
Problem(s)
Figure BDA00039976585900000424
The solving mode of (2) is as follows:
problem pairing using the dual method
Figure BDA00039976585900000429
Solving, the Lagrangian dual equation g (a, b) is defined as the following optimization equation problem
Figure BDA00039976585900000426
The optimization (Karush-Kuhu-Tucker, KKT) condition of g (a, b) can be expressed as
Figure BDA0003997658590000051
The dual problem is defined as the problem of maximizing g (a, b) or minimizing-g (a, b);
in order to obtain a maximum g (a, b) relative to b, a g (a, b) gradient equal to 0 can be obtained
Figure BDA0003997658590000052
Thus, +.>
Figure BDA0003997658590000053
Can be carried into g (a, b)
Figure BDA0003997658590000054
The coefficient of the mismatch filter h can be calculated by optimizing the parameters a and b;
the solution of parameter a may be obtained by solving a maximized unconstrained problem ζ (a) using Newton's method or a linear search strategy, and the Lagrangian multiplier a may be based on a given parameter
Figure BDA0003997658590000055
Determining the corresponding range interval as +.>
Figure BDA0003997658590000056
or
Figure BDA0003997658590000057
wherein
Figure BDA0003997658590000058
Has characteristic decomposition->
Figure BDA0003997658590000059
Σ is a diagonal matrix, e= [ E ] 1 e 2 …e M ]Is a symmetric matrix, M is a matrix +.>
Figure BDA00039976585900000510
Rank of (c);
maximizing ζ (a) given the transmitted signal sequence s gives the value of a, while the value of b can also be obtained by solving, in which case obtaining optimal parameter values a and b brings the Lagrangian dual function to an optimal value, equivalent to the problem
Figure BDA00039976585900000511
The optimal value is reached, so that the coefficient of the mismatch filter h can be calculated by optimizing the parameters a and b.
For the fixed mismatch filter coefficients, the problem of optimizing the signal from whom
Figure BDA00039976585900000512
Since it is a non-convex problem, it is difficult to solve, so the re-optimization problem is->
Figure BDA00039976585900000513
For the question->
Figure BDA00039976585900000514
The sub-problem of optimizing the transmit signal while fixing the mismatched filter coefficients is described as
Figure BDA00039976585900000515
Figure BDA00039976585900000516
s.t.h H s＝1
|s n |＝1,n＝1,2,…,N
In the optimization problem
Figure BDA00039976585900000522
Constant modulus constraint, re-write optimization problem->
Figure BDA00039976585900000518
Is->
Figure BDA00039976585900000519
Figure BDA00039976585900000520
s.t.h H s＝1
Figure BDA00039976585900000521
Solution optimization by Lagrangian dual methodProblem(s)
Figure BDA0003997658590000061
The Lagrangian function equation for a problem can be expressed as
Figure BDA0003997658590000062
Wherein c and { d } n Respectively expressed as }
Figure BDA0003997658590000063
The corresponding constraint in the problem is a dual variable, d= [ d ] 1 d 2 ...d N ] T ；
At the same time, the method comprises the steps of,
Figure BDA0003997658590000064
is four times equation, and matrix Q (h) +Diag (d) is a positive definite matrix, the standing point of the Lagrangian function is satisfied +.>
Figure BDA0003997658590000065
So that the following relation s=cq exists between the transmit signal and the mismatch filter (h) +Diag(d)] -1 h。
Preferably, in order to solve the problem
Figure BDA0003997658590000066
Its lagrangian dual function is shown below,
h(c,{d n })＝-c 2 h H [Q (h) +Diag(d)] -1 h+c+c * -1 T d
the purpose is to find the optimal dual variables c and d n The dual function h (c, { d) n }) reaches a maximum value, and thus, the maximization of h (c, { d) n }), in which case the dual variable c=1/h H [Q (h) +Diag(d)] -1 h, the maximized dual optimization problem corresponding to the dual variable d is written as
Figure BDA0003997658590000067
According to given parameters
Figure BDA0003997658590000068
The lagrangian multiplier d should be located +.>
Figure BDA0003997658590000069
Or->
Figure BDA00039976585900000610
Between them;
d and c can be determined by maximizing ζ (d), and the optimized transmit signal s can be calculated by optimizing c, d, and h.
The initial content of the above-mentioned transmit waveform and receive filter joint optimization algorithm includes:
setting an iteration flag k=0, initializing a transmission sequence s (0) Let h be using a random coding sequence (0) ＝s (0) and v(0) ＝1。
In an ASL-based transmitting signal and receiving filter joint design algorithm, the optimizing step optimizes the transmitting signal and the mismatched filter coefficient by using an alternate iterative optimization mode;
the alternating optimizing step includes:
first optimizing a mismatch filter
Figure BDA00039976585900000611
By->
Figure BDA00039976585900000612
Calculation of v (k) At the same time calculate Lagrangian multiplier a (k) Fix s (k) Calculate h (k+1) Alternate optimization of the transmit signal +.>
Figure BDA00039976585900000613
By c=1/h H [Q (h) +Diag(d)] -1 h can obtain c (k) Fix h (k) Calculate s (k+1) 。
The above-described alternately optimized stop conditions are:
judging given iteration stop condition s (k+1) -s (k) ||+||h (k+1) -h (k) ||＜∈ 1 Whether or not to meet, where E 1 For the predefined convergence range, if not, repeating the alternative optimization step, and if the iteration stop condition is satisfied, outputting the optimized emission waveform s (k+1) And the optimized adaptive filter coefficient h (k+1) . Namely, in the ASL-based transmitting signal and receiving filter joint design algorithm, the stopping step uses the step length iteration norm as a stopping condition, and when the transmitting signal iteration step length norm and the mismatch filter iteration step length norm are smaller than a set value epsilon 1 And when the algorithm stops optimizing iteration, outputting the transmitting signal parameter and the mismatch filter parameter at the moment.
The invention has the following beneficial effects:
compared with a typical joint optimization algorithm of a transmitting signal and a receiving filter, the method disclosed by the invention has the advantages that the optimization problem is included in the dynamic range of the receiver, and the side lobe level and the interference level after pulse compression are balanced under the premise of simultaneously considering the minimized target scattering coefficient root mean square error (Mean Square Error, MSE) and the dynamic range of the receiver. Meanwhile, for the calculation difficulty brought by the non-convex nature of each optimization sub-problem, a conversion form of the optimization sub-problem is provided to reduce the calculation complexity, the minimum average sidelobe level (Average Sidelobe Level, ASL) is taken as an objective function, the interference level range is restrained, the output of a target signal mismatch filter is maximized as a constraint condition, and for the transmitted signal under the main lobe interference suppression, a transmitting waveform and receiving filter combined optimization algorithm (Joint Transmit Signal and Receiving Filter Design, JTRD) based on the average sidelobe level (Average Sidelobe Level, ASL) is provided, and the JTRD optimization algorithm can simultaneously restrain the interference and the received signal sidelobe level, and improve the dynamic range of the receiver, so that the method is very important for multi-target detection and is particularly suitable for weak target detection under the main lobe interference suppression condition. Compared with a cognitive receiving filter and waveform design (Cognitive Receiver and Waveform, CREW) algorithm, the JTRD-ASL optimization algorithm improves the dynamic range after the combined optimization of the transmitting signal and the receiving filter by 22dB and 12dB respectively, and obtains the optimized dynamic range under different input Interference Signal Ratios (ISR).
Drawings
FIG. 1 is a schematic diagram of an ASL-based receive mismatch filter output dynamic range in an embodiment;
FIG. 2 is a diagram of Frank sequence mismatch filtering output in an embodiment;
FIG. 3 is a CREW sequence mismatch filtered output graph in an embodiment;
FIG. 4 is a graph of the output of a JTRD-ASL algorithm optimizing transmit signal and receive filter mismatch filtering in an embodiment;
FIG. 5 is a graph showing convergence of JTRD-ASL algorithm in an embodiment;
FIG. 6 is a plot of mismatch filtered outputs of an un-optimized transmit signal and an interfering signal at different ISRs in an embodiment;
FIG. 7 is a graph showing the mismatch filtered output of the optimized transmit and interference signals as a function of ISR in an embodiment;
FIG. 8 is a Frank sequence mismatch filtered output map for a multi-objective scenario in an embodiment;
FIG. 9 is a graph of CREW sequence mismatch filtering output for a multi-objective scenario in an embodiment;
FIG. 10 is a graph of the JTRD-ASL optimized mismatch filtered output for a multi-objective scenario in an embodiment;
FIG. 11 is a flow chart of the method of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
Although the steps of the present invention are arranged by reference numerals, the order of the steps is not limited, and the relative order of the steps may be adjusted unless the order of the steps is explicitly stated or the execution of a step requires other steps as a basis. It is to be understood that the term "and/or" as used herein relates to and encompasses any and all possible combinations of one or more of the associated listed items.
As shown in fig. 11, a method for suppressing interference and optimizing the joint design of a transmit waveform and a receive filter includes:
s1: establishing a transmitting signal sequence model, a receiving signal sequence model and an ASL-based receiving mismatch filter model; the method comprises the steps of constructing a discrete point target signal superposition suppression interference receiving signal model, and constructing a mismatch filter model based on minimum mean square error (ASL) characteristics;
s2: aiming at the model established in the step S1, constructing a transmitting waveform and receiving filter joint optimization model considering the dynamic range of a receiver;
s3: and solving a joint optimization model by adopting a joint optimization algorithm of the transmitting waveform and the receiving filter to obtain an optimal solution of the transmitting signal and the mismatched filter parameters so as to guide the design of the transmitting signal sequence and the receiving filter.
This step decomposes into two sub-problems of transmit signal design and receive filter design using an alternating direction method based on a mismatch filter model based on minimum mean square error characteristics of the Average Sidelobe Level (ASL). By taking Average Sidelobe Level (ASL) reduction as an evaluation index, a JTRD optimization method based on ASL criteria and Lagrangian dual method is provided aiming at two sub-problems of transmitting signal design and receiving filter design. And solving the transmission optimized waveform and the mismatch optimized filter by a transmission waveform and reception filter joint waveform design (JTRD) optimization method to obtain an optimal solution of the parameters of the transmission signal and the mismatch filter.
In the embodiment, in step S1, a mismatch filter model of the discrete point target signal superposition suppression interference receiving signal model and the minimum mean square error characteristic based on ASL is constructed as follows:
the transmitted sequence is expressed as s= [ s ] 1 ,s 2 ,…,s N ] T I.e. the transmitted signal is in the form of a phase-keyed signal
Assuming that the received baseband signal contains a point target signal and a suppressed interference signal, the receiver acceptance signal is modeled as r=sx+w, where,
Figure BDA0003997658590000091
wherein, the S matrix stores the transmitted signal models at different distances, x k The scattering coefficients representing the different distance elements, w, are defined as the interference independent of the target signal.
Let w and { x } k And are independent of each other. If the electromagnetic scattering amplitude of a point target is x 0 Then the scattering power of the target at the point is E [ |x 0 | 2 ]＝α 2 The interference can be characterized by an interference covariance matrix W (1) Represented as
Figure BDA0003997658590000092
wherein ,/>
Figure BDA0003997658590000093
Defined as the average power of the interference, W (1) Is a diagonal element in the interference covariance matrix.
At a desired distance unit x 0 A mismatch filter with minimum mean square error is adopted, and the mismatch filter h satisfies h for maximizing filtering output H s=1, at distance x 0 The mean square error MSE at this point can be modeled as
Figure BDA0003997658590000094
wherein ,hH Q (s)h and sH Q (h) s represents the average sidelobe level, h H W (1) h represents the interference level after the mismatch filtering process,
Figure BDA0003997658590000095
Figure BDA0003997658590000096
/>
wherein ,Jk Representing the shift matrix to satisfy
Figure BDA0003997658590000097
Taking into account h H Q (s)h and sH Q (h) s represents the average sidelobe level ASL and the maximized filter output constraint h, respectively H s=1, the ASL-based reception mismatch filter can be defined as
Figure BDA0003997658590000098
wherein ,
Figure BDA0003997658590000099
is Signal-to-interference Ratio (SIR). When h H When s is constant, kappa h H Q (s)h and hH W (1) The maximum of both h can be used to determine the dynamic range of the receive mismatch filter, and fig. 1 presents a schematic diagram of the output dynamic range of the ASL-based receive mismatch filter.
In a more specific implementation, in order to minimize the average sidelobe level kh H Q (s) h and mismatch filter interference level h H W (1) And h, enabling the interference level processed by the mismatch filter to be equal to the side lobe level as far as possible, and simultaneously designing the transmitting signal and the mismatch filter to maximally promote the receiving degree of freedom. The optimization problem can be written in the following compact form
Figure BDA0003997658590000101
s.t.h H s＝1
h H W (1) h＝c (κ)
|s n |＝1,n＝1,2,...,N
wherein ,c(κ) The interference level, defined as the mismatch filtered output, is related to a predetermined signal-to-interference ratio k. Problem(s)
Figure BDA0003997658590000102
Is intended to minimize the mismatch filtered signal sidelobe levels. And given h H The s=1 constraint can maximize the mismatch filtered output of the target signal, h H W (1) h suppresses the interference level to a given c (κ) Range at the same time of |s n I=1, n=1, 2.
In the embodiment, the decomposition and optimization problem using the alternate direction method in step S2 is two sub-problem processes of transmit signal design and receive filter design as follows:
optimizing the mismatched filter coefficients when fixing the transmitted signal according to the concept of the alternating direction method can result in sub-problems
Figure BDA0003997658590000103
Optimizing the transmitted signal while fixing the mismatched filter coefficients gives the sub-problem +.>
Figure BDA0003997658590000104
Figure BDA0003997658590000105
s.t.s H h＝1 s.t.h H s＝1
h H W (1) h＝c (κ) |s n |＝1,n＝1,2,...,N
In an embodiment, the problem of optimizing the mismatched filter coefficients for a fixed transmit signal
Figure BDA0003997658590000106
To reduce the operation complexity, eigenvalue decomposition of the interference covariance matrix can be obtained +.>
Figure BDA0003997658590000107
wherein ,V(1) Is a feature vector matrix;
order the
Figure BDA0003997658590000108
Simultaneous overwriting problem->
Figure BDA0003997658590000109
Is->
Figure BDA00039976585900001010
Figure BDA00039976585900001011
Figure BDA00039976585900001012
v H v＝c (κ)
wherein ,
Figure BDA00039976585900001013
in a more specific implementation, in step S3, with reduced Average Sidelobe Level (ASL) as an evaluation index, a JTRD optimization method based on an ASL criterion and a lagrangian dual method is proposed for two sub-problems of transmit signal design and receive filter design, as follows:
problem pairing using Lagrangian dual method
Figure BDA0003997658590000111
Solving the problem
Figure BDA0003997658590000112
The Lagrangian equation form may be expressed as
Figure BDA0003997658590000113
Wherein a and b correspond to problems respectively
Figure BDA0003997658590000114
Real and complex variables in the constraint.
Figure BDA0003997658590000115
Equivalent to
Figure BDA0003997658590000116
Thus, for a given parameter a and b, one can obtain
Figure BDA0003997658590000117
Minimum solution, denoted->
Figure BDA0003997658590000118
In an embodiment, a Lagrangian function may be written
Figure BDA0003997658590000119
The dual function g (a, b) of (a) is defined as follows
Figure BDA00039976585900001110
The first order optimality condition (Karush-Kuhu-Tucker, KKT) of the dual function g (a, b) is
Figure BDA00039976585900001111
The dual problem is thus defined as the problem of maximizing g (a, b), parameter a being set so as to obtain the maximized g (a, b) of parameter b, the gradient of g (a, b) over parameter b being equal to0 can be obtained
Figure BDA00039976585900001112
Thereby can be obtained
Figure BDA00039976585900001113
So when the parameter b and the parameter a satisfy the relation of the above formula, the dual equation g (a, b) can be written as a formula containing only the parameter a
Figure BDA00039976585900001114
In an embodiment, where a back tracking linear search method is used to find the maximum parameter a, a method based on Armijo Goldstein condition search may be used to search for the maximum in a given direction. The algorithm design starts with a relatively large step size estimate that moves in the search direction and iteratively reduces the step size (i.e., "back-tracking") until the objective function value calculated from the gradient value of the objective function becomes smaller.
In an embodiment, the lagrangian multiplier a may be solved by the following method. Order the
Figure BDA0003997658590000121
Wherein Σ is a diagonal matrix, e= [ E ] 1 e 2 …e M ]Is a symmetrical matrix lambda i and ei Respectively is a matrix->
Figure BDA0003997658590000122
Is described, and feature vectors. M is matrix->
Figure BDA0003997658590000123
Rank of (2) may give lambda 1 ≥λ 2 ≥…≥λ M ，/>
Figure BDA0003997658590000124
Order the
Figure BDA0003997658590000125
Can obtain
Figure BDA0003997658590000126
I.e. the
Figure BDA0003997658590000127
wherein ,
Figure BDA0003997658590000128
thus, the Lagrangian multiplier a is a positive integer and is not equal to 0, with the following relationship
Figure BDA0003997658590000129
If there is
Figure BDA00039976585900001210
Can obtain
Figure BDA00039976585900001211
If it is
Figure BDA00039976585900001212
There is->
Figure BDA00039976585900001213
Because of
Figure BDA00039976585900001214
And->
Figure BDA00039976585900001215
Thus->
Figure BDA00039976585900001216
When it is available
Figure BDA00039976585900001217
If it is
Figure BDA00039976585900001218
Can obtain
Figure BDA0003997658590000131
If it is
Figure BDA0003997658590000132
There is->
Figure BDA0003997658590000133
Because of
Figure BDA0003997658590000134
And->
Figure BDA0003997658590000135
Thus->
Figure BDA0003997658590000136
Can obtain
Figure BDA0003997658590000137
/>
The lagrangian multiplier a can be based on given parameters
Figure BDA0003997658590000138
Determining the corresponding range interval as +.>
Figure BDA0003997658590000139
Or->
Figure BDA00039976585900001310
wherein
Figure BDA00039976585900001311
Has characteristic decomposition->
Figure BDA00039976585900001312
Σ is a diagonal matrix, e= [ E ] 1 e 2 …e M ]Is a symmetric matrix, M is a matrix +.>
Figure BDA00039976585900001313
Rank of (c);
in an embodiment, maximizing ζ (a) given the transmitted signal s yields the value of parameter a, while also yielding parameter b based on the relationship between parameter b and parameter a, by optimizing the dual problem g (a, b), the Lagrange problem
Figure BDA00039976585900001314
And the optimal solution of the filter h is obtained, so that the coefficient of the optimized mismatch filter h is obtained.
In an embodiment, the problem of optimizing the transmitted signal when the mismatched filter coefficients are fixed
Figure BDA00039976585900001315
In order to accelerate the solving of the problem, the problem is rewritten +.>
Figure BDA00039976585900001316
For the question->
Figure BDA00039976585900001317
Figure BDA00039976585900001318
s.t.h H s＝1
Figure BDA00039976585900001319
In an embodiment, the problem is solved using the Lagrangian dual method
Figure BDA00039976585900001320
Solving the problem->
Figure BDA00039976585900001326
The Lagrangian equation form may be expressed as
Figure BDA00039976585900001322
Wherein c and { d } n Respectively expressed as }
Figure BDA00039976585900001323
The corresponding constraint in the problem is a dual variable, d= [ d ] 1 d 2 ...d N ] T
Figure BDA00039976585900001324
Is a fourth order polynomial due to matrix Q (h) +Diag (d) is a positive definite matrix, so +.>
Figure BDA00039976585900001325
Is bounded. The transmitted signal sequence s is graded to be equal to 0 to obtain
Figure BDA0003997658590000141
s＝c[Q (h) +Diag(d)] -1 h
The dual function h (c, { d n }) is defined as an optimized result that maximizes the following problem
h(c,{d n })＝-c 2 h H [Q (h) +Diag(d)] -1 h+c+c * -1 T d
In an embodiment, the dual variable c and the dual variable { d } n The relation of } is
c＝1/h H [Q (h) +Diag(d)] -1 h
So the dual problem h (c, { d) n }) can be written as problem ζ (d)
Figure BDA0003997658590000142
In an embodiment, the lagrangian multiplier d may be solved by the following method. Order the
Figure BDA0003997658590000143
wherein ,Σh As a diagonal matrix, f= [ F 1 f 2 …f M ]Is a symmetric matrix, eta i and fi Respectively is a matrix Q (h) Is described, and feature vectors. M is a matrix Q (h) Rank of (1), may be given η 1 ≥η 2 ≥…≥η M . Let->
Figure BDA0003997658590000144
wherein ,
Figure BDA0003997658590000145
recording device
Figure BDA0003997658590000146
Can obtain
Figure BDA0003997658590000147
and
Figure BDA0003997658590000151
Finally, the following relationship can be obtained
Figure BDA0003997658590000152
Wherein there are
Figure BDA0003997658590000153
If it is
Figure BDA0003997658590000154
|d min I > 0, then it should be satisfied
Figure BDA0003997658590000155
If it is
Figure BDA0003997658590000156
There is->
Figure BDA0003997658590000157
Thus, when->
Figure BDA0003997658590000158
Corresponding |d n I should satisfy +.>
Figure BDA0003997658590000159
Can obtain
Figure BDA00039976585900001510
If it is
Figure BDA00039976585900001511
|d min I > 0, then it should be satisfied
Figure BDA00039976585900001512
If it is
Figure BDA00039976585900001513
There is->
Figure BDA00039976585900001514
Thus, when->
Figure BDA00039976585900001515
Corresponding |d n I should satisfy +.>
Figure BDA00039976585900001516
Can obtain
Figure BDA00039976585900001517
So according to given parameters
Figure BDA00039976585900001518
The lagrangian multiplier d should be located +.>
Figure BDA00039976585900001519
Or->
Figure BDA00039976585900001520
Between, wherein->
Figure BDA00039976585900001521
In an embodiment, maximizing ζ (d) given a mismatch filter coefficient h yields a value of a dual variable d, while based on a dual variable c and a dual variable { d } n The relation of the two can obtain a dual variable c by optimizing the dual problem h (c,{d n }) may beTo get Lagrangian problem
Figure BDA0003997658590000161
And thus an optimized transmit signal s.
In a more specific implementation, the process of solving the transmit optimized waveform and the mismatch optimized filter by the transmit waveform and receive filter joint waveform design (JTRD) optimization method in step S4 to obtain the optimal solution of the transmit signal and the mismatch filter parameters is divided into an initial step, an iterative step and a stop step.
An initial step of an ASL-based transmit signal and receive filter joint design algorithm sets an iteration count index k=0 while initializing the transmit signal to s using a random phase encoded signal (0) Let the receiving filter coefficient h (0) ＝s (0) and v(0) =1. Simultaneously, the signal-to-interference ratio kappa is set, and the interference level c of mismatched filtering output is set (κ) . Initializing Lagrangian multiplier a (0) ，d (0) 。
The iterative steps of the ASL-based transmitting signal and receiving filter joint design algorithm are as follows: optimizing mismatch filters
Figure BDA0003997658590000162
Lagrangian multiplier a (k) According to the relation
Figure BDA0003997658590000163
Calculation b (k) By means of
Figure BDA0003997658590000164
Calculation of v (k) Fix the transmitted signal s (k) Calculating a mismatch filter coefficient h (k+1) 。
Thereafter optimizing the transmitted signal
Figure BDA0003997658590000165
Opposite Lagrangian multiplier d (k) According to the relation
c＝1/h H [Q (h) +Diag(d)] -1 h
Calculation c (k) Fix the mismatch filter coefficient h (k) Calculating the transmitted signal s (k+1) 。
The stop step of the ASL-based transmitting signal and receiving filter joint design algorithm is as follows:
judging whether the optimized coefficient meets the step length stopping condition, namely the step length s (k+1) -s (k) ||+||h (k+1) -h (k) ||＜∈ 1 Wherein, E1 is a preset stop step. When the iteration step norm meets the stop condition, stopping the iteration and simultaneously outputting the optimized transmission signal s (k+1) And optimized mismatch filter h (k+1) If the iteration stop condition is not satisfied, k=k+1, and the steps of the iteration step are repeated at the same time.
Simulation experiment:
in order to ensure the consistency of experimental results, noise frequency modulation interference in the suppression type interference is used, and the corresponding mathematical expression is
Figure BDA0003997658590000166
The instantaneous frequency f (t) of the noise-modulated disturbance w (t) is f (t) =f 0 +k fm n(t)。
Assuming n (t) is band-limited white noise, the interference spectrum can be expressed by the following equation
Figure BDA0003997658590000171
Let the frequency modulation factor be defined as m f ＝k fm δ/B n > 1, when m f When > 1, the spectral shape approximates a Gaussian distribution, and the interference bandwidth can be written as
Figure BDA0003997658590000172
Assuming a spectrum determination, the cross-correlation coefficient and covariance matrix are fixed.
Let the carrier frequency be f 0 =9.4 GHz, the transmit sequence contains n=100 rectangular sub-pulses, perThe time width of the sub-pulse is t p =100 ns. For noisy fm interferers, the interferer bandwidth is set to 2.5MHz.
Using average sidelobe levels, which may be defined as asl=10log, to scale the transmit signal and interference signal joint optimization receive filter output results 10 h H κQ (s) h (dB). And meanwhile, comparing the mismatch filtering output of the optimized transmitting signal with the mismatch filtering output of the Frank sequence and the CREW sequence.
The autocorrelation function of the Frank sequence as shown in fig. 2 has lower side lobe levels, and the ASL response results in about-37 dB. When the Interference-to-Signal Ratio (ISR) is 10dB, the output result of the Interference Signal after the mismatch filter processing is about-10 dB. This greatly limits the dynamic range of the receive filter output.
Fig. 3 shows the output of a mismatched filter after the joint optimization of the transmit waveform and the receive filter by a cognitive receive filter and waveform design (Cognitive Receiver and Waveform, brew) algorithm. ASL of the mismatch filter output is suppressed to around-34 dB. However, the interfering signal output by the mismatch filter is suppressed to-18 dB.
Fig. 4 shows the result of a mismatched filter output for joint optimization of transmit waveforms and receive filters using the JTRD-ASL optimization algorithm. The mismatch filter output ASL and the interfering signal are suppressed at-30 dB simultaneously. The dynamic range of the combined optimization of the transmit signal and the receive filter is improved by 22dB and 12dB, respectively, in contrast to Frank code and brew sequences.
Fig. 5 shows an output level curve of the disturbance, with the ordinate representing the mismatch filter outputs ASL and is (k+1) -s (k) ||+||h (k+1) -h (k) The abscissa is the number of iterations. From the graph, the algorithm converges after about 8 iterations of optimization.
Fig. 6 shows the mismatch filtered output of the pre-optimized transmit signal and the interference signal along with the ISR change, and fig. 7 shows the mismatch filtered output of the post-optimized transmit signal and the interference signal along with the ISR change. Fig. 6 and 7 depict the output range of the mismatch filter, the transmitted signal and the interfering signal compared to the input ISR. The input ISR range is defined as 0 to 20dB, and the suppression range of the transmitted signal remains unchanged until the output of the mismatch filter is optimized, and the suppression range of the interfering signal decreases as the input ISR increases. However, for a mismatch filter output where the transmit signal and the receive filter are jointly optimized, the degree of suppression of the transmit signal and the interference signal is unchanged and an optimized dynamic range can be obtained at different inputs ISR.
Meanwhile, the simulation laboratory is performed on point targets, and the method provided by the invention is also applicable to multi-target scenes. The multi-objective simulation parameters are as follows, assuming ISR equal to 10dB, the three objectives are divided into units at-40, 0, 20 distances, corresponding amplitudes of-10 dB,0dB and 12dB, respectively.
Fig. 8 shows the result of the Frank encoded mismatch filter output in a multi-object scenario.
Fig. 9 shows the output result of a mismatch filter optimized by the brew algorithm in a multi-target scenario, where two weak targets are submerged in the side lobes of the strong signal and interference, and cannot be detected.
Fig. 10 shows that the output result of the mismatch filter optimized by the JTRD-ASL algorithm in the multi-target scene is marked by circles after the transmission signal and the mismatch filter are optimized, so that the two weak targets can be smoothly detected by the radar receiver, and the signal sidelobes and the interference are obviously reduced after the optimization. Weak targets are effectively detected.
It will be evident to those skilled in the art that the invention is not limited to the details of the foregoing illustrative embodiments, and that the present invention may be embodied in other specific forms without departing from the spirit or essential characteristics thereof. The present embodiments are, therefore, to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. Any reference sign in a claim should not be construed as limiting the claim concerned.
Furthermore, it should be understood that although the present disclosure describes embodiments, not every embodiment is provided with a separate embodiment, and that this description is provided for clarity only, and that the disclosure is not limited to the embodiments described in detail below, and that the embodiments described in the examples may be combined as appropriate to form other embodiments that will be apparent to those skilled in the art.

Claims (10)

1. The suppression interference suppression method for the joint design of the transmitting waveform and the receiving filter is characterized by comprising the following steps of:
s1: establishing a transmitting signal sequence model, a receiving signal sequence model and an ASL-based receiving mismatch filter model;
s2: aiming at the model established in the step S1, constructing a transmitting waveform and receiving filter joint optimization model considering the dynamic range of a receiver;
s3: and solving a joint optimization model by adopting a joint optimization algorithm of the transmitting waveform and the receiving filter to obtain an optimal solution of the transmitting signal and the mismatched filter parameters so as to guide the design of the transmitting signal sequence and the receiving filter.
2. The method for suppressing interference according to claim 1, wherein the process of establishing the model of the transmission signal sequence and the reception signal sequence in S1 is as follows:
the transmitted signal sequence is expressed as s= [ s ] 1 ,s 2 ,...,s N ] T ；
The received baseband signal contains a point target signal and a suppressed interference signal, which satisfies the following equation
r＝Sx+w
wherein ,
Figure QLYQS_1
representing the transmitted sequence at different distance units, x= [ x ] 0 ,x 1 ,…,x N-1 ,x -(N-1) ,…,x -1 ] T ，x k Scattering coefficients representing different distance units, w being defined as the distance to the targetInterference of signals independent of each other, assuming w and { x } k -independent of each other;
the electromagnetic scattering amplitude of the point target is x 0 Average clutter power E [ |x 0 | 2 ]＝α 2 ；
The feature of suppressing interference uses an interference covariance matrix w (1) Represented as
Figure QLYQS_2
wherein ,/>
Figure QLYQS_3
Defined as the average power of the interference, w (1) Is a diagonal element in the interference covariance matrix.
3. The method for suppressing interference according to claim 1, wherein the establishing process of the ASL-based receiving mismatch filter model in S1 is as follows:
the receiving filter uses a mismatch filter with a minimum mean square error MSE, at a desired distance element x 0 Where the mismatch filter h satisfies h H s=1, then at distance x 0 The mean square error MSE at this point is expressed as
Figure QLYQS_4
wherein ,hH Q (s)h and sH Q (h) s represents the average sidelobe level, h H W (1) h represents the interference level after the mismatch filtering process,
Figure QLYQS_5
J k representing a shift matrix with the expression +.>
Figure QLYQS_6
Delta is the unit dirac function;
average sidelobe level ASL and h H s=1 are denoted as h respectively H Q (s)h and sH Q (h) s, the ASL based receive mismatch filter is expressed as:
Figure QLYQS_7
wherein ,
Figure QLYQS_8
is the signal-to-interference ratio;
when h H When s is constant, kappa h H Q (s)h and hH W (1) The maximum of both h is used to determine the dynamic range of the receive mismatch filter.
4. The method for suppressing interference by joint design of a transmit waveform and a receive filter according to claim 1, wherein the constructing process of the joint optimization model of the transmit waveform and the receive filter in S2 is as follows:
to obtain a larger dynamic range of the receiver, the average sidelobe level kh of the mismatch filtered signal is minimized H Q (s) h is used as an objective function, and the interference level h of a mismatch filter under the signal-to-interference ratio kappa is used H W (1) h. Maximizing the mismatched filtering output of the target signal as a constraint condition, and constructing an optimization model in the following form:
Figure QLYQS_9
s.t.h H s＝1
h H W (1) h＝c (κ)
|s n |＝1,n＝1,2,...,N
wherein ,c(κ) The interference level defined as the mismatch filtering output is related to the preset signal-to-interference ratio kappa; h is a H s=1 constraint maximizes the mismatch filtered output of the target signal, h H W (1) h suppressing the interference level to a given levelC of (2) (κ) Range at the same time of |s n I=1, n=1, 2.
5. The method for suppressing interference by joint design of a transmit waveform and a receive filter according to claim 1, wherein S3 the transmit waveform and receive filter joint optimization algorithm uses an alternative optimization method to decompose an optimization model into two sub-problems for alternative iterative optimization, the two sub-problems are respectively: an optimization sub-problem when optimizing the filter coefficients when fixing the transmit waveform and a sub-problem when optimizing the transmit signal when fixing the mismatched filter coefficients.
6. The method for suppressing interference by joint design of transmit waveform and receive filter as set forth in claim 5, wherein said optimization sub-problem in optimizing filter coefficients while fixing transmit waveform is described as
Figure QLYQS_10
Figure QLYQS_11
s.t.s H h＝1
h H W (1) h＝c (κ)
Figure QLYQS_12
Is a convex optimization problem, and the eigenvalue decomposition is carried out on the interference covariance matrix to obtain +.>
Figure QLYQS_13
wherein ,V(1) Is a feature vector matrix;
order the
Figure QLYQS_14
Rewriten optimization problem->
Figure QLYQS_15
Described as optimization problem->
Figure QLYQS_16
Figure QLYQS_17
Figure QLYQS_18
v H v＝c (κ)
wherein ,
Figure QLYQS_19
/>
problem pairing using Lagrangian dual method
Figure QLYQS_20
Solving the problem->
Figure QLYQS_21
Expressed in Lagrangian equation form as
Figure QLYQS_22
Wherein a and b correspond to the problems +.>
Figure QLYQS_23
Real and complex variables in the constraint, +.>
Figure QLYQS_24
Equivalent to
Figure QLYQS_25
For a given parameter a and b, we get
Figure QLYQS_27
Minimum solution, denoted->
Figure QLYQS_29
The method is equivalent to solving unconstrained minimisation +.>
Figure QLYQS_31
Lagrangian equation by letting +.>
Figure QLYQS_28
Gradient equal to 0, i.e.)>
Figure QLYQS_30
I.e. by letting +.>
Figure QLYQS_32
Gradient equal to 0, get->
Figure QLYQS_33
The least solution, expressed as
Figure QLYQS_26
Problem(s)
Figure QLYQS_34
The solving mode of (2) is as follows:
problem pairing using the dual method
Figure QLYQS_35
Solving, the Lagrangian dual equation g (a, b) is defined as the following optimization equation problem
Figure QLYQS_36
The optimization conditions of g (a, b) are expressed as
Figure QLYQS_37
The dual problem is defined as the problem of maximizing g (a, b) or minimizing-g (a, b);
in order to obtain a maximum g (a, b) relative to b, a g (a, b) gradient equal to 0 is obtained
Figure QLYQS_38
Thus, get +.>
Figure QLYQS_39
Can be carried into g (a, b)
Figure QLYQS_40
Calculating the coefficient of the mismatch filter h through optimizing the parameters a and b;
solving the parameter a is obtained by solving a maximized unconstrained problem ζ (a) using Newton's method or a linear search strategy, and the Lagrangian multiplier a is based on a given parameter
Figure QLYQS_41
Determining the corresponding range interval as +.>
Figure QLYQS_42
Or->
Figure QLYQS_43
wherein
Figure QLYQS_44
Has characteristic decomposition->
Figure QLYQS_45
Σ is a diagonal matrix, e= [ E ] 1 e 2 …e M ]Is a symmetric matrix, M is a matrix +.>
Figure QLYQS_46
Rank of (c);
maximizing ζ (a) given the transmitted signal sequence s yields a value of a, while b is also obtained by solving, where obtaining optimal parameter values a and b results in an optimal value of the Lagrangian dual function, equivalent to the problem
Figure QLYQS_47
The optimal value is reached, so the coefficient of the mismatch filter h can be calculated by optimizing the parameters a and b.
7. The method for suppressing interference in a joint design of a transmit waveform and a receive filter according to claim 5, wherein the sub-problem of optimizing the transmit signal while fixing the mismatched filter coefficients is described as
Figure QLYQS_48
Figure QLYQS_49
s.t.h H s＝1
|s n |＝1,n＝1,2,...,N
In the optimization problem
Figure QLYQS_50
Constant modulus constraint, re-write optimization problem->
Figure QLYQS_51
Is->
Figure QLYQS_52
Figure QLYQS_53
s.t.h H s＝1
Figure QLYQS_54
Solving the optimization problem by Lagrangian dual method
Figure QLYQS_55
Figure QLYQS_56
The Lagrangian function equation of the problem is expressed as
Figure QLYQS_57
Wherein c and { d } n Respectively expressed as }
Figure QLYQS_58
The corresponding constraint in the problem is a dual variable, d= [ d ] 1 d 2 …d N ] T ；
Maximizing the dual variable d the dual optimization problem is written as
Figure QLYQS_59
According to given parameters
Figure QLYQS_60
The lagrangian multiplier d should be located +.>
Figure QLYQS_61
Or->
Figure QLYQS_62
Between them;
d and c are determined by maximizing ζ (d), then the optimized transmit signal s is calculated from the optimized c, d and h.
8. The method for suppressing interference suppression in combination with a transmit waveform and a receive filter according to claim 5, wherein the initial content of the transmit waveform and receive filter combination optimization algorithm comprises:
setting an iteration flag k=0, initializing a transmission sequence s (0) Let h be using a random coding sequence (0) ＝s (0) and v(0) ＝1。
9. The method of suppressing interference for a transmit waveform and receive filter joint design of claim 5, wherein said alternately optimizing step comprises:
first optimizing a mismatch filter
Figure QLYQS_63
By->
Figure QLYQS_64
Calculation of v (k) At the same time calculate Lagrangian multiplier a (k) Fix s (k) Calculate h (k+1) Alternate optimization of the transmit signal +.>
Figure QLYQS_65
By c=1/h H [Q (h) +Diag(d)] -1 h gives c (k) Fix h (k) Calculate s (k+1) 。
10. The method for suppressing interference in combination with a transmit waveform and receive filter design of claim 5, wherein the alternate optimization stop condition is:
judging given iteration stop condition s (k+1) -s (k) ||+||h (k+1) -h (k) ||＜∈ 1 Whether or not to meet, where E 1 For the predefined convergence range, if not, repeating the alternative optimization step, and if the iteration stop condition is satisfied, outputting the optimized emission waveform s (k+1) And the optimized adaptive filter coefficient h (k+1) 。
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