CN116381612B - Cognitive radar waveform design method and device based on split quadratic programming - Google Patents
Cognitive radar waveform design method and device based on split quadratic programming Download PDFInfo
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Abstract
The application relates to a cognitive radar waveform design method and device based on fractional quadratic programming. The method comprises the following steps: calculating the signal-to-interference-and-noise ratio of a signal at a receiving end according to a pulse signal sequence sent in a pulse period of a single-base radar system; respectively constructing a first problem model of signal-to-interference-and-noise ratio under the constant modulus constraint of the pulse signal sequence and constructing a second problem model of signal-to-interference-and-noise ratio under the low PAR constraint of the pulse signal sequence; converting the non-convex quadratic programming problem into a quadratic programming problem through the quadratic programming, and obtaining a first constant modulus quadratic programming problem and a second quadratic programming problem; when the problem iteration solution is carried out, solving a quadratic programming problem model corresponding to the constraint condition according to the constraint condition met by the pulse signal sequence, calculating a current iteration step, and solving and outputting an optimal waveform through alternate iteration. The method improves the waveform design efficiency and simultaneously adapts to more hardware application scenes.
Description
Technical Field
The application relates to the technical field of cognitive radar waveform design, in particular to a cognitive radar waveform design method and device based on partial quadratic programming.
Background
The blur function (Ambiguity Function, AF) is an effective tool for waveform design and analysis that can control the range-doppler resolution of a radar system, while also being used to evaluate the interference immunity of waveforms. For achieving good resolution measurements of target range and doppler, the designed radar system is usually tack-like, i.e. with a single peak at the range-doppler cell of the target, but due to its equal volume characteristics, it is often difficult to design the waveforms described above, and thus prior studies have chosen methods of shaping by a fuzzy function to improve the target detection performance of the radar system.
At present, a great deal of research is focused on fuzzy function design matched with a transmitting filter and a receiving filter, and the mutual fuzzy function design research is less, and the mutual fuzzy function shaping method fully utilizes the freedom degree of radar receiving and transmitting joint processing, improves waveform performance and shortens convergence time of optimization problems. In addition, most researches define the constraint of a transmitting sequence as a single mode, but in practical application, strict constant mode requirements cannot be achieved, so that the efficiency in the waveform design process is low, the transmitting waveform is limited by hardware, and the application range is limited.
Disclosure of Invention
In view of the foregoing, it is desirable to provide a method and apparatus for designing a cognitive radar waveform based on a split quadratic programming, which can improve the degree of freedom and applicability of the waveform.
A cognitive radar waveform design method based on fractional quadratic programming, the method comprising:
and calculating the signal-to-interference-and-noise ratio of the signal at the receiving end according to the pulse signal sequence sent in the pulse period of the single-base radar system.
And respectively constructing a first problem model of the signal-to-interference-and-noise ratio under the constant modulus constraint of the pulse signal sequence and constructing a second problem model of the signal-to-interference-and-noise ratio under the low PAR constraint of the pulse signal sequence. The first problem model and the second problem model are both non-convex quadratic programming problems.
And converting the non-convex quadratic programming problem into a quadratic programming problem through the quadratic programming, and obtaining a first constant modulus quadratic programming problem and a second quadratic programming problem.
When the problem iteration solving is carried out, if the pulse signal sequence meets the constant modulus constraint, the first constant modulus quadratic programming problem is solved to calculate the current iteration step, if the pulse signal sequence meets the low PAR constraint, the second quadratic programming problem is solved to calculate the current iteration step, and the optimal waveform is solved and output through alternate iteration.
In one embodiment, the method further comprises: according to a pulse signal sequence sent in a pulse period of a single-base radar system, calculating the signal-to-interference-and-noise ratio of a signal at a receiving end by adopting a mutual blurring function:
；
；
wherein ,for code length +.>Pulse signal sequence,/-for (a)>For receiving the filter, +.>To interfere with the distribution of the doppler cells at different ranges, and (2)>Is noise energy>Representing the range bin and Doppler bin indices, respectively, +.>For the frequency of the current Doppler unit index, +.>For the shift matrix of the distance cell, superscript +.>Is conjugate transpose->Is Doppler direction vector,>is->Normalized Doppler frequency of individual scattering elements, +.>In the form of a diagonal matrix representation of the steering vector, +.>For receiving the square of the euclidean norm of the filter,/->For Doppler frequency->Corresponding to the diagonal matrix representation of the steering vector,is an intermediate variable.
In one embodiment, the method further comprises: by equally dividing the Doppler frequency interval intoAnd setting Doppler frequency of the pulse signal sequence, and generating a displacement matrix of the pulse signal sequence:
；
wherein ,for distance toNumber of intervals from unit>For the code length of the pulse signal sequence, +.>For the displacement matrix of the pulse signal sequence, +.>，/>Respectively, different distance units.
In one embodiment, the method further comprises: under the constant mode constraint of a pulse signal sequence, a first problem model of signal-to-interference-and-noise ratio is constructed by a pulse signal and receiving filter through a mutual blurring function shaping method:
；
wherein ,for signal-to-interference-and-noise ratio of pulse signal, +.>Is pulse signal sequence, +.>Is a receive filter.
In one embodiment, the method further comprises: when the PAR of the pulse signal is not larger than the preset peak-to-average power ratio, the pulse signal sequence is in low PAR constraint, and a second problem model of signal-to-interference-and-noise ratio is constructed:
；
wherein ,for a preset peak averagePower ratio->For signal-to-interference-and-noise ratio of pulse signal, +.>Is pulse signal sequence, +.>For receiving the filter, +.>Is the square of the 2 norms of the pulse signal sequence.
In one embodiment, the method further comprises: by constructing an objective function of the split quadratic programming:
；
；
；
wherein ,is pulse signal sequence, +.>For receiving the filter, +.>Is noise energy>In the form of a diagonal matrix representation of the steering vector, +.>Is an intermediate variable +.>Is the square of the euclidean norm of the receive filter.
Substituting the objective function into the non-convex quadratic score programming problem to convert the quadratic programming problem, and obtaining a first constant modulus quadratic programming problem:
；
wherein ,for pulse signal sequences, superscript +.>Is conjugate transpose->As an intermediate variable, the number of the variables,
and a second quadratic programming problem:
；
wherein ,for pulse signal sequences, superscript +.>Is conjugate transpose->For a preset peak-to-average power ratio, < >>Is the square of the 2 norms of the pulse signal sequence, < >>Is an intermediate variable.
In one embodiment, the method further comprises: substituting the objective function into the first problem modelObtaining problems：
；
The objective function is setIs satisfied with->Substitution question->Get questions->：
；
wherein ,is a super parameter.
By solving the problemsPerforming transformation to obtain quadratic programming problem->：
；
wherein ,to optimize the variables +.>For the purpose of +.>Is super-parameter (herba Cinchi Oleracei)>Is the identity matrix of the optimization variables.
Order theConverting the quadratic programming problem into a first constant modulus quadratic programming problem:
；
wherein ,，/>for optimizing the identity matrix of the variables, +.>For pulse signal sequences, superscript +.>Is conjugate transpose->Is greater than->A parameter of the maximum eigenvalue of (c).
In one embodiment, the method further comprises: when the problem iteration solution is carried out, if the pulse signal sequence meets the constant modulus constraint, a power-like iterative algorithm is adopted to generate a constant modulus iterative algorithm, and the current iterative step is calculated according to the constant modulus iterative solution first constant modulus quadratic programming problem. And if the pulse signal sequence meets the low PAR constraint, generating a low peak average power ratio iteration by adopting a nearest neighbor vector method, and solving a second quadratic programming problem in an iteration mode according to the low peak average power ratio to calculate the current iteration step. And outputting an optimal pulse signal sequence according to the current iteration step, outputting an optimal receiving filter after the optimal pulse signal sequence is processed by the receiving filter, and outputting an optimal waveform through alternately iterating the optimal pulse signal sequence and the optimal receiving filter.
In one embodiment, the method further comprises: updating outer layer iteration parameters according to the optimal waveform and the optimal receiving filter, and updating super parameters, optimal variables, objective functions and intermediate variables if the outer layer iteration parameters are not equal to preset iteration conditionsIntermediate variable +.>Otherwise, the update is terminated.
A cognitive radar waveform design device based on split quadratic programming, the device comprising:
and the signal-to-interference-and-noise ratio calculation module is used for calculating the signal-to-interference-and-noise ratio of the signal at the receiving end according to the pulse signal sequence sent in the pulse period of the single-base radar system.
The problem building module is used for building a first problem model of signal-to-interference-and-noise ratio under the constant modulus constraint of the pulse signal sequence and building a second problem model of the signal-to-interference-and-noise ratio under the low PAR constraint of the pulse signal sequence respectively. The first problem model and the second problem model are both non-convex quadratic programming problems.
And the problem conversion module is used for converting the non-convex quadratic programming problem into a quadratic programming problem through the quadratic programming, so as to obtain a first constant modulus quadratic programming problem and a second quadratic programming problem.
And the waveform design module is used for solving the first constant modulus quadratic programming problem to calculate the current iteration step when the pulse signal sequence meets the constant modulus constraint and solving the second quadratic programming problem to calculate the current iteration step when the pulse signal sequence meets the low PAR constraint when the pulse signal sequence meets the constant modulus constraint, and solving and outputting the optimal waveform through alternate iteration.
According to the cognitive radar waveform design method and device based on the partial quadratic programming, the signal-to-interference-plus-noise ratio of the signal at the receiving end is calculated according to the pulse signal sequence sent in the pulse period of the single-base radar system, and the non-convex quadratic partial programming problem model is respectively constructed under the constant modulus constraint and the low PAR constraint of the pulse signal sequence. And further, the signal-to-interference-and-noise ratio of a receiving end signal in the single-base radar system is calculated and optimized, corresponding problem models are respectively constructed under the constant modulus constraint and the low PAR constraint of the pulse signal sequence, and the non-convex quadratic programming problem is converted into the quadratic programming problem through the quadratic programming, so that the waveform design is more flexible and efficient by simplifying the problem models according to different radar scenes. In addition, the problem solving is performed in an alternate iteration mode, so that the optimal waveform can be obtained in a short time, the waveform design efficiency is improved, and meanwhile, more hardware application scenes are adapted.
Drawings
FIG. 1 is a flow chart of a cognitive radar waveform design method based on partial quadratic programming in one embodiment;
FIG. 2 is a flowchart illustrating steps for implementing a cognitive radar waveform design based on a split quadratic programming in one embodiment;
FIG. 3 is a disturbance energy profile in one embodiment;
FIG. 4 is a graph illustrating convergence of response values of an objective function according to one embodiment;
FIG. 5 is a schematic diagram of waveforms corresponding to the transmitting and receiving filters in one embodiment, wherein FIG. 5 (a) is a graph of a mutual ambiguity function of the waveforms, and FIG. 5 (b) is a response of the waveforms at different Doppler frequencies in a distance dimension section;
FIG. 6 is a schematic diagram of signal-to-interference-and-noise ratio performance in one embodiment;
FIG. 7 is a diagram illustrating real and imaginary parts of a transmitted sequence under different PAR constraints in one embodiment;
fig. 8 is a schematic structural diagram of a cognitive radar waveform design device based on a split quadratic programming in an embodiment.
Detailed Description
The present application 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 application 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 application.
In one embodiment, as shown in fig. 1, a cognitive radar waveform design method based on a partial quadratic programming is provided, which includes the following steps:
step 102, calculating the signal-to-interference-and-noise ratio of the signal at the receiving end according to the pulse signal sequence sent in the pulse period of the single-base radar system.
The radar system can be loaded on a single-shot and single-received cognitive radar, and the code length of the radar transmitter transmitted in one PRT (pulse period) isThe code sequence of (2) is a pulse signal sequence, which is received by a radar receiver. Specifically, according to a pulse signal sequence sent in a pulse period of a single-base radar system, calculating the signal-to-interference-and-noise ratio of a signal at a receiving end by adopting a mutual blurring function:
；
；
wherein ,for code length +.>Pulse signal sequence,/-for (a)>For receiving the filter, +.>To interfere with the distribution of the doppler cells at different ranges, and (2)>Is noise energy>Representing the range bin and Doppler bin indices, respectively, +.>For the frequency of the current Doppler unit index, +.>For the shift matrix of the distance cell, superscript +.>Is conjugate transpose->Is a Doppler steering vector, wherein>Represents->Normalized Doppler frequency of individual scattering elements, +.>In the form of a diagonal matrix representation of the steering vector, +.>For receiving the square of the euclidean norm of the filter,/->For Doppler frequency->Diagonal matrix representation of the corresponding steering vector, +.>Is an intermediate variable.
Further, the Doppler frequency interval is uniformly divided intoAnd sets Doppler frequency of pulse signal sequenceThen->，/>Is a Doppler steering vector, wherein>Represents->Normalized Doppler frequency of individual scattering elements, +.>Representing the diagonal matrix to which the construction vector corresponds.Is a shift matrix, and the specific expression form is as follows:
；
wherein ,is the distance unit distance%>，/>Respectively, different distance units.
Step 104, respectively constructing a first problem model of signal-to-interference-and-noise ratio under the constant modulus constraint of the pulse signal sequence and constructing a second problem model of signal-to-interference-and-noise ratio under the low PAR constraint of the pulse signal sequence. The first problem model and the second problem model are both non-convex quadratic programming problems.
Specifically, under the constant mode constraint of a pulse signal sequence, a first problem model of signal-to-interference-and-noise ratio is constructed by a pulse signal and receiving filter through a mutual blurring function shaping method:
；
wherein ,for signal-to-interference-and-noise ratio of pulse signal, +.>Is pulse signal sequence, +.>Is a receive filter. In addition, when the PAR (ratio of peak value to average power) of the pulse signal is not greater than the preset peak value average power ratio, the pulse signal sequence is in low PAR constraint, and a second problem model of signal-to-interference-and-noise ratio is constructed:
；
wherein ,for a preset peak-to-average power ratio, < >>For signal-to-interference-and-noise ratio of pulse signal, +.>Is pulse signal sequence, +.>For receiving the filter, +.>Is the square of the 2 norms of the pulse signal sequence.
And 106, converting the non-convex quadratic programming problem into a quadratic programming problem through the quadratic programming, and obtaining a first constant modulus quadratic programming problem and a second quadratic programming problem.
Specifically, by constructing a split quadratic programming objective function:
；
；
；
wherein ,is pulse signal sequence, +.>For receiving the filter, +.>Is noise energy>In the form of a diagonal matrix representation of the steering vector, +.>Is an intermediate variable +.>Is the square of the euclidean norm of the receive filter.
Further, the first problem model converts the problem into the problem by using the split quadratic programming under the constraint condition of the constant modulus：
；
wherein ,the constraint condition for the objective function as the first problem model is thatTherefore, the problem is substituted into the constraint term of the objective function in consideration of the satisfaction condition>Get questions->：
；
wherein ,is a super parameter.
Further, by solving the problemsPerforming transformation to obtain quadratic programming problem->：
；
wherein ,to optimize the variables +.>For the purpose of +.>Is super-parameter (herba Cinchi Oleracei)>In order to optimize the identity matrix of the variables,、/>the parameter vectors of the optimization variables respectively. In addition, the unitary matrix of the variable is optimized on the premise of not changing the modular lengthThe function of (1) is to add vector->Rotate to and->The same direction, namely, the partial quadratic programming formula of the optimized variable is obtained:
；
due to the introduction of optimization variablesIt needs to be solved, and then the problem is +.>Conversion to the optimization variable solution +.>：
；
wherein ,unit moment for optimizing variablesMatrix, superscript->Is a conjugate transpose. It can be seen that the optimization variable solves +.>Only the minimization problem of the orthogonal constraint, optimizing the unitary matrix of variables>The set of solution spaces that are located are called step manifold spaces, which can be expressed as:
；
wherein ,for dimension +.>Is a complex matrix of->、/>Coordinate index of manifold space, respectively, +.>For the code length of the pulse signal sequence, superscript +.>Is conjugate transposed, so the flow space is solved by conjugate gradient descent method +.>From this, a solution to the unitary matrix of the optimization variable can be obtained.
Further, unitary matrices for given optimization variablesAnd pulse signal sequenceColumn->By giving the question->Conversion to question->Thus, solving the objective function +.>And Supermarameter->：
；
Obtaining problems according to simple derivative operationThe optimal solution of (a) is:
；
wherein ,，/>，/>is an algorithmic super parameter greater than 1.
Further, for the determined fractional quadratic programming objective functionAnd optimizing a variable unitary matrix>Problem->Can be converted into a quadratic programming problem:
；
wherein ,is provided with->，/>Is greater than->Ensuring +.>Positive nature of (2), thus the question->The method can be further converted into a quadratic programming problem and a first constant modulus quadratic programming problem:
；
further, for the case that the PAR of the pulse signal is not greater than the preset peak-to-average power ratio, the pulse signal sequence is under the low PAR constraint, the second problem model may be converted by the above method, and the second quadratic programming problem may be obtained only by changing the constraint condition:
；
wherein ,for pulse signal sequences, superscript +.>Is conjugate transpose->For a preset peak-to-average power ratio, < >>Is the square of the 2 norms of the pulse signal sequence, < >>Is an intermediate variable.
And step 108, when carrying out problem iteration solving, if the pulse signal sequence meets the constant modulus constraint, solving a first constant modulus quadratic programming problem to calculate a current iteration step, and if the pulse signal sequence meets the low PAR constraint, solving the second quadratic programming problem to calculate the current iteration step, and solving and outputting an optimal waveform through alternate iteration.
Specifically, when carrying out problem iteration solution, if the pulse signal sequence meets the constant modulus constraint, adopting a power-like iterative algorithm to generate constant modulus iterative algorithm:
；
according to the constant modulus iteration solution, calculating the current iteration step, namely solving the following formula:
；
wherein ,the optimal solution of the current iteration step is the optimal pulse signal sequence.
Further, if the pulse signal sequence satisfies the low PAR constraint, the nearest neighbor vector method is adopted to give the pulse signal waveform according to the energy constraintSelecting a transmission pulse signal sequence +.>With the smallest intermediate mould lengthThe indices of the individual elements form a set->If->Not only, but also->Performing inner layer iteration, and->For the inner layer iteration times under the constraint condition of low PAR, the iteration number for generating the low peak average power ratio is as follows:
；
wherein ,is an intermediate variable.
Further, if the index set is obtainedAll elements->Corresponding transmit pulse signal sequence +.>All haveObtaining the optimal transmitted pulse signal sequence solving type of the second quadratic programming problemThe method comprises the following steps:
；
otherwise, letIf the obtained index set->All elements->Corresponding transmit pulse signal sequence +.>There is->And returning to the inner layer iteration, and re-selecting the index set, otherwise, obtaining an optimal transmitted pulse signal sequence solution of the second quadratic programming problem, wherein the solution formula is as follows:
；
outputting an optimal pulse signal sequence through inner layer iteration solution, processing the optimal pulse signal sequence through a receiving filter, outputting an optimal receiving filter, updating outer layer iteration parameters according to the optimal receiving filter, and updating super parameters, optimization variables, objective functions and intermediate variables if the outer layer iteration parameters are not equal to preset iteration conditionsIntermediate variable +.>Otherwise, the update is terminated. And then according to the non-matched filter corresponding to the optimal pulse signal sequence as an optimal closed solution, the method comprises the following steps:
；
wherein ,is an intermediate variable +.>Is a diagonal matrix representation of the steering vector.
According to the cognitive radar waveform design method and device based on the partial quadratic programming, the signal-to-interference-plus-noise ratio of the signal at the receiving end is calculated according to the pulse signal sequence sent in the pulse period of the single-base radar system, and the non-convex quadratic partial programming problem model is respectively constructed under the constant modulus constraint and the low PAR constraint of the pulse signal sequence. And further, the signal-to-interference-and-noise ratio of a receiving end signal in the single-base radar system is calculated and optimized, corresponding problem models are respectively constructed under the constant modulus constraint and the low PAR constraint of the pulse signal sequence, and the non-convex quadratic programming problem is converted into the quadratic programming problem through the quadratic programming, so that the waveform design is more flexible and efficient by simplifying the problem models according to different radar scenes. In addition, the problem solving is performed in an alternate iteration mode, so that the optimal waveform can be obtained in a short time, the waveform design efficiency is improved, and meanwhile, more hardware application scenes are adapted.
In one embodiment, the signal-to-interference-and-noise ratio of the signal at the receiving end is calculated by adopting a mutual ambiguity function according to a pulse signal sequence sent in a pulse period of the monostatic radar system:
；
；
wherein ,for code length +.>Pulse signal sequence,/-for (a)>For receiving the filter, +.>To interfere with the distribution of the doppler cells at different ranges, and (2)>Is noise energy>Representing the range bin and Doppler bin indices, respectively, +.>For the frequency of the current Doppler unit index, +.>For the shift matrix of the distance cell, superscript +.>Is conjugate transpose->Is a Doppler steering vector, wherein>Represents->Normalized Doppler frequency of individual scattering elements, +.>In the form of a diagonal matrix representation of the steering vector, +.>For receiving the square of the euclidean norm of the filter,/->For Doppler frequency->Diagonal matrix representation of the corresponding steering vector, +.>Is an intermediate variable.
In one embodiment, the Doppler frequency interval is divided into equal intervalsAnd setting Doppler frequency of the pulse signal sequence, and generating a displacement matrix of the pulse signal sequence:
；
wherein ,is the number of distances apart from the cell, and (2)>For the code length of the pulse signal sequence, +.>For the displacement matrix of the pulse signal sequence, +.>，/>Respectively, different distance units. />
In one embodiment, under the constant modulus constraint of the pulse signal sequence, a first problem model of signal-to-interference-and-noise ratio is constructed by a pulse signal and receiving filter through a mutual blurring function shaping method:
；
wherein ,for signal-to-interference-and-noise ratio of pulse signal, +.>Is pulse signal sequence, +.>Is a receive filter.
It is worth to say that, the traditional fuzzy function design only uses the degree of freedom of one dimension of the transmitted waveform, and the method adopts a method of combined optimization of the transmitted pulse signal sequence and the receiving filter, so that the waveform design performance and the calculation operation speed are improved.
In one embodiment, when the PAR of the pulse signal is not greater than the preset peak-to-average power ratio, the pulse signal sequence is under low PAR constraint, and a second problem model of the signal-to-interference-and-noise ratio is constructed:
；
wherein ,for a preset peak-to-average power ratio, < >>For signal-to-interference-and-noise ratio of pulse signal, +.>Is pulse signal sequence, +.>For receiving the filter, +.>Is the square of the 2 norms of the pulse signal sequence.
In one embodiment, the objective function is calculated by constructing a split quadratic programming:
；
；
；
wherein ,is pulse signal sequence, +.>For receiving the filter, +.>Is noise energy>In the form of a diagonal matrix representation of the steering vector, +.>Is an intermediate variable +.>Is the square of the euclidean norm of the receive filter.
Substituting the objective function into the non-convex quadratic score programming problem to convert the quadratic programming problem, and obtaining a first constant modulus quadratic programming problem:
；
wherein ,for pulse signal sequences, superscript +.>Is conjugate transpose->As an intermediate variable, the number of the variables,
and a second quadratic programming problem:
；/>
wherein ,for pulse signal sequences, superscript +.>Is conjugate transpose->For a preset peak-to-average power ratio, < >>Is the square of the 2 norms of the pulse signal sequence, < >>Is an intermediate variable.
It is worth to say that, the constraint condition of the traditional method is usually a strict constant modulus, the constraint of the constant modulus and the constraint of the low peak average power ratio are comprehensively considered, and because the constraint of the constant modulus is strict to the hardware requirement, the design of the transmitted pulse signal sequence under any constraint of the low peak average power ratio can be realized by relaxing the constraint of the transmitted pulse signal waveform to the low peak average power ratio, so that the practicability is stronger and the application range is wider.
In one embodiment, the objective function is substituted into the first problem model to obtain the problem：
；
The objective function is setIs satisfied with->Substitution question->Get questions->：
；
wherein ,is a super parameter.
By solving the problemsPerforming transformation to obtain quadratic programming problem->：
；
wherein ,to optimize the variables +.>For the purpose of +.>Is super-parameter (herba Cinchi Oleracei)>Is the identity matrix of the optimization variables.
Order theConverting the quadratic programming problem into a first constant modulus quadratic programming problem:
；
wherein ,，/>for optimizing the identity matrix of the variables, +.>For pulse signal sequences, superscript +.>Is conjugate transpose->Is greater than->Ensuring +.>Is the positive nature of (3).
In one embodiment, when the problem is solved in an iterative manner, if the pulse signal sequence meets the constraint of the constant modulus, a power-like iterative algorithm is adopted to generate the constant modulus iterative method, and the current iterative step is calculated according to the first constant modulus quadratic programming problem solved in the constant modulus iterative method. And if the pulse signal sequence meets the low PAR constraint, generating a low peak average power ratio iteration by adopting a nearest neighbor vector method, and calculating the current iteration step by solving a second constant modulus quadratic programming problem according to the low peak average power ratio iteration. And outputting an optimal pulse signal sequence according to the current iteration step, outputting an optimal receiving filter after the optimal pulse signal sequence is processed by the receiving filter, and outputting an optimal waveform through alternately iterating the optimal pulse signal sequence and the optimal receiving filter.
In one embodiment, the outer layer iteration parameters are updated according to the optimal waveform and the optimal receiving filter, and if the outer layer iteration parameters are not equal to the preset iteration conditions, the super parameters, the optimal variables, the objective function and the intermediate variables are updatedIntermediate variable +.>Otherwise, the update is terminated.
It is worth to say that, the alternating loop iterative algorithm is adopted, the signal-to-interference-and-noise ratio performance is good, after the problem is converted, the inner layer iteration of the quadratic programming problem under different constraint conditions is firstly carried out, after the optimal pulse signal sequence is obtained, the given parameters are updated, and the outer layer iteration is carried out by the convergence non-matching receiving filter, so that compared with the traditional waveform design, the method has higher signal-to-interference-and-noise ratio and shorter convergence time.
In one embodiment, the simulation data is further illustrated by the following experiments:
1. experimental scenario: performed on a computer (kernel 2.30 GHz i7-12700H,RAM 16.0GB), MATLAB version R2022a was used. The adopted initialization transmitting sequence and the receiving filter are random sequences, and target scattering coefficients are setNoise energy->. Initializing the transmission sequence to->Receiving filter, wherein /> and />Is mutually independent random variable and is uniformly distributed in +.>. Assume the length of the transmit sequence and the receive filter +.>Clutter interference region->The distribution over the range-doppler cell is shown in fig. 3, expressed as:
；
the optimization problem end conditions are:
；
since the cyclic iteration process comprises two layers of inner and outer iteration, in the stop conditionIn particular to outer layer iteration.
2. The experimental content is shown in fig. 2:
2.1 Modeling of the problem: modeling the optimization problem according to the step 1. Initializing transmit waveformsInitializing the receive filter->Parameter->Parameter->. And (5) iteration termination conditions.
2.2 External(s)Layer iteration: and (3) converting the optimization problem form according to the step (2), and converting the non-convex split optimization problem into a secondary optimization problem. Updating matrix、/>Solving +.A conjugate gradient method in the Steifel manifold space>Simultaneously updating parameters、/>Sum matrix->。
2.3 Inner layer iteration: according to the step 3, two conditions are divided, when the problem meets the constraint of constant modulus, the optimal transmitting sequence is solved by adopting a power-like iterative methodThe method comprises the steps of carrying out a first treatment on the surface of the When the problem satisfies the low PAR constraint, solving the optimal transmitting sequence by adopting a nearest neighbor vector method>。
2.4 Calculating a receive filter based on the optimal transmit sequence。
2.5 Judging convergence: if the iteration stop condition is satisfied, outputAnd->The method comprises the steps of carrying out a first treatment on the surface of the Otherwise, repeating the steps 2.2-2.4 until convergence.
It should be noted that, as shown in fig. 4, the objective function value varies with the iteration number of the inner layer, and the convergence curve has a stepwise rising trend, in which the inner layer iteratively updates the transmission sequenceOuter layer iterative update receiving filter>And other relevant parameters. The convergence curve illustrates that the target response value monotonically increases and eventually converges to a plateau. FIG. 5 shows the response values of the waveform designed by the method under different Doppler frequencies in the cross section of the distance dimension, and the mutual ambiguity function diagram in FIG. 5 (a) has notches in the distance units where clutter is located, thus proving the effectiveness of the method on the waveform design of the cognitive radar. Meanwhile, the transmitting signal sequence and the receiving filter are designed to respectively perform inner-outer layer iterative computation, so that the notch is obvious, the edge is clear, and the performance of the mutual blurring function is good. FIG. 5 (b) shows that the blurring function is +.>Wherein the hatched area is where the disturbance energy distribution is concentrated. />For the range-Doppler unit where the target is located, at the normalized Doppler frequencyIn the interval, i.e. at the clutter interference concentration, it is seen that there are more pronounced notches for different range cells and pronounced spikes in the range-doppler cell where the target is located.
It is noted that by changing the code length of the transmission sequence to n=20:10:100, the signal-to-interference-and-noise ratio performance and the convergence time are compared at different code lengths. As can be seen from fig. 6, as the code length of the transmission sequence increases, the signal-to-interference-and-noise ratio value obtained by the transmission-reception pair increases, and there is a significant advantage in terms of the operation time and convergence time.
Finally, when the constant modulus constraint is relaxed to the low peak-to-average power ratio constraint, the real and imaginary parts of the transmitted sequence designed using nearest neighbor vector method are as shown in FIG. 7, whenWhen the method is used, the point corresponding to the generated emission waveform is positioned on the unit circle, and the generation of the constant-mode waveform is proved; when->The distribution radii of the points are relatively dispersed, but also meet the low peak to average power ratio constraint. It can be seen that due to +.>Only in the radar receiver, no hardware constraint of peak-to-average power ratio is satisfied, and no constraint is imposed on its modular length.
Therefore, compared with the traditional mutual blurring function shaping method, the method has higher signal-to-interference-and-noise ratio and higher operation efficiency under short code length, can realize the joint design of the transmitting and receiving filter under the constraint of any low peak average power ratio, and has higher application value.
It should be understood that, although the steps in the flowcharts of fig. 1-2 are shown in order as indicated by the arrows, these steps are not necessarily performed in order as indicated by the arrows. The steps are not strictly limited to the order of execution unless explicitly recited herein, and the steps may be executed in other orders. Moreover, at least some of the steps in fig. 1-2 may include multiple sub-steps or multiple stages that are not necessarily performed at the same time, but may be performed at different times, nor does the order in which the sub-steps or stages are performed necessarily occur in sequence, but may be performed alternately or alternately with at least a portion of the other steps or sub-steps or stages of other steps.
In one embodiment, as shown in fig. 8, there is provided a cognitive radar waveform design apparatus based on a split quadratic programming, including: a signal-to-interference-and-noise ratio calculation module 802, a construction problem module 804, a problem transformation module 806, and a waveform design module 808, wherein:
the signal-to-interference-and-noise ratio calculating module 802 is configured to calculate the signal-to-interference-and-noise ratio of the signal at the receiving end according to the pulse signal sequence sent in the pulse period of the monostatic radar system.
A problem building module 804 is configured to build a first problem model of signal-to-interference-and-noise ratio under a constant modulus constraint of the pulse signal sequence and a second problem model of signal-to-interference-and-noise ratio under a low PAR constraint of the pulse signal sequence, respectively. The first problem model and the second problem model are both non-convex quadratic programming problems.
The problem transformation module 806 is configured to transform the non-convex quadratic programming problem into a quadratic programming problem through a quadratic programming, and obtain a first constant modulus quadratic programming problem and a second quadratic programming problem.
The waveform design module 808 is configured to, when performing problem iteration solution, solve a first constant modulus quadratic programming problem to calculate a current iteration step if the pulse signal sequence satisfies a constant modulus constraint, and solve a second quadratic programming problem to calculate a current iteration step if the pulse signal sequence satisfies a low PAR constraint, and solve and output an optimal waveform through alternate iteration.
For specific limitations of the cognitive radar waveform design device based on the fractional quadratic programming, reference may be made to the above limitation of the cognitive radar waveform design method based on the fractional quadratic programming, and the description thereof will not be repeated here. All or part of each module in the cognitive radar waveform design device based on the split quadratic programming can be realized by software, hardware and a combination thereof. The above modules may be embedded in hardware or may be independent of a processor in the computer device, or may be stored in software in a memory in the computer device, so that the processor may call and execute operations corresponding to the above modules.
It will be appreciated by those skilled in the art that the structure shown in FIG. 8 is merely a block diagram of some of the structures associated with the present inventive arrangements and is not limiting of the computer device to which the present inventive arrangements may be applied, and that a particular computer device may include more or fewer components than shown, or may combine some of the components, or have a different arrangement of components.
Those skilled in the art will appreciate that implementing all or part of the above described methods may be accomplished by way of a computer program stored on a non-transitory computer readable storage medium, which when executed, may comprise the steps of the embodiments of the methods described above. Any reference to memory, storage, database, or other medium used in embodiments provided herein may include non-volatile and/or volatile memory. The nonvolatile memory can include Read Only Memory (ROM), programmable ROM (PROM), electrically Programmable ROM (EPROM), electrically Erasable Programmable ROM (EEPROM), or flash memory. Volatile memory can include Random Access Memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in a variety of forms such as Static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double Data Rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous Link DRAM (SLDRAM), memory bus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), among others.
The technical features of the above embodiments may be arbitrarily combined, and all possible combinations of the technical features in the above embodiments are not described for brevity of description, however, as long as there is no contradiction between the combinations of the technical features, they should be considered as the scope of the description.
The above examples merely represent a few embodiments of the present application, which are described in more detail and are not to be construed as limiting the scope of the application. It should be noted that it will be apparent to those skilled in the art that several variations and modifications can be made without departing from the spirit of the application, which are all within the scope of the application. Accordingly, the scope of the application should be assessed as that of the appended claims.
Claims (8)
1. The cognitive radar waveform design method based on the split quadratic programming is characterized by comprising the following steps of:
calculating the signal-to-interference-and-noise ratio of a signal at a receiving end according to a pulse signal sequence sent in a pulse period of a single-base radar system;
respectively constructing a first problem model of the signal-to-interference-and-noise ratio under the constant modulus constraint of the pulse signal sequence, and constructing a second problem model of the signal-to-interference-and-noise ratio under the low PAR constraint of the pulse signal sequence; the first problem model and the second problem model are both non-convex quadratic programming problems;
converting the non-convex quadratic division planning problem into a quadratic programming problem through division quadratic programming, and obtaining a first constant modulus quadratic programming problem and a second quadratic programming problem;
when carrying out problem iteration solving, if the pulse signal sequence meets constant modulus constraint, solving the first constant modulus quadratic programming problem to calculate a current iteration step, if the pulse signal sequence meets low PAR constraint, solving the second quadratic programming problem to calculate the current iteration step, and solving and outputting an optimal waveform through alternate iteration;
by constructing an objective function of the split quadratic programming:
；
；
；
wherein ,for the pulse signal sequence, < > for>For receiving the filter, +.>Is noise energy>Is a diagonal matrix of steering vectors, < >>Is an intermediate variable +.>Squaring the euclidean norm of the receive filter;
substituting the objective function into the non-convex quadratic score planning problem to convert the quadratic programming problem, and obtaining a first constant modulus quadratic programming problem:
；
wherein ,for the pulse signal sequence, superscript +.>Is conjugate transpose->As an intermediate variable, the number of the variables,
and a second quadratic programming problem:
；
wherein , for the pulse signal sequence, superscript +.>Is conjugate transpose->For a preset peak-to-average power ratio, < >>Is the square of the 2 norms of the pulse signal sequence,/->Is an intermediate variable;
substituting the objective function into a first problem model to obtain a problem：
；
-applying said objective functionIs satisfied with->Substitution question->Get questions->：
；
wherein ,is a super parameter;
by addressing the problemsPerforming transformation to obtain quadratic programming problem->：
；
wherein , to optimize the variables +.>For the objective function, +.>Is super-parameter (herba Cinchi Oleracei)>A unit matrix for the optimization variables;
order theConverting the quadratic programming problem into a first constant modulus quadratic programming problem:
；
wherein ,，/>for the identity matrix of the optimization variables, +.>For the pulse signal sequence, superscript +.>Is conjugate transpose->Is greater than->A parameter of the maximum eigenvalue of (c).
2. The method of claim 1, wherein calculating the signal-to-interference-and-noise ratio of the receiver signal from the sequence of pulse signals transmitted during the pulse period of the monostatic radar system comprises:
according to a pulse signal sequence sent in a pulse period of a single-base radar system, calculating the signal-to-interference-and-noise ratio of a signal at a receiving end by adopting a mutual blurring function:
；
；
wherein ,for code length +.>Pulse signal sequence,/-for (a)>In order to receive the filter(s),to interfere with the distribution of the doppler cells at different ranges, and (2)>Is noise energy>Representing the range bin and Doppler bin indices, respectively, +.>For the frequency of the current Doppler unit index, +.>Superscript for the shift matrix of the distance unitIs conjugate transpose->Is Doppler direction vector,>is->Normalized Doppler frequency of individual scattering elements, +.>In the form of a diagonal matrix representation of the steering vector, +.>For receiving the square of the euclidean norm of the filter,/->For Doppler frequency->Corresponding to the diagonal matrix representation of the steering vector,is an intermediate variable.
3. The method according to claim 2, characterized in that before the step of constructing the first problem model of the signal-to-interference-and-noise ratio under constant modulus constraints of the pulse signal sequence, respectively, it comprises:
by equally dividing the Doppler frequency interval intoAnd setting Doppler frequency of the pulse signal sequence, and generating a displacement matrix of the pulse signal sequence:
；
wherein ,is the number of distances apart from the cell, and (2)>For the code length of the pulse signal sequence, < >>For the displacement matrix of the pulse signal sequence, < >>，/>Respectively, different distance units.
4. A method according to claim 3, wherein constructing the first problem model of the signal-to-interference-and-noise ratio under constant modulus constraints of the pulse signal sequence comprises:
under the constant mode constraint of the pulse signal sequence, constructing a first problem model of the signal-to-interference-and-noise ratio by a pulse signal and receiving filter through a mutual blurring function shaping method:
；
wherein ,for the signal-to-interference-and-noise ratio of the pulse signal, < >>For the pulse signal sequence, < > for>Is the receiving filter.
5. The method of claim 4, wherein constructing the second problem model for the signal-to-interference-and-noise ratio under low PAR constraints of the pulse signal sequence comprises:
when the PAR of the pulse signal is not larger than the preset peak-to-average power ratio, the pulse signal sequence is in low PAR constraint, and a second problem model of the signal-to-interference-and-noise ratio is constructed:
；
wherein ,for a preset peak-to-average power ratio, < >>For the signal-to-interference-and-noise ratio of the pulse signal, < >>For the pulse signal sequence, < > for>For the receiving filter, < >>Is the square of the 2 norms of the pulse signal sequence.
6. The method of claim 5, wherein in performing the iterative problem solving, if the pulse signal sequence satisfies a constant modulus constraint, the first constant modulus quadratic programming problem is solved to calculate a current iteration step, if the pulse signal sequence satisfies a low PAR constraint, the second quadratic programming problem is solved to calculate a current iteration step, and the optimal waveform is output by the iterative problem solving alternately, comprising:
when carrying out problem iteration solving, if the pulse signal sequence meets constant modulus constraint, adopting a power-like iterative algorithm to generate constant modulus iteration, and calculating a current iteration step according to the constant modulus iteration solving first constant modulus quadratic programming problem;
if the pulse signal sequence meets the low PAR constraint, generating a low peak average power ratio iteration by adopting a nearest neighbor vector method, and solving the second quadratic programming problem in an iteration mode according to the low peak average power ratio to calculate a current iteration step;
and outputting an optimal pulse signal sequence according to the current iteration step, processing the optimal pulse signal sequence by the receiving filter, outputting an optimal receiving filter, and outputting an optimal waveform by alternately iterating the optimal pulse signal sequence and the optimal receiving filter.
7. The method of claim 6, wherein outputting an optimal waveform by alternately iterating the optimal pulse signal sequence and the optimal receive filter, further comprises:
updating outer layer iteration parameters according to the optimal waveform and the optimal receiving filter, if the outer layer iteration parameters are the sameIf the layer iteration parameter is not equal to the preset iteration condition, updating the super parameter, the optimization variable, the objective function and the intermediate variableSaid intermediate variable +.>Otherwise, the update is terminated.
8. Cognitive radar waveform design device based on split quadratic programming, characterized in that, the device includes:
the signal-to-interference-and-noise ratio calculation module is used for calculating the signal-to-interference-and-noise ratio of the signal of the receiving end according to the pulse signal sequence sent in the pulse period of the single-base radar system;
the problem building module is used for building a first problem model of the signal-to-interference-and-noise ratio under the constant modulus constraint of the pulse signal sequence and building a second problem model of the signal-to-interference-and-noise ratio under the low PAR constraint of the pulse signal sequence respectively; the first problem model and the second problem model are both non-convex quadratic programming problems;
the problem conversion module is used for converting the non-convex quadratic programming problem into a quadratic programming problem through fractional quadratic programming to obtain a first constant modulus quadratic programming problem and a second quadratic programming problem; by constructing an objective function of the split quadratic programming:
；
；
；
wherein ,for the pulse signal sequence, < > for>For receiving the filter, +.>Is noise energy>Is a diagonal matrix of steering vectors, < >>Is an intermediate variable +.>Squaring the euclidean norm of the receive filter;
substituting the objective function into the non-convex quadratic score planning problem to convert the quadratic programming problem, and obtaining a first constant modulus quadratic programming problem:
；
wherein ,for the pulse signal sequence, superscript +.>Is conjugate transpose->As an intermediate variable, the number of the variables,
and a second quadratic programming problem:
；
wherein , for the pulse signal sequence, superscript +.>Is conjugate transpose->For a preset peak-to-average power ratio, < >>Is the square of the 2 norms of the pulse signal sequence,/->Is an intermediate variable;
substituting the objective function into a first problem model to obtain a problem：
；
-applying said objective functionIs satisfied with->Substitution question->Get questions->：
；
wherein ,is a super parameter;
by addressing the problemsPerforming transformation to obtain quadratic programming problem->：
；
wherein , to optimize the variables +.>For the objective function, +.>Is super-parameter (herba Cinchi Oleracei)>A unit matrix for the optimization variables;
order theConverting the quadratic programming problem into a first constant modulus quadratic programming problem:
；
wherein ,，/>for the identity matrix of the optimization variables, +.>For the pulse signal sequence, superscript +.>Is conjugate transpose->Is greater than->A parameter of a maximum eigenvalue of (a);
and the waveform design module is used for solving the first constant modulus quadratic programming problem to calculate the current iteration step when the pulse signal sequence meets the constant modulus constraint and solving the second quadratic programming problem to calculate the current iteration step when the pulse signal sequence meets the low PAR constraint and solving the output optimal waveform through alternate iteration when the pulse signal sequence meets the constant modulus constraint.
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