CN116482621B - Initial phase agile pulse train waveform design method based on distance gating performance optimization - Google Patents
Initial phase agile pulse train waveform design method based on distance gating performance optimization Download PDFInfo
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Abstract
The invention belongs to the field of radar waveform optimization design, and particularly relates to a method for designing a waveform of a pulse train with initial phase agility based on range gating performance optimization. The invention uses the fuzzy function of the initial phase-agile pulse train waveformpThe norm intuitively describes the distance gating performance of the initial phase-agile pulse train waveform and constructs an optimal design model of the initial phase-agile pulse train waveform based on the optimal distance gating performance; the agent function of the optimization target is constructed through the minimization of the principal component, so that the computational complexity of the solved optimization problem is reduced, and further, the Newton method is utilized for iterative solution, and the effective waveform optimization design is realized; compared with a randomly generated initial phase agile pulse train waveform, the waveform designed by the method has better range gating performance.
Description
Technical Field
The invention belongs to the field of radar waveform optimization design, and particularly relates to a method for designing a waveform of a pulse train with initial phase agility based on range gating performance optimization.
Background
Search radars mostly employ a narrow Pulse Doppler (PD) regime, and transmit waveform parameters such as: pulse repetition time (Pulse Repetition Time, PRT), carrier frequency, intra-pulse modulation scheme, etc. are fixed. The fixed waveform parameters will cause periodic ambiguity, i.e. range ambiguity, in the echo with a delay exceeding one PRT, which makes it impossible for the radar to determine which transmit period the detected echo is in. A classical way of solving the distance ambiguity is to transmit a plurality of groups of signals with different PRTs, and for a remote target with the distance ambiguity, the method uses the Chinese remainder theorem to solve the ambiguity because the echo time delays measured by the signals with different repetition frequencies are different, so as to obtain the real time delay of the target. However, the defuzzification processing needs to use a plurality of groups of echo data, the data rate is lower, meanwhile, the coherent accumulation of signals with different repetition frequencies can not be realized, the echo energy can not be effectively utilized, and the defuzzification processing is easy to generate ghosts or false targets in a multi-target environment. Feng-ling Lin and Michael steper in the united states navy laboratories of 2001 first proposed using the initial phase-change pulse train waveform to resolve distance ambiguity. They point out that the transmitting end adopts the initial phase agile pulse train waveform and sets up a filter group matched with the echo phase of each distance section at the receiving end, so as to realize the distance ambiguity resolution. The modulation initial phase of the initial phase agile pulse train waveform is mostly obtained by adopting a random generation mode, and the distance ambiguity suppression capability (also called distance gating performance) has stronger uncertainty, so that the waveform also has larger optimization design space.
Disclosure of Invention
The technical solution of the invention is as follows: the method is characterized by solving the problems of the prior art, providing a method for designing a pulse waveform of initial phase agility based on the optimization of the range gating performance, and from the aspect of a fuzzy functionpThe norm minimization is an optimization criterion, an initial phase agile pulse train waveform optimization design model with optimal distance gating performance is constructed, and the optimization design of the waveform is realized through principal component minimization and Newton method iteration solution.
The technical scheme of the invention is as follows:
initial phase agile pulse train waveform design method based on distance gating performance optimization, wherein the initial phase agile pulse train waveformThe expression of (2) is shown as the formula (1):
（1）
wherein ,for the complex envelope of the signal fast time dimension, +.>For fast time->In order to be the pulse sequence number,，/>is->The modulation phase of the individual pulses,/->For pulse number +.>Is imaginary unit, ++>For the pulse repetition period, a pulse repetition period +.>Corresponding distance range>For a distance segment, i.e.)>, wherein />Is the speed of light;
the initial phase agile pulse train waveform design method based on the distance gating performance optimization can be realized by solving the optimization problem shown in the formula (2).
（2）
wherein ,for the modulation primary phase to be optimized, +.>For transposition->For taking the modulus value, +.>For distance segment number>Representing the number of optimized distance segments>For Doppler channel number, +.>A fuzzy function of the initial phase agile pulse train waveform, < >>Represents infinite norm>The physical meaning of (a) is that the peak value of the fuzzy function in the range of the optimized distance section, namely corresponding to the initial phase agile pulse train waveform +.>The range gating performance of the echo of each range section refers to the capability of gating the echo of the range section and inhibiting the echo of other range sections, and directly reflects the waveform of the initial phase agile pulse train +.>Ability to suppress distance blur.
The method steps for solving the optimization problem as shown in formula (2) include:
step 1, utilizepOptimization objective shown in norm conversion (2)Due to the optimization objective +.>Difficult to explicitly represent, resulting in an inability to solve the optimization problem, employingpThe norm may approximate the optimization objective, thereby converting the optimization objective into the one shown in equation (3),
（3）
representation ofpNorms, whenpWhen the temperature of the liquid crystal approaches to infinity,pthe norm becomes infinite.
By usingpAfter the norm approximation, the optimization problem of equation (2) can be translated into,
（4）
step 2: the proxy function is constructed using a principal component minimization algorithm. Optimization objectives of (4) can be constructed using principal component minimization algorithmsAs shown in the expression (5),
（5）
wherein Is a conjugate transpose.
The expression of (2) is shown as a formula (6),
（6）
for initial modulation of the initial phase +.>And->The expressions of (a) are shown as the expression (7) and the expression (8) respectively,
（7）
（8）
wherein ,a fuzzy function of complex envelope +.>Output of Doppler channel,/, of>And->The expression of (2) is shown as the expression (9) and the expression (10),
（9）
（10）
representation->Go (go)/(go)>Column 0 matrix, ">Representation->Go (go)/(go)>Column 0 matrix, ">Is->Unit matrix of dimension,/->Is diagonalized.
The optimization problem shown in the formula (4) can be converted into the formula (11) by using the proxy function shown in the formula (5),
（11）
step 3: solving the optimization problem represented by the formula (11) by Newton's method. The optimization problem shown in the formula (11) is a non-convex optimization problem because of constant modulus constraint, and is required to be converted into an unconstrained convex problem through optimization variable substitution, and then is solved by utilizing a Newton method.
Due toThe optimization variable in formula (11)>Can use->In the alternative to this, the first and second,is the primary phase of inter-pulse modulation->Thereby converting the non-convex optimization problem of the formula (11) containing the constant modulus constraint into the unconstrained convex optimization problem of the formula (12),
（12）
by solving forFor->Gradient of->And Heisen matrix->The iterative formula of Newton's method is shown in formula (13),
（13）
is->Optimizing variable +.>Value of->Representing the matrix inversion.
When gradient is formed2 norms of>Less than a set threshold->When the newton method converges, the algorithm ends.
Step 4: and (5) iterating until the whole algorithm converges. Repeating the step 2-3, and updating the optimizing result obtained in the step 3 each time as an initial value in the step 2Until the modulation initial phase obtained by optimizing the two times before and after +.>Corresponding->The difference of (2) is smaller than the set threshold +.>The overall algorithm may be considered to converge. The->The initial phase is modulated based on the optimization of the distance gating performance, and the initial phase is substituted into the (1) to obtain the initial phase agile pulse train waveform based on the optimization of the distance gating performance.
Advantageous effects
The invention uses the fuzzy function of the initial phase-agile pulse train waveformpThe norm intuitively describes the distance gating performance of the initial phase-agile pulse train waveform and constructs an optimal design model of the initial phase-agile pulse train waveform based on the optimal distance gating performance;the agent function of the optimization target is constructed through the minimization of the principal component, so that the computational complexity of the solved optimization problem is reduced, and further, the Newton method is utilized for iterative solution, and the effective waveform optimization design is realized; compared with a randomly generated initial phase agile pulse train waveform, the waveform designed by the method has better range gating performance.
Drawings
FIG. 1a is a three-dimensional view of a chirp waveform blur function;
FIG. 1b is a distance-amplitude projection of a chirp waveform blur function;
FIG. 2a is a three-dimensional view of a randomly generated initial phase agile pulse train waveform blur function;
FIG. 2b is a distance-amplitude projection of a randomly generated initial phase agile pulse train waveform blur function;
FIG. 3a is a three-dimensional view of a waveform blur function of an initial phase-change pulse train optimally designed according to the method of the present invention;
FIG. 3b is a distance-amplitude projection of a fuzzy function of a waveform of a pulse train of a short-cut variation in an optimization design of the method of the present invention.
Detailed Description
The invention is further described below with reference to the drawings and examples.
Examples
Currently, the search radar mostly uses a waveform with fixed parameters as a transmitting waveform, such as a chirp pulse train waveform. From fig. 1a and 1b, it can be seen that the echo between the distance segments of the parameter-fixed chirp waveform from the dimension is completely blurred by the blurring function of the chirp waveform.
Initial phase agile pulse train waveformThe expression of (2) is shown as the formula (1):
（1）
wherein ,for the complex envelope of the signal fast time dimension, +.>For fast time->In order to be the pulse sequence number,，/>is->The modulation phase of the individual pulses,/->For pulse number +.>Is imaginary unit, ++>For pulse repetition period, a pulse repetition period is defined for convenience of description>Corresponding distance range>For a distance segment, i.e.)>, wherein />Is the speed of light.
The initial phase agile pulse train waveform design method based on the distance gating performance optimization can be realized by solving the optimization problem shown in the formula (2).
（2）
wherein For the modulation primary phase to be optimized, +.>For transposition->For taking the modulus value, +.>For distance segment number>Representing the number of optimized distance segments>For Doppler channel number, +.>A fuzzy function of the initial phase agile pulse train waveform, < >>Represents infinite norm>The physical meaning of (a) is that the peak value of the fuzzy function in the range of the optimized distance section, namely corresponding to the initial phase agile pulse train waveform +.>Range gating performance for each range echo. The range gating performance refers to the capability of gating the echo of the range section and inhibiting the echo of other range sections, and directly reflects the waveform of the pulse train of the initial phase agility +.>Ability to suppress distance blur.
The method comprises the following steps:
step 1, utilizepOptimization objective shown in norm conversion (2). Due to the optimization objective +.>It is difficult to explicitly represent, resulting in an optimization problem that cannot be solved. By usingpThe norm may approximate the optimization objective, thereby converting the optimization objective into the one shown in equation (3),
（3）
representation ofpNorms, whenpWhen the temperature of the liquid crystal approaches to infinity,pthe norm becomes infinite.
By usingpAfter the norm approximation, the optimization problem of equation (2) can be translated into,
（4）
step 2: the proxy function is constructed using a principal component minimization algorithm. Optimization objectives of (4) can be constructed using principal component minimization algorithmsAs shown in the expression (5),
（5）
wherein Is a conjugate transpose.
The expression of (2) is shown as a formula (6),
（6）
for initial modulation of the initial phase +.>And->The expressions of (a) are shown as the expression (7) and the expression (8) respectively,
（7）
（8）
wherein ,a fuzzy function of complex envelope +.>Output of Doppler channel,/, of>And->The expression of (2) is shown as the expression (9) and the expression (10),
（9）
（10）
representation->Go (go)/(go)>Column 0 matrix, ">Representation->Go (go)/(go)>Column 0 matrix, ">Is->Unit matrix of dimension,/->Is diagonalized.
The optimization problem shown in the formula (4) can be converted into the formula (11) by using the proxy function shown in the formula (5),
（11）
step 3: solving the optimization problem represented by the formula (11) by Newton's method. The optimization problem shown in the formula (11) is a non-convex optimization problem because of constant modulus constraint, and is required to be converted into an unconstrained convex problem through optimization variable substitution, and then is solved by utilizing a Newton method.
Due toThe optimization variable in formula (11)>Can use->In the alternative to this, the first and second,is the primary phase of inter-pulse modulation->Thereby converting the non-convex optimization problem of the formula (11) containing the constant modulus constraint into the unconstrained convex optimization problem of the formula (12),
（12）
by solving forFor->Gradient of->And Heisen matrix->The iterative formula of Newton's method is shown in formula (13),
（13）
is->Optimizing variable +.>Value of->Representing the matrix inversion.
When gradient is formed2 norms of>Less than a set threshold->When the newton method converges, the algorithm ends.
Step 4: and (5) iterating until the whole algorithm converges. Repeating the step 2-3, and updating the optimizing result obtained in the step 3 each time as an initial value in the step 2Until the modulation initial phase obtained by optimizing the two times before and after +.>Corresponding->The difference of (2) is smaller than the set threshold +.>The overall algorithm may be considered to converge. The->The initial phase is modulated based on the optimization of the distance gating performance, and the initial phase is substituted into the (1) to obtain the initial phase agile pulse train waveform based on the optimization of the distance gating performance.
Verifying and explaining the range gating performance of the designed initial phase agile pulse train waveform:
the effectiveness of the proposed waveform design method is verified in a simulation manner. The number of pulses is set to be 100 in the simulation, the number of concerned distance segments is 3, a complex envelope adopts a linear frequency modulation pulse train waveform, the pulse width is 50us, the PRT is 500us, the bandwidth is 4MHz, the sampling rate is 5MHz, and the carrier frequency is 1GHz. FIGS. 2a and 2b show the followingMechanically generated initial phase-change pulse train waveformAs can be seen from fig. 2a and 2b, the randomly generated initial phase-change pulse train waveform ∈>The range gating performance for the range segment of interest is 10.3dB, 10.5dB, 9.8dB, respectively. By randomly generated initial phase agile pulse train waveform +.>As an initial value, the initial phase agile pulse train waveform obtained by adopting the method provided by the invention after optimization design>As shown in fig. 3a and 3b, the range gating performance of the concerned range section is 17.4dB, 17.5dB and 17.4dB respectively; />Compared with +.>The range gating performance of the range segment of interest improves by 7.1dB, 7.0dB, 7.6dB, respectively.
Of course, the present invention is capable of other various embodiments and its several details are capable of modification and variation in light of the present invention, as will be apparent to those skilled in the art, without departing from the spirit and scope of the invention as defined in the appended claims.
Claims (5)
1. A method for designing a waveform of an initial phase agile pulse train based on optimization of range gating performance is characterized by comprising the following steps:
step 1, designing a waveform of a pulse train with initial phase agilityAs shown in formula (1):
（1）
wherein ,for the complex envelope of the signal fast time dimension, +.>For fast time->In order to be the pulse sequence number,，/>is->The modulation phase of the individual pulses,/->For pulse number +.>Is imaginary unit, ++>Is a pulse repetition period;
step 2, constructing the initial phase agile pulse train waveform designed in step 1The optimization problem based on the optimization of the range gating performance is as shown in the formula (2):
（2）
wherein ,for the modulation primary phase to be optimized, +.>For transposition->For taking the modulus, a pulse repetition period +.>Corresponding distance range>For a distance segment, i.e.)>, wherein />For the speed of light->For distance segment number>Representing the number of optimized distance segments>For Doppler channel number, +.>A fuzzy function of the initial phase agile pulse train waveform, < >>Represents an infinite norm;
step 3, utilizepThe norm targets the optimization problem constructed in step 2 to the optimizationThe conversion is as shown in formula (3):
（3）
wherein ,representation ofpA norm;
step 4, converting the optimization problem constructed in the step 2 into a formula (4) according to the optimization target converted in the step 3:
（4）
step 5, constructing an optimization target of the optimization problem shown in the formula (4)As shown in the formula (5):
（5）
wherein ,is a conjugate transpose;
the expression of (2) is shown as a formula (6),
（6）
for initial modulation of the initial phase +.>And->The expressions of (a) are shown as the expression (7) and the expression (8) respectively,
（7）
（8）
wherein ,a fuzzy function of complex envelope +.>Output of Doppler channel,/, of>And->The expression of (2) is shown as the expression (9) and the expression (10),
（9）
（10）
representation->Go (go)/(go)>Column 0 matrix, ">Representation->Go (go)/(go)>Column 0 matrix, ">Is thatUnit matrix of dimension,/->Is diagonalized;
step 6, converting the optimization problem shown in the formula (4) into a formula (11) according to the proxy function obtained in the step 5:
（11）
and 7, solving the optimization problem shown in the formula (11) by utilizing a Newton method to obtain the initial phase agile pulse train waveform based on the optimization of the range gating performance.
2. The method for designing the initial phase agile pulse train waveform based on the optimization of the range gating performance according to claim 1, wherein the method comprises the following steps:
in the step 2, the range gating performance refers to the capability of gating the echo of the range section and suppressing the echo of other range sections.
3. The method for designing the initial phase agile pulse train waveform based on the optimization of the range gating performance according to claim 2, wherein the method comprises the following steps:
in the step 5, a principal component minimization algorithm is used to construct a proxy function.
4. The method for designing the initial phase agile pulse train waveform based on the optimization of the range gating performance according to claim 3, wherein the method comprises the following steps of:
in the step 7, the optimization problem shown in the formula (11) is solved by newton method specifically as follows:
the optimization variable in the formula (11)Use->For replacement of->Is the primary phase of inter-pulse modulation->Converting the non-convex optimization problem of formula (11) containing constant modulus constraints into the unconstrained convex optimization problem of formula (12):
（12）
by solving forFor->Gradient of->And Heisen matrix->The iterative formula for obtaining Newton's method is shown as formula (13):
（13）
is->Optimizing variable +.>Value of->Representing matrix inversion;
when gradient is formed2 norms of>Less than a set threshold->At this time, newton's method converges and ends.
5. The method for designing the initial phase agile pulse train waveform based on the optimization of the range gating performance according to claim 4, wherein the method comprises the following steps:
repeating the steps 5-7, and updating the optimization result obtained in each step 7 as an initial value in the step 5Up to two times of optimizationModulating primary phase->Corresponding->The difference of (2) is smaller than the set threshold +.>Converging, at this time, the obtainedThe initial phase modulation based on the optimization of the range gating performance is substituted into the (1) to obtain the initial phase agile pulse train waveform based on the optimization of the range gating performance.
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