CN111736133B - Orthogonal Waveform Design Method for MIMO Radar Based on Improved GA-SQP - Google Patents
Orthogonal Waveform Design Method for MIMO Radar Based on Improved GA-SQP Download PDFInfo
- Publication number
- CN111736133B CN111736133B CN202010542057.XA CN202010542057A CN111736133B CN 111736133 B CN111736133 B CN 111736133B CN 202010542057 A CN202010542057 A CN 202010542057A CN 111736133 B CN111736133 B CN 111736133B
- Authority
- CN
- China
- Prior art keywords
- individual
- population
- chromosome
- individuals
- sqp
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 238000000034 method Methods 0.000 title claims abstract description 43
- 238000013461 design Methods 0.000 title claims abstract description 23
- 210000000349 chromosome Anatomy 0.000 claims abstract description 66
- 239000011159 matrix material Substances 0.000 claims abstract description 35
- 238000005457 optimization Methods 0.000 claims abstract description 26
- 230000002068 genetic effect Effects 0.000 claims abstract description 20
- 230000035772 mutation Effects 0.000 claims abstract description 17
- 239000012634 fragment Substances 0.000 claims description 20
- 108090000623 proteins and genes Proteins 0.000 claims description 12
- 230000008569 process Effects 0.000 claims description 6
- 238000004364 calculation method Methods 0.000 claims 1
- 238000004088 simulation Methods 0.000 description 13
- 230000005540 biological transmission Effects 0.000 description 6
- 238000005314 correlation function Methods 0.000 description 4
- 230000000694 effects Effects 0.000 description 4
- 230000035485 pulse pressure Effects 0.000 description 4
- 238000005311 autocorrelation function Methods 0.000 description 3
- 230000006872 improvement Effects 0.000 description 3
- 230000008859 change Effects 0.000 description 2
- 238000005516 engineering process Methods 0.000 description 2
- 238000012986 modification Methods 0.000 description 2
- 230000004048 modification Effects 0.000 description 2
- 238000012935 Averaging Methods 0.000 description 1
- 108091026890 Coding region Proteins 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 230000001427 coherent effect Effects 0.000 description 1
- 238000011161 development Methods 0.000 description 1
- 238000010586 diagram Methods 0.000 description 1
- 238000011478 gradient descent method Methods 0.000 description 1
- 230000009191 jumping Effects 0.000 description 1
- 238000011160 research Methods 0.000 description 1
- 238000010845 search algorithm Methods 0.000 description 1
- 238000002922 simulated annealing Methods 0.000 description 1
Images
Classifications
-
- 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
- G01S7/42—Diversity systems specially adapted for radar
Landscapes
- Engineering & Computer Science (AREA)
- Radar, Positioning & Navigation (AREA)
- Remote Sensing (AREA)
- Computer Networks & Wireless Communication (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Radar Systems Or Details Thereof (AREA)
Abstract
The invention discloses a MIMO radar orthogonal waveform design method based on improved GA-SQP, which adopts an improved GA-SQP algorithm to optimize a phase coding matrix, and uses the optimized phase coding matrix to design an orthogonal waveform; after the crossover and mutation of the traditional genetic algorithm, the SQP optimization stage is added, and a certain number of individuals are selected to perform SQP iteration for a plurality of times so as to improve the local optimizing performance of the algorithm; meanwhile, on the basis of the original genetic algorithm, the cross operation and the mutation operation are continuously refined, an operation object is changed into a chromosome from an individual, the solution space is enlarged, the convergence of the whole algorithm is further improved, and the optimization speed of the phase coding matrix is improved.
Description
Technical Field
The invention relates to the technical field of civil security radar, in particular to a MIMO radar orthogonal waveform design method based on improved GA-SQP, which has better convergence, and the designed waveform can be used as a transmitting waveform of a MIMO system radar.
Background
Along with the development of radar technology and the improvement of the functional requirements of the radar technology, the multiple-input multiple-output (MIMO) radar has the advantages of better distance and Doppler resolution, improved system freedom, capability of resisting the flicker of the cross sectional area of a target and the like, and becomes a main radar system. The performance of the MIMO radar has quite close relation with the transmitted waveforms, the waveform design is a scientific research direction which is important in the field of the MIMO radar, and the coherent MIMO radar requires the transmitted waveforms to be mutually orthogonal, so that a wide-beam low-gain waveform is obtained. Waveforms of MIMO radars can be generally classified into phase, frequency codes, and orthogonal waveforms with good pulse pressure performance are the basis of high resolution radar systems. There are two general goals for MIMO radar waveform design tasks: firstly, in order to ensure higher resolution performance of the radar and avoid that a large target covers a small target, the pulse pressure main and side lobe ratio of the waveform is required to be high enough; in addition, in order to avoid the mutual interference of signals between the MIMO radar channels, the signals of different transmitting array elements are required to meet the requirement of low cross correlation.
Phase-encoding waveform design algorithms can be categorized into two main categories according to their properties: one is a heuristic algorithm with certain global searching capability such as a simulated annealing algorithm (SA), a Genetic Algorithm (GA) and the like, but the heuristic algorithm has the problems of more iteration times, large data volume, large resource consumption and weak local optimizing capability; the other is an iterative gradient descent algorithm, the objective of optimizing is achieved by converting given constraint conditions into functions and then performing iterative optimization on the functions in gradient directions, and the method depends on the selection of initial points and is easy to fall into local extremum. There are therefore many ways to combine two algorithms, for example: the design of the orthogonal two-phase code is completed by utilizing the global convergence of the GA algorithm and the local optimizing capability of the gradient descent method by the Western-type electronic technology university Tao Haigong. The hybrid search algorithm has both global convergence and local optimizing capability, and shows better performance in waveform design. However, the existing method of combining GA and SQP (sequence quadratic programming) algorithms has the problems of coarse granularity and limited convergence capability during crossover operation and mutation operation, and the convergence is still required to be further improved.
Disclosure of Invention
Aiming at the problems in the prior art, the invention aims to provide the MIMO radar orthogonal waveform design method based on the improved GA-SQP.
In order to achieve the above purpose, the present invention is realized by the following technical scheme.
The MIMO radar orthogonal waveform design method based on the improved GA-SQP comprises the following steps:
wherein phi is i (l) The i-th phase of the i-th transmission channel is represented, the phase encoding matrix Φ is formed by m×l encoding phases, each row of which is a transmission channel, and each column represents symbols transmitted by M array elements at the same time.
The transmit waveform of the ith element can be expressed as
Wherein a is i (l) Is of amplitude phi i (l) Then the i-th phase of the i-th element transmission is indicated.
2.1, setting N individuals in a population, wherein each phase coding matrix corresponds to one individual; randomly initializing each individual in the population, namely randomly taking values between [0,2 pi ] for each element in each phase coding matrix;
2.2, judging whether each individual in the population performs segment crossing, if so, performing segment crossing on the current individual, otherwise, keeping the current individual unchanged, judging whether the next individual performs segment crossing, and so on until all the individuals in the population are judged to be finished, and obtaining the population after segment crossing;
2.3, judging whether each individual in the population after the segment crossing is mutated, if so, mutating the current individual, otherwise, keeping the current individual unchanged, judging whether the next individual is crossed by the segment, and so on until all the individuals in the population are judged to be finished, and obtaining the mutated population;
2.4, judging whether each individual in the mutated population is subjected to chromosome crossover, if so, carrying out chromosome crossover on the current individual, otherwise, keeping the current individual unchanged, judging whether the next individual is subjected to chromosome crossover, and the like until all the individuals in the population are judged to be finished, and obtaining the population after chromosome crossover.
And 2.5, judging whether the population after chromosome crossing is locally optimized, if so, locally optimizing the population after chromosome crossing, otherwise, switching to the step 2.6.
2.6, calculating the fitness value of all individuals in the current population, sorting according to the fitness value, selecting the individual with the largest fitness as the optimal individual in the iteration, directly reserving the optimal individual to enter the next iteration, and selecting the rest (N-1) individuals by adopting a roulette manner to obtain the population after optimization of the current iteration times.
2.7, after the iteration times are added with 1, judging whether the current iteration times reach IterNum, if so, stopping iteration, and outputting the optimal individual in 2.6 as an optimized phase coding matrix; otherwise, turning to step 2.2 for the next iteration;
and step 3, designing orthogonal transmitting waveforms by adopting the optimized phase encoding matrix, and completing the orthogonal waveform design of the MIMO radar.
Compared with the prior art, the invention has the beneficial effects that:
according to the invention, after the crossover and mutation of the traditional genetic algorithm, an SQP optimization stage is added, and a certain number of individuals are selected to perform SQP multiple iterations so as to improve the local optimizing performance of the algorithm. Meanwhile, the invention improves the genetic algorithm, and on the basis of the original genetic algorithm, the crossover operation and the mutation operation are continuously refined, the operation object is changed into a chromosome from an individual, the solution space is enlarged, the convergence of the whole algorithm is further improved, and the optimization speed of the phase encoding matrix is improved.
Drawings
The invention will now be described in further detail with reference to the drawings and to specific examples.
FIG. 1 is a flow chart of an implementation of the present invention;
FIG. 2 is a graph of an autocorrelation function of a waveform obtained under the condition that the code length is 48 and the number of waveforms is 4 according to an embodiment of the present invention; wherein 2 (a) corresponds to waveform 1,2 (b) corresponds to waveform 2,2 (c) corresponds to waveform 3,2 (d) corresponds to waveform 4;
FIG. 3 is a cross-correlation function diagram of waveforms obtained under the condition that the code length is 48 and the number of waveforms is 4 according to the embodiment of the present invention; wherein, 3 (a) corresponds to waveform 1 and waveforms 2,3 (b) corresponds to waveform 1 and waveforms 3,3 (c) corresponds to waveform 1 and waveforms 4,3 (d) corresponds to waveform 2 and waveforms 3,3 (e) waveform 2 and waveforms 4,3 (f) waveform 3 and waveform 4;
FIG. 4 is a graph showing the performance of the method of the present invention compared with the GA algorithm and the SQP algorithm, respectively, in the embodiment of the present invention; wherein, (a) the corresponding parameters are m=2, l=8 to 48, and (b) the corresponding parameters are m=3, l=8 to 48;
FIG. 5 is a graph showing the performance of the method of the present invention compared with the original GA-SQP method, respectively, in the example of the present invention; wherein, (a) the corresponding parameter is m=2, l=24; (b) the corresponding parameter is m=3, l=24; (c) the corresponding parameter is m=4, l=24.
Detailed Description
Embodiments of the present invention will be described in detail below with reference to examples, but it will be understood by those skilled in the art that the following examples are only for illustrating the present invention and should not be construed as limiting the scope of the present invention.
Referring to fig. 1, the method for designing the MIMO radar orthogonal waveforms based on the improved GA-SQP provided by the invention comprises the following steps:
wherein phi is i (l) The i-th phase of the i-th transmission channel is represented, the phase encoding matrix Φ is formed by m×l encoding phases, each row of which is a transmission channel, and each column represents symbols transmitted by M array elements at the same time.
The transmit waveform of the ith element can be expressed as
Wherein a is i (l) Is of amplitude phi i (l) Then the i-th phase of the i-th element transmission is indicated.
In this embodiment, m=3, l=8.
2.1, setting N individuals in a population, wherein each phase coding matrix corresponds to one individual; randomly initializing each individual in the population, namely randomly taking values between [0,2 pi ] for each element in each phase coding matrix;
specifically, a random strategy is generally adopted during population initialization, namely, each gene of all individuals in the population is randomly valued between [0,2 pi ], so that the individuals in the population can cover as many 'traits', namely phases, as possible at the initial moment.
2.2, judging whether each individual in the population performs segment crossing, if so, performing segment crossing on the current individual, otherwise, keeping the current individual unchanged, judging whether the next individual performs segment crossing, and so on until all the individuals in the population are judged to be finished, and obtaining the population after segment crossing;
further, the determining whether each individual in the population performs fragment crossover is specifically: randomly generating a random number rand1 of [0, 1), if rand1 < P c Then segment crossing is carried out on the current individual;
wherein P is c The segment crossing probability is preset. P (P) c Take [0.65,0.9 ]]The effect is optimal.
Further, the fragment crossover is specifically: randomly selecting a plurality of continuous gene loci on each chromosome of the current individual as a male parent genetic fragment; and randomly selecting one individual from the remaining (N-1) individuals as a female parent, taking a genetic locus at a position corresponding to the male parent genetic fragment on the female parent as a female parent genetic fragment, and exchanging the male parent genetic fragment with the female parent genetic fragment to finish the fragment intersection of the current individual.
Specifically, it is assumed that the phase encoding matrices of a pair of male parent individuals in the population are S 1 And S is 2 ：
The crossover operation of individual segments involves multiple loci of all chromosomes, meaning that once this operation occurs, the auto-and cross-correlations of all orthogonal waveforms will change for the corresponding individual (the coding matrix). To further reduce the granularity, individual fragments are cross-refined in the improved method, the cross-over operation is still performed between two individuals, but the cross-over fragments are selected in chromosome units instead of individual units. If the male parent and female parent individuals are S respectively 1 And S is 2 Randomly selecting chromosome fragments for crossing, selecting gene loci contained in a dotted line frame, and storing S 1 Genes in the dashed box and replaced with S 2 Dotted line frame part, get S' 1 ：
At the same time, using the S stored in the previous step 1 Middle segment overlay individual S 2 Corresponding part of (a) is denoted as S' 2 ：
2.3, judging whether each individual in the population after the segment crossing is mutated, if so, mutating the current individual, otherwise, keeping the current individual unchanged, judging whether the next individual is crossed by the segment, and so on until all the individuals in the population are judged to be finished, and obtaining the mutated population;
further, the determining whether each individual in the population after the segment crossing is mutated specifically is: generating a random number rand2 of [0, 1), if rand2 < P v When the mutation is performed;
wherein P is v Is a predetermined variation probability.
Further, the mutation of the current individual is specifically as follows: randomly selecting a locus on each chromosome of the current individual, and changing the gene variation at the selected locus into a new gene randomly generated in [0,2H ], thereby completing the variation of the current individual.
The mutation process can generate genes which do not exist in the current individual, and in the optimization problem, the probability of jumping out of local optimum is improved by the emergency. The crossover operation is to obtain offspring with the advantages of both male parent and female parent, while the mutation operation has stronger randomness, so as to ensure the stability P of the algorithm v Not too large, P v Take [0.05,0.2 ]]The effect is optimal.
To further reduce the granularity, mutation operations are refined in the improved method, and mutation gene sites are selected in units of chromosomes instead of whole individuals. The individual performing the mutation operation is S' 1 Specific details of the variation are as follows:
if the mutation site is a site in a dotted line frame, randomly generating [0,2 pi ]]New phase in interval to obtain S 1 ：
2.4, judging whether each individual in the mutated population is subjected to chromosome crossover, if so, carrying out chromosome crossover on the current individual, otherwise, keeping the current individual unchanged, judging whether the next individual is subjected to chromosome crossover, and the like until all the individuals in the population are judged to be finished, and obtaining the population after chromosome crossover.
Further, the determining whether each individual in the mutated population performs segment crossover is specifically: randomly generating a random number rand3 of [0, 1), if rand3 < P cc Then the current individual is subjected to chromosome crossover;
wherein P is cc Is a preset chromosome crossover probability.
Further, the chromosome crossover is specifically: randomly selecting one chromosome of the current individual as a male parent chromosome; randomly selecting one individual from the rest (N-1) individuals as a female parent, taking the position on the female parent corresponding to the male parent chromosome as a female parent chromosome, and exchanging the male parent chromosome with the female parent chromosome to complete the chromosome crossing of the current individual; one chromosome corresponds to each row in the phase encoding matrix.
Individual segment crossover will change the auto-correlation, cross-correlation properties of all waveforms, and in order to increase the diversity of the search, the trend of the optimization process is controlled more finely, and another crossover operation, chromosome crossover, is adopted.
The chromosome crossing is introduced to optimize the original crossing operation, and the 'fragment crossing is mainly used and the chromosome crossing is auxiliary', so that the probability value is smaller. A large amount of priori data show, P cc Take [0.05,0.2 ]]The effect is good.
The male parent individual and the female parent individual are respectively S 1 And S' 2 Randomly selecting one chromosome for chromosome crossing, selecting the first chromosome with the segment in the dotted line frame, and storing S' 1 Line 1 of (C) and replaced by S' 2 Line 1 of (B), denoted S'. 1 ：
At the same time, individual S′ 2 Line 1 of (1) is saved by the last step 1 Line 1 of (B) is denoted as S 2 ：
And 2.5, judging whether the population after chromosome crossing is locally optimized, if so, locally optimizing the population after chromosome crossing, otherwise, switching to the step 2.6.
Further, the judging whether the population after chromosome crossing is locally optimized specifically includes: generating a random number rand4 of [0, 1), if rand4 < P s Then carrying out local optimization; p (P) s The probability is optimized for the preset.
Further, the local optimization of the population after chromosome crossing is specifically as follows: randomly selecting x individuals from the population after chromosome crossing, and optimizing the selected x individuals by adopting sequence quadratic programming to obtain x optimized individuals; x is more than 1 and less than N;
P s take [0.85,0.95 ]]The effect is optimal. The SQP algorithm has local super linear convergence, SQP optimization is introduced into the GA algorithm, so that efficient local optimization of the sub-generation part individuals can be realized, and the overall convergence of the algorithm is improved.
The optimization process for each individual is:
(a) Setting an initial value
The initial value of the iteration times is 0, and the maximum iteration times is SQPiterNum;
(b) The objective function is determined as:
where t is an auxiliary variable, ω is a weighting coefficient, |A (s i K) represents the autocorrelation side lobe peak of the ith waveform, |c(s) p ，s q K) represents the cross correlation peak of the p-th waveform and the q-th waveform;
(c) Solving an optimal solution of the objective function by adopting the fmincon function, and terminating iteration when the iteration number reaches the set maximum iteration number SQPiternum to obtain an optimized individual
Specifically, assume that the optimized individual is s 6 Can be written as
Wherein s is 6 The autocorrelation of the first waveform i can be expressed as:
in order to meet the pulse pressure performance requirement, the self-correlation peak sidelobes of the waveform should be as small as possible, and can be expressed as follows by virtue of an auxiliary variable r
|A(s i ，k)|≤t，k≠0，i＝1，…M
In addition, s 6 The cross-correlation of the p, q two waveforms in (c) can be expressed as:
to meet the orthogonality requirement, the cross-correlation of the waveforms should be as small as possible, again by means of the auxiliary variable t, which can be expressed as:
|C(s p ，s q ，k)|≤t，p≠q，p，q＝1，…M
it can be known that the auxiliary variable t is the upper bound of the side lobe of the auto-correlation and the cross-correlation, and the t is continuously reduced in the optimization process. The SQP algorithm is mainly used to provide the direction of descent, where SQPiterNum is typically chosen 10 to 20 times. So the result of the sqpidernum iteration is the optimized result and is recorded as:
2.6, calculating the fitness value of all individuals in the current population, sorting according to the fitness value, selecting the individual with the largest fitness as the optimal individual in the iteration, directly reserving the optimal individual to enter the next iteration, and selecting the rest (N-1) individuals by adopting a roulette manner to obtain the population after optimization of the current iteration times.
2.7, after the iteration times are added with 1, judging whether the current iteration times reach IterNum, if so, stopping iteration, and outputting the optimal individual in the step 2.6 as an optimized phase encoding matrix; otherwise, go to step 2.2 to perform the next iteration.
The roulette mode is as follows: : a wheel disc is arranged and divided into N parts; the area of the area occupied by each individual on the wheel disc is proportionally divided according to the adaptability of the individual; and rotating the wheel disc, selecting an individual corresponding to the area pointed by the fixed pointer after the wheel disc stops as a first individual, and repeating the operation until the rest (N-1) individuals are selected.
For example, 40 individuals exist in the population, after the optimal individual is selected to enter the next generation, the population individuals of the next generation are 39, and then the 39 individuals are obtained through roulette.
The specific method is that the wheel discs are divided according to the adaptability of 40 individuals in the previous round, one wheel disc is obtained once every rotation, 39 wheels are rotated, 39 individuals are obtained, 40 individuals are obtained together with the previous optimal individuals, and the new population enters the next iteration. After each rotation of the turntable one individual is obtained, the next rotation of the turntable is still the same, i.e. of the 39 individuals obtained after 39 rotations, it is possible to include the same individual several times, since it may be rotated several times.
And step 3, designing orthogonal transmitting waveforms by adopting the optimized phase encoding matrix, and completing the orthogonal waveform design of the MIMO radar.
Further, the calculating the fitness value of all the individuals in the current population is to select the main and side lobe ratio mps r as the fitness function to calculate the fitness of each individual, and the calculating formula is as follows:
MPSR＝-max{APSL，PCCL}
wherein,,
an autocorrelation side lobe peak representing the ith waveform,/->
Autocorrelation sidelobe peak representing orthogonal waveforms, +.>
Representing the peak of the cross correlation of the p-th waveform and the q-th waveform,
representing the cross-correlation peak of the orthogonal waveforms.
In particular, the quality of the quadrature-phase encoded waveform can be measured by APSL and PCCL, and the autocorrelation function of the signal form can be expressed as
Where x represents the conjugate and Σ represents the summation. When l is not 0, A (s i I) is the autocorrelation sidelobes of the waveform i.
The cross-correlation function is expressed as
Wherein p+.q, p, q=1, 2, …, M, C (s p ，s q K) is the cross-correlation side lobe.
In order to have higher resolution performance, the radar can avoid that a large target covers a small target, and the pulse pressure main and side lobe ratio of the waveform is required to be high enough; in addition, in order to avoid the mutual interference of signals between the MIMO radar channels, the signals of different transmitting array elements are required to meet the requirement of low cross correlation. Therefore, the quality of the quadrature-phase code waveform can be measured by an Autocorrelation Peak Sidelobe Level (APSL) and a Peak Cross Correlation Level (PCCL), strict orthogonality means that the autocorrelation is an impulse function and the cross correlation is zero, but due to the constraint of various conditions, the ideal quadrature-phase code waveform does not exist, so that the APSL and the PCCL can be reduced as much as possible when the waveform is designed, and the proper quadrature-phase code optimization criterion can be selected according to different requirements when the waveform is actually applied.
Strict orthogonality means that autocorrelation is an impulse function and cross correlation is zero, but due to constraints of various conditions, ideal quadrature phase code waveforms do not exist, APSL and PCCL can only be reduced as much as possible, suitable quadrature phase code optimization criteria can be selected according to different requirements in practical application,
when the genetic algorithm is used for designing the orthogonal phase code waveforms, one code matrix corresponds to one individual, one population contains a plurality of individuals, so that the genetic algorithm has certain parallelism, each row of the code matrix corresponds to one chromosome, the number of the chromosomes of each individual is the number of orthogonal waveforms to be designed, and the genes correspond to the elements of the matrix one by one. Before executing the algorithm, the population is initialized, and a random value-taking mode is generally adopted. After initialization, iteration is carried out according to the sequence of crossover, mutation and fitness selection, and the optimal solution of the problem is continuously approached.
Simulation experiment
1.1 Parameter setting)
The simulation parameters are shown in table 1.
Table 1 modified GA-SQP algorithm simulation parameter Table
1.2 Simulation content
The method of the invention is adopted to design the MIMO quadrature phase coding waveform, the obtained phase coding sequence is shown in table 2, and the autocorrelation function and the cross correlation function are shown in fig. 2 and 3.
Table 2 design of the phase encoding table of the resulting waveforms
Fig. 2 and3 show graphs of autocorrelation and cross-correlation functions of a phase-coded sequence designed by the improved GA-SQP algorithm of the present invention, respectively, normalized by the abscissa time delay. It can be seen that the APSL is maintained at about-18.47 dB, the main lobe is very narrow, and the side lobes are relatively gentle, because the optimization criterion for minimizing the peak side lobes is adopted, the fitness function of the GA algorithm promotes peak drop, so that the side lobes tend to be consistent. Since the weight is 1, the values of the finally generated phase code sequences PCCL and APSL are identical, and the cross correlation of each code sequence is kept low, indicating good orthogonality.
2.1 Parameter setting)
The parameters adopted for algorithm performance comparison are shown in table 3, and all data are selected in a mode of calculating an average value through multiple simulation in order to ensure objectivity and reality.
TABLE 3 target motion parameter Table
| Parameters (parameters) | Numerical value | Parameters (parameters) | Numerical value |
| Population number N of |
20 | Probability of variation P v | 0.1 |
| Phase encoding length L | 8-48 | SQP |
1 |
| Number of orthogonal waveforms M | 2-3 | SQP iteration |
3 |
| Probability of segment crossing P c | 0.85 | |
10 |
| Chromosome crossover probability P cc | 0.15 | Number of iterations | 100 |
2.2 Simulation content
Fig. 4 shows the performance comparison of the method, GA algorithm and SQP algorithm according to the present invention, with the main and side lobe ratios as reference indices, with the code length taken from 8 to 48. It can be seen from fig. 3 (a) and (b) that the performance of the method of the present invention is improved compared with both GA algorithm and SQP algorithm. Comparing the method and SQP algorithm of the invention can see that when the code length is 16, the main-side lobe ratio difference of the waveforms obtained by the two algorithms is 0.6dB, and when the code length is 48, the main-side lobe ratio difference is increased to 1.2dB, because the SQP algorithm has limited global optimizing capability, and as the code length is increased, the solution space is greatly expanded, the probability of sinking into local optimum is also increased, and finally the difference between the SQP algorithm and the method is increased. In contrast, the performance of the GA algorithm is less affected by the problem scale, and the gap in performance of the GA-SQP algorithm remains within a certain range all the time. As the number of signals becomes larger, the main lobe ratio and the side lobe ratio are reduced, and the algorithm performance comparison result is that the method of the invention is that the GA algorithm is larger than the SQP algorithm.
3.1 Parameter setting)
The simulation parameters are shown in Table 4
Table 4 performance versus simulation parameters table
| Parameters (parameters) | Numerical value | Parameters (parameters) | Numerical value |
| Population number N of |
40 | Probability of variation P v | 0.1 |
| Phase encoding length L | 24 | SQP |
1 |
| Number of orthogonal waveforms M | 2-4 | SQP iteration |
3 |
| Probability of segment crossing P c | 0.85 | |
15 |
| Chromosome crossover probability P cc | 0.15 | Number of |
50 |
3.2 Simulation content
The comparison condition of the convergence rate of the method and the original GA-SQP algorithm is provided, in order to ensure objective and real comparison results, the curve is obtained by carrying out 20 times of averaging by the algorithm, the code length L is 24, and the signal numbers are 2,3 and4 respectively. As shown in fig. 5, the peak sidelobe of the waveform of the improved method is reduced more rapidly than that of the original method, the convergence is better, and the final result obtained by iterating 50 times is better than that of the original algorithm. The invention refines the crossing and mutation operation of the original algorithm, and the optimization process can make more choices, so that lower APSL and PCCL can be obtained, and a group of waveforms with higher main-side lobe ratio and lower cross-correlation can be further designed.
In conclusion, the simulation experiment verifies the correctness, the effectiveness and the reliability of the invention.
While the invention has been described in detail in this specification with reference to the general description and the specific embodiments thereof, it will be apparent to one skilled in the art that modifications and improvements can be made thereto. Accordingly, such modifications or improvements may be made without departing from the spirit of the invention and are intended to be within the scope of the invention as claimed.
Claims (8)
1. The MIMO radar orthogonal waveform design method based on the improved GA-SQP is characterized by comprising the following steps:
step 1, let the number of transmitting array elements of the MIMO radar be M, and the code length be L, then the phase encoding matrix is expressed as:
wherein phi is i (l) Represents the i-th phase of the i-th transmit channel, i=1, … M; the phase coding matrix phi consists of M multiplied by L coding phases, each row of the phase coding matrix is a transmitting channel, and each column represents code elements transmitted by M array elements at the same moment;
step 2, optimizing the phase coding matrix by adopting an improved GA-SQP algorithm to obtain an optimized phase coding matrix;
2.1, setting N individuals in a population, wherein each phase coding matrix corresponds to one individual; randomly initializing each individual in the population, namely randomly taking values between [0,2 pi ] for each element in each phase coding matrix;
2.2, judging whether each individual in the population performs segment crossing, if so, performing segment crossing on the current individual, otherwise, keeping the current individual unchanged, judging whether the next individual performs segment crossing, and so on until all the individuals in the population are judged to be finished, and obtaining the population after segment crossing;
2.3, judging whether each individual in the population after the segment crossing is mutated, if so, mutating the current individual, otherwise, keeping the current individual unchanged, judging whether the next individual is crossed by the segment, and so on until all the individuals in the population are judged to be finished, and obtaining the mutated population;
2.4, judging whether each individual in the mutated population is subjected to chromosome crossover, if so, carrying out chromosome crossover on the current individual, otherwise, keeping the current individual unchanged, judging whether the next individual is subjected to chromosome crossover, and so on until all the individuals in the population are judged to be finished, and obtaining the population after chromosome crossover;
2.5, judging whether the population after the chromosome intersection is locally optimized, if so, locally optimizing the population after the chromosome intersection, otherwise, switching to the step 2.6;
2.6, calculating the fitness value of all individuals in the current population, sorting according to the fitness value, selecting the individual with the largest fitness as the optimal individual in the iteration, directly reserving the optimal individual to enter the next iteration, and selecting the rest (N-1) individuals in a roulette manner to obtain the population after optimization of the current iteration times;
2.7, after the iteration times are added with 1, judging whether the current iteration times reach IterNum, if so, stopping iteration, and outputting the optimal individual in the step 2.6 as an optimized phase encoding matrix; otherwise, turning to step 2.2 for the next iteration;
and step 3, designing orthogonal transmitting waveforms by adopting the optimized phase encoding matrix, and completing the orthogonal waveform design of the MIMO radar.
2. The improved GA-SQP-based MIMO radar orthogonal waveform design method of claim 1, wherein in step 2.2, the determining whether each individual in the population is performingThe segment crossover is specifically: randomly generating a random number rand1 of [0, 1), if rand1 < P c Then segment crossing is carried out on the current individual; wherein P is c The method is a preset fragment crossover probability;
the fragment crossover is specifically: randomly selecting a plurality of continuous gene loci on each chromosome of the current individual as a male parent genetic fragment; and randomly selecting one individual from the remaining (N-1) individuals as a female parent, taking a genetic locus at a position corresponding to the male parent genetic fragment on the female parent as a female parent genetic fragment, and exchanging the male parent genetic fragment with the female parent genetic fragment to finish the fragment intersection of the current individual.
3. The improved GA-SQP-based MIMO radar orthogonal waveform design method according to claim 1, wherein in step 2.3, the determining whether each individual in the population after the segment crossing is mutated is specifically: generating a random number rand2 of [0, 1), if rand2 < P v When the mutation is performed; wherein P is v The variation probability is preset;
the mutation of the current individual is specifically as follows: randomly selecting a locus on each chromosome of the current individual, and changing the gene variation at the selected locus into a new gene randomly generated in [0,2 pi ], thereby completing the variation of the current individual.
4. The method for designing MIMO radar orthogonal waveforms based on improved GA-SQP of claim 1, wherein in step 2.4, the determining whether each individual in the mutated population performs segment crossing is specifically: randomly generating a random number rand3 of [0, 1), if rand3 < P cc Then the current individual is subjected to chromosome crossover; wherein P is cc The chromosome crossover probability is preset;
the chromosome crossover is specifically as follows: randomly selecting one chromosome of the current individual as a male parent chromosome; randomly selecting one individual from the rest (N-1) individuals as a female parent, taking the position on the female parent corresponding to the male parent chromosome as a female parent chromosome, and exchanging the male parent chromosome with the female parent chromosome to complete the chromosome crossing of the current individual; one chromosome corresponds to each row in the phase encoding matrix.
5. The method for designing MIMO radar orthogonal waveforms based on improved GA-SQP according to claim 1, wherein in step 2.5, the determining whether the population after chromosome crossing is locally optimized is specifically: generating a random number rand4 of [0, 1), if rand4 < P s Then carrying out local optimization; p (P) s The optimization probability is preset;
the local optimization of the population after chromosome crossing is specifically as follows: randomly selecting x individuals from the population after chromosome crossing, and optimizing the selected x individuals by adopting sequence quadratic programming to obtain x optimized individuals; x is more than 1 and less than N.
6. The improved GA-SQP based MIMO radar orthogonal waveform design method of claim 5, wherein the optimization process for each individual is:
(a) Setting an initial value
The initial value of the iteration times is 0, and the maximum iteration times is SQPiterNum;
(b) The objective function is determined as:
where t is an auxiliary variable, ω is a weighting coefficient, |A (s i K) represents the autocorrelation side lobe peak of the ith waveform, |c(s) p ，s q K) represents the cross correlation peak of the p-th waveform and the q-th waveform;
(c) Solving an optimal solution of the objective function by adopting the fmincon function, and terminating iteration when the iteration number reaches the set maximum iteration number SQPiternum to obtain an optimized individual
7. The improved GA-SQP-based MIMO radar orthogonal waveform design method of claim 1, wherein the calculating the fitness value of all the individuals in the current population is to select a main-side lobe ratio mps r as a fitness function to calculate the fitness of each individual, and the calculation formula is as follows:
MPSR＝-max{APSL，PCCL}
wherein,,
an autocorrelation side lobe peak representing the ith waveform,/->
Autocorrelation sidelobe peak representing orthogonal waveforms, +.>
Representing the peak of the cross correlation of the p-th waveform and the q-th waveform,
representing the cross-correlation peak of the orthogonal waveforms.
8. The improved GA-SQP based MIMO radar orthogonal waveform design method of claim 1, wherein the roulette scheme is: a wheel disc is arranged and divided into N parts; the area of the area occupied by each individual on the wheel disc is proportionally divided according to the adaptability of the individual; and rotating the wheel disc, selecting an individual corresponding to the area pointed by the fixed pointer after the wheel disc stops as a first individual, and repeating the operation until the rest (N-1) individuals are selected.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202010542057.XA CN111736133B (en) | 2020-06-15 | 2020-06-15 | Orthogonal Waveform Design Method for MIMO Radar Based on Improved GA-SQP |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202010542057.XA CN111736133B (en) | 2020-06-15 | 2020-06-15 | Orthogonal Waveform Design Method for MIMO Radar Based on Improved GA-SQP |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN111736133A CN111736133A (en) | 2020-10-02 |
| CN111736133B true CN111736133B (en) | 2023-06-30 |
Family
ID=72649207
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202010542057.XA Active CN111736133B (en) | 2020-06-15 | 2020-06-15 | Orthogonal Waveform Design Method for MIMO Radar Based on Improved GA-SQP |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN111736133B (en) |
Families Citing this family (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113075623B (en) * | 2021-03-31 | 2024-10-15 | 吉林大学 | MIMO radar orthogonal waveform design method based on quantum particle swarm optimization |
| CN113472400A (en) * | 2021-05-17 | 2021-10-01 | 西安电子科技大学 | SQP-GA-based MIMO orthogonal phase coding waveform generation method |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102353938A (en) * | 2011-07-25 | 2012-02-15 | 电子科技大学 | Method for generating orthogonal phase coded signal |
| WO2018161468A1 (en) * | 2017-03-10 | 2018-09-13 | 东莞理工学院 | Global optimization, searching and machine learning method based on lamarck acquired genetic principle |
-
2020
- 2020-06-15 CN CN202010542057.XA patent/CN111736133B/en active Active
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102353938A (en) * | 2011-07-25 | 2012-02-15 | 电子科技大学 | Method for generating orthogonal phase coded signal |
| WO2018161468A1 (en) * | 2017-03-10 | 2018-09-13 | 东莞理工学院 | Global optimization, searching and machine learning method based on lamarck acquired genetic principle |
Non-Patent Citations (1)
| Title |
|---|
| 基于约束非线性规划的MIMO雷达正交波形设计;胡亮兵;刘宏伟;吴顺君;;系统工程与电子技术(第01期);全文 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN111736133A (en) | 2020-10-02 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| EP3611799A1 (en) | Array element arrangement method for l-type array antenna based on inheritance of acquired characteristics | |
| CN111832219B (en) | Orthogonal waveform design algorithm of MIMO radar based on niche genetic algorithm | |
| CN111736133B (en) | Orthogonal Waveform Design Method for MIMO Radar Based on Improved GA-SQP | |
| CN111143983B (en) | Low side lobe comprehensive optimization method for sparse antenna array based on improved water circulation algorithm | |
| CN107462875B (en) | Cognitive radar maximum MI (maximum MI) waveform optimization method based on IGA-NP (ensemble-nearest neighbor) algorithm | |
| CN104504442A (en) | Neural network optimization method | |
| CN113472400A (en) | SQP-GA-based MIMO orthogonal phase coding waveform generation method | |
| Uray et al. | Metaheuristics-based pre-design guide for cantilever retaining walls | |
| CN110376557B (en) | A Grating Lobe Suppression Method Based on Non-Uniform Nested MIMO Radar | |
| CN104376363B (en) | A kind of multiphase orthogonal code generating method based on improved immune genetic algorithm | |
| Li et al. | Improving the performance of GA–ML DOA estimator with a resampling scheme | |
| CN105093190A (en) | Design method of quadrature phase coding signal | |
| CN106372726B (en) | A kind of MIMO radar orthogonal intersection code signal optimization method based on GASA | |
| CN114675237B (en) | An Optimal Design Method for Inter-Pulse Phase Coding Waveform of Wideband Radar | |
| CN112488831B (en) | Block chain network transaction method and device, storage medium and electronic equipment | |
| CN119719701A (en) | Array antenna sidelobe optimization method and system based on improved crossover genetic algorithm | |
| CN113093146A (en) | Orthogonal waveform design method of MIMO radar based on quantum jump escape mechanism | |
| CN112162243B (en) | Method for generating MIMO radar orthogonal waveform based on DDPG model | |
| CN110910164A (en) | Product sales forecasting method, system, computer device and storage medium | |
| Jiang et al. | Modulation recognition of underwater acoustic communication signals based on neural architecture search | |
| Qi et al. | A distributed subarray position optimization method based on DE-MIFT algorithm | |
| Alden et al. | Eugenic evolution utilizing a domain model | |
| CN115032589B (en) | A method for generating orthogonal waveform of ultrasonic signal based on genetic algorithm | |
| CN120724870B (en) | Radar waveform phase design method based on KAN network | |
| JP2990101B2 (en) | Directional synthesis method for conformal array antenna and medium storing the method |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |