CN104376363B - A kind of multiphase orthogonal code generating method based on improved immune genetic algorithm - Google Patents
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Abstract
A kind of multiphase orthogonal code generating method based on improved immune genetic algorithm of the disclosure of the invention, belongs to radar emission waveform and produces field, be related to a kind of Multiphase Orthogonal Sequences generation method based on improved immune genetic algorithm.First Polyphase Orthogonal Code collection is modeled；Set up initial population；Calculate adaptive weighted coefficient；The selection of genetic algorithm is carried out, is intersected, mutation operation；Calculate individual comentropy H and its similarity A；The renewal of colony；The renewal of mnemon.The method introduces the memory function of immune algorithm, and impact of the growth to multiphase orthogonal code collection performance for sequence number employs follow-up system of selection, so that algorithm has good convergence, the diversity of population is maintained, and has obtained the performance better than conventional algorithm.
Description
Technical field
The invention belongs to radar emission waveform produces field, just it is being related to a kind of multiphase based on improved immune genetic algorithm
Hand over sequence generating method.
Background technology
Orthogonal sequence is widely used in the every field of radar and communications.Multiple-input and multiple-output (multiple-input
Multiple-output, MIMO) radar as a kind of new system, just ground because of its superior performance since the proposition
The extensive concern of the person of studying carefully.Wherein, phased-array radar, synthetic aperture radar etc. are all the special cases of MIMO radar.In MIMO radar,
To avoid interfering between portion's messenger passage, usually require that the signal of MIMO radar transmitting terminal is mutually orthogonal, so sending out
The quality of ejected wave shape affects very big for the detection performance of whole radar.So the optimization of transmitted waveform is also the weight of MIMO radar
Want research direction.For MIMO radar, independent information can be received from each target echo, and is avoided interference, be launched
Signal demand is mutually orthogonal, it is desirable to have poor cross correlation between signal, i.e., orthogonal.And for each transmission signal
For, need signal to have low autocorrelation sidelobe level (ASP).So finding and generating with good auto-correlation and poor mutual
The orthogonal code collection of correlation properties just becomes the particularly important research direction of MIMO radar.
Orthogonal signalling can be designed by phase code, frequency coding two ways, and wherein phase code is divided into many again
Mutually coding and binomial are encoded, and polyphase codes are encoded relative to binomial, generally with bigger main-side lobe ratio, and are had
More complicated signal structure, it is difficult to by place detection, so polyphase codes increasingly become the selection of radar signal.Orthogonal multiphase
The searching and generation problem of code is a combinatorial optimization problem, and the generation method of the Polyphase Orthogonal Code for adopting so far mainly has
Simulated annealing, genetic algorithm, TABU searching algorithms, discrete particle cluster algorithm etc..Wherein, genetic algorithm is used as high parallel
Degree, self adaptation, random global search optimized algorithm, are especially suitable for for generating Polyphase Orthogonal Code.Exist in existing algorithm
That convergence rate is excessively slow, easily occur in optimization process precocious so as to stay in the situation of locally optimal solution.
The content of the invention
Present invention mainly solves be：For the convergence rate mistake existing for the existing method for generating Polyphase orthogonal code
Slowly, the problems such as easily there is precocity so as to stay in locally optimal solution in optimization process, it is proposed that a kind of to be based on improved immunity
The method that genetic algorithm generates Polyphase Orthogonal Code sequence.The method introduces the memory function of immune algorithm, and is directed to sequence
Impact of the growth of number to multiphase orthogonal code collection performance employs follow-up system of selection so that algorithm has good receipts
Holding back property, the diversity of population are maintained, and have obtained the performance better than conventional algorithm.
The technical proposal for solving the technical problem of the invention is：A kind of multiphase based on improved immune genetic algorithm is just
Sequence generating method is handed over, realizes that step is as follows：First Polyphase Orthogonal Code collection is modeled；Set up initial population；Calculate adaptive
Answer weight coefficient；The selection of genetic algorithm is carried out, is intersected, mutation operation；Calculate individual comentropy H and its similarity A；Colony
Renewal；The renewal of mnemon.Specifically include following steps：
Step 1：For a code length is N, signal number is that multiphase code collection S of L is modeled：
Wherein M represents optional phase place；
Step 2：Initial population of the individual sum for S is set up, one is obtained through first encoding to the model that step 1 is set up
Individuality, obtains some other individual, the M system sequences of each individuality for L × N using identical method；
Step 3：Calculate each individual fitness in population；
Step 4：According to each individual adaptation degree that step 3 is obtained, the selection of genetic algorithm is carried out, intersected, mutation operation is obtained
To new population；
Step 5：Each individual comentropy H in new population is calculated, and similarity A is calculated using comentropy, if similarity is big
Step 6, otherwise return to step 3 are entered then in similarity critical value A0；
Step 6：According to similarity by the individuality cluster in population, the ratio of population at individual sum shared by the individual sum of each class
Weight is individual concentration in such, using individual concentration and the polymerization fitness of the fitness COMPREHENSIVE CALCULATING individuality；Then adopt
P new individual is produced with the model based coding in step 1, the individuality sum of step 4 new population is NP, new from new the P for producing
NP individual, the new population of composition is selected according to polymerization fitness during the NP of individual and new population is individual；
Step 7：Setting can store Y individual mnemon, according to polymerization fitness in the new population obtained from step 6
Choose Y individuality to update mnemon, judge whether to reach the evolutionary generation of setting after renewal, step 8 is entered if reaching,
If not up to, return to step 3；
Step 8：Judge whether to reach evolutionary circulation number of times, if not up to evolutionary circulation number of times, newly produce NP-Y newly
Individuality, it is individual with Y in mnemon together with constitute new population, return again to step 3；Export if evolutionary circulation number of times is reached
Optimum individuality；
Step 9：The optimum individual of step 8 output is that code length is N, M phase orthogonal sequence of the yardage for L, using in graph theory
Minimal path shot, the n code composition code length that optimum is selected from yardage L is N, and yardage is the M phase orthogonal sequences of n.
In the step 2, individual sum is 100 for S.
The adaptive weighted coefficient of the step 3 is calculated as follows：
Individual fitness is calculated, fitness function is：
Wherein：
A (φ in formulal, k) and C (φp,φq, k) it is respectively polyphase code sequence SlAperiodic auto-correlation and SpWith SqIt is mutual
Correlation function, the Optimality Criteria for adopting is for minimum autocorrelation peak secondary lobe and cross-correlation peak value and minimizes autocorrelation sidelobe
Energy and cross-correlation energy；
Weight coefficient [w1,w2,w3,w4] be set as, population is ranked up according to the size of adaptive value, and adaptive value is most
Little individuality is standard, sets weight coefficient [w1,w2,w3,w4] the order of magnitude, make four order of magnitude phases in fitness function
When.
The selection of step 4 genetic algorithm, cross compile operation are as follows：
The method selected using order in the selection operation of genetic algorithm；Handed over using single-point in the crossover operation of genetic algorithm
Fork is come individuality of recombinating, and crossover probability is taken as 0.9；Made a variation using single-point in the mutation operation of genetic algorithm.
The step 5 calculates individual information entropy H and similarity A is as follows：
The population of the individual composition in evolutionary process is a uncertain system, is come by the average information entropy H (N) of Shannon
Its degree of irregularity, p are describedijThe probability of the jth position of individual UVR exposure sequence is occurred in for i-th coded sequence, i.e.,：
Hj(N) be j-th gene comentropy, be defined as：
Colony's average information entropy is：
Swarm similarity
Wherein, A (N) characterizes the similarity degree of whole colony, and A (N) is bigger, and colony's similarity degree is higher, various degree
It is lower；
Similarity critical value A0=0.1.
The individuality that similarity is more than 0.9 is gathered for a class in the step 6, obtain each individual concentration Ci, root
Simultaneous adaptation degree is calculated according to individual fitness fitness and concentration, computing formula is：
Fitness'=fitness × exp (k × Ci)
Polymerization fitness is the amendment to individual fitness, and k is constant, takes 0.8 herein；
Then P new individual is produced, the quantity of the new individual of generation is the 40% of population at individual sum.
Half of the individual amount Y of mnemon storage for population at individual sum NP in the step 7.
The concrete grammar of the step 9 is：
If sequence i, the normalized autocorrelation side lobe peak of j is respectively ai, aj, the normalized crosscorrelation peak value of sequence i and j
For cij, then the distance between sequence i and j are ai+aj+cijIf being S by the code collection of L Sequence composition, from L sequence arbitrarily
N sequence is selected, code collection S' is constitutedi(1≤i≤m), wherein m are represented from L sequence, are arbitrarily selected n sequence altogether can
There are m kind systems of selection, i.e.,, calculate each S'iMiddle n sequence between any two apart from sum fi, therefrom select optimum
, i.e. fiN minimum sequence is used as new Polyphase Orthogonal Code collection.
Advantage is the present invention compared with prior art：
1. improved immune genetic algorithm is applied to the present invention generation of Polyphase Orthogonal Code, solves traditional genetic algorithm
The slow and easily precocious problem of convergence rate.
2. the present invention by the number of code length and code to Polyphase Orthogonal Code collection for autocorrelation performance and cross correlation
Impact summary, devise the scheme of second selecting so that the performance of resulting code collection is further optimized.
3. in contrast to most of recent for the document for generating Polyphase Orthogonal Code collection, performance will be more excellent for the present invention
More.
Description of the drawings
Fig. 1 is flow chart of the present invention based on improved immune genetic algorithm；
Fig. 2 be generate code length L=40, sequence number N=4, the autocorrelation of the sequence of optional number of phases M=4.Fig. 2 (a)
For sequence 1, Fig. 2 (b) is sequence 2, and Fig. 2 (c) is sequence 3, and Fig. 2 (d) is sequence 4；
Fig. 3 be generate code length L=40, sequence number N=4, the cross correlation of the sequence of optional number of phases M=4.Fig. 3 (a)
For sequence 1 and the cross correlation of sequence 2, Fig. 3 (b) is the cross correlation of sequence 1 and sequence 3, and Fig. 3 (c) is sequence 1 and sequence 4
Cross correlation, Fig. 3 (d) is the cross correlation of sequence 2 and sequence 3, and Fig. 3 (e) is the cross correlation of sequence 2 and sequence 4, Fig. 3
F () is sequence 3 and the cross correlation of sequence 4,
Convergence curves of the Fig. 4 for algorithm fitness function.Convergence curves of the Fig. 4 (a) for traditional genetic algorithm, Fig. 4 (b) are this
The convergence of algorithm curve of invention, it can be seen that for convergence rate has high lifting.
Specific embodiment
Below in conjunction with the accompanying drawings and specific embodiment is discussed in detail the present invention.
The example that this introduction is adopted is to produce a sequence number for 4 by the method for the present invention, and code length is 40, optional
Number of phases is 4 orthogonal sequence.The flow chart which is implemented is as shown in Figure 1.
Polyphase Orthogonal Code collection is modeled：
Assume that Polyphase Orthogonal Code collection has L sequence, each has N number of subpulse, then signal collection can be expressed as：
If in polyphase codes, available phases number is M, then the phase place of subpulse can only be selected from following phase set：
For a code length is N, signal number is multiphase code collection S of L, can be represented with the phasing matrix of L × N：
Matrix in formula is the object of optimization, contains all information of multiphase code collection S.
Its auto-correlation and cross correlation properties can be expressed as：
A (φ in formulal, k) and C (φp,φq, k) it is respectively polyphase code sequence SlAperiodic auto-correlation and SpWith SqIt is mutual
Correlation function, for radar MIMO Radar Polyphase Code Design problem, adoptable Optimality Criteria for minimize autocorrelation peak secondary lobe and
Cross-correlation peak value and minimum autocorrelation sidelobe energy and cross-correlation energy.
For combinatorial optimization algorithm, fitness function is particularly important.The selection course of optimization is all by suitable
Response function is realizing.So for the optimization of Polyphase Orthogonal Code collection is generated, fitness function can be constructed as：
Four optimal values in formula have the different orders of magnitude, so needing the weight coefficient [w of cost function1,w2,w3,w4]
To be adjusted so that in optimization process, four optimal values can access optimization.
Set up initial population：
For primary response, initial individuals randomly generate (identical with standard genetic algorithm)；And for replying again, then borrow
Help immune memory mechanism, half initial individuals by and a unit obtain, remaining individuality is randomly generated.This test is carried out
Cubic response, wherein randomly generating initial individuals when first secondary response.
Adaptive weighted coefficient is calculated：
Individual fitness is calculated, fitness function is provided by above formula.For the weight coefficient [w in formula1,w2,w3,w4]
Setting, in each response, population is ranked up according to the size of adaptive value, the individuality of adaptive value minimum (i.e. optimum) is
Standard, sets weight coefficient [w1,w2,w3,w4] the order of magnitude, wherein w4=1, added by being divided by with Section 4 respectively afterwards
Weight coefficient.
The selection of genetic algorithm, the concrete operations of cross and variation：
The selection operation of genetic algorithm：According to fitness function, using corresponding selection opertor, the present invention is selected in roulette
It is tested in selecting operator and order selection opertor, order selection opertor performance is slightly better than roulette selection operator, so choosing
The method that order is selected is selected.In order selection algorithm, the select probability of excellent individual is q=0.6, j-th after sequence
The select probability of body is：
The crossover operation of genetic algorithm：This is the important operation in genetic algorithm, for the selection of crossover probability is particularly weighed
Will, the present invention takes single-point to intersect come individuality of recombinating, and crossover probability is taken as 0.9.
The mutation operation of genetic algorithm：By mutation operation, the gene of the individuality in population enters row variation.The present invention takes
Mutation operation be single-point variation, and because being directed to M system code, to the gene point chosen, if its value is m,
M-1 optional phase place, i.e. M optional phase place is removed.The variation behaviour of genetic algorithm
Originally it was the search vigor for keeping population, but if mutation probability is excessive, then it was slack-off to easily cause convergence rate, and
Mutation probability is too low for the great problem of solution space, the generation problem of such as Polyphase Orthogonal Code collection, then easily cause precocity.
Calculate individual information entropy H and similarity A：
The system of the individual composition in evolutionary process is a uncertain system, and degree of irregularity can be by the average information of Shannon
Upper H (N) is describing.pijOccur on locus j for the i-th symbol value of i (in this problem be M optional phase place)
Probability, i.e.,：
Hj(N) be j-th gene comentropy, be defined as：
Entirely the average information entropy of colony is：
Swarm similarity
Wherein, A (N) characterizes the total similarity degree of whole colony, and A (N) is bigger, and colony's similarity degree is higher, Duo Yangcheng
Degree is lower.If swarm similarity A (N)>A0, wherein A0For similarity critical value, then diversity is unsatisfactory for requiring, into step
(6), the optimization in otherwise this generation terminates, into step (4).
The renewal of colony is as follows：
P new individuality is randomly generated, the number for taking P herein is the 40% of individual number NP, individual sum is NP+P,
A bulk concentration and the fitness that is polymerized are calculated, the renewal of colony is carried out based on polymerization fitness.Individual bulk concentration refers to individuality in colony
In the proportion that occupied with its similar individuals, i.e.,：
Wherein λ is similarity constant, typically takes 0.9≤λ≤1.
Polymerization fitness is the result that individual fitness is evaluated with equalization of concentration：
Fitness'=fitness × exp (k × Ci)
Polymerization fitness is the amendment to individual fitness, and k is constant, takes 0.8 herein.
Update mnemon as follows：
The adaptive value of the individuality in newly-generated individuality and mnemon is compared, if better than in mnemon
New individual, then mnemon is updated.This update mode is not only able to greatly increase convergence rate, and with compared with
Good solution group distribution.Determine whether to reach evolution cut-off algebraically after having updated, reach, determine whether to reach evolution number of times, reach
Evolution number of times then exports optimization solution, not up to evolution number of times then return to step 2, return to step 4 if such as not up to ending algebraically.
It is as follows that orthogonal code collection to producing carries out second selecting：
By step before, and multiple mnemon renewal is carried out, the code length of generation is N, and yardage is L0M phases just
Sequence is handed over, using the minimal path shot in graph theory, can be from sequence number L0In select optimum L code, it is new so as to constitute
Polyphase Orthogonal Code collection, compared to n code is directly generated, possesses more excellent performance.The specifically chosen method for using is as follows：
If sequence i, the normalized autocorrelation side lobe peak of j is respectively ai, aj, the normalized crosscorrelation peak value of sequence i and j
For cij, then the distance between sequence i and j are ai+aj+cijIf being S by the code collection of L Sequence composition, from L sequence arbitrarily
N sequence is selected, code collection S' is constitutedi(1≤i≤m), wherein m are represented from L sequence, are arbitrarily selected n sequence altogether can
There are m kind systems of selection, i.e.,, calculate each S'iMiddle n sequence between any two apart from sum fi, therefrom select optimum
, i.e. fiN minimum sequence is used as new Polyphase Orthogonal Code collection.
Code length N=40 is optimized by algorithm above in realization, sequence number L=4, optional number of phases M=4 it is orthogonal many
Phase code collection, during parameter is selected, takes L0=16, evolutionary generation was 100 generations, and the number of times of evolution is 3, the orthogonal sequence for drawing from phase
Pass function and cross-correlation function are as shown in Figures 2 and 3.The convergence curve of the convergence curve and inventive algorithm of traditional genetic algorithm
As shown in Figure 4.As shown in table 1, performance passes through the maximum of normalized autocorrelation functions and returns the performance of the orthogonal sequence for obtaining
The maximum of one change cross-correlation function is represented.Sequence obtained by the present invention and the parameter identical produced by recent pertinent literature
The performance comparison of sequence such as table 2, wherein ASP represent autocorrelation sidelobe peak value, and CP represents cross-correlation peak value.
The N=40 that 1 inventive algorithm of table is generated, the Polyphase Orthogonal Code sequence performance of L=4, M=4
The Performance comparision of 2 various algorithms of table
Claims (6)
1. a kind of multiphase orthogonal code generating method based on improved immune genetic algorithm, the method include：
Step 1：For a code length is N, signal number is that multiphase code collection S of L is modeled：
Wherein M represents optional phase place；
Step 2：Initial population of the individual sum for S is set up, the model that step 1 is set up is obtained one by one through first encoding
Body, obtains some other individual, the M system sequences of each individuality for L × N using identical method；
Step 3：Calculate each individual fitness in population；
Step 4：According to each individual adaptation degree that step 3 is obtained, the selection of genetic algorithm is carried out, intersected, mutation operation, obtain new
Population；
Step 5：Each individual comentropy H in new population is calculated, similarity A is calculated using comentropy, if similarity is more than phase
Like degree critical value A0Step 6, otherwise return to step 3 are entered then；
Step 6：According to similarity by the individuality cluster in population, shared by the individual sum of each class, the proportion of population at individual sum is
Individual concentration in such, using individual concentration and the polymerization fitness of the fitness COMPREHENSIVE CALCULATING individuality；Then using step
Model based coding in rapid 1 produces P new individual, and the individuality sum of step 4 new population is NP, from the new P new individual for producing
NP individual, the new population of composition is selected according to polymerization fitness in individual with the NP of new population；
Step 7：Setting can store Y individual mnemon, be chosen according to polymerization fitness in the new population obtained from step 6
Y individuality judges whether to reach the evolutionary generation of setting after renewal updating mnemon, enters step 8, if not if reaching
Reach, then return to step 3；
Step 8：Judge whether to reach evolutionary circulation number of times, if not up to evolutionary circulation number of times, newly produce NP-Y new
Body, it is individual with Y in mnemon together with constitute new population, return again to step 3；Export most if evolutionary circulation number of times is reached
Excellent individuality；
Step 9：The optimum individual of step 8 output is that code length is N, M phase orthogonal sequence of the yardage for L, using the minimum in graph theory
Path method, the n code composition code length that optimum is selected from yardage L is N, and yardage is the M phase orthogonal sequences of n.
2. a kind of multiphase orthogonal code generating method based on improved immune genetic algorithm as claimed in claim 1, its feature
It is that individual sum is 100 for S in the step 2.
3. a kind of multiphase orthogonal code generating method based on improved immune genetic algorithm as claimed in claim 1, its feature
It is that the adaptive weighted coefficient of the step 3 is calculated as follows：
Individual fitness is calculated, fitness function is：
Wherein：
A (φ in formulal, k) and C (φp,φq, k) it is respectively polyphase code sequence SlAperiodic auto-correlation and SpWith SqCross-correlation
Function, the Optimality Criteria for adopting is for minimum autocorrelation peak secondary lobe and cross-correlation peak value and minimizes autocorrelation sidelobe energy
With cross-correlation energy；
Weight coefficient [w1,w2,w3,w4] be set as, population is ranked up according to the size of adaptive value, adaptive value it is minimum
Body is standard, sets weight coefficient [w1,w2,w3,w4] the order of magnitude, make four orders of magnitude in fitness function suitable.
4. a kind of multiphase orthogonal code generating method based on improved immune genetic algorithm as claimed in claim 1, its feature
It is the selection of step 4 genetic algorithm, cross compile operates as follows：
The method selected using order in the selection operation of genetic algorithm；In the crossover operation of genetic algorithm using single-point intersect come
Restructuring is individual, and crossover probability is taken as 0.9；Made a variation using single-point in the mutation operation of genetic algorithm；
The step 5 calculates individual information entropy H and similarity A is as follows：
The population of the individual composition in evolutionary process is a uncertain system, is described by the average information entropy H (N) of Shannon
Its degree of irregularity, pijThe probability of the jth position of individual UVR exposure sequence is occurred in for i-th coded sequence, i.e.,：
Hj(N) be j-th gene comentropy, be defined as：
Colony's average information entropy is：
Swarm similarity
Wherein, A (N) characterizes the similarity degree of whole colony, and A (N) is bigger, and colony's similarity degree is higher, and various degree is got over
It is low；
Similarity critical value A0=0.1.
5. a kind of multiphase orthogonal code generating method based on improved immune genetic algorithm as claimed in claim 1, its feature
It is to gather the individuality that similarity is more than 0.9 for a class in the step 6, obtains each individual concentration Ci, according to individual
The fitness fitness of body and concentration calculate simultaneous adaptation degree, and computing formula is：
Fitness'=fitness × exp (k × Ci)
Polymerization fitness is the amendment to individual fitness, and k is constant, takes 0.8 herein；
Then P new individual is produced, the quantity of the new individual of generation is the 40% of population at individual sum；
Half of the individual amount Y of mnemon storage for population at individual sum NP in the step 7.
6. a kind of multiphase orthogonal code generating method based on improved immune genetic algorithm as claimed in claim 1, its feature
It is that the concrete grammar of the step 9 is：
If sequence i, the normalized autocorrelation side lobe peak of j is respectively ai, aj, sequence i is c with the normalized crosscorrelation peak value of jij,
Then the distance between sequence i and j are ai+aj+cijIf being S by the code collection of L Sequence composition, n is arbitrarily selected from L sequence
Individual sequence, constitutes code collection S'i(1≤i≤m), wherein m are represented from L sequence, are arbitrarily selected n sequence have altogether m kinds
System of selection, i.e.,Calculate each S'iMiddle n sequence between any two apart from sum fi, optimum is therefrom selected, i.e.,
fiN minimum sequence is used as new Polyphase Orthogonal Code collection.
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