CN104376363B - A kind of multiphase orthogonal code generating method based on improved immune genetic algorithm - Google Patents

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

A Method for Generating Polyphase Orthogonal Codes Based on Improved Immune Genetic Algorithm

technical field

The invention belongs to the field of radar emission waveform generation, and relates to a multiphase orthogonal sequence generation method based on an improved immune genetic algorithm.

Background technique

Orthogonal sequences are widely used in various fields of radar and communication. Multiple-input multiple-output (MIMO) radar, as a new system, has been widely concerned by researchers because of its superior performance since it was proposed. Among them, phased array radar and synthetic aperture radar are special cases of MIMO radar. In MIMO radar, in order to avoid mutual interference between communication signal channels, the signals at the transmitting end of MIMO radar are usually required to be orthogonal to each other, so the quality of the transmitting waveform has a great influence on the detection performance of the entire radar. Therefore, the optimization of transmitting waveform is also an important research direction of MIMO radar. For MIMO radar, independent information can be received from each target echo, and interference can be avoided. The transmitted signals need to be orthogonal to each other, and the signals are required to have poor cross-correlation, that is, they are orthogonal to each other. And for each transmitted signal, it is required that the signal has a low autocorrelation sidelobe level (ASP). Therefore, finding and generating orthogonal code sets with good autocorrelation and poor cross-correlation characteristics has become an extremely important research direction for MIMO radars.

Orthogonal signals can be designed by phase encoding and frequency encoding. Phase encoding is divided into polyphase encoding and binomial encoding. Compared with binomial encoding, polyphase encoding generally has a larger main-sidelobe ratio. , and has a more complex signal structure, which is difficult to be detected locally, so polyphase encoding is increasingly becoming the choice of radar signals. The problem of finding and generating orthogonal polyphase codes is a combinatorial optimization problem. So far, the generation methods of orthogonal polyphase codes mainly include simulated annealing algorithm, genetic algorithm, TABU search algorithm, discrete particle swarm optimization algorithm and so on. Among them, the genetic algorithm is a high-parallel, self-adaptive, random global search optimization algorithm, which is very suitable for generating orthogonal polyphase codes. In the existing algorithm, the convergence speed is too slow, and the optimization process tends to be premature and stay in the local optimal solution.

Contents of the invention

The main solution of the present invention is: in view of the existing methods for generating polyphase orthogonal codes, the convergence speed is too slow, and the optimization process tends to be precocious and stay in the local optimal solution, etc., and proposes an improved A method for generating orthogonal polyphase code sequences by immune genetic algorithm. This method introduces the memory function of the immune algorithm, and adopts a subsequent selection method for the impact of the increase in the number of sequences on the performance of polyphase orthogonal code sets, so that the algorithm has good convergence and the diversity of the population is maintained. And get better performance than previous algorithms.

The technical scheme adopted by the present invention to solve the technical problem is: a polyphase orthogonal sequence generation method based on the improved immune genetic algorithm, and the realization steps are as follows: first, the orthogonal polyphase code set is modeled; the initial population is established; Adapt to the weighting coefficient; perform genetic algorithm selection, crossover, and mutation operations; calculate the individual information entropy H and its similarity A; update the population; update the memory unit. Specifically include the following steps:

Step 1: Model a polyphase code set S with code length N and number of signals L:

Where M represents an optional phase;

Step 2: Establish an initial population with a total number of individuals of S, encode the model established in step 1 once to obtain an individual, and use the same method to obtain several other individuals, each individual is an M-ary sequence of L×N;

Step 3: Calculate the fitness of each individual in the population;

Step 4: According to the fitness of each individual obtained in step 3, perform genetic algorithm selection, crossover, and mutation operations to obtain a new population;

Step 5: Calculate the information entropy H of each individual in the new population, use the information entropy to calculate the similarity A, if the similarity is greater than the similarity critical value A0, go to step 6, otherwise return to step 3;

Step 6: Cluster the individuals in the population according to the similarity, the proportion of the total number of individuals in each category to the total number of individuals in the population is the concentration of individuals in this category, and use the concentration and fitness of individuals to comprehensively calculate the aggregation fitness of the individual; Then use the model coding in step 1 to generate P new individuals, the total number of individuals in the new population in step 4 is NP, select NP individuals from the newly generated P new individuals and the NP individuals of the new population according to the aggregation fitness, and form new species;

Step 7: Set up a memory unit that can store Y individuals, select Y individuals from the new population obtained in step 6 according to the aggregation fitness to update the memory unit, and judge whether the set evolutionary algebra has been reached after updating, and if so, enter the step 8. If not reached, return to step 3;

Step 8: Determine whether the number of evolutionary cycles has been reached. If the number of evolutionary cycles has not been reached, NP—Y new individuals will be newly generated to form a new population with Y individuals in the memory unit, and then return to step 3; if the number of evolutionary cycles is reached Then output the best individual;

Step 9: The optimal individual output in step 8 is an M-phase orthogonal sequence with a code length of N and a code number of L. Using the minimum path method in graph theory, select the optimal n codes from the code number L An M-phase orthogonal sequence with a code length of N and a number of codes of n.

The total number of individuals in step 2 is S is 100.

The step 3 adaptive weighting coefficient is calculated as follows:

Calculate the fitness of the individual, and the fitness function is:

in:

where A(φ _l , k) and C(φ _p ,φ _q ,k) are the aperiodic autocorrelation function of polyphase code sequence S _l and the cross-correlation function of S _p and S _q respectively, and the optimization criterion adopted is the minimum Maximize autocorrelation peak sidelobe and cross-correlation peak and minimize autocorrelation sidelobe energy and cross-correlation energy;

The weighting coefficient [w ₁ ,w ₂ ,w ₃ ,w ₄ ] is set to sort the population according to the size of the fitness value, the individual with the smallest fitness value is the standard, and the weighting coefficient [w ₁ ,w ₂ ,w ₃ , w ₄ ], so that the four items in the fitness function have the same magnitude.

The selection of the genetic algorithm in step 4, the cross-compilation operation is as follows:

The method of sequential selection is adopted in the selection operation of the genetic algorithm; the single-point crossover is used in the crossover operation of the genetic algorithm to recombine individuals, and the crossover probability is taken as 0.9; the single-point mutation is used in the mutation operation of the genetic algorithm.

The step 5 calculates the individual information entropy H and similarity A as follows:

The population composed of individuals in the evolution process is an uncertain system, and its irregularity is described by Shannon's average information entropy H(N), p _ij is the i-th coding sequence that appears in the j-th position of the individual coding sequence probability, that is:

H _j (N) is the information entropy of the jth gene, defined as:

The average information entropy of the group is:

group similarity

Among them, A(N) represents the degree of similarity of the entire group, the larger the A(N), the higher the degree of group similarity and the lower the degree of diversity;

Similarity critical value A ₀ =0.1.

In the step 6, individuals with a similarity of 0.9 or more are grouped into one group, the concentration C _i of each individual is obtained, and the joint fitness is calculated according to the fitness and concentration of the individual, and the calculation formula is:

fitness'=fitness×exp(k×C _i )

Aggregate fitness is the correction of individual fitness value, k is a constant, 0.8 is taken in this paper;

Then P new individuals are generated, and the number of new individuals generated is 40% of the total number of individuals in the population.

The number of individuals Y stored in the memory unit in step 7 is half of the total number of individuals in the population NP.

The concrete method of described step 9 is:

Let the normalized autocorrelation side lobe peaks of sequence i and j be a _i , a _j respectively, and the normalized cross-correlation peak value of sequence i and j be c _ij , then the distance between sequence i and j is a _i + a _j +c _ij , let the code set composed of L sequences be S, randomly select n sequences from the L sequences to form a code set S' _i (1≤i≤m), where m means from the L sequences There can be a total of m selection methods for arbitrarily selecting n sequences in , that is, , calculate the sum of the distances f _i between each pair of n sequences in each S' _i , and select the optimal n sequences with the smallest f _i as a new orthogonal polyphase code set.

Compared with the prior art, the present invention has the advantages that:

1. The present invention applies the improved immune genetic algorithm to the generation of orthogonal polyphase codes, which solves the problems of slow convergence and premature maturity of the traditional genetic algorithm.

2. The present invention designs the scheme of secondary selection by summarizing the influence of the code length and the number of codes of orthogonal polyphase code sets on autocorrelation characteristics and cross-correlation characteristics, so that the performance of the obtained code sets can be obtained further optimization.

3. Compared with most recent literatures for generating orthogonal polyphase code sets, the performance of the present invention is superior.

Description of drawings

Fig. 1 is the flow chart based on the improved immune genetic algorithm of the present invention;

Fig. 2 shows the autocorrelation of the generated sequence with code length L=40, sequence number N=4, and optional phase number M=4. Figure 2(a) is sequence 1, Figure 2(b) is sequence 2, Figure 2(c) is sequence 3, and Figure 2(d) is sequence 4;

Fig. 3 shows the cross-correlation of the generated sequence with code length L=40, sequence number N=4, and optional phase number M=4. Figure 3(a) is the cross-correlation between sequence 1 and sequence 2, figure 3(b) is the cross-correlation between sequence 1 and sequence 3, figure 3(c) is the cross-correlation between sequence 1 and sequence 4, figure 3 (d) is the cross-correlation between sequence 2 and sequence 3, Fig. 3(e) is the cross-correlation between sequence 2 and sequence 4, Fig. 3(f) is the cross-correlation between sequence 3 and sequence 4,

Figure 4 is the convergence curve of the algorithm fitness function. Fig. 4(a) is the convergence curve of the traditional genetic algorithm, and Fig. 4(b) is the convergence curve of the algorithm of the present invention, it can be seen that the convergence speed is greatly improved.

specific embodiment

The present invention will be described in detail below in conjunction with the accompanying drawings and specific embodiments.

The example used in this introduction is to use the method of the present invention to generate an orthogonal sequence with 4 sequences, 40 code lengths and 4 optional phases. The flow chart of its implementation is shown in Figure 1.

Model an orthogonal polyphase codeset:

Assuming that the orthogonal polyphase code set has L sequences, each with N sub-pulses, then the signal set can be expressed as:

If the number of phases available in polyphase encoding is M, then the phase of the sub-pulse can only be selected from the following phase sets:

For a polyphase code set S whose code length is N and the number of signals is L, it can be represented by an L×N phase matrix:

The matrix in the formula is the optimized object, which contains all the information of the polyphase code set S.

Its autocorrelation and cross-correlation properties can be expressed as:

where A(φ _l ,k) and C(φ _p ,φ _q ,k) are the aperiodic autocorrelation function of the polyphase code sequence S _l and the cross-correlation function of S _p and S _q respectively. For radar quadrature polyphase For the code design problem, the optimization criterion that can be adopted is to minimize the autocorrelation peak sidelobe and cross-correlation peak and minimize the autocorrelation sidelobe energy and cross-correlation energy.

For combinatorial optimization algorithms, the fitness function is extremely important. The optimal selection process is realized through the fitness function. So for the optimal generation of orthogonal polyphase code sets, the fitness function can be constructed as:

The four optimal values in the formula have different orders of magnitude, so the weighting coefficients [w ₁ , w ₂ , w ₃ , w ₄ ] of the cost function are needed to adjust, so that the four optimal values can be optimized during the optimization process.

Create an initial population:

For the first response, the initial individuals are randomly generated (same as the standard genetic algorithm); for the second response, with the help of the memory mechanism of the immune system, half of the initial individuals are obtained by the first unit, and the rest are randomly generated. In this experiment, three responses were performed, and the initial individuals were randomly generated during the first response.

Calculation of adaptive weighting coefficients:

Calculate the fitness of the individual, and the fitness function is given by the above formula. For the setting of the weighting coefficient [w ₁ , w ₂ , w ₃ , w ₄ ] in the formula, the population is sorted according to the size of the fitness value at each response, and the individual with the smallest fitness value (that is, the best) is Standard, set the magnitude of the weighting coefficient [w ₁ , w ₂ , w ₃ , w ₄ ], where w ₄ =1, and then obtain the weighting coefficient by dividing it with the fourth term respectively.

The selection of genetic algorithm, the specific operation of cross mutation:

The selection operation of the genetic algorithm: according to the fitness function, the corresponding selection operator is adopted. The present invention is tested in the roulette selection operator and the sequence selection operator, and the performance of the sequence selection operator is slightly better than that of the roulette selection operator. child, so the method of sequential selection was chosen. In the sequential selection algorithm, the selection probability of an excellent individual is q=0.6, and the selection probability of the jth individual after sorting is:

Crossover operation of genetic algorithm: this is an important operation in genetic algorithm, especially important for the selection of crossover probability. The present invention adopts single-point crossover to recombine individuals, and the crossover probability is taken as 0.9.

Mutation operation of genetic algorithm: Through mutation operation, the genes of individuals in the population are mutated. The mutation operation adopted by the present invention is a single-point mutation, and because it is coded for M-ary, so for the selected gene point, if its value is m, then in the M-1 optional phases, that is, the M optional phases remove m A point is randomly selected as its new value. The mutation operation of the genetic algorithm is originally used to maintain the search vitality of the population, but if the mutation probability is too large, it is easy to cause the convergence speed to slow down, and the mutation probability is too low for problems with a large solution space, such as orthogonal polyphase code sets The formation problem of the child is likely to cause premature maturity.

Calculate individual information entropy H and similarity A:

The system composed of individuals in the evolution process is an uncertain system, and the degree of irregularity can be described by Shannon's average information H(N). p _ij is the probability that the i-th symbol (in this question, the value of i is M optional phases) appears on the locus j, namely:

H _j (N) is the information entropy of the jth gene, defined as:

The average information entropy of the whole group is:

group similarity

Among them, A(N) represents the overall similarity degree of the entire group, and the larger A(N) is, the higher the similarity degree of the group is, and the lower the degree of diversity is. If the group similarity A(N)>A ₀ , where A ₀ is the critical value of similarity, then the diversity does not meet the requirements and go to step (6); otherwise, the optimization of this generation ends and go to step (4).

The groups are updated as follows:

Randomly generate P new individuals. In this paper, the number of P is 40% of the number of individuals NP, and the total number of individuals is NP+P. The individual concentration and aggregation fitness are calculated, and the group is updated based on the aggregation fitness. Individual concentration refers to the proportion of an individual in the group and its similar individuals, that is:

Where λ is a similarity constant, generally 0.9≤λ≤1.

Aggregate fitness is the result of individual fitness and concentration equilibrium evaluation:

fitness'=fitness×exp(k×C _i )

Aggregate fitness is the correction of individual fitness value, k is a constant, 0.8 is taken in this paper.

Update the memory unit as follows:

Compare the fitness value of the newly generated individual with the individual in the memory unit, if there is better than the new individual in the memory unit, the memory unit will be updated. This update method can not only greatly increase the convergence speed, but also has a better solution group distribution. After updating, determine whether the cut-off algebra of evolution has been reached. If reached, determine whether the number of evolution has been reached. If the number of evolution is reached, the optimal solution will be output. If the number of evolution has not been reached, return to step 2. If the cut-off algebra has not been reached, return to step 4.

The secondary selection of the generated orthogonal code set is as follows:

Through the previous steps and multiple memory unit updates, the generated M-phase orthogonal sequence with a code length of N and a code number of L ₀ can be selected from the sequence number L ₀ by using the minimum path method in graph theory The optimal L codes are used to form a new orthogonal polyphase code set, which has better performance than directly generating n codes. The specific selection method used is as follows:

Let the normalized autocorrelation side lobe peaks of sequence i and j be a _i , a _j respectively, and the normalized cross-correlation peak value of sequence i and j be c _ij , then the distance between sequence i and j is a _i + a _j +c _ij , let the code set composed of L sequences be S, randomly select n sequences from the L sequences to form a code set S' _i (1≤i≤m), where m means from the L sequences There can be a total of m selection methods for arbitrarily selecting n sequences in , that is , calculate the sum of the distances f _i between each pair of n sequences in each S' _i , and select the optimal n sequences with the smallest f _i as a new orthogonal polyphase code set.

In the implementation, the code length N=40, the number of sequences L=4, and the number of optional phases M=4 are optimized through the above algorithm. In the parameter selection, L ₀ =16, and the evolution algebra is 100 generations , the number of evolutions is 3, and the autocorrelation function and cross-correlation function of the obtained orthogonal sequence are shown in Figure 2 and Figure 3. The convergence curve of the traditional genetic algorithm and the convergence curve of the algorithm of the present invention are shown in FIG. 4 . The performance of the obtained orthogonal sequence is shown in Table 1, and the performance is represented by the maximum value of the normalized autocorrelation function and the maximum value of the normalized cross-correlation function. The performance comparison of the sequence obtained by the present invention and the sequence with the same parameters as those produced by recent related literature is shown in Table 2, where ASP represents the peak value of the autocorrelation sidelobe, and CP represents the peak value of the cross-correlation.

Table 1 The performance of N=40, L=4, M=4 orthogonal polyphase code sequence generated by the algorithm of the present invention

Table 2 Performance comparison of various algorithms

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：

$A({\mathrm{\&phi;}}_l,k)=\left\{\begin{array}{cc}\frac{1}{N}\underset{n=1}{\overset{N-k}{\&Sigma;}}\exp \left\{j\&lsqb;{\mathrm{\&phi;}}_l\left(n\right)-{\mathrm{\&phi;}}_l\left(n+k\right)\&rsqb;\right\}& 0<k<N\\ \frac{1}{N}\underset{n=-k+1}{\overset{N}{\&Sigma;}}\exp \left\{j\&lsqb;{\mathrm{\&phi;}}_l\left(n\right)-{\mathrm{\&phi;}}_l\left(n+k\right)\&rsqb;\right\}& -N<k<0\end{array}\right\},l=1,2,\mathrm{...},L$

$C({\mathrm{\&phi;}}_p,{\mathrm{\&phi;}}_q,k)=\left\{\begin{array}{cc}\frac{1}{N}\underset{n=1}{\overset{N-k}{\&Sigma;}}\exp j\&lsqb;{\mathrm{\&phi;}}_p\left(n\right)-{\mathrm{\&phi;}}_q\left(n+k\right)\&rsqb;& 0<k<N\\ \frac{1}{N}\underset{n=-k+1}{\overset{N}{\&Sigma;}}\exp j\&lsqb;{\mathrm{\&phi;}}_p\left(n\right)-{\mathrm{\&phi;}}_q\left(n+k\right)\&rsqb;& -N<k<0\end{array}\right\},\left(\begin{array}{c}p\&NotEqual;q\\ p,q=1,2,\mathrm{...},L\end{array}\right)$

A (φ in formula_l, k) and C (φ_p,φ_q, k) it is respectively polyphase code sequence S_lAperiodic auto-correlation and S_pWith S_qCross-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, p_ijThe probability of the jth position of individual UVR exposure sequence is occurred in for i-th coded sequence, i.e.,：

H_j(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 C_i, according to individual The fitness fitness of body and concentration calculate simultaneous adaptation degree, and computing formula is：

Fitness'=fitness × exp (k × C_i)

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 a_i, a_j, sequence i is c with the normalized crosscorrelation peak value of j_ij, Then the distance between sequence i and j are a_i+a_j+c_ijIf 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 f_i, optimum is therefrom selected, i.e., f_iN minimum sequence is used as new Polyphase Orthogonal Code collection.