CN108694390B - Modulation signal classification method for cuckoo search improved wolf optimization support vector machine - Google Patents

Abstract

The invention discloses a modulated signal classification method for cuckoo search and improved gray wolf optimization support vector machine, wherein the method selects high-order cumulant and local mean decomposition approximate entropy for characteristic parameters of modulated signals, and uses cuckoo Search and update the position of the wolf pack twice to optimize the two key parameters of the least squares support vector machine model, the penalty coefficient γ and the kernel parameter σ, so as to obtain the optimal kernel extreme learning machine parameter value. The method involved in the present invention reduces noise The influence of factors on the signal recognition results makes up for the defects of under-envelope, over-envelope and boundary effects in the traditional modal empirical decomposition, and effectively improves the weak global search ability of gray wolf optimization, which is easy to fall into when dealing with high-dimensional data. The shortcomings of the local optimal solution are compared with the optimization results of the original gray wolf through MATLAB simulation, and it is proved that the invention can intelligently classify the modulated signal more efficiently and accurately, and has a good application prospect.

Description

A Modulated Signal Classification Method Based on Cuckoo Search and Improved Grey Wolf Optimized Support Vector Machine

technical field

The invention relates to the field of modulation signal classification and swarm intelligence optimization, in particular to a modulation signal classification method for cuckoo search and improved gray wolf optimization support vector machine.

Background technique

Signal modulation mode identification refers to identifying the modulation mode and various parameters of each signal in the environment of multi-modulated signals and noise interference. In general, the receiver can only intercept signals whose prior knowledge is unknown, so it becomes more and more important to effectively identify the modulation method of the signal.

In the published literature related to modulation identification, the intelligent identification of signals can be roughly divided into two types: the most likely hypothesis testing method based on decision theory and the statistical pattern classification and identification method based on feature extraction. When solving the modulation signal classification problem, the biggest feature of the former is that the waveform of the signal to be classified needs to be observed, and then it is assumed to be one of the candidate modulation methods, and then the similarity judgment is performed according to the selected decision threshold to determine the signal to be classified. In the latter, the characteristic parameters of the received signal need to be extracted first, and then the signal type is determined by the pattern recognition system. Generally, the pattern recognition framework of modulated signal mainly includes three main modules: signal preprocessing, feature parameter extraction and classifier. The research field of the present invention focuses on the classifier module, and the quality of the classifier will be directly related to the correct rate of recognition. There are three popular classifier design structures: the recognition method based on decision tree theory, the method based on support vector machine and the recognition method based on neural network.

Support Vector Machine (SVM) is an advanced pattern recognition method based on minimum empirical risk theory and VC dimension theory. SVM has the property of minimizing structural statistics, which is beneficial to deal with nonlinear, small sample, and high-dimensional pattern recognition problems.

Least Squares Support Vector Machine (LSSVM) is an improvement over the standard SVM. Different from the inequality constraints adopted by the standard SVM, the LSSVM adopts the equality constraints to obtain a linear equation system, which greatly simplifies the calculation process, reduces the calculation cost, and makes the support vector machine easier to train. The penalty coefficients and kernel parameters in the LSSVM model are collectively referred to as hyperparameters. The above analysis shows that the establishment of the LSSVM estimation model is the problem of the selection of hyperparameters. Improper selection of hyperparameters will reduce the credibility of the prediction results. The choice of appropriate parameters plays a decisive role in the estimation accuracy and complexity of the model.

Grey Wolf Optimization (GWO) is inspired by the intelligent behavior of grey wolf packs living in Eurasia. GWO mainly simulates the leadership hierarchy and hunting mechanism of wolves in nature, and divides wolves into four types by simulating the leadership hierarchy of wolves, as shown in Figure 1. α, β, δ are regarded as the top three wolves with the best performance (the best fitness) in the wolf pack, and they guide the other wolves (ω) towards the best region in the search space (the global with the solving problem). Optimal solution). In the whole iterative search process, three kinds of wolves, α, β, and δ, are used to predict and evaluate the possible location of the prey, that is, jump to the key group through trend search—individuals with high fitness value.

The optimization process of GWO is: randomly generate a group of gray wolves in the search space. During the evolution process, α, β, δ are responsible for evaluating the position of the prey (global optimal solution), and the rest of the individuals in the group take this as the The standard calculates the distance between itself and the prey, and completes the behavior of approaching, encircling, and attacking the prey in all directions, and finally captures the prey. The defect of this position update method of GWO is very obvious: the global search ability is weak, and there is a high probability of falling into the local optimal solution, especially when using high-dimensional data.

The idea of cuckoo search (CS) is based on the parasitic feeding mechanism and Levi flight of a specific population of cuckoos. Studies have shown that cuckoo search does not need to perform multiple matching of parameters in solving optimization problems, and has the advantages of fewer parameters and easy to set. realization and other advantages. The initial solution of the cuckoo search represents the existing eggs in the host bird’s nest, and the new solution generated by the cuckoo search represents the location of the cuckoo’s eggs. The final implementation needs to be based on the following three assumptions:

1. The cuckoo randomly selects the host bird's nest to lay eggs, and the cuckoo only lays one egg at a time, that is, only one is allowed in the end;

2. The optimal host bird's nest and its cuckoo eggs with the highest priority (the optimal solution) are reserved for the next iteration;

3. The host bird decides whether to find cuckoo eggs according to the probability P _a , and if found, either discard the eggs and keep the nest, or abandon the bird and rebuild a new nest elsewhere. P _a ∈ [0, 1] is a transition probability through which the third hypothesis can be estimated.

According to the above three assumptions, the nesting path and position update of cuckoo can be deduced. Based on the above rules, it can be seen that when the cuckoo search updates the position of the host bird's nest, it is mainly realized through the two operations of fostering behavior and Levi's flight, so the cuckoo search step length is almost equal to the probability of long or short, and the direction of the movement is different. The choice is highly random. In addition, cuckoo search makes it easier to jump from the current area to other areas to complete a global search.

From the above background analysis, it can be seen that in the process of pattern recognition and classification of modulated signals, what plays a key role in the quality of the classification results is whether it is possible to find a kind of strong search ability and high efficiency, and the result is not easy due to the high complexity of the data. The method of getting stuck in a local optimal solution determines the hyperparameters in the least squares support vector machine estimation model.

SUMMARY OF THE INVENTION

Purpose of the invention: In view of the above problems in the prior art, the present invention proposes a method combining cuckoo search and gray wolf optimization to determine the hyperparameters in the least squares support vector machine estimation model. has a good classification effect.

Technical scheme: In order to realize the purpose of the present invention, the technical scheme adopted in the present invention is: a modulated signal classification method of cuckoo search and improved gray wolf optimization support vector machine, including training phase and testing phase, including the following steps:

The training phase includes the following steps:

(1) Randomly extract N modulation signals from five digital modulation signals of M BPSK, QPSK, 8PSK, 16QAM and 64QAM to form a training signal set array1, to ensure that the N modulation signals include the above 5 signals, and the remaining M-N modulation signals The signal naturally forms the test signal set array2;

(2) Extract high-order cumulant-based feature parameters F ₁ , F ₂ for each signal x _i , i=1, 2, 3, . . . N in the training signal set array1, and an approximation based on local mean decomposition The entropy feature parameters ApFn ₁ , ApFn ₂ , the extracted feature parameters constitute the four-dimensional feature vector of the training signal: f _i ^k , k=1, 2, 3, 4; the feature vectors of all training signals constitute the data training samples f _i , i=1,2,3,...N;

(3) Substitute the training sample data obtained in step (2) as one of the equation constraints into the following least squares support vector machine estimation model for training:

Make it satisfy the equality constraints:

是将调制信号映射到高维特征空间的非线性函数，u表示偏差量，e_i则为第i组训练样本的实际结果与估计输出的误差量，γ为惩罚系数；where y _i is the modulated signal type corresponding to the ith training sample, 1, 2, 3, 4, and 5 represent different categories of BPSK, QPSK, 8PSK, 16QAM, and 64QAM, respectively, and w is the weight vector,

is the nonlinear function that maps the modulated signal to the high-dimensional feature space, u represents the deviation, e _i is the error between the actual result and the estimated output of the i-th group of training samples, and γ is the penalty coefficient;

用来校准权重的大小，第二个部分

描述训练数据中的误差，使用拉格朗日法寻找最优惩罚系数γ和核参数σ以使得目标函数值达到最小：The first part of the objective function minJ(w, e _i ) optimized by the above formula

Used to calibrate the size of the weights, the second part

To describe the error in the training data, use the Lagrangian method to find the optimal penalty coefficient γ and kernel parameter σ to minimize the objective function value:

where μ _i is the Lagrangian multiplier, differentiate w, u, e _i , and μ _i in the above expressions respectively and make them all equal to 0, to obtain the optimization condition of this problem:

Eliminating w and e _i , the optimal solution problem is transformed into the following system of linear equations:

where y=[y ₁ ;...;y _N ], μ=[μ ₁ ;...; μ _N ], I is an identity matrix, 1 _v =[1;...;1],Ω is a square matrix, the elements of the mth row and the nth column are Ω _mn =K(f _m , f _n ), m, n=1, 2, 3,...,N, and the introduced kernel function is:

Finally, the decision function of the modulated signal is obtained;

The testing phase includes the following steps:

(4) to the test signal in the test signal set as above-mentioned step (2) extract the characteristic value that constitutes the four-dimensional eigenvector of this test signal, constitute the data test sample;

(5) Substitute the data test sample into the decision function, and output the classification result of the signal.

Wherein, the decision function obtained in step (3) of the modulated signal is as follows;

Among them, f _j , f _i represent the test samples formed by the eigenvectors of the test signal, y(f _j ) represents the result of signal recognition, and represents the Lagrange multiplier. The kernel function in the formula adopts the RBF kernel function:

where σ denotes the kernel parameter and i is not equal to j.

Among them, the characteristic parameters of the training signal in step (2) are selected from high-order cumulants F ₁ , F ₂ , and approximate entropy ApFn ₁ , ApFn ₂ of local mean decomposition quantities, and the specific extraction method is as follows:

(2.1)x(t) is the modulation signal expression, which is regarded as a stationary complex random process. The second, fourth and sixth higher-order cumulants are expressed as follows: M _pq =E[x(t) ^pq x ^* (t) ^q ], which is the p-order mixing moment of x(t);

C ₂₁ =M ₂₁

C ₄₀ =M ₄₀ -3M ₂₀ ²

C ₆₃ =M ₆₃ -6M ₂₀ M ₄₁ -9M ₄₂ M ₂₁ +18M ₂₀ ² M ₂₁ +12M ₂₁ ³

Among them, C ₂₁ , C ₄₀ , and C ₆₃ are the second, fourth, and sixth order cumulants, respectively. The characteristic parameter expressions based on the above high-order cumulants are:

(2.2) The approximate entropy characteristic parameters of the two local mean decomposition quantities of ApEn ₁ and ApEn ₂ are calculated as follows:

The original modulated signal x(t) is decomposed into the sum of k PF components and a monotonic function by the method of local mean decomposition, namely:

where PF _i is the local mean value decomposition of the original modulated signal, h _k (t) is a monotone function, take the first two local mean decomposition quantities PF ₁ and PF ₂ to calculate the approximate entropy value respectively, the steps are as follows:

(2.2.1) The local mean decomposition is regarded as a one-dimensional time series PF(i) of length s, i=1, 2, ..., s, and the z-dimensional vector P _i is reconstructed as follows, i= 1, 2, ..., sz-1:

P _i ={PF(i), PF(i+1), ..., PF(i+z-1)}

(2.2.2) Calculate the distance between vectors P _i and P _j , i, j=1, 2, ..., sz-1:

d=max|PF(i+j)-PF(j+k)|, k=0, 1, ..., z-1

(2.2.3) Given a threshold r, count the number of d≤r for each vector P _i and the ratio of this number to the total distance (sz), denoted as

取对数，然后将所有的i求平均值，记为Φ^z(r)：(2.2.4) to

Take the logarithm, then average over all i and denote it as Φ ^z (r):

和Φ^z+1(r)；(2.2.5) Add 1 to z and repeat the steps (3.2.1)-(3.2.4) to obtain

and Φ ^z+1 (r);

(2.2.6) The expression of approximate entropy is obtained from Φ ^z and Φ ^z+1 :

Through the above steps, approximate entropy can be obtained for the first two PF components PF ₁ and PF ₂ of the modulated signal, respectively, which are denoted as ApEn ₁ and ApEn ₂ .

Among them, in step (3), the least squares support vector machine estimation model is trained, and the optimal penalty coefficient γ and kernel parameter σ in the model are determined, and the steps are as follows:

(3.1) Initialize the hyperparameter pair population: the total number of hyperparameter pairs is Q, the space for hyperparameter pair population search is a two-dimensional space, and the value of the i-th hyperparameter pair in the two-dimensional space can be expressed as X _i = (X _i1 , X _i2 ), the maximum allowable number of iterations t _max , the value range of the penalty coefficient γ and the kernel parameter σ, and randomly generate the initial values of a group of hyperparameter pairs in the search space;

(3.2) The least squares support vector machine estimation model starts training based on the initial values of γ, σ, and calculates the size of the objective function value to be optimized in the least squares support vector machine estimation model under the current γ, σ hyperparameters , where the objective function expression is as follows:

(3.3) Classify the hyperparameter population according to the size of the obtained objective function value. The first three pairs of hyperparameters with smaller objective function values are in turn the three pairs with the best fitness. According to the definition of gray wolf optimization, these three pairs Named α, β, δ hyperparameter pairs in turn, and the remaining hyperparameter pairs are ω groups;

(3.4) Numerically update the population of hyperparameters according to the following formulas:

D _α =|C ₁ ·X _α (t)-X(t)|

D _β =|C ₂ ·X _β (t)-X(t)|

D _δ =|C ₃ ·X _δ (t)-X(t)|

X ₁ =X _α (t)-A ₁ ·D _α

X ₂ =X _β (t)-A ₂ ·D _β

X ₃ =X _δ (t)-A ₃ ·D _δ

where D _α , D _β , and D _δ represent the distance between the current ω population and the α, β, and δ hyperparameter pairs, respectively, t represents the number of current iterations, X _α (t), X _β (t), X _δ (t) represents the position of the current α, β, δ hyperparameter pair respectively, X(t) represents the position of the current hyperparameter pair, where C ₁ , C ₂ , C ₃ are swing factors, determined by the formula C _i =2r ₁ , i=1, 2, 3, r ₁ ∈ [0, 1], A ₁ , A ₂ , A ₃ are convergence factors, which are determined by the formula A _i =2ar ₂ -a,i=1,2,3,r ₂ ∈ [0, 1], a is the iteration factor, with the number of iterations decreasing linearly from 2 to 0, X ₁ , X ₂ , and X ₃ define the direction and step of the ω population toward the α, β, and δ hyperparameter pairs, respectively. long, X(t+1) can comprehensively judge the moving direction of the current hyperparameter pair;

(3.5) update parameters a, A _i , C _i ;

(3.6) Calculate the objective function value of each hyperparameter pair in the new position, and compare the two objective function values before and after the position update of each hyperparameter pair. If the updated value is less than the value before the update, keep the updated hyperparameter pair, Otherwise, the hyperparameter pair before the update is retained, and the current hyperparameter group is classified according to step (3.3);

(3.7) Compare the current number of iterations with the maximum allowable number of iterations. If the number of iterations t _max is not reached, jump to step (3.4) to continue parameter optimization; otherwise, the training is over, and the obtained hyperparameter pair is the least squares support The vector machine estimates the optimal solution output of the model.

Further, in the above-mentioned step (3.4), the following steps are also included:

According to the following formula, calculate the updated position of the group by hyperparameters again, and select a random number in the interval of random number v∈[0, 1] that obeys uniform distribution. If the random number is greater than the discovery probability P _a , update the current The value of the hyperparameter pair, otherwise it will not be updated;

表示内积乘法，X_i(t)表示第t次迭代第i对超参数的值，，X_i(t+1)为第i对超参数的值当次迭代后的值，ε为步长因子，由于ε＞0确定步长，与问题的刻度相关联，在极大多数情况下，ε取值为1，随机飞行的步长为Levy(λ)，服从列维分布。where i=1, 2, 3, ..., N, N represents the number of host bird nests, that is, the total number of hyperparameter pairs to be selected,

Represents inner product multiplication, X _i (t) represents the value of the i-th pair of hyperparameters in the t-th iteration, X _i (t+1) is the value of the i-th pair of hyperparameters after the current iteration, and ε is the step size The factor, since ε>0 determines the step size, is related to the scale of the problem. In most cases, the value of ε is 1, and the step size of the random flight is Levy (λ), which obeys the Levy distribution.

Beneficial effects: Compared with the prior art, the technical scheme of the present invention has the following beneficial effects:

(1) The method of the present invention selects the high-order cumulant characteristic parameters F ₁ , F ₂ and the approximate entropy characteristic parameters ApFn ₁ and ApFn ₂ of the local mean decomposition for the characteristic parameters of the training signal and the test signal, which improves the effect of noise factors on the The influence of the signal identification results makes up for the defects of under-envelope, over-envelope and boundary effects in the traditional modal empirical decomposition.

(2) The method of the present invention adopts the intelligent swarm algorithm-grey wolf optimization strategy to search for the optimal hyperparameters of the least squares support vector machine model, which improves the problem that the hyperparameters of the traditional least squares support vector machine cannot be adaptively changed. insufficient.

(3) The method of the present invention uses cuckoo search to perform secondary optimization on the updated wolf group position in the gray wolf optimization, expands the search space for the optimal solution, and compares the traditional group intelligent optimization with high computational cost and low robustness. Insufficiency, the present invention reduces the number of iterations, accelerates the convergence speed, and improves the recognition rate.

Description of drawings

Figure 1 is a schematic diagram of a simulated wolf pack hierarchy.

Figure 2 is a schematic diagram of finding the optimal solution using grey wolf optimization.

Fig. 3 is a flow chart of the modulated signal classification method of cuckoo search and improved gray wolf optimization support vector machine.

Figure 4 is a flow chart of cuckoo search to improve gray wolf optimization parameters.

Figure 5 is a comparison of the convergence curves of MAPE values under the condition of low signal-to-noise ratio between Gray Wolf Optimized Least Squares Support Vector Machine (GWO-LSSVM) and Cuckoo Search Improved Gray Wolf Optimized Least Squares Support Vector Machine (CS-IGWO-LSSVM) picture.

Figure 6 is a comparison of the convergence curves of MAPE values under the condition of high signal-to-noise ratio between Gray Wolf Optimized Least Squares Support Vector Machine (GWO-LSSVM) and Cuckoo Search Improved Gray Wolf Optimized Least Squares Support Vector Machine (CS-IGWO-LSSVM) picture.

Figure 7 is a comparison chart of the recognition rates of the Gray Wolf Optimized Least Squares Support Vector Machine (GWO-LSSVM) and the Cuckoo Search Improved Gray Wolf Optimized Least Squares Support Vector Machine (CS-IGWO-LSSVM) under different signal-to-noise ratios.

Detailed ways

The technical solutions of the present invention will be further described below with reference to the accompanying drawings and embodiments.

As shown in Figure 3, the further detailed steps of the technical solution of the present invention are described as follows:

(1) N times of Monte Carlo experiments are carried out in this example. The simulation signals are: BPSK, QPSK, 8PSK, 16QAM and 64QAM five commonly used digital modulation signals. The simulation software environment is MATLAB r2014b, the hardware environment is ASUS notebook, processor: Intel Core i5-5200U@2.20GHz 2.19GHz, memory: 8GB. The selected carrier signal frequency f _c is 2 kHz, the symbol rate _rs is 1000 Baud, the sampling rate f _s is 8 kHz, and the channel environment is zero-mean additive white Gaussian noise. The signal-to-noise ratio (SNR) is defined by the following formula, and the value range is [-6, 12], and the unit is dB.

where E _S and n ₀ represent symbol energy and noise energy, respectively.

N modulation signals are randomly selected from five commonly used digital modulation signals including M BPSK, QPSK, 8PSK, 16QAM and 64QAM to form a training signal set array1, and the remaining N-M modulation signals naturally form a test signal set array2; The number of the extracted training signals is counted, and the variance value of the extracted number of 5 kinds of signals is calculated. If it is less than the variance limit value ξ=0.5, it can be ensured that the extracted training signal set takes into account each signal and the number of Balanced, if the limit of the variance limit value is not met, random sampling is performed again until it is met.

The following description takes M=300 and N=200 as an example.

(2) Extract high-order cumulant feature parameters F ₁ , F ₂ , and local mean decomposition approximate entropy feature parameter ApFn for each signal x _i , i=1, 2, 3, ... 200 in the training signal set array1 ₁ , ApFn ₂ , the extracted feature parameters constitute the four-dimensional feature vector of the training signal: f _i ^k , k=1, 2, 3, 4, the feature vectors of all training signals constitute the data training sample f _i , i=1, 2, 3, ... 200. The specific extraction method is as follows: x(t) is the expression of the modulated signal, which is regarded as a stationary complex random process.

First, the calculation of high-order cumulant characteristic parameters is introduced. The fourth and sixth high-order cumulant expressions of the modulated signal are as follows:

C ₂₁ =M ₂₁

C ₄₀ =M ₄₀ -3M ₂₀ ²

C ₆₃ =M ₆₃ -6M ₂₀ M ₄₁ -9M ₄₂ M ₂₁ +18M ₂₀ ² M ₂₁ +12M ₂₁ ³

理论计算值如下表：Wherein, M _pq =E[x(t) ^pq x ^* (t) ^q ] is the p-order mixing moment of x(t), and C ₂₁ , C ₄₀ , and C ₆₃ are the second-, fourth-, and sixth-order cumulants, respectively. The characteristic parameter expression based on the above-mentioned higher-order cumulants is:

The theoretical calculation values are as follows:

Characteristic Parameters BPSK QPSK 8PSK 16QAM 64QAM F₁ 2 1 0 0.68 2.08 F₂ 16 4 4 0.619 1.797

It can be seen from the above table that the above two parameters can be used for intra-class identification and classification of MPSK, namely BPSK, QPSK, 8PSK and MQAM, namely 16QAM and 64QAM.

Secondly, the calculation of the approximate entropy characteristic parameters of the two local mean decomposition quantities of ApEn ₁ and ApEn ₂ is introduced, as follows:

The original modulated signal x(t) is decomposed into the sum of k PF components and a monotonic function according to the steps of local mean decomposition, namely:

where PF _i is the local mean value decomposition of the original modulated signal, h _k (t) is a monotone function, take the first two local mean decomposition quantities PF ₁ and PF ₂ to calculate the approximate entropy value respectively, the steps are as follows:

(a) The local mean decomposition quantity PF is regarded as a one-dimensional time series {PF(i), i=1, 2, ..., s} of length s, and the z-dimensional vector P _i , i is reconstructed as follows =1,2,...,sz-1.:

P _i ={PF(i), PF(i+1), ..., PF(i+z-1)}

(b) Calculate the distance between vectors P _i and P _j , j=1, 2, ..., sz-1:

d=max|PF(i+j)-PF(j+k)|, k=0, 1, ..., z-1

(c) Given a threshold r, count the number of _d≤r for each vector Pi and the ratio of this number to the total distance (sz), denoted as

取对数，然后将所有的

累加，再求得平均值，记为Φ^z(r)：(d) Yes

Take the logarithm, then put all the

Accumulate, and then obtain the average value, denoted as Φ ^z (r):

和Φ^z+1(r)。(e) Add 1 to z and repeat steps (1)-(4) to obtain

and Φ ^z+1 (r).

(f) The approximate entropy expression is obtained from Φ ^z and Φ ^z+1 as follows:

Through the above steps, the approximate entropy can be obtained for PF ₁ and PF ₂ respectively, which are denoted as ApEn ₁ and ApEn ₂ , and together with F ₁ and F ₂ are used as characteristic parameters for subsequent training.

(3) Substitute the instance specific data of the training sample f _i obtained in step (2) as one of the equation constraints into the following least squares support vector machine estimation model for training:

Make it satisfy the equality constraints:

是能够将输入空间映射为高维空间的非线性变换，u表示偏差量，e_i(i＝1，2，3，...，200)则为第i组训练样本的实际结果与估计输出的误差量，γ为惩罚系数。where y _i , i=1, 2, 3, . different categories of , w is the weight vector,

is a nonlinear transformation that can map the input space into a high-dimensional space, u represents the deviation, and e _i (i=1, 2, 3,..., 200) is the actual result and estimated output of the i-th group of training samples The amount of error, γ is the penalty coefficient.

用来校准权重的大小并惩罚大权重，第二个部分

描述训练数据中的误差。用拉格朗日法求解这个优化问题：The first part of the objective function minJ(w, e _i ) optimized by the above formula

Used to calibrate the size of the weights and penalize large weights, the second part

Describe the error in the training data. Solve this optimization problem using the Lagrangian method:

where μ _i is the Lagrangian multiplier, we will differentiate w, u, e _i and μ _i respectively and make them all equal to 0 to obtain the optimization condition of this problem:

Eliminating w and e _i , the optimal solution problem is transformed into the following system of linear equations:

where y=[y ₁ ;...;y ₂₀₀ ], μ=[μ ₁ ;...; μ ₂₀₀ ], I is an identity matrix, 1 _v =[1;...;1],Ω is a square matrix, the element of the mth row and the nth column is Ω _mn =K(f _m , f _n ), where m, n=1, 2, 3,..., 200, and the introduced kernel function is:

The final decision function of the modulated signal is:

where f _j ( _j =1, 2, 3, . Represent different categories of BPSK, QPSK, 8PSK, 16QAM, and 64QAM, respectively, and represent Lagrange multipliers. The kernel function in the formula adopts the RBF kernel function:

where σ denotes the kernel parameter.

The least squares support vector machine estimation model is trained, that is, the determination of the optimal value of the penalty coefficient γ and the kernel parameter σ in the model, the penalty parameter and the kernel parameter are both hyperparameters, and the hyperparameter pairs are used to refer to the penalty parameters γ and Kernel parameter σ.

The present invention adopts the method of cuckoo search to improve gray wolf optimization to help the least squares support vector machine model to select the optimal value of the hyperparameter pair, and the specific method is to introduce the cuckoo search for secondary position when the hyperparameter updates the position of the group. Update, improve the problem that the original gray wolf optimization is easy to fall into the local optimum in the high-dimensional data set environment, the two-dimensional coordinate solution of the output optimal α wolf is the optimal value of the hyperparameter pair, and the fitness of the gray wolf corresponds to the target The size of the value of the function, and meet the corresponding constraints, the specific steps are as follows:

Step 3.1: Initialize the hyperparameter pair population: the total number of hyperparameter pairs is 20, the space for hyperparameter pair population search is a two-dimensional space, and the value of the i-th hyperparameter pair in the two-dimensional space can be expressed as X _i = (X _i1 , X _i2 ), the maximum allowable number of iterations t _max is 200, the value ranges of the penalty coefficient γ and the kernel parameter σ are γ∈[0, 100], σ∈[0, 1], respectively, in the search space Randomly generate initial values for a group of hyperparameter pairs;

Step 3.2: The LSSVM model starts training according to the initial values of (γ, σ), and calculates the size of the objective function value to be optimized in the LSSVM model under the current γ, σ hyperparameters.

Step 3.3: Classify the hyperparameter population according to the obtained objective function value. The first three pairs of hyperparameters with smaller objective function values are the three pairs with the best fitness in order. Name these three pairs in turn according to the definition of gray wolf optimization. is the α, β, δ hyperparameter pair, and the remaining hyperparameter pairs are the ω population.

Step 3.4: Numerically update the population of hyperparameters separately according to the following formulas:

D _α =|C ₁ ·X _α (t)-X(t)|

D _β =|C ₂ ·X _β (t)-X(t)|

D _δ =|C ₃ ·X _δ (t)-X(t)|

X ₁ =X _α (t)-A ₁ ·D _α

X ₂ =X _β (t)-A ₂ ·D _β

X ₃ =X _δ (t)-A ₃ ·D _δ

where D _α , D _β , and D _δ represent the distance between the current ω population and the α, β, and δ hyperparameter pairs, respectively, t represents the number of current iterations, X _α (t), X _β (t), X _δ (t) represents the position of the current α, β, δ hyperparameter pair respectively, X(t) represents the position of the current hyperparameter pair, where C ₁ , C ₂ , C ₃ are swing factors, determined by the formula C _i =2r ₁ , i=1, 2, 3, r ₁ ∈ [0, 1], A ₁ , A ₂ , A ₃ are convergence factors, which are determined by the formula A _i =2ar ₂ -a,i=1,2,3,r ₂ ∈ [0, 1], a is the iteration factor, with the number of iterations decreasing linearly from 2 to 0, X ₁ , X ₂ , and X ₃ define the direction and step of the ω population toward the α, β, and δ hyperparameter pairs, respectively. long, X(t+1) can comprehensively judge the moving direction of the current hyperparameter pair.

When the hyperparameters are used to update the position of the group, the cuckoo search is introduced to perform the secondary position update, which improves the problem that the original gray wolf optimization is easy to fall into the local optimum in the high-dimensional data set environment. So add the following additional steps to step 3.4 above:

Step 3.4.1: Calculate the updated position of the population by hyperparameters again according to the following formula, and select a random number in the interval of uniformly distributed random numbers v∈[0, 1], if the random number is greater than the discovery probability P _a =0.5, then update the current value of the hyperparameter pair, otherwise do not update.

表示内积乘法，X_i(t)表示第t次迭代第i对超参数的值，X_i(t+1)为第i对超参数的值当次迭代后的值。ε为步长因子，由于ε＞0确定步长，与问题的刻度相关联，ε取值为1。随机飞行的步长为Levy(λ)，服从列维分布。where i=1, 2, 3, ..., 20, indicating that the number of searchable host bird nests is 20 (that is, the total number of hyperparameter pairs to be selected),

Represents the inner product multiplication, X _i (t) represents the value of the i-th pair of hyperparameters in the t-th iteration, and X _i (t+1) is the value of the i-th pair of hyperparameters after the current iteration. ε is the step size factor. Since ε>0 determines the step size, it is related to the scale of the problem, and the value of ε is 1. The step size of the random flight is Levy(λ), which obeys the Levy distribution.

Step 3.5: Update parameters a, A _i , C _i .

Step 3.6: Calculate the objective function value of each hyperparameter pair at the new position, compare the two objective function values before and after the position update of each hyperparameter pair, if the updated value is less than the value before the update, keep the updated hyperparameter pair, Otherwise, the hyperparameter pair before the update is retained, and the current hyperparameter population is classified according to step 3.3.

Step 3.7: Compare the current number of iterations with the maximum allowable number of iterations. If it does not reach 200, skip to step 3.4 to continue parameter optimization; otherwise, the training is over, and the obtained α hyperparameter pair is the output of the optimal solution of the LSSVM model, which is obtained. The optimal penalty parameter γ is 4.9278, and the optimal kernel parameter σ is 0.3112.

Step 4: Extract the eigenvalues of the signals in the test signal set array2 as in the above step 2 to form a four-dimensional feature vector of the test signal, and form a data test sample f _j , j=1, 2, . . . , 100.

Step 5: Substitute the data test sample into the decision function, and output the classification result of the signal.

In the research of the present embodiment, in order to compare and evaluate the accuracy of the modulated signal method, the mean absolute percentage error (Mean Absolute Percentage Error, MAPE) is selected, and the calculation method is as follows:

Among them, M is the total number of signals of the training sample 200, and y _i and y _p represent the actual value and estimated value of the ith signal, respectively. The final accuracy of the method can be expressed as:

est_acc=100%-(MAPE×100%)

In order to better illustrate the superiority of cuckoo search improved gray wolf optimization on the classification effect of modulated signals, the following is a comparison of the classification results with the original gray wolf optimization:

It can be seen from the convergence curve graph given in Figure 5 that both the original gray wolf optimization (the legend in the figure is GWO) and the cuckoo search improved gray wolf optimization (the legend in the figure is CS-GWO) have a high convergence speed, and the cuckoo The improved gray wolf optimization of bird search converges to the optimal solution in about 65 iterations, and the original gray wolf optimization converges at about 85 times. Therefore, the speed of the improved gray wolf optimization of cuckoo search in the convergence process is improved. In addition, it can be clearly seen from Figure 5 that the final recognition rate of the improved gray wolf optimization by cuckoo search is also improved. The MAPE value of the original gray wolf optimization finally converges to 94.1085% under the low signal-to-noise ratio of -3dB, while the improvement of cuckoo search Under the signal-to-noise ratio of gray wolf optimization, the MAPE value reaches 96.7426%. It can be concluded that under low signal-to-noise ratio, the modulation signal classification method of cuckoo search improved gray wolf optimization needs more than the original gray wolf optimization modulation signal classification method. Fewer iterations and more accurate recognition rates.

FIG. 6 is a simulation diagram of the average recognition rate convergence curve of the modulation signal classification by the reference LSSVM classification method under the signal-to-noise ratio of 12dB. Figure 6 shows intuitively that the classification method of the original gray wolf optimization has the same recognition rate of 100% as the cuckoo search improved gray wolf optimization, and observing the number of convergence iterations, it is found that the original gray wolf optimization converges to the maximum at about 90 iterations. The optimal solution, the improved gray wolf optimization of cuckoo search converges at about 65 times. Therefore, under the high signal-to-noise ratio, the improved gray wolf optimization of cuckoo search is compared with the original gray wolf optimization, which reduces the local maximum in the optimization process of this method. good probability.

Figure 7 shows the simulation results in the signal-to-noise ratio in the range of -6dB to 12dB, the classification method of the original gray wolf optimization and the cuckoo search improved gray wolf optimization classification method to the recognition rate of the modulated signal. The broken line of the recognition rate in Figure 7 shows that under the experimental signal-to-noise ratio, the performance of the classification method improved by cuckoo search and improved gray wolf optimization is significantly improved. When the signal-to-noise ratio is greater than 3dB, the recognition rates of the two classification methods have reached the convergence value. And under the experimental condition that the signal-to-noise ratio is lower than 3dB, the performance of the cuckoo search improved gray wolf optimization classification method is better than that of the original gray wolf optimization classification method.

Combining the above simulation results, it can be concluded that the classification method of cuckoo search improved gray wolf optimized least squares support vector machine has faster convergence speed, improves efficiency, and also improves the recognition rate of modulated signals, especially in the real world. The advantages of the improved method are particularly obvious under the low signal-to-noise ratio of significance.

The present invention uses cuckoo search to update the position of wolves twice to improve the global search ability, and better optimizes the parameters of the LSSVM function estimation model, so that it has good robustness in the classification application of modulated signals, and the present invention has more accurate It also has important application value in other applications.

Claims (5)

1. A modulation signal classification method of a cuckoo search improved wolf optimization support vector machine comprises a training stage and a testing stage, and is characterized in that:

the training phase comprises the steps of:

(1) randomly extracting N modulation signals from five digital modulation signals of M BPSK, QPSK, 8PSK, 16QAM and 64QAM to form a training signal set array1, ensuring that the N modulation signals comprise the 5 digital modulation signals, and naturally forming a test signal set array2 by the rest M-N modulation signals;

(2) For each signal x in training signal set array1_iExtracting characteristic parameters F based on high-order cumulant₁，F₂And an approximate entropy characterizing parameter ApFn based on the local mean decomposition₁，ApFn₂And the extracted characteristic parameters form a four-dimensional characteristic vector of the training signal: f. of_i ^kK is 1, 2, 3, 4; all the feature vectors of the training signal constitute the data training sample f_i，i＝1，2，3，...N；

(3) Substituting the training sample data obtained in the step (2) as one item in an equation constraint into the following least square support vector machine estimation model for training:

so that it satisfies the equality constraint:

wherein y is_iFor the modulation signal type corresponding to the ith training sample, 1, 2, 3, 4, 5 respectively represent different classes of BPSK, QPSK, 8PSK, 16QAM, 64QAM, w is a weight vector,

is a non-linear function mapping the modulation signal to a high-dimensional feature space, u represents the deviation, e_iThe error amount between the actual result of the ith group of training samples and the estimation output is determined, and gamma is a penalty coefficient;

objective function minJ (w, e) optimized by the above formula_i) First part of

For calibrating the magnitude of the weights, the second part

Describing error in training data, using Lagrange method to find optimal punishment coefficient gamma and decision function of modulation signal

So that the value of the objective function is minimized:

Wherein mu_iFor Lagrange multiplier, the values of w, u and e in the above expression are respectively compared_i，μ_iDifferentiating and making them all equal to 0, the optimum condition for the problem is found:

elimination of w and e_iThe optimal solution problem will be converted to the form of the following system of linear equations:

wherein y is [ y ]₁；...；y_N]，μ＝[μ₁；...；μ_N]I is an identity matrix, 1_v＝[1；...；1]Omega is a square matrix, the mth row and nth column elements are omega_mn＝K(f_m，f_n) N, where the introduced kernel function is:

finally, a decision function of the modulation signal is obtained;

the testing phase comprises the following steps:

(4) extracting characteristic values from the test signals in the test signal set to form a four-dimensional characteristic vector of the test signals in the step (2) to form a data test sample;

(5) and substituting the data test sample into a decision function, and outputting a classification result of the signal.

2. The method as claimed in claim 1, wherein the decision function of obtaining the modulation signal is as follows:

wherein f is_j，f_iA test sample consisting of a feature vector representing the test signal, y (f)_j) Representing the result of signal recognition, mu_iRepresenting Lagrange multiplier, wherein the kernel function in the formula adopts RBF kernel function:

where σ denotes the nuclear parameter and i is not equal to j.

3. The method of claim 1, wherein the method comprises the following steps: selecting high-order cumulant F as characteristic parameter of training signal in step (2)₁，F₂And approximate entropy of local mean decomposition (APFn)₁，ApFn₂The specific extraction method is as follows:

(2.1) x (t) is a modulation signal expression and is regarded as a smooth complex random process, and the second, fourth and sixth high-order cumulant expressions are as follows: m_pq＝E[x(t)^p-qx^*(t)^q]A mixture moment of order p of x (t), where q is expressed as a high order accumulation coefficient of a stationary complex random process;

C₂₁＝M₂₁

C₄₀＝M₄₀-3M₂₀ ²

C₆₃＝M₆₃-6M₂₀M₄₁-9M₄₂M₂₁+18M₂₀ ²M₂₁+12M₂₁ ³

wherein C is₂₁、C₄₀、C₆₃Respectively are second order cumulant, fourth order cumulant and sixth order cumulant, and the characteristic parameter expression based on the high order cumulant is as follows:

(2.2)ApEn₁and ApEn₂The approximate entropy characteristic parameters of the two local mean decomposition quantities are calculated as follows:

decomposing an original modulation signal x (t) into the sum of k PF components and 1 monotonic function by using a local mean decomposition method, namely:

wherein the PF_iIs the local mean decomposition quantity, h, of the original modulation signal_k(t) is a monotonic function, the first two local mean decomposition quantities PF are taken₁、PF₂Respectively carrying out approximate entropy calculation on the obtained data, and the steps are as follows:

(2.2.1) considering the local mean decomposition as a one-dimensional time series pf (i) of length s, i 1, 2 _i，i＝1，2，...，s-z-1：

P_i＝{PF(i)，PF(i+1)，...，PF(i+z-1)}

(2.2.2) calculating the vector P_iAnd P_j，1, 2, s-z-1:

d＝max|PF(i+j)-PF(j+k)|，k＝0，1，...，z-1

(2.2.3) given a threshold r, for each vector P_iCounting the number of d ≦ r and the ratio of the number to the total distance (s-z), and recording

(2.2.4) pairs

Taking logarithm, then averaging all i, and recording as phi^z(r)：

(2.2.5) adding z to 1, repeating the steps (3.2.1) - (3.2.4) to obtain

And phi^z+1(r)；

(2.2.6) from Φ^zAnd phi^z+1Obtaining a representation of approximate entropyFormula (II):

the first two PF components PF of the modulated signal can be modulated by the above steps₁，PF₂Respectively calculating approximate entropy, and marking as ApEn₁And ApEn₂。

4. The method of claim 1, wherein the method comprises the following steps: in the step (3), training the least square support vector machine estimation model, and determining the optimal penalty coefficient gamma and the nuclear parameter sigma in the model, the steps are as follows:

(3.1) initializing hyperparameter versus population: the total number of the hyper-parameter pairs is Q, the space searched by the hyper-parameter pair group is a two-dimensional space, wherein the value of the ith pair of hyper-parameter pairs in the two-dimensional space can be represented as X_i＝(X_i1，X_i2) Maximum number of allowed iterations t_maxThe value ranges of the penalty coefficient gamma and the nuclear parameter sigma randomly generate a group of initial values of the hyper-parameter pairs in a search space;

(3.2) training the estimation model of the least square support vector machine according to the initial values of gamma and sigma, and calculating the value of an objective function value to be optimized in the estimation model of the least square support vector machine under the current gamma and sigma hyper-parameters, wherein the expression of the objective function is as follows:

(3.3) carrying out grade division on the hyper-parameter groups according to the size of the obtained objective function value, wherein the first three pairs of hyper-parameters with smaller objective function values are sequentially the three pairs with the best fitness, the three pairs are sequentially named as alpha, beta and delta hyper-parameter pairs according to the definition of wolf optimization, and the rest hyper-parameter pairs are omega groups;

(3.4) respectively carrying out numerical update on the hyperparameter population according to the following formula:

D_α＝|C₁·X_α(t)-X(t)|

D_β＝|C₂·X_β(t)-X(t)|

D_δ＝|C₃·X_δ(t)-X(t)|

X₁＝X_α(t)-A₁·D_α

X₂＝X_β(t)-A₂·D_β

X₃＝X_δ(t)-A₃·D_δ

wherein D_α、D_β、D_δRespectively representing the distances between the current omega population and alpha, beta and delta hyper-parameter pairs, respectively, t representing the number of current iterations, X_α(t)、X_β(t)、X_δ(t) respectively represents the positions of the current alpha, beta and delta hyper-parameter pairs, X (t) represents the position of the current hyper-parameter pair, wherein C₁、C₂、C₃Is the wobble factor, expressed by the formula C_i＝2r₁Determining i as 1, 2, 3, r₁∈[0，1]，A₁、A₂、A₃Is a convergence factor, represented by formula A_i＝2ar₂-a，i＝1，2，3，r₂∈[0，1]A is an iteration factor, X decreases linearly from 2 to 0 with the number of iterations₁、X₂、X₃Respectively defining the advancing direction and the step length of an omega group to alpha, beta and delta hyper-parameter pairs, wherein X (t +1) can comprehensively judge the moving direction of the current hyper-parameter pair;

(3.5) updating the parameters a, A_i、C_i；

(3.6) calculating objective function values of all hyper-parameter pairs at the new position, comparing two objective function values before and after position updating of all hyper-parameter pairs, if the updated value is smaller than the value before updating, keeping the updated hyper-parameter pairs, otherwise, keeping the hyper-parameter pairs before updating, and grading the current hyper-parameter group according to the step (3.3);

(3.7) comparing the current iteration times with the maximum allowable iteration times, and if the iteration times t are not reached_maxSkipping to the step (3.4) to continue parameter optimization; otherwise, the training is finished, and the obtained hyperparameter pair, namely the optimal solution of the least square support vector machine estimation model is output.

5. The method for classifying modulation signals of the blackbird search improved graying support vector machine according to claim 3, wherein the step (3.4) further comprises the following steps:

respectively calculating the positions of the super parameters after the group is updated according to the following formula, and simultaneously calculating the random number upsilon ∈ [0, 1) which obeys uniform distribution]Selecting a random number in the interval, if the random number is larger than the discovery probability P_aIf not, updating the numerical value of the current hyper-parameter pair;

wherein i is 1, 2, 3, …, N, N represents the number of host bird nests, i.e. the total number of pairs of candidate hyperparameters,

Representing inner product multiplication, X_i(t) values of the ith pair of hyperparameters, X, for the tth iteration_iAnd (t +1) is the value of the ith pair of hyperparameter after the current iteration, epsilon is a step-size factor, the step size of random flight is Levy (lambda), and the column-dimensional distribution is obeyed.

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