CN114172770B - Modulation signal identification method of quantum root tree mechanism evolution extreme learning machine - Google Patents

Abstract

The invention provides a modulation signal identification method of a quantum root tree mechanism evolution extreme learning machine, which utilizes a weighted Myriad filter to inhibit impact noise, provides a quantum root tree mechanism for carrying out efficient solution, and breaks through some application limitations of the existing modulation signal identification method based on the evolution extreme learning machine. The modulation signal identification method of the quantum root tree mechanism evolution extreme learning machine designs the quantum root tree mechanism, can carry out high-precision solution on the weight and the threshold value of the extreme learning machine under impact noise, and effectively improves the modulation identification rate. Simulation experiments prove that the effectiveness of the modulation signal identification method of the quantum root tree mechanism evolution extreme learning machine under impact noise breaks through the application limitation of the traditional method that the performance is deteriorated or even fails under the impact noise and low signal-to-noise ratio environment, and compared with the traditional method, the identification rate is greatly improved.

Description

Modulation signal recognition method based on extreme learning machine evolved by quantum rooted tree mechanism

Technical Field

The invention relates to a modulation signal recognition method based on a quantum root tree mechanism in an impact noise environment, and belongs to the field of communication signal processing.

Background Art

In recent years, the automatic modulation recognition technology of communication signals has been widely used in spectrum allocation, electronic countermeasures, cognitive radio and other scenarios. In the military field, it is necessary to distinguish the modulation types of various communication signals and radar signals emitted by enemy electronic equipment before the next step of demodulation, even monitoring and interference can be carried out. In the civilian field, the application of modulation recognition technology in the field of cognitive radio can cooperate with modules such as parameter estimation and signal demodulation to effectively avoid radio interference and optimize spectrum allocation.

With the advancement of science and technology and social development, the electromagnetic environment of wireless communication has become more and more complex, the types and spectrum of signals have gradually expanded upward, and there are various interferences and noises in the environment, such as receiving noise in radar and satellite communications, and impact noise generated by electrocardiogram signals and interstellar gravitational fields. Since the actual impact noise has the characteristics of spike pulses and a thick probability density function tail, as well as the complexity of the electromagnetic environment, this poses a huge challenge to the recognition task of modulated signals. Most traditional modulation signal recognition methods require the acquisition of prior information of the signal in advance. Factors such as frequency deviation and noise will lead to inaccurate parameter estimation or feature extraction, resulting in unsatisfactory accuracy in modulation signal recognition under low signal-to-noise ratio. In addition, traditional modulation recognition methods mainly study the modulation recognition problem in Gaussian noise environment. The performance of the original method drops sharply or even fails in the impact noise environment.

With the continuous development of machine learning, artificial neural networks, support vector machines and other technologies have gradually been applied in many fields such as image processing and signal processing. Since machine learning methods do not require manual design of decision thresholds or calculation of complex likelihood functions, more and more scholars have applied machine learning to modulated signal recognition methods. Neural networks have powerful pattern recognition capabilities. Each node automatically and adaptively updates weights and thresholds, and can handle complex nonlinear problems well. Therefore, neural networks can be used as classifiers to identify the types of modulated signals.

The modulation signal recognition method based on neural network generally includes three basic steps: feature extraction, network training and classification recognition. In the back propagation training process of BP neural network, the training results and convergence of the network are highly dependent on the initial weights, thresholds and network structure. Therefore, how to determine the appropriate initial weights and thresholds becomes an important issue. Generally, BP neural network uses the method of random initialization of weights and thresholds before training, which is easy to fall into local convergence during the training process, and the recognition accuracy is not ideal in low signal-to-noise ratio or impact noise environment.

Since the BP neural network needs to gradually iterate and adjust the weights and thresholds of the network during the training process, the amount of calculation is large and it is easy to fall into the local optimum. Compared with the BP algorithm, the extreme learning machine has the characteristics of fast learning speed. Therefore, the extreme learning machine belonging to the single hidden layer feedforward neural network can be used as a classifier to realize the modulation signal recognition. This helps to realize the real-time processing of modulation signal recognition and has greater engineering application value.

However, the characteristic of the random initialization of hidden layer parameters of the extreme learning machine makes it need more hidden layer nodes than the BP neural network to achieve similar classification effects, which makes the network more complex and reduces the generalization ability of the network. Therefore, after determining the objective function, the intelligent optimization algorithm can be used to evolve the input layer and hidden layer weights and hidden layer thresholds of the extreme learning machine to improve the accuracy of modulated signal recognition. Therefore, it is of great significance and value to study the modulation signal recognition method based on the quantum root tree mechanism evolution extreme learning machine under impulse noise.

Through searching the existing technical literature, it is found that Song Lihui et al. published "Digital Communication Modulation Recognition Based on Extreme Learning Machine" in Laser Journal (2016, 37(3): 119-122), using extreme learning machine to realize the recognition of 7 types of digital modulation signals under Gaussian noise, but did not consider the influence of impulse noise, nor did they evolve the extreme learning machine, making it difficult to obtain the optimal parameters; Zhang Hui (Harbin Engineering University, 2016) published "Research on Communication Signal Modulation Recognition Method Based on Machine Learning" using particle swarm algorithm and principal component analysis to evolve the parameters and structure of extreme learning machine, and the recognition rate was improved under Gaussian noise, but did not consider the influence of impulse noise environment.

The search results of existing literature show that most of the existing modulation signal recognition methods based on evolutionary extreme learning machines are implemented in Gaussian noise environments, and their performance deteriorates in impulse noise environments. Therefore, a modulation signal recognition method based on an evolutionary extreme learning machine with a quantum root tree mechanism under impulse noise is proposed. The overall process is to use a weighted Myriad filter to suppress impulse noise, perform feature extraction on this basis, and then evolve the parameters of the extreme learning machine through the quantum root tree mechanism to solve the problem of performance degradation of existing modulation signal recognition methods based on evolutionary extreme learning machines under impulse noise environments.

Summary of the invention

In view of the shortcomings and deficiencies of the existing modulation signal recognition method based on evolutionary extreme learning machine, the present invention designs a modulation signal recognition method based on quantum root tree mechanism evolutionary extreme learning machine under impulse noise. This method uses a weighted Myriad filter to suppress impulse noise and proposes a quantum root tree mechanism for efficient solution, breaking through some application limitations of the existing modulation signal recognition method based on evolutionary extreme learning machine.

The object of the present invention is achieved by comprising the following steps:

Step 1: Obtain the communication modulation signal and signal preprocessing to obtain the modulation signal preprocessing data set under the impact noise background. Signal preprocessing includes shaping filtering, power normalization, adding impact noise and suppressing it.

Step 2: Use weighted Myriad filter to suppress impulse noise, and obtain the modulated signal preprocessing data set through segment processing.

Step three, extract instantaneous feature parameters from the modulated signal preprocessing data set to obtain a feature data set for training an extreme learning machine.

Step 4: Determine the objective function of the optimal parameters of the extreme learning machine.

Step 5: Initialize the quantum root tree mechanism parameters.

Step 6: Calculate the fitness and moisture content of all roots in the population and arrange the population in ascending order of moisture content.

Step seven, use simulated quantum revolving door to update different individuals in the population respectively.

Step 8: Calculate the fitness and wetness of the new generation of roots, update the global optimal root, and arrange the population in ascending order of wetness.

是否达到最大迭代次数G_max，若达到最大迭代次数，则终止迭代，输出最优权值和阈值向量；否则返回步骤七。Step 9: Determine the number of iterations

Whether the maximum number of iterations G _max is reached, if so, the iteration is terminated and the optimal weight and threshold vector are output; otherwise, return to step seven.

Step 10: Use the extreme learning machine with the optimal weights and thresholds as a classifier to identify the modulated signal under the impact noise background. The optimal weights and thresholds are obtained by evolving the extreme learning machine through the quantum root tree mechanism, and are used as the initial weights and thresholds of the extreme learning machine. The training set data is used for training, and the trained extreme learning machine with the optimal weights and thresholds is used as a classifier for modulated signal recognition under the impact noise background. Finally, the test set or collected data is used to output the modulation recognition result.

-3T＜t＜3T，式中，t为采样时间，μ为升余弦滚降系数，T为码元周期。之后进行功率归一化，将每种调制方式的信号平均功率归一化为1。Furthermore, step 1 specifically includes: adding a shaping filter at the transmitting end, and the shaping filter adopts a raised cosine roll-off function to shape the digital baseband signal, and the expression is:

-3T＜t＜3T, where t is the sampling time, μ is the raised cosine roll-off coefficient, and T is the symbol period. Then power normalization is performed to normalize the average power of the signal of each modulation mode to 1.

The Alpha stable distribution theory S _α (β,γ,δ) is used to construct the impact noise simulation model, where α is called the characteristic index, which represents the impact degree of the Alpha stable distribution. The value range is 0＜α≤2. The smaller α is, the greater the impact degree is. β is called the symmetry parameter or skew factor, which represents the skewness of the Alpha stable distribution relative to the center. The value range is -1≤β≤1. If β＜0, it is a negatively skewed distribution; if β＞0, it is a positively skewed distribution. γ is called the scale parameter, which represents the deviation degree of the Alpha stable distribution from the center. The value range is γ＞0. The larger γ is, the greater the deviation degree from the center is. δ is called the location parameter, which represents the location of the Alpha stable distribution. The value range is -∞＜δ＜∞. When 1＜α≤2, δ represents the mean; when 0＜α≤1, δ represents the median.

和权重集合

定义输入向量x＝[x₁,x₂,...,x_N]^T和权值向量

对于给定的非线性度参数K＞0，假设随机变量

相互独立且服从位置参数θ和尺度参数

的柯西分布，可得其概率密度函数为

定义

加权Myriad使得似然函数

最大，可得

定义

引入函数ρ(v)＝ln(1+v²)，其中v是自变量，则加权Myriad输出为

称Q(θ)为加权Myriad目标函数。定义函数ρ(v)的导数

其中v是自变量，加权Myriad输出

是Q(θ)的一个局部极小值，因此有

定义函数

其中v是自变量，引入正函数

其中i＝1,2,...,N，则

因此有如下结论：包括

在内的所有目标函数Q(θ)的局部极小值点都可以表示成对输入x_i求加权均值的形式，即

定义映射

可将Q(θ)的局部极小点，即Q'(θ)＝0的根视为T(θ)的定点，利用定点迭代算法计算这些定点，即

其中m是定点迭代次数。Furthermore, step 2 specifically includes: given a set of N observation samples

and weight set

Define the input vector x = [x ₁ , x ₂ , ..., x _N ] ^T and the weight vector

For a given nonlinearity parameter K>0, assuming that the random variable

Independent of each other and subject to the location parameter θ and the scale parameter

The Cauchy distribution has a probability density function of

definition

The weighted Myriad makes the likelihood function

Maximum, available

definition

Introducing the function ρ(v)=ln(1+v ² ), where v is the independent variable, the weighted Myriad output is

Q(θ) is called the weighted Myriad objective function. Define the derivative of the function ρ(v)

Where v is the independent variable, weighted Myriad output

is a local minimum of Q(θ), so we have

Defining functions

Where v is the independent variable, introduce the positive function

Where i = 1, 2, ..., N, then

Therefore, the following conclusions are drawn:

All local minimum points of the objective function Q(θ) can be expressed as the weighted mean of the input _xi , that is,

Defining the Mapping

The local minimum points of Q(θ), i.e., the roots of Q'(θ) = 0, can be regarded as fixed points of T(θ), and these fixed points can be calculated using the fixed-point iterative algorithm, i.e.

Where m is the number of fixed-point iterations.

The segmentation process divides the modulated signal of each modulation mode into a plurality of data segments of equal length and a collection of labels corresponding to each data segment.

式中，s(t)是原信号y(t)的解析信号，而

是y(t)的希尔伯特变换，有

式中，

代表卷积运算。其频率响应为

Furthermore, step three specifically includes: after the receiver receives the signal, it performs Hilbert transform on it to obtain its analytical form, that is,

Where s(t) is the analytical signal of the original signal y(t), and

is the Hilbert transform of y(t), we have

In the formula,

represents the convolution operation. Its frequency response is

的离散序列y(n)，其解析形式为

瞬时幅度为A(n)，则

瞬时相位为θ(n)，有

The original signal y(t) is sampled with sampling frequency _fs , and the total number of points is

The discrete sequence y(n) of

The instantaneous amplitude is A(n), then

The instantaneous phase is θ(n), and we have

有

Since the main value interval of the inverse tangent function is (-π/2,π/2), θ(n) may produce a sudden change of ±π at this time, and it is adjusted to obtain a phase value in [0,2π)

have

的关系是

式中，mod代表求余运算。因此，

存在相位卷叠。由于去卷叠瞬时相位φ(n)满足φ(n)＝2πf_cT_sn+ε(n)+θ，式中，f_c是载波频率，T_s采样是周期，θ是初始相位。从上式可知，去卷叠瞬时相位是由载波频率引起的线性相位分量和ε(n)与θ引起的非线性分量。需要对序列

加上一个矫正序列{c(n)}实现去卷叠，定义为

此时，去卷叠瞬时相位估计值为

在载波、码元完全同步的情况下，去卷叠瞬时相位非线性分量的估计值为

The actual instantaneous phase ε(n) is related to

The relationship is

Here, mod represents the remainder operation. Therefore,

There is phase wrapping. Since the dewrapped instantaneous phase φ(n) satisfies φ(n)＝2πf _c T _s n+ε(n)+θ, where f _c is the carrier frequency, T _s sampling is the period, and θ is the initial phase. From the above formula, it can be seen that the dewrapped instantaneous phase is the linear phase component caused by the carrier frequency and the nonlinear component caused by ε(n) and θ. It is necessary to

Add a correction sequence {c(n)} to achieve deconvolution, defined as

At this time, the deconvolution instantaneous phase estimate is

When the carrier and code element are completely synchronized, the estimated value of the de-warping instantaneous phase nonlinear component is

式中，f_s是采样频率。The instantaneous frequency sequence can be obtained by differentiating the deconvolved instantaneous phase sequence, that is,

Where _fs is the sampling frequency.

零中心归一化瞬时幅度绝对值的标准偏差σ_aa，零中心非弱信号段瞬时相位非线性分量的标准差σ_dp，零中心非弱信号段瞬时相位非线性分量绝对值的标准差σ_ap，零中心归一化非弱信号段瞬时频率绝对值的标准差σ_af，归一化瞬时频率的方差

通过特征参数的提取，得到一个包含六种特征参数的数据集，将特征参数数据集按一定比例分成训练集和测试集，用训练集来训练数字调制信号识别的极限学习机。Based on the instantaneous amplitude, frequency and phase of the signal obtained in the impact noise environment, multiple characteristic quantities of the instantaneous information of the digital modulation signal are further extracted to obtain six characteristic parameters, including the maximum value of the spectral density of the zero-centered normalized instantaneous amplitude

The standard deviation of the absolute value of the normalized instantaneous amplitude at the zero center is _σaa , the standard deviation of the instantaneous phase nonlinear component of the non-weak signal segment at the zero center is _σdp , the standard deviation of the absolute value of the instantaneous phase nonlinear component of the non-weak signal segment at the zero center is _σap , the standard deviation of the absolute value of the instantaneous frequency of the normalized non-weak signal segment at the zero center is _σaf , and the variance of the normalized instantaneous frequency is

By extracting characteristic parameters, a data set containing six characteristic parameters is obtained. The characteristic parameter data set is divided into a training set and a test set according to a certain ratio, and the training set is used to train an extreme learning machine for digital modulation signal recognition.

Furthermore, step 4 specifically includes: the learning process of the extreme learning machine is as follows:

隐含层节点数为l，输出层节点数为m，输入层与隐含层权值矩阵为

有

式中，

是输入层第i个节点与隐含层第k个节点的连接权值。设隐含层与输出层权值矩阵为

有

式中，

是隐含层第i个节点与输出层第k个节点的连接权值。设隐含层阈值为b＝[b₁,b₂,...,b_l]^T，极限学习机输入特征矩阵

包含q个样本，对应的期望输出矩阵为

有

和

第i个样本对应的输入向量为

期望输出向量为

Assume the number of input layer nodes is

The number of nodes in the hidden layer is l, the number of nodes in the output layer is m, and the weight matrix of the input layer and the hidden layer is

have

In the formula,

is the connection weight between the i-th node in the input layer and the k-th node in the hidden layer. Let the weight matrix of the hidden layer and the output layer be

have

In the formula,

is the connection weight between the i-th node in the hidden layer and the k-th node in the output layer. Assume that the hidden layer threshold is b = [b ₁ ,b ₂ ,...,b _l ] ^T , and the extreme learning machine input feature matrix is

Contains q samples, and the corresponding expected output matrix is

have

and

The input vector corresponding to the i-th sample is

The expected output vector is

式中，

Assume that the hidden layer node activation function is g(x), H is the hidden layer output matrix, then

In the formula,

Suppose the network output matrix is O, then O = [o ₁ ,o ₂ ,...,o _q ] _m×q , the output vector of the kth input sample is o _k , and we have

式中，

因此，存在一个单隐含层前馈神经网络，使得

成立，这q个方程可以用矩阵表示为

The output of a single hidden layer feedforward neural network can approximate the q sample feature vectors with zero error under the conditions that the weights and thresholds are real numbers, the number of hidden layer nodes is the same as the number of samples, and the activation function is infinitely differentiable.

In the formula,

Therefore, there exists a single hidden layer feedforward neural network such that

The q equations can be expressed as a matrix.

和

单隐含层前馈神经网络的隐含层节点数l通常远小于输入样本个数q，因此可能不存在满足上式的单隐含层前馈神经网络。对于传统的学习算法，寻找一组

和b，使得误差最小，即

其中

和

分别代表误差最小时的输入层与隐含层权值、输出层阈值和隐含层与输出层权值，该式等价于最小化损失函数

For a given sample

and

The number of hidden layer nodes l of a single hidden layer feedforward neural network is usually much smaller than the number of input samples q, so there may not be a single hidden layer feedforward neural network that satisfies the above equation. For traditional learning algorithms, finding a set of

and b, so that the error is minimized, that is

in

and

Respectively represent the input layer and hidden layer weights, output layer threshold and hidden layer and output layer weights when the error is minimum. This formula is equivalent to minimizing the loss function

和隐含层阈值b，在给定样本

的情况下，隐含层输出矩阵H被唯一确定。因此，极限学习机学习等价于找到使线性系统

的最小二乘解，即

其最小范数最小二乘解为

式中，

是H的Moore-Penrose广义逆。In the extreme learning machine, the weights of the input layer and the hidden layer can be randomly initialized

And hidden layer threshold b, given a sample

In the case of , the hidden layer output matrix H is uniquely determined. Therefore, extreme learning machine learning is equivalent to finding a linear system

The least squares solution of

Its minimum norm least squares solution is

In the formula,

is the Moore-Penrose generalized inverse of H.

隐含层节点数为l，输出层节点数为m，样本个数为q，则最优求解方程可以描述为

式中，

为网络输出层第i个节点第k个样本的期望输出，o_ik为输出层第i个节点第k个样本的预测输出，

为神经网络权值和阈值向量，

为最优的网络权值和阈值向量，M为极限学习机权值和阈值总个数，有

After training the extreme learning machine with the feature training set, the system output is predicted, and the mean absolute error between the predicted output and the expected output is used as the objective function. Assume that the number of nodes in the input layer is

The number of hidden layer nodes is l, the number of output layer nodes is m, and the number of samples is q, then the optimal solution equation can be described as

In the formula,

is the expected output of the kth sample of the ith node in the network output layer, _oik is the predicted output of the kth sample of the ith node in the output layer,

are the neural network weights and threshold vectors,

is the optimal network weight and threshold vector, M is the total number of extreme learning machine weights and thresholds,

每个根的量子位置维数是M，上界设为U＝[U₁,U₂,...,U_M]，下界设为L＝[L₁,L₂,...,L_M]，设置最大迭代次数为G_max，迭代次数

设置三种更新方程的比例分别为R_r、R_n和R_c，更新公式中可调整参数分别为c₁、c₂和c₃，量子旋转角为0时的变异概率分别为e₁、e₂和e₃。在量子位置定义域内随机产生每个根的量子位置，每一维量子位置都限制在[0,1]，第

次迭代第i个根的量子位置是

对应的位置为

且

式中，

L_d是第d维位置下界，U_d是第d维位置上界。Furthermore, step five specifically includes: the parameters of the quantum root tree mechanism are set as follows: the root population size is

The quantum position dimension of each root is M, the upper bound is U = [U ₁ ,U ₂ ,...,U _M ], the lower bound is L = [L ₁ ,L ₂ ,...,L _M ], the maximum number of iterations is G _max , and the number of iterations is

The proportions of the three update equations are set to R _r , R _n and R _c , the adjustable parameters in the update formula are c ₁ , c ₂ and c ₃ , and the mutation probabilities when the quantum rotation angle is 0 are e ₁ , e ₂ and e ₃ . The quantum position of each root is randomly generated in the quantum position definition domain, and each dimension of the quantum position is restricted to [0,1].

The quantum position of the ith root of the iteration is

The corresponding position is

and

In the formula,

L _d is the lower bound of the d-th dimension position, and U _d is the upper bound of the d-th dimension position.

次迭代第i个根的适应度

将平均绝对误差作为适应度函数，因此

其中，

是第

次迭代输出层第i个节点第k个样本的预测输出，

是输出层第i个节点第k个样本的期望输出。根据

计算第

次迭代第i个根对应的湿润度，然后根据湿润度

升序排列种群中所有的根，全局最优的根的位置记为

对应量子位置记为

Furthermore, step six specifically includes: evaluating the

The fitness of the i-th root in the iteration

The mean absolute error is used as the fitness function, so

in,

It is

The predicted output of the kth sample of the i-th node in the output layer of the iteration,

is the expected output of the kth sample of the i-th node in the output layer.

Calculate the

The wetness corresponding to the i-th root is iterated, and then according to the wetness

Arrange all the roots in the population in ascending order, and the position of the global optimal root is recorded as

The corresponding quantum position is recorded as

个根，第

次迭代第i个根的量子位置第d维更新公式是

式中，e₁是变异概率，取值是[0,1/M]之间的常数，

是取值范围在(0,1)之间的随机数，

是前一代随机选择的根的第d维量子位置，

是对应的量子旋转角。量子旋转角的第d维更新公式是

式中，randn是取值范围在[-1,1]之间的高斯分布随机数。Furthermore, step seven specifically includes: updating process 1, for the first

Root,

The update formula for the d-dimensional quantum position of the ith root of the iteration is

In the formula, e ₁ is the mutation probability, and its value is a constant between [0,1/M].

is a random number in the range (0,1).

is the d-th quantum position of a randomly chosen root from the previous generation,

is the corresponding quantum rotation angle. The d-th dimension update formula of the quantum rotation angle is

Where randn is a Gaussian distributed random number in the range of [-1,1].

个根，第

次迭代第i个根的量子位置第d维更新公式是

式中，e₂是变异概率，取值是[0,1/M]之间的常数，

是全局最优的根的第d维量子位置，

是对应的量子旋转角。量子旋转角的第d维更新公式是

Update process 2, for the population with lower humidity

Root,

The update formula for the d-dimensional quantum position of the ith root of the iteration is

In the formula, e ₂ is the mutation probability, which is a constant between [0,1/M].

is the d-th quantum position of the globally optimal root,

is the corresponding quantum rotation angle. The d-th dimension update formula of the quantum rotation angle is

个根，第

次迭代第i个根的量子位置第d维更新公式是

式中，e₃是变异概率，取值是[0,1/M]之间的常数，

是对应的量子旋转角。量子旋转角的第d维更新公式是

式中，

是具有全局最优适应度的根的第d维位置，rand代表[0,1]之间的均匀随机数。Update process 3, for the population with lower humidity

Root,

The update formula for the d-dimensional quantum position of the ith root of the iteration is

Where e ₃ is the mutation probability, which is a constant between [0, 1/M].

is the corresponding quantum rotation angle. The d-th dimension update formula of the quantum rotation angle is

In the formula,

is the d-th dimension position of the root with the global optimal fitness, and rand represents a uniform random number between [0,1].

其中

第

次迭代量子位置更新后第i个根的位置是

设输入层与隐含层之间权值是

其中F＝n×l，隐含层阈值是

其中M＝n×l+l。计算第

次迭代更新后第i个根的适应度，有

其中

是第

次迭代输出层第i个节点第k个样本的预测输出，

是输出层第i个节点第k个样本的期望输出。根据湿润度定义计算更新后的湿润度，有

更新全局最优根的位置

和对应的量子位置

按照湿润度升序排列种群，迭代次数

Further, step eight specifically includes: after the quantum positions of all roots are updated, define “*” as the multiplication of the elements in the corresponding dimensions of the two vectors before and after, and map the quantum position of each root into a position, and the mapping relationship is

in

No.

The position of the i-th root after the iterative quantum position update is

Assume that the weight between the input layer and the hidden layer is

Where F = n × l, the hidden layer threshold is

Where M = n × l + l. Calculate the

The fitness of the i-th root after the iterative update is

in

It is

The predicted output of the kth sample of the i-th node in the output layer of the iteration,

is the expected output of the kth sample of the i-th node in the output layer. According to the definition of wetness, the updated wetness is calculated as follows:

Update the position of the global optimal root

and the corresponding quantum position

Arrange the population in ascending order of wetness, and the number of iterations

Compared with the prior art, the present invention has the following beneficial effects:

(1) Aiming at the problem that the performance of existing modulation signal recognition methods based on extreme learning machines deteriorates in impulse noise environments, a modulation signal recognition method based on quantum root tree mechanism evolution extreme learning machines is designed, which can effectively suppress impulse noise, and a weighted Myriad filter is used to suppress impulse noise.

(2) The modulation signal recognition method of the extreme learning machine evolved by the quantum root tree mechanism designed in the present invention designs a quantum root tree mechanism, which can solve the weights and thresholds of the extreme learning machine under impulse noise with high precision, effectively improving the modulation recognition rate.

(3) Simulation experiments have demonstrated the effectiveness of the modulation signal recognition method of the extreme learning machine evolved by the quantum root tree mechanism under impulsive noise. This method breaks through the application limitations of traditional methods, which suffer from performance deterioration or even failure in the environment of impulsive noise and low signal-to-noise ratio, and significantly improves the recognition rate compared with traditional methods.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a flow chart of a modulation signal recognition method of a quantum rooted tree mechanism evolution extreme learning machine designed in the present invention.

FIG. 2 is a comparison chart of the recognition accuracy of the method proposed in the present invention and the original method.

DETAILED DESCRIPTION

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

In conjunction with Figures 1 and 2, the steps of the present invention are as follows:

Step 1: Obtain communication modulation signals and signal preprocessing to construct a modulation signal data set under the impact noise background.

The communication modulation signal types used in the present invention are 2ASK, 4ASK, 2PSK, 4PSK, 2FSK, 4FSK and MSK, and are not limited to these modulation modes. The symbol rate _fd = 38400 bit/s, the carrier frequency _fc = 408kHz, the carrier frequencies for 2FSK are 204kHz and 408kHz, respectively, and the carrier frequencies for 4FSK are 102kHz, 204kHz, 306kHz and 408kHz, respectively. The sampling frequency _fs = 3.264MHz, the sampling time _t0 = 0.25s, and the number of sampling points for each symbol is 85.

-3T＜t＜3T，式中，t为采样时间，μ为升余弦滚降系数，T为码元周期。之后进行功率归一化，将每种调制方式的信号平均功率化为1。A shaping filter is added at the transmitting end. The shaping filter uses a raised cosine roll-off function to shape the digital baseband signal. The expression is:

-3T＜t＜3T, where t is the sampling time, μ is the raised cosine roll-off coefficient, and T is the symbol period. Then power normalization is performed to normalize the average power of the signal of each modulation mode to 1.

The Alpha stable distribution theory S _α (β,γ,δ) is used to construct the impact noise simulation model, where α is called the characteristic index, which represents the impact degree of the Alpha stable distribution. The value range is 0＜α≤2. The smaller α is, the greater the impact degree is. β is called the symmetry parameter or skew factor, which represents the skewness of the Alpha stable distribution relative to the center. The value range is -1≤β≤1. If β＜0, it is a negatively skewed distribution; if β＞0, it is a positively skewed distribution. γ is called the scale parameter, which represents the deviation degree of the Alpha stable distribution from the center. The value range is γ＞0. The larger γ is, the greater the deviation degree from the center is. δ is called the location parameter, which represents the location of the Alpha stable distribution. The value range is -∞＜δ＜∞. When 1＜α≤2, δ represents the mean; when 0＜α≤1, δ represents the median.

式中，

是信号的方差，γ是Alpha稳定分布的尺度参数，GSNR范围是-10dB到20dB，5dB间隔。The impulse noise parameters are set as: α = 1.5, β = 0, γ = 1, δ = 0. The generalized signal-to-noise ratio GSNR is used to measure the relationship between the signal and noise intensity, that is,

In the formula,

is the variance of the signal, γ is the scale parameter of the Alpha stable distribution, and the GSNR range is -10dB to 20dB with 5dB intervals.

Step 2: Use weighted Myriad filter to suppress impulse noise, and obtain the modulated signal preprocessing data set through segment processing.

和权重集合

定义输入向量x＝[x₁,x₂,...,x_N]^T和权值向量w＝[w₁,w₂,...,w_N]^T，对于给定的非线性度参数K＞0，假设随机变量

相互独立且服从位置参数θ和尺度参数

的柯西分布，可得其概率密度函数为

定义

加权Myriad使得似然函数

最大，可得

定义

引入函数ρ(v)＝ln(1+v²)，其中v是自变量，则加权Myriad输出为

称Q(θ)为加权Myriad目标函数。定义函数ρ(v)的导数

其中v是自变量，加权Myriad输出

是Q(θ)的一个局部极小值，因此有

定义函数

其中v是自变量，引入正函数

其中i＝1,2,...,N，则

因此有如下结论：包括

在内的所有目标函数Q(θ)的局部极小值点都可以表示成对输入x_i求加权均值的形式，即

定义映射

可将Q(θ)的局部极小点，即Q'(θ)＝0的根视为T(θ)的定点，利用定点迭代算法计算这些定点，即

其中m是定点迭代次数。Given a set of N observation samples

and weight set

Define the input vector x = [x ₁ ,x ₂ ,...,x _N ] ^T and the weight vector w = [w ₁ ,w ₂ ,...,w _N ] ^T , for a given nonlinearity parameter K>0, assume that the random variable

Independent of each other and subject to the location parameter θ and the scale parameter

The Cauchy distribution has a probability density function of

definition

The weighted Myriad makes the likelihood function

Maximum, available

definition

Introducing the function ρ(v)=ln(1+v ² ), where v is the independent variable, the weighted Myriad output is

Q(θ) is called the weighted Myriad objective function. Define the derivative of the function ρ(v)

Where v is the independent variable, weighted Myriad output

is a local minimum of Q(θ), so we have

Defining functions

Where v is the independent variable, introduce the positive function

Where i = 1, 2, ..., N, then

Therefore, the following conclusions are drawn:

All local minimum points of the objective function Q(θ) can be expressed as the weighted mean of the input _xi , that is,

Defining Mappings

The local minimum points of Q(θ), i.e., the roots of Q'(θ) = 0, can be regarded as fixed points of T(θ), and these fixed points can be calculated using the fixed-point iterative algorithm, i.e.

Where m is the number of fixed-point iterations.

The segmentation process divides the modulated signal of each modulation mode into a plurality of data segments of equal length and a collection of labels corresponding to each data segment.

Step three, extract instantaneous feature parameters from the modulated signal preprocessing data set to obtain a feature data set for training an extreme learning machine.

Based on the instantaneous amplitude, frequency and phase of the signal obtained in the impulse noise environment, multiple characteristic quantities of the instantaneous information of the digital modulation signal are further extracted to obtain 6 characteristic parameters.

式中，a_cn(i)为零中心归一化瞬时幅度，有a_cn(i)＝a_n(i)-1，

式中，a(i)是信号瞬时幅度，

是信号的长度。γ_max体现了信号瞬时幅度的变化特征。Characteristic parameter 1. Maximum value of the spectral density of the zero-centered normalized instantaneous amplitude

Where _acn (i) is the zero-centered normalized instantaneous amplitude, and _acn (i)=a _n (i)-1,

Where a(i) is the instantaneous amplitude of the signal,

is the length of the signal. _{γ max} reflects the changing characteristics of the instantaneous amplitude of the signal.

σ_aa反映了信号的绝对幅度信息。Characteristic parameter 2. Standard deviation of the absolute value of the zero-centered normalized instantaneous amplitude _σaa ,

σ _aa reflects the absolute amplitude information of the signal.

式中，a_t为设定的幅度阈值，一般取1。

是零中心瞬时相位非线性分量，有

式中，

为信号瞬时相位。σ_dp体现了信号瞬时相位的变化特征。Characteristic parameter 3. Standard deviation of the instantaneous phase nonlinear component of the zero-centered non-weak signal segment σ _dp ,

In the formula, a _t is the set amplitude threshold, which is generally 1.

is the zero-centered instantaneous phase nonlinear component,

In the formula,

is the instantaneous phase of the signal. _{σ dp} reflects the changing characteristics of the instantaneous phase of the signal.

σ_ap体现信号瞬时绝对相位的变化特征。Characteristic parameter 4. Standard deviation σ _ap of the absolute value of the instantaneous phase nonlinear component of the zero-centered non-weak signal segment,

σ _ap reflects the changing characteristics of the instantaneous absolute phase of the signal.

式中，f_cn(i)是零中心归一化瞬时频率，有f_cn(i)＝f(i)/m_f-1，

f(i)是瞬时频率。σ_af体现了瞬时绝对频率的变化特征。特征参数6.归一化瞬时频率的方差

式中，f_n(i)是归一化瞬时频率，f_n(i)＝f(i)/m_f。

体现了瞬时频率的变化特征。Characteristic parameter 5. Standard deviation of the absolute value of the instantaneous frequency of the zero-centered normalized non-weak signal segment σ _af ,

Where _fcn (i) is the zero-centered normalized instantaneous frequency, and _fcn (i)=f(i)/ _mf -1,

f(i) is the instantaneous frequency. _{σ af} reflects the variation characteristics of the instantaneous absolute frequency. Characteristic parameter 6. Variance of normalized instantaneous frequency

Wherein, _fn (i) is the normalized instantaneous frequency, _fn (i)=f(i)/ _mf .

It reflects the changing characteristics of instantaneous frequency.

By extracting characteristic parameters, a data set containing six characteristic parameters is obtained. The characteristic parameter data set is divided into a training set and a test set in a ratio of 3:1, and the training set is used to train the extreme learning machine for digital modulation signal recognition.

Step 4: Determine the objective function of the optimal parameters of the extreme learning machine.

式中，

为网络输出层第i个节点第k个样本的期望输出，o_ik为输出层第i个节点第k个样本的预测输出，

为神经网络权值和阈值向量，

为最优的网络权值和阈值向量，M是极限学习机权值和阈值总个数，也是量子根树机制的维数，有

After training the extreme learning machine with the feature training set, the system output is predicted, and the mean absolute error between the predicted output and the expected output is used as the objective function. Assuming the number of input layer nodes is n, the number of hidden layer nodes is l, the number of output layer nodes is m, and the number of samples is q, the optimal solution equation can be described as

In the formula,

is the expected output of the kth sample of the ith node in the network output layer, _oik is the predicted output of the kth sample of the ith node in the output layer,

are the neural network weights and threshold vectors,

is the optimal network weight and threshold vector, M is the total number of extreme learning machine weights and thresholds, and is also the dimension of the quantum root tree mechanism.

Step 5: Initialize the quantum root tree mechanism parameters.

隐含层节点数l＝20，输出层节点数m＝7，隐含层激活函数为sigmoid。The parameters of the extreme learning machine are set as follows: The number of input layer nodes is

The number of hidden layer nodes is l=20, the number of output layer nodes is m=7, and the hidden layer activation function is sigmoid.

计算得维数M＝140，上界设为U＝[U₁,U₂,...,U_M]＝[1,1,...,1]，下界设为L＝[L₁,L₂,...,L_M]＝[-1,-1,...,-1]，最大迭代次数G_max＝100，迭代次数

三种更新策略的比例分别为R_r＝0.3、R_n＝0.1和R_c＝0.6；可调整参数分别正c₁＝30，c₂＝c₃＝10；量子旋转角为0时的变异概率e₁＝e₂＝e₃＝1/M。在量子位置定义域内随机产生每个根的量子位置，每一维量子位置都限制在[0,1]，第

次迭代第i个根的量子位置是

对应的位置为

且

式中，

L_d是第d维下界，U_d是第d维上界。The parameters of the quantum root tree mechanism are set as follows: population size

The calculated dimension is M = 140, the upper bound is U = [U ₁ , U ₂ , ..., U _M ] = [1, 1, ..., 1], the lower bound is L = [L ₁ , L ₂ , ..., L _M ] = [-1, -1, ..., -1], the maximum number of iterations G _max = 100, and the number of iterations

The ratios of the three update strategies are R _r = 0.3, R _n = 0.1 and R _c = 0.6 respectively; the adjustable parameters are c ₁ = 30, c ₂ = c ₃ = 10 respectively; the mutation probability when the quantum rotation angle is 0 is e ₁ = e ₂ = e ₃ = 1/M. The quantum position of each root is randomly generated in the quantum position definition domain, and each dimension of the quantum position is restricted to [0,1].

The quantum position of the ith root of the iteration is

The corresponding position is

and

In the formula,

L _d is the lower bound of the d-th dimension, and U _d is the upper bound of the d-th dimension.

Step 6: Calculate the fitness and moisture content of all roots in the population and arrange the population in ascending order of moisture content.

次迭代第i个根的适应度

将平均绝对误差作为适应度函数，因此

其中，

是第

次迭代输出层第i个节点第k个样本的预测输出，

是输出层第i个节点第k个样本的期望输出。根据

计算第

次迭代第i个根对应的湿润度，然后根据湿润度

升序排列种群中所有的根，全局最优的根的位置记为

对应量子位置记为

Evaluation

The fitness of the i-th root in the iteration

The mean absolute error is used as the fitness function, so

in,

It is

The predicted output of the kth sample of the i-th node in the output layer of the iteration,

is the expected output of the kth sample of the i-th node in the output layer.

Calculate the

The wetness corresponding to the i-th root is iterated, and then according to the wetness

Arrange all the roots in the population in ascending order, and the position of the global optimal root is recorded as

The corresponding quantum position is recorded as

Step seven, use simulated quantum revolving door to update different individuals in the population respectively.

个根，，第

次迭代第i个根的量子位置第d维更新公式是

式中，e₁是变异概率，取值是[0,1/M]之间的常数，

是取值范围在(0,1)之间的随机数，

是前一代随机选择的根的第d维量子位置，

是对应的量子旋转角。量子旋转角的第d维更新公式是

式中，randn是取值范围在[-1,1]之间的高斯分布随机数。Update process 1: for the population with the lowest humidity

Root,

The update formula for the d-dimensional quantum position of the ith root of the iteration is

In the formula, e ₁ is the mutation probability, and its value is a constant between [0,1/M].

is a random number in the range (0,1).

is the d-th quantum position of a randomly chosen root from the previous generation,

is the corresponding quantum rotation angle. The d-th dimension update formula of the quantum rotation angle is

Where randn is a Gaussian distributed random number in the range of [-1,1].

个根，第

次迭代第i个根的量子位置第d维更新公式是

式中，e₂是变异概率，取值是[0,1/M]之间的常数，

是全局最优的根的第d维量子位置，

是对应的量子旋转角。量子旋转角的第d维更新公式是

Update process 2, for the population with lower humidity

Root,

The update formula for the d-dimensional quantum position of the ith root of the iteration is

In the formula, e ₂ is the mutation probability, which is a constant between [0,1/M].

is the d-th quantum position of the globally optimal root,

is the corresponding quantum rotation angle. The d-th dimension update formula of the quantum rotation angle is

个根，第

次迭代第i个根的量子位置第d维更新公式是

式中，e₃是变异概率，取值是[0,1/M]之间的常数，

是对应的量子旋转角。量子旋转角的第d维更新公式是

式中，

是具有全局最优适应度的根的第d维位置，rand为[0,1]之间的均匀随机数。Update process 3, for the population with lower humidity

Root,

The update formula for the d-dimensional quantum position of the ith root of the iteration is

Where e ₃ is the mutation probability, which is a constant between [0, 1/M].

is the corresponding quantum rotation angle. The d-th dimension update formula of the quantum rotation angle is

In the formula,

is the d-th dimension position of the root with the global optimal fitness, and rand is a uniform random number between [0,1].

Step 8: Calculate the fitness and wetness of the new generation of roots, update the global optimal root, and arrange the population in ascending order of wetness.

其中

“*”表示前后两向量对应维度内的元素相乘。第

次迭代量子位置更新后第i个根的位置是

设输入层与隐含层之间权值是

其中F＝n×l，隐含层阈值是

其中M＝n×l+l。计算第

次迭代更新后第i个根的适应度，有

其中，

是第

次迭代输出层第i个节点第k个样本的预测输出，

是输出层第i个节点第k个样本的期望输出。根据湿润度定义计算更新后的湿润度，有

更新全局最优根的位置

和对应的量子位置

按照湿润度升序排列种群，迭代次数

After the quantum positions of all roots are updated, the quantum position of each root is mapped to the position. The mapping relationship is

in

"*" means multiplying the elements in the corresponding dimensions of the two vectors.

The position of the i-th root after the iterative quantum position update is

Assume that the weight between the input layer and the hidden layer is

Where F = n × l, the hidden layer threshold is

Where M = n × l + l. Calculate the

The fitness of the i-th root after the iterative update is

in,

It is

The predicted output of the kth sample of the i-th node in the output layer of the iteration,

is the expected output of the kth sample of the i-th node in the output layer. According to the definition of wetness, the updated wetness is calculated as follows:

Update the position of the global optimal root

and the corresponding quantum position

Arrange the population in ascending order of wetness, and the number of iterations

是否达到最大迭代次数G_max，若达到最大迭代次数，则终止迭代，输出最优权值和阈值向量；否则返回步骤七。Step 9: Determine the number of iterations

Whether the maximum number of iterations G _max is reached, if so, the iteration is terminated and the optimal weight and threshold vector are output; otherwise, return to step seven.

Step 10: Use the extreme learning machine with the optimal weights and thresholds as a classifier to identify the modulated signal under the impact noise background. The optimal weights and thresholds are obtained by evolving the extreme learning machine through the quantum root tree mechanism, and are used as the initial weights and thresholds of the extreme learning machine. The training set data is used for training, and the trained extreme learning machine with the optimal weights and thresholds is used as a classifier for modulated signal recognition under the impact noise background. Finally, the test set or collected data is used to output the modulation recognition result.

In FIG2 , the modulation signal recognition method of the quantum rooted tree mechanism evolution extreme learning machine designed in the present invention is denoted as WMy-QRTO-ELM, and the modulation signal recognition method of the original extreme learning machine is denoted as ELM.

搜索上下界为[-1,1]，计算权值和阈值总个数M＝140，最大迭代次数G_max＝100，三种更新策略的比例R_r＝0.3，R_n＝0.1，R_c＝0.6，c₁＝30，c₂＝c₃＝10，量子旋转角为0时的变异概率e₁＝e₂＝e₃＝1/M。The simulation experiment parameters of the modulation signal recognition method of the quantum root tree mechanism evolution extreme learning machine are set as follows: the number of input layer nodes of the extreme learning machine is 6, the number of hidden layer nodes is 20, the number of output layer nodes is 7, and the hidden layer activation function is sigmoid.

The search upper and lower bounds are [-1,1], the total number of calculated weights and thresholds is M=140, the maximum number of iterations is _Gmax =100, the ratios of the three update strategies are _Rr =0.3, _Rn =0.1, _Rc =0.6, _c1 =30, _c2 = _c3 =10, and the mutation probability when the quantum rotation angle is 0 is _e1 = _e2 = _e3 =1/M.

As can be seen from Figure 2, after the weighted Myriad filter and quantum rooted tree mechanism evolution, the recognition rate under low generalized signal-to-noise ratio is greatly improved, breaking through the application limit of traditional methods.

Claims (1)

1. A modulation signal recognition method for an extreme learning machine evolved by a quantum root tree mechanism, characterized in that the steps are as follows: Step 1: Obtain the communication modulation signal, perform signal preprocessing, and obtain the modulation signal preprocessing data set under the impact noise background; the signal preprocessing includes shaping filtering, power normalization, adding impact noise and suppressing it; Step 2: Use weighted Myriad filter to suppress impulse noise, and obtain the modulated signal preprocessing data set through segment processing; Given a set of N observation samples

and weight set

Define the input vector x = [x ₁ , x ₂ , ..., x _N ] ^T and the weight vector

For a given nonlinearity parameter K>0, assuming that the random variable

Independent of each other and subject to the location parameter θ and the scale parameter

The Cauchy distribution has a probability density function of

definition

The weighted Myriad makes the likelihood function

Maximum, available

definition

Introducing the function ρ(v)=ln(1+v ² ), where v is the independent variable, the weighted Myriad output is

Q(θ) is called the weighted Myriad objective function; define the derivative of the function ρ(v)

Where v is the independent variable, weighted Myriad output

is a local minimum of Q(θ), so we have

Defining functions

Where v is the independent variable, introduce the positive function

Where i = 1, 2, ..., N, then

Therefore, the following conclusions are drawn:

All local minimum points of the objective function Q(θ) can be expressed as the weighted mean of the input _xi , that is,

Defining Mappings

The local minimum points of Q(θ), i.e., the roots of Q'(θ) = 0, can be regarded as fixed points of T(θ), and these fixed points can be calculated using the fixed-point iterative algorithm, i.e.

Where m is the number of fixed-point iterations; Segment processing divides the modulated signal of each modulation mode into a plurality of data segments of equal length and a collection form of labels corresponding to each data segment; Step 3: extract instantaneous feature parameters from the modulated signal preprocessing data set to obtain a feature data set for training the extreme learning machine; After the receiver receives the signal, it performs Hilbert transform on it to obtain its analytical form, that is,

Where s(t) is the analytical signal of the original signal y(t), and

is the Hilbert transform of y(t), we have

In the formula,

represents the convolution operation, and its frequency response is

The original signal y(t) is sampled with sampling frequency _fs , and the total number of points is

The discrete sequence y(n) of

The instantaneous amplitude is A(n), then

The instantaneous phase is θ(n), and we have

Since the main value interval of the inverse tangent function is (-π/2,π/2), θ(n) may produce a sudden change of ±π at this time, and it is adjusted to obtain a phase value in [0,2π)

have

The actual instantaneous phase ε(n) is related to

The relationship is

In the formula, mod represents the remainder operation,

There is phase wrapping. Since the dewrapping instantaneous phase φ(n) satisfies φ(n)＝2πf _c T _s n+ε(n)+θ, where f _c is the carrier frequency, T _s sampling is the period, and θ is the initial phase, it can be seen from the above formula that the dewrapping instantaneous phase is the linear phase component caused by the carrier frequency and the nonlinear component caused by ε(n) and θ.

Add a correction sequence {c(n)} to achieve deconvolution, defined as

At this time, the deconvolution instantaneous phase estimate is

When the carrier and code element are completely synchronized, the estimated value of the de-wrapped instantaneous phase nonlinear component is

The instantaneous frequency sequence can be obtained by differentiating the deconvolved instantaneous phase sequence, that is,

Where _fs is the sampling frequency; Step 4: Determine the objective function of the optimal parameters of the extreme learning machine; Use the feature training set to train the extreme learning machine and then predict the system output. Take the mean absolute error between the predicted output and the expected output as the objective function. Suppose the number of input layer nodes is

The number of hidden layer nodes is l, the number of output layer nodes is m, and the number of samples is q, then the optimal solution equation can be described as

In the formula,

is the expected output of the kth sample of the ith node in the network output layer, _oik is the predicted output of the kth sample of the ith node in the output layer,

are the neural network weights and threshold vectors,

is the optimal network weight and threshold vector, M is the total number of extreme learning machine weights and thresholds,

Step 5: Initialize the parameters of the quantum root tree mechanism; The parameters of the quantum root tree mechanism are set as follows: the root population size is

The quantum position dimension of each root is M, the upper bound is U = [U ₁ ,U ₂ ,...,U _M ], the lower bound is L = [L ₁ ,L ₂ ,...,L _M ], the maximum number of iterations is G _max , and the number of iterations is

The proportions of the three update equations are set to R _r , R _n and R _c , the adjustable parameters in the update formula are c ₁ , c ₂ and c ₃ , and the mutation probabilities when the quantum rotation angle is 0 are e ₁ , e ₂ and e ₃ ; the quantum position of each root is randomly generated in the quantum position definition domain, and each dimension of the quantum position is restricted to [0,1].

The quantum position of the ith root of the iteration is

The corresponding position is

and

In the formula,

L _d is the lower bound of the d-th dimension position, and U _d is the upper bound of the d-th dimension position; Step 6: Calculate the fitness and moisture content of all roots in the population, and arrange the population in ascending order of moisture content; Evaluation

The fitness of the i-th root in the iteration

The mean absolute error is used as the fitness function, so

in,

It is

The predicted output of the kth sample of the i-th node in the output layer of the iteration,

is the expected output of the kth sample of the i-th node in the output layer; according to

Calculate the

The wetness corresponding to the i-th root is iterated, and then according to the wetness

Arrange all the roots in the population in ascending order, and the position of the global optimal root is recorded as

The corresponding quantum position is recorded as

Step 7: Use simulated quantum revolving door to update different individuals in the population; Update process 1: for the population with the lowest humidity

Root,

The update formula for the d-dimensional quantum position of the ith root of the iteration is

In the formula, e ₁ is the mutation probability, and its value is a constant between [0,1/M].

is a random number in the range (0,1).

is the d-th quantum position of a randomly chosen root from the previous generation,

is the corresponding quantum rotation angle; the d-th dimension update formula of the quantum rotation angle is

Where randn is a Gaussian distributed random number in the range of [-1,1]; Update process 2, for the population with lower humidity

Root,

The update formula for the d-dimensional quantum position of the ith root of the iteration is

In the formula, e ₂ is the mutation probability, which is a constant between [0,1/M].

is the d-th quantum position of the globally optimal root,

is the corresponding quantum rotation angle; the d-th dimension update formula of the quantum rotation angle is

Update process 3, for the population with lower humidity

Root,

The update formula for the d-dimensional quantum position of the ith root of the iteration is

Where e ₃ is the mutation probability, which is a constant between [0, 1/M].

is the corresponding quantum rotation angle; the d-th dimension update formula of the quantum rotation angle is

In the formula,

is the d-th dimension position of the root with the global optimal fitness, and rand represents a uniform random number between [0,1]; Step 8: Calculate the fitness and wetness of the new generation of roots, update the global optimal root, and arrange the population in ascending order of wetness; After the quantum positions of all roots are updated, define “*” as the multiplication of the elements in the corresponding dimensions of the two vectors before and after, and map the quantum position of each root to the position. The mapping relationship is

in

No.

The position of the i-th root after the iterative quantum position update is

Assume that the weight between the input layer and the hidden layer is

Where F = n × l, the hidden layer threshold is

Where M = n × l + l; calculate the

The fitness of the i-th root after the iterative update is

in

It is

The predicted output of the kth sample of the i-th node in the output layer of the iteration,

is the expected output of the kth sample of the i-th node in the output layer; the updated wetness is calculated according to the definition of wetness,

Update the position of the global optimal root

and the corresponding quantum position

Arrange the population in ascending order of wetness, and the number of iterations

Step 9: Determine the number of iterations

Whether the maximum number of iterations G _max is reached, if so, the iteration is terminated and the optimal weight and threshold vector are output; otherwise, return to step 7; Step 10: Use the extreme learning machine with optimal weights and thresholds as a classifier to identify the modulated signal under the impact noise background. Evolve the extreme learning machine through the quantum root tree mechanism to obtain the optimal weights and thresholds, which are used as the initial weights and thresholds of the extreme learning machine. Use the training set data for training, and use the trained extreme learning machine with optimal weights and thresholds as a classifier for modulated signal identification under the impact noise background. Finally, use the test set or collected data to output the modulation recognition result.

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