CN108449295A - Combined modulation recognition methods based on RBM networks and BP neural network - Google Patents

Abstract

The combined modulation recognition methods based on RBM networks and BP neural network that the invention discloses a kind of, including：(1) modulated signal is pre-processed；(2) characteristic parameter is extracted；(3) training sample and test sample of every class modulation system are randomly generated；(4) BP input layers are trained with first layer hidden layer as a RBM；(5) intersection of the parameter of initialization RBM；(6) training RBM, obtains the intersection of parameter and the output feature of hidden layer；(7) visible layer and hidden layer by the first layer hidden layer of BP and next layer as second RBM are trained, input of the output of first RBM as second RBM, repeats the intersection of the parameter of (5) (6) (7) until obtaining all RBM；(8) re -training BP, until reaching optimal solution state；(9) test data is normalized, inputs trained BP, calculate Modulation Mode Recognition rate.The invention has the beneficial effects that：Input dimension is reduced, Modulation Identification rate is improved.

Description

Combined modulation identification method based on RBM network and BP neural network

Technical Field

The invention relates to a modulation identification method, in particular to a combined modulation identification method based on an RBM (radial basis function) network and a BP (back propagation) neural network, and belongs to the technical field of communication.

Background

With the development of communication technology, the application of signal modulation mode identification covers almost the whole commercial and military communication fields, has important functions in the aspects of signal authentication, interference identification, electronic countermeasure and the like, and has very wide application value and prospect.

Modulation identification refers to identifying a modulation scheme before demodulation of a received signal. Generally, there are three methods of modulation identification: decision tree classifier, cluster analysis, neural network classifier.

Nandi and Azzouz propose a decision tree algorithm for classification based on characteristic parameters. Decision tree classification is a low complexity and intuitive method that is susceptible to noise, and is therefore often combined with other methods in practical applications. The cluster analysis is a multivariate statistical classification method, which performs blind classification according to the pattern similarity in unlabeled samples, but the cluster analysis method is susceptible to noise, and different extracted characteristic parameters have great influence on the recognition performance. As the most common method, a Back Propagation (BP) and Radial Basis Function (RBF) neural network with self-learning and generalization capability is very suitable for the classification problem of potential nonlinear mapping of input signals and outputs, but the neural network classification method is easy to fall into the problem of local optimal solution. In addition, the neural network classification method has too slow convergence rate when approaching the optimal solution, poor generalization capability and low recognition rate under the condition of low signal-to-noise ratio (SNR).

The Restricted Boltzmann Machine (RBM) is a non-connected structure network in a layer, which is proposed on the basis of the Boltzmann Machine (BM) proposed by Hinton and Sejnowski, and can fit any discrete distribution under the condition that the hidden units are enough; after Hinton proposed the fast learning algorithm-Contrast Divergence (CD) for RBM in 2002, RBM has been successfully applied to various machine learning problems such as classification, regression, dimensionality reduction, etc.

Disclosure of Invention

In order to overcome the defects in the prior art, the invention aims to provide a combined modulation identification method which is based on an RBM network and a BP neural network and can improve the modulation identification rate.

In order to achieve the above object, the present invention adopts the following technical solutions:

the joint modulation identification method based on the RBM network and the BP neural network is characterized by comprising the following steps of:

step 1: preprocessing a modulation signal to be classified;

step 2: extracting characteristic parameters of the preprocessed signals, wherein the characteristic parameters are characteristic parameters based on a time domain, a frequency domain and statistics;

step 3: randomly generating a training sample and a testing sample of each type of modulation mode according to the characteristic parameters extracted at Step2 to obtain a training sample set, a testing data set and a corresponding class label set;

step 4: setting relevant parameters of a BP neural network, and taking an input layer and a first hidden layer of the BP neural network as an RBM network for training;

step 5: initializing a collection of parameters theta of the RBM network, wherein theta is (W, a, b), wherein W is a weight matrix between a hidden layer and a visible layer of the RBM network, a is a bias vector of the visible layer, and b is a bias vector of the hidden layer;

step 6: dividing the training samples generated by Step3 into small batch of data, normalizing the data and then training the RBM network to obtain a parameter collection theta of the RBM network and an output characteristic p (h) of a hidden layer_j1| v), where h is the state vector of the hidden layer, h_jRepresenting the state of the jth neuron in the hidden layer, and v is the state vector of the visible layer;

step 7: training a first hidden layer and a next layer of the BP neural network as a visible layer and a hidden layer of a second RBM network, and outputting p (h) of the first RBM network_j1| v) as input to the second RBM network, repeating Step5, Step6 and Step7 until a collection θ of parameters for all RBM networks is obtained;

step 8: setting an initial parameter theta 'of the BP neural network as a parameter set theta of the trained RBM network, retraining the BP neural network with supervision, and finely adjusting the parameter theta' to achieve an optimal solution state;

step 9: and (4) normalizing the test data, inputting the normalized test data into the trained BP neural network, and calculating the recognition rate of the modulation mode.

The joint modulation identification method based on the RBM network and the BP neural network is characterized in that, in Step1, the preprocessing includes: zero averaging and normalization.

The joint modulation identification method based on the RBM network and the BP neural network is characterized in that, in Step2, the characteristic parameters include: instantaneous amplitude characteristics, spectral characteristics of the signal, and higher order spectral characteristics of the signal.

The joint modulation identification method based on the RBM network and the BP neural network is characterized in that, in Step4, the relevant parameters include: the number of nodes of each layer of the BP neural network and the number of hidden layers.

The joint modulation identification method based on the RBM network and the BP neural network is characterized in that in Step5, a specific process of initializing a parameter set θ of the RBM network is as follows:

(5a) dividing the training samples generated by Step3 into small batches of data containing 20 samples of each type, and setting the number n of visible layer units_vSetting the number n of hidden layer units for the number of input layer nodes of BP neural network_hThe number of nodes of a first hidden layer of the BP neural network is;

(5b) the weight matrix W is initialized to random numbers from a normal distribution N (0,0.01), and a_iAnd b_jInitialized to 0, and the objective function is related to w at each iteration_ijApproximation of partial derivative of (a) Δ w_ijObjective function with respect to a_iApproximation of partial derivative of (a) Δ a_iObjective function with respect to b_jApproximation of partial derivative of (a) Δ b_jAll are initialized to 0, and the weight learning rate epsilon between the visible layer and the hidden layer is set_wLearning rate between visible layer biases ε_aAnd learning rate between hidden layer biases ε_bAre both set to 0.01, the momentum learning rate and the final momentum learning rate are set to 0.5 and 0.9, respectively, and the weight is setThe attenuation coefficient lambda takes any value between 0.01 and 0.0001, and a parameter k in the k-step contrast divergence algorithm is set to be 1.

The joint modulation identification method based on the RBM network and the BP neural network is characterized in that in Step6, the specific process of training the RBM network is as follows:

(6a) when the modulated signal to be classified is transferred in the forward direction, v_i ⁽⁰⁾Representing the input value at the first forward pass, the output of the hidden layer of the RBM network is:

wherein,is an activation function of the RBM network, using input v_i ⁽⁰⁾Calculating output probability;

(6b) p (h)_j ⁽⁰⁾＝1|v⁽⁰⁾) Binarization as h_j ⁽⁰⁾If this number is less than p (h)_j ⁽⁰⁾＝1|v⁽⁰⁾) Then h is_j ⁽⁰⁾If the number is greater than or equal to p (h)_j ⁽⁰⁾＝1|v⁽⁰⁾) Then h is_j ⁽⁰⁾Has a value of 1;

(6c) when the modulation signal to be classified is transmitted reversely, the calculated h_j ⁽⁰⁾As inputs, the output of the visible layer of the RBM network is:

(6d) from v calculated in back propagation_i ⁽¹⁾Repeating the step (6a) and the step (6b), and calculating p (h) after the second iteration_j ⁽¹⁾＝1|v⁽¹⁾) And h_j ⁽¹⁾A value of (d);

(6e) using a CD-k algorithm to perform k-step alternating Gibbs sampling to obtain the w of the objective function at each iteration_ij、a_i、b_jSince k is 1, Δ w is an approximation of the partial derivative of (c)_ij、Δa_i、Δb_jAre respectively formulated as:

Δw_ij≈p(h_i ⁽⁰⁾＝1|v⁽⁰⁾)·v_j ⁽⁰⁾-p(h_i ⁽¹⁾＝1|v⁽¹⁾)·v_j ⁽¹⁾(4)

Δa_i＝v_i ⁽⁰⁾-v_i ⁽¹⁾(5)

Δb_i＝p(h_i ⁽⁰⁾＝1|v⁽⁰⁾)-p(h_i ⁽¹⁾＝1|v⁽¹⁾) (6)

(6f) when iterating to l +1 times, updating w by gradient ascending method_ij、a_i、b_jThe update formula is:

w_ij ^(l+1)＝w_ij ^(l)+Δw_ij ^(l+1)(7)

a_i ^(l+1)＝a_i ^(l)+Δa_i ^(l+1)(8)

b_j ^(l+1)＝b_j ^(l)+Δb_j ^(l+1)(9)

wherein, Δ w_ij、Δa_i、Δb_jCan be expressed as:

where ρ is the momentum learning rate, n_blockIs the number of small batches of data,is the weight decay term.

The joint modulation identification method based on the RBM network and the BP neural network is characterized in that in Step8, the process of training the BP neural network and finely adjusting the parameter θ' to reach the optimal solution state specifically includes the following steps:

(8a) initializing parameters theta' of the BP neural network into a parameter collection theta of the trained RBM network, and then setting a transfer function of the BP neural network into a Sigmoid function:

(8b) when modulation signals to be classified are transmitted in the forward direction, a new training set pair formed by original training samples and class labels is transmitted from an input layer, the new training set pair is transmitted to an output layer after being processed layer by layer through hidden layers, and if the actual output error and the expected output error of the output layer are too large, the error is transmitted in the backward direction;

(8c) when the modulation signals to be classified are reversely propagated, the output is reversely propagated to the input layer by layer through the hidden layer, errors are distributed to all units of all the input layers, so that error signals of all the units of all the input layers are obtained, the weight parameters of all the input layers are corrected by the error signals, and when the errors are smaller than the minimum errors, the training is completed.

The invention has the advantages that:

1. the modulation signals to be classified are preprocessed in a zero-mean (zero center) mode, a normalization mode and the like, characteristic parameters are extracted, and input dimensionality is reduced;

2. the problems that the BP neural network training is trapped in a local minimum value, the convergence speed is too low at the optimal solution and the like are effectively solved, and the modulation recognition rate of the system is improved.

Drawings

FIG. 1 is a general flow chart of the joint modulation identification method of the present invention;

FIG. 2 is a schematic diagram of the modulation performed by the RBM network in conjunction with the BP neural network;

FIG. 3 is a flow chart of RBM network training.

Detailed Description

The invention carries out preprocessing such as zero equalization, normalization and the like on the modulation signals to be classified, extracts characteristic parameters, reduces input dimension, trains an input layer, a multilayer hidden layer and an output layer of the BP neural network according to a multilayer RBM network mode, obtains the weight of the BP neural network and the initial value of an offset parameter, and trains the BP neural network to finely adjust the parameter, thereby carrying out signal modulation mode identification.

The invention is described in detail below with reference to the figures and the embodiments.

Referring to fig. 1, the joint modulation identification method based on the RBM network and the BP neural network of the present invention is specifically implemented as follows:

step 1: and carrying out zero equalization and normalization preprocessing on the modulation signals x (n) to be classified.

The signal sequence s (n) after zero-averaging and normalization is expressed by the formula:

wherein,is a zero-averaged sequence of the modulated signal x (n) to be classified, HT(s)_Z) Is s_z(N) Hilbert change, N being the length of the signal sequence.

Step 2: extracting characteristic parameters of the preprocessed signals, wherein the characteristic parameters mainly refer to characteristic parameters based on a time domain, a frequency domain and statistics, and the characteristic parameters comprise:

(1) the characteristic parameter based on the time domain is an instantaneous amplitude characteristic, and the characteristic parameter is used for distinguishing a MASK modulation mode and an MQAM modulation mode;

(2) the characteristic parameter based on the frequency domain is the frequency spectrum characteristic of the signal, and the characteristic parameter is used for distinguishing the MFSK modulation mode;

(3) the characteristic parameter based on the statistic is the high-order spectral characteristic of the signal, and the characteristic parameter is used for distinguishing the modulation mode of the MPSK.

Step 3: and randomly generating a training sample and a testing sample of each type of modulation mode according to the characteristic parameters extracted at Step2 to obtain a training sample set, a testing data set and a corresponding class label set.

Steps 4 to 7 show the joint modulation process of the RBM network and the BP neural network, and refer to fig. 2.

Step 4: setting relevant parameters of the BP neural network, and taking an input layer and a first hidden layer of the BP neural network as an RBM network for training.

Step 5: initializing a set of parameters of the RBM network, θ ═ (W, a, b), where W is a weight matrix between the hidden and visible layers of the RBM network, W ═ W { (W)_ij}，w_ijIs the connection weight of the ith neuron in the hidden layer and the jth neuron in the visible layer; a is the bias vector for the visible layer, a ═ a_i}，a_iIs made bySee bias of the ith neuron in the layer; b is the bias vector of the hidden layer, b ═ b_j}，b_jIs the bias of the jth neuron in the hidden layer.

The specific process of initializing the parameter set theta of the RBM network is as follows:

(5a) divide the training samples generated at Step3 into small batches of data containing 20 samples per class (to improve computational efficiency), set the number of visible layer cells n_vSetting the number n of hidden layer units for the number of input layer nodes of BP neural network_hThe number of nodes of the first hidden layer of the BP neural network.

(5b) The weight matrix W is initialized to random numbers from a normal distribution N (0,0.01), and a_iAnd b_jInitialized to 0, and the objective function is related to w at each iteration_ijApproximation of partial derivative of (a) Δ w_ijObjective function with respect to a_iApproximation of partial derivative of (a) Δ a_iObjective function with respect to b_jApproximation of partial derivative of (a) Δ b_jAre all initialized to 0, i.e. Δ w_ij＝0，Δa_i＝0，Δb_j0; learning the weight between the visible layer and the hidden layer_wLearning rate between visible layer biases ε_aAnd learning rate between hidden layer biases ε_bAre all set to 0.01, i.e. epsilon_w＝ε_a＝ε_bThe momentum learning rate and the final momentum learning rate are set to 0.5 and 0.9, respectively, the weight attenuation coefficient λ may take any value between 0.01 and 0.0001, and the parameter k in the k-step contrast divergence algorithm is set to 1.

Step 6: dividing the training samples generated by Step3 into small batch of data, normalizing the data and then training the RBM network to obtain a parameter collection theta of the RBM network and an output characteristic p (h) of a hidden layer_j1| v), wherein h_jIs the state of the jth neuron in the hidden layer, h_jE h, h is the state vector of the hidden layer, v is the state vector of the visible layer, v ═ v_i}，v_iIs the state of the ith neuron in the visible layer.

Referring to fig. 3, the specific process of training the RBM network is as follows:

(6a) when the modulated signal to be classified is transferred in the forward direction, v_i ⁽⁰⁾Representing the input value at the first forward pass, the output of the hidden layer of the RBM network is:

wherein,is an activation function of the RBM network, using input v_i ⁽⁰⁾And calculating the output probability.

(6b) P (h)_j ⁽⁰⁾＝1|v⁽⁰⁾) Binarization as h_j ⁽⁰⁾I.e. a number between 0 and 1 is randomly generated, if this number is smaller than p (h)_j ⁽⁰⁾＝1|v⁽⁰⁾) Then h is_j ⁽⁰⁾If the number is greater than or equal to p (h)_j ⁽⁰⁾＝1|v⁽⁰⁾) Then h is_j ⁽⁰⁾Has a value of 1.

(6c) When the modulation signal to be classified is transmitted reversely, the calculated h_j ⁽⁰⁾As inputs, the output of the visible layer of the RBM network is:

due to input v_i ⁽⁰⁾Is at [0,1 ]]In between, so after calculating the output probability of the visible layer, the binary is not needed, and the method can be directly regarded as the input v of the next forward propagation_i ⁽¹⁾。

(6d) From v calculated in back propagation_i ⁽¹⁾Repeating the step (6a) and the step (6b), and calculating p (h) after the second iteration_j ⁽¹⁾＝1|v⁽¹⁾) And h_j ⁽¹⁾The value of (c).

(6e) Using a CD-k algorithm to perform k-step alternating Gibbs sampling to obtain the w of the objective function at each iteration_ij、a_i、b_jSince k is 1, Δ w is an approximation of the partial derivative of (c)_ij、Δa_i、Δb_jAre respectively formulated as:

Δw_ij≈p(h_i ⁽⁰⁾＝1|v⁽⁰⁾)·v_j ⁽⁰⁾-p(h_i ⁽¹⁾＝1|v⁽¹⁾)·v_j ⁽¹⁾(4)

Δa_i＝v_i ⁽⁰⁾-v_i ⁽¹⁾(5)

Δb_i＝p(h_i ⁽⁰⁾＝1|v⁽⁰⁾)-p(h_i ⁽¹⁾＝1|v⁽¹⁾) (6)

(6f) when iterating to l +1 times, updating w by gradient ascending method_ij、a_i、b_jThe update formula is:

w_ij ^(l+1)＝w_ij ^(l)+Δw_ij ^(l+1)(7)

a_i ^(l+1)＝a_i ^(l)+Δa_i ^(l+1)(8)

b_j ^(l+1)＝b_j ^(l)+Δb_j ^(l+1)(9)

wherein, Δ w_ij、Δa_i、Δb_jCan be expressed as:

where ρ is the momentum learning rate, n_blockIs the number of small batches of data,is the weight decay term.

Step 7: training a first hidden layer and a next layer of the BP neural network as a visible layer and a hidden layer of a second RBM network, and outputting p (h) of the first RBM network_j1| v) as input to the second RBM network, and repeating Step5, Step6, and Step7 until a collection θ of parameters for all RBM networks is obtained.

Step 8: setting an initial parameter theta 'of the BP neural network as a parameter set theta of the trained RBM network, retraining the BP neural network with supervision, and finely adjusting the parameter theta' to reach an optimal solution state, wherein the whole process specifically comprises the following steps:

(8a) initializing parameters theta 'of the BP neural network into a parameter set theta of the RBM network which is trained, wherein theta is (W, a, b), namely the parameters theta' of the BP neural network are initialized into a weight matrix W which is trained, a bias vector a and a bias vector b, and then setting a transfer function of the BP neural network into a Sigmoid function:

(8b) when the modulation signals to be classified are transmitted in the forward direction, a new training set pair formed by original training samples and class labels is transmitted from an input layer, the training set pair is transmitted to an output layer after being processed layer by layer through hidden layers, and if the actual output error and the expected output error of the output layer are too large, the error is transmitted in the backward direction.

(8c) When the modulation signals to be classified are reversely propagated, the output is reversely propagated to the input layer by layer through the hidden layer, errors are distributed to all units of all the input layers, so that error signals of all the units of all the input layers are obtained, the weight parameters of all the input layers are corrected by the error signals, and when the errors are smaller than the minimum errors, the training is completed.

Step 9: and (4) normalizing the test data, inputting the normalized test data into the trained BP neural network, and calculating the recognition rate of the modulation mode.

Because the trained parameters of the RBM network are used as the initial parameters of the BP neural network, the selection of the initial parameters of the BP neural network is close to the optimal solution, the method effectively avoids the problems that the training of the BP neural network is trapped in a local minimum value, the convergence speed at the optimal solution is too slow and the like, and improves the modulation recognition rate of the system.

The combined modulation identification method based on the RBM network and the BP neural network can be used for identification of a modulation mode in a communication signal transmission process.

It should be noted that the above-mentioned embodiments do not limit the present invention in any way, and all technical solutions obtained by using equivalent alternatives or equivalent variations fall within the protection scope of the present invention.

Claims (7)

1. The joint modulation identification method based on the RBM network and the BP neural network is characterized by comprising the following steps of:

step 1: preprocessing a modulation signal to be classified;

step 2: extracting characteristic parameters of the preprocessed signals, wherein the characteristic parameters are characteristic parameters based on a time domain, a frequency domain and statistics;

step 3: randomly generating a training sample and a testing sample of each type of modulation mode according to the characteristic parameters extracted at Step2 to obtain a training sample set, a testing data set and a corresponding class label set;

step 4: setting relevant parameters of a BP neural network, and taking an input layer and a first hidden layer of the BP neural network as an RBM network for training;

step 5: initializing a collection of parameters theta of the RBM network, wherein theta is (W, a, b), wherein W is a weight matrix between a hidden layer and a visible layer of the RBM network, a is a bias vector of the visible layer, and b is a bias vector of the hidden layer;

step 6: dividing the training samples generated by Step3 into small batch of data, normalizing the data and then training the RBM network to obtain a parameter collection theta of the RBM network and an output characteristic p (h) of a hidden layer_j1| v), where h is the state vector of the hidden layer, h_jRepresenting the state of the jth neuron in the hidden layer, and v is the state vector of the visible layer;

step 7: training a first hidden layer and a next layer of the BP neural network as a visible layer and a hidden layer of a second RBM network, and outputting p (h) of the first RBM network_j1| v) as input to the second RBM network, repeating Step5, Step6 and Step7 until a collection θ of parameters for all RBM networks is obtained;

step 8: setting an initial parameter theta 'of the BP neural network as a parameter set theta of the trained RBM network, retraining the BP neural network with supervision, and finely adjusting the parameter theta' to achieve an optimal solution state;

step 9: and (4) normalizing the test data, inputting the normalized test data into the trained BP neural network, and calculating the recognition rate of the modulation mode.

2. The joint modulation recognition method based on the RBM network and the BP neural network as claimed in claim 1, wherein in Step1, the preprocessing comprises: zero averaging and normalization.

3. The joint modulation recognition method based on the RBM network and the BP neural network as claimed in claim 1, wherein in Step2, the characteristic parameters comprise: instantaneous amplitude characteristics, spectral characteristics of the signal, and higher order spectral characteristics of the signal.

4. The RBM network and BP neural network-based joint modulation recognition method of claim 1, wherein at Step4, the related parameters comprise: the number of nodes of each layer of the BP neural network and the number of hidden layers.

5. The joint modulation recognition method based on the RBM network and the BP neural network as claimed in claim 1, wherein in Step5, the specific process of initializing the parameter set θ of the RBM network is as follows:

(5a) dividing the training samples generated by Step3 into small batches of data containing 20 samples of each type, and setting the number n of visible layer units_vSetting the number n of hidden layer units for the number of input layer nodes of BP neural network_hThe number of nodes of a first hidden layer of the BP neural network is;

(5b) the weight matrix W is initialized to random numbers from a normal distribution N (0,0.01), and a_iAnd b_jInitialized to 0, and the objective function is related to w at each iteration_ijApproximation of partial derivative of (a) Δ w_ijObjective function with respect to a_iApproximation of partial derivative of (a) Δ a_iObjective function with respect to b_jApproximation of partial derivative of (a) Δ b_jAll are initialized to 0, and the weight learning rate epsilon between the visible layer and the hidden layer is set_wLearning rate between visible layer biases ε_aAnd learning rate between hidden layer biases ε_bThe momentum learning rate and the final momentum learning rate are respectively set to 0.5 and 0.9, the weight attenuation coefficient lambda takes any value between 0.01 and 0.0001, and the parameter k in the k-step contrast divergence algorithm is set to be 1.

6. The joint modulation recognition method based on the RBM network and the BP neural network as claimed in claim 1, wherein in Step6, the specific process of training the RBM network is as follows:

(6a) when the modulated signal to be classified is transferred in the forward direction, v_i ⁽⁰⁾Representing the input value at the first forward pass,the output of the hidden layer of the RBM network is:

wherein,is an activation function of the RBM network, using input v_i ⁽⁰⁾Calculating output probability;

(6b) p (h)_j ⁽⁰⁾＝1|v⁽⁰⁾) Binarization as h_j ⁽⁰⁾If this number is less than p (h)_j ⁽⁰⁾＝1|v⁽⁰⁾) Then h is_j ⁽⁰⁾If the number is greater than or equal to p (h)_j ⁽⁰⁾＝1|v⁽⁰⁾) Then h is_j ⁽⁰⁾Has a value of 1;

(6c) when the modulation signal to be classified is transmitted reversely, the calculated h_j ⁽⁰⁾As inputs, the output of the visible layer of the RBM network is:

(6d) from v calculated in back propagation_i ⁽¹⁾Repeating the step (6a) and the step (6b), and calculating p (h) after the second iteration_j ⁽¹⁾＝1|v⁽¹⁾) And h_j ⁽¹⁾A value of (d);

(6e) using a CD-k algorithm to perform k-step alternating Gibbs sampling to obtain the w of the objective function at each iteration_ij、a_i、b_jSince k is 1, Δ w is an approximation of the partial derivative of (c)_ij、Δa_i、Δb_jAre respectively formulated as:

Δw_ij≈p(h_i ⁽⁰⁾＝1|v⁽⁰⁾)·v_j ⁽⁰⁾-p(h_i ⁽¹⁾＝1|v⁽¹⁾)·v_j ⁽¹⁾(4)

Δa_i＝v_i ⁽⁰⁾-v_i ⁽¹⁾(5)

Δb_i＝p(h_i ⁽⁰⁾＝1|v⁽⁰⁾)-p(h_i ⁽¹⁾＝1|v⁽¹⁾) (6)

(6f) when iterating to l +1 times, updating w by gradient ascending method_ij、a_i、b_jThe update formula is:

w_ij ^(l+1)＝w_ij ^(l)+Δw_ij ^(l+1)(7)

a_i ^(l+1)＝a_i ^(l)+Δa_i ^(l+1)(8)

b_j ^(l+1)＝b_j ^(l)+Δb_j ^(l+1)(9)

wherein, Δ w_ij、Δa_i、Δb_jCan be expressed as:

where ρ is the momentum learning rate, n_blockIs the number of small batches of data,is the weight decay term.

7. The joint modulation recognition method based on the RBM network and the BP neural network as claimed in claim 1, wherein in Step8, the process of training the BP neural network and fine-tuning the parameter θ' to reach the optimal solution state specifically comprises the following steps:

(8a) initializing parameters theta' of the BP neural network into a parameter collection theta of the trained RBM network, and then setting a transfer function of the BP neural network into a Sigmoid function:

(8b) when modulation signals to be classified are transmitted in the forward direction, a new training set pair formed by original training samples and class labels is transmitted from an input layer, the new training set pair is transmitted to an output layer after being processed layer by layer through hidden layers, and if the actual output error and the expected output error of the output layer are too large, the error is transmitted in the backward direction;

(8c) when the modulation signals to be classified are reversely propagated, the output is reversely propagated to the input layer by layer through the hidden layer, errors are distributed to all units of all the input layers, so that error signals of all the units of all the input layers are obtained, the weight parameters of all the input layers are corrected by the error signals, and when the errors are smaller than the minimum errors, the training is completed.