CN114239657A - Time sequence signal identification method based on complex value interference neural network - Google Patents

Time sequence signal identification method based on complex value interference neural network Download PDF

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CN114239657A
CN114239657A CN202111557195.6A CN202111557195A CN114239657A CN 114239657 A CN114239657 A CN 114239657A CN 202111557195 A CN202111557195 A CN 202111557195A CN 114239657 A CN114239657 A CN 114239657A
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庄连生
李奥迪
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Abstract

The invention provides a time sequence signal identification method based on a complex value interference neural network, which comprises the following steps: preprocessing the time sequence signal and calculating a complex value time-frequency diagram of the signal; constructing a complex value interference neural network comprising an interference convolution layer and a frequency domain full-link layer; calculating a classification loss function, and carrying out complex value interference neural network training based on a gradient descent method; and deploying and testing a complex value interference neural network model.

Description

Time sequence signal identification method based on complex value interference neural network
Technical Field
The invention relates to a time sequence signal identification method based on a complex value interference neural network, mainly aims at the signal identification problem of complex value time-frequency graph data, and belongs to the technical field of machine learning and time sequence signal processing.
Background
Time series data often occurs in many fields, such as voice, communications, finance, and biomedicine. The conventional timing problem usually requires human labor for feature engineering to input the preprocessed data into the machine learning algorithm, and such feature engineering usually requires professional knowledge in some specific fields, thereby further increasing the preprocessing cost. However, with the advent of deep learning, the convolutional neural network can process computer vision tasks more perfectly, and the network can automatically combine the most basic features into more advanced and abstract features layer by layer, thereby completing the computer vision tasks. However, the convolutional neural network algorithm based on the one-dimensional time series signal often cannot fully exert the strong self-learning capability of the convolutional neural network. Researches show that the convolutional neural network can efficiently extract the characteristics of spatial data, so that the convolutional neural network time sequence signal identification method based on the time sequence signal two-dimensional time frequency diagram becomes a mainstream algorithm.
However, the signal time-frequency diagram is very different from the natural image, the horizontal axis and the vertical axis of the time-frequency diagram represent time and frequency, respectively, and the horizontal axis and the vertical axis of the natural image represent space. The network structure layer designed for natural images, such as convolutional layer, does not take into account the difference between the horizontal axis and the vertical axis in physical meaning, so although it has achieved some success in the task of time sequence signal identification, it still lacks due robustness and interpretability. Aiming at the problems, the invention provides a time sequence signal identification method based on a complex value interference neural network, which has the core thought that the autocorrelation characteristic of time sequence signals is fully mined by constructing the complex value interference network comprising an interference convolution layer and a frequency domain full-link layer, so that the distinguishing characteristic of various time sequence signals is extracted, and the time sequence signal classification or identification is finally realized.
Disclosure of Invention
The technical problems solved by the invention are as follows: the method is used for time sequence signal identification of complex-valued time-frequency diagram data. The problem can be described as constructing a complex neural network structure containing optimizable parameters, and optimizing the parameters by a gradient descent method, so that the structure can automatically find distinctive features of different types of time-sequence signals from a complex-valued time-frequency graph, and finally realize certain given targets by using the features. In the process, the structure of the neural network directly influences the quality of the extracted features, and the neural network structure with good interpretability and noise robustness is provided.
The invention discloses a time sequence signal identification method based on a complex value interference neural network, which comprises the following steps: preprocessing the time sequence signal and calculating a complex value time-frequency diagram of the signal; constructing a complex value interference neural network comprising an interference convolution layer and a frequency domain full-link layer; calculating a classification loss function, and carrying out complex value interference neural network training based on a gradient descent method; and deploying and testing a complex value interference neural network model.
A flow chart of performing radio frequency fingerprint identification by using a complex value interference neural network is shown in fig. 1, and mainly comprises the following steps: the method comprises the following steps:
step S1, preprocessing the time sequence signal and calculating a complex value time-frequency diagram of the time sequence signal;
step S2, constructing a complex value interference neural network, wherein the complex value interference neural network is characterized in that an interference convolution layer and a frequency domain full-link layer are sequentially and alternately connected, the interference convolution layer performs time-dimension complex value convolution operation on a complex value time-frequency graph to simulate the interference process of waves, and the frequency domain full-link layer performs frequency-dimension complex value full-link operation on the complex value time-frequency graph to simulate the nonlinear process of waves;
step S3, calculating a classification loss function, and performing complex value interference neural network training based on a gradient descent method to obtain a complex value interference neural network model;
and S4, obtaining complex value time-frequency diagram data to be tested from the time sequence signal to be tested according to the step S1, obtaining the probability that the time sequence signal to be tested belongs to each category by utilizing the complex value interference neural network model and the complex value time-frequency diagram data to be tested, and finally taking the category corresponding to the maximum probability value as the final prediction result of the complex value interference neural network, thereby realizing the identification of the time sequence signal.
In step S2, the frequency domain full link layer includes: carrying out dimensionality transformation on the input tensor to enable the last dimension of the tensor after transformation to be the frequency dimension; defining two full connection layers which are equivalent to a complex full connection layer; calculating the real part tensor and the imaginary part tensor of the output tensor of the equivalent complex value fully-connected layer according to the tensor after dimensionality transformation and the two fully-connected layers; and performing dimensionality splicing on the real part tensor and the imaginary part tensor, and converting the spliced tensor into a five-dimensional tensor with the same meaning as the input tensor, wherein the five-dimensional tensor is used as a final output result of the frequency domain full-connection layer.
In step S2, the interference convolution layer includes: taking a real part and an imaginary part of input data, and then carrying out dimension transformation on a real part tensor and an imaginary part tensor to ensure that the last dimension of the tensor after the transformation is a time dimension; defining two convolutional layers which are equivalent to a complex value convolutional layer, wherein the weight parameters of the two convolutional layers are initialized by using a Kaiming normal initialization method; calculating a real part tensor and an imaginary part tensor of an output tensor of the equivalent complex value convolution layer according to the tensor after dimensionality transformation and the two convolution layers; and performing dimensionality splicing on the real part tensor and the imaginary part tensor, and converting the spliced tensor into a five-dimensional tensor which has the same meaning as the input tensor, wherein the five-dimensional tensor is used as a final output result of the interference convolution layer.
The constructed complex value interference neural network comprises a frequency domain full-connection layer and an interference convolution layer which are repeatedly stacked for a plurality of times so as to increase the depth of the network; accessing a statistical pooling layer, converting complex value data into real value data, and obtaining a feature vector of each sample; and finally, accessing two common full-connection layers for feature transformation, and outputting the probability that the sample belongs to each category.
In the structure complex value interference neural network, when a frequency domain full connection layer and an interference convolution layer are repeatedly stacked, a layer jump connection or dense connection mode in a ResNet and DenseNet network architecture is adopted to further increase the network depth.
Step S1: and preprocessing the time sequence signal and calculating a complex value time-frequency diagram of the signal.
This step includes the following two substeps.
Step S101: the timing signal is pre-processed, such as normalized, filtered, etc.
Step S102: and calculating a complex-value time-frequency diagram of the signal after preprocessing.
The embodiment of the invention adopts a classic short-time Fourier transform method, and the short-time Fourier transform process comprises the following steps: the fourier transform is preceded by a time-limited window function w (n) and the non-stationary signal is assumed to be stationary during a short time interval of the analysis window, and the signal is analyzed segment by shifting the window function on the time axis to obtain a set of local "spectra" of the signal. The calculation formula is as follows:
Figure BDA0003419258550000031
where X (n) is an input timing signal which can be either a complex or a real signal, w (n) is a window function which can employ a Hamming window, R is the number of signal sample points moved by adjacent signal windows, and XmAnd (omega) is complex-valued time-frequency diagram data, wherein m represents time (representing an mth frame short-time signal), and omega represents frequency. The complex-valued time-frequency diagram data after frequency discretization is recorded as X, wherein X is a three-dimensional tensor, each dimension of the tensor represents a real part, an imaginary part (2 dimensions), a frequency dimension and a time dimension respectively, and the method is recorded as follows:
X：＝[2，Freq，Time]。
and finally, carrying out dimension transformation on the three-dimensional tensor X, wherein the transformed tensor X _ ReSize is a five-dimensional tensor, namely:
X_ReSize：＝[1，2，Freq，1，Time]。
x _ ReSize is the input of the complex-valued interferometric neural network.
Step S2: and constructing a complex-valued interference neural network comprising an interference convolution layer and a frequency domain full-link layer.
The invention mainly provides a new neural network structure, namely a complex value interference network, which is a key step of the invention. The invention improves the traditional convolution neural network, is similar to the traditional convolution neural network in principle, achieves the aim of respectively considering time domain and frequency domain by replacing the convolution layer of the traditional convolution network with a frequency domain full-connection layer and an interference convolution layer, and has stronger interpretability and robustness. This step therefore comprises the following substeps.
Step S201: and constructing a frequency domain full-connection layer.
The frequency domain fully-connected layer input data is denoted as FcIn, which is a five-dimensional tensor expressed as:
FcIn：＝[Batch，2，Freq_FcIn，FeatureMaps，Time]。
wherein, Batch represents the sample number of each Batch of samples, 2 represents two dimensions of a real part and an imaginary part of a complex value, Freq _ FcIn represents the frequency dimension degree of input data of a frequency domain full connection layer, FeatureMaps represents the feature map number (the dimension of an initial Time-frequency map is 1), and Time represents the Time dimension degree and the frame number of the Time-frequency map.
(1) Performing dimension transformation on the input FcIn, so that the last dimension of the transformed data FcIn _ ReSize is a frequency dimension, namely:
FcIn_ReSize:＝[Batch*FeatureMaps*Time,2,Freq_FcIn]。
wherein, Batch [ FeatureMaps ] Time represents the product of the number of samples Batch, the number of feature maps FeatureMaps, and the Time dimension number Time.
The following steps (2) to (4) are the process of FcIn _ ReSize passing through the equivalent complex value full connection layer.
(2) Full connection layers fc _ re and fc _ im are defined, representing the real and imaginary parts of the frequency domain full connection layer, respectively. This step can be implemented directly using the torch.
(3) Calculating the output of the equivalent complex value full-connection layer:
FcOut_re＝fc_re(FcIn_ReSize[:,0,:])-fc_im(FcIn_ReSize[:,1,:])，
FcOut_im＝fc_re(FcIn_ReSize[:,1,:])+fc_im(FcIn_ReSize[:,0,:])。
for ease of description, the above formula uses the notation in python for the array slice, which will be followed below.
(4) Carrying out dimension splicing on FcOut _ re and FcOut _ im, converting the spliced tensor into a five-dimensional tensor, and keeping the meaning of each dimension of the converted tensor to be the same as that of the input tensor FcIn:
FcOut:＝[Batch,2,Freq_FcOut,FeatureMaps,Time]。
wherein, Batch represents the sample number of each Batch of samples, 2 represents two dimensions of a real part and an imaginary part of complex value output, Freq _ FcOut represents the frequency dimension degree of frequency domain full connection layer output data, FeatureMaps represents the feature map number, and Time represents the Time dimension degree and the frame number of a real-Time frequency map.
Step S202: an interference convolution layer is constructed.
The interference convolution layer input data is denoted as ConvIn, which is a five-dimensional tensor expressed as:
ConvIn:＝[Batch,2,Freq,FeatureMaps_ConvIn,Time]。
wherein, Batch represents the sample number of each Batch of samples, 2 represents two dimensions of a real part and an imaginary part of a complex value, Freq represents the frequency dimension degree, FeatureMaps _ Convin represents the number of input feature maps of the interference convolution layer (the dimension of an initial Time-frequency map is 1), and Time represents the Time dimension degree and the frame number of the Time-frequency map.
(1) Taking the real part and imaginary part of the input data as ConvIn _ re and ConvIn _ im, namely:
ConvIn_re＝ConvIn[:,0]，
ConvIn_im＝ConvIn[:,1]。
performing dimensionality transformation on ConvIn _ re and ConvIn _ im respectively to enable the transformed tensor to be a three-dimensional tensor, namely:
ConvIn_re_ReSize:＝[Batch,Freq*FeatureMaps_ConvIn,Time]，
ConvIn_im_ReSize:＝[Batch,Freq*FeatureMaps_ConvIn,Time]。
wherein Freq _ FeatureMaps _ ConvIn represents the frequency dimension number Freq multiplied by the number FeatureMaps _ ConvIn of the input feature map of the interference convolution layer.
The following steps (2) to (4) are the processes of ConvIn _ re _ ReSize and ConvIn _ im _ ReSize passing through the equivalent complex-valued interference convolution layer.
(2) Defining the optimizable parameters weight _ re and weight _ im, the three-dimensional tensor can be expressed as weight _ re: not [ Freq [ ] FeatureMaps _ ConvOut, FeatureMaps _ ConvIn, KernelSize ], weight _ im: freq, FeatureMaps _ ConvOut, FeatureMaps _ ConvIn, KernelSize.
Wherein, KernelSize, FeatureMaps _ ConvIn, FeatureMaps _ ConvOut represent the convolution kernel size, the number of input feature maps, and the number of output feature maps of the interference convolution layer, respectively. Freq _ FeatureMaps _ ConvOut represents the frequency dimension number Freq multiplied by the number of interference convolution layer output signatures FeatureMaps _ ConvIOut. This step can be implemented using a torch. The above parameters can all be initialized using the Kaiming normal initialization method.
(3) Calculating the output of the equivalent complex value convolution layer:
ConvOut_re＝F.conv1d(ConvIn_re_ReSize，weight＝self.weight_re，bias＝None，groups
＝Freq)-F.conv1d(ConvIn_im_ReSize，weight＝self.weight_im，bias
＝None，groups＝Freq)
ConvOut_im＝F.conv1d(ConvIn_re_ReSize，weight＝self.weight_im，bias＝None，groups
＝Freq)+F.conv1d(ConvIn_im_ReSize，weight＝self.weight_re，bias
＝None，groups＝Freq)
in the formula, the variable convIn _ re _ ReSize and the variable ConvIn _ im _ ReSize respectively represent the result of the dimensional transformation of the real part and the imaginary part of the input of the interference convolutional layer, and the variable ConvOut _ re and the variable ConvOut _ im respectively represent the real part and the imaginary part of the output of the interference convolutional layer. Conv1d is the one-dimensional convolution operation of the torch. nn. functional, weight, bias, and groups are three parameters of the function f. conv1d, which respectively represent the weight, bias, and number of groups of the convolution layer, and self. Weight _ re and weight _ im are weight _ re and weight _ im after initialization using Kaiming normal, respectively; bias-free f.conv1d operation, group Freq equal to frequency dimension degree, which is the most key characteristic of the interference convolutional layer to distinguish from the common convolutional layer.
(4) Performing dimension splicing on ConvOut _ re and ConvOut _ im, converting the spliced tensor into a five-dimensional tensor, and keeping the meaning of each dimension of the converted tensor ConvOut the same as that of the input tensor ConvIn, namely:
ConvOut：＝[Batch，2，Freq，FeatureMaps_ConvOut，Time]。
wherein, Batch represents the sample number of each Batch of samples, 2 represents two dimensions of real part and imaginary part of complex value output, Freq represents frequency dimension degree, FeatureMaps _ ConvOut represents the feature map number of the output data of the interference convolution layer, and Time represents Time dimension degree, i.e. the frame number of the frequency map.
Step S203: and constructing a complete complex value interference neural network.
The construction method is as follows:
(1) the frequency domain full link layer and the interference convolution layer are repeatedly stacked for several times, and the network depth is increased.
(2) And accessing a statistical pooling layer. The input Poolingin for this layer is the five dimensional tensor as follows:
PoolingIn：＝[Batch，2，Freq，FeatureMaps，Time]。
wherein, Batch represents the sample number of each Batch of samples, 2 represents two dimensions of a real part and an imaginary part, Freq represents the frequency dimension degree, FeatureMaps represents the feature map number, and Time represents the Time dimension degree and the frame number of the instant frequency map.
The output of the statistical pooling layer can be used as a time sequence signal Feature extracted by the network, and is a two-dimensional tensor, namely:
Feature：＝[Batch，FeatureMaps]。
therefore, the statistical pooling layer can convert complex-valued data into real-valued data, and simultaneously convert the features of each sample into vectors with lengths of FeatureMaps, and the specific calculation formula of the layer is as follows:
Figure BDA0003419258550000061
the above formula adopts notation of logarithmic array element index In python, that is, Feature [ i, n ] represents the value of two-dimensional tensor Feature when the first dimension is i and the second dimension is n, In [ i, 0, k, n, m ] and In [ i, 1, k, n, m ] respectively represent the value of input tensor In when the values of the dimensions are i, 0, k, n, m and i, 1, k, n, m respectively.
(3) And finally, two common full-connection layers are used for feature transformation, and the probability that the sample belongs to each category is output, namely:
Out：＝[Batch，Num_Classes]。
where Out represents the final output of the complex-valued interference network, Batch represents the number of samples per Batch, and Num _ Classes represents the number of communication terminals to be classified.
Step S3: and calculating a classification loss function, and performing complex value interference neural network training based on a gradient descent method.
Firstly, the network input complex value time-frequency graph data passes through the complex value interference neural network layer by layer to obtain the output of the complex value interference neural network, and the loss function of the network output relative to the real label of the sample can be calculated according to the output of the complex value interference neural network. As cross entropy loss function:
Figure BDA0003419258550000062
in the above formula, L represents the value of the loss function, N is the number of samples per batch, xiRepresenting the input of the last fully-connected layer, yiRepresenting the sample true label, W, b representing the weight parameter to be optimized and the bias parameter of the last fully-connected layer.
Then, by using an automatic derivation mechanism in the torch, the gradient of the loss function relative to each parameter to be optimized in the complex interference network is calculated, and each parameter is updated by using a gradient descent method.
Figure BDA0003419258550000063
Wherein, theta is any parameter to be optimized in the complex value interference network, theta' is the value of the parameter to be optimized theta after gradient descent updating,
Figure BDA0003419258550000071
the gradient of the loss function relative to each parameter to be optimized in the complex interference network, wherein eta is a learning rate, belongs to a hyper-parameter, and can be adjusted, for example, 5 e-4.
And finally, repeating and iterating the loss function calculation and gradient descending process for a plurality of times until convergence.
Step S4: and deploying and testing a complex value interference neural network model.
The implementation process of this step is simple, firstly according to the method described in step S1, the time sequence signal to be tested obtains the complex value time-frequency diagram data to be tested, the complex value time-frequency diagram data to be tested utilizes the complex value interference neural network obtained in step S3 to obtain the probability that the time sequence signal to be tested belongs to each category, and finally the category corresponding to the maximum probability value is taken as the final prediction result of the complex value interference neural network.
Compared with the prior art, the invention has the advantages that:
(1) the invention mainly considers the difference between the time axis and the frequency axis of the time-frequency diagram and the natural image in the physical meaning, designs the complex value interference network comprising the interference convolution layer and the frequency domain full connection layer, and the interference convolution layer and the frequency domain full connection layer in the network have definite physical meaning for each layer output of the network because the interference process and the nonlinear process of the wave are respectively simulated, which shows that the time sequence signal identification algorithm based on the complex value interference network has good interpretability. On the other hand, the time sequence signal identification algorithm based on the complex value interference network not only can improve the distinguishability of the learned characteristics (as shown in fig. 2) and obtain higher identification accuracy, but also has stronger robustness (as shown in fig. 3).
(2) Timing signal identification (including voice signal identification, communication signal identification, stock signal identification and the like) has wide application prospect in real life. The traditional time sequence signal identification technology mainly utilizes characteristics of manual design to carry out identification, and has the defects of low efficiency and limited application range. The mainstream method at present is to convert a time sequence signal into an image signal and perform identification by means of a deep convolutional neural network. However, the method does not consider the characteristics of the time sequence signal, and lacks of clear physical meaning, so that the performance has a certain improvement space. The invention designs a novel neural network structure by referring to the wave interference theory to realize the time sequence signal identification, has more definite physical meaning and also obtains better experimental results. The method can be applied to the fields of voice recognition, Internet of things, communication and the like.
Drawings
FIG. 1 is a flow chart of a timing signal identification method based on a complex-valued interferometric neural network according to the present invention;
FIG. 2 shows two connection modes of a frequency domain full connection layer and an interference convolution layer in a complex-valued interference network according to the present invention; (a) a direct connection type; (b) dense connection type;
FIG. 3 is a dimension reduction distribution diagram, in which (a) and (b) are dimension reduction distribution diagrams of features extracted by a conventional complex ResNet network and a complex interferometric neural network, respectively;
fig. 4 is a histogram of signal recognition accuracy for a conventional complex ResNet network and a complex interferometric neural network.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and examples.
Timing signals typically take many forms, such as speech signals, communication signals, bioelectric signals, and the like. The time sequence signal identification method based on the complex value interference network is suitable for any time sequence signal. The following explains the implementation of the present invention in detail by taking the communication signal as an example. The radio frequency fingerprint identification technology extracts essential difference information of different sending terminal devices from a received radio frequency signal through a signal processing method so as to distinguish a sending terminal communication individual, and therefore the radio frequency fingerprint identification problem essentially belongs to the time sequence signal identification problem.
As shown in FIG. 1, the method comprises the following steps:
step S1: and preprocessing the communication signal and calculating a complex value time-frequency diagram of the signal.
This step includes the following two substeps.
Step S101: the communication signal is pre-processed, such as burst detection, power normalization, linear filtering, etc. The operation has stronger flexibility and any reasonable pretreatment method can be adopted.
Step S102: and calculating a complex-value time-frequency diagram of the signal after preprocessing.
The embodiment of the invention adopts a classic short-time Fourier transform method, and the short-time Fourier transform process comprises the following steps: the fourier transform is preceded by a time-limited window function w (n) and the non-stationary signal is assumed to be stationary during a short time interval of the analysis window, and the signal is analyzed segment by shifting the window function on the time axis to obtain a set of local "spectra" of the signal. The calculation formula is as follows:
Figure BDA0003419258550000081
where X (n) is the input communication signal, which may be complex IQ signal or real signal, w (n) is the window function, which may be Hamming window, R is the number of signal sampling points moved by the adjacent signal window, and X (n) is the number of sampling points moved by the adjacent signal windowmAnd (omega) is complex-valued time-frequency diagram data, wherein m represents time (representing an mth frame short-time signal), and omega represents frequency. The complex-valued time-frequency diagram data after frequency discretization is recorded as X, wherein X is a three-dimensional tensor, each dimension of the tensor represents a real part, an imaginary part (2 dimensions), a frequency dimension and a time dimension respectively, and the method is recorded as follows:
X：＝[2，Freq，Time]。
and finally, carrying out dimension transformation on the three-dimensional tensor X, wherein the transformed tensor X _ ReSize is a five-dimensional tensor, namely:
X_Resize：＝[1，2，Freq，1，Time]。
x _ ReSize is the input of the complex-valued interferometric neural network.
Step S2: and constructing a complex-valued interference neural network comprising an interference convolution layer and a frequency domain full-link layer.
The invention provides a new neural network structure, namely a complex value interference network, which is a key step of the invention. The invention improves the traditional convolution neural network, is similar to the traditional convolution neural network in principle, but achieves the aim of respectively considering time domain and frequency domain by replacing the convolution layer of the traditional convolution network with a frequency domain full-connection layer and an interference convolution layer, and has stronger interpretability and robustness.
This step therefore comprises the following substeps.
Step S201: and constructing a frequency domain full-connection layer.
The frequency domain fully-connected layer input data is denoted as FcIn, which is a five-dimensional tensor expressed as:
FcIn:＝[Batch,2,Freq_FcIn,FeatureMaps,Time]。
wherein, Batch represents the sample number of each Batch of samples, 2 represents two dimensions of a real part and an imaginary part of a complex value, Freq _ FcIn represents the frequency dimension degree of input data of a frequency domain full connection layer, FeatureMaps represents the feature map number (the dimension of an initial Time-frequency map is 1), and Time represents the Time dimension degree and the frame number of the Time-frequency map.
(1) Performing dimension transformation on the input FcIn, so that the last dimension of the transformed data FcIn _ ReSize is a frequency dimension, namely:
FcIn_ReSize:＝[Batch*FeatureMaps*Time,2,Freq_FcIn]。
wherein, Batch [ FeatureMaps ] Time represents the product of the number of samples Batch, the number of feature maps FeatureMaps, and the Time dimension number Time.
The following steps (2) to (4) are the process of FcIn _ ReSize passing through the equivalent complex value full connection layer.
(2) Full connection layers fc _ re and fc _ im are defined, representing the real and imaginary parts of the frequency domain full connection layer, respectively. This step can be implemented directly using the torch.
(3) Calculating the output of the equivalent complex value full-connection layer:
FcOut_re＝fc_re(FcIn_ReSize[:,0,:])-fc_im(FcIn_ReSize[:,1,:])，
FcOut_im＝fc_re(FcIn_ReSize[:,1,:])+fc_im(FcIn_ReSize[:,0,:])。
for ease of description, the above formula uses the notation in python for groups of slices.
(4) Carrying out dimension splicing on FcOut _ re and FcOut _ im, converting the spliced tensor into a five-dimensional tensor, and keeping the meaning of each dimension of the converted tensor to be the same as that of the input tensor FcIn:
FcOut:＝[Batch,2,Freq_FcOut,FeatureMaps,Time]。
wherein, Batch represents the sample number of each Batch of samples, 2 represents two dimensions of a real part and an imaginary part of complex value output, Freq _ FcOut represents the frequency dimension degree of frequency domain full connection layer output data, FeatureMaps represents the feature map number, and Time represents the Time dimension degree and the frame number of a real-Time frequency map.
Step S202: an interference convolution layer is constructed.
The interference convolution layer input data is denoted as ConvIn, which is a five-dimensional tensor expressed as:
ConvIn:＝[Batch,2,Freq,FeatureMaps_ConvIn,Time]。
wherein, Batch represents the sample number of each Batch of samples, 2 represents two dimensions of a real part and an imaginary part of a complex value, Freq represents the frequency dimension degree, FeatureMaps _ Convin represents the number of input feature maps of the interference convolution layer (the dimension of an initial Time-frequency map is 1), and Time represents the Time dimension degree and the frame number of the Time-frequency map.
(1) Taking the real part and imaginary part of the input data as ConvIn _ re and ConvIn _ im, namely:
ConvIn_re＝ConvIn[：，0]，
ConvIn_im＝ConvIn[：，1]。
performing dimensionality transformation on ConvIn _ re and ConvIn _ im respectively to enable the transformed tensor to be a three-dimensional tensor, namely:
ConvIn_re_ReSize：＝[Batch，Freq*FeatureMaps_ConvIn，Time]，
ConvIn_im_ReSize：＝[Batch，Freq*FeatureMaps_ConvIn，Time]。
wherein Freq _ FeatureMaps _ ConvIn represents the frequency dimension number Freq multiplied by the number FeatureMaps _ ConvIn of the input feature map of the interference convolution layer.
The following steps (2) to (4) are the processes of ConvIn _ re _ ReSize and ConvIn _ im _ ReSize passing through the equivalent complex-valued interference convolution layer.
(2) Defining the optimizable parameters weight _ re and weight _ im, and expressing the three-dimensional tensor as weight _ re: not [ Freq [ ] FeatureMaps _ ConvOut, FeatureMaps _ ConvIn, KernelSize ], weight _ im: freq, FeatureMaps _ ConvOut, FeatureMaps _ ConvIn, KernelSize.
Wherein, KernelSize, FeatureMaps _ ConvIn, FeatureMaps _ ConvOut represent the convolution kernel size, the number of input feature maps, and the number of output feature maps of the interference convolution layer, respectively. Freq _ FeatureMaps _ ConvOut represents the frequency dimension number Freq multiplied by the number of interference convolution layer output signatures FeatureMaps _ ConvIOut. This step can be implemented using a torch. The above parameters can all be initialized using the Kaiming normal initialization method.
(3) Calculating the output of the equivalent complex value convolution layer:
ConvOut_re＝F.conv1d(ConvIn_re_ReSize，weight＝self.weight_re，bias＝None，groups
＝Freq)-F.conv1d(ConvIn_im_ReSize，weight＝self.weight_im，bias
＝None，groups＝Freq)
ConvOut_im＝F.conv1d(ConvIn_re_ReSize，weight＝self.weight_im，bias＝None，groups
＝Freq)+F.conv1d(ConvIn_im_ReSize，weight＝self.weight_re，bias
＝None，groups＝Freq)
in the formula, the variable convIn _ re _ ReSize and the variable ConvIn _ im _ ReSize respectively represent the result of the dimensional transformation of the real part and the imaginary part of the input of the interference convolutional layer, and the variable ConvOut _ re and the variable ConvOut _ im respectively represent the real part and the imaginary part of the output of the interference convolutional layer. Conv1d is the one-dimensional convolution operation of the torch. nn. functional, weight, bias, and groups are three parameters of the function f. conv1d, which respectively represent the weight, bias, and number of groups of the convolution layer, and self. Weight _ re and weight _ im are weight _ re and weight _ im after initialization using Kaiming normal, respectively; bias-free f.conv1d operation, group Freq equal to frequency dimension degree, which is the most key characteristic of the interference convolutional layer to distinguish from the common convolutional layer.
(4) Performing dimension splicing on ConvOut _ re and ConvOut _ im, converting the spliced tensor into a five-dimensional tensor, and keeping the meaning of each dimension of the converted tensor ConvOut the same as that of the input tensor ConvIn, namely:
ConvOut：＝[Batch，2，Freq，FeatureMaps_ConvOut，Time]。
wherein, Batch represents the sample number of each Batch of samples, 2 represents two dimensions of real part and imaginary part of complex value output, Freq represents frequency dimension degree, FeatureMaps _ ConvOut represents the feature map number of the output data of the interference convolution layer, and Time represents Time dimension degree, i.e. the frame number of the frequency map.
Step S203: and constructing a complete complex value interference neural network.
The construction method is as follows:
(1) the frequency domain full link layer and the interference convolution layer are repeatedly stacked for several times, and the network depth is increased. The complex-valued interference network is mainly characterized in that frequency domain full-link layers and interference convolution layers are alternately stacked in sequence, but the specific connection modes of the frequency domain full-link layers and the interference convolution layers can be various, and two possible connection modes are shown in fig. 2. The method is generally only suitable for the condition of less network layer number, and the instability of the calculated numerical value generally causes difficulty in optimization along with the increase of the network layer number; (b) the interference convolution layer outputs of different layers are finally spliced and connected through a statistical pooling layer and a dimensionality, and the dense connection type is generally easier to optimize than a direct connection type under the condition of a deeper network.
The number of repetitions (i.e., the number of network layers) can be freely set (e.g., 5). In each repetition, the frequency domain full-link layer and the interference convolution layer can exchange positions, and an activation layer and a batch normalization layer can be added. The parameters of each frequency domain full-link layer can be adjusted (for example, Freq _ FcOut parameters of 5 frequency domain full-link layers are sequentially set to 256, 128, 64, 32 and 16), and each interference convolution layer parameter can also be flexibly set (for example, FeatureMaps _ ConvOut parameters of 5 interference convolution layers are sequentially 64, 64, 64, 128 and 128, and KernelSize parameters are sequentially 3, 3, 3, 3 and 1).
(2) And accessing a statistical pooling layer.
The input PoolingIn for this layer is the five-dimensional tensor,
PoolingIn：＝[Batch，2，Freq，FeatureMaps，Time]。
wherein, Batch represents the sample number of each Batch of samples, 2 represents two dimensions of a real part and an imaginary part, Freq represents the frequency dimension degree, FeatureMaps represents the feature map number, and Time represents the Time dimension degree and the frame number of the instant frequency map.
The output of the statistical pooling layer can be used as a time sequence signal Feature extracted by the network, and is a two-dimensional tensor, namely:
Feature：＝[Batch，FeatureMaps]。
in the layer, the total energy of the signal at each time is calculated along the frequency axis of the data, and then the average value is calculated along the time axis of the data, so as to obtain the characteristic of each time sequence signal sample, wherein the specific calculation formula is as follows:
Figure BDA0003419258550000121
the above formula adopts notation of logarithmic array element index In python, that is, Feature [ i, n ] represents the value of two-dimensional tensor Feature when the first dimension is i and the second dimension is n, In [ i, 0, k, n, m ] and In [ i, 1, k, n, m ] respectively represent the value of input tensor In when the values of the dimensions are i, 0, k, n, m and i, 1, k, n, m respectively.
(3) And finally, two common full-connection layers are used for feature transformation, and the probability that the sample belongs to each category is output, namely: out: batch, Num _ Classes ].
Where Out represents the final output of the complex-valued interference network, Batch represents the number of samples per Batch, and Num _ Classes represents the number of communication terminals to be classified.
Step S3: and calculating a classification loss function, and performing complex value interference neural network training based on a gradient descent method.
Firstly, the network input complex value time-frequency graph data passes through the complex value interference neural network layer by layer to obtain the output of the complex value interference neural network, and the loss function of the network output relative to the real label of the sample can be calculated according to the output of the complex value interference neural network. As cross entropy loss function:
Figure BDA0003419258550000122
in the above formula, L represents the value of the loss function, N is the number of samples per batch, xiRepresenting the input of the last fully-connected layer, yiRepresenting the sample true label, W, b representing the weight parameter to be optimized and the bias parameter of the last fully-connected layer.
Then, by using an automatic derivation mechanism in the torch, the gradient of the loss function relative to each parameter to be optimized in the complex interference network is calculated, and each parameter is updated by using a gradient descent method.
Figure BDA0003419258550000123
Wherein, theta is any parameter to be optimized in the complex value interference network, theta' is the value of the parameter to be optimized theta after gradient descent updating,
Figure BDA0003419258550000124
the gradient of the loss function relative to each parameter to be optimized in the complex interference network, wherein eta is a learning rate, belongs to a hyper-parameter, and can be adjusted, for example, 5 e-4.
And finally, repeating and iterating the loss function calculation and gradient descending process for a plurality of times until convergence.
Step S4: and deploying and testing a complex value interference neural network model.
Firstly, according to the method described in step S1, obtaining complex-valued time-frequency diagram data to be tested from the time sequence signal to be tested, obtaining the probability that the time sequence signal to be tested belongs to each class by using the complex-valued interference neural network obtained in step S3 for the complex-valued time-frequency diagram data to be tested, and finally, taking the class corresponding to the maximum probability value as the final prediction result of the complex-valued interference neural network.
As shown in fig. 3, the dimension reduction distribution maps of the features extracted by the conventional complex ResNet network and the complex interference neural network are shown in (a) and (b), respectively, and the dimension reduction method is t-SNE. Comparing (a) and (b) in fig. 3, it can be seen that the characteristics of the same kind of signals basically present the characteristics of aggregation distribution no matter the complex-valued ResNet network or the complex-valued interference network; however, the intra-class distribution of the characteristic learned by the complex interference neural network is more compact and regular compared with the traditional complex ResNet network.
Fig. 4 is a histogram of signal recognition accuracy for a conventional complex ResNet network and a complex interferometric neural network. As can be seen from fig. 4, when the test set timing signal-to-noise ratio is equal to the training set signal-to-noise ratio (20dB), the recognition accuracy of the complex-valued interference network is slightly higher than the complex-valued residual; when the signal-to-noise ratio of the test set time sequence signal is lower than the signal-to-noise ratio (20dB) of the training set, the recognition accuracy of the complex residual error network is reduced sharply, and under the test environment of 10dB, the recognition rate is reduced to 70.37%, and the accuracy of the interference network is still over 80%. The above results show that the complex interference network has stronger noise robustness compared to the conventional complex ResNet network.
The above description is only an embodiment of the present invention in the context of an application of radio frequency fingerprinting of communication signals. The present invention is not limited to the above-described embodiments. The description of the invention is intended to be illustrative, and not to limit the scope of the claims. Many alternatives, modifications, and variations will be apparent to those skilled in the art. All technical solutions formed by adopting equivalent substitutions or equivalent transformations fall within the protection scope of the claims of the present invention.

Claims (5)

1. A time sequence signal identification method based on a complex value interference neural network is characterized by comprising the following steps:
firstly, preprocessing a time sequence signal and calculating a complex value time-frequency diagram of the time sequence signal;
constructing a complex value interference neural network, wherein the complex value interference neural network is characterized in that an interference convolution layer and a frequency domain full-connection layer are sequentially and alternately connected, the interference convolution layer performs time-dimension complex value convolution operation on a complex value time-frequency graph to simulate the interference process of the wave, and the frequency domain full-connection layer performs frequency-dimension complex value full-connection operation on the complex value time-frequency graph to simulate the nonlinear process of the wave;
thirdly, calculating a classification loss function, and carrying out complex value interference neural network training based on a gradient descent method to obtain a complex value interference neural network model;
and fourthly, according to the first step, obtaining complex value time-frequency graph data to be tested from the time sequence signal to be tested, obtaining the probability that the time sequence signal to be tested belongs to each class by utilizing the complex value interference neural network model and the complex value time-frequency graph data to be tested, and finally taking the class corresponding to the maximum probability value as the final prediction result of the complex value interference neural network, thereby realizing the identification of the time sequence signal.
2. The method of claim 1, wherein the method comprises: in the second step, the frequency domain full link layer includes: carrying out dimensionality transformation on the input tensor to enable the last dimension of the tensor after transformation to be the frequency dimension; defining two full connection layers which are equivalent to a complex full connection layer; calculating the real part tensor and the imaginary part tensor of the output tensor of the equivalent complex value fully-connected layer according to the tensor after dimensionality transformation and the two fully-connected layers; and performing dimensionality splicing on the real part tensor and the imaginary part tensor, and converting the spliced tensor into a five-dimensional tensor with the same meaning as the input tensor, wherein the five-dimensional tensor is used as a final output result of the frequency domain full-connection layer.
3. The method of claim 1, wherein the method comprises: in a second step, the interference convolution layer includes: taking a real part and an imaginary part of input data, and then carrying out dimension transformation on a real part tensor and an imaginary part tensor to ensure that the last dimension of the tensor after the transformation is a time dimension; defining two convolutional layers which are equivalent to a complex value convolutional layer, wherein the weight parameters of the two convolutional layers are initialized by using a Kaiming normal initialization method; calculating a real part tensor and an imaginary part tensor of an output tensor of the equivalent complex value convolution layer according to the tensor after dimensionality transformation and the two convolution layers; and performing dimensionality splicing on the real part tensor and the imaginary part tensor, and converting the spliced tensor into a five-dimensional tensor which has the same meaning as the input tensor, wherein the five-dimensional tensor is used as a final output result of the interference convolution layer.
4. The method of claim 1, wherein the method comprises: the constructed complex value interference neural network comprises a frequency domain full-connection layer and an interference convolution layer which are repeatedly stacked for a plurality of times so as to increase the depth of the network; accessing a statistical pooling layer, converting complex value data into real value data, and obtaining a feature vector of each sample; and finally, accessing two common full-connection layers for feature transformation, and outputting the probability that the sample belongs to each category.
5. The method of claim 4, wherein the method comprises: in the structure complex value interference neural network, when a frequency domain full connection layer and an interference convolution layer are repeatedly stacked, a layer jump connection or dense connection mode in a ResNet and DenseNet network architecture is adopted to further increase the network depth.
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Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114866311A (en) * 2022-04-29 2022-08-05 东南大学 Radio frequency fingerprint extraction method based on time sequence representation
CN115130385A (en) * 2022-07-04 2022-09-30 贵州省人民医院 Time sequence signal prediction classification identification method and device
CN115296758A (en) * 2022-07-07 2022-11-04 中山大学 Method, system, computer device and storage medium for identifying interference signal

Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114866311A (en) * 2022-04-29 2022-08-05 东南大学 Radio frequency fingerprint extraction method based on time sequence representation
CN114866311B (en) * 2022-04-29 2024-03-22 东南大学 Radio frequency fingerprint extraction method based on time sequence characterization
CN115130385A (en) * 2022-07-04 2022-09-30 贵州省人民医院 Time sequence signal prediction classification identification method and device
CN115296758A (en) * 2022-07-07 2022-11-04 中山大学 Method, system, computer device and storage medium for identifying interference signal
CN115296758B (en) * 2022-07-07 2023-08-11 中山大学 Method, system, computer equipment and storage medium for identifying interference signals

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