A Parameter Estimation Method for LFM Signals under the Influence of Sinusoidal Nonlinear Interference

Abstract

The present invention discloses a method for estimating the parameters of an LFM signal under the influence of sinusoidal non-linear interference. First, the LFM signal is modeled, with the sinusoidal non-linear interference regarded as the "multiplicative noise" of the signal and the Gaussian noise regarded as the "additive noise" of the signal. The formed noise signal model includes a sinusoidal non-linear interference term, a Gaussian noise term, and an ideal signal model. Then, the noise signal model and the ideal signal model are used to train the CAE model. The trained CAE model can not only remove the conventional Gaussian noise in the signal but also remove the sinusoidal non-linear interference existing in the real environment. The method of the present invention then uses the "clean" signal from which the sinusoidal non-linear interference and Gaussian noise have been removed and the signal modulation parameters corresponding to the signal to train the CNN model. The trained CNN model can quickly complete parameter estimation and obtain accurate signal modulation parameters.

Description

Technical Field

[0001] The present invention belongs to the technical field of communication signal processing, and relates to a method for estimating LFM signal parameters, specifically to a method for estimating LFM signal parameters under the influence of sinusoidal non-linear interference, and is applicable to the technical field of radar signal processing. Background Art

[0002] The Linear Frequency Modulation (LFM) signal, also known as the chirp signal, is a typical time-varying signal whose frequency changes linearly with time. LFM signals are often applied in the fields of radar, communication, sonar, etc. Especially in the radar field, LFM signals are very suitable for target positioning, tracking and other position information perception due to their large time-bandwidth product and strong anti-Doppler frequency shift ability. At the same time, due to the advantage of low probability of intercept, LFM signals are widely used in the field of radar signal processing technology. Currently, radar devices using LFM signals are widely applied to various military fields. Taking the electronic warfare scenario as an example, radar reconnaissance equipment needs to search, intercept and estimate the parameters of LFM signals emitted by enemy radars in the battlefield environment to obtain key parameters and other intelligence carried by the LFM signals. Quickly and accurately obtaining these key intelligence information is of crucial significance for analyzing the battlefield situation and commanding operations. Therefore, how to accurately and quickly estimate the parameters of LFM signals is very important.

[0003] However, in the real environment, LFM signals are often affected by sinusoidal non-linear phase errors caused by hardware defects in the transmitting end of linear frequency modulation radars. Such hardware defects are usually considered to be caused by inaccurate radar digital circuits or the transient response of phase-locked loops. [1] . Under the influence of sinusoidal non-linear interference, the LFM signal model has changed. For example, traditional methods such as time-frequency analysis - straight line detection method [2] , fractional Fourier transform method [3] only consider the Gaussian noise received by LFM signals in the simulation environment and cannot exclude the influence of real environment hardware devices on LFM signals. Therefore, the accuracy of their parameter estimation results is not high.

[0004] Reference [4] proposed a method for denoising time-domain signals based on a deep denoising network. The LFM signal after noise filtering is subjected to parameter estimation by the Fractional Fourier Transform (FRFT) technique. This method belongs to an indirect parameter estimation method. The noise signal is first filtered by the proposed denoising network, and then the signal parameters are estimated by traditional methods. When estimating the LFM signal, this method has relatively cumbersome steps. Since the fractional Fourier transform requires a two-stage search method from coarse to fine, this method requires a large amount of computing time and cannot meet the real-time requirements of LFM signal parameter estimation. At the same time, the denoising performance of the denoising network adopted in this method is not strong, and it also cannot eliminate the influence of sinusoidal non-linear phase error on the LFM signal.

[0005] Reference [5] adopted a deep learning regression prediction method. This method was the first to successfully apply the deep learning method to the problem of LFM signal parameter estimation, and it can directly estimate the parameters of the LFM signal. The proposed complex-valued deep neural network in this method takes the time-domain LFM signal as the input, uses a complex-valued fully connected network to map the one-dimensional input into a two-dimensional image, and then extracts the image features by a complex-valued convolutional neural network and realizes signal parameter estimation. However, this method still does not consider the influence of sinusoidal non-linear phase error on the LFM signal, and in practical applications, the parameter estimation accuracy is poor. Summary of the Invention

[0006] To solve the problems existing in the prior art, the present invention provides a method for estimating the parameters of an LFM signal under the influence of sinusoidal non-linear interference. After the network model training is completed, this method can quickly obtain the parameter estimation results, and at the same time, the parameter estimation accuracy is high.

[0007] The present invention adopts the following technical solutions:

[0008] A method for estimating the parameters of an LFM signal under the influence of sinusoidal non-linear interference, comprising:

[0009] 1) Generating a noise signal model of the LFM signal; the noise signal model includes a sinusoidal non-linear interference term, a Gaussian noise term, and an ideal signal model; the ideal signal model includes signal modulation parameters;

[0010] 2) Constructing a CAE model, using the noise signal model as a sample to form a CAE input set for CAE model training; using the ideal signal model in the noise signal model as a sample to form a CAE label set corresponding to the CAE input set; training the constructed CAE model based on the CAE input set and the CAE label set;

[0011] 3) Construct a CNN model, input the samples in the CAE input set into the trained CAE model, and use the output result of the CAE model as the CNN input set for training the CNN model; use the signal modulation parameter items corresponding to the samples in the CAE input set as the CNN label set corresponding to the CNN input set; train the constructed CNN model based on the CNN input set and the CNN label set;

[0012] 4) Preprocess the target LFM signal, input the preprocessed signal into the trained CAE model for denoising, and input the output result of the CAE model into the trained CNN model for parameter estimation.

[0013] Further, the signal modulation parameter items include the initial frequency and the frequency modulation frequency of the signal.

[0014] Further, the noise signal model is s(t) = x(t)m(t) + n(t)

[0015] where s(t) is the noise signal model; m(t) is the sine non - linear interference term; n(t) is the Gaussian noise term; x(t) is the ideal signal model, f0 is the initial frequency; μ is the frequency modulation slope; [f0, μ] are the signal modulation parameters in the ideal signal model.

[0016] Further, the CAE input set s i is the i - th sample in the CAE input set, corresponding to the i - th noise signal model;

[0017] The CAE label set x i is the i - th sample in the CAE label set, corresponding to the i - th ideal signal model; P is the total number of models;

[0018] The CNN input set is the i - th sample in the CNN input set, corresponding to the i - th noise signal model after denoising by the CAE model;

[0019] The CNN label set [f 0,i ,μ i is the i - th sample in the CNN label set, corresponding to the signal modulation parameter items corresponding to the i - th noise signal model.

[0020] Further, in the CAE input set, the sample

[0021] In the CAE label set, the sample

[0022] Among them, and are respectively taking the real part and the imaginary part; s[1]... s[L] are respectively the signals of the 1st... the Lth sampling points corresponding to the i-th sample in the CAE input set; x[1]... x[L] are respectively the signals of the 1st... the Lth sampling points corresponding to the i-th sample in the CAE label set; is the set of all real numbers;

[0023] Furthermore, the CAE model includes an encoder and a decoder; among them,

[0024] The encoder includes an input layer and three A-Block modules. The input layer performs a normalization operation on the preprocessed signal data and outputs a feature matrix. The A-Block module includes four convolutional layers, one BN layer, and one Dropout layer. The convolutional layer uses a convolutional kernel to perform convolution on the input data, extracts signal features, and outputs them as a feature map. The BN layer performs a normalization operation on the output of the convolutional layer. The Dropout layer randomly deactivates neurons in the neural network and outputs the feature information contained in the remaining neurons;

[0025] The decoder uses the output of the encoder as input data. The decoder includes three B-Block modules and an output layer. The B-Block module includes four deconvolutional layers, one BN layer, and one Dropout layer. The deconvolutional layer performs a restoration operation on the encoder output features and outputs a feature vector. The BN layer performs a normalization operation on the output of the convolutional layer. The Dropout layer randomly deactivates neurons in the network and outputs the feature information contained in the remaining neurons. The output layer uses a deconvolutional layer with 2 convolutional kernels. The output layer performs an integration operation on the feature information and outputs the denoised signal data.

[0026] Furthermore, the input data size of the CAE model is 512×2, and the output data size is 512×2. The Dropout layer parameter is set to 0.1. The training uses the Adam optimization algorithm, and the initial learning rate is set to 0.002. The loss function uses the mean square error function.

[0027] Furthermore, in the a-th A-Block module, the input and the output Y y a (s) The relationship between them is expressed as:

[0028]

[0029]

[0030] Among them, R{·} is the ReLU activation function;

[0031] is the weight of the y-th convolutional layer;

[0032] is the offset of the y-th convolutional layer;

[0033] * is the dot product; n y a is the size of the convolutional kernel and m y a is the number of convolutional kernels; a = 1, 2, 3; y = 1, 2, 3, 4;

[0034] In the b-th B-Block module, the input and output of the t-th transposed convolutional layer are related as follows:

[0035]

[0036] Among them, and are the weight and offset of the t-th transposed convolutional layer of the b-th module respectively; is the size of the convolutional kernel of the transposed convolutional layer; is the number of convolutional kernels; b = 1, 2, 3; t = 1, 2, 3, 4;

[0037] The batch normalization layer is expressed as:

[0038]

[0039] Among them, E[Y4 a (s)] and Var[Y4 a (s)] are the mean and variance of the output Y4 a (s) of the 4th convolutional layer respectively, ε is an extremely small number, γ a is the coefficient, and β a is the offset.

[0040] Furthermore, the CNN network includes three C-Block modules, a Flatten layer, and an FC-Block module; the C-Block module includes a convolutional layer, a BN layer, and a Dropout layer;

[0041] The Flatten layer is used to flatten the data of the previous layer to form an input vector suitable for the FC-Block module The FC-Block module contains 4 fully connected layers.

[0042] For the input of the h-th fully connected layer and the output The relationship between them is expressed as:

[0043]

[0044] wherein, and are the weights and offsets of the h-th fully connected layer respectively; k h is the number of neurons in this layer; h = 1, 2, 3, 4.

[0045] Furthermore, the input data size of the CNN model is 512×2, and the output data size is 2×1; the Dropout layer parameter is set to 0.2; the training adopts the Adam optimization algorithm, and the initial learning rate is set to 0.0004; the loss function adopts the root mean square error function of weights.

[0046] The present invention has the following beneficial effects compared with the prior art

[0047] Considering that the LFM signal in the real environment may be affected by sinusoidal non-linear interference due to hardware device defects at the signal transmitting end, the present invention provides a method for estimating the parameters of the LFM signal under the influence of sinusoidal non-linear interference. This method first models the LFM signal, takes the sinusoidal non-linear interference as the "multiplicative noise" of the signal and the Gaussian noise as the "additive noise" of the signal, and the formed noise signal model includes a sinusoidal non-linear interference term, a Gaussian noise term and an ideal signal model. Then, the noise signal model and the ideal signal model are used to train the CAE model. The trained CAE model can not only remove the conventional Gaussian noise in the signal, but also remove the sinusoidal non-linear interference existing in the real radar working environment; the method of the present invention then uses the "clean" signal after removing the sinusoidal non-linear interference and Gaussian noise and the signal modulation parameters corresponding to the signal to train the CNN model. The trained CNN model can quickly complete parameter estimation and obtain the signal modulation parameters. Therefore, the trained CAE model and CNN model in the present invention have a fast processing speed for the target signal, can quickly obtain the signal modulation parameters, and at the same time, the filtering effect of the CAE model is strong, and more accurate signal modulation parameters can be obtained.

[0048] In the parameter estimation method of the present invention, the CAE model uses the BN layer and the Dropout layer to replace the pooling layer and the upsampling layer. This design enhances the noise reduction performance of the CAE network and can better remove the sinusoidal non-linear interference and Gaussian noise in the LFM signal.

[0049] The parameter estimation method of the present invention is applicable to the technical field of communication signal processing, and is especially applicable to scenarios such as radar signal fast processing and electronic warfare. Description of the Drawings

[0050] Figure 1 It is a flowchart of a parameter estimation method;

[0051] Figure 2 It is a schematic diagram of the CAE model architecture;

[0052] Figure 3 It is a schematic diagram of the CNN model architecture;

[0053] Figure 4 It is a schematic diagram of the processing flow of the target LFM signal;

[0054] Figure 5(a) is the time-frequency diagram of the ideal transmitted signal of the radar;

[0055] Figure 5(b) is the time-frequency diagram of the signal actually intercepted by the receiver;

[0056] Figure 5(c) is the time-frequency diagram of the signal after noise reduction using Model A;

[0057] Figure 6(a) is the comparison diagram of the estimation accuracy of the frequency modulation slope;

[0058] Figure 6(b) is the comparison of the estimation accuracy of the initial frequency. Specific implementation manners

[0059] The present invention will be further described below in conjunction with specific embodiments and corresponding drawings.

[0060] Embodiment 1:

[0061] A method for estimating the parameters of an LFM signal under the influence of sinusoidal non-linear interference according to the present invention, as Figure 1 shown, includes:

[0062] 1) Generating a noise signal model of the LFM signal; the noise signal model includes a sinusoidal non-linear interference term, a Gaussian noise term, and an ideal signal model; the ideal signal model includes signal modulation parameters composed of the initial frequency and the frequency modulation frequency of the signal.

[0063] 2) Constructing a CAE model (Convolutional Auto-encoder, convolutional auto-encoding network), using the noise signal model as a sample to form a CAE input set for training the CAE model; using the ideal signal model in the noise signal model as a sample to form a CAE label set corresponding to the CAE input set; training the constructed CAE model based on the CAE input set and the CAE label set;

[0064] 3) Construct a CNN model (Convolutional Neural Network), input the samples in the CAE input set into the trained CAE model, and use the output result of the CAE model as the CNN input set for training the CNN model; use the signal modulation parameter items corresponding to the samples in the CAE input set as the CNN label set corresponding to the CNN input set; train the constructed CNN model based on the CNN input set and the CNN label set;

[0065] 4) Preprocess the target LFM signal, and the preprocessing includes storing the target LFM signal in the I / Q form. Input the preprocessed signal into the trained CAE model for denoising. The trained CAE model can not only remove the conventional Gaussian noise in the signal, but also remove the sine nonlinear interference existing in the real environment; then input the output result of the CAE model into the trained CNN model for parameter estimation, which can quickly obtain the signal modulation parameters, and the obtained signal modulation parameters are accurate.

[0066] Example 2:

[0067] A further optional design in this example is that the noise signal model in this example is s(t) = x(t)m(t) + n(t); where, s(t) is the noise signal model; m(t) is the sine nonlinear interference term; n(t) is the Gaussian noise term; x(t) is the ideal signal model, f0 is the initial frequency; μ is the frequency modulation slope; [f0, μ] is the signal modulation parameter in the ideal signal model.

[0068] Example 3:

[0069] A further optional design in this example is that the CAE input set s i is the i-th sample in the CAE input set, corresponding to the i-th noise signal model;

[0070] CAE label set x i is the i-th sample in the CAE label set, corresponding to the i-th ideal signal model; P is the total number of models;

[0071] CNN input set is the i-th sample in the CNN input set, corresponding to the i-th noise signal model after denoising by the CAE model;

[0072] CNN label set [f 0,i ,μ i is the i-th sample in the CNN label set, corresponding to the signal modulation parameter item corresponding to the i-th noise signal model;

[0073] The output result of the CNN model is corresponding to the signal modulation parameter items after being processed by the CNN model.

[0074] Example 4:

[0075] A further optional design of this example is that in the CAE input set of this example, the samples

[0076] In the CAE label set, the samples

[0077] where, and are respectively taking the real part and the imaginary part; s[1]... s[L] are the signals of the 1st... the Lth sampling points corresponding to the ith sample in the CAE input set; x[1]... x[L] are the signals of the 1st... the Lth sampling points corresponding to the ith sample in the CAE label set; is the set of all real numbers;

[0078] Example 5:

[0079] A further optional design of this example is that in this example, the CAE model includes an encoder and a decoder; where,

[0080] The encoder includes an input layer and three A-Block modules. The input layer performs a normalization operation on the preprocessed signal data and outputs a feature matrix; the A-Block module includes four one-dimensional convolutional layers (1D-Convolutional), one BN layer (Batch Normalization), and one Dropout layer; the role of the convolutional layer is to perform convolution on the signal using a convolutional kernel, extract the signal features and transform them into a feature map for output; the BN layer performs a normalization operation on the output of the convolutional layer; the Dropout layer randomly deactivates neurons in the neural network and outputs the feature information contained in the remaining neurons;

[0081] The decoder takes the output of the encoder as input data; the decoder includes three B-Block modules and an output layer; the B-Block module includes four one-dimensional transposed convolutional layers (1D-ConvTranspose), a BN layer, and a Dropout layer; the transposed convolutional layer performs a recovery operation on the encoder output features and outputs a feature vector; the BN layer performs a normalization operation on the output of the convolutional layer; the Dropout layer randomly deactivates the network neurons and outputs the feature information contained in the remaining neurons; the output layer uses a transposed convolutional layer with 2 convolutional kernels, and the output layer integrates the feature information and outputs the denoised LFM signal data.

[0082] The input data size of the CAE model is 512×2, and the output data size is 512×2; the Dropout layer parameter is set to 0.1; the Adam optimization algorithm is used for training, and the initial learning rate is set to 0.002; the mean square error function is used as the loss function.

[0083] In the a-th A-Block module, the input of the y-th convolutional layer and the output Y y a (s) are related as:

[0084]

[0085]

[0086] where R{`} is the ReLU activation function;

[0087] is the weight of the y-th convolutional layer;

[0088] is the offset of the y-th convolutional layer;

[0089] * is the dot product; n y a is the size of the convolutional kernel and m y a is the number of convolutional kernels; a = 1, 2, 3; y = 1, 2, 3, 4;

[0090] In the b-th B-Block module, the input of the t-th transposed convolutional layer and the output are related as:

[0091]

[0092] where, and are the weight and offset of the t-th transposed convolutional layer of the b-th module, respectively; is the convolution kernel size of the deconvolution layer; is the number of convolution kernels; b = 1, 2, 3; t = 1, 2, 3, 4;

[0093] The batch normalization layer is expressed as:

[0094]

[0095] where, E[Y4 a (s)] and Var[Y4 a (s)] are the mean and variance of the output Y4 a (s) of the 4th convolution layer respectively, ε is a very small number, γ a is a coefficient, and β a is an offset.

[0096] Example Six:

[0097] A further optional design of this example is that: the CNN network includes three C-Block modules, a Flatten layer and an FC-Block module; the C-Block module includes a convolution layer, a BN layer and a Dropout layer;

[0098] The Flatten layer is used to flatten the data of the previous layer to form an input vector suitable for the FC-Block module The FC-Block module contains 4 fully connected layers.

[0099] For the input and output of the hth fully connected layer, the relationship is expressed as:

[0100]

[0101] where, and are the weight and offset of the hth fully connected layer respectively; k h is the number of neurons in this layer; h = 1, 2, 3, 4.

[0102] The input data size of the CNN model is 512×2, and the output data size is 2×1; the Dropout layer parameter is set to 0.2; the training adopts the Adam optimization algorithm, and the initial learning rate is set to 0.0004; the loss function adopts the root mean square error function of the weights;

[0103] Example Seven:

[0104] A method for estimating the parameters of an LFM signal under the influence of sinusoidal non - linear interference, which combines the CAE model and the CNN model. The formed CAE - CNN model can not only reduce the time for signal parameter estimation and meet the requirements of battlefield real - time performance, but also improve the accuracy of LFM signal parameter estimation under the influence of sinusoidal non - linear phase error and Gaussian white noise.

[0105] The specific analysis and implementation steps of the method of the present invention are as follows:

[0106] S1. Analyze and generate a signal model and construct a data set.

[0107] An ideal linear frequency - modulated signal is generally defined as:

[0108]

[0109] Among them, A is the signal amplitude, f0 is the initial frequency of the signal, μ is the frequency - modulation slope, T is the signal time - width; (f0, μ) are the modulation parameters to be estimated. The phase term of this signal can be expressed as the following formula:

[0110]

[0111] The instantaneous frequency of the signal x(t) at time t is defined as:

[0112] f ideal (t)=2π(f0 + kt)(3)

[0113] It can be observed from formula (3) that the instantaneous frequency of an ideal LFM signal shows a linear transformation. However, in practical applications, some linear frequency - modulated radars may have certain hardware defects. For example, as introduced in reference [1], during the signal generation stage, due to the spurs of the direct digital synthesizer (DDS) itself, the DDS clock, and the power supply voltage spurs, the instantaneous frequency of the LFM signal shows a non - linear transformation. At this time, the instantaneous frequency of the LFM signal can be expressed as:

[0114] f real =f ideal +ε e (t)(4)

[0115] Among them, ε e (t) is the non - linear interference term. At the same time, considering the influence of background noise, the LFM signal can be described as:

[0116]

[0117] Among them, n(t) is the noise with a power of σ 2Additive white Gaussian noise, ε(t) = ∫ε e (t)dt is a non-linear interference. According to reference [6], ε(t) is defined as a sinusoidal non-linear phase term:

[0118] ε(t) = (A e / f e )(1 - cos2πf e t) (6)

[0119] where A e represents the sinusoidal non-linear amplitude, and f e represents the sinusoidal non-linear frequency. It should be noted that formula (5) can be expressed as follows:

[0120]

[0121] where m(t) = exp[jε(t)]. It can be seen that the sinusoidal non-linear frequency ramp affects the signal (1) in the form of multiplicative noise and hinders the traditional methods for estimating the parameters of the LFM signal.

[0122] After sampling the received LFM signal is completed, the discrete form of the signal (7) can be expressed as,

[0123] s[l] = x[l]m[l] + n[l], l = 1,..., L (8)

[0124] where s[l] represents the l-th sampling point of the received signal, and L is the total number of sampling points. x[l] is the discrete form of the signal (1). The data set constructed in this step mainly includes the data set of CAE and the data set of CNN. The value, the data set of CAE contains the input set and the corresponding label set where s i and x i are the input data and label data of the i-th training data respectively. where, represents the set of all real numbers, and respectively refer to taking the real part and the imaginary part. After the CAE network noise reduction processing, the output refers to the signal s i after noise reduction.

[0125] The data set of the CNN data set contains the input set and the label set where [f 0,i , μ i refers to the signal s iThe modulation parameters. Finally, the output of the CNN is where is the parameter estimation result of the signal s i .

[0126] To make the parameter estimation method of the present invention have wide applicability, this step generates a large training data set for different modulation parameters and signal-to-noise ratios (SNRs). The modulation parameters include {f0, μ, A e , f e}, and they traverse a certain parameter range at a fixed step size. The data contains a total of 4 SNR levels, and 194,400 pieces of data are generated for each SNR. Therefore, the data set contains a total of 777,600 pieces of data. For the sampled signal, it is assumed that the time width T of the signal is 400e -6 seconds, the number of sampling points is fixed at L = 512, and the sampling rate is 1.28 MHz. Table 1 gives the detailed content of the modulation parameters.

[0127] Table 1 Modulation parameter settings of training samples

[0128] Modulation parameter Parameter range Parameter step size Unit Number of steps <![CDATA[f0]]> 200～400 25 kHz 9 μ 0.1～0.5 0.05 GHz / s 9 <![CDATA[A e > 16～22 2 kHz 4 <![CDATA[f e > 5～11 2 kHz 4 SNR -12～-9 1 dB 4

[0129] S2. Construction and training settings of the CAE-CNN model architecture

[0130] The framework of the CAE network constructed in the present invention is as Figure 2 shown, which includes an encoder network and a decoder network. Different from the traditional CAE network structure, the present invention cancels the pooling layer and the upsampling layer to improve the noise reduction performance of the CAE network model.

[0131] In the encoder network, it includes 1 input layer and 3 A-Block modules. Each A-Block module contains 4 one-dimensional convolutional layers (1D-Convolutional), 1 batch normalization layer (BN), and 1 Dropout layer. For the a-th A-Block module (a = 1, 2, 3), the input of the y-th convolutional layer (y = 1, 2, 3, 4) and the output Y y a (s) can be expressed as:

[0132]

[0133] where R(·) refers to the activation function ReLU [7] , refers to the weight of the y-th convolutional layer, refers to the offset of the y-th convolutional layer, * refers to the dot product, n ya is the size of the convolutional kernel and m y a is the number of convolutional kernels. The batch normalization layer performs a normalization operation on Y4 a (s), which can reduce the training time of the network and can be defined as:

[0134]

[0135] where E[Y4 a (s)] and Var[Y4 a (s)] are the mean and variance of the input data Y4 a (s) respectively, ε is an extremely small number, γ a is a coefficient, and β a is an offset.

[0136] The decoder network contains 3 B-Block modules and an output layer. Among them, the decoder network takes the output of the encoder network as its input data and outputs Each B-Block module contains 4 transposed convolutional layers (1D-ConvTranspose), a BN layer, and a Dropout layer. For the b-th B-Block module (b = 1, 2, 3), the input and output of the t-th transposed convolutional layer (t = 1, 2, 3, 4) can be expressed as:

[0137]

[0138] where and are the weights and offsets of the t-th transposed convolutional layer of the b-th module respectively, represents the size of the convolutional kernel of the transposed convolutional layer, represents the number of convolutional kernels. Subsequently, the operation of the BN layer is the same as that introduced in the encoder part. Finally, the output layer consists of a transposed convolutional layer with 2 convolutional kernels to obtain the final output.

[0139] The structure of the CNN network in the present invention is as Figure 3 shown, including 3 C-Block modules, 1 Flatten layer, and 1 FC-Block module. The CNN network takes the output of the CAE as its input data and outputs the parameter estimation result The C-Block module contains a one-dimensional convolutional layer, a BN layer, and a Dropout layer. Their principles are the same as those in the encoder network and will not be elaborated here. The Flatten layer is used to flatten the data of the previous layer into a vector. Suitable for the input of the FC-Block module. The FC-Block module contains 4 fully connected layers. For the input and output of the h-th fully connected layer (h = 1, 2, 3, 4), the relationship can be described as:

[0140]

[0141] where and are the weights and biases of the h-th fully connected layer respectively, and k h is the number of neurons in this layer.

[0142] The following are the training details of the CAE-CNN network model.

[0143] In the CAE network model, the input data size of its output layer is 512×8, and the output data size is 512×2. The parameter settings of other A-Block and B-Block modules are shown in Tables 2 and 3. The parameter setting of the Dropout layer in CAE is 0.1. The optimizer used for training is the Adam algorithm, and the initial learning rate is set to 0.002. Considering that signal denoising is a regression problem, the mean squared error (MSE) is used as the loss function, and its definition is:

[0144]

[0145] where Ν = 256 refers to the size of each training batch data. A training strategy with callback functions is used, and the loss of the validation set is a monitor for updating the learning rate in a timely manner. When the loss does not decrease for 5 consecutive training epochs, the initial learning rate will be multiplied by a factor of 0.9 to update the learning rate. This network was trained for 30 epochs.

[0146] Table 2. Parameter settings of A-Block

[0147]

[0148] Table 3. Parameter settings of B-Block

[0149]

[0150] Table 4. Parameter settings of C-Block

[0151]

[0152] Table 5. FC-Block Parameter Settings

[0153]

[0154] In the CNN network, the parameter settings for the C-Block and FC-Block modules are shown in Tables 4 and 5. The parameter setting of the Dropout layer is 0.2. The optimizer of CNN also uses Adam, and the initial learning rate is 0.0004. The root mean square error of the weights is selected as the loss function, and its definition is as follows:

[0155]

[0156] where Ν = 128 refers to the size of each training batch data, and w1 = 0.67 and w2 = 0.33 are the weight settings of the root mean square error of the weights. CNN uses the same training strategy as CAE and is trained for 100 epochs in total.

[0157] For the received and adopted target LFM signal as the input of the constructed CAE-CNN model, as Figure 4 shown, in the first stage, the CAE model performs noise reduction filtering on the LFM signal and outputs a clean signal. In the second stage, the CNN model performs parameter estimation on the clean LFM signal, and the finally output modulation parameters include the initial frequency and frequency modulation slope of the signal.

[0158] Application Example 1:

[0159] In this example, an electronic warfare scenario is simulated and parameter estimation is performed on a radar LFM signal intercepted in the simulation. The hardware device at the transmitting end of this signal is a certain type of miniaturized FMCW radar. The initial frequency of this signal is set to 215 kHz, and the modulation frequency is 0.4 GHz / s. Due to defects in the hardware device at the transmitting end, there is a sinusoidal non-linear term in the phase of this LFM signal, where the sinusoidal non-linear frequency is 6 kHz and the sinusoidal non-linear amplitude is 16 kHz.

[0160] First, the intercepted LFM signal is sampled, and the length of the obtained single-component LFM signal is 512, and the signal-to-noise ratio of this signal is -6 dB.

[0161] Then, the pre-trained CAE model A is used to perform denoising processing on this signal, and the time-frequency diagrams of the LFM signal before and after noise reduction are shown using the Wigner-Ville distribution. Figure 5(a) is the time-frequency diagram of the ideal transmitted signal of the radar, Figure 5(b) is the time-frequency diagram of the signal actually intercepted by the receiver, and Figure 5(c) is the time-frequency diagram of the signal after noise reduction using model A.

[0162] By comparing Fig. 5(a) and Fig. 5(c), it can be seen that the denoised LFM signal basically restores the ideal transmitted signal, which is very beneficial for subsequent parameter estimation.

[0163] Finally, the pre-trained CNN model A is used to estimate the parameters of the intercepted signal processed by the CAE model A. In this example, the methods in Ref. [4] and Ref. [5] are also used to estimate the parameters of the same signal, and a comparison is made in terms of estimation accuracy and calculation time. The comparison method uses the same dataset as the present invention during training, and parameter settings such as the initial learning rate and the number of training epochs are the same. At the same time, 300 Monte Carlo experiments are calculated in this example to verify the estimation accuracy of each method, and the root mean square error (RMSE) is used as the parameter estimation accuracy evaluation criterion, which can be defined as follows:

[0164]

[0165] Fig. 6(a) is the comparison chart of the estimation accuracy of the frequency modulation slope, and Fig. 6(b) is the comparison of the estimation accuracy of the initial frequency.

[0166] It can be seen from Fig. 6(a) and Fig. 6(b) that the method of the present invention has higher estimation accuracy when the signal-to-noise ratio is higher than -13 dB. In Fig. 6(a), when the signal-to-noise ratio is greater than -12 dB, the estimation accuracies of the methods in Ref. [4] (the corresponding line of DCNN-FrFT) and Ref. [5] (the corresponding line of CVDNN) are both lower than that of the present invention (the corresponding line of CAE-CNN). Among them, the estimation accuracy of the method in Ref. [5] always remains at about 79 dB, while the accuracy of the method in Ref. [4] gradually increases with the increase of the signal-to-noise ratio. When the signal-to-noise ratio is greater than -9 dB, the accuracy is higher than that of the method in Ref. [5], but the estimation performance is still lower than that of the method of the present invention. In Fig. 6(b), when the signal-to-noise ratio is greater than -13 dB, the estimation accuracies of the methods in Ref. [4] (the corresponding line of DCNN-FrFT in the figure) and Ref. [5] (the corresponding line of CVDNN) are both lower than that of the present invention (the corresponding line of CAE-CNN). Among them, the estimation accuracies of the methods in Ref. [4] and Ref. [5] are about 45 dB and 50 dB respectively, and the signal parameters cannot be accurately estimated.

[0167] Table 6 shows the time required for 300 Monte Carlo experiments calculated by the present invention and other methods. It can be seen that the calculation time required by the present invention is relatively short, which is completely suitable for real-time estimation of signal parameters, especially suitable for scenarios such as radar signal fast processing and electronic warfare.

[0168] Table 6 Comparison of calculation times of different methods

[0169] Method Consumption time The present invention - CAE - CNN 0.4146s Reference [4] - DCNN - FrFT 0.4124 s (+11.1627 s) Reference [5] - CVDNN 0.2507s

[0170] References:

[0171] [1] Ayhan, S., Scherr, S., Bhutani, A., Fischbach, B., Pauli, M., & Zwick, T. (2016). Impact of frequency ramp nonlinearity, phase noise, and SNR on FMCW radar accuracy. IEEE Transactions on Microwave Theory and Techniques, 64(10), 3290 - 3301.

[0172] [2] S. Barbarossa, "Analysis of multicomponent LFM signals by a combined Wigner - Hough transform", IEEE Transactions on Signal Processing, vol. 43, no. 6, pp. 1511 - 1515, June 1995.

[0173] [3] R. Chen and Y. Wang, "Universal FRFT - based algorithm for parameter estimation of chirp signals," in Journal of Systems Engineering and Electronics, vol. 23, no. 4, pp. 495 - 501, Aug. 2012, doi: 10.1109 / JSEE.2012.00063.

[0174] [4] Ben, G., Zheng, X., Wang, Y., Zhang, X., & Zhang, N. (2021). Chirp Signal Denoising Based on Convolution Neural Network. Circuits, systems, and signal processing, 40(11), 5468 - 5482.

[0175] [5]Su, H., Bao, Q., & Chen, Z. (2019). Parameter estimation processor for chirp signals based on a complex-valued deep neural network. IEEE Access, 7, 176278-176290.

[0176] [6]Piper, S. O. (1995, May). Homodyne FMCW radar range resolution effects with sinusoidal nonlinearities in the frequency sweep. In Proceedings international radar conference (pp. 563-567). IEEE.

[0177] [7]Glorot, X., Bordes, A., & Bengio, Y. (2011, June). Deep sparse rectifier neural networks. In Proceedings of the fourteenth international conference on artificial intelligence and statistics (pp. 315-323). JMLR Workshop and Conference Proceedings.

Claims

1. A method for estimating the parameters of an LFM signal under the influence of sinusoidal non - linear interference, characterized in that: Including: 1) A noise signal model for generating an LFM signal; The noise signal model includes a sine nonlinear interference term, a Gaussian noise term, and an ideal signal model; the ideal signal model includes signal modulation parameters; 2) Construct a CAE model, use the noise signal model as a sample to form a CAE input set for CAE model training; Use the ideal signal model in the noise signal model as a sample to form a CAE label set corresponding to the CAE input set; train the constructed CAE model based on the CAE input set and the CAE label set; 3) Construct a CNN model, input the samples in the CAE input set into the trained CAE model, and use the output result of the CAE model as a CNN input set for CNN model training; Use the signal modulation parameter terms corresponding to the samples in the CAE input set as a CNN label set corresponding to the CNN input set; train the constructed CNN model based on the CNN input set and the CNN label set; 4) Preprocess the target LFM signal, input the preprocessed signal into the trained CAE model for denoising, and input the output result of the CAE model into the trained CNN model for parameter estimation; The noise signal model is s(t) = x(t)m(t) + n(t) where \(s(t)\) is the noise signal model; \(m(t)\) is the sinusoidal non - linear interference term; \(n(t)\) is the Gaussian noise term; \(x(t)\) is the ideal signal model, \(f_0\) is the initial frequency; \(\mu\) is the frequency modulation slope; \([f_0,\mu]\) are the signal modulation parameters in the ideal signal model; The CAE input set s i is the i-th sample in the CAE input set, corresponding to the i-th noise signal model; The CAE tag set x i is the i-th sample in the CAE tag set, corresponding to the i-th ideal signal model; P is the total number of models; The CNN input set is the i-th sample in the CNN input set, corresponding to the i-th noise signal model after noise reduction by the CAE model; The CNN tag set [f 0,i ,μ i is the i-th sample in the CNN tag set, corresponding to the signal modulation parameter item of the i-th noise signal model; In the CAE input set, the sample In the CAE tag set, the sample Among them, and respectively take the real part and the imaginary part; s[1]... s[L] are the signals of the 1st... the Lth sampling points corresponding to the ith sample in the CAE input set; x[1]... x[L] are the signals of the 1st... the Lth sampling points corresponding to the ith sample in the CAE label set; is the set of all real numbers; The CAE model includes an encoder and a decoder; where, The encoder includes an input layer and three A-Block modules. The input layer performs a normalization operation on the preprocessed signal data and outputs a feature matrix; the A-Block module includes four convolutional layers, a BN layer, and a Dropout layer; the convolutional layer uses a convolutional kernel to perform convolution on the input data, extracts signal features and transforms them into a feature map for output; the BN layer performs a normalization operation on the output of the convolutional layer; the Dropout layer randomly deactivates neurons in the neural network and outputs the feature information contained in the remaining neurons; The decoder uses the output of the encoder as input data; the decoder includes three B-Block modules and an output layer; the B-Block module includes four deconvolutional layers, a BN layer, and a Dropout layer; the deconvolutional layer performs a recovery operation on the encoder output features and outputs a feature vector; the BN layer performs a normalization operation on the output of the convolutional layer; the Dropout layer randomly deactivates neurons in the network and outputs the feature information contained in the remaining neurons; the output layer uses a deconvolutional layer with 2 convolutional kernels, and the output layer performs an integration operation on the feature information and outputs the denoised signal data; In the a-th A-Block module, the input of the y-th convolutional layer and the output are related as follows: where, R{·} is the activation function ReLU; is the weight of the y-th convolutional layer; is the offset for the y-th convolutional layer; * is the dot product; n y a is the size of the convolutional kernel and m y a is the number of convolutional kernels; a = 1, 2, 3; y = 1, 2, 3, 4; In the b-th B-Block module, the input and output of the t-th transposed convolutional layer are related as follows: Among them, and are the weights and offsets of the t-th deconvolution layer of the b -th module respectively; is the convolution kernel size of the deconvolution layer; is the number of convolution kernels; b = 1, 2, 3; t = 1, 2, 3, 4; The batch normalization layer is expressed as: Among them, E[Y4 a (s)] and Var[Y4 a (s)] are the mean and variance of the output Y4 a (s) of the fourth convolutional layer respectively, ε is an extremely small number, γ a is a coefficient, and β a is an offset.

2. The method for estimating the parameters of an LFM signal under the influence of sinusoidal non - linear interference according to claim 1, characterized in that: The signal modulation parameter terms include the initial signal frequency and the frequency modulation frequency.

3. The method for estimating the parameters of an LFM signal under the influence of sinusoidal non - linear interference according to claim 2, characterized in that: The input data size of the CAE model is 512×2, and the output data size is 512×2; the Dropout layer parameter is set to 0.1; the training uses the Adam optimization algorithm, and the initial learning rate is set to 0.002; the loss function uses the mean square error function.

4. The method for estimating LFM signal parameters under the influence of sinusoidal non - linear interference according to claim 3, wherein: The CNN model includes three C-Block modules, a Flatten layer, and an FC-Block module; the C-Block module includes a convolutional layer, a BN layer, and a Dropout layer; The Flatten layer is used to flatten the data of the previous layer to form an input vector suitable for the FC-Block module. The FC-Block module contains 4 fully connected layers. For the input of the h th fully connected layer and the output The relationship between them is expressed as: Among them, and are the weights and offsets of the h-th fully connected layer respectively; k h is the number of neurons in this layer; h = 1, 2, 3, 4.

5. The method for estimating LFM signal parameters under the influence of sinusoidal non - linear interference according to claim 4, wherein: The input data size of the CNN model is 512×2, and the output data size is 2×1; the Dropout layer parameter is set to 0.2; the Adam optimization algorithm is used for training, and the initial learning rate is set to 0.0004; the weighted root mean square error function is used as the loss function.

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