A satellite suppression jamming identification method based on a multi semantic feature fusion network
By reconstructing satellite suppression jamming signals from images and fusing multiple semantic features, the problem of insufficient input dimensions of residual networks was solved, enabling efficient identification of seven types of suppression jamming signals and improving identification accuracy and generalization ability.
Patent Information
- Application Number
- CN202210183503.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-02-25
- Publication Date
- 2025-11-04
- Estimated Expiration
- 2042-02-25
AI Technical Summary
In existing technologies, residual networks based on time-domain construction have small input sample dimensions when identifying satellite navigation signals, which makes it impossible to provide sufficient feature discrimination and affects the accuracy of identifying interference signals.
By reconstructing the satellite suppression jamming signal into an image, a multi-semantic feature fusion network is constructed. A residual network with skip connections is used to extract high-dimensional signal time-frequency domain features. The feature fusion module is then used to fuse low-level and high-level semantic features to improve the signal feature extraction capability.
It has achieved effective identification of seven typical suppression interference signals, improving the identification accuracy and generalization ability, especially performing well under conditions of high signal-to-noise ratio and high interference signal ratio.
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Figure CN114624739B_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application is mainly directed to the identification of 7 types of active suppression jamming of satellite navigation signals, mainly relates to a satellite suppression jamming identification method based on a multi-semantic feature fusion network. BACKGROUND
[0002] In military and civilian fields, with the development of satellite navigation systems and their applications, global navigation satellite systems (GNSS) have become an important and indispensable space infrastructure. With the in-depth application of navigation and positioning technology, "navigation jamming war" has gradually become an important branch of electronic countermeasures. In a complex communication environment, satellite navigation suppression jamming from the outside poses a serious threat to the safe, efficient and stable operation of infrastructure that relies on satellite navigation services. Therefore, effective detection and identification of suppression jamming is still a research hotspot in the field of GNSS.
[0003] For the identification of multiple types of active suppression jamming, in recent years, some scholars have used deep learning network structure to automatically extract signal features, and have made good breakthroughs in signal identification. A residual network suppression jamming identification algorithm based on time domain construction is proposed, which uses one-dimensional data constructed in the time domain of the signal as the network input. The dimension scale of the network input sample is small, which cannot provide more effective distinguishing features for the network as classification and identification basis. To this end, the present application proposes a satellite suppression jamming signal identification algorithm based on a multi-semantic feature fusion network. Through signal image reconstruction and multi-semantic feature fusion network, the low-level and high-level semantic feature extraction of the residual network through the skip connection is used to construct more perfect high-dimensional signal time-frequency domain features and extract more rich multi-semantic features, which has better identification performance than the residual network suppression jamming identification algorithm based on time domain construction.
[0004] Therefore, the satellite suppression jamming identification algorithm based on the multi-semantic feature fusion network has a very wide application prospect in the identification of satellite navigation signal jamming. SUMMARY
[0005] Due to the simple principle of suppression jamming, it has the advantages of low implementation difficulty and high suppression efficiency, so artificial suppression jamming has become the main interference factor of satellite communication systems.
[0006] The technical solution adopted by the present application to solve its technical problems comprises the following steps:
[0007] Step 1, analyze 7 types of suppression jamming signals, and receive the time domain signal of the mixed signal of the satellite navigation signal and the suppression jamming signal and the Gaussian noise signal;
[0008] Step 2: Perform image reconstruction processing on the received time-domain signal to obtain a two-dimensional image affected by different suppression interference signals.
[0009] Step 3: Build an interference identification model.
[0010] First, a residual network model is built; then, the output features of each residual unit in the residual network model are further spliced and fused to finally obtain an interference recognition model based on feature fusion network.
[0011] Step 4: Obtain multi-semantic fusion features, classify them, and calculate the recognition accuracy.
[0012] Step 1 is implemented as follows:
[0013] 1-1. For the seven typical suppression interference signals, the expression for J(t) can be represented by Table 1.
[0014] Table 1 shows the expression for suppressing interference signals.
[0015]
[0016] In Table 1, f c The carrier frequency of the interference signal. The initial phase is usually set to 0. a(t), a1(t), and a2(t) are the baseband data of the BPSK and QPSK interference signals. u(t) is the pulse signal of the time-domain pulse interference signal, τ is the pulse duration, and T is the time-domain pulse period. n(t) is random Gaussian white noise, K... FM K is the slope of the frequency modulation characteristic curve of the noise frequency modulation interference. K1 is the sweep rate of the sweep frequency interference. The comb spectrum interference signal is synthesized from 5 noise frequency modulation signals, and K is the slope of the frequency modulation characteristic curve of the comb spectrum interference. c,i The carrier frequency of the comb spectrum interference signal is determined by the communication frequency band to be interfered with.
[0017] 1-2. The time-domain model of the satellite to be identified suppressing interference signals can be expressed as:
[0018] S(t)=ρ1b(t)c(t)exp(j2πft)+ρ2J(t)+N(t) (1)
[0019] In the above formula, ρ1 and ρ2 are the amplitudes of the satellite navigation signal and the jamming signal, respectively; b(t) is the baseband data of the satellite navigation signal; c(t) is the spread spectrum sequence data of the satellite navigation signal; f is the carrier frequency of the satellite navigation signal; J(t) is the jamming signal; and N(t) is the noise signal, which follows the rule N(0, σ). 2 Gaussian white noise, σ 2 This represents the noise variance.
[0020] Therefore, the sampling of the received signal can be expressed as I and Q two-way data signals respectively:
[0021]
[0022] Where f s is the sampling frequency, M represents the number of symbols, and N is the number of sampling points.
[0023] Step 2 is implemented as follows:
[0024] 2-1. Because the input of the network structure is usually a one-dimensional data form of training samples when solving signal recognition problems by traditional deep learning processing, the number of features that can be extracted by the network is insufficient, resulting in low signal recognition accuracy. Therefore, after combining satellite suppression jamming signal recognition with deep learning, the present application proposes to image reconstruct one-dimensional suppression jamming signal to obtain high-dimensional data images, which facilitates the deep learning network to extract signal features with effective distinguishing degree.
[0025] In order to ensure the same data constraint conditions as the network used in the present application, first, the received signal is sampled, and the sampled I and Q two-way one-dimensional time sequence signals are expressed as a data matrix block of 1xMN, then the data matrix block is spliced and expanded to expand the data set of the network input signal, achieving the effect of data enhancement. Finally, the data matrix blocks of I and Q two-way are matrix transformed and spliced to obtain high-dimensional data as the two-dimensional image input of the network model of the present application.
[0026] The specific process of signal image reconstruction is as follows: the time domain signal obtained from formula (2) and formula (3) is cut and transformed according to the symbol length to obtain a data matrix block of 1xMN. Therefore, the data matrix block obtained by preliminarily image reconstructing the sampled data can be expressed as:
[0027] S mod,I,1 = [S I (1), S I (2), S I (3), …, S I (MN) 1×MN (4)
[0028] S mod,Q,1 = [S Q (1), S Q (2), S Q (3), …, S Q (MN) 1×MN (5)
[0029] To provide as many extractable signal features as possible for the network model, the data matrix blocks obtained from formula (4) and formula (5) are further spliced and expanded accordingly, and the data matrix blocks are filled D times to obtain new data blocks. The filling process can be represented as
[0030] S mod,I mod,I,1 mod,I,2 mod,I,16 1×DMN (6)
[0031] mod,Q mod,Q,1 mod,Q,2 mod,Q,16 1×DMN (7) To make the constructed two-dimensional image better reflect the time-frequency characteristics of the interference signal, the two expanded data blocks obtained from formula (6) and formula (7) are matrix transformed and spliced to obtain a two-dimensional image of DNx2M size, and the two-dimensional image can be represented as:
[0032]
[0033] 2-2. In the image reconstruction process, the signal is filled and converted to enhance the data set of the signal to be identified, to provide more extractable signal features for the network of the application, thereby improving the recognition accuracy of the interference signal.
[0034] The received signals under different types of suppressed interference signals are respectively image reconstructed to obtain the two-dimensional images input into the network of the application as shown in Figures 2.1 to 2.8 It is found through observation that the received signals can more intuitively present the differences between various signals after image reconstruction. In a Gaussian noise environment, the depth change of the pixel points in the horizontal direction on the grayscale image can reflect the change of the signal with frequency and time, and the depth of the pixel points in the vertical direction can reflect the signal data information of the signal at different times.
[0035] Step 3 is specifically implemented as follows:
[0036] 3-1. To meet the multi-semantics feature fusion, it is necessary to ensure that the network can obtain more rich time domain and frequency domain features, and the application proposes to use a nonlinear mapping residual network structure to extract signal features. To better adapt to the input of the residual network, the single-channel input image is first changed in channel and changed in size, and then a convolution layer and a maximum pooling layer are used to obtain an input image more suitable for the residual network.
[0037] To extract as many local details and texture features as possible from the signal, this invention employs a four-level residual network in the feature extraction module. Each residual unit involves two convolutional layers with small kernels, avoiding the loss of detail in interference signals caused by a large receptive field of view. This allows the network to accurately extract more detailed and realistic signal features from the interference signal. Simultaneously, each convolutional layer is accompanied by a ReLU activation function layer, and the skip connections between the various levels of the residual network form a deep network, increasing the non-linearity of the convolutional operations. This enables the network to extract features from different perspectives, obtaining more accurate semantic features of the signal to be identified at various levels, thereby improving the accuracy of suppressing interference signals.
[0038] 3-2. The received signal is a complex mixture of satellite navigation signals, suppressed interference signals, and Gaussian noise. When extracting signal features, a residual network is used. The lower-level convolutional parts of the signal processing layer have a small receptive field, primarily extracting local details such as edges and textures of the interference signal. As the number of layers increases, more signal features can be extracted. Similarly, higher layers can obtain abstract and complex semantic features of the interference signal. Therefore, to simultaneously obtain both low-level and high-level semantic features, a feature fusion process is proposed for the extracted semantic features at each level. The feature fusion module includes four feature preprocessing layers, an average pooling layer, and a flattening layer.
[0039] The feature fusion method employed is concatenation fusion. To maintain a consistent proportion of signal feature effects across layers, preprocessing is required to change the size and channels of the output feature maps from each residual unit. Therefore, this invention proposes a feature preprocessing unit, primarily composed of a 1×1 convolutional layer, a max pooling layer, an instance normalization layer, and a ReLU activation layer. To avoid the problem of a significant increase in parameters caused by directly using convolutional layer downsampling, this invention uses a 1×1 convolutional layer to achieve feature channel changes, followed by pooling layer downsampling to change the feature map size. The feature preprocessing unit is as follows: Figure 3 As shown.
[0040] pass Figure 3 The feature preprocessing unit shown standardizes the semantic features of different sizes and number of channels output by each level of the residual network to obtain standardized features.
[0041] Step 4 is implemented as follows:
[0042] 4-1. Figure 3The output standardized features are dimensionally spliced, fused and pooled to reduce dimension, and the multi-semantics fused features of the signals are obtained.
[0043] The present application has the following advantages:
[0044] Therefore, the present application mainly researches on seven typical active jamming signals, which are BPSK jamming, single-tone jamming, time-domain pulse jamming, noise frequency modulation jamming, QPSK jamming, linear sweep jamming and comb spectrum jamming. The present application proposes to reconstruct the time-domain signals into images, and uses the residual network with skip connection to extract the time-frequency domain features and abstract semantic features, and then fuses the low-level and high-level output features through the feature fusion module to obtain more complex and abstract multi-semantics features, so as to realize the effective identification of the seven typical jamming signals.
[0045] The present application proposes the multi-semantics feature fusion network based on image reconstruction to realize the satellite jamming signal identification. On the one hand, the image reconstruction achieves the data enhancement effect and provides more extractable signal features for the network. On the other hand, the multi-semantics feature fusion improves the feature extraction and classification ability of the network, which is more helpful for classification and identification, and the algorithm has good generalization ability. Therefore, the algorithm of the present application can effectively deal with complex and multi-type jamming and obtain good classification and identification effect. BRIEF DESCRIPTION OF DRAWINGS
[0046] Table 1: Expression of jamming signal
[0047] Table 2: Generation parameters of jamming signal
[0048] Figure 1 Jamming signal identification framework based on multi-semantics feature fusion network
[0049] Figure 2.1 BPSK jamming exists
[0050] Figure 2.2 Single-tone jamming exists
[0051] Figure 2.3 Time-domain pulse jamming exists
[0052] Figure 2.4 Noise frequency modulation jamming exists
[0053] Figure 2.5 QPSK jamming exists
[0054] Figure 2.6 Linear sweep jamming exists
[0055] Figure 2.7 There is a comb spectrum interference;
[0056] Figure 2.8 There is no satellite navigation signal image of suppressing interference;
[0057] Figure 3 Feature preprocessing unit;
[0058] Figure 4 The interference recognition rates of three networks at different jamming-to-signal ratios;
[0059] Figure 5 The interference recognition rates of three networks at different signal-to-noise ratios; DETAILED DESCRIPTION
[0060] The specific embodiments of the present application will be further described below in conjunction with the accompanying drawings. The multi-semantics feature fusion network realizes the satellite suppressing interference signal recognition method, and the specific implementation steps are as follows:
[0061] Step 1: Obtain the expressions of the specific 7 types of suppressing interference signals as shown in Table 1, and obtain the time domain sampling signals S I (n) and S Q (n) under different suppressing interferences.
[0062] Table 1 is the expression of the suppressing interference signal
[0063]
[0064] In Table 1, f c is the carrier frequency of the interference signal, is the initial phase, which is usually set to 0. a(t), a1(t) and a2(t) are the baseband data of BPSK and QPSK interference signals. u(t) is the pulse signal of the time domain pulse interference signal, τ is the pulse duration, and T is the time domain pulse period. n(t) is random Gaussian white noise, K FM is the frequency modulation characteristic curve slope of the noise frequency modulation interference. K1 is the sweep frequency rate of the sweep interference. The comb spectrum interference signal is composed of 5 noise frequency modulation signals, K is the frequency modulation characteristic curve slope of the comb spectrum interference, f c,i is the carrier frequency of the comb spectrum interference signal, and the selection of the frequency point is determined by the communication frequency band to be interfered.
[0065] Step 2: Database making. The received time domain signal is image reconstructed with symbol number M = 112, sampling number N = 14, splicing expansion number D = 16, and a two-dimensional image with a size of 224x224 is obtained. According to the parameters of each type of suppression jamming obtained in Table 2, 500 frequency points are uniformly selected in the carrier frequency range, 4 pictures are generated for each frequency point, the number of data image of each type of signal is 500x4 = 2000, and the size of the training set data image library is 500x4x7 = 140000. As for the test set image, 500 frequency points are randomly selected in the carrier frequency range, and 1 picture is generated for each frequency point, so the size of the test set image library is 500x1x7 = 3500.
[0066] Table 2: Suppression jamming signal generation parameters
[0067] Jammer type Jammer parameters BPSK jammer Random frequency location in the range 3-9 kHz Single tone jammer Random frequency location in the range 3-9 kHz Time domain pulse jammer Random duty cycle in the range 0-100% Noise FM jammer Random frequency location in the range 3-9 kHz, FM slope 200 QPSK jammer Random frequency location in the range 3-9 kHz Linear sweep jammer Random sweep rate in the range 4.8-14.4 kHz / s, start frequency 3 kHz Comb spectrum jammer 5 noise FM signals combined, random frequency location in the range 3-9 kHz
[0068] Step 3: According to Figure 1 The feature fusion network model is built, mainly composed of convolution layer, pooling layer, activation function, residual module and feature fusion module. The visual range of the convolution layer is 7x7, the residual module is composed of 4-level residual unit skip connection with a distribution of (2, 2, 2, 2), wherein the convolution kernel size in the residual module is 3x3, and the feature fusion module adopts splicing fusion. After the output size of each level of residual module is standardized, it is added. First, the single channel signal image (224x224x1 dimension) is changed in size and channel to obtain an input image with a size of 112x112, an input channel of 64, and after passing through 4-level residual unit, the features output by each level of residual unit are obtained. Then the standardized features of different sizes and different channel numbers output by each level of residual network are standardized (7x7x512 dimensions) by the feature preprocessing unit shown in the figure. Figure 3
[0069] Step 4: The standardized features output by the feature preprocessing unit in step 3 are dimensionally spliced and fused and pooled to reduce the dimension to obtain multi semantic fusion features of the signal (1x2048 dimensions). Finally, the output features are classified, and the recognition accuracy is counted to obtain the simulation results of Figure 4 and Figure 5
[0070] Embodiment:
[0071] The server GPU used in the experimental training of the present application is NVIDIA TITAN RTX, the deep learning framework used is Pytorch, the training is carried out by using the multi semantic feature fusion network of the present application, the global learning rate is 0.05, the training batch is 16, the training round is 100, the loss function adopts cross entropy, the optimizer is Adam, and the signal feature vector dimension after feature fusion is 2048. At the same time, the simulation of the widely used residual network interference suppression algorithm based on time domain is carried out, which is used as the comparison result of the present application.
[0072] The simulation of 7 types of satellite suppression interference signals is realized by means of MATLAB software, the signal data preprocessing is carried out to obtain training set and test set image samples, and the two are not crossed. The signal-to-noise ratio SNR is [–10:10] dB, the jamming-to-signal ratio JSR is [–10:15] dB, the sampling frequency is 22.4 kHz, the spread spectrum code speed is 100 Hz, the interference information rate is 1.6 kHz, and the other parameters of each type of interference are shown in table 2.
[0073] The training set and test set samples of the residual network interference suppression algorithm based on time domain in the comparison algorithm are based on time domain, the satellite receiving signals containing 7 types of suppression interference are obtained by MATLAB simulation in the simulation, and the I and Q signals after sampling are spliced into one-dimensional data. In order to observe the comparison effect, the interference parameters are set as shown in table 2, the size of the training set and test set, the signal-to-noise ratio and the jamming-to-signal ratio range are consistent with the present application.
[0074] The trained network is used to verify the signal, the multi semantic feature fusion network of the present application and the network without feature fusion, and the network of the comparison algorithm are used to realize the identification of each type of suppression interference signal, and the correct identification rate of each type of suppression interference in the three network algorithms when the signal-to-noise ratio is 0 dB and the jamming-to-signal ratio changes is as shown in Figure 4 The correct identification rate of each type of suppression interference in the three network algorithms when the jamming-to-signal ratio is 0 dB and the signal-to-noise ratio changes is as shown in Figure 5 .
[0075] As can be seen from Figure 4 and Figure 5 , the identification accuracy of the feature fusion network and the feature non fusion network proposed in the present application is higher than that of the comparison algorithm. When the signal-to-noise ratio is greater than 0 dB or the jamming-to-signal ratio is greater than 0 dB, the interference identification accuracy of the network of the present application can reach more than 90%. This is because the present application proposes to reconstruct the received signal into an image, enhances the network input data set, provides more extractable signal features, and improves the interference identification performance. And the multi semantic feature fusion obtains more effective signal features with large distinguishing degree, so as to obtain better identification performance.
[0076] Finally, it is to be understood that the embodiments are for purposes of illustration only and that various changes and modifications can be made by those skilled in the art without departing from the scope of the application as disclosed in the specification and appended claims. Therefore, the scope of the application is not to be limited to the embodiments disclosed but is to be accorded the full scope permissible by the appended claims.
Claims
1. A satellite suppression interference identification method based on a multi-semantic feature fusion network, characterized in that... Includes the following steps: Step 1: Analyze the 7 types of suppression jamming signals and receive the time-domain signal of the mixed signal of satellite navigation signal, suppression jamming signal and Gaussian noise signal; Step 2: Perform image reconstruction processing on the received time-domain signal to obtain a two-dimensional image affected by different suppression interference signals; Step 3: Build an interference identification model; First, a residual network model is built; then, the output features of each residual unit in the residual network model are further spliced and fused to finally obtain an interference recognition model based on feature fusion network. Step 4: Obtain multi-semantic fusion features, perform classification, and calculate the recognition accuracy. Step 2 is implemented as follows: 2-1. By combining satellite jamming signal recognition with deep learning, a method is proposed to reconstruct high-dimensional data images from one-dimensional jamming signals. First, the received signal is sampled, and the sampled one-dimensional time-series signals of the I and Q channels are represented as 1×MN data matrix blocks. Then, the data matrix blocks are spliced and expanded to extend the dataset of the network input signal, achieving data augmentation. Finally, matrix transformation and splicing are performed on the data matrix blocks of the I and Q channels to obtain high-dimensional data as a two-dimensional image input to the network model. The specific process of signal image reconstruction is as follows: The received signal is sampled, and the resulting I and Q data signals are represented as follows: Among them, f s Where M is the sampling frequency, M represents the number of symbols, and N is the number of sampling points. The time-domain signal obtained from formulas (2) and (3) is used to cut and transform the received signal according to the symbol length to obtain a data matrix block of size 1×MN. Therefore, the data matrix block obtained by performing preliminary image reconstruction on the sampled data is represented as: S mod,I,1 =[S I (1),S I (2),S I (3),…,S I (MN)] 1×MN (4)S mod,Q,1 =[S Q (1),S Q (2),S Q (3),…,S Q (MN)] 1×MN (5) To provide the network model with as many extractable signal features as possible, the data matrix blocks obtained from formulas (4) and (5) are further spliced and expanded accordingly, filling the data matrix blocks D times to obtain new data blocks; the filling process is represented as S mod,I =[S mod,I,1 ,S mod,I,2 ,…,S mod,I,16 ] 1×DMN (6)S mod,Q =[S mod,Q,1 ,S mod,Q,2 ,…,S mod,Q,16 ] 1×DMN (7) To make the constructed two-dimensional image better reflect the time-frequency characteristics of the interference signal, matrix transformation and splicing are performed on the two-channel extended data blocks obtained by formulas (6) and (7) to obtain a two-dimensional image of size DN×2M. The two-dimensional image is represented as follows: 2-2. In the process of image reconstruction, the signal is padded and transformed to enhance the dataset of the signal to be identified; Step 3 is implemented as follows: 3-1. A nonlinear mapping residual network structure is used to extract signal features; the single-channel input image is transformed and resized, and then passed through convolutional layers and max pooling layers to obtain an input image that is more suitable for the residual network; The feature extraction module employs a 4-level residual network; each residual unit involves two convolutional layers, and each convolutional layer is accompanied by a ReLU activation function layer, with each level of the residual network skipping connections to form a deep network; 3-2. In order to obtain both low-level and high-level semantic features at the same time, a feature fusion process is proposed for the extracted semantic features at all levels of the signal. The feature fusion module includes four feature preprocessing layers, an average pooling layer, and a flattening layer. The feature fusion method adopted is concatenation fusion; the feature preprocessing unit preprocesses the output feature maps of each residual unit to change size and channel; the feature preprocessing unit mainly consists of a 1×1 convolutional layer, a max pooling layer, an instance normalization layer, and a ReLU activation layer; the feature preprocessing unit normalizes the semantic features of different sizes and different numbers of channels output by each residual network to obtain standardized features; Step 4 is implemented as follows: The standardized features of the output are dimensionally concatenated and fused, and then pooled to reduce dimensionality, to obtain the multi-semantic fusion features of the signal. The signal is then passed through a fully connected layer to classify the types of interference signals and to calculate the recognition accuracy.
2. The satellite suppression interference identification method based on a multi-semantic feature fusion network according to claim 1, characterized in that... Step 1 is implemented as follows: 1-1. The expression for J(t) for seven typical suppression interference signals is shown in the following table; f in the table c The carrier frequency of the interference signal. The initial phase is usually set to 0; a(t), a1(t), and a2(t) are the baseband data of the BPSK and QPSK interference signals; u(t) is the pulse signal of the time-domain pulse interference signal, τ is the pulse duration, and T is the time-domain pulse period; n(t) is random Gaussian white noise, K FM K is the slope of the frequency modulation characteristic curve of the noise frequency modulation interference; K1 is the sweep rate of the sweep frequency interference; the comb spectrum interference signal is synthesized from 5 noise frequency modulation signals, and K is the slope of the frequency modulation characteristic curve of the comb spectrum interference. c,i The carrier frequency of the comb spectrum interference signal is determined by the communication frequency band to be interfered with; 1-2. The time-domain model of the interference signal suppressed by the satellite to be identified is expressed as follows: S(t)=ρ1b(t)c(t)exp(j2πft)+ρ2J(t)+N(t) (1) In the above formula, ρ1 and ρ2 are the amplitudes of the satellite navigation signal and the jamming signal, respectively; b(t) is the baseband data of the satellite navigation signal; c(t) is the spread spectrum sequence data of the satellite navigation signal; f is the carrier frequency of the satellite navigation signal; J(t) is the jamming signal; and N(t) is the noise signal, which follows the rule N(0, σ). 2 Gaussian white noise, σ 2 This represents the noise variance.
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