Signal modulation recognition method based on dual-branch wavelet convolutional network
The signal modulation recognition method using a dual-branch wavelet convolutional network combined with GRU and CICM modules solves the problems of large parameters and low accuracy of deep learning models on edge devices, and achieves efficient signal modulation recognition.
Patent Information
- Application Number
- CN202511038812.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2025-07-28
- Publication Date
- 2025-10-03
- Estimated Expiration
- 2045-07-28
AI Technical Summary
Existing deep learning models have problems in signal modulation recognition, such as a huge number of parameters, cumbersome data preprocessing, and limited application in miniaturized devices. After being lightweighted, the accuracy is reduced, and it is difficult to run efficiently on edge devices with limited computing resources.
A signal modulation recognition method based on a dual-branch wavelet convolutional network is adopted, which combines wavelet convolution and GRU for multi-scale feature extraction. The CICM module is used to compress the parameters and optimize the balance between the accuracy and complexity of the model.
It significantly improves the feature extraction capability of signal modulation recognition and reduces model complexity. At the same time, it is suitable for edge devices with limited computing resources while ensuring high performance.
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Figure CN120547030B_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of electrical communications, relates to the classification of modulation modes of radio signals, and particularly to a signal modulation recognition method based on a dual-branch wavelet convolutional network. Background Art
[0002] Signal modulation recognition, a key step in communication signal processing, plays a vital role in connecting the detection and demodulation processes. It is widely used in tasks such as electronic countermeasures, spectrum monitoring, and communication network management. To date, scholars both domestically and internationally have achieved extensive research results on modulation signal recognition methods. Traditional modulation signal recognition algorithms are mostly based on likelihood theory and feature extraction, while the latest modulation signal recognition algorithms are mostly based on deep learning. Compared with traditional cumulant and machine learning-based algorithms, deep learning methods offer significant performance advantages and application feasibility.
[0003] To further improve the performance of deep learning models, existing technologies have proposed hybrid deep learning frameworks. By using various traditional features and raw IQ signal sequences as inputs to hybrid networks for feature extraction, they can achieve better results than single-input deep learning networks. Furthermore, Zheng et al. proposed a hybrid heterogeneous framework, DeepSIG, which converts IQ signals into image and graph representations and uses these three input forms, along with the raw IQ signals, as inputs to ResNet18, graph neural networks, and LSTM networks for feature extraction. This significantly improves performance, particularly in the case of few samples. Through its complex structure and multiple data input forms, the network can adapt to more complex environments. However, the large number of parameters and cumbersome data preprocessing limit its practical application. This is especially true given the trend toward miniaturization and intelligentization of modern devices, where the problems of complex networks are becoming more prominent.
[0004] To balance algorithm efficiency and accuracy, some researchers have designed lightweight network structures. However, as the model size decreases, the accuracy also decreases significantly. Therefore, the recognition rate of most lightweight structures still lags behind that of hybrid networks. Summary of the Invention
[0005] In response to the shortcomings of the existing technology, the present invention proposes a signal modulation recognition method based on a dual-branch wavelet convolutional network, which relies on wavelet convolution and GRU for multi-scale feature extraction and temporal dependency modeling, and further compresses the parameter amount through the CICM module to optimize the balance between the model parameter amount and accuracy.
[0006] The signal modulation recognition method based on a dual-branch wavelet convolutional network specifically includes the following steps:
[0007] Step 1: Collect the I (in-phase) and Q (quadrature) sequences of the radio modulation signal, perform energy normalization on them, and mark the modulation type as training samples and labels.
[0008] Step 2: Construct a feature extraction network to extract features from the training samples. This network consists of a shallow feature extraction block and two deep feature extraction blocks cascaded in sequence. A feature compression block (CICM) is placed between the feature extraction blocks. By evaluating feature importance, it divides features into key features and auxiliary features. Key features are roughly compressed, while auxiliary features are finely compressed, resulting in a more compact feature representation in terms of channels and space.
[0009] The shallow feature extraction block first performs a wavelet transform on the input training sample to extract frequency information. It then uses a large convolution kernel to extract features from the training sample and its frequency information, adding them together to produce large-scale features. It then uses a small convolution kernel to extract features from the input and frequency information separately, adding them together to produce small-scale features. Attention enhancement is performed on both large-scale and small-scale features, and these features are concatenated to produce shallow features.
[0010] The deep feature extraction block first divides the input features into X1, X2, and X3 along the channel dimension, and performs large-core multi-scale feature extraction and small-core multi-scale feature extraction respectively. After splicing, the residual connection is performed with the input features to obtain deep features. The large-core multi-scale feature extraction first performs a wavelet transform on X1 to extract frequency information, and uses a large convolution kernel to extract features of X1 and its frequency information and add them to obtain the primary features. The primary features are spliced with X2, and the above operation is repeated to obtain the secondary features. The secondary features are enhanced and then spliced with X3 to obtain large-core multi-scale features. The small-core multi-scale feature extraction replaces the convolution kernel in the large-core multi-scale feature extraction with a small convolution kernel to obtain a small-core multi-scale feature.
[0011] Step 3: Max pool the features output by the second deep feature extraction block and then send them to the gated recurrent unit (GRU) for temporal modeling. Finally, a fully connected layer and a softmax function are used to classify and map the temporal features output by the gated recurrent unit to obtain the predicted modulation mode of the training sample.
[0012] Step 4: Use the cross entropy function to calculate the network loss and train the network parameters. Input the I and Q sequences of the radio modulation signal into the trained network to identify the modulation mode.
[0013] The present invention has the following beneficial effects:
[0014] This paper utilizes a dual-branch wavelet convolutional network architecture, combining wavelet transforms with multiscale convolution operations to extract multiscale features of signals, significantly improving the network's feature extraction capabilities. Furthermore, the proposed CICM module employs a feature separation and compression strategy to reduce model complexity while retaining key feature information, further balancing parameter count and accuracy. Finally, the GRU is used to model temporal dependencies, improving the recognition accuracy of long-sequence signals. Compared to existing technologies, this network structure is relatively lightweight and suitable for edge devices with limited computing resources, meeting deployment requirements while ensuring high performance. BRIEF DESCRIPTION OF THE DRAWINGS
[0015] Figure 1 Schematic diagram of the DPWCN network structure constructed in the embodiment;
[0016] Figure 2 Schematic diagram of the dual-scale reconstruction wavelet convolution structure;
[0017] Figure 3 Schematic diagram of the ICA structure to improve the coordinate attention mechanism;
[0018] Figure 4 This is a structural diagram of the feature compression block CICM;
[0019] Figure 5 Schematic diagram of large kernel multi-scale feature extraction;
[0020] Figure 6 The results of the test using the RML2016.10a dataset in the examples are shown below.
[0021] Figure 7 These are the results of the test using the RML2016.10b dataset in the examples. DETAILED DESCRIPTION
[0022] The present invention will be further explained below with reference to the accompanying drawings;
[0023] like Figure 1 As shown in FIG, the signal modulation recognition method based on the dual-branch wavelet convolutional network specifically includes the following steps:
[0024] Step 1: This embodiment uses the public datasets RML2016.10a and RML2016.10b as training and testing data. The main information is shown in Table 1.
[0025] Table 1
[0026]
[0027] Each sample in the data set consists of 128 sampling points of I (in-phase) and Q (quadrature) sequences. The I and Q sequences are energy-normalized and then used as training samples.
[0028] Step 2: Construct a feature extraction network to extract features from the training samples. This includes a shallow feature extraction block and two deep feature extraction blocks cascaded in sequence. A feature compression block (CICM) is placed between the feature extraction blocks to obtain a more compact feature representation in terms of channels and space, as follows:
[0029] s2.1. The shallow feature extraction block first extracts large-scale and small-scale features through dual-scale reconstruction wavelet convolution, then performs attention enhancement operation, and obtains shallow features after splicing.
[0030] The dual-scale reconstruction wavelet convolution guides the corresponding branch to focus on macro features through large-scale feature reconstruction, and guides the corresponding branch to focus on detail features through small-scale feature reconstruction. Figure 2 As shown, the dual-scale reconstruction wavelet convolution first passes through the convolution kernel For input samples Each channel of the convolution is convolved with a step size of 2 to achieve a two-dimensional Haar wavelet transform and decompose the features containing high and low frequency information. , C, H and W are the number of channels, height and width of a single sample respectively, H F and W F are the height and width of feature F respectively:
[0031]
[0032] Among them, GConv represents group convolution and WT() represents wavelet transform.
[0033] Then use the shape 1xk l Large convolution kernel Perform depth convolution on feature F and use weight vector Perform adaptive adjustment, and finally implement the inverse wavelet transform IWT () through the transpose convolution TransposeConv with a group number of C, and output large-scale reconstruction features :
[0034]
[0035]
[0036] in, Denotes element-by-element multiplication. The two-dimensional wavelet transform captures local feature variations at different frequencies of the input X. Using the inverse wavelet transform, adaptive feature reconstruction is achieved, overcoming the limitations of traditional convolution kernels in terms of feature representation. Reconstructing large-scale information allows for the overall trend of changes between the I and Q signals.
[0037] In order to supplement the important information that may be lost in the reconstruction process, the input sample X is also given a shape of 1xk l Large convolution kernel , and through learnable weights and large-scale reconstruction features Perform adaptive addition to output large-scale features :
[0038]
[0039] Also using shape 1xk s Small convolution kernel Process the feature F and input sample X, extract the time series details, and output the small-scale reconstruction features , and based on learnable weights Reconstructing features at small scales Adaptively add the features of the input sample X and output the small-scale feature X s .
[0040] Considering that wavelet convolution leads to insufficient interaction between channel and spatial information due to the deep convolution characteristics, the coordinate attention mechanism CA is introduced to respectively l and small-scale features X s Feature enhancement is performed, and then after a convolution layer, batch normalization layer and ReLu activation function, the features of the two scales are spliced along the channel dimension to output shallow features.
[0041] In one embodiment, considering that the amount of information in the horizontal direction (i.e., the temporal direction) of radio modulation signals is significantly higher than that in the vertical direction, an improved coordinate attention mechanism ICA with an asymmetric structure is proposed to enhance the attention generation capability in the horizontal direction and reduce the number of parameters consumed in the attention generation in the vertical direction. l Take feature enhancement as an example, Figure 3 As shown in the figure, the improved coordinate attention mechanism ICA maintains the original global average pooling method in vertical encoding, and introduces a combined structure of 3x1 group convolution and average pooling in horizontal encoding to independently capture the feature correlation of each channel in the vertical dimension, avoiding direct pooling to blur the key information representation in the vertical dimension:
[0042]
[0043]
[0044]
[0045] in, Represents large-scale features X lThe c-th channel, the eigenvalue at (h, j), express The c-th channel, the eigenvalue at (i, w), and Represents horizontal features and vertical features In order to reduce the parameter scale and avoid overfitting of the network to the vertical direction attention with less information, and After splicing, input a single-channel uncompressed shared 1x1 convolution and Sigmoid function to generate horizontal and vertical attention weights and , for large-scale features X l Perform element-wise multiplication to obtain enhanced features :
[0046]
[0047] in, To enhance features The i-th row and j-th column element of the c-th channel of .
[0048] s2.2. In order to reduce computational redundancy, a feature compression block CICM is set between feature extraction blocks. By evaluating the importance of features, the features are divided into key features and auxiliary features, and rough and fine compression operations are performed on these two types of features respectively; finally, the two are fused to obtain a more compact feature representation in terms of channels and space. Figure 4 As shown, the feature compression block CICM includes a feature evaluation layer, a feature decoupling layer, a feature compression layer and a feature fusion layer.
[0049] The feature evaluation layer uses global average pooling and global maximum pooling to extract the average value A of each channel in the feature map. c and the maximum value M c , and form the mean eigenvector and the maximum eigenvector , where r is a real number used to adjust the number of output channels to reduce the amount of calculation. Then, the vectors M and A are mapped and concatenated separately through independent fully connected layers, and then input into a shared fully connected layer to perform secondary modeling of the overall channel relationship. Finally, the channel weight vector is obtained by scaling it to [0,1] through the Sigmoid gating function. .
[0050] The feature decoupling layer pre-sets a hard threshold T, when the weight channel of the cth channel When the mask is set to 1, otherwise it is set to 0. The important channel mask mask is formed in the order of channels to identify the more important channels. The important channel mask mask is negated to obtain the non-important channel mask nomask. The key sparse features X containing more important information can be separated by multiplying the mask and nomask with the feature map respectively. I and auxiliary sparse features X containing less important feature information NI .
[0051] The feature compression layer is used to compress the key sparse features X I and auxiliary sparse features X NI Adopt differentiated processing strategies to further optimize feature representation. For key sparse features X I , point convolution is used to compress the channel and obtain rough features , where C o is the channel dimension after compression. For the auxiliary sparse feature X NI First, a 2D grouped convolution with a kernel shape of 1x3 is used to extract local information. Grouped convolution focuses on a specific subspace to improve sensitivity to weak effective features and extract more detailed information. The ReLU activation function is then used to further sparse the redundant representation in the space and retain positive significant information. Finally, point convolution is used to perform channel compression to reduce channel feature redundancy and obtain detailed features. .
[0052] The feature fusion layer is used to combine the rough features O r and detail features O f Perform weighted fusion and output compressed features .
[0053] s2.3. In order to achieve fine-tuning of model performance and parameter quantity, the deep feature extraction block first transforms the input features along the channel dimension. Split into 、 、 .in, 、 Respectively represent the number of channels of X1 and X2, C o –C α –C β Indicates the number of channels of X3, α and β are the channel division ratios, 0<α, β<1, and α+β<1, Indicates taking the maximum value, Then, through parallel large-core multi-scale feature extraction and small-core multi-scale feature extraction, the concatenation is performed with the input feature O for residual connection to obtain the deep feature Y out .
[0054] like Figure 5 As shown, the large kernel multi-scale feature extraction first performs wavelet transform on X1 to extract frequency information, and then uses a large convolution kernel Extract and add the features of X1 and its frequency information, and extract the initial feature X from a relatively large scale ls :
[0055]
[0056]
[0057] Then the initial feature X ls Concatenate with X2 and concatenate the features X cat1 Perform wavelet transform to extract frequency information and use relatively small large convolution kernel To X cat1 and its frequency information to extract features and add them, extracting secondary features X from a relatively smaller scale ss :
[0058]
[0059]
[0060] Finally, enhance the secondary feature X ss The key features in F are expressed as e , F e Splice with X3, and obtain the large-core multi-scale feature O through the convolution layer, batch standard layer and ReLu activation function l .
[0061] Small kernel multi-scale feature extraction uses the convolution kernel in large kernel multi-scale feature extraction 、 Replace with 、 , and obtain the small kernel multi-scale feature O s .in, , .
[0062] Step 3: Max pool the features output by the second deep feature extraction block and then send them to the gated recurrent unit (GRU) for temporal modeling. Finally, a fully connected layer and a softmax function are used to classify and map the temporal features output by the gated recurrent unit to obtain the predicted modulation mode of the training sample.
[0063] Step 4: In this embodiment, set the network parameters according to Table 2:
[0064] Table 2
[0065]
[0066] We then set the training batch size to 128, the initial learning rate to 0.001, the maximum number of training epochs to 300, and the cross-entropy function to calculate the loss. We also used the Adam optimizer. We also employed a learning rate adjustment strategy: if the validation set loss did not decrease for five consecutive epochs, we halved the learning rate. If the validation set loss did not decrease for 10 consecutive epochs, we considered the model fully converged and terminated training.
[0067] In order to verify the contribution of the improved coordinate attention mechanism ICA and feature compression block CICM to the method, an ablation experiment was conducted. On the RML2016.10a dataset, the impact of different attention mechanisms on the results was compared. The channel compression ratio of the coordinate attention mechanism CA was set to 1. The results are shown in Table 3:
[0068] Table 3
[0069]
[0070] The results in Table 3 show that when no attention mechanism is used to enhance the reconstructed features (DPWCN-NoAttention), the model achieves the lowest accuracy, only 61.9%. However, using the full coordinate attention mechanism (DPWCN (CA)) improves the model's accuracy to 62.6%. Comparing the results of retaining only horizontal attention (DPWCN (CA-W)) and retaining only vertical attention (DPWCN (CA-H)), it is found that horizontal attention plays a dominant role. Therefore, when using the coordinate attention mechanism (ICA) (DPWCN), an asymmetric design strengthens horizontal attention modeling and simplifies the vertical encoding and terminal attention generation structure, achieving higher accuracy while reducing the number of parameters.
[0071] Define the compression ratio ρ as the number of input feature channels C of the feature compression block CICM in and the number of output feature channels C out On the RML2016.10a dataset, the effects of different compression ratios ρ and feature compression block CICM under hard threshold T on the results are compared. The results are shown in Table 4:
[0072] Table 4
[0073]
[0074] Table 4 shows that when ρ = 1 / 4, the network parameters are reduced by approximately 39% compared to DPWCN, while the floating-point operations are reduced by approximately 48%. Furthermore, the average accuracy is improved by approximately 3.1%. As ρ decreases to 1 / 8, the number of parameters and average accuracy also decrease accordingly. When ρ is further reduced to 1 / 16, the accuracy decreases by approximately 0.6% compared to ρ = 1 / 8, and the number of parameters is only 0.032M. However, while over-compressing features can keep the network parameter count low, it can also lead to excessive information loss, affecting network performance. Overall, the model with T = 0.3 and ρ = 1 / 4 achieves optimal performance and a low parameter count.
[0075] In order to demonstrate the effectiveness of the proposed model DPWCN-CICM, comparative experiments were conducted on the RML2016.10a and RML2016.10b datasets with CNN1, CNN2, LSTM-AP, CNN-LSTM, PET-CGDNN, MCLDNN, and MCMBNN. The results are shown in Tables 5 and 6, where F1 is calculated under a signal-to-noise ratio of 4 dB:
[0076] Table 5
[0077]
[0078] Table 6
[0079]
[0080] Figure 6 The results of testing each model using the RML2016.10a dataset under different signal-to-noise ratios are as follows: in the [0,18]dB signal-to-noise ratio range, the average recognition rates of MCMBNN and PET-CGDNN are 91.6% and 89.7% respectively, while DPWCN-CICM reaches 92.5%, which is about 0.9% higher than the superior MCMBNN; in the [-20,-10]dB signal-to-noise ratio range, DPWCN-CICM also has an advantage. In this range, the average recognition rates of MCMBNN and PET-CGDNN are 14.2% and 13.9% respectively, while DPWCN-CICM reaches 23.3%, which is about 9.1% higher than MCMBNN.
[0081] Figure 7The results of testing various models using the RML2016.10b dataset at different signal-to-noise ratios (SNRs) show that at high SNRs, DPWCN-CICM achieves comparable recognition rates to MCMBNN, which has a higher recognition rate. However, at low SNRs, particularly in the [-20, -12] dB SNR range, DPWCN-CICM significantly outperforms other models. While MCMBNN and PET-CGDNN achieve average recognition rates of 14.5% and 14.6%, respectively, DPWCN-CICM achieves 26.5%, approximately 12% higher than MCMBNN. These results demonstrate the potential of DPWCN-CICM for low-SNR signal recognition across various datasets. Combined with the data in Tables 5 and 6, DPWCN-CICM outperforms other compared models in terms of parameter count, computational complexity, and recognition performance, making it particularly suitable for applications with limited memory and computing power.
Claims
1. A signal modulation recognition method based on a dual-branch wavelet convolutional network is proposed. A feature extraction network is constructed to extract features from the I and Q sequences of radio modulation signals. The features are input into a classifier to identify the modulation mode of the radio modulation signals. The method is characterized by: The feature extraction network includes a shallow feature extraction block and two deep feature extraction blocks cascaded in sequence; A feature compression block CICM is set between the feature extraction blocks to compress the features to different degrees based on their importance, thereby obtaining a more compact feature representation in terms of channels and space; The feature compression block CICM includes a feature evaluation layer, a feature decoupling layer, a feature compression layer and a feature fusion layer; The feature evaluation layer is based on the average value A of each channel in the feature map c and the maximum value M c , the weight of the output channel ; The feature decoupling layer compares the weight of each channel in turn The relationship between the size of the preset hard threshold T is When , set the mask to 1, otherwise set it to 0, form the important channel mask mask in channel order, and negate it to get the non-important channel mask nomask; use mask and nomask respectively to extract the key feature X from the feature map I and auxiliary feature X NI ; The feature compression layer is used for the key sparse feature X I , directly perform channel compression to obtain the rough feature O r ; For the auxiliary sparse feature X NI , compressed by two-dimensional group convolution, ReLu activation function and point convolution in turn, to obtain the detail feature O f ; The feature fusion layer is used to combine the rough features O r and detail features O f Perform weighted fusion and output compressed feature O; The shallow feature extraction block first performs a wavelet transform on the input sequence, and then uses convolution kernels of different sizes to reconstruct feature extraction, and adds them to the results of the wavelet transform to obtain large-scale features and small-scale features, which are then spliced together to output shallow features; the deep feature extraction block first divides the input features along the channel dimension, and performs large-core multi-scale feature extraction and small-core multi-scale feature extraction respectively. After splicing, they are residually connected with the input features to obtain deep features, which are then sent to the gated recurrent unit for time series modeling and finally input into the classifier to identify the modulation mode of the input sequence.
2. The signal modulation identification method based on a dual-branch wavelet convolutional network according to claim 1, characterized in that: The feature compression block CICM divides features into key features and auxiliary features by evaluating their importance, and performs coarse and fine compression operations on these two types of features respectively.
3. The signal modulation identification method based on a dual-branch wavelet convolutional network according to claim 1, characterized in that: The shallow feature extraction block first decomposes the input sequence X into features F containing high- and low-frequency information through two-dimensional Haar wavelet transform; Use shape 1xk l The large convolution kernel performs depth convolution on the feature F and uses the weight vector ω l Perform adaptive adjustment and finally perform inverse wavelet transform to output large-scale reconstruction features ; Then directly use the shape 1xk for the input sample X l large convolution kernels and learnable weights and large-scale reconstruction features Perform adaptive addition and output large-scale features X l ; Use shape 1xk s The small convolution kernel extracts small-scale reconstruction features from the feature F , and based on learnable weights Reconstructing features at small scales Adaptively add the features of the input sample X and output the small-scale feature X s .
4. The signal modulation identification method based on a dual-branch wavelet convolutional network according to claim 3, characterized in that: Through the coordinate attention mechanism CA, the large-scale features X l and small-scale features X s Perform feature enhancement.
5. The signal modulation identification method based on a dual-branch wavelet convolutional network according to claim 3, characterized in that: Through the improved coordinate attention mechanism ICA of the asymmetric structure, the large-scale features X l and small-scale features X s Perform feature enhancement; the improved coordinate attention mechanism ICA maintains the original global average pooling method in vertical encoding, and introduces a combined structure of grouped convolution and average pooling in horizontal encoding to independently capture the feature correlation of the vertical dimension of each channel.
6. The signal modulation identification method based on a dual-branch wavelet convolutional network according to claim 3, characterized in that: Set k s =3, k l =3.
7. The signal modulation identification method based on a dual-branch wavelet convolutional network according to claim 1, characterized in that: The deep feature extraction block compresses the features output by the feature compression block CICM along the channel dimension Split into 、 、 Among them, C o , H, W represent the number of channels, height and width of the compressed feature O respectively; 、 Respectively represent the number of channels of X1 and X2, C o –C α –C β Indicates the number of channels of X3, α and β are the channel division ratios, 0<α, β<1, and α+β<1, max() means taking the maximum value, Indicates rounding down.
8. The signal modulation identification method based on a dual-branch wavelet convolutional network according to claim 7, characterized in that: The large kernel multi-scale feature extraction first performs wavelet transform on X1 to extract frequency information, and then uses the shape of 1xk l The large convolution kernel extracts and adds the features of X1 and its frequency information to obtain the initial feature X ls ; Then the initial feature X ls Joined with X2 to form feature X cat1 , then for feature X cat1 Perform wavelet transform to extract frequency information and use the shape The large convolution kernel of X cat1 And its frequency information is extracted and added to obtain the secondary feature X ss ; Finally, enhance the secondary feature X ss The key features in F are expressed as e , F e Splice with X3, and obtain the large-core multi-scale feature O through the convolution layer, batch standard layer and ReLu activation function l The small-core multi-scale feature extraction modifies the size of the convolution kernel in the large-core multi-scale feature extraction to 1xk s 、 ;in, 、 .
9. The signal modulation identification method based on a dual-branch wavelet convolutional network according to claim 1 or 8, characterized in that: The features output by the second deep feature extraction block are max-pooled and then fed into the gated recurrent unit for temporal modeling. Finally, they are fed into the classifier to identify the modulation mode of the input sequence.
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