Modulation recognition method and system based on stacked denoising encoder and edge device

Abstract

The present invention relates to a modulation recognition method and system based on a stacked denoising encoder and an edge device, and belongs to the field of artificial intelligence technology. It includes: generating a modulated signal based on GNU Radio; simulating the actual communication environment by adding different types of noise in the process of generating the modulated signal; performing channel simulation after adding different types of noise; data storage and output; performing modulation recognition based on a decision tree and a network; and refers to: signal denoising based on a stacked denoising encoder and signal modulation recognition based on multiple features such as instantaneous features, spectral features, high-order cumulants, phase, and constellation diagrams. The present invention enhances the robustness of feature extraction through a stacked denoising encoder, and combines the computing advantages of edge devices to achieve efficient and accurate modulation recognition.

Description

Technical Field

[0001] The invention relates to a modulation recognition method and system based on a stacked denoising encoder and an edge device, and belongs to the technical field of artificial intelligence. Background Art

[0002] In wireless communication systems, signal modulation recognition is one of the core links to achieve intelligent communication. With the continuous development of communication technology, especially the widespread application of the Internet of Things and edge computing, how to effectively identify the modulation mode of signals in complex wireless environments has become an important research topic. Existing modulation recognition methods mainly include traditional methods based on feature extraction and classification and emerging methods based on deep learning. These methods show certain advantages in specific application scenarios, but there are still many shortcomings and challenges in practical applications.

[0003] Traditional modulation recognition methods usually rely on manually designed feature extraction techniques. These methods extract features by analyzing the time domain, frequency domain or statistical characteristics of the signal, and combine them with machine learning algorithms such as support vector machine (SVM), k-nearest neighbor (KNN) or decision tree for classification. A notable feature of this type of method is that feature design often needs to rely on the domain knowledge of experts. Based on their understanding of signal characteristics, experts design feature sets that can describe the characteristics of different modulation modes, such as high-order statistics, cyclostationary characteristics, instantaneous amplitude and phase. However, these manually designed features are easily affected by noise, interference and multipath effects when facing complex wireless communication environments, resulting in a significant decrease in recognition accuracy. In addition, since these methods rely on specific signal features, when the signal morphology or environment changes, their generalization ability is poor and it is difficult to adapt to new scenarios.

[0004] With the rise of deep learning technology, more and more researchers have begun to try to use deep neural networks for modulation recognition. Deep learning methods can automatically learn features from raw signals, reducing reliance on artificial feature design. For example, convolutional neural networks (CNNs) are widely used in signal processing and image classification tasks. They capture local features of signals through a hierarchical structure and also show good performance in modulation recognition. Recurrent neural networks (RNNs) use their modeling capabilities for time series data to capture temporal correlations in signals. In addition, unsupervised learning models such as deep belief networks (DBNs) and autoencoders are also used to automatically extract features from large amounts of unlabeled data, and then classify and identify modulation methods.

[0005] However, although the application of deep learning methods in modulation recognition has shown great potential, these methods still face some challenges in practical applications. First, the training and inference of deep learning models usually require a lot of computing and storage resources, which makes it difficult to directly deploy these models on resource-constrained edge devices. With the popularity of IoT devices, many application scenarios require real-time signal processing on edge devices, and the application of existing deep learning models in these scenarios is limited. Secondly, deep learning models usually require a large amount of labeled data for training, which makes the data acquisition and labeling costly for modulation recognition tasks in wireless communications. In addition, the computational complexity of deep learning models is high. In application scenarios with high real-time requirements, the processing delay of existing methods may be difficult to meet actual needs.

[0006] The development and application of illegal electromagnetic signal monitoring and identification technology is to deal with fake base stations, black broadcasts, illegal radio stations; but also for illegal drones, espionage activities, electronic countermeasures, tactical radio stations, etc. However, electromagnetic information security testing and analysis technology is difficult, widely used, and complex scenarios. The core difficulty is illegal electromagnetic signal monitoring and classification technology. In addition, due to the development of information technology, illegal electromagnetic signal detection faces two major problems, namely:

[0007] 1. Rapid and real-time detection of large amounts of illegal electromagnetic signals;

[0008] 2. Accurate identification and analysis of complex illegal electromagnetic signals. Summary of the invention

[0009] In view of the shortcomings of the above existing methods, the present invention proposes a modulation recognition method and system based on stacked denoising autoencoder (SDAE) and edge devices. The core innovation of this method is to enhance the robustness of feature extraction through stacked denoising autoencoder, and combine the computing advantages of edge devices to achieve efficient and accurate modulation recognition.

[0010] In order to meet the needs of edge computing scenarios, the present invention is also specially optimized for edge devices. Edge devices, based on the system deployment of Huawei Atlas 200 DK, a localized developer kit for edge devices, usually have certain computing capabilities, but their resources are still relatively limited compared to traditional cloud servers. To this end, the present invention adopts a lightweight strategy in model design, and reduces the computational complexity and storage requirements of the model through technologies such as model pruning and quantization, so that it can run efficiently on edge devices. In addition, the application of edge devices also improves the real-time processing capabilities of the system, avoids data transmission delays, and enables the system to respond quickly in a dynamically changing wireless environment.

[0011] In summary, the modulation recognition method and system based on stacked denoising encoders and edge devices not only perform well in noisy environments, but also can run efficiently on resource-constrained edge devices to meet the real-time requirements in practical applications. This innovative method provides a solution with practical application value for intelligent modulation recognition in wireless communications and has broad application prospects.

[0012] To achieve the above object, the present invention provides the following technical solutions:

[0013] Modulation recognition method based on stacked denoising encoder and edge device, including:

[0014] Generate modulated signals based on GNU Radio; simulate the actual communication environment by adding different types of noise during the generation of modulated signals; perform channel simulation after adding different types of noise; store and output data;

[0015] Modulation recognition based on decision trees and networks; refers to: signal denoising based on stacked denoising encoders and signal modulation recognition based on the combination of multiple features such as instantaneous features, spectral features, high-order cumulants, phase and constellation diagrams.

[0016] Preferably, according to the present invention, generating a modulated signal based on GNU Radio means: using GNU Radio to generate a final real modulated signal from an input 01 sequence of an input signal; including:

[0017] First, input the 01 sequence to the vector source module. The input 01 sequence refers to the bit stream to be modulated. GNU Radio includes a vector source module, which converts the input 01 sequence into a vector format.

[0018] Subsequently, the bit stream to be modulated passes through a stream conversion module to a labeled stream; the stream conversion module to a labeled stream adds a length label to each frame of the bit stream;

[0019] Next, the data stream is input into the signal modulation module, which modulates the input bit stream according to the set number of symbols and sensitivity parameters to generate a modulated signal; at the same time, the modulated signal enters the signal demodulation module, and the original bit stream is restored through the corresponding parameter settings; the demodulated bit stream is bit-repacked and converted into floating-point representation;

[0020] Finally, the generated modulated signal is input into the visualization module to show the characteristics of the modulated signal.

[0021] Preferably, according to the present invention, data is generated by GNU Radio; comprising:

[0022] Determine the range of modulation mode and signal-to-noise ratio; define modulation transmitters of various modulation modes, including discrete modulation transmitters and continuous modulation transmitters.

[0023] Further preferably, the discrete modulation transmitter includes BPSK, QPSK, 8PSK, PAM4, QAM16, QAM64, GFSK, CPFSK and GMSK; the discrete modulation transmitter maps the input bit stream into corresponding modulation symbols, and then filters it through a pulse shaping filter to generate a modulated signal.

[0024] Further preferably, the continuous modulation transmitter includes FM, AM-DSB and AM-SSB; the continuous modulation transmitter is used to generate a continuous carrier signal.

[0025] Preferably, according to the present invention, different types of noise are added to simulate the actual communication environment; the different types of noise include Gaussian noise, impulse noise, Rayleigh noise, Laplace noise and uniform noise;

[0026] The generation process of Gaussian noise is as follows:

[0027] Compute the amplitude of the noise for a specified signal-to-noise ratio:

[0028] ;

[0029] in, represents the amplitude of the noise, is the average power of the signal, SNR is the signal-to-noise ratio; the noise signal follows a normal distribution, Gaussian noise It is expressed as:

[0030] ;

[0031] in, represents a normal distribution with a mean of 0 and a variance of 1, and j is an imaginary unit;

[0032] Impulse noise is expressed as follows:

[0033] ;

[0034] in, represents the impulse noise value of the i-th sample point, represents the amplitude of the pulse noise, p is the probability of the pulse occurring;

[0035] The formula for generating Rayleigh noise is:

[0036] ;

[0037] in, represents the Rayleigh noise value of the i-th sample point, is the noise amplitude, U and V are uniformly distributed random variables in the interval [0,1], is the natural logarithm function, and denote the cosine and sine functions respectively;

[0038] The generation formula of Laplace noise is:

[0039] ;

[0040] in, represents the Laplace noise value of the i-th sample point, is the noise amplitude, X is a uniformly distributed random variable in the interval [-0.5, 0.5], represents the sign function of X, is the natural logarithm function;

[0041] The formula for generating uniform noise is:

[0042] ;

[0043] in, represents the uniform noise value of the i-th sample point, is the noise amplitude, and U is a uniformly distributed random variable in the interval [0,1].

[0044] Preferably, according to the present invention, after adding different types of noise, channel simulation is performed; comprising:

[0045] After adding noise, choose whether to apply the channel model to further simulate the channel effect in wireless communication. The channel model uses the dynamic channel model in GNU Radio. After the signal is processed by the dynamic channel model, a sample vector of fixed length is generated by random sampling; each sample vector is normalized.

[0046] Preferably, according to the present invention, data storage and output include:

[0047] After generating and processing the signal data for all modulation modes and signal-to-noise ratio conditions, the data is saved in MAT file format.

[0048] Preferably, according to the present invention, modulation recognition is performed based on a decision tree and a network; it refers to: signal denoising based on a stacked denoising encoder; including:

[0049] The denoising process of the stacked denoising encoder includes:

[0050] Noise addition and input perturbation: For an original noise-free signal, it is expressed as , by adding noise Generate a noisy signal :

[0051] ;

[0052] in, Represents different types of noise;

[0053] The encoder is used to extract features and reduce dimension; the input noisy signal Mapped to a low-dimensional feature space; assuming the encoder consists of a set of weight matrices and the bias vector , the encoding process is expressed as:

[0054] ;

[0055] in, is the feature representation of the hidden layer, It is an activation function. The encoder extracts the deep features of the signal and maps the deep features to a low-dimensional space.

[0056] The signal is reconstructed by a decoder; the decoder includes a set of weight matrices and the bias vector , the reconstruction process is expressed as:

[0057]

[0058] in, is the signal reconstructed by the decoder, is the activation function of the decoder;

[0059] Loss function and model optimization; define the loss function to measure the reconstruction signal With the original signal The difference between; loss function is the mean square error, expressed as:

[0060] ;

[0061] Where N is the sample size, are the original signal and the reconstructed signal of the i-th sample respectively; by minimizing the loss function, the stacked denoising encoder gradually adjusts its parameters so that the reconstructed signal is closer to the original signal;

[0062] Multi-layer stacking and deep denoising; stack multiple layers of encoders and decoders to form a deep structure; the encoder of each layer takes the hidden representation of the previous layer as input and further extracts features, while the decoder reconstructs the signal layer by layer.

[0063] The final output is the denoising effect.

[0064] Preferably, according to the present invention, signal modulation identification is performed based on the combination of multiple features such as instantaneous features, spectral features, high-order cumulants, phase and constellation diagram; comprising:

[0065] (1) Determine whether the signal to be identified is noise: For the received discrete signal sequence , find the Fourier transform and calculate the eigenvalue according to the following formula ;

[0066] ;

[0067] in, U ( f ) represents the normalized first-order spectrum of the signal, var[·] represents the variance calculation, mean [·] indicates mean calculation.

[0068] like , then it is determined to be noise, otherwise, step (2) is executed; where, is the discrimination threshold;

[0069] (2) Determine whether the signal to be identified is quadrature offset phase shift keying (OQPSK):

[0070] 2a) Signal Seek its envelope , and Fourier transform its square to get , take the positive spectrum part , and remove the DC component;

[0071] 2b) Traversal , select , the relative prominence of the spectral line at frequency f is calculated according to the following formula ;

[0072] ;

[0073] Where |U( f )| represents the amplitude of the spectral line at frequency f. , , , They represent the maximum and second largest values ​​of the amplitude of the spectrum line in the left k neighborhood and the maximum and second largest values ​​of the amplitude of the spectrum line in the right k neighborhood of frequency f respectively;

[0074] 2c) Extract the maximum value , if mav> , then it is determined to be {OQPSK}, otherwise, go to Step 3; where, is the discrimination threshold, =2;

[0075] (3) The symbol rate of the signal to be identified is estimated to perform blind matching and sampling rate conversion. The output sequence is ;

[0076] (4) Determine whether the signal to be identified is of the M-order amplitude keying MASK category:

[0077] Signal Taking its Fourier transform we get , calculate the relative prominence S1 of the maximum value of the primary spectrum according to the following formula;

[0078] ;

[0079] In the above formula, U ( f ) represents the normalized signal first-order spectrum, and the numerator max(| U ( f )|) represents the maximum spectral line value;

[0080] If S1< , then it is determined to be {binary amplitude keying 2ASK, quaternary amplitude keying 4ASK, octal amplitude keying 8ASK}, and step (5) is executed; otherwise, step (6) is executed;

[0081] (5) M-order amplitude keying MASK intra-class recognition:

[0082] 5a) Signal Perform frequency offset estimation to obtain carrier frequency offset estimation value ;

[0083] 5b) According to Signal After frequency offset compensation, the output sequence is ,in, is a complex exponential signal used for compensation, whose frequency is equal to the estimated frequency deviation , is the sampling period;

[0084] 5c) Perform high-order accumulation on the output sequence of the previous step and Calculate and find its eigenvalue ;

[0085] like , then it is judged as {2ASK}; if , then it is determined as {4ASK}, otherwise, it is determined as {8ASK}, and the branch identification ends; among them, , is the discrimination threshold;

[0086] (6) Determine whether the signal to be identified is {binary phase shift keying BPSK, 8th order quadrature amplitude modulation 8QAM}: Calculate , and take Fourier transform to get ;like , then it is determined to be {BPSK, 8QAM} and step 7 is executed, otherwise step 8 is executed; wherein, is the discrimination threshold;

[0087] (7) {BPSK, 8QAM} Intra-subset Identification:

[0088] 7a) Signal Perform symbol synchronization to obtain an output sequence;

[0089] 7b) Calculate the eigenvalue of the output sequence of step 7a) according to the following formula :

[0090] ;

[0091] In the formula, It refers to the average value of the absolute value of the instantaneous amplitude normalized at the zero center; N refers to the total number of samples of the signal, which indicates the number of discrete sampling points contained in the signal on the time axis; It refers to the operation of summing all sampling points i, which means accumulating all the absolute values ​​of the instantaneous amplitudes of the signal; represents the instantaneous amplitude after zero-center normalization of the i-th sampling point, It represents the absolute value of this value; is the instantaneous amplitude after zero-centered normalization;

[0092] like , then it is determined to be {BPSK}, otherwise it is determined to be {8QAM}, and the branch identification ends; among them, is the discrimination threshold;

[0093] (8) Determine whether the signal to be identified belongs to the subset of {quadrature phase shift keying QPSK, 8-phase shift keying 8PSK, 16-phase shift keying 16PSK, π / 4-offset quadrature phase shift keying π / 4DQPSK} or {16-order quadrature amplitude modulation 16QAM, 32-order quadrature amplitude modulation 32QAM, 64-order quadrature amplitude modulation 64QAM};

[0094] Signal Perform symbol synchronization to restore the baseband modulation symbol sequence, calculate the high-order cumulative quantities C63 and C42 of the sequence, and find the eigenvalue H2=|C63|2 / |C42|3; if H2>th7, the signal belongs to the {QPSK, 8PSK, 16PSK, π / 4DQPSK} subset, and execute step (8); otherwise, the signal belongs to the {16QAM, 32QAM, 64QAM} subset, and execute step (9); where, is the discrimination threshold;

[0095] (9) Identification within the {QPSK, 8PSK, 16PSK, π / 4DQPSK} subset:

[0096] 9a) Calculation , and the Fourier transform is obtained ,like , then the signal belongs to the {QPSK, π / 4DQPSK} subset, and execute step 8b); otherwise, it belongs to the {8PSK, 16PSK} subset, and execute step 8c); wherein, is the discrimination threshold;

[0097] 9b) Traverse the spectrum obtained in step 9a) and calculate the number of spectrum lines with normalized amplitude greater than 0.5 ,like , then it is determined to be {π / 4DQPSK}, otherwise, it is determined to be {QPSK}, and the branch identification ends; among them, is the discrimination threshold;

[0098] 9c) Calculation , and find its Fourier transform ,like , then it is determined as {8PSK}, otherwise, it is determined as {16PSK}, and the branch identification ends, where, is the discrimination threshold;

[0099] (10) {16QAM, 32QAM, 64QAM} subset identification:

[0100] 10a) Signal Carrier synchronization and symbol synchronization are performed to obtain an output sequence;

[0101] 10b) Perform a high-order accumulation on the output sequence of the previous step C 80 and C 42 Calculate and find its eigenvalue H 3=| C 80 | / | C 42 | 2 ,like , then it is determined to be {16QAM, 64QAM}, and step 10c) is executed; otherwise, it is determined to be {32QAM}; wherein, is the discrimination threshold;

[0102] 10c) Calculate the average value of the recursive zero-centered normalized instantaneous amplitude absolute value for the output sequence of step 10a) according to the following formula: M 2:

[0103] ;

[0104] In the above formula, ;

[0105] like M 2> th 12 , then it is determined to be {16QAM}, otherwise it is determined to be {64QAM}, and the branch identification ends; wherein, is the discrimination threshold.

[0106] Further preferably, in step 5a), the signal Carrier frequency offset estimation is performed to obtain the carrier frequency offset estimation value ;include:

[0107] The signal is transmitted from the transmitter to the receiver through the wireless channel, and the received signal sequence r(t) is transformed to its fourth power, and we get {y(t)}={r 4 (t)}; let {y in (t)}={y(t)}, and we can get {y 1 (t)};

[0108] The output sequence of the previous step is used as the input of the next autocorrelation operation. The autocorrelation operation is repeated m times. The output of the mth autocorrelation operation is the final output, that is, {y out (t)}={y m (t)};

[0109] Traverse {y out (t)}, search for the position of the maximum normalized amplitude and obtain ∆f coa ;

[0110] Using CZT to measure ∆f coa Nearby narrow band [(1-ε) ∆f coa , (1+ε) ∆f coa ] performs frequency selection analysis, including: transforming the input signal x(n) using the CZT algorithm, and the obtained spectrum data corresponds to the signal components within the selected frequency range;

[0111] Select a value greater than 0 and much less than 1 to get the frequency offset estimate .

[0112] More preferably, is 0.5, is 2, is 2, is 150, is 97, is 2, is 0.35, is 15, is 2, is 10, is 2, is 1.3, is 0.6.

[0113] Modulation recognition system based on stacked denoising encoders and edge devices, including:

[0114] The modulation signal generation unit is configured to: generate a modulation signal based on GNU Radio; during the generation of the modulation signal, simulate the actual communication environment by adding different types of noise; perform channel simulation after adding different types of noise; and store and output data;

[0115] The signal denoising and identification unit is configured to: perform signal modulation identification based on stacked denoising encoder signal denoising and based on multiple features such as instantaneous features, spectral features, high-order cumulants, phase and constellation diagram.

[0116] Compared with the prior art, the present invention has the following advantages:

[0117] 1. Data generation: highly customized modulation signal production based on GNU Radio;

[0118] The present invention utilizes GNU Radio, a powerful open source software development toolkit, to generate modulated signals. GNU Radio provides a wide range of signal processing modules, enabling users to flexibly design and implement various wireless communication systems. It supports different modulation modes, filter design, and spectrum analysis, and users can combine and customize these modules according to specific needs. In addition, the open source nature of GNU Radio allows users to modify and expand existing modules or develop new modules as needed, greatly increasing the flexibility and scalability of system design. By cooperating with hardware front-ends such as USRP, RTL-SDR, etc., GNU Radio can run on actual radio hardware, thereby realizing real-time acquisition, processing, and transmission of real signals.

[0119] 2. Data processing: efficient signal denoising and feature extraction using stacked denoising encoders;

[0120] In the data processing stage, the present invention effectively denoises the collected noisy signals through a stacked denoising encoder (SDAE). This method adds noise during the training process so that the encoder learns the ability to denoise the input data, thereby improving the robustness of the model in a high-noise environment. SDAE extracts the deep features of the signal layer by layer through a multi-layer neural network structure, and uses a denoising mechanism to enhance the robustness of the features, so that high recognition performance can still be maintained in a high-noise environment. This deep learning method reduces the reliance on traditional manual feature design, automatically learns complex features from the original signal, and improves the accuracy and efficiency of data processing.

[0121] 3. Data recognition: complex modulation recognition based on multiple features;

[0122] In the data recognition stage, this system combines the signal denoising results based on SDAE and the multi-feature joint analysis method to realize modulation recognition in complex wireless environments. This method comprehensively utilizes multiple features such as instantaneous features, spectral features, high-order cumulants, phase and constellation diagrams for joint analysis, which makes up for the shortcomings of a single feature in a complex environment. For example, instantaneous features can reflect the changes in the signal in the time domain, spectral features reveal the distribution of the signal in the frequency domain, and high-order cumulants can be used to capture non-Gaussian and nonlinear characteristics. This fusion of multiple features enables this system to have stronger discrimination ability and higher recognition accuracy when identifying complex modulation methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0123] Figure 1 Generate data flow diagrams for modulated signals based on GNU Radio;

[0124] Figure 2 A time domain waveform diagram of the data generated for the modulated signal based on GNU Radio;

[0125] Figure 3 A diagram of the frequency domain waveform of the modulated signal generated by GNU Radio;

[0126] Figure 4 A diagram showing the constellation diagram for generating data for a modulated signal based on GNU Radio.

[0127] Figure 5 Schematic diagram of the stacked denoising encoder structure;

[0128] Figure 6 Schematic diagram of the modulation recognition rate curve of the joint recognition algorithm. DETAILED DESCRIPTION

[0129] In order to have a clearer understanding of the technical features of the present invention, the specific implementation methods of the present invention are described below in conjunction with the accompanying drawings. The technical solutions in the present invention are clearly and completely described. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0130] To facilitate understanding of the present invention, the present invention will be described more comprehensively below with reference to the relevant drawings. Several embodiments of the present invention are given. However, the present invention can be implemented in many different forms and is not limited to the embodiments described herein. On the contrary, the purpose of providing these embodiments is to make the disclosure of the present invention more thorough and comprehensive.

[0131] Example 1

[0132] Modulation recognition method based on stacked denoising encoder and edge device, including:

[0133] Generate modulated signals based on GNU Radio; simulate the actual communication environment by adding different types of noise during the generation of modulated signals; perform channel simulation after adding different types of noise; store and output data;

[0134] Modulation recognition based on decision trees and networks; refers to: signal denoising based on stacked denoising encoders and signal modulation recognition based on the combination of multiple features such as instantaneous features, spectral features, high-order cumulants, phase and constellation diagrams.

[0135] Example 2

[0136] The modulation recognition method based on the stacked denoising encoder and the edge device according to Embodiment 1 is different in that:

[0137] Generate a modulated signal based on GNU Radio; means: use GNU Radio to generate the final real modulated signal from the input 01 sequence; such as Figure 1 As shown, including:

[0138] First, input the 01 sequence to the Vector Source module. The input 01 sequence refers to the bit stream to be modulated. GNU Radio includes a Vector Source module, which converts the input 01 sequence (i.e., bit stream) into a vector format suitable for subsequent processing.

[0139] Subsequently, the bit stream to be modulated is converted to a tagged stream module (Stream to TaggedStream); the tagged stream module adds a length tag to each frame of the bit stream; this helps the subsequent modules to correctly identify the boundaries of the data frame and ensure that the data packets can be effectively identified and processed during the transmission and reception process, so that the data packets can be correctly identified and processed in the subsequent processing.

[0140] Next, the data stream is input into the signal modulation module, which modulates the input bit stream according to the set number of symbols and sensitivity parameters to generate a modulated signal. At the same time, the modulated signal enters the signal demodulation module, which restores the original bit stream through the corresponding parameter settings. This step ensures the correctness of the modulated signal and provides a basis for further analysis and visualization. The demodulated bit stream is repacked and converted to floating point representation through a series of processing modules to be compatible with various GUI visualization tools.

[0141] Finally, generate Figure 2 , Figure 3 and Figure 4 The modulated signal shown is input into visualization modules such as time domain diagram, spectrum diagram and constellation diagram to display the characteristics of the modulated signal. These graphical tools can display the spectrum distribution, time waveform and constellation point distribution of the signal in real time, thus providing users with an intuitive means of analyzing the modulated signal.

[0142] At the same time, using the function interface of GNU Radio in Python, a more convenient signal generation method can be designed for users, and a series of noises can be added to the modulated signal to enrich the data set. The present invention uses the GNU Radio framework to generate modulated signal data, and adds different noises to the signal to simulate the actual communication environment. The generated data set can be used to train and test the modulation recognition algorithm in wireless communication. The data generation process and the method of adding noise are introduced in detail below.

[0143] Generate data via GNU Radio; including:

[0144] Determine the modulation mode and the range of signal-to-noise ratio (SNR); the present invention sets different modulation modes and SNR ranges to generate modulated signal data under various conditions; specifically, the code uses a modulation transmitter, a modulation signal transmitter framework based on GNU Radio, which can generate a variety of discrete and continuous modulation signals. It realizes the signal generation and processing of different modulation modes by defining a series of transmitter classes and combining the signal processing modules in GNU Radio. Each transmitter class represents a specific modulation mode by inheriting the hier_block2 class of GNU Radio. The hier_block2 class is the basic building block for creating complex signal processing links in GNU Radio. It can be used to easily combine different signal processing modules to build complex signal processing systems. Define modulation transmitters for multiple modulation modes, including discrete modulation transmitters and continuous modulation transmitters.

[0145] Discrete modulation transmitters include BPSK, QPSK, 8PSK, PAM4, QAM16, QAM64, GFSK, CPFSK, and GMSK; discrete modulation transmitters map the input bit stream to the corresponding modulation symbols, and then filter them through a pulse shaping filter to generate a modulated signal. For example, the transmitter_bpsk class implements BPSK (Binary Phase Shift Keying) modulation, which achieves modulation by mapping the input bit stream to a signal with two phases. Other modulation methods such as QPSK, 8PSK, QAM, etc. use more phase or amplitude combinations on this basis to achieve higher-order modulation.

[0146] Continuous modulation transmitters include FM (frequency modulation), AM-DSB (double-sideband amplitude modulation), and AM-SSB (single-sideband amplitude modulation); continuous modulation transmitters are used to generate a continuous carrier signal. Unlike discrete modulation, the amplitude or frequency of a continuously modulated signal changes continuously over time. For example, the transmitter_fm class implements wideband FM modulation by calling the analog.wfm_tx module of GNU Radio. The transmitter_am class implements double-sideband amplitude modulation by multiplying the input signal with the carrier and then passing the result to the modulator. The transmitter_amssb class implements single-sideband amplitude modulation by generating a single-sideband signal through a Hilbert transform filter.

[0147] OFDM transmitters such as OFDM-BPSK+BPSK, the OFDM frame header uses BPSK modulation, and the OFDM frame payload also uses BPSK modulation; OFDM-BPSK+QPSK, the OFDM frame header uses BPSK modulation, and the subcarriers of the OFDM payload use QPSK modulation; OFDM-BPSK+8PSK, the OFDM frame header uses BPSK modulation, and the subcarriers of the OFDM payload use 8PSK modulation; OFDM-QPSK+BPSK, the OFDM frame header uses QPSK modulation, and the subcarriers of the OFDM payload use BPSK modulation; OFDM-QPSK+QPSK, the OFDM frame header uses QPSK modulation, and the subcarriers of the OFDM payload also use QPSK modulation; OFDM-QPSK+8PSK, the OFDM frame header uses QPSK modulation, and the subcarriers of the OFDM payload use 8PSK modulation. OFDM is a multi-carrier modulation technology that increases the data transmission rate by sending multiple symbols simultaneously on different carriers. These classes internally use the GNU Radio digital.ofdm_tx module to implement OFDM modulation and configure the generation of OFDM signals by defining parameters such as synchronization words, carrier mapping, and convolutional coding.

[0148] The framework can not only easily expand new modulation methods, but also be integrated with actual hardware systems to achieve real-time wireless signal processing, which is of great significance for studying wireless communication systems and developing modulation recognition algorithms.

[0149] In wireless communication systems, it is very important to generate and study the performance of modulated signals under different channel conditions. This paper introduces how to use the GNU Radio framework to generate modulated signals and simulate the actual communication environment by adding different types of noise (including Gaussian noise, impulse noise, Rayleigh noise, Laplace noise and uniform noise). These noise sources are used to evaluate the robustness of modulation recognition algorithms in different environments. The following details the methods of adding various noises in the process of signal data generation.

[0150] Simulate the actual communication environment by adding different types of noise; different types of noise include Gaussian noise, impulse noise, Rayleigh noise, Laplace noise and uniform noise;

[0151] ;

[0152] in, represents the average power of the signal, N is the number of signal samples, and x[i] is the amplitude value of the i-th signal sample.

[0153] In order to simulate the real communication environment, the present invention adds various types of noise to the generated modulated signal, including Gaussian noise, impulse noise, Rayleigh noise, Laplace noise and uniform noise. Each type of noise is added as follows:

[0154] The generation process of Gaussian noise is as follows:

[0155] Gaussian noise is the most common type of noise and is widely used to simulate thermal noise or background noise in communication systems.

[0156] Compute the amplitude of the noise for a specified signal-to-noise ratio:

[0157] ;

[0158] in, represents the amplitude of the noise, is the average power of the signal, SNR is the signal-to-noise ratio (in decibels); the noise signal follows a normal distribution, Gaussian noise It is expressed as:

[0159] ;

[0160] in, represents a normal distribution with a mean of 0 and a variance of 1, j is an imaginary unit; the real and imaginary parts of the noise are both independently normally distributed, and after being multiplied by the noise amplitude coefficient, they are added to the signal to form composite noise.

[0161] Impulse noise is expressed as follows:

[0162] Impulse noise may be caused by brief interference or switching operations of electronic equipment in communication systems. It is characterized by large amplitude and short duration.

[0163] ;

[0164] in, represents the impulse noise value of the i-th sample point, Indicates the amplitude of the impulse noise, usually large, p is the probability of the pulse occurring; usually small (such as 0.01 to 0.1). This noise is characterized by occasional high-amplitude interference.

[0165] The formula for generating Rayleigh noise is:

[0166] Rayleigh noise is often used to simulate signal fading in a multipath fading environment, and its amplitude follows the Rayleigh distribution.

[0167]

[0168] in, represents the Rayleigh noise value of the i-th sample point, is the noise amplitude, U and V are uniformly distributed random variables in the interval [0,1], is the natural logarithm function, and Represent the cosine and sine functions respectively; the formula uses the inverse transform sampling method to generate Rayleigh distributed noise signals.

[0169] The generation formula of Laplace noise is:

[0170] Laplace noise has a peaky nature and is often used to simulate outliers that may occur in image processing.

[0171] ;

[0172] in, represents the Laplace noise value of the i-th sample point, is the noise amplitude, X is a uniformly distributed random variable in the interval [-0.5, 0.5], represents the sign function of X, is a natural logarithmic function; the noise is generated in such a way that it has the characteristic of producing sharp peaks around the original signal.

[0173] The generation formula of uniform noise is:

[0174] The amplitude of uniform noise is evenly distributed within a certain range and is often used to simulate quantization errors.

[0175]

[0176] in, represents the uniform noise value of the i-th sample point, is the noise amplitude, and U is a uniformly distributed random variable on the interval [0,1]. The characteristic of this noise is that its values ​​are uniformly distributed within a given range.

[0177] After adding different types of noise, channel simulation is performed; including:

[0178] After adding noise, choose whether to apply the channel model to further simulate the channel effect in wireless communication. The channel model uses the dynamic channel model (channels.dynamic_channel_model) in GNU Radio, which can simulate multipath effects, Rayleigh fading, Doppler shift and other phenomena in actual communication. Specifically, set the Doppler shift (Doppler frequency shift), delays(delays) and relative amplitudes(magnitudes) and other parameters are used to more realistically simulate the propagation characteristics of signals in complex wireless channels. After the signal is processed by the dynamic channel model, a sample vector with a fixed length is generated by random sampling; each sample vector is normalized to ensure the energy consistency of the signal. The formula for normalization is:

[0179] ;

[0180] Among them, x represents the extracted signal vector, xs is the extracted signal vector, and N is the length of the vector, that is, 1000. The normalization process ensures that the total energy of each vector is consistent by dividing by the total energy of the vector.

[0181] Data storage and output; including:

[0182] After generating and processing the signal data for all modulation modes and signal-to-noise ratio conditions, the data is saved in MAT file format. This format is widely used in the MATLAB environment to facilitate further data analysis and processing. The generated files are named according to the modulation mode and signal-to-noise ratio, for example, "QAM16_SNR_10.mat" represents the signal data under the condition of QAM16 modulation mode and signal-to-noise ratio of 10dB.

[0183] The data includes 18 signal types, with a signal-to-noise ratio range of -20dB to 20dB, and the length of each combined signal vector is 1000.

[0184] Modulation recognition based on decision trees and networks; refers to: signal denoising based on stacked denoising encoders; includes:

[0185] The modulation recognition method of the present invention has significant advantages over traditional methods, especially in the case of complex wireless environments and the coexistence of multiple modulation modes, it shows higher robustness and accuracy. First, through the signal denoising technology based on the stacked denoising encoder, the present invention can effectively eliminate the interference of noise on the signal and improve the accuracy of feature extraction. The stacked denoising encoder extracts the deep features of the signal layer by layer through a multi-layer neural network structure, and uses the denoising mechanism to enhance the robustness of the features, so that it can still maintain a high recognition performance in a high noise environment. Secondly, the present invention combines multiple features such as instantaneous features, spectral features, high-order cumulants, phase and constellation diagrams for joint analysis. This multi-feature joint method can more comprehensively capture the different dimensional characteristics of the signal and make up for the shortcomings of a single feature in a complex environment. For example, the instantaneous feature can reflect the change of the signal in the time domain, the spectral feature reveals the distribution of the signal in the frequency domain, and the high-order cumulant can be used to capture non-Gaussian and nonlinear characteristics. This fusion of multiple features enables the present invention to have stronger discrimination ability and higher recognition accuracy when identifying complex modulation modes. Finally, combined with the recognition algorithm based on the network and decision tree, the present invention also performs well in terms of computational efficiency and real-time performance. The decision tree algorithm is widely used because of its easy implementation and low computational overhead, and can quickly process large-scale data. After combining with the network model, the present invention can further improve the accuracy and generalization ability of recognition, especially when facing unknown signals, it can make accurate judgments more effectively. These advantages make the present invention have significant competitiveness and application prospects in the field of modulation recognition. The recognition process is described in detail below:

[0186] The denoising process of the stacked denoising encoder includes:

[0187] Stacked Denoising Autoencoder (SDAE) is a deep learning-based model that aims to recover the original noise-free signal from noisy input data. It introduces noise perturbations to train the encoder and decoder, giving the model the ability to denoise, thereby enhancing its robustness to noise. The following is a detailed introduction to the denoising process of SDAE when processing noisy signals.

[0188] Noise addition and input perturbation: For an original noise-free signal, it is expressed as , by adding noise Generate a noisy signal :

[0189] ;

[0190] in, Represent different types of noise; such as Gaussian noise, impulse noise, Rayleigh noise, Laplace noise or uniform noise. This step will simulate the noise interference in the real environment and provide more challenging training samples for the model.

[0191] The encoder is used to extract features and reduce dimensionality; in SDAE, the encoder is responsible for converting the input noisy signal Mapped to a low-dimensional feature space; assuming the encoder consists of a set of weight matrices and the bias vector , the encoding process is expressed as:

[0192] ;

[0193] in, is the feature representation of the hidden layer, is the activation function. Common activation functions include ReLU (linear rectification function) and Sigmoid (logistic function). Through this process, the encoder extracts the deep features of the signal and maps the deep features to a low-dimensional space to retain the main information of the signal.

[0194] The decoder is used to reconstruct the signal; next, the decoder is responsible for extracting the hidden layer features Reconstruct the original noise-free signal as close as possible The decoder consists of a set of weight matrices and the bias vector , the reconstruction process is expressed as:

[0195] ;

[0196] in, is the signal reconstructed by the decoder, is the activation function of the decoder (usually the same as the encoder); the reconstructed signal Try to restore the original signal structure and characteristics.

[0197] Loss function and model optimization; In order to enable SDAE to effectively denoise, a loss function is defined to measure the reconstructed signal With the original signal The difference between; loss function is the mean square error (MSE), expressed as:

[0198] ;

[0199] Where N is the sample size, are the original signal and the reconstructed signal of the i-th sample respectively; by minimizing the loss function, the stacked denoising encoder gradually adjusts its parameters so that the reconstructed signal is closer to the original signal;

[0200] Multi-layer stacking and deep denoising: The key feature of SDAE is the stacking of multiple denoising encoders, which enables the model to extract more abstract and higher-level features layer by layer. In practical applications, multiple layers of encoders and decoders are stacked to form a deep structure; the encoder of each layer takes the hidden representation of the previous layer as input and further extracts features, while the decoder reconstructs the signal layer by layer.

[0201] like Figure 5 As shown, with three layers of encoder and decoder, the entire denoising process can be described as follows:

[0202] Layer 1 encoder:

[0203] ;

[0204] Layer 2 encoder:

[0205] ;

[0206] Layer 3 encoder:

[0207] ;

[0208] The signal is then reconstructed layer by layer through the decoder: Layer 1 decoder:

[0209] ;

[0210] Layer 2 decoder:

[0211] ;

[0212] Layer 3 Decoder:

[0213] ;

[0214] in, is the weight matrix of the decoder, is the bias vector, is the activation function of the decoder.

[0215] Finally, the denoising effect is output. Through the above multi-layer denoising process, SDAE can eliminate the noise components in the input signal layer by layer, and finally output a reconstruction result close to the original noise-free signal. When faced with complex noise environments in practical applications, the trained SDAE can effectively restore the main features and structures of the signal, thereby greatly improving the accuracy of subsequent modulation recognition.

[0216] In summary, the stacked denoising encoder achieves effective denoising of noisy signals by introducing noise disturbance, feature extraction, signal reconstruction and multi-layer stacking. It can not only eliminate various types of noise, but also maintain high signal recovery quality in complex wireless environments, providing high-quality input data for tasks such as modulation recognition.

[0217] The detailed parameters of the stacked denoising encoder are shown in Table 1.

[0218] Table 1 Detailed parameter table of stacked denoising encoder;

[0219]

[0220] The training, verification and testing process of the stacked denoising encoder is as follows:

[0221] Input: training dataset , where each sample is a noisy signal;

[0222] Output: reconstructed signal Each reconstruction sample is the signal after denoising;

[0223] Step 1: Dataset Division

[0224] The dataset Divided into training set, validation set and test set; the training set is used for model training, the validation set is used to monitor the performance of the model, and the test set is used to evaluate the final effect of the model.

[0225] Step 2: Set training parameters

[0226] The stacked denoising encoder consists of three layers of encoders and three layers of decoders; set the training parameters:

[0227] Batch size: 256

[0228] Number of epochs: 50

[0229] Optimizer: Adam (Adaptive Moment Estimation), because it performs well in handling large-scale data and non-stationary targets.

[0230] Step 3: Set the learning rate and early stopping strategy for training

[0231] Initial learning rate: 0.001

[0232] Learning rate update strategy: When the loss function (val_loss) of the validation set does not improve in 5 consecutive epochs, the learning rate is reduced to 0.1 times the original value. The minimum learning rate is set to 10 -6 .

[0233] Early stopping strategy: If the loss function of the validation set does not decrease by 0.001 within 20 epochs, the training is terminated early.

[0234] Step 4: Initialize model parameters;

[0235] Randomly initialize the weights and biases of all layers in the SDAE network. Specifically, use a uniform distribution or a Gaussian distribution to initialize the weights of the model to ensure that the initial values ​​of the model parameters are diverse.

[0236] Step 5: Training process

[0237] Entering the training loop, the following steps are performed for each epoch:

[0238] Step 5.1: Input training data;

[0239] Input the training set data into the model. Each training sample is a signal containing noise.

[0240] Step 5.2: Encoder output features:

[0241] The input noisy signal is processed by the three-layer encoder of SDAE. Encode layer by layer to extract low-dimensional feature representation .

[0242] The encoding process is as follows:

[0243] Layer 1 encoding: , the output shape is (None, 2, 512).

[0244] Layer 2 encoding: , the output shape is (None, 2, 256).

[0245] Layer 3 encoding: , the output shape is (None, 2, 128).

[0246] Step 5.3: The decoder reconstructs the data;

[0247] Use decoder to extract features from the encoded Reconstruct the signal .

[0248] The decoding process is as follows:

[0249] Layer 1 decoding: , the output shape is (None, 2, 256).

[0250] Layer 2 decoding: , the output shape is (None, 2, 512).

[0251] Layer 3 decoding: , the output shape is (None, 2, 1000).

[0252] Step 5.4: Calculate the loss function;

[0253] Calculate the loss function for the training set And the loss function of the validation set The loss function usually uses the mean square error (MSE) to measure the reconstructed signal. With the original signal The difference between:

[0254] ;

[0255] Step 5.5: Update model parameters;

[0256] The gradient of the loss function to the model parameters (weights and biases) is calculated through the back-propagation algorithm, and the optimizer (such as Adam) is used to update the weights and biases of each layer to gradually reduce the loss function value.

[0257] Step 5.6 Verify the early stopping condition;

[0258] Based on the performance of the loss function on the validation set, check whether you need to adjust the learning rate or stop training early.

[0259] Step 6: Save the model;

[0260] After the training process is completed, the stacked denoising encoder and its parameters are saved. These parameters can be used for subsequent signal denoising or other modulation recognition tasks. Through the above training process, SDAE gradually learns to extract useful features from noisy signals and restore noise-free signals through the decoder. In the repeated training and verification process, the model continuously optimizes its internal parameters to achieve the best denoising effect and provide higher quality input data for subsequent modulation recognition tasks.

[0261] Signal modulation recognition based on the combination of instantaneous features, spectral features, high-order cumulants, phase and constellation diagram; including:

[0262] In the frequency deviation state, for 13 digital modulation modes among the above 28 modulation signals and the noise type without signal, the present invention proposes a joint recognition algorithm based on multiple features. The recognition process is described as follows:

[0263] (1) Determine whether the signal to be identified is noise: For the received discrete signal sequence , find the Fourier transform. The signal is transmitted from the transmitter to the receiver through the wireless channel. The initial signal is an analog signal. At the receiver, this analog signal needs to be converted into digital form through analog-to-digital conversion for subsequent digital signal processing. Discrete signal sequence It is a series of sampling points obtained after analog-to-digital conversion. The eigenvalue is calculated according to the following formula ;

[0264]

[0265] in, U ( f ) represents the normalized first-order spectrum of the signal, var[·] represents the variance calculation, mean [·] indicates mean calculation.

[0266] like , then it is determined to be noise, otherwise, step (2) is executed; where, is the discrimination threshold;

[0267] (2) Determine whether the signal to be identified is quadrature offset phase shift keying (OQPSK):

[0268] 2a) Signal Seek its envelope , and Fourier transform its square to get , take the positive spectrum part , and remove the DC component;

[0269] 2b) Traversal , select , the relative prominence of the spectral line at frequency f is calculated according to the following formula ;

[0270] ;

[0271] Where |U( f )| represents the amplitude of the spectral line at frequency f. , , , They represent the maximum and second largest values ​​of the amplitude of the spectrum line in the left k neighborhood and the maximum and second largest values ​​of the amplitude of the spectrum line in the right k neighborhood of frequency f respectively;

[0272] 2c) Extract the maximum value , if mav> , then it is determined to be {OQPSK}, otherwise, go to Step 3; where, is the discrimination threshold, =2;

[0273] (3) The symbol rate of the signal to be identified is estimated to perform blind matching and sampling rate conversion. The output sequence is ; Among them, symbol rate estimation is the process of determining the symbol rate by analyzing the received signal spectrum. First, the signal is Fourier transformed to estimate the spectrum characteristics, and then the estimated rate is compared with the standard symbol rate through blind matching, and the closest value is selected. Next, the signal is sampled and converted so that the sampling rate of the signal matches the symbol rate, and the output sequence is obtained. , so that the subsequent modulation feature extraction and identification are more accurate.

[0274] (4) Determine whether the signal to be identified is of the M-order amplitude keying MASK category:

[0275] Signal Taking its Fourier transform we get , calculate the relative prominence S1 of the maximum value of the primary spectrum according to the following formula;

[0276] ;

[0277] In the above formula, U ( f ) represents the normalized signal first-order spectrum, and the numerator max(| U ( f )|) represents the maximum spectral line value;

[0278] If S1< , then it is determined to be {binary amplitude keying 2ASK, quaternary amplitude keying 4ASK, octal amplitude keying 8ASK}, and step (5) is executed; otherwise, step (6) is executed;

[0279] (5) M-order amplitude keying MASK intra-class recognition:

[0280] 5a) Signal Carrier frequency offset estimation is performed to obtain the carrier frequency offset estimation value ;

[0281] 5b) According to Signal After frequency offset compensation, the output sequence is ,in, is a complex exponential signal used for compensation, whose frequency is equal to the estimated frequency deviation , is the sampling period;

[0282] 5c) Perform high-order accumulation on the output sequence of the previous step and Calculate and find its eigenvalue ;

[0283] like , then it is judged as {2ASK}; if , then it is determined as {4ASK}, otherwise, it is determined as {8ASK}, and the branch identification ends; among them, , is the discrimination threshold;

[0284] (6) Determine whether the signal to be identified is {binary phase shift keying BPSK, 8th order quadrature amplitude modulation 8QAM}: Calculate , and take Fourier transform to get ;like , then it is determined to be {BPSK, 8QAM} and step 7 is executed, otherwise step 8 is executed; wherein, is the discrimination threshold;

[0285] (7) {BPSK, 8QAM} Intra-subset Identification:

[0286] 7a) Signal Perform symbol synchronization to obtain an output sequence;

[0287] 7b) Calculate the eigenvalue of the output sequence of step 7a) according to the following formula :

[0288] ;

[0289] In the formula, It refers to the average value of the absolute value of the instantaneous amplitude normalized to the zero center; it indicates the average level of the absolute value of the instantaneous amplitude of the signal after the signal is normalized to the zero center; N refers to the total number of samples of the signal, indicating the number of discrete sampling points contained in the signal on the time axis; It refers to the operation of summing all sampling points i, which means accumulating all the absolute values ​​of the instantaneous amplitudes of the signal; represents the instantaneous amplitude after zero-center normalization of the i-th sampling point, It represents the absolute value of this value; is the instantaneous amplitude after zero-centered normalization;

[0290] like , then it is determined to be {BPSK}, otherwise it is determined to be {8QAM}, and the branch identification ends; among them, is the discrimination threshold;

[0291] (8) Determine whether the signal to be identified belongs to the subset of {quadrature phase shift keying QPSK, 8-phase shift keying 8PSK, 16-phase shift keying 16PSK, π / 4-offset quadrature phase shift keying π / 4DQPSK} or {16-order quadrature amplitude modulation 16QAM, 32-order quadrature amplitude modulation 32QAM, 64-order quadrature amplitude modulation 64QAM};

[0292] Signal Perform symbol synchronization to restore the baseband modulation symbol sequence, calculate the high-order cumulative quantities C63 and C42 of the sequence, and find the eigenvalue H2=|C63|2 / |C42|3; if H2>th7, the signal belongs to the {QPSK, 8PSK, 16PSK, π / 4DQPSK} subset, and execute step (8); otherwise, the signal belongs to the {16QAM, 32QAM, 64QAM} subset, and execute step (9); where, is the discrimination threshold;

[0293] (9) Identification within the {QPSK, 8PSK, 16PSK, π / 4DQPSK} subset:

[0294] 9a) Calculation , and the Fourier transform is obtained ,like , then the signal belongs to the {QPSK, π / 4DQPSK} subset, and execute step 8b); otherwise, it belongs to the {8PSK, 16PSK} subset, and execute step 8c); wherein, is the discrimination threshold;

[0295] 9b) Traverse the spectrum obtained in step 9a) and calculate the number of spectrum lines with normalized amplitude greater than 0.5 ,like , then it is determined to be {π / 4DQPSK}, otherwise, it is determined to be {QPSK}, and the branch identification ends; among them, is the discrimination threshold;

[0296] 9c) Calculation , and find its Fourier transform ,like , then it is determined as {8PSK}, otherwise, it is determined as {16PSK}, and the branch identification ends, where, is the discrimination threshold;

[0297] (10) {16QAM, 32QAM, 64QAM} subset identification:

[0298] 10a) Signal Carrier synchronization and symbol synchronization are performed to obtain an output sequence; the specific steps are the same as steps 5a) to 5b);

[0299] 10b) Perform a high-order accumulation on the output sequence of the previous step C 80 and C 42 Calculate and find its eigenvalue H 3=| C 80 | / | C 42 | 2 ,like , then it is determined to be {16QAM, 64QAM}, and step 10c) is executed; otherwise, it is determined to be {32QAM}; wherein, is the discrimination threshold;

[0300] 10c) Calculate the average value of the recursive zero-centered normalized instantaneous amplitude absolute value for the output sequence of step 10a) according to the following formula: M 2:

[0301] ;

[0302] In the above formula, ;

[0303] like M 2> th 12 , then it is determined to be {16QAM}, otherwise it is determined to be {64QAM}, and the branch identification ends; wherein, is the discrimination threshold.

[0304] In step 5a), the signal Perform frequency offset estimation to obtain carrier frequency offset estimation value ;include:

[0305] The signal is transmitted from the transmitter to the receiver through the wireless channel, and the received signal sequence r(t) is transformed to its fourth power, and we get {y(t)}={r 4 (t)}; let {y in (t)}={y(t)}, and we can get {y 1 (t)};

[0306] The output sequence of the previous step is used as the input of the next autocorrelation operation. The autocorrelation operation is repeated m times. The output of the mth autocorrelation operation is the final output, that is, {y out (t)}={y m (t)};

[0307] Traverse {y out (t)}, search for the position of the maximum normalized amplitude and obtain ∆f coa ;

[0308] Using CZT to measure ∆f coa Nearby narrow band [(1-ε) ∆f coa , (1+ε) ∆f coa ] to perform frequency selection analysis, including: using the CZT algorithm to transform the input signal x(n). The core idea of ​​CZT is to convolve the signal and then calculate the spectrum value by selecting the appropriate path after the convolution. After the CZT transformation, the obtained spectrum data corresponds to the signal component within the selected frequency range;

[0309] Select a value greater than 0 and much less than 1 to get the frequency offset estimate .

[0310] is 0.5, is 2, is 2, is 150, is 97, is 2, is 0.35, is 15, is 2, is 10, is 2, is 1.3, is 0.6.

[0311] Depend on Figure 6 It can be seen that when there is a normalized frequency deviation of 0.2, the joint recognition algorithm proposed in the present invention can achieve a recognition rate of more than 90% when the signal-to-noise ratio is greater than 7dB; except for 4ASK, the recognition rates of other types reach more than 90% when the signal-to-noise ratio is greater than 5dB, which meets the needs of subsequent projects.

[0312] Example 3

[0313] Modulation recognition system based on stacked denoising encoders and edge devices, including:

[0314] The modulation signal generation unit is configured to: generate a modulation signal based on GNU Radio; during the generation of the modulation signal, simulate the actual communication environment by adding different types of noise; perform channel simulation after adding different types of noise; and store and output data;

[0315] The signal denoising and identification unit is configured to: perform signal modulation identification based on stacked denoising encoder signal denoising and based on multiple features such as instantaneous features, spectral features, high-order cumulants, phase and constellation diagram.

Claims

1. A modulation recognition method based on a stacked denoising encoder and an edge device, characterized in that: Including: Generating a modulated signal based on GNU Radio; During the process of generating the modulated signal, simulating the actual communication environment by adding different types of noise; After adding different types of noise, performing channel simulation; data storage and output; Performing modulation recognition based on decision trees and networks; Refers to: signal denoising based on stacked denoising autoencoders and multi-feature joint signal modulation recognition based on instantaneous features, spectral features, high-order cumulants, phase, and constellations; Multi-feature joint signal modulation recognition based on instantaneous features, spectral features, high-order cumulants, phase, and constellations; including: (1) Determining whether the signal to be recognized is noise: For the received discrete signal sequence r(n), taking the Fourier transform and calculating the eigenvalue P according to the following formula; where U(f) represents the normalized first-order power spectrum of the signal, var[·] represents variance calculation, and mean[·] represents mean calculation; If P < th0, then determine it as noise, otherwise execute step (2); where th0 is the discrimination threshold; (2) Determining whether the signal to be recognized is offset quadrature phase shift keying (OQPSK); 2a) Find the envelope of the signal r(n) |r(n)|, perform Fourier transform on its square to get U(f), and take its positive spectrum part I + (f), and remove the DC component; 2b) Traverse U + (f), select k = 32, and calculate the relative prominence R of the spectral line at frequency f according to the following formula p (f); Among them, |U(f)| represents the amplitude value of the spectral line at frequency f, |U l1 (f)|、|U l2 (f)|、|U r1 (f)|、|U r2 (f)|represents the maximum and second largest values ​​of the amplitude of the spectrum line in the left k neighborhood and the maximum and second largest values ​​of the amplitude of the spectrum line in the right k neighborhood of frequency f respectively; 2c) Extract the maximum value max=max[R p (f)], if mav>th1, it is determined to be {OQPSK}, otherwise, go to Step 3; where th1 is the discrimination threshold, th1=2; (3) Estimating the symbol rate of the signal to be recognized for blind matching and sampling rate conversion, and the output sequence is r′(n); (4) Determining whether the signal to be recognized belongs to the M-ary amplitude shift keying (MASK) category; Taking the Fourier transform of the signal r′(n) to obtain U1(f), and calculating the relative prominence S1 of the maximum value of the first-order spectrum according to the following formula; In the above formula, U(f) represents the normalized first-order power spectrum of the signal, and the numerator max(|U(f)|) represents the maximum spectral line value; If S1 < th2, then determine it as {binary amplitude shift keying (2ASK), quaternary amplitude shift keying (4ASK), octal amplitude shift keying (8ASK)}, and execute step (5), otherwise execute step (6); (5) Intra-class recognition of M-ary amplitude shift keying (MASK); 5a) Estimating the frequency offset of the signal r′(n) to obtain the estimated value of the carrier frequency offset 5b) According to After frequency offset compensation of signal r′(n), the output sequence is in, is a complex exponential signal used for compensation, whose frequency is equal to the estimated frequency deviation T3 is the sampling period; 5c) Perform a high-order accumulation C on the output sequence of the previous step 80 and C 21 Calculate the characteristic value H1=|C 80 | / |C 21 | 4 ; If H1 > th3, then determine it as {2ASK}; if H1 > th4, then determine it as {4ASK}, otherwise determine it as {8ASK}, and the branch recognition ends; where th3 and th4 are discrimination thresholds; (6) Determining whether the signal to be recognized is {binary phase shift keying (BPSK), 8-ary quadrature amplitude modulation (8QAM)}: Calculating r′(n)r′(n - 1) and taking its Fourier transform to obtain S2; if S2 > th5, then determine it as {BPSK, 8QAM} and execute step 7, otherwise execute step 8; where th5 is the discrimination threshold; (7) Intra-subset recognition of {BPSK, 8QAM}; 7a) Performing symbol synchronization on the signal r′(n) to obtain the output sequence; 7b) Calculating the eigenvalue M1 of the output sequence in step 7a) according to the following formula; Where M1 refers to the average value of the zero-centered normalized instantaneous amplitude absolute value; N refers to the total number of samples of the signal, indicating the number of discrete sampling points contained in the signal on the time axis; It refers to the operation of summing all sampling points i, which means accumulating all the instantaneous absolute values ​​of the signal amplitude; A cn (i) represents the instantaneous amplitude of the i-th sampling point after zero-center normalization, |A cn (i)| represents the absolute value of this value; A cn (i) is the instantaneous amplitude after zero-centered normalization; If M1 < th6, then determine it as {BPSK}, otherwise determine it as {8QAM}, and the branch recognition ends; where th6 is the discrimination threshold; (8) determining whether the signal to be identified belongs to the subset {quadrature phase shift keying QPSK, 8-phase shift keying 8PSK, 16-phase shift keying 16PSK, π / 4-offset quadrature phase shift keying π / 4DQPSK} or {16-order quadrature amplitude modulation 16QAM, 32-order quadrature amplitude modulation 32QAM, 64-order quadrature amplitude modulation 64QAM}; Perform symbol synchronization on the signal r′(n) to restore it into a baseband modulation symbol sequence, calculate the high-order cumulative quantities C63 and C42 of the sequence, and find the eigenvalue H2=|C63|2 / |C42|3; if H2>th7, the signal belongs to the {QPSK, 8PSK, 16PSK, π / 4DQPSK} subset, and execute step (8); otherwise, the signal belongs to the {16QAM, 32QAM, 64QAM} subset, and execute step (9); wherein th7 is the discrimination threshold; (9) {QPSK, 8PSK, 16PSK, π / 4DQPSK} subset identification: 9a) Calculate r′(n)r′(n-1)r′(n-2)r′(n-3), perform Fourier transform on it to obtain S4, if S4>th8, the signal belongs to the {QPSK,π / 4DQPSK} subset, execute step 9b), otherwise it belongs to the {8PSK, 16PSK} subset, execute step 9c); wherein th8 is the discrimination threshold; 9b) Traverse the spectrum obtained in step 9a) and calculate the number of spectrum lines num4 with normalized amplitude greater than 0.

5. If num4 = th 10 , then it is determined to be {π / 4DQPSK}, otherwise, it is determined to be {QPSK}, and the branch identification ends; among them, th 10 is the discrimination threshold; 9c) Calculate r′(n)r′(n-1)r′(n-2)r′(n-3)r′(n-4)r′(n-5)r′(n-6)r′(n-7) and find its Fourier transform S8. If S8>th 11 , then it is determined as {8PSK}, otherwise, it is determined as {16PSK}, and the branch recognition ends, where th 11 is the discrimination threshold; (10) {16QAM, 32QAM, 64QAM} subset identification: 10a) performing carrier synchronization and symbol synchronization on the signal r′(n) to obtain an output sequence; 10b) Perform a high-order accumulation C on the output sequence of the previous step 80 and C 42 Calculate the characteristic value H3=|C 80 | / |C 42 | 2 If H3>th9, it is determined to be {16QAM, 64QAM}, and step 10c) is executed; otherwise, it is determined to be {32QAM}; wherein th9 is the discrimination threshold; 10c) Calculate the average value M2 of the recursive zero-centered normalized instantaneous amplitude absolute value for the output sequence of step 10a) according to the following formula: In the above formula, If M2>th 12 , then it is determined as {16QAM}, otherwise it is determined as {64QAM}, and the branch identification ends; among them, th 12 is the discrimination threshold.

2. The modulation recognition method based on stacked denoising encoder and edge device according to claim 1, characterized in that: Generate modulated signals based on GNU Radio; It means: using GNU Radio to generate the final real modulation signal from the input 01 sequence; including: First, input the 01 sequence to the vector source module. The input 01 sequence refers to the bit stream to be modulated. GNURadio includes a vector source module, which converts the input 01 sequence into a vector format. Subsequently, the bit stream to be modulated passes through a stream conversion module to a labeled stream; the stream conversion module to a labeled stream adds a length label to each frame of the bit stream; Next, the data stream is input into the signal modulation module, which modulates the input bit stream according to the set number of symbols and sensitivity parameters to generate a modulated signal; at the same time, the modulated signal enters the signal demodulation module, and the original bit stream is restored through the corresponding parameter settings; the demodulated bit stream is bit-repacked and converted into floating-point representation; Finally, the generated modulated signal is input into the visualization module to show the characteristics of the modulated signal.

3. The modulation recognition method based on stacked denoising encoder and edge device according to claim 1, characterized in that: Generate modulated signals based on GNU Radio; including: Determine the range of modulation modes and signal-to-noise ratios; define modulation transmitters with multiple modulation modes, including discrete modulation transmitters and continuous modulation transmitters; Discrete modulation transmitters include BPSK, QPSK, 8PSK, PAM4, QAM16, QAM64, GFSK, CPFSK, and GMSK; Discrete modulation transmitters map the input bit stream into corresponding modulation symbols, which are then filtered through a pulse shaping filter to generate a modulated signal; Continuous modulation transmitters include FM, AM-DSB and AM-SSB; continuous modulation transmitters are used to generate continuous carrier signals.

4. The modulation recognition method based on stacked denoising encoder and edge device according to claim 1, characterized in that: Simulate the actual communication environment by adding different types of noise; different types of noise include Gaussian noise, impulse noise, Rayleigh noise, Laplace noise and uniform noise; The generation process of Gaussian noise is as follows: Compute the amplitude of the noise for a specified signal-to-noise ratio: Among them, A 噪声 Represents the amplitude of the noise, P 信号 is the average power of the signal, SNR is the signal-to-noise ratio; the noise signal follows a normal distribution, and the Gaussian noise n 高斯噪声 [i] is represented by: Where N(0,1) represents a normal distribution with a mean of 0 and a variance of 1, and j is an imaginary unit; Impulse noise is expressed as follows: Among them, n 脉冲噪声 [i] represents the impulse noise value of the i-th sample point, A 脉冲噪声 represents the amplitude of the impulse noise, and p is the probability of the pulse occurring; The formula for generating Rayleigh noise is: Among them, n 瑞利噪声 [i] represents the Rayleigh noise value of the i-th sample point, A 噪声 is the noise amplitude, U and V are uniformly distributed random variables on the interval [0,1], ln(·) is the natural logarithm function, cos(·) and sin(·) represent the cosine and sine functions, respectively; The generation formula of Laplace noise is: n 拉普拉斯噪声 [i]=A 噪声 ×sign(X)×ln(1-2∣X∣) Among them, n 拉普拉斯噪声 [i] represents the Laplace noise value of the i-th sample point, A 噪声 is the noise amplitude, X is a uniformly distributed random variable in the interval [-0.5, 0.5], sign(X) represents the sign function of X, and ln(·) is the natural logarithm function; The formula for generating uniform noise is: n 均匀噪声 [i]=A 噪声 ×(2U-1) Among them, n 均匀噪声 [i] represents the uniform noise value of the i-th sample point, A 噪声 is the noise amplitude, and U is a uniformly distributed random variable in the interval [0,1].

5. The modulation recognition method based on stacked denoising encoder and edge device according to claim 1, characterized in that: After adding different types of noise, channel simulation is performed; including: After adding noise, choose whether to apply the channel model to further simulate the channel effect in wireless communication. The channel model uses the dynamic channel model in GNU Radio. After the signal is processed by the dynamic channel model, a sample vector of fixed length is generated by random sampling; each sample vector is normalized.

6. The modulation recognition method based on stacked denoising encoder and edge device according to claim 1, characterized in that: Data storage and output; including: After generating and processing the signal data for all modulation modes and signal-to-noise ratio conditions, the data is saved in MAT file format.

7. The modulation recognition method based on stacked denoising encoder and edge device according to claim 1, characterized in that: Modulation recognition based on decision trees and networks; Refers to: signal denoising based on stacked denoising encoder; including: The denoising process of the stacked denoising encoder includes: Noise addition and input perturbation: For an original noise-free signal represented as x, a noisy signal x is generated by adding noise n 噪 : x 噪 =x+n Where n represents different types of noise; The encoder is used to extract features and reduce dimension; the input noisy signal x 噪 Mapped to a low-dimensional feature space; assuming that the encoder consists of a set of weight matrices W k and the bias vector b k , the encoding process is expressed as: h=f(W e x 噪 +b e ) Where h is the feature representation of the hidden layer, f(·) is the activation function, the encoder extracts the deep features of the signal and maps the deep features to a low-dimensional space; The signal is reconstructed by the decoder; the decoder includes a set of weight matrices W n and the bias vector b n , the reconstruction process is expressed as: x 重建 =g(W n h+b n ) Where xreconstruct is the signal reconstructed by the decoder, and g(·) is the activation function of the decoder; Loss function and model optimization; define the loss function to measure the reconstructed signal x 重建 The difference between the original signal x and the loss function is the mean square error, expressed as: Where N is the number of samples, x E and are the original signal and the reconstructed signal of the i-th sample respectively; by minimizing the loss function, the stacked denoising encoder gradually adjusts its parameters so that the reconstructed signal is closer to the original signal; Multi-layer stacking and deep denoising; stacking multiple layers of encoders and decoders to form a deep structure; the encoder of each layer takes the hidden representation of the previous layer as input and further extracts features, while the decoder reconstructs the signal layer by layer; The final output is the denoising effect.

8. The modulation recognition method based on stacked denoising encoder and edge device according to claim 7, characterized in that: In step 5a), the frequency offset of the signal r'(n) is estimated to obtain the carrier frequency offset estimate value include: The signal is transmitted from the transmitter to the receiver through the wireless channel. The received signal sequence r(t) is transformed to its fourth power and we get {y(t)} = {r 4 (t)}; let {y in (t)}={y(t)} and perform autocorrelation operation to obtain {y 1 (t)}; The output sequence of the previous step is used as the input of the next autocorrelation operation. The autocorrelation operation is repeated m times. The output of the mth autocorrelation operation is the final output, that is, {y out (t)}={y m (t)}; Traverse {y out (t)}, search for the position of the maximum normalized amplitude and obtain Δf coa ; Using CZT to measure Δf coa Nearby narrow band [(1-ε)Δf coa ,(1+ε)Δf coa ] performs frequency selection analysis, including: transforming the input signal x(n) using the CZT algorithm, and the obtained spectrum data corresponds to the signal components within the selected frequency range; ε is selected to be greater than 0 and much less than 1, that is, the frequency offset estimate is obtained. th0 is 0.5, th1 is 2, th2 is 2, th3 is 150, th4 is 97, th5 is 2, th6 is 0.35, th7 is 15, th8 is 2, th9 is 10, th 10 2,th 11 is 1.3,th 12 is 0.

6.

9. A modulation recognition system based on a stacked denoising encoder and an edge device, characterized in that: include: The modulation signal generating unit is configured to: generate a modulation signal based on GNU Radio; In the process of generating the modulated signal, different types of noise are added to simulate the actual communication environment; after adding different types of noise, channel simulation is performed; data is stored and output; A signal denoising and identification unit is configured to: perform signal modulation identification based on signal denoising of a stacked denoising encoder and based on a combination of instantaneous features, spectral features, high-order cumulants, phases and constellation diagrams; Signal modulation recognition based on the combination of instantaneous features, spectral features, high-order cumulants, phase and constellation diagram; including: (1) Determine whether the signal to be identified is noise: For the received discrete signal sequence r(n), calculate the Fourier transform and calculate the eigenvalue P according to the following formula; Among them, U(f) represents the first - order normalized spectrum of the signal, var[·] represents variance calculation, and mean[·] represents mean calculation; If P < th0, it is determined to be noise, otherwise step (2) is executed; where th0 is the discrimination threshold; (2) Determine whether the signal to be recognized is Offset Quadrature Phase Shift Keying (OQPSK); 2a) Find the envelope of the signal r(n) |r(n)|, perform Fourier transform on its square to get U(f), and take its positive spectrum part U + (f), and remove the DC component; 2b) Traverse U + (f), select k = 32, and calculate the relative prominence R of the spectral line at frequency f according to the following formula p (f); Among them, |U(f)| represents the amplitude value of the spectral line at frequency f, |U l1 (f)|、|U l2 (f)|、|U r1 (f)|、|U r2 (f)|represents the maximum and second largest values ​​of the amplitude of the spectrum line in the left k neighborhood and the maximum and second largest values ​​of the amplitude of the spectrum line in the right k neighborhood of frequency f respectively; 2c) Extract the maximum value mav = max[R p (f)], if mav>th1, it is determined to be {OQPSK}, otherwise, go to Step 3; where th1 is the discrimination threshold, th1=2; (3) Estimate the symbol rate of the signal to be recognized for blind matching and sampling rate conversion, and the output sequence is r′(n); (4) Determine whether the signal to be recognized belongs to the large category of M - ary Amplitude Shift Keying (MASK); Perform the Fourier transform on the signal r′(n) to obtain U1(f), and calculate the relative prominence S1 of the maximum value of the first - order spectrum according to the following formula; In the above formula, U(f) represents the first - order normalized spectrum of the signal, and the numerator max(|U(f)|) represents the maximum spectral line value; If S1 < th2, it is determined to be {Binary Amplitude Shift Keying (2ASK), Quaternary Amplitude Shift Keying (4ASK), Octal Amplitude Shift Keying (8ASK)}, and step (5) is executed, otherwise step (6) is executed; (5) Intra - class recognition of M - ary Amplitude Shift Keying (MASK); 5a) Estimating the frequency offset of the signal r′(n) to obtain the estimated value of the carrier frequency offset 5b) According to After frequency offset compensation of signal r′(n), the output sequence is in, is a complex exponential signal used for compensation, whose frequency is equal to the estimated frequency deviation T3 is the sampling period; 5c) Perform a high-order accumulation C on the output sequence of the previous step 80 and C 21 Calculate the characteristic value H1=|C 80 | / |C 21 | 4 ; If H1 > th3, it is determined to be {2ASK}; if H1 > th4, it is determined to be {4ASK}, otherwise it is determined to be {8ASK}, and the branch recognition ends; where th3 and th4 are discrimination thresholds; (6) Determine whether the signal to be recognized is {Binary Phase Shift Keying (BPSK), 8 - Quadrature Amplitude Modulation (8QAM)}: Calculate r′(n)r′(n - 1) and perform its Fourier transform to obtain S2; if S2 > th5, it is determined to be {BPSK, 8QAM} and step Step7 is executed, otherwise step Step8 is executed; where th5 is the discrimination threshold; (7) Intra - subset recognition of {BPSK, 8QAM}; 7a) Perform symbol synchronization on the signal r′(n) to obtain the output sequence; 7b) Calculate the eigenvalue M1 of the output sequence in step 7a) according to the following formula; Where M1 refers to the average value of the zero-centered normalized instantaneous amplitude absolute value; N refers to the total number of samples of the signal, indicating the number of discrete sampling points contained in the signal on the time axis; It refers to the operation of summing all sampling points i, which means accumulating all the instantaneous absolute values ​​of the signal amplitude; A cn (i) represents the instantaneous amplitude of the i-th sampling point after zero-center normalization, |A cn (i)| represents the absolute value of this value; A cn (i) is the instantaneous amplitude after zero-centered normalization; If M1 < th6, it is determined to be {BPSK}, otherwise it is determined to be {8QAM}, and the branch recognition ends; where th6 is the discrimination threshold; (8) Determine whether the signal to be recognized belongs to the subset of {Quadrature Phase Shift Keying (QPSK), 8 - Phase Shift Keying (8PSK), 16 - Phase Shift Keying (16PSK), π / 4 - Offset Quadrature Phase Shift Keying (π / 4DQPSK)} or the subset of {16 - Quadrature Amplitude Modulation (16QAM), 32 - Quadrature Amplitude Modulation (32QAM), 64 - Quadrature Amplitude Modulation (64QAM)}; Perform symbol synchronization on the signal r′(n) to restore it to the base - band modulation symbol sequence, calculate the high - order cumulants C63 and C42 of this sequence, and find the eigenvalue H2 = |C63|2 / |C42|3; if H2 > th7, the signal belongs to the subset of {QPSK, 8PSK, 16PSK, π / 4DQPSK}, and step (8) is executed, otherwise the signal belongs to the subset of {16QAM, 32QAM, 64QAM}, and step (9) is executed; where th7 is the discrimination threshold; (9) Intra - subset recognition of {QPSK, 8PSK, 16PSK, π / 4DQPSK}; 9a) Calculate r′(n)r′(n-1)r′(n-2)r′(n-3), perform Fourier transform on it to obtain S4, if S4>th8, the signal belongs to the {QPSK,π / 4DQPSK} subset, execute step 9b), otherwise it belongs to the {8PSK, 16PSK} subset, execute step 9c); wherein th8 is the discrimination threshold; 9b) Traverse the spectrum obtained in step 9a) and calculate the number of spectrum lines num4 with normalized amplitude greater than 0.

5. If num4 = th 10 , then it is determined to be {π / 4DQPSK}, otherwise, it is determined to be {QPSK}, and the branch identification ends; among them, th 10 is the discrimination threshold; 9c) Calculate r′(n)r′(n-1)r′(n-2)r′(n-3)r′(n-4)r′(n-5)r′(n-6)r′(n-7) and find its Fourier transform S8. If S8>th 11 , then it is determined as {8PSK}, otherwise, it is determined as {16PSK}, and the branch recognition ends, where th 11 is the discrimination threshold; (10) {16QAM, 32QAM, 64QAM} subset identification: 10a) performing carrier synchronization and symbol synchronization on the signal r′(n) to obtain an output sequence; 10b) Perform a high-order accumulation C on the output sequence of the previous step 80 and C 42 Calculate the characteristic value H3=|C 80 | / |C 42 | 2 If H3>th9, it is determined to be {16QAM, 64QAM}, and step 10c) is executed; otherwise, it is determined to be {32QAM}; wherein th9 is the discrimination threshold; 10c) Calculate the average value M2 of the recursive zero-centered normalized instantaneous amplitude absolute value for the output sequence of step 10a) according to the following formula: In the above formula, If M2>th 12 , then it is determined as {16QAM}, otherwise it is determined as {64QAM}, and the branch identification ends; among them, th 12 is the discrimination threshold.

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