CN113452637A - Underwater acoustic communication signal modulation identification method based on feature selection and support vector machine - Google Patents

Underwater acoustic communication signal modulation identification method based on feature selection and support vector machine Download PDF

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CN113452637A
CN113452637A CN202111017690.8A CN202111017690A CN113452637A CN 113452637 A CN113452637 A CN 113452637A CN 202111017690 A CN202111017690 A CN 202111017690A CN 113452637 A CN113452637 A CN 113452637A
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吕曜辉
刘炜琪
李兴顺
殷昊
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Abstract

The invention discloses an underwater acoustic communication signal modulation and identification method based on feature selection and a support vector machine. The method comprises the following steps: extracting instantaneous characteristics, high-order cumulant and power spectrum characteristics of each sample from underwater acoustic communication data samples obtained in a simulated or actual mode to form series characteristics; calculating a weight coefficient of the series connection features by adopting an entropy weight method, and regarding the corresponding features of which the weight coefficients are larger than a preset weight threshold as sensitive features; taking the sensitive characteristics of each sample as sample data, marking the same label on the underwater sound data sample with the same modulation mode, and marking different labels on the underwater sound data sample with different modulation modes to form training; training by taking a training set as the input of a support vector machine, adopting a Gaussian kernel function and taking a multi-class cross entropy function as a target function to obtain an identification model based on the support vector machine; and modulating and identifying the underwater acoustic communication data subjected to the feature extraction by using the trained identification model. The method has the advantages of high efficiency and accurate identification.

Description

Underwater acoustic communication signal modulation identification method based on feature selection and support vector machine
Technical Field
The invention relates to the field of signal processing, in particular to a modulation identification method for underwater acoustic communication.
Background
With the development and application of machine learning technology, the research of modulation identification methods gradually becomes a hotspot in the field of underwater acoustic communication. Among them, a modulation identification method based on feature extraction is one of important research directions.
Generally, a modulation identification method based on feature extraction is divided into two parts, namely feature extraction and a classifier. However, the underwater acoustic channel is a time-frequency-space variant parameter channel with strong multipath, large doppler spread and multiple transmission attenuation, and the characteristics of the underwater acoustic channel cause serious distortion of an underwater acoustic communication signal at a receiving end, which affects the selection of characteristics and the quality of the characteristics, and further affects the identification performance of the classifier. Theoretically, the more the feature vectors are, the better the identification capability among underwater acoustic communication signals in different modulation modes can be enhanced, but meanwhile, redundant information is increased, the calculation complexity is improved, and the identification efficiency of a classifier is reduced. The support vector machine is used as a classic classifier algorithm, has a complete theoretical basis and has good generalization capability. But when the dimensionality of the input features is low, the recognition effect is poor.
Therefore, for complex underwater acoustic channels, a robust underwater acoustic communication signal modulation identification method which effectively combines a feature selection technology and a support vector machine needs to be established.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a method for realizing underwater acoustic communication signal modulation identification based on sensitive feature selection and a support vector machine.
In order to achieve the purpose, the invention adopts the following technical scheme:
a method for realizing underwater acoustic communication signal modulation identification based on feature selection and a support vector machine comprises the following steps:
(1) extracting instantaneous characteristics, high-order cumulant and power spectrum characteristics of each sample from simulated or actually acquired underwater acoustic communication data samples to form series characteristics;
(2) calculating a weight coefficient of the series connection features by adopting an entropy weight method, determining a weight threshold value, and regarding the corresponding features of which the weight coefficients are greater than the weight threshold value as sensitive features;
(3) taking the sensitive characteristics of each sample as sample data, marking the same label on the underwater sound data sample with the same modulation mode, and marking different labels on the underwater sound data sample with different modulation modes to form a training set;
(4) training by taking a training set as the input of a support vector machine, adopting a Gaussian kernel function and taking a multi-classification cross entropy function as a target function to obtain an identification model of the support vector machine;
(5) and modulating and identifying the underwater acoustic communication data subjected to the feature extraction by using the trained identification model of the support vector machine.
In a preferred embodiment of the invention, the temporal characteristics of each sample comprise a zero-center normalized temporal amplitude spectral density maximum, a standard deviation of the temporal amplitudes of the zero-center normalized non-weak signal segments, a compactness of the zero-center normalized temporal amplitudes, a standard deviation of the temporal phase non-linear components of the zero-center non-weak signal segments, a standard deviation of the absolute values of the temporal phase non-linear components of the zero-center non-weak signal segments, a compactness of the zero-center normalized temporal frequencies, and a standard deviation of the absolute values of the temporal frequencies of the zero-center normalized non-weak signal segments. The higher-order cumulants for each sample include the second-order cumulants, the fourth-order cumulants, and the sixth-order cumulants. The power spectrum features comprise single-frequency component detection values of the primary spectrum, double-frequency component detection values of the primary spectrum, single-frequency component detection values of the secondary spectrum and waveform feature values.
Compared with the prior art, the invention has the following beneficial effects:
the invention provides an underwater acoustic communication signal modulation and identification method based on feature selection and a support vector machine, which reduces information redundancy by extracting a plurality of relevant features of instantaneous features, high-order cumulant and power spectrum features of each data sample and selecting sensitive features by adopting an entropy weight method; the support vector machine recognition algorithm takes the series sensitive features as input samples, and utilizes a Gaussian kernel function to map the input samples into a linearly separable feature space so as to realize the classification recognition of the input samples. Aiming at the complex underwater acoustic channel condition, the invention reduces the data dimension and the redundant information on the premise of not reducing the identification precision, and improves the efficiency of modulating and identifying the underwater acoustic communication signal.
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FIG. 1 is a schematic diagram of an underwater acoustic communication signal modulation identification method based on sensitive feature selection and a support vector machine according to the present invention;
FIG. 2 is a schematic flow chart of a sensitive feature selection technique according to the present invention;
FIG. 3 is a comparison graph of recognition results under different weight thresholds in the embodiment of the present invention;
FIG. 4 is a diagram of a simulation confusion matrix in an embodiment of the invention.
Detailed Description
The technical scheme of the invention is further explained by combining the attached drawings.
The invention provides an underwater acoustic communication signal modulation and identification method based on sensitive feature selection and a support vector machine, and with reference to fig. 1, the method mainly comprises two stages: sensitive feature selection and support vector machine identification. The sensitive feature selection part selects the sensitive features by giving different weights to each feature through an entropy weight method on the basis of extracting 18 features such as instantaneous features, high-order cumulant, power spectrum features and the like of the underwater acoustic communication signals. The more the weight corresponding to the features is, the more the role in the subsequent modulation identification is, and the features with the larger weight are regarded as sensitive features. The support vector machine identification part takes the serially connected sensitive features as input samples, and utilizes a Gaussian kernel function to map the input samples into a linearly separable feature space so as to realize the classification identification of the input samples. In the embodiment, after underwater acoustic communication data are obtained, the underwater acoustic communication data are divided into training samples and testing samples according to a certain proportion, and a training set and a testing set are formed through feature extraction, sensitive feature selection and labeling; and taking the training set as the input of the support vector machine to obtain an identification model based on the support vector machine, and taking the test set as the input of the identification model to verify the identification performance of the support vector machine.
The following describes the implementation and the effect of the present invention with reference to a simulation example. The method specifically comprises the following steps:
001, the simulation conditions of the invention are as follows: the method is characterized in that the gradient of shallow sea is 'micro positive', the water depth is 50m, the sound source laying depth is 10m, the receiver laying depth is 30m, the transmission distance is 5km, the background noise is Gaussian noise, and the signal-to-noise ratio is 10 dB.
Step 002, for the simulated 2ASK, 4ASK, 2FSK, 4FSK, 2PSK, QPSK, 16QAM and DSSS underwater acoustic communication signals, the sampling frequency is 51.2 kHz, 5000 data samples are generated for each type of communication signal simulation, and each data sample has 2048 discrete data. And dividing the data sample generated by simulation into a training sample and a test sample according to a certain proportion. The ASK (Amplitude Shift keying) is also called Amplitude keying, the 2ASK is binary Amplitude keying, the 4ASK is quaternary Amplitude keying, the FSK (Frequency Shift keying) is Frequency Shift keying, the qpsk (quadrature Phase Shift keying) is quadrature Phase Shift keying, the qam (quadrature Amplitude modulation) is quadrature Amplitude modulation, and the dsss (direct Sequence Spread spectrum) is direct Sequence Spread spectrum.
And step 003, extracting the transient characteristics of each data sample, wherein the transient characteristics specifically comprise 7 characteristics of a maximum value of zero-center normalized transient amplitude spectral density, a standard deviation of transient amplitude of a zero-center normalized non-weak signal segment, compactness of the zero-center normalized transient amplitude, a standard deviation of transient phase nonlinear component of the zero-center non-weak signal segment, a standard deviation of an absolute value of the transient phase nonlinear component of the zero-center non-weak signal segment, compactness of zero-center normalized transient frequency and a standard deviation of an absolute value of the transient frequency of the zero-center normalized non-weak signal segment, and the 7 characteristics are derived from transient characteristics (transient amplitude, transient phase and transient frequency) of the signal. The specific expressions are respectively as follows:
(1) zero-center normalized instantaneous amplitude spectral density maximum:
Figure 531536DEST_PATH_IMAGE001
wherein, N is the number of sampling points,
Figure 448677DEST_PATH_IMAGE002
the instantaneous amplitude is normalized for the center of zero,
Figure 539998DEST_PATH_IMAGE003
is instantaneous amplitude, and
Figure 935208DEST_PATH_IMAGE004
，
Figure 749580DEST_PATH_IMAGE005
，
Figure 634359DEST_PATH_IMAGE006
(ii) a The DFT is a discrete fourier transform. The maximum value of the zero-center normalized instantaneous amplitude spectrum density represents the change condition of the instantaneous amplitude of the signal and can reflect the change characteristic of the envelope of the modulation signal.
(2) Standard deviation of zero-center normalized non-weak signal segment instantaneous amplitude:
Figure 901393DEST_PATH_IMAGE007
Figure 100293DEST_PATH_IMAGE008
the method is an amplitude judgment threshold, generally taking the average value of instantaneous amplitude, and judging whether the amplitude is a weak signal segment or not, wherein the amplitude is a non-weak signal segment if the amplitude is greater than the threshold; c is the number of non-weak signal segments in all the sampled data;
Figure 582221DEST_PATH_IMAGE009
a non-linear component of zero central instantaneous amplitude. The standard deviation of the zero-center normalized non-weak signal segment instantaneous amplitude is used to distinguish the normalized center instantaneous amplitude as zero within a symbol intervalAnd a modulation scheme other than zero.
(3) Compactness of zero-centered normalized instantaneous amplitude:
Figure 575585DEST_PATH_IMAGE010
Figure 329914DEST_PATH_IMAGE011
representing a statistical average. Compactness of zero-center normalized instantaneous amplitude can be used to distinguish signals with a high dense distribution of instantaneous amplitude from signals with a more sparse distribution of instantaneous amplitude.
(4) Standard deviation of the instantaneous phase nonlinear component of the zero center non-weak signal segment:
Figure 66926DEST_PATH_IMAGE012
wherein the content of the first and second substances,
Figure 652628DEST_PATH_IMAGE013
is the non-linear component of the instantaneous phase. The standard deviation of the zero center non-weak signal segment instantaneous phase nonlinear component characterizes the change in the instantaneous phase of the signal and can be used to distinguish between signals containing direct phase and signals that do not contain direct phase information.
(5) Standard deviation of absolute value of instantaneous phase nonlinear component of zero center non-weak signal segment:
Figure 82472DEST_PATH_IMAGE014
the standard deviation of the absolute value of the instantaneous phase nonlinear component of the zero center non-weak signal segment can be used to distinguish between signals containing absolute phase information and signals that do not contain absolute phase information.
(6) Compactness of zero-center normalized instantaneous frequency:
Figure 324098DEST_PATH_IMAGE015
wherein the content of the first and second substances,
Figure 599221DEST_PATH_IMAGE016
，
Figure 554277DEST_PATH_IMAGE017
. The compactness of zero-center normalized instantaneous frequencies can be used to distinguish signals with highly dense and sparsely distributed instantaneous frequencies.
(7) Standard deviation of zero-center normalized non-weak signal instantaneous frequency absolute value:
Figure 889443DEST_PATH_IMAGE018
wherein the content of the first and second substances,
Figure 618365DEST_PATH_IMAGE019
，
Figure 697179DEST_PATH_IMAGE020
，
Figure 257473DEST_PATH_IMAGE021
。
Figure 29120DEST_PATH_IMAGE022
in order to be able to determine the signal rate,
Figure 979759DEST_PATH_IMAGE023
is the instantaneous frequency of the signal. The standard deviation of the zero-center normalized non-weak signal segment instantaneous frequency absolute value represents the absolute frequency information of the signal, and can be used for distinguishing a modulation mode with the normalized center instantaneous frequency absolute value as a constant and a modulation mode with absolute and direct frequency information.
Step 004, extracting high-order cumulant characteristics of each data sample, specifically including 7 characteristics of second-order cumulant, fourth-order cumulant and sixth-order cumulant, assuming that a received signal is received
Figure 862264DEST_PATH_IMAGE024
The expressions are respectively:
(1) second order cumulant:
Figure 27797DEST_PATH_IMAGE025
Figure 970346DEST_PATH_IMAGE026
(2) fourth order cumulant:
Figure 408280DEST_PATH_IMAGE027
Figure 828897DEST_PATH_IMAGE028
Figure 363784DEST_PATH_IMAGE029
(3) sixth-order cumulant:
Figure 477233DEST_PATH_IMAGE030
Figure 402464DEST_PATH_IMAGE031
the invention has the advantage that the high-order cumulant can not be influenced by the noise for the received signal mixed with the Gaussian noise. Other parameters in the signals generate different high-order cumulant information data after different order operations, and the signals can be classified and identified according to the principle. In the above-described expression, the expression,
Figure 626772DEST_PATH_IMAGE032
an estimated value representing a high-order accumulation amount,
Figure 999853DEST_PATH_IMAGE033
represents an estimate of the higher order moment,
Figure 284204DEST_PATH_IMAGE034
which represents the modulus of the received signal,
Figure 696731DEST_PATH_IMAGE035
representing the conjugate of the received signal. The high-order statistics comprise a high-order Moment (Moment) and a high-order Cumulant (Cumulant), wherein the high-order Cumulant is approximately obtained by the high-order Moment, and the high-order Cumulant is defined by the second-order Cumulant, the fourth-order Cumulant and the sixth-order Cumulant.
Step 005, extracting power spectrum characteristics of each data sample, specifically including a single-frequency component detection value of a primary spectrum, a double-frequency component detection value of a primary spectrum, a single-frequency component detection value of a secondary spectrum, and a waveform characteristic value, wherein the expressions are respectively:
(1) single-frequency component detection value of primary spectrum:
Figure 724730DEST_PATH_IMAGE036
wherein the content of the first and second substances,
Figure 968629DEST_PATH_IMAGE037
is the maximum amplitude of the power spectrum;
Figure 158302DEST_PATH_IMAGE038
the next largest amplitude. The single-frequency component detection value of the primary spectrum is used for judging the position of the maximum power spectrum value, and can be used for distinguishing M-ary Amplitude-Shift Keying (MASK), multi-ary frequency Shift Keying (MFSK) and multi-ary phase Shift Keying (MPSK).
(2) Detection value of dual-frequency component of primary spectrum:
Figure 58125DEST_PATH_IMAGE039
wherein the maximum amplitude value of the power spectrum corresponds to a frequency of
Figure 624236DEST_PATH_IMAGE040
The frequency corresponding to the sub-maximum is
Figure 738953DEST_PATH_IMAGE041
，
Figure 99527DEST_PATH_IMAGE042
Is the power spectrum of the signal. The detection value of the double-frequency component of the primary spectrum is used for describing whether two single-frequency components exist in the power spectrum, so that the modulation mode of the 2FSK is identified.
(3) Single-frequency component detection value of quadratic spectrum:
Figure 486646DEST_PATH_IMAGE043
the single-frequency component detection values of the quadratic spectrum can be used to distinguish 2PSK and QPSK signals.
(4) The waveform characteristic value:
Figure 856448DEST_PATH_IMAGE044
wherein the content of the first and second substances,
Figure 809360DEST_PATH_IMAGE045
respectively, the mean and variance of the signal power spectral envelope. The waveform characteristics reflect the degree of change in the signal power spectral envelope.
And 006, selecting sensitive characteristics according to the instantaneous characteristics, the high-order cumulant and the power spectrum characteristics obtained in the steps 003-005.
Referring to fig. 2, the 18 series characteristics of the instantaneous characteristics, the high-order cumulant and the power spectrum characteristics of each data sample are stacked in a row to form a characteristic matrix. Wherein, the line number is the sample number, the column number is the characteristic number 18, adopt the entropy weight method, obtain the weighted value of each characteristic.
The entropy weight method specifically comprises:
(1) for feature matrix
Figure 606415DEST_PATH_IMAGE046
And (6) carrying out normalization processing.
Figure 215251DEST_PATH_IMAGE047
Where m is the number of samples and n is the number of features 18 extracted from the samples.
(2) Calculating the proportion of the ith sample in the jth feature:
Figure 388743DEST_PATH_IMAGE048
(3) calculating the entropy value of the jth feature:
Figure 399425DEST_PATH_IMAGE049
in particular, if
Figure 678965DEST_PATH_IMAGE050
Then, then
Figure 775097DEST_PATH_IMAGE051
Is 0.
(4) Calculating a weight coefficient corresponding to each feature:
Figure 486701DEST_PATH_IMAGE052
after the weight corresponding to each feature is obtained, a weight threshold is determined, and the corresponding feature larger than the weight threshold is regarded as a sensitive feature. In the embodiment of the present invention, the sensitivity characteristic selection is performed with the maximum weight value and the maximum weight value as the threshold value, which are 0.1 time, 0.2 time, 0.3 time, 0.4 time, 0.5 time, 0.6 time, 0.7 time, 0.8 time, and 0.9 time, respectively.
And 007, marking a label on each sample data by taking the sensitive characteristic of each sample as the sample data, marking the same label on the underwater sound data samples with the same modulation mode, and marking different labels on the underwater sound data samples with different modulation modes to form a training set and a test set. In the embodiment of the invention, according to 8: 2 into training and test sets.
And step 008, taking the training set as the input of the support vector machine, selecting a Gaussian kernel function, training by using a cross validation strategy and a multi-class cross entropy function as a cost function, and storing the trained model. It is prior art to train the multi-class cross entropy function as the cost function, and it is not described here any more.
The Gaussian kernel function is:
Figure 351889DEST_PATH_IMAGE053
wherein the content of the first and second substances,
Figure 553063DEST_PATH_IMAGE054
representing original spatial samples
Figure 136491DEST_PATH_IMAGE055
To high dimensional space samples
Figure 386207DEST_PATH_IMAGE056
The Euclidean distance of (a) is,
Figure 371481DEST_PATH_IMAGE057
is a hyperparameter unique to the Gaussian kernel function, and
Figure 494289DEST_PATH_IMAGE057
greater than 0. Description of the kernel function: in most cases, the data is non-linear. Support vector machines employ kernel functions to map data into a high dimensional space so that samples are linearly separable within this space.
And step 009, verifying the recognition performance of the support vector machine by taking the test set as the input of the training model.
As shown in fig. 3, the recognition rates under 10 kinds of thresholds are compared, and the maximum weight value and the training model, which is 0.1 times the threshold corresponding to the highest recognition rate, are selected.
The following is a measure of performance for the recognition model with a weight maximum of 0.1 times as a threshold.
With reference to fig. 4, each row of the confusion matrix represents a true modulation class, each column represents a predicted modulation class, and the values on the diagonal are the correct number of predictions for the modulation class; taking a 2ASK underwater acoustic communication signal as an example, there are 1499 test samples, where the number of samples predicted to be correct is 1295, the number of samples predicted to be in the 4ASK modulation class is 179, the number of samples predicted to be in the 2PSK modulation class is 24, and the number of samples predicted to be in the QPSK modulation class is 1.
With reference to fig. 4 and table 1 below, the recall ratio R is the ratio of the number of correctly predicted samples to the total number of samples that the class should be correctly predicted, and the precision ratio P is the ratio of the number of correctly predicted samples to the total number of samples predicted by the class. F1 is based on the harmonic mean of recall and precision and is defined as:
Figure 565013DEST_PATH_IMAGE058
。
TABLE 1 simulation confusion matrix calculation results
Figure 618419DEST_PATH_IMAGE059
As can be seen from the verification result of the test set, the method has good identification effect on recall ratio and precision ratio. In practical application, the underwater acoustic communication data which is actually collected can be input into the model after feature extraction based on the trained recognition model, and the modulation mode is recognized.
In summary, the invention provides an underwater acoustic communication signal modulation identification method based on sensitive feature selection and a support vector machine, and the technology can be used for modulation identification in underwater acoustic communication. Under simulation conditions, modulation classification of 8 communication signals of 2ASK, 4ASK, 2FSK, 4FSK, 2PSK, QPSK, 16QAM, and DSSS can be achieved.
The invention provides a thought of an underwater acoustic communication signal modulation identification method based on sensitive feature selection and a support vector machine, and a plurality of methods and ways for specifically realizing the technical scheme are provided, and the methods and the ways are only preferred embodiments of the invention. It should be noted that, for those skilled in the art, without departing from the principle of the present invention, several improvements and modifications can be made, and these improvements and modifications should also be construed as the protection scope of the present invention. All the components not specified in the present embodiment can be realized by the prior art.

Claims (7)

1. An underwater acoustic communication signal modulation identification method based on feature selection and a support vector machine is characterized by comprising the following steps:
(1) extracting instantaneous characteristics, high-order cumulant and power spectrum characteristics of each sample from simulated or actually acquired underwater acoustic communication data samples to form series characteristics;
(2) calculating a weight coefficient of the series connection features by adopting an entropy weight method, determining a weight threshold value, and regarding the corresponding features of which the weight coefficients are greater than the weight threshold value as sensitive features;
(3) taking the sensitive characteristics of each sample as sample data, marking the same label on the underwater sound data sample with the same modulation mode, and marking different labels on the underwater sound data sample with different modulation modes to form a training set;
(4) training by taking a training set as the input of a support vector machine, adopting a Gaussian kernel function and taking a multi-class cross entropy function as a target function to obtain an identification model based on the support vector machine;
(5) and modulating and identifying the underwater acoustic communication data subjected to the feature extraction by using the trained identification model.
2. The feature selection and support vector machine based underwater acoustic communication signal modulation identification method according to claim 1, characterized in that the instantaneous feature of each sample in the step (1) comprises a zero-center normalized instantaneous amplitude spectrum density maximum value, a standard deviation of the instantaneous amplitude of the zero-center normalized non-weak signal segment, compactness of the zero-center normalized instantaneous amplitude, a standard deviation of the instantaneous phase nonlinear component of the zero-center non-weak signal segment, a standard deviation of the absolute value of the instantaneous phase nonlinear component of the zero-center non-weak signal segment, compactness of the zero-center normalized instantaneous frequency and a standard deviation of the absolute value of the instantaneous frequency of the zero-center normalized non-weak signal,
wherein the maximum value of the zero-center normalized instantaneous amplitude spectral density is:
Figure 746346DEST_PATH_IMAGE001
wherein N is the number of data samples,
Figure 227006DEST_PATH_IMAGE002
the instantaneous amplitude is normalized for the center of zero,
Figure 831032DEST_PATH_IMAGE003
is instantaneous amplitude, and
Figure 688129DEST_PATH_IMAGE004
，
Figure 382416DEST_PATH_IMAGE005
，
Figure 33977DEST_PATH_IMAGE006
(ii) a DFT is discrete Fourier transform;
the standard deviation of the zero-center normalized non-weak signal segment instantaneous amplitude is:
Figure 141610DEST_PATH_IMAGE007
wherein the content of the first and second substances,
Figure 536820DEST_PATH_IMAGE008
the amplitude judgment threshold is used for judging whether the signal is a weak signal segment or not, and the signal is a non-weak signal segment if the signal is larger than the threshold; c is the number of non-weak signal segments in all the sampled data;
Figure 85613DEST_PATH_IMAGE009
a non-linear component of zero-center instantaneous amplitude;
the compactness of the zero-center normalized instantaneous amplitude is:
Figure 986704DEST_PATH_IMAGE010
the standard deviation of the instantaneous phase nonlinear component of the zero-center non-weak signal segment is:
Figure 253737DEST_PATH_IMAGE011
wherein the content of the first and second substances,
Figure 452637DEST_PATH_IMAGE012
is the non-linear component of the instantaneous phase;
the standard deviation of the absolute value of the instantaneous phase nonlinear component of the zero-center non-weak signal segment is as follows:
Figure 855937DEST_PATH_IMAGE013
the compactness of the zero-center normalized instantaneous frequency is:
Figure 177197DEST_PATH_IMAGE014
wherein the content of the first and second substances,
Figure 931526DEST_PATH_IMAGE015
；
the standard deviation of the absolute value of the zero-center normalized non-weak signal instantaneous frequency is:
Figure 668538DEST_PATH_IMAGE016
wherein the content of the first and second substances,
Figure 191923DEST_PATH_IMAGE017
，
Figure 933352DEST_PATH_IMAGE018
in order to be able to determine the signal rate,
Figure 909398DEST_PATH_IMAGE019
is the instantaneous frequency of the signal.
3. The feature selection and support vector machine based underwater acoustic communication signal modulation identification method according to claim 1, characterized in that the high order cumulant of each sample in the step (1) includes a second order cumulant, a fourth order cumulant and a sixth order cumulant,
wherein the second order cumulant is:
Figure 450101DEST_PATH_IMAGE020
Figure 93572DEST_PATH_IMAGE021
the fourth order cumulant is:
Figure 491055DEST_PATH_IMAGE022
Figure 219977DEST_PATH_IMAGE023
Figure 298791DEST_PATH_IMAGE024
the sixth order cumulant is:
Figure 796769DEST_PATH_IMAGE025
Figure 115886DEST_PATH_IMAGE026
in the formula (I), the compound is shown in the specification,
Figure 332103DEST_PATH_IMAGE027
the moment estimate is represented as a function of time,
Figure 214609DEST_PATH_IMAGE028
which is indicative of the receipt of data,
Figure 567093DEST_PATH_IMAGE029
a modulus representing the received data is shown,
Figure 571958DEST_PATH_IMAGE030
representing the conjugate of the received data and N is the number of data samples.
4. The feature selection and support vector machine-based underwater acoustic communication signal modulation identification method according to claim 1, wherein the power spectrum feature of each sample in the step (1) comprises a single-frequency component detection value of a primary spectrum, a dual-frequency component detection value of a primary spectrum, a single-frequency component detection value of a secondary spectrum and a waveform feature value,
wherein, the single-frequency component detection value of the primary spectrum is:
Figure 9892DEST_PATH_IMAGE031
wherein the content of the first and second substances,
Figure 430509DEST_PATH_IMAGE032
is the maximum amplitude of the power spectrum;
Figure 903079DEST_PATH_IMAGE033
is the next largest amplitude;
the detection value of the dual-frequency component of the primary spectrum is as follows:
Figure 898471DEST_PATH_IMAGE034
wherein the content of the first and second substances,
Figure 823702DEST_PATH_IMAGE035
for the frequency corresponding to the maximum value of the amplitude of the power spectrum,
Figure 48010DEST_PATH_IMAGE036
is the frequency corresponding to the sub-maximum,
Figure 437403DEST_PATH_IMAGE037
is the power spectrum of the signal, and N is the number of data samples;
the single-frequency component detection value of the quadratic spectrum is as follows:
Figure 721754DEST_PATH_IMAGE038
the waveform eigenvalues are:
Figure 134281DEST_PATH_IMAGE039
wherein the content of the first and second substances,
Figure 896700DEST_PATH_IMAGE040
respectively, the mean and variance of the signal power spectral envelope.
5. The underwater acoustic communication signal modulation identification method based on feature selection and support vector machine according to claim 1, wherein the step (2) specifically comprises:
(21) for feature matrix
Figure 891332DEST_PATH_IMAGE041
And (3) carrying out normalization treatment:
Figure 346584DEST_PATH_IMAGE042
wherein m is the number of samples, and n is the number of features extracted from the samples;
(22) calculating the proportion of the ith sample in the jth feature:
Figure 246407DEST_PATH_IMAGE043
(23) calculating the entropy value of the jth feature:
Figure 812518DEST_PATH_IMAGE044
(24) calculating a weight coefficient corresponding to each feature:
Figure 910924DEST_PATH_IMAGE045
(25) and determining a weight threshold value, and taking the corresponding characteristic with the weight coefficient larger than the weight threshold value as a sensitive characteristic.
6. The method for modulating and identifying underwater acoustic communication signals based on feature selection and support vector machine according to claim 1, wherein the Gaussian kernel function in the step (4) is as follows:
Figure 537077DEST_PATH_IMAGE046
wherein the content of the first and second substances,
Figure 924196DEST_PATH_IMAGE047
representing original spatial samples
Figure 28418DEST_PATH_IMAGE048
To high dimensional space samples
Figure 496178DEST_PATH_IMAGE049
The Euclidean distance of (a) is,
Figure 293232DEST_PATH_IMAGE050
is a hyperparameter unique to the Gaussian kernel function, and
Figure 902068DEST_PATH_IMAGE050
greater than 0.
7. The feature selection and support vector machine-based underwater acoustic communication signal modulation identification method according to any one of claims 1 to 6, wherein the modulation modes of the underwater acoustic communication signal include 2ASK, 4ASK, 2FSK, 4FSK, 2PSK, QPSK, 16QAM and DSSS.
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