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CN111814703B - A joint feature extraction method for signals based on HB under non-reconstruction conditions - Google Patents

A joint feature extraction method for signals based on HB under non-reconstruction conditions Download PDF

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CN111814703B
CN111814703B CN202010671516.4A CN202010671516A CN111814703B CN 111814703 B CN111814703 B CN 111814703B CN 202010671516 A CN202010671516 A CN 202010671516A CN 111814703 B CN111814703 B CN 111814703B
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order cumulant
radiation source
signal
bispectrum
order
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CN111814703A (en
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李智
吴俊�
王宇阳
解建兰
李健
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Sichuan University
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Abstract

The invention belongs to the field of signal processing, provides an HB-based signal combined feature extraction method under a non-reconstruction condition aiming at the problem that a single feature has an identification result which is easy to drift, and is particularly used for processing the problem of radiation source signal classification and identification. The single feature is extracted as the identification feature, and sometimes the feature classification boundary is fuzzy, which may reduce the identification effect. The joint feature of high order cumulants combined with bispectrum is used to solve this problem. The high-order cumulant can well retain information such as amplitude, phase and the like, and the bispectrum is the lowest-order high-order spectrum and has the advantage of simple calculation. The radiation source signal is first generated, and the received signal is then compressively sampled by the MWC and its amplitude is normalized. And then calculating the three-six-order cumulant and the square eight-order cumulant, and extracting the characteristics of the high-order cumulant. And meanwhile, extracting the estimation characteristics of the bispectrum coefficients of the sampling matrix. And finally, transmitting the three different high-order cumulant features and the bispectrum coefficient estimation features into an SVM classifier for classification by using the three different high-order cumulant features and the bispectrum coefficient estimation features as joint features.

Description

一种非重构条件下基于HB的信号联合特征提取方法A Joint Feature Extraction Method of Signal Based on HB under Non-reconstruction Condition

技术领域technical field

本发明属于信号处理领域，涉及一种非重构条件下基于HB的信号联合特征提取方法，具体用于处理辐射源信号分类识别问题。The invention belongs to the field of signal processing, and relates to a signal joint feature extraction method based on HB under non-reconstruction conditions, which is specifically used for processing the problem of classification and identification of radiation source signals.

背景技术Background technique

特定辐射源识别根据其独特特征将单个发射器与其他发射器区分开，从而识别出不同的发射器。辐射源识别技术主要用于军事通信中。随着新技术的出现，例如认知无线电和自组织网络，它变得越来越重要。Specific radiation source identification identifies different emitters by distinguishing individual emitters from other emitters based on their unique characteristics. Radiation source identification technology is mainly used in military communications. It becomes increasingly important with the advent of new technologies, such as cognitive radios and self-organizing networks.

基于发射器的工作方式，辐射源识别可以对瞬态或稳态信号进行发射器识别。瞬态信号又称为开/关信号，所得的发射器特异性可用来提取特征。 要提取瞬态信号的特征，主要方法是通过检测噪声的起点和终点来提取瞬态信号。但是，瞬态信号的持续时间短且难以捕获。 它也容易受到复杂信道的干扰，并影响发射器的识别效果。稳态信号在整个信号的瞬态开始和结束之间传输。与瞬态信号相比，稳态信号的检测和采集更加简单。然而，由于稳态特征容易被破坏，使得稳态特征的提取变得困难。 对于稳态信号，研究了各种特征提取方案。 最常用的方法是基于时频分析算法，如短时傅里叶变换、小波等。除了这些方法，像累积量，双谱也被大量采用。Based on how the transmitter works, source identification enables transmitter identification for transient or steady-state signals. Transient signals are also known as on/off signals, and the resulting transmitter specificity can be used to extract features. To extract the characteristics of the transient signal, the main method is to extract the transient signal by detecting the start and end points of the noise. However, transient signals are short in duration and difficult to capture. It is also susceptible to interference from complex channels and affects the recognition effect of the transmitter. Steady-state signals are transmitted between the start and end of the transient across the signal. Compared with transient signals, the detection and acquisition of steady-state signals is simpler. However, since the steady state features are easily destroyed, the extraction of steady state features becomes difficult. For steady-state signals, various feature extraction schemes are investigated. The most commonly used method is based on time-frequency analysis algorithms, such as short-time Fourier transform, wavelet, etc. In addition to these methods, like cumulant, bispectral is also widely used.

传统的提取特征方式虽然能够有效的提取辐射源特征，但是作为单一特征有时会造成识别结果漂移，降低正确识别率。本发明提出一种基于高阶累积量和双谱系数估计的联合指纹特征（HB,Joint Fingerprint features based on Higher-order cumulantsand Bispectrum coefficient estimation）提取算法。它能解决单一特征存在识别结果易漂移的问题，提高辐射源识别稳定性。Although the traditional feature extraction method can effectively extract the radiation source features, as a single feature, sometimes the recognition result will drift and the correct recognition rate will be reduced. The invention proposes a joint fingerprint feature (HB, Joint Fingerprint features based on Higher-order cumulants and Bispectrum coefficient estimation) extraction algorithm based on higher-order cumulants and bispectrum coefficient estimation. It can solve the problem that the identification result of a single feature is easy to drift, and improve the stability of radiation source identification.

发明内容SUMMARY OF THE INVENTION

本发明针对单一特征存在识别结果易漂移的问题，提出一种多特征联合特征识别方法。Aiming at the problem that the recognition result of a single feature is easy to drift, the invention proposes a multi-feature joint feature recognition method.

本发明所用的技术方案如下：The technical scheme used in the present invention is as follows:

非重构条件下基于HB的信号联合特征提取，主要有以下几步：The signal joint feature extraction based on HB under non-reconstruction conditions mainly includes the following steps:

步骤1、生成辐射源信号；Step 1. Generate a radiation source signal;

步骤2、利用MWC对辐射源进行预处理；Step 2, using MWC to preprocess the radiation source;

步骤3、提取高阶累积量特征；Step 3. Extract high-order cumulant features;

步骤4、提取双谱系数估计特征；Step 4, extracting bispectral coefficient estimation features;

步骤5、使用支持向量机（SVM）对辐射源信号进行分类识别。Step 5. Use support vector machine (SVM) to classify and identify the radiation source signal.

有益效果：1）本发明的方法在有三个辐射源的情况下，与VMD_SF算法和EMD_EM算法对比，识别效果更好；2）随着待识别的辐射源数目增加，识别难度会越来越大，但是当5个辐射源在信噪比达到10dB时，识别率仍能达到90%。Beneficial effects: 1) In the case of three radiation sources, compared with VMD_SF algorithm and EMD_EM algorithm, the method of the present invention has better recognition effect; 2) With the increase of the number of radiation sources to be recognized, the recognition difficulty will become more and more difficult , but when the signal-to-noise ratio of five radiation sources reaches 10dB, the recognition rate can still reach 90%.

附图说明Description of drawings

图1是MWC系统结构图；Figure 1 is a structural diagram of the MWC system;

图2是MWC频谱搬移图；Fig. 2 is the MWC spectrum shift diagram;

图3是非重构条件下基于HB的信号联合特征提取算法流程图；Fig. 3 is the flow chart of the signal joint feature extraction algorithm based on HB under the condition of non-reconstruction;

图4是本发明的TSOC特征分布图；Fig. 4 is the TSOC characteristic distribution diagram of the present invention;

图5是本发明的SEOC特征分布图；Fig. 5 is the SEOC characteristic distribution figure of the present invention;

图6是本发明的双谱系数估计特征分布图；Fig. 6 is the bispectral coefficient estimation characteristic distribution diagram of the present invention;

图7是本发明的HB联合特征分布图；Fig. 7 is the HB joint feature distribution diagram of the present invention;

图8是本发明与VMD_SF和EMD_EM算法在高斯白噪声信道的识别率对比图；Fig. 8 is the identification rate contrast figure of the present invention and VMD_SF and EMD_EM algorithm in Gaussian white noise channel;

图9是本发明与VMD_SF和EMD_EM算法在衰落信道的识别率对比图；Fig. 9 is the identification rate contrast figure of the present invention and VMD_SF and EMD_EM algorithm in fading channel;

图10是本发明与VMD_SF和EMD_EM算法在4个辐射源下的识别率对比图；Fig. 10 is the identification rate contrast diagram of the present invention and VMD_SF and EMD_EM algorithm under 4 radiation sources;

图11是本发明与VMD_SF和EMD_EM算法在5个辐射源下的识别率对比图。FIG. 11 is a comparison chart of the recognition rate of the present invention and VMD_SF and EMD_EM algorithms under five radiation sources.

具体实施方式Detailed ways

1. 生成辐射源信号1. Generate the radiation source signal

在发射机中包含很多非线性器件，建立的系统模型主要考虑功率放大器的非线性为辐射源指纹产生的机理。建立泰勒级数模型，令

Figure 142498DEST_PATH_IMAGE001
为泰勒多项式的阶数，对于发射机
Figure 894554DEST_PATH_IMAGE002
的输出可表示为The transmitter contains many nonlinear devices, and the established system model mainly considers the nonlinearity of the power amplifier as the mechanism of the fingerprint of the radiation source. To build a Taylor series model, let
Figure 142498DEST_PATH_IMAGE001
is the order of the Taylor polynomial, for the transmitter
Figure 894554DEST_PATH_IMAGE002
The output can be expressed as

Figure 717016DEST_PATH_IMAGE003
（1）
Figure 717016DEST_PATH_IMAGE003
(1)

其中in

Figure 171000DEST_PATH_IMAGE004
（2）
Figure 171000DEST_PATH_IMAGE004
(2)

Figure 838742DEST_PATH_IMAGE005
是功率放大器的输入信号，其中
Figure 507621DEST_PATH_IMAGE006
为第
Figure 500984DEST_PATH_IMAGE007
个发射机在时间
Figure 724155DEST_PATH_IMAGE008
处的基带调制信号，
Figure 461167DEST_PATH_IMAGE009
是总的辐射源数目。
Figure 984552DEST_PATH_IMAGE010
为载波频率，
Figure 414397DEST_PATH_IMAGE011
为采样周期，
Figure 374131DEST_PATH_IMAGE012
是泰勒多项式的系数。
Figure 649255DEST_PATH_IMAGE013
表示辐射源功率放大器
Figure 292726DEST_PATH_IMAGE014
的输出信号。时间
Figure 627892DEST_PATH_IMAGE015
接收信号可以表示为
Figure 838742DEST_PATH_IMAGE005
is the input signal of the power amplifier, where
Figure 507621DEST_PATH_IMAGE006
for the first
Figure 500984DEST_PATH_IMAGE007
transmitters at time
Figure 724155DEST_PATH_IMAGE008
The baseband modulated signal at ,
Figure 461167DEST_PATH_IMAGE009
is the total number of radiation sources.
Figure 984552DEST_PATH_IMAGE010
is the carrier frequency,
Figure 414397DEST_PATH_IMAGE011
is the sampling period,
Figure 374131DEST_PATH_IMAGE012
are the coefficients of the Taylor polynomial.
Figure 649255DEST_PATH_IMAGE013
Represents radiation source power amplifier
Figure 292726DEST_PATH_IMAGE014
output signal. time
Figure 627892DEST_PATH_IMAGE015
The received signal can be expressed as

Figure 825655DEST_PATH_IMAGE016
（3）
Figure 825655DEST_PATH_IMAGE016
(3)

其中

Figure 904470DEST_PATH_IMAGE017
是从辐射源
Figure 402447DEST_PATH_IMAGE018
到接收机的信道衰落系数，
Figure 174094DEST_PATH_IMAGE019
是加性噪声。 把式（1）代入式（3）得到信号
Figure 593574DEST_PATH_IMAGE020
为in
Figure 904470DEST_PATH_IMAGE017
from the radiation source
Figure 402447DEST_PATH_IMAGE018
the channel fading coefficient to the receiver,
Figure 174094DEST_PATH_IMAGE019
is additive noise. Substitute equation (1) into equation (3) to get the signal
Figure 593574DEST_PATH_IMAGE020
for

Figure 476079DEST_PATH_IMAGE021
（4）
Figure 476079DEST_PATH_IMAGE021
(4)

在接收端接收信号

Figure 828563DEST_PATH_IMAGE020
，从
Figure 771112DEST_PATH_IMAGE020
中提取特征来识别不同辐射源。Receive the signal at the receiver
Figure 828563DEST_PATH_IMAGE020
,from
Figure 771112DEST_PATH_IMAGE020
feature extraction to identify different radiation sources.

2.辐射源信号预处理2. Radiation source signal preprocessing

在信号预处理部分，我们用到调制宽带转换器（MWC），其采样系统的原理框图如图1所示。输入信号

Figure 677888DEST_PATH_IMAGE022
被分成m路输入MWC采样系统，其中每一个欠采样通道分别由伪随机混频、低通滤波（LPF）和低速 ADC 组成，输出结果为原信号的压缩采样序列。图2为MWC各个通道的频谱搬移图，经过频谱切割之后整个频带被分为L个频谱，各子频带相互搬移混合之后包含了这个通道中信号的全局信息。In the signal preprocessing part, we use a Modulated Wideband Converter (MWC), and the block diagram of its sampling system is shown in Figure 1. input signal
Figure 677888DEST_PATH_IMAGE022
It is divided into m-channel input MWC sampling system, in which each under-sampling channel is composed of pseudo-random mixing, low-pass filtering (LPF) and low-speed ADC, and the output result is the compressed sampling sequence of the original signal. Figure 2 is the spectrum transfer diagram of each channel of MWC. After spectrum cutting, the entire frequency band is divided into L spectrums, and each sub-band is transferred and mixed with each other to contain the global information of the signal in this channel.

接收信号

Figure 98505DEST_PATH_IMAGE023
经过MWC压缩采样之后得到一个
Figure 571074DEST_PATH_IMAGE024
维矩阵，记为
Figure 684524DEST_PATH_IMAGE025
receive signal
Figure 98505DEST_PATH_IMAGE023
After MWC compression sampling, a
Figure 571074DEST_PATH_IMAGE024
dimension matrix, denoted as
Figure 684524DEST_PATH_IMAGE025

Figure 826399DEST_PATH_IMAGE026
(5)
Figure 826399DEST_PATH_IMAGE026
(5)

其中

Figure 50707DEST_PATH_IMAGE027
是
Figure 112204DEST_PATH_IMAGE028
维列向量。避免在提取特征时由于强度敏感、幅度敏感性造成影响，采用包络对齐方法实现样本数据的平移补偿，如下式进行幅度归一化处理in
Figure 50707DEST_PATH_IMAGE027
Yes
Figure 112204DEST_PATH_IMAGE028
Dimension column vector. To avoid the influence of intensity sensitivity and amplitude sensitivity when extracting features, the envelope alignment method is used to realize the translation compensation of the sample data, and the amplitude is normalized as follows:

Figure 396555DEST_PATH_IMAGE029
(6)
Figure 396555DEST_PATH_IMAGE029
(6)

双谱是被广泛应用于高阶统计分析中的特征，信号三阶累积量的二维离散傅里叶变换（DFT, Discrete Fourier transform)就是双谱。对于确定的离散时间信号

Figure 809081DEST_PATH_IMAGE030
，它的三阶累积量为Bispectrum is a feature that is widely used in high-order statistical analysis. The two-dimensional discrete Fourier transform (DFT, Discrete Fourier transform) of the third-order cumulant of the signal is bispectrum. For a deterministic discrete-time signal
Figure 809081DEST_PATH_IMAGE030
, its third-order cumulant is

Figure 305922DEST_PATH_IMAGE031
(7)
Figure 305922DEST_PATH_IMAGE031
(7)

其中

Figure 487504DEST_PATH_IMAGE032
是
Figure 677177DEST_PATH_IMAGE033
的共轭。in
Figure 487504DEST_PATH_IMAGE032
Yes
Figure 677177DEST_PATH_IMAGE033
the conjugate.

3.提取高阶累积量特征3. Extract high-order cumulant features

提取不同的高阶累积量（HOC，Higher-Order Cumulants）特征，包括三-六阶累积量 （TSOC, Tri-Sixth-Order Cumulant）、方形八阶累积量（SEOC, Square Eight-OrderCumulant）。经过MWC压缩采样获得了接收信号的CSD。对于

Figure 577000DEST_PATH_IMAGE034
，信号的时变矩定义为Extract different higher-order cumulants (HOC, Higher-Order Cumulants) features, including third-sixth-order cumulants (TSOC, Tri-Sixth-Order Cumulant), square eight-order cumulants (SEOC, Square Eight-Order Cumulant). The CSD of the received signal is obtained through MWC compression sampling. for
Figure 577000DEST_PATH_IMAGE034
, the time-varying moment of the signal is defined as

Figure 611952DEST_PATH_IMAGE035
(8)
Figure 611952DEST_PATH_IMAGE035
(8)

其中（8）中

Figure 913621DEST_PATH_IMAGE036
称为信号
Figure 274195DEST_PATH_IMAGE037
的滞后积,
Figure 661314DEST_PATH_IMAGE038
是
Figure 499957DEST_PATH_IMAGE039
的共轭，
Figure 390552DEST_PATH_IMAGE040
是共轭总数。Among them (8)
Figure 913621DEST_PATH_IMAGE036
signal
Figure 274195DEST_PATH_IMAGE037
The lag product of ,
Figure 661314DEST_PATH_IMAGE038
Yes
Figure 499957DEST_PATH_IMAGE039
the conjugate of ,
Figure 390552DEST_PATH_IMAGE040
is the total number of conjugates.

索引集

Figure 187607DEST_PATH_IMAGE041
的不同分区命名为
Figure 796443DEST_PATH_IMAGE042
,
Figure 969935DEST_PATH_IMAGE043
是分区中元素的数量，并且属于分区的索引集用
Figure 698726DEST_PATH_IMAGE044
表示。根据矩-累积量（MC, Moment-cumulative）转换公式，
Figure 666682DEST_PATH_IMAGE045
的
Figure 762814DEST_PATH_IMAGE046
阶累积量表示为index set
Figure 187607DEST_PATH_IMAGE041
different partitions named
Figure 796443DEST_PATH_IMAGE042
,
Figure 969935DEST_PATH_IMAGE043
is the number of elements in the partition and belongs to the index set of the partition with
Figure 698726DEST_PATH_IMAGE044
express. According to the moment-cumulative (MC, Moment-cumulative) conversion formula,
Figure 666682DEST_PATH_IMAGE045
of
Figure 762814DEST_PATH_IMAGE046
The order cumulant is expressed as

Figure 474418DEST_PATH_IMAGE047
(9)
Figure 474418DEST_PATH_IMAGE047
(9)

因此我们可以得到如下的矩-累积量之间的关系So we can get the following moment-cumulant relationship

Figure 808447DEST_PATH_IMAGE048
(10)
Figure 808447DEST_PATH_IMAGE048
(10)

可以分别从上述参数中提取TSOC、SEOC，TSOC 特征

Figure 947305DEST_PATH_IMAGE049
可以表示为TSOC, SEOC, TSOC features can be extracted from the above parameters respectively
Figure 947305DEST_PATH_IMAGE049
It can be expressed as

Figure 530733DEST_PATH_IMAGE050
(11)
Figure 530733DEST_PATH_IMAGE050
(11)

SEOC 特征

Figure 780448DEST_PATH_IMAGE051
可以表示为SEOC features
Figure 780448DEST_PATH_IMAGE051
It can be expressed as

Figure 234564DEST_PATH_IMAGE052
(12)
Figure 234564DEST_PATH_IMAGE052
(12)

如上述公式提取TSOC和SEOC作为两个高阶累积量特征。TSOC and SEOC are extracted as two higher-order cumulant features as above formula.

图4和图5分别画出了三个具有不同泰勒系数辐射源个体的TSOC特征、SEOC特征的对比图，其中辐射源1的泰勒系数为

Figure 544322DEST_PATH_IMAGE053
，辐射源2的泰勒系数为
Figure 615046DEST_PATH_IMAGE054
，辐射源3的泰勒系数为
Figure 668453DEST_PATH_IMAGE055
，基带调制方式都为8QAM。图4为TSOC特征分布图，图中横轴表示辐射源的信号点数，纵轴表示TSOC特征值。我们可以看出，三个辐射源信号能够大致分类识别，但是区分边界有混淆，如果受到外界干扰，会导致识别率下降。以TSOC单一特征作为分类判别依据不利于辐射源信号分类。图5为SEOC特征分布图，图中横轴表示辐射源的信号点数，纵轴表示SEOC特征值。图中，辐射源信号1的SEOC特征值平均值为11.4，辐射源信号2的SEOC特征值平均值为10.9，辐射源信号3的SEOC特征值平均值为12.0。三种信号的SEOC特征值混淆比较严重，但作为联合特征其中之一依然可行，若单独使用这个特征分类识别，将造成结果严重失真。Figures 4 and 5 show the comparison of TSOC characteristics and SEOC characteristics of three radiation sources with different Taylor coefficients, where the Taylor coefficient of radiation source 1 is
Figure 544322DEST_PATH_IMAGE053
, the Taylor coefficient of radiation source 2 is
Figure 615046DEST_PATH_IMAGE054
, the Taylor coefficient of radiation source 3 is
Figure 668453DEST_PATH_IMAGE055
, the baseband modulation mode is 8QAM. FIG. 4 is a TSOC characteristic distribution diagram, in which the horizontal axis represents the number of signal points of the radiation source, and the vertical axis represents the TSOC characteristic value. We can see that the three radiation source signals can be roughly classified and recognized, but the distinction boundary is confused. If it is disturbed by the outside world, the recognition rate will drop. Taking the single feature of TSOC as the classification criterion is not conducive to the classification of radiation source signals. Fig. 5 is a distribution diagram of SEOC characteristics, the horizontal axis represents the number of signal points of the radiation source, and the vertical axis represents the SEOC characteristic value. In the figure, the average value of the SEOC characteristic value of the radiation source signal 1 is 11.4, the average value of the SEOC characteristic value of the radiation source signal 2 is 10.9, and the average value of the SEOC characteristic value of the radiation source signal 3 is 12.0. The SEOC eigenvalues of the three signals are seriously confused, but it is still feasible as one of the joint features. If this feature is used alone for classification and identification, the results will be seriously distorted.

4.提取双谱系数估计特征4. Extract bispectral coefficient estimation features

公式(7)已经给出了离散时间信号

Figure 508233DEST_PATH_IMAGE056
的三阶累积量
Figure 457734DEST_PATH_IMAGE057
计算公式，故
Figure 750176DEST_PATH_IMAGE058
的双谱
Figure 607273DEST_PATH_IMAGE059
为Equation (7) already gives the discrete-time signal
Figure 508233DEST_PATH_IMAGE056
The third-order cumulant of
Figure 457734DEST_PATH_IMAGE057
calculation formula, so
Figure 750176DEST_PATH_IMAGE058
bispectrum
Figure 607273DEST_PATH_IMAGE059
for

Figure 301560DEST_PATH_IMAGE060
(13)
Figure 301560DEST_PATH_IMAGE060
(13)

双谱是将一个频率用其他两个频率表示，本发明采用直接估计法，对

Figure 172695DEST_PATH_IMAGE061
进行双谱估计。将采样数据
Figure 218011DEST_PATH_IMAGE062
分为
Figure 613220DEST_PATH_IMAGE063
段，每段包含
Figure 162013DEST_PATH_IMAGE064
个数据，相邻两端数据之间可以有重叠，为了方便描述记为
Figure 718897DEST_PATH_IMAGE065
。求每段数据的DFT系数Bispectrum is to represent one frequency with other two frequencies, the present invention adopts the direct estimation method,
Figure 172695DEST_PATH_IMAGE061
Perform bispectral estimation. will sample data
Figure 218011DEST_PATH_IMAGE062
divided into
Figure 613220DEST_PATH_IMAGE063
segments, each containing
Figure 162013DEST_PATH_IMAGE064
There can be overlap between the data at the adjacent two ends. For the convenience of description, it is recorded as
Figure 718897DEST_PATH_IMAGE065
. Find the DFT coefficients of each piece of data

Figure 985930DEST_PATH_IMAGE066
(14)
Figure 985930DEST_PATH_IMAGE066
(14)

其中

Figure 184830DEST_PATH_IMAGE067
，
Figure 588130DEST_PATH_IMAGE068
。设
Figure 847073DEST_PATH_IMAGE069
为采样率，计算每个DFT系数的三重相关，得到相关序列
Figure 70244DEST_PATH_IMAGE070
in
Figure 184830DEST_PATH_IMAGE067
,
Figure 588130DEST_PATH_IMAGE068
. Assume
Figure 847073DEST_PATH_IMAGE069
is the sampling rate, calculate the triple correlation of each DFT coefficient, and get the correlation sequence
Figure 70244DEST_PATH_IMAGE070

Figure 807256DEST_PATH_IMAGE071
(15)
Figure 807256DEST_PATH_IMAGE071
(15)

其中

Figure 330641DEST_PATH_IMAGE072
表示第
Figure 760485DEST_PATH_IMAGE073
段数据的三重相关
Figure 205373DEST_PATH_IMAGE074
，
Figure 746076DEST_PATH_IMAGE075
。样本数据的双谱系数估计为in
Figure 330641DEST_PATH_IMAGE072
means the first
Figure 760485DEST_PATH_IMAGE073
Triple Correlation of Segment Data
Figure 205373DEST_PATH_IMAGE074
,
Figure 746076DEST_PATH_IMAGE075
. The bispectral coefficients of the sample data are estimated as

Figure 389547DEST_PATH_IMAGE076
(16)
Figure 389547DEST_PATH_IMAGE076
(16)

其中

Figure 724713DEST_PATH_IMAGE077
。in
Figure 724713DEST_PATH_IMAGE077
.

图6给出了双谱系数估计特征分布情况，图中横轴表示辐射源的信号点数，纵轴表示双谱系数估计特征值。我们可以看出，辐射源信号1和其他两种信号能有效区分，但依然避免不了辐射源信号2和辐射源信号3的边界混淆。图7为HB联合特征分布图，该图为表示三维特征，三条坐标轴分别表示TSOC特征、SEOC特征和双谱系数估计特征。我们能清晰地看出，当三个特征组成一联合三维特征是时，能够将不同辐射源个体完全区分开来。Fig. 6 shows the characteristic distribution of bispectral coefficient estimation. In the figure, the horizontal axis represents the number of signal points of the radiation source, and the vertical axis represents the bispectral coefficient estimation characteristic value. We can see that the radiation source signal 1 and the other two signals can be effectively distinguished, but the boundary confusion between the radiation source signal 2 and the radiation source signal 3 cannot be avoided. Fig. 7 is a distribution diagram of the HB joint feature, which represents a three-dimensional feature, and the three coordinate axes represent the TSOC feature, the SEOC feature, and the bispectral coefficient estimation feature, respectively. We can clearly see that when the three features form a joint three-dimensional feature, the individual radiation sources can be completely distinguished.

5.使用支持向量机（SVM）对辐射源信号进行分类识别5. Use support vector machine (SVM) to classify and identify radiation source signals

支撑向量机是一种用于二分类问题的监督学习分类器。训练集

Figure 171744DEST_PATH_IMAGE078
，
Figure 250558DEST_PATH_IMAGE079
是训练向量，
Figure 748536DEST_PATH_IMAGE080
是标签的类。我们考虑最简单的情况，正负标签数据可以用简单超平面
Figure 254603DEST_PATH_IMAGE081
来分离，SVM is a supervised learning classifier for binary classification problems. Training set
Figure 171744DEST_PATH_IMAGE078
,
Figure 250558DEST_PATH_IMAGE079
is the training vector,
Figure 748536DEST_PATH_IMAGE080
is the class of the label. We consider the simplest case, the positive and negative label data can use a simple hyperplane
Figure 254603DEST_PATH_IMAGE081
to separate,

Figure 470821DEST_PATH_IMAGE082
(17)
Figure 470821DEST_PATH_IMAGE082
(17)

其中，

Figure 822168DEST_PATH_IMAGE083
是超平面的法向量；
Figure 174652DEST_PATH_IMAGE084
是原点到超平面的垂直距离。支撑向量机的目的是优化超平面，使其边缘
Figure 117200DEST_PATH_IMAGE085
达到最大（
Figure 555135DEST_PATH_IMAGE086
表示正点到超平面的最近距离，
Figure 444593DEST_PATH_IMAGE087
表示负点到超平面的最近距离）。以此找出的超平面作为不同类别数据的分离边界。对于类数大于2的情况，一般来说，多分类问题可以通过将其简化为几个二分类问题来处理。in,
Figure 822168DEST_PATH_IMAGE083
is the normal vector of the hyperplane;
Figure 174652DEST_PATH_IMAGE084
is the vertical distance from the origin to the hyperplane. The purpose of the SVM is to optimize the hyperplane so that its edges
Figure 117200DEST_PATH_IMAGE085
to reach maximum(
Figure 555135DEST_PATH_IMAGE086
represents the closest distance from the punctuation point to the hyperplane,
Figure 444593DEST_PATH_IMAGE087
represents the closest distance from the negative point to the hyperplane). The hyperplane found in this way is used as the separation boundary of different categories of data. For the case where the number of classes is greater than 2, in general, the multi-classification problem can be handled by reducing it to several binary classification problems.

使用SVM对图7给出的联合特征进行识别，得到识别结果。图8为本发明与VMD_SF和EMD_EM算法在3类辐射源信号的情况下经过加性高斯白噪声信道的识别率对比图。从图中可以看出，本发明在各SNR时的识别正确率都高于另外两种算法，在SNR=-5db时，本发明的正确识别率为90%，识别率比VMD_SF高20%，比EMD_EM高21%。在低SNR下，基于HB的识别算法在辐射源识别领域中识别效果优于其他两种算法。Use SVM to identify the joint features given in Figure 7, and get the identification result. FIG. 8 is a comparison diagram of the recognition rate of the present invention and the VMD_SF and EMD_EM algorithms through the additive white Gaussian noise channel in the case of three types of radiation source signals. As can be seen from the figure, the recognition accuracy rate of the present invention at each SNR is higher than that of the other two algorithms. When SNR=-5db, the correct recognition rate of the present invention is 90%, and the recognition rate is 20% higher than VMD_SF. 21% higher than EMD_EM. Under low SNR, the identification algorithm based on HB is better than the other two algorithms in the field of radiation source identification.

图9是本发明与VMD_SF和EMD_EM算法在3类辐射源信号的情况下经过衰落信道的识别率对比图，对比于图8，在衰落信道中三种算法的识别率都下降了，本发明的识别率在SNR>8db后能达到90%以上，VMD_SF和EMD_EM算法在SNR=20db时识别率分别是81%、73%，由此可以看出本发明在衰落信道下依然能够成功识别辐射源个体。FIG. 9 is a comparison diagram of the recognition rates of the present invention and VMD_SF and EMD_EM algorithms through a fading channel in the case of three types of radiation source signals. Compared with FIG. The recognition rate can reach more than 90% after SNR>8db, and the recognition rates of VMD_SF and EMD_EM algorithms are 81% and 73% respectively when SNR=20db. It can be seen that the present invention can still successfully identify individual radiation sources under fading channels. .

图10为本发明与VMD_SF和EMD_EM算法在4类辐射源信号的情况下经过加性高斯白噪声信道的识别性能图。图11表示在5类辐射源信号的情况下经过加性高斯白噪声信道的识别性能图。从图中可以看出随着辐射源数目增加，三个算法的识别率都有所降低，但是与其它两种算法相比，本发明的识别率始终最高。FIG. 10 is a graph showing the identification performance of the present invention and the VMD_SF and EMD_EM algorithms through the additive white Gaussian noise channel in the case of four types of radiation source signals. FIG. 11 shows a graph of the identification performance through an additive white Gaussian noise channel in the case of a 5-type radiation source signal. It can be seen from the figure that as the number of radiation sources increases, the recognition rates of the three algorithms all decrease, but compared with the other two algorithms, the recognition rate of the present invention is always the highest.

Claims (3)

1. A signal joint feature extraction method based on HB under the non-reconstruction condition is characterized by comprising the following steps:
step 1, generating a radiation source signal;
step 2, preprocessing the radiation source signal;
step 3, extracting high-order cumulant features, wherein the formula for extracting the high-order cumulant is
Figure DEST_PATH_IMAGE001
，
And obtaining the relation between the moment and the cumulant through the formula as
Figure DEST_PATH_IMAGE002
，
Next, the three-Sixth Order Cumulant (TSOC, Tri-six-Order Cumulant) and the Square Eight Order Cumulant (SEOC, Square elevation-Order Cumulant) are extracted as characteristics, wherein
Figure DEST_PATH_IMAGE003
，
Figure DEST_PATH_IMAGE004
；
Step 4, extracting estimation characteristics of bispectrum coefficients, firstly sampling data
Figure DEST_PATH_IMAGE005
Segmentation, as
Figure DEST_PATH_IMAGE006
，
The DFT coefficients for each piece of data are then found,
Figure DEST_PATH_IMAGE007
，
then, according to the triple correlation of each DFT coefficient, a correlation sequence is obtained,
Figure DEST_PATH_IMAGE008
，
finally, the estimation characteristics of the bispectrum coefficient are obtained,
Figure DEST_PATH_IMAGE009
；
and 5, using a Support Vector Machine (SVM) and adopting a combined characteristic consisting of three-six-order cumulant, square eight-order cumulant and double-spectrum coefficient as input to classify and identify the radiation source signals.
2. The method according to claim 1, wherein the HB-based signal joint feature extraction method under the non-reconstruction condition is characterized in that: step 1, modulating QAM signals in the process of generating signals
Figure DEST_PATH_IMAGE010
Performing Taylor nonlinear processing, and adding fading coefficient
Figure DEST_PATH_IMAGE011
And noise
Figure DEST_PATH_IMAGE012
Generating a source signal, is
Figure DEST_PATH_IMAGE013
And is and
Figure DEST_PATH_IMAGE014
。
3. the method according to claim 1, wherein the HB-based signal joint feature extraction method under the non-reconstruction condition is characterized in that: receiving signals in step 2
Figure 966900DEST_PATH_IMAGE013
After MWC compression sampling, one is obtained
Figure DEST_PATH_IMAGE015
Dimension matrix, denoted as
Figure DEST_PATH_IMAGE016
And is made of
Figure DEST_PATH_IMAGE017
Will be
Figure 946357DEST_PATH_IMAGE016
The amplitude is obtained after the normalization processing of the amplitude is carried out,
Figure DEST_PATH_IMAGE018
。
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