CN107147599A - A kind of figure characteristic of field method for auto constructing for Modulation Recognition of Communication Signal - Google Patents
A kind of figure characteristic of field method for auto constructing for Modulation Recognition of Communication Signal Download PDFInfo
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Abstract
The invention discloses a kind of figure characteristic of field method for auto constructing for Modulation Recognition of Communication Signal, using the Cyclic Spectrum of signal of communication, the automatic figure characteristic of field for building signal of communication is realized in the case where any computational complexity will not be caused.The present invention extracts adjacency matrix from circulation spectrogram domain representation first, and count the stability characteristic (quality) of adjacency matrix entry, the KL divergences of these entries are calculated on the basis of statistical property is stablized, the modulation signature of training signal finally is set up according to the average of adjacency matrix entry, it is achieved thereby that setting up figure domain modulation signature model automatically.Compared with prior art, inappropriate training characteristics sequence will not artificially be chosen, it is ensured that AMCGThe robustness and accuracy of algorithm;The figure characteristic of field sequence of use is based on AMCGIt can keep constant in the whole assorting process of algorithm, and it can set up and prestore automatically in memory, will not cause any computational complexity.
Description
Technical field
The invention belongs to signal processing technology field, more specifically, it is related to a kind of for Modulation Recognition of Communication Signal
Figure characteristic of field method for auto constructing.
Background technology
Automatic Modulation is classified (Automatic Modulation Classification, abbreviation AMC), also referred to as communication letter
Number Modulation Identification can recognize the modulation type for receiving signal in the case of little or no priori, and be widely used in
Many military and civilian communications fields.
Existing AMC is built upon on the basis of signal statistics, the mould of feature based (Feature-Based, abbreviation FB)
Formula recognizes (Pattern Recognition, abbreviation PR) method and based on likelihood function (Likelihood-Based
Influence, abbreviation LB) decision theory recognition method be required for system to provide higher operational capability, thus be difficult to use in
Some requirement of real-time are higher and the limited particular application of system resource.Existing communication signal modulate method is in processing
Poor robustness in performance severe exacerbation during the processing of actual wireless Modulation Recognition of Communication Signal, practical engineering application, and for logical
Believe the Modulation Identification of signal, there is no the theoretical system and method for complete set.
Automatic Modulation classification (Graph-based Automatic Modulation based on figure domain
Classification abbreviations AMCG) AMC is introduced into graphic field for the first time, and have been realized in than existing PR and based on LB's
The more excellent performance of decision theory algorithm.The Modulation Recognition of Communication Signal method utilizes the Cyclic Spectrum of modulated signal, according to circulation frequency
Rate is configured to the weighting directed loop in graphic field, and the nonzero term of its manually recorded adjacency matrix minor diagonal, and these are non-
The line index of zero is built as effective characteristic parameters.However, in AMCGIn whole figure characteristic of field build be by manually entering
Capable, and calculate cumbersome.Characteristic sequence is selected if inappropriate as figure characteristic of field, it will usually caused unsatisfactory
Performance.This is accomplished by a kind of figure characteristic of field method for auto constructing for Modulation Recognition of Communication Signal, not only whole figure characteristic of field
Building process avoids artificial participation, and ensures AMCGRobustness.
The content of the invention
It is an object of the invention to overcome the deficiencies in the prior art, a kind of figure domain for Modulation Recognition of Communication Signal is proposed
Feature method for auto constructing, it is artificial constructed to avoid, select inappropriate characteristic sequence to be used as figure characteristic of field, it is ensured that Modulation Identification
Robustness and accuracy, meanwhile, reduce computational complexity.
For achieving the above object, the present invention is used for the figure characteristic of field method for auto constructing of Modulation Recognition of Communication Signal,
It is characterised in that it includes following steps:
(1) adjacency matrix of kth class modulation type signal, is obtainedThe set of matrices that element is constituted on minor diagonalWherein:
Wherein, P is cycle frequency number, αpFor cycle frequency (p=1,2 ..., P);M is test number (TN), and m represents the m times examination
Test (m=1,2 ..., M);It is adjacency matrixElement on the minor diagonal being right against directly over leading diagonal, its
Middle q=1,2 ..., Q, Q are the element numbers in minor diagonal;It is by matrixIn q arrange the sub- square of M × 1 to be formed
Battle array;
(2), calculating matrixIn q row be submatrixThe probability of middle element non-zero
Wherein,For submatrixThe quantity of middle element non-zero, q=1,2 ..., Q;If probabilityThen
From matrixMiddle this row of removal are submatrixObtain matrix
Wherein, τ is the probability threshold value of setting, is set as the case may be;Representing matrixIn the row that carry over
Vector, subscript rl Represent the corresponding adjacency matrix of the column vector(m ∈ 1,2 ..., M }) secondary diagonal
The line index of element on line;It is the cycle frequency α of kth class modulation type signalpThe row that corresponding adjacency matrix is carried over
The number of vector,
If adjacency matrixMiddle column vector is less than τ simultaneously for the probability of non-zero, then corresponding matrixIt is changed into sky square
Battle array, and remove, obtain the corresponding V of non-zero adjacency matrixkIndividual cycle frequency, and correspondingly kth class modulation type signal is represented
ForVk≤ P, is usedInstead ofIn αp, then construct a matrix stack
Wherein,
Due toSubscript rl,Represent adjacency matrix(m ∈ { 1,2 ..., M }) it is time diagonal
The line index of element on line, for kth class modulation type signal, extracts matrix stackThe subscript of middle element, is produced stable
Line index sequenceWherein,Correspond to the cycle frequency of kth class modulated signal
Stable line index sequence, v=1,2 ..., Vk, VkTo stablize the length of line index sequence;
For modulation type collectionWhereinRepresent kth kind modulation type, k=1,2 ...,
K, passes through set of rows index sequence(k=1,2 ..., K) collectively constitute one group of stable line index sequenceI.e.And be expressed as again forWherein, line index sequenceIn h-th son
SequenceIt is to stablize line index sequenceCombination, they correspond to identical cycle frequencyT=1,2 ..., Th, ThFor subsequenceLength, H be line index sequenceThe quantity of middle subsequence;
(3), kth class modulation type signal is in cycle frequencyLine index is on corresponding adjacency matrix minor diagonal
KL divergences at position are:
Wherein,For stochastic variable absolute valueProbability density function,For stochastic variable absolute valueProbability density function, k be current modulation type, kiAll it is modulated signal Candidate Set with kThe rope of middle modulation type
Draw, ki∈ { 1,2 ..., K }, k ∈ { 1,2 ..., K }, and ki≠k;
(4), whenWhen, stable line index sequenceIt is alsoSubset, for kth class modulated signal correspondence
Adjacency matrix minor diagonal on line index be that KL divergences at l positions areIfThen record line indexAnd its average of corresponding elementWherein, ζ is KL divergence threshold values;
(5), according to the absolute value of the average of the line index corresponding element of recordDropped using them
The new sequence of sequence array structureWherein, If
It is empty sequence, then deletes, for kth class modulation type, new sequence sets is expressed asWherein
(6), for kth class modulation type, using corresponding to line index sequenceMean absolute value sequenceTo produce the characteristic sequence of training signal;
Check one by oneIfBlock sequenceIn
Its line index corresponds toElement afterwards;Wherein, ξ1And ξ2It is default threshold value, can be generally respectively set to 0.04 He
0.6, Δ is the quantized interval used in figure domain mapping;
IfIn all entries condition is not satisfied, then accordinglyAlso it is removed, kth class may finally be obtained
The characteristic sequence collection of modulation type training signalAnd it is used as figure characteristic of field, its corresponding cycle frequency
Collection is combined into
The object of the present invention is achieved like this.
The present invention is used for the figure characteristic of field method for auto constructing of Modulation Recognition of Communication Signal, utilizes the circulation of signal of communication
Spectrum, the automatic figure characteristic of field for building signal of communication is realized in the case where that will not cause any computational complexity.It is of the invention first
Adjacency matrix is first extracted from circulation spectrogram domain representation, and counts the stability characteristic (quality) of adjacency matrix entry, it is special in stable statistics
Property on the basis of calculate the KL divergences of these entries, the last average according to adjacency matrix entry sets up the modulation of training signal
Feature, it is achieved thereby that setting up figure domain modulation signature model automatically.Compared with prior art, will not artificially it choose incorrect
Training characteristics sequence, it is ensured that AMCGThe robustness and accuracy of algorithm, it is possible to ignore because training signal transmits symbol
The inconsistency of the modulation signature sequence of more modulation type caused by randomness;The figure characteristic of field sequence of use based on
AMCGIt can keep constant in the whole assorting process of algorithm, and it can set up and prestore automatically in memory,
Any computational complexity will not be caused.
Brief description of the drawings
Fig. 1 is signal of communication figure domain mapping step schematic diagram;
Fig. 2 is figure domain mapping and transition diagram based on bpsk signal Cyclic Spectrum;
Fig. 3 is training signal figure domain line index feature locations schematic diagram.
Embodiment
The embodiment to the present invention is described below in conjunction with the accompanying drawings, so as to those skilled in the art preferably
Understand the present invention.Requiring particular attention is that, in the following description, when known function and design detailed description perhaps
When can desalinate the main contents of the present invention, these descriptions will be ignored herein.
Describe, the relevant speciality term occurred in embodiment is illustrated for convenience first:
BPSK(binary phase-shift keying):Binary phase shift keying;
QPSK(quadrature phase-shift keying):QPSK;
OQPSK(offset quadrature phase-shift keying):Offset quadraphase shift keying;
2FSK(binary frequency-shift keying):Binary Frequency Shift Keying;
4FSK(quadrature frequency-shift keying):Quaternary frequency shift keying;
MSK(minimum shift keying):MSK;
FB(feature-based):Feature based
PR(pattern recognition):Pattern-recognition
LB(Likelihood-based influence):Based on likelihood function
AMCG(graph-based automatic modulation classification):Based on the automatic of figure domain
Modulation classification;
KL divergences (Kullback-Leibler divergence):KL divergences, also known as relative entropy;
FAM(FFT(fast Fourier transform)accumulation method):FFT accumulation algorithms, are used for
Calculate Cyclic spectrum density;
PDF(probability density function):Probability density function;
It is higher that existing the PR methods based on FB and the decision theory recognition method based on LB can not meet some real-times
And need the strong occasion of system robustness, AMCGAlthough more excellent performance can be realized, feature construction process can only be manually realized.This
Invention proposes a kind of for AMCGFeature method for auto constructing.The present invention extracts adjoining from circulation spectrogram domain representation first
Matrix, and the stability characteristic (quality) of entry on adjacency matrix minor diagonal is counted, entry is calculated on the basis of statistical property is stablized
KL divergences, the last average according to adjacency matrix entry sets up the modulation signature of training signal, so as to realize automatic foundation
Modulation signature model is simultaneously prestored in memory, and AMC is ensure that in the case where that will not cause any computational complexityGRobust
Property and accuracy.
1. signal of communication figure domain mapping is theoretical
Most of modulated signals show corresponding second-order statisticses periodically in a communications system, this provide by signal from
Circulation spectral domain transforms to the channel of graphic field.Fig. 1 gives the signal of communication figure domain mapping step based on Cyclic Spectrum, calculates first
The Cyclic Spectrum of input signal, is then normalized, quantification treatment to Cyclic Spectrum, status switch therein is extracted, then these
Sequence mapping is figure.
For the modulated signal x (n) with N number of sampling point, corresponding Cyclic SpectrumCan smoothly it be calculated by the time domain optimized
Method --- FAM algorithms are estimated.For given a frequency f and cycle frequency α, the smooth cycle diagram of time domain can be under
Formula is represented:
Wherein g (n) is that width is NTsThe unified weighting function of second, f1And f2It is the centre frequency of FAM algorithm median filters,
TsIt is the sampling period, wherein, f1=f+ α/2, f2=f- α/2, XT(r,f1) and XT(r,f2) be x (n) complex demodulation, can be under
Formula is calculated.
It is T=N ' T the duration that wherein a (r), which is,sThe cone data window of second, its width is the frequency point of Cyclic Spectrum
Resolution Δ f, if a (r) is normalized, Cyclic Spectrum can realize unbiased esti-mator, such as following formula by time domain smoothness period figure:
In FAM algorithms, frequency resolution Δ f=fsThe Δ t=f of/N ', cycle frequency resolution ax α=1/s/ N, wherein,
fsFor the sampling interval, N ' is the points of data used in complex demodulation, and N is the data points of input in the Δ t times.Therefore, adopt above
The circulation spectrum matrix calculated with FAM algorithmsFor (N '+1) × (2N+1) matrix, i.e., circulation spectrum matrix, which is one, has
The Three Dimensional Spectrum of non-negative range value, there is 2N+1 cycle frequency α=αp(p=-N ,-N+1 ..., N) and+1 spectral frequencies f=of N '
fq(q=-N '/2 ,-N '/2+1 ..., N '/2).
It requires, in fact, the circulation spectrum matrix calculated is normalized and quantification treatment, obtained matrix isIts maximum is 1, shown in normalization, quantitative formula such as formula (4):
Wherein, Represent maximizing function, floor functions and quantized interval respectively with Δ.
Due to the symmetry of Cyclic Spectrum, takeA quarter quadrant carry out figure domain mapping.Here, forEach cycle frequency α=αp(p=0,1 ..., N), can build a figureBuild the rule of figure such as
Under:1) vertex setIt is made up of all non-negative spectral frequencies;2) side collection
Defined by formula (5):
It therefore, it can constitute N+1 figureThe corresponding cycle frequency α=α of each figure correspondencep, p=0,
1,...,N.Obviously schemeIt is a ring or an empty graph (without side).So, for each figureIts adjacency matrixIt is easy to build.
Fig. 2 illustrates figure domain mapping and conversion method based on Cyclic Spectrum by taking bpsk signal as an example.Fig. 2 (a) gives
The quantization of Cyclic Spectrum is carried out in the normalization Cyclic Spectrum of bpsk signal, Fig. 2 (b), Fig. 2 (c) gives by taking cycle frequency α=0 as an example
Its frequency spectrum and periodic extension method in first quartile is gone out, the corresponding figure domain tables of Fig. 2 (c) is finally given in Fig. 2 (d)
The adjacency matrix shown.
2. the feature method for auto constructing proposed
If modulation type collection isWhereinExpression kth kind modulation type, k=1,
2,...,K.The figure characteristic of field of training signal and test signal is built automatically below and inquired into.
The figure characteristic of field of 2.1 training signals is built automatically
For muting kth class modulation type training signal, its Cyclic Spectrum can be calculated, is begged in then being saved according to upper one
The block graphics of figure domain transition structure one of opinion.Here, training signal sample sequence is divided into M sections, and carries out M figure domain mapping
Experiment.Delete the cycle frequency that empty graph is all produced in all M experiments, it is possible to achieve experiment all retains P figure every time.For
M experiment, atlas can be expressed asWhereinP=1,2 ..., P, represent that kth kind is adjusted
The cycle frequency α that the training signal of type processed is remainedpCorresponding figure.Adjacency matrix set expression is accordinglyIt is then possible to extractIn any adjacency matrix leading diagonal directly over minor diagonal institute
There is entry, and one group of sequence of kth class modulation type can be obtained in the m times experimentIts
InElementIt isIn any adjacency matrixIt is being right against leading diagonal
Entry on the minor diagonal of surface, wherein q=1,2 ..., Q, Q is the entry number in minor diagonal.
2.1.1 stable line index sequence is produced
M times all experiments are considered, for given cycle frequency αp, p=1,2 ..., P, we can be based on(m
=1,2 ..., M) in subsequenceTo form M × Q matrixMeanwhile, the matrix of kth class modulation type can be obtained
SetWherein
Wherein,Be byIn q arrange the submatrix of M × 1 to be formed.Note, in any adjacency matrix(m∈
{ 1,2 ..., M }) in,In all entry there is identical line index (position), arrange, can calculate for qIn
The quantity of non-zero entry, it can be expressed asSo as to nonzero probabilityIt can be calculated by following formula:
IfThen from matrixMiddle this column vector of removalThen it can obtain what a dimension diminished
MatrixWhereinRepresenting matrixIn the column vector that carries over;Subscript rl
Represent the corresponding adjacency matrix of the column vectorThe line index of entry on (m ∈ { 1,2 ..., M }) minor diagonal;It is kth
The cycle frequency α of class modulation typepThe number for the column vector that corresponding adjacency matrix is carried over,Note adjacent square
Battle arrayMiddle column vector may be less than τ simultaneously for the probability of non-zero, in this case corresponding matrixIt is changed into empty matrix, and
It can remove.Therefore the corresponding V of non-zero adjacency matrix can be obtainedkIndividual cycle frequency, also, correspondence kth class modulation type can
To be expressed asVk≤P.Here useInstead ofIn αp, then construct a dimension and subtract
Small matrix stackWherein
Due toSubscript rl,Represent any adjacency matrix(m ∈ { 1,2 ..., M }) it is secondary right
The line index of entry on linea angulata, for kth class modulation type, can extract matrix stackThe subscript of middle element, is produced steady
Fixed line index sequenceWhereinCorrespond to the cycle frequency of kth class modulation system's
Stable line index sequence.For whole modulation Candidate SetSet can be passed through(k=1,2 ..., K) collectively constitute one group
Stable line index sequenceAndWherein
It isThe combination of (k=1,2 ..., K),In subsequenceIt is(k=1,2 ...,
K combination), they correspond to identical cycle frequencyIt has to be noticed thatLength or Th(h=1,2 ..., H) no
It is certain identical.
2.1.2 the calculating of KL divergences
For the m times experiment, the cycle frequency of kth class modulation typeCorresponding adjacency matrixOn minor diagonal,
Its line index isEntry useRepresent.Here, cycle frequencyAnd line indexIt is belonging respectively to stable circulation frequency sequence
RowWith stablize line index sequenceTherefore,Stochastic variable by(setIn the corresponding bar of all line index
Mesh) represent,Corresponding PDF is defined as
Wherein,
Note, ifSo
Due to using entry in the present inventionAbsolute value, thusProbability density can be asked by following formula
:
On this basis, kth class modulation type can be defined in cycle frequencyOn corresponding adjacency matrix minor diagonal
Line index isKL divergences at position are
WhereinRepresent the logarithm relative to radix 10;K is current modulation type, kiAll it is that modulation type is waited with k
Selected worksThe index of middle modulation type, ki∈ { 1,2 ..., K }, k ∈ { 1,2 ..., K }, and ki≠k.Note for specific modulation
Type k a, demand goes out line indexIn setIn position KL divergences.
2.1.3 modulation signature sequence construct
Now, it is considered to the stable line index arrangement set of kth class modulation typeIt must be noted that cycle frequency sequence
RowIt isSubset beWhenWhen, stable line index sequenceIt is alsoSubset.Therefore, for
Kth class is modulated, and can calculate adjacency matrixMinor diagonal on each entry joint KL divergencesWhereinIn
Line index isIfThen record line indexAnd its it is correspondingWherein ζ is predetermined threshold value.Then,
According to the corresponding mean absolute value of the line index of collectionThe arrangement of their descendings can be utilized
The new sequence of constructionWherein,It must also be noted that,Can
To be empty sequence.Therefore, for kth class modulation type, new sequence sets can be expressed as
WhereinHere for symbol uniformity, useInstead of subscript
Finally, for kth class modulation type, using corresponding to line index sequenceMean absolute value sequenceTo produce the characteristic sequence of training signal.Check one by one In
Entry.IfBlock sequenceIn its line index correspond toEntry afterwards.
Here, ξ1And ξ2It is default threshold value, can be generally respectively set to 0.04 and 0.6.Δ is between the quantization used in figure domain mapping
Every.IfIn all entries condition is not satisfied, then accordinglyAlso it is removed.Therefore, kth may finally be obtained
The characteristic sequence collection for the training signal that class modulation type has,Its corresponding cycle frequency set
ForIt is obvious that these line index sequencesThere need not be identical length.
It is automatic that Fig. 3 (a)~(f) sets forth BPSK, 2FSK, 4FSK, QPSK, OQPSK and msk signal under simulated conditions
Abscissa in the figure domain line index feature locations schematic diagram of foundation, Fig. 3 (a)~(f) indexes for cycle frequency, represents feature sequence
The cycle frequency of row concentrates corresponding position in cycle frequency, and this cycle frequency collection is all modulation type characteristic sequences built
The union of place cycle frequency;Position of the ordinate for the line index in figure characteristic of field sequence in correspondence adjacency matrix;In figure
The solid diamond of blueness represents the line index of training signal figure characteristic of field, notices that schematic diagram 3 (a)~(f) does not provide same neighbour
Connect the sequencing of line index in matrix.
The figure characteristic of field of 2.2 test signals is built
For the test signal with kth class modulation type, one group of figure can also be generatedAnd
Its corresponding adjacency matrix, adjacency matrix can be expressed asHere,WithCorrespond to respectively
In the cycle frequency of the test signal of kth class modulation typeCorresponding figure and adjacency matrix, in general, test signalCycle frequency collection and training signalCycle frequency collection it is different.But test can be constructed
The figure feature set of signalMake its feature set with training signalWith identical form and greatly
It is small.For kth class modulation type, featureExtracting rule it is as follows:
1) feature set provided according to kth category calibration signalOrderTable
Show respective cycle frequencyThe length of descending index sequence;
2) for zk=jk=1,2 ..., Jk, make Zk=Jk,For jk=1,2 ..., Jk, order
The line index sequence of test signalBuilt with following rule:
According to the absolute value of these non-zero entries, to adjacency matrixNon-zero entry on minor diagonal is with descending
Mode is ranked up.
Before collectionIndividual adjacency matrixElement sorted line index on minor diagonal, is formed
3) feature set of test signal can finally, be built
Finally, for each modulated signal, once establishWithThe normalization Hamming between them can just be utilized
DistanceTo recognize modulation type.
Although illustrative embodiment of the invention is described above, in order to the technology of the art
Personnel understand the present invention, it should be apparent that the invention is not restricted to the scope of embodiment, to the common skill of the art
For art personnel, as long as various change is in the spirit and scope of the present invention that appended claim is limited and is determined, these
Change is it will be apparent that all utilize the innovation and creation of present inventive concept in the row of protection.
Claims (1)
1. a kind of figure characteristic of field method for auto constructing for Modulation Recognition of Communication Signal, it is characterised in that comprise the following steps:
(1) adjacency matrix of kth class modulation type signal, is obtainedThe set of matrices that element is constituted on minor diagonalWherein:
Wherein, P is cycle frequency number, αpFor cycle frequency (p=1,2 ..., P);M represents the m times experiment (m=1,2 ..., M);It is adjacency matrixElement on the minor diagonal being right against directly over leading diagonal, wherein q=1,2 ..., Q, Q
It is the element number in minor diagonal;It is by matrixIn q arrange the submatrix of M × 1 to be formed;
(2), calculating matrixIn q row be submatrixThe probability of middle element non-zero
Wherein,For submatrixThe quantity of middle element non-zero, q=1,2 ..., Q;If probabilityThen from square
Battle arrayMiddle this row of removal are submatrixObtain matrix
Wherein, τ is the probability threshold value of setting, is set as the case may be;Representing matrixIn the column vector that carries over,
Subscript rl Represent the corresponding adjacency matrix of the column vectorMember on (m ∈ { 1,2 ..., M }) minor diagonal
The line index of element;It is the cycle frequency α of kth class modulation type signalpThe column vector that corresponding adjacency matrix is carried over
Number,
If adjacency matrixMiddle column vector is less than τ simultaneously for the probability of non-zero, then corresponding matrixIt is changed into empty matrix, and
And remove, obtain the corresponding V of non-zero adjacency matrixkIndividual cycle frequency, and correspondingly kth class modulation type signal is expressed asVk≤ P, is usedInstead ofIn αp, then construct a matrix stack
Wherein,
Due toSubscript rl,Represent adjacency matrixMinor diagonal
The line index of upper element, for kth class modulation type signal, extracts matrix stackThe subscript of middle element, produces stabilization
Line index sequenceWherein,Correspond to the cycle frequency of kth class modulated signal's
Stable line index sequence, v=1,2 ..., Vk, VkTo stablize the length of line index sequence;
For whole modulation type collectionWherein,Kth kind modulation type is represented, passes through set of rows
Index sequenceCollectively constitute one group of stable line index sequenceI.e.And be expressed as again
ForWherein, line index sequenceIn h-th of subsequence
It is to stablize line index sequenceCombination, they correspond to identical cycle frequencyT=1,2 ..., Th, ThFor son
SequenceLength, H be line index sequenceThe quantity of middle subsequence;
(3), kth class modulation type signal is in cycle frequencyLine index is on corresponding adjacency matrix minor diagonalPosition
The KL divergences at place are:
Wherein,For stochastic variable absolute valueProbability density function,For stochastic variable absolute value
Probability density function, k be current modulation type, kiAll it is modulated signal Candidate Set with kThe index of middle modulation type, ki
∈ { 1,2 ..., K }, k ∈ { 1,2 ..., K }, and ki≠k;
(4), whenWhen, stable line index sequenceIt is alsoSubset, neighbour corresponding for kth class modulated signal
It is that the KL divergences at l positions are to connect line index on matrix minor diagonalIfThen record line indexAnd
The average of its corresponding elementWherein, ζ is KL divergence threshold values;
(5), according to the absolute value of the average of the line index corresponding element of recordDropped using them
The new sequence of sequence array structureWherein, If
It is empty sequence, then deletes, for kth class modulation type, new sequence sets is expressed asWherein
(6), for kth class modulation type, using corresponding to line index sequenceMean absolute value sequence
To produce the characteristic sequence of training signal;
Check one by oneIfBlock sequenceIn its row
Index corresponds toElement afterwards;Wherein, ξ1And ξ2It is default threshold value, can be generally respectively set to 0.04 and 0.6,
Δ is the quantized interval used in figure domain mapping;
IfIn all entries condition is not satisfied, then accordinglyAlso it is removed, the modulation of kth class may finally be obtained
The characteristic sequence collection of type training signalAnd it is used as figure characteristic of field, its corresponding cycle frequency set
For
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CN110798419A (en) * | 2019-10-28 | 2020-02-14 | 北京邮电大学 | Modulation mode identification method and device |
CN112787964A (en) * | 2021-02-18 | 2021-05-11 | 金陵科技学院 | BPSK and QPSK signal modulation identification method based on range median domain features |
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