CN103051367A - Clustering-based blind source separation method for synchronous orthogonal frequency hopping signals - Google Patents

Abstract

The invention discloses a clustering-based blind source separation method for synchronous orthogonal frequency hopping signals. The method comprises the following steps of: acquiring M sampled paths of discrete time-domain mixed signals; obtaining M time-frequency domain matrixes of the mixed signals; preprocessing the time-frequency domain matrixes of the frequency hopping mixed signals; estimating frequency hopping moments, normalized mixed matrix column vectors and frequency hopping frequency; estimating time-frequency domain frequency hopping source signals by utilizing the estimated normalized mixed matrix column vectors; splicing the time-frequency domain frequency hopping source signals between different frequency hopping points; and recovering time-domain source signals according to time-frequency domain estimate values of the source signals. According to the method, the frequency hopping source signals are estimated only according to the received mixed signals of a plurality of frequency hopping signals under the condition of unknown channel information, and the frequency hopping signals can be subjected to blind estimation under the condition that the number of receiving antennae is smaller than that of the source signals; short-time Fourier transform is utilized, so that the method is low in computation amount; and the frequency hopping signals are subjected to blind separation, and meanwhile, a part of parameters can also be estimated, so that the method is high in practicability.

Description

A kind of synchronized orthogonal Frequency Hopping Signal blind source separation method based on cluster

Technical field

The invention belongs to communication and signal processing technology field, relate in particular to a kind of synchronized orthogonal Frequency Hopping Signal blind source separation method based on cluster.

Background technology

The separation of blind source refers to is not knowing under the condition of any channel information, only estimates the process of source signal according to the mixed signal that observes.When observation signal number during greater than the source signal number, be called the blind separation of overdetermination; When the observation signal number equals the source signal number, be called suitable fixed blind separation; When observation signal number during less than the source signal number, become and owe fixed blind separation.

Blind source separate technology obtains using more and more widely in the signal of communication process field, the at present research of blind source separate technology more is more than or equal to the overdetermination of source signal number or suitable fixed blind separation for the observation signal number, EASI (Equivariant adaptive source separation such as classics, Deng the variation self adaptation) algorithm, FastICA (Fast Independent Component Analysis, Fast Independent Component Analysis) algorithm etc.Owing to satisfy statistical independence between the different Frequency Hopping Signals, and satisfy certain correlation between the different frequency hopping points of identical Frequency Hopping Signal, the thought that therefore has document to propose to utilize blind source to separate is carried out blind estimation to a plurality of Frequency Hopping Signals that receive.

The blind separation algorithm of Frequency Hopping Signal that provides in the existing document requires the observation signal number more than or equal to the source signal number.But in the practical communication process, because the restriction of reception antenna number, when frequency hopping synthesizer signal number was more, the observation signal number was often less than the source signal number, therefore existing algorithm can't in the less situation of reception antenna number, carry out blind estimation to a plurality of Frequency Hopping Signals.

Summary of the invention

The invention provides a kind of synchronized orthogonal Frequency Hopping Signal blind source separation method based on cluster, be intended to solve the blind separation algorithm requirement of existing Frequency Hopping Signal observation signal number more than or equal to the source signal number, but in the practical communication process, because the restriction of reception antenna number, when frequency hopping synthesizer signal number is more, the observation signal number is often less than the source signal number, and therefore existing algorithm can't be in the less situation of reception antenna number, the problem of a plurality of Frequency Hopping Signals being carried out blind estimation.

The object of the present invention is to provide a kind of synchronized orthogonal Frequency Hopping Signal blind source separation method based on cluster, the method may further comprise the steps:

Step 1 is utilized and is contained the array antenna received of M array element from the Frequency Hopping Signal of a plurality of synchronized orthogonal frequency hopping radio sets, each road is received signal sample, and rear M road discrete time-domain mixed signal obtains sampling

M=1,2, L, M;

Step 2 is carried out overlapping windowing Short Time Fourier Transform to M road discrete time-domain mixed signal, obtains the time-frequency domain matrix of M mixed signal P=0,1, L P-1, q=0,1, L N _Fft-1;

Step 3 is to the frequency-hopping mixing signal time-frequency domain matrix that obtains in the step 2

Carry out preliminary treatment;

Step 4 utilizes clustering algorithm to estimate jumping moment and corresponding normalized hybrid matrix column vector, the frequency hopping frequency of each jumping of each jumping;

Step 5, the normalization hybrid matrix column vector that estimation obtains according to step 4 is estimated time-frequency domain frequency hopping synthesizer signal;

Step 6 is spliced the time-frequency domain frequency hopping synthesizer signal between the different frequency hopping points;

Step 7, root signal time-frequency domain estimated value is recovered the time domain source signal.

Further, in step 2, (p, q) expression time-frequency index, concrete time-frequency value is

Here N _FftThe length of expression FFT conversion, P represents the windowing number of times, C is integer, the sampling number at expression Short Time Fourier Transform windowing interval, general C＜N _Fft, and K _c=N _Fft/ C is integer, and what that is to say employing is the Short Time Fourier Transform of overlapping windowing.

Further, in step 3, to frequency-hopping mixing signal time-frequency domain matrix Carry out preliminary treatment, specifically comprise following two steps:

The first step is right

Go low-yield preliminary treatment, namely at each sampling instant p, will

Amplitude sets to 0 less than the value of thresholding ε, obtains The setting of thresholding ε can be determined according to the average energy that receives signal;

Second step is found out the constantly time-frequency domain data of (p=0,1,2, L P-1) non-zero of p, uses

Expression, wherein

Constantly time-frequency response of expression p

Corresponding frequency indices when non-zero to these non-zero normalization preliminary treatment, obtains pretreated vectorial b (p, q)=[b ₁(p, q), b ₂(p, q), L, b _M(p, q)] ^T, wherein

$b_m(p,q)=\left\{\begin{array}{cc}\frac{{\stackrel{V}{X}}_m^{\%}(p,q)}{{\stackrel{V}{X}}_1^{\%}(p,q)},& q={\stackrel{V}{q}}_{\mathrm{<figure-callout\; id="0"\; label="p"\; filenames="HSA00000819859700021.png,HSA00000819859700022.png"\; state="\{\{state\}\}">p</figure-callout>}}\\ 0,& q\&NotEqual;{\stackrel{V}{q}}_p\end{array}\right.,m=\mathrm{1,2},\mathrm{L\; M}.$

Further, in step 4, when utilizing clustering algorithm to estimate that the jumping moment of each jumping and each are jumped corresponding normalized hybrid matrix column vector, frequency hopping frequency, may further comprise the steps:

The first step, p (p=0,1,2 ... P-1) constantly, right

The frequency values of expression carries out cluster, the cluster centre number that obtains

The carrier frequency number that expression p exists constantly,

Individual cluster centre then represents the size of carrier frequency, uses respectively

Expression;

Second step, to each sampling instant p (p=0,1,2 ... P-1), utilize clustering algorithm pair Carry out cluster, can obtain equally Individual cluster centre is used

Expression;

The 3rd step is to all

Average and round, obtain the estimation of source signal number Namely

$\hat{N}=\mathrm{round}\left(\frac{1}{p}\underset{p=0}{\overset{P-1}{\mathrm{\&Sigma;}}}{\hat{N}}_p\right);$

In the 4th step, find out

The moment, use p _hExpression is to the p of the continuous value of each section _hAsk intermediate value, use

Represent the l section p that links to each other _hIntermediate value, then

Represent the estimation constantly of l frequency hopping;

The 5th step is according to what estimate in the second step to obtain

P ≠ p _hAnd the 4th estimate that the frequency hopping obtain constantly estimates each and jumps corresponding in the step

Individual hybrid matrix column vector

Concrete formula is:

${\hat{a}}_n\left(l\right)=\left\{\begin{array}{cc}\frac{1}{{\stackrel{\&OverBar;}{p}}_h\left(1\right)}\&CenterDot;\underset{p=1,p\&NotEqual;p_h}{\overset{{\stackrel{\&OverBar;}{p}}_h\left(1\right)}{\mathrm{\&Sigma;}}}{b}_{n,p}^0& l=1,\\ \frac{1}{{\stackrel{\&OverBar;}{p}}_h\left(l\right)-{\stackrel{\&OverBar;}{p}}_h(l-1)}\&CenterDot;\underset{p={\stackrel{\&OverBar;}{p}}_h(l-1)+1,p\&NotEqual;p_h}{\overset{{\stackrel{\&OverBar;}{p}}_h\left(l\right)}{\mathrm{\&Sigma;}}}{b}_{n,p}^0& l>1,\end{array}\right.n=\mathrm{1,2},...,\hat{N}$

Here ${\hat{a}}_n\left(l\right)={[{\hat{a}}_{n,1}\left(l\right),{\hat{a}}_{n,2}\left(l\right),L,{\hat{a}}_{n,M}\left(l\right)]}^T(n=\mathrm{1,2},...,\hat{N})$ It is corresponding to represent that l jumps

Individual hybrid matrix column vector estimated value;

The 6th step, estimate the carrier frequency frequency that each jumping is corresponding, use

It is corresponding to represent that l jumps

Individual frequency estimation, computing formula is as follows:

${\hat{f}}_{c,n}\left(l\right)=\left\{\begin{array}{cc}\frac{1}{{\stackrel{\&OverBar;}{p}}_h\left(1\right)}\&CenterDot;\underset{p=1,p\&NotEqual;p_h}{\overset{{\stackrel{\&OverBar;}{p}}_h\left(1\right)}{\mathrm{\&Sigma;}}}{f}_o^n\left(p\right)& l=1,\\ \frac{1}{{\stackrel{\&OverBar;}{p}}_h\left(l\right)-{\stackrel{\&OverBar;}{p}}_h(l-1)}\&CenterDot;\underset{p={\stackrel{\&OverBar;}{p}}_h(l-1)+1,p\&NotEqual;p_h}{\overset{{\stackrel{\&OverBar;}{p}}_h\left(l\right)}{\mathrm{\&Sigma;}}}{f}_o^n\left(p\right)& l>1,\end{array}\right.n=\mathrm{1,2},...,\hat{N}.$

Further, in step 5, estimate time-frequency domain frequency hopping synthesizer signal according to the normalization hybrid matrix column vector of estimating in the step 4 to obtain, concrete steps are as follows:

The first step judges that to all sampling instant index p which this moment index belongs to and jump, and concrete grammar is: if

Represent that then p belongs to the l jumping constantly; If

Represent that then p belongs to the 1st jumping constantly;

Second step is to l (l=1,2, all moment p that L) jump _l, estimate that this jumps the time-frequency domain data of each frequency hopping synthesizer signal, computing formula is as follows:

$\left\{\begin{array}{c}{S}_j^{\%}(p_l,q)=\frac{1}{{\left|\right|{\hat{a}}_j\left(l\right)\left|\right|}^2}\&CenterDot;{\hat{a}}_j^H\left(l\right)\&times;\left[\begin{array}{c}{X}_1^{\%}(p_l,q)\\ X_2^{\%}(p_l,q)\\ M\\ X_M^{\%}(p_l,q)\end{array}\right]\\ j=\underset{j_{}}{\mathrm{<figure-callout\; id="0"\; label="arg\; max\; j"\; filenames="HSA00000819859700021.png,HSA00000819859700022.png"\; state="\{\{state\}\}">arg</figure-callout>}\max }\left(\right|{[X_1^{\%}(p_l,q),X_2^{\%}(p_l,q),L,X_M^{\%}(p_l,q)]}^H\&times;{\hat{a}}_{j_0}\left(l\right)\left|\right)\\ S_m^{\%}(p_l,q)=0m=\mathrm{1,2},L,M,m\&NotEqual;j\\ q=\mathrm{0,1,2},L,N_{\mathrm{fft}}-1\end{array}\right..$

Further, in step 6, the time-frequency domain frequency hopping synthesizer signal between the different frequency hopping points is spliced,

Concrete steps are:

The first step, it is corresponding to estimate that l jumps

Individual incident angle is used

Represent that l jumps n the incident angle that source signal is corresponding,

Computing formula as follows:

${\widehat{\mathrm{\&theta;}}}_n\left(l\right)=\frac{1}{M-1}\underset{m=2}{\overset{M}{\mathrm{\&Sigma;}}}{\sin }^{-1}\left[\frac{\mathrm{angle}({\hat{a}}_{n,m}\left(l\right)/{\hat{a}}_{n,m-1}\left(l\right))*\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="HSA00000819859700021.png,HSA00000819859700022.png"\; state="\{\{state\}\}">c</figure-callout>}}{2\mathrm{\&pi;}{\hat{f}}_{c,n}\left(l\right)d}\right]n=\mathrm{1,2},...,\hat{N}$

Represent that l jumps n the hybrid matrix column vector that estimation obtains M element;

Second step, judge the 1st (1=2,3 ...) jump the source signal and first of estimating and jump corresponding relation between the source signal of estimation, judgment formula is as follows:

${m_n}^{\left(l\right)}=\underset{m}{\arg \min }|{\widehat{\mathrm{\&theta;}}}_m^{\left(l\right)}-{\widehat{\mathrm{\&theta;}}}_n^{\left(1\right)}|,n=\mathrm{1,2},L,\hat{N}$

M wherein _n ^(l)Represent that l jumps the m that estimates _n ^(l)Individual signal and first is jumped n the signal of estimating and is belonged to same source signal;

The 3rd step, with different frequency hopping point estimation to the signal that belongs to same source signal be stitched together, estimate as final time-frequency domain source signal, use Y _nN source signal of (p, q) expression the time time-frequency domain estimated value on frequency (p, q), p=0,1,2 ...., P, q=0,1,2 ..., N _Fft-1, namely

Further, in step 7, when root signal time-frequency domain estimated value was recovered the time domain source signal, concrete steps were as follows:

The first step, to each sampling instant p (p=0,1,2 ...) and frequency domain data Y _n(p, q), q=0,1,2, L, N _Fft-1 is N _FftThe IFFT conversion of point obtains time domain source signal corresponding to p sampling instant, uses y _n(p, q _t) (q _t=0,1,2, L, N _Fft-1) expression;

Second step is to above-mentioned all time domain source signal y that constantly obtain _n(p, q _t) merge processing, obtain final time domain source signal and estimate, concrete formula is as follows:

$s_n[\mathrm{kC}:(k+1)C-1]=\left\{\begin{array}{cc}\underset{m=0}{\overset{k}{\mathrm{\&Sigma;}}}{y}_n[m,(k-m)C:(k-m+1)C-1]& k<K_c\\ \underset{m=k-K_c+1}{\overset{k}{\mathrm{\&Sigma;}}}{y}_n[m,(k-m)C:(k-m+1)C-1]& k\&GreaterEqual;K_c\end{array}\right.k=\mathrm{0,1,2},L$

Here K _c=N _Fft/ C, the sampling number at C windowing interval.

Synchronized orthogonal Frequency Hopping Signal blind source separation method based on cluster provided by the invention, do not knowing under the condition of any channel information, only according to the mixed signal of a plurality of Frequency Hopping Signals of receiving, estimate the frequency hopping synthesizer signal, can be under the condition of reception antenna number less than the source signal number, a plurality of Frequency Hopping Signals are carried out blind estimation, only utilized Short Time Fourier Transform, amount of calculation is little, realize that easily the method can also be estimated partial parameters when Frequency Hopping Signal is carried out blind separation, practical, have stronger propagation and employment and be worth.

Description of drawings

Fig. 1 is the realization flow figure based on the synchronized orthogonal Frequency Hopping Signal blind source separation method of cluster that the embodiment of the invention provides;

Fig. 2 is the 1st source signal and the estimated signal time domain waveform figure thereof that the embodiment of the invention provides;

Fig. 3 is the 2nd source signal and the estimated signal time domain waveform figure thereof that the embodiment of the invention provides;

Fig. 4 is the 3rd source signal and the estimated signal time domain waveform figure thereof that the embodiment of the invention provides;

Fig. 5 is the 4th source signal and the estimated signal time domain waveform figure thereof that the embodiment of the invention provides;

Fig. 6 is the embodiment of the invention original Frequency Hopping Signal that provides and Frequency Hopping Signal coefficient correlation and the Between Signal To Noise Ratio curve chart estimated.

Embodiment

In order to make purpose of the present invention, technical scheme and advantage clearer, below in conjunction with drawings and Examples, the present invention is further described in detail.Should be appreciated that specific embodiment described herein only in order to explaining the present invention, and be not used in and limit invention.

The realization flow based on the synchronized orthogonal Frequency Hopping Signal blind source separation method of cluster that Fig. 1 shows that the embodiment of the invention provides.

The method may further comprise the steps:

Step S101 utilizes and contains the array antenna received of M array element from the Frequency Hopping Signal of a plurality of synchronized orthogonal frequency hopping radio sets, respectively each road frequency-hopping mixing signal is sampled, and establishing sample frequency is f _s, the sampling interval is T _s=1/f _s, the discrete data of field frequency-hopping mixing signal is used during m road after the sampling

Expression then has M=1,2, L, M;

Step S102 is to the discrete time domain mixed signal in M road

Carry out overlapping windowing Short Time Fourier Transform, obtain the time-frequency domain matrix of M frequency-hopping mixing signal P=0,1, L P-1, q=0,1, L N _Fft-1;

Step S103 is to the time-frequency domain matrix of frequency-hopping mixing signal

Carry out preliminary treatment, obtain vectorial a (p, q);

Step S104 utilizes clustering algorithm to estimate jumping moment and corresponding normalized hybrid matrix column vector, the frequency hopping frequency of each jumping of each jumping;

Step S105, the normalization hybrid matrix column vector that estimation obtains according to step S104 is estimated the time-frequency domain source signal;

Step S106 splices the time-frequency domain frequency hopping synthesizer signal between the different frequency hopping points;

Step S107 according to frequency hopping synthesizer signal time-frequency domain estimated value, recovers time domain frequency hopping synthesizer signal.

In embodiments of the present invention, in step S102, (p, q) expression time-frequency index, concrete time-frequency value is

Here N _FftThe length of expression FFT conversion, P represents the windowing number of times, C is integer, the sampling number at expression Short Time Fourier Transform windowing interval, general C＜N _Fft, and K _c=N _Fft/ C is integer, and what that is to say employing is the Short Time Fourier Transform of overlapping windowing.

In embodiments of the present invention, in step S103, to the time-frequency domain data

Carry out preliminary treatment, when obtaining vectorial a (p, q), specifically comprise following two steps:

The first step is right

Go low-yield preliminary treatment, namely at each sampling instant p, will

Amplitude sets to 0 less than the value of thresholding ε, obtains

The setting of thresholding ε can be determined according to the average energy that receives signal;

Second step is found out the constantly time-frequency domain data of (p=0,1,2, L P-1) non-zero of p, uses

Expression, wherein

Constantly time-frequency response of expression p

Corresponding frequency indices when non-zero to these non-zero normalization preliminary treatment, obtains pretreated vectorial b (p, q)=[b ₁(p, q), b ₂(p, q), L, b _M(p, q)] ^T, wherein

$b_m(p,q)=\left\{\begin{array}{cc}\frac{{\stackrel{V}{X}}_m^{\%}(p,q)}{{\stackrel{V}{\mathrm{<figure-callout\; id="1"\; label="X\; V"\; filenames="HSA00000819859700021.png,HSA00000819859700022.png"\; state="\{\{state\}\}">X</figure-callout>}}}_1^{\%}(p,q)},& q={\stackrel{V}{\mathrm{<figure-callout\; id="0"\; label="q\; V\; p"\; filenames="HSA00000819859700021.png,HSA00000819859700022.png"\; state="\{\{state\}\}">q</figure-callout>}}}_p\\ 0,& q\&NotEqual;{\stackrel{V}{q}}_p\end{array}\right.,m=\mathrm{1,2},\mathrm{L\; M}.$

In embodiments of the present invention, in step S104, when utilizing clustering algorithm to estimate that the jumping moment of each jumping and each are jumped corresponding normalized hybrid matrix column vector, frequency hopping frequency, may further comprise the steps:

The first step, p (p=0,1,2 ... P-1) constantly, right

The frequency values of expression carries out cluster, the cluster centre number that obtains

The carrier frequency number that expression p exists constantly,

Individual cluster centre then represents the size of carrier frequency, uses respectively

Expression;

Second step to each sampling instant p, utilizes clustering algorithm pair

Carry out cluster, can obtain equally Individual cluster centre is used

Expression;

The 3rd step is to all

Average and round, obtain the estimation of source signal number

Namely

$\hat{N}=\mathrm{round}\left(\frac{1}{p}\underset{p=0}{\overset{P-1}{\mathrm{\&Sigma;}}}{\hat{N}}_p\right);$

In the 4th step, find out

The moment, use p _hExpression is to the p of the continuous value of each section _hAsk intermediate value, use Represent the l section p that links to each other _hIntermediate value, then

Represent the estimation constantly of the 1st frequency hopping;

The 5th step is according to what estimate in the second step to obtain

P ≠ p _hAnd the 4th estimate that the frequency hopping obtain constantly estimates each and jumps corresponding in the step

Individual hybrid matrix column vector

Concrete formula is:

${\hat{a}}_n\left(l\right)=\left\{\begin{array}{cc}\frac{1}{{\stackrel{\&OverBar;}{p}}_h\left(1\right)}\&CenterDot;\underset{p=1,p\&NotEqual;p_h}{\overset{{\stackrel{\&OverBar;}{p}}_h\left(1\right)}{\mathrm{\&Sigma;}}}{b}_{n,p}^0& l=1,\\ \frac{1}{{\stackrel{\&OverBar;}{p}}_h\left(l\right)-{\stackrel{\&OverBar;}{p}}_h(l-1)}\&CenterDot;\underset{p={\stackrel{\&OverBar;}{p}}_h(l-1)+1,p\&NotEqual;p_h}{\overset{{\stackrel{\&OverBar;}{p}}_h\left(l\right)}{\mathrm{\&Sigma;}}}{b}_{n,p}^0& l>1,\end{array}\right.n=\mathrm{1,2},...,\hat{N}$

Here ${\hat{a}}_n\left(l\right)={[{\hat{a}}_{n,1}\left(l\right),{\hat{a}}_{n,2}\left(l\right),L,{\hat{a}}_{n,M}\left(l\right)]}^T(n=\mathrm{1,2},...,\hat{N})$ It is corresponding to represent that l jumps

Individual hybrid matrix column vector estimated value;

The 6th step, estimate the carrier frequency frequency that each jumping is corresponding, use

It is corresponding to represent that l jumps

Individual frequency estimation, computing formula is as follows:

${\hat{f}}_{c,n}\left(l\right)=\left\{\begin{array}{cc}\frac{1}{{\stackrel{\&OverBar;}{p}}_h\left(1\right)}\&CenterDot;\underset{p=1,p\&NotEqual;p_h}{\overset{{\stackrel{\&OverBar;}{p}}_h\left(1\right)}{\mathrm{\&Sigma;}}}{f}_o^n\left(p\right)& l=1,\\ \frac{1}{{\stackrel{\&OverBar;}{p}}_h\left(l\right)-{\stackrel{\&OverBar;}{p}}_h(l-1)}\&CenterDot;\underset{p={\stackrel{\&OverBar;}{p}}_h(l-1)+1,p\&NotEqual;p_h}{\overset{{\stackrel{\&OverBar;}{p}}_h\left(l\right)}{\mathrm{\&Sigma;}}}{f}_o^n\left(p\right)& l>1,\end{array}\right.n=\mathrm{1,2},...,\hat{N}.$

In embodiments of the present invention, in step S105, estimate the time-frequency domain source signal according to the normalization hybrid matrix column vector of estimating among the step S104 to obtain, concrete steps are as follows:

The first step judges that to all sampling instant index p which this moment index belongs to and jump, and concrete grammar is: if Represent that then p belongs to the l jumping constantly; If

Represent that then p belongs to the 1st jumping constantly;

Second step is to l (l=1,2, all moment p that L) jump _l, estimate that this jumps the time-frequency domain data of each source signal, computing formula is as follows:

$\left\{\begin{array}{c}{S}_j^{\%}(p_l,q)=\frac{1}{{\left|\right|{\hat{a}}_j\left(l\right)\left|\right|}^2}\&CenterDot;{\hat{a}}_j^H\left(l\right)\&times;\left[\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="X"\; filenames="HSA00000819859700021.png,HSA00000819859700022.png"\; state="\{\{state\}\}">X</figure-callout>}}_1^{\%}(p_l,q)\\ {\mathrm{<figure-callout\; id="2"\; label="X"\; filenames="HSA00000819859700021.png,HSA00000819859700022.png"\; state="\{\{state\}\}">X</figure-callout>}}_2^{\%}(p_l,q)\\ M\\ X_M^{\%}(p_l,q)\end{array}\right]\\ j=\underset{j_{}}{\mathrm{<figure-callout\; id="0"\; label="arg\; max\; j"\; filenames="HSA00000819859700021.png,HSA00000819859700022.png"\; state="\{\{state\}\}">arg</figure-callout>}\max }\left(\right|{[{\mathrm{<figure-callout\; id="1"\; label="X"\; filenames="HSA00000819859700021.png,HSA00000819859700022.png"\; state="\{\{state\}\}">X</figure-callout>}}_1^{\%}(p_l,q),{\mathrm{<figure-callout\; id="2"\; label="X"\; filenames="HSA00000819859700021.png,HSA00000819859700022.png"\; state="\{\{state\}\}">X</figure-callout>}}_2^{\%}(p_l,q),L,X_M^{\%}(p_l,q)]}^H\&times;{\hat{a}}_{j_0}\left(l\right)\left|\right)\\ S_m^{\%}(p_l,q)=0m=\mathrm{1,2},L,M,m\&NotEqual;j\\ q=\mathrm{0,1,2},L,N_{\mathrm{fft}}-1\end{array}\right..$

In embodiments of the present invention, in step S106, the frequency hopping synthesizer signal between the different frequency hopping points is spliced, concrete steps are:

The first step, it is corresponding to estimate that l jumps Individual incident angle is used Represent that l jumps n the incident angle that source signal is corresponding,

Computing formula as follows:

${\widehat{\mathrm{\&theta;}}}_n\left(l\right)=\frac{1}{M-1}\underset{m=2}{\overset{M}{\mathrm{\&Sigma;}}}{\sin }^{-1}\left[\frac{\mathrm{angle}({\hat{a}}_{n,m}\left(l\right)/{\hat{a}}_{n,m-1}\left(l\right))*\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="HSA00000819859700021.png,HSA00000819859700022.png"\; state="\{\{state\}\}">c</figure-callout>}}{2\mathrm{\&pi;}{\hat{f}}_{c,n}\left(l\right)d}\right]n=\mathrm{1,2},...,\hat{N}$

Represent that l jumps n the hybrid matrix column vector that estimation obtains

M element;

Second step, judge l (l=2,3 ...) and source signal and first that jump to estimate jumps the corresponding relation between the source signal of estimation, judgment formula is as follows:

${m_n}^{\left(l\right)}=\underset{m}{\arg \min }|{\widehat{\mathrm{\&theta;}}}_m^{\left(l\right)}-{\widehat{\mathrm{\&theta;}}}_n^{\left(1\right)}|,n=\mathrm{1,2},L,\hat{N}$

M wherein _n ^(l)Represent that l jumps the m that estimates _n ^(l)Individual signal and first is jumped n the signal of estimating and is belonged to same source signal;

The 3rd the step, with different frequency hopping point estimation to the signal that belongs to same source signal be stitched together, as final time-frequency domain frequency hopping synthesizer Signal estimation, use Y _nN source signal of (p, q) expression the time time-frequency domain estimated value on frequency (p, q), p=0,1,2 ...., P, q=0,1,2 ..., N _Fft-1, namely

In embodiments of the present invention, in step S107, when recovering time domain frequency hopping synthesizer signal according to frequency hopping synthesizer signal time-frequency domain estimated value, concrete steps are as follows:

The first step, to each sampling instant p (p=0,1,2 ...) and frequency domain data Y _n(p, q), q=0,1,2, L, N _Fft-1 is N _FftThe IFFT conversion of point obtains time domain source signal corresponding to p sampling instant, uses y _n(p, q _t) (q _t=0,1,2, L, N _Fft-1) expression;

Second step is to above-mentioned all time domain source signal y that constantly obtain _n(p, q _t) merge processing, obtain final time domain frequency hopping synthesizer Signal estimation, concrete formula is as follows:

$s_n[\mathrm{kC}:(k+1)C-1]=\left\{\begin{array}{cc}\underset{m=0}{\overset{k}{\mathrm{\&Sigma;}}}{y}_n[m,(k-m)C:(k-m+1)C-1]& k<K_c\\ \underset{m=k-K_c+1}{\overset{k}{\mathrm{\&Sigma;}}}{y}_n[m,(k-m)C:(k-m+1)C-1]& k\&GreaterEqual;K_c\end{array}\right.k=\mathrm{0,1,2},L$

Here K _c=N _Fft/ C, the sampling number at C windowing interval.

Below in conjunction with drawings and the specific embodiments application principle of the present invention is further described.

The object of the invention is to owe surely blind separation problem for Frequency Hopping Signal, propose a kind of synchronized orthogonal Frequency Hopping Signal blind source separation method based on cluster, the method comprises:

(1) utilization contains the aerial array reception of M array element from the Frequency Hopping Signal of a plurality of synchronized orthogonal frequency hopping radio sets, each road frequency-hopping mixing signal is sampled the discrete time-domain frequency-hopping mixing signal after obtaining sampling

M=1,2, L, M.

(2) to M road discrete time-domain Frequency Hopping Signal

Carry out overlapping windowing Short Time Fourier Transform (employing rectangular window function), obtain the time-frequency domain matrix of M mixed signal

P=0,1, L P-1, q=0,1, L N _Fft-1.Wherein (p, q) represents the time-frequency index, and concrete time-frequency value is

Here N _FftThe length of expression FFT conversion, P represents the windowing number of times, C is integer, the sampling number at expression Short Time Fourier Transform windowing interval, general C＜N _Fft, and K _c=N _Fft/ C is integer, and what that is to say employing is the Short Time Fourier Transform of overlapping windowing.

(3) to mixed signal time-frequency domain matrix

Carry out preliminary treatment, obtain vectorial a (p, q), specifically comprise following two steps:

3.1) right

Go low-yield preliminary treatment, namely at each sampling instant p, will

Amplitude sets to 0 less than the value of thresholding ε, obtains

The setting of thresholding can be determined according to the average energy that receives signal.

3.2) find out the constantly time-frequency domain data of (p=0,1,2, L P-1) non-zero of p, use

Expression, wherein

Constantly time-frequency response of expression p Corresponding frequency indices when non-zero to these non-zero normalization preliminary treatment, obtains pretreated vectorial b (p, q)=[b ₁(p, q), b ₂(p, q), L, b _M(p, q)] ^T, wherein

$b_m(p,q)=\left\{\begin{array}{cc}\frac{{\stackrel{V}{X}}_m^{\%}(p,q)}{{\stackrel{V}{\mathrm{<figure-callout\; id="1"\; label="X\; V"\; filenames="HSA00000819859700021.png,HSA00000819859700022.png"\; state="\{\{state\}\}">X</figure-callout>}}}_1^{\%}(p,q)},& q={\stackrel{V}{\mathrm{<figure-callout\; id="0"\; label="q\; V\; p"\; filenames="HSA00000819859700021.png,HSA00000819859700022.png"\; state="\{\{state\}\}">q</figure-callout>}}}_p\\ 0,& q\&NotEqual;{\stackrel{V}{q}}_p\end{array}\right.,m=\mathrm{1,2},\mathrm{L\; M}---\left(1\right)$

(4) utilize clustering algorithm to estimate jumping moment and corresponding normalized hybrid matrix column vector, the frequency hopping frequency of each jumping of each jumping.May further comprise the steps:

4-1) p (p=0,1,2 ... P-1) constantly, right

The frequency values of expression carries out cluster, the cluster centre number that obtains

The carrier frequency number that expression p exists constantly, Individual cluster centre then represents the size of carrier frequency, uses respectively

Expression;

4-2) to each sampling instant p, utilize clustering algorithm pair

Carry out cluster, can obtain equally

Individual cluster centre is used

Expression.

4-3) to all Average and round, obtain the estimation of source signal number

Namely

$\hat{N}=\mathrm{round}\left(\frac{1}{p}\underset{p=0}{\overset{P-1}{\mathrm{\&Sigma;}}}{\hat{N}}_p\right)---\left(2\right)$

4-4) find out

The moment, use p _hExpression is to the p of the continuous value of each section _hAsk intermediate value, use

Represent the l section p that links to each other _hIntermediate value, then

Represent the estimation constantly of l frequency hopping.

4-5) obtain according to estimation in the step (4-2) P ≠ p _hAnd estimate in the step (4-3) that the frequency hopping obtain constantly estimates each and jumps corresponding

Individual hybrid matrix column vector

Concrete formula is as follows:

${\hat{a}}_n\left(l\right)=\left\{\begin{array}{cc}\frac{1}{{\stackrel{\&OverBar;}{p}}_h\left(1\right)}\&CenterDot;\underset{p=1,p\&NotEqual;p_h}{\overset{{\stackrel{\&OverBar;}{p}}_h\left(1\right)}{\mathrm{\&Sigma;}}}{b}_{n,p}^0& l=1,\\ \frac{1}{{\stackrel{\&OverBar;}{p}}_h\left(l\right)-{\stackrel{\&OverBar;}{p}}_h(l-1)}\&CenterDot;\underset{p={\stackrel{\&OverBar;}{p}}_h(l-1)+1,p\&NotEqual;p_h}{\overset{{\stackrel{\&OverBar;}{p}}_h\left(l\right)}{\mathrm{\&Sigma;}}}{b}_{n,p}^0& l>1,\end{array}\right.n=\mathrm{1,2},...,\hat{N}---\left(3\right)$

Here ${\hat{a}}_n\left(l\right)={[{\hat{a}}_{n,1}\left(l\right),{\hat{a}}_{n,2}\left(l\right),L,{\hat{a}}_{n,M}\left(l\right)]}^T(n=\mathrm{1,2},...,\hat{N})$ It is corresponding to represent that l jumps

Individual hybrid matrix column vector estimated value.

4-6) estimate the carrier frequency frequency that each jumping is corresponding, use

It is corresponding to represent that l jumps

Individual frequency estimation, computing formula is as follows:

${\hat{f}}_{c,n}\left(l\right)=\left\{\begin{array}{cc}\frac{1}{{\stackrel{\&OverBar;}{p}}_h\left(1\right)}\&CenterDot;\underset{p=1,p\&NotEqual;p_h}{\overset{{\stackrel{\&OverBar;}{p}}_h\left(1\right)}{\mathrm{\&Sigma;}}}{f}_o^n\left(p\right)& l=1,\\ \frac{1}{{\stackrel{\&OverBar;}{p}}_h\left(l\right)-{\stackrel{\&OverBar;}{p}}_h(l-1)}\&CenterDot;\underset{p={\stackrel{\&OverBar;}{p}}_h(l-1)+1,p\&NotEqual;p_h}{\overset{{\stackrel{\&OverBar;}{p}}_h\left(l\right)}{\mathrm{\&Sigma;}}}{f}_o^n\left(p\right)& l>1,\end{array}\right.n=\mathrm{1,2},...,\hat{N},---\left(4\right)$

(5) estimate the time-frequency domain source signal according to the normalization hybrid matrix column vector of estimating in the step (4) to obtain, concrete steps are as follows:

5-1) all sampling instant index p are judged which this moment index belongs to and jump, concrete grammar is as follows:

If Represent that then p belongs to the l jumping constantly;

If

Represent that then p belongs to the 1st jumping constantly.

5-2) to l (l=1,2, all of L) jumping are pl constantly, utilize formula (5) to estimate that this jumps the time-frequency domain data of each source signal, computing formula is as follows:

$\left\{\begin{array}{c}{S}_j^{\%}(p_l,q)=\frac{1}{{\left|\right|{\hat{a}}_j\left(l\right)\left|\right|}^2}\&CenterDot;{\hat{a}}_j^H\left(l\right)\&times;\left[\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="X"\; filenames="HSA00000819859700021.png,HSA00000819859700022.png"\; state="\{\{state\}\}">X</figure-callout>}}_1^{\%}(p_l,q)\\ {\mathrm{<figure-callout\; id="2"\; label="X"\; filenames="HSA00000819859700021.png,HSA00000819859700022.png"\; state="\{\{state\}\}">X</figure-callout>}}_2^{\%}(p_l,q)\\ M\\ X_M^{\%}(p_l,q)\end{array}\right]\\ j=\underset{j_{}}{\mathrm{<figure-callout\; id="0"\; label="arg\; max\; j"\; filenames="HSA00000819859700021.png,HSA00000819859700022.png"\; state="\{\{state\}\}">arg</figure-callout>}\max }\left(\right|{[{\mathrm{<figure-callout\; id="1"\; label="X"\; filenames="HSA00000819859700021.png,HSA00000819859700022.png"\; state="\{\{state\}\}">X</figure-callout>}}_1^{\%}(p_l,q),{\mathrm{<figure-callout\; id="2"\; label="X"\; filenames="HSA00000819859700021.png,HSA00000819859700022.png"\; state="\{\{state\}\}">X</figure-callout>}}_2^{\%}(p_l,q),L,X_M^{\%}(p_l,q)]}^H\&times;{\hat{a}}_{j_0}\left(l\right)\left|\right)\\ S_m^{\%}(p_l,q)=0m=\mathrm{1,2},L,M,m\&NotEqual;j\\ q=\mathrm{0,1,2},L,N_{\mathrm{fft}}-1\end{array}\right.---\left(5\right)$

(6) splicing of source signal between the different frequency hopping points, concrete steps are as follows:

6-1) estimation l jumps correspondence

Individual incident angle is used Represent that l jumps n the incident angle that source signal is corresponding,

Computing formula as follows:

${\widehat{\mathrm{\&theta;}}}_n\left(l\right)=\frac{1}{M-1}\underset{m=2}{\overset{M}{\mathrm{\&Sigma;}}}{\sin }^{-1}\left[\frac{\mathrm{angle}({\hat{a}}_{n,m}\left(l\right)/{\hat{a}}_{n,m-1}\left(l\right))*\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="HSA00000819859700021.png,HSA00000819859700022.png"\; state="\{\{state\}\}">c</figure-callout>}}{2\mathrm{\&pi;}{\hat{f}}_{c,n}\left(l\right)d}\right]n=\mathrm{1,2},...,\hat{N}---\left(6\right)$

Represent that l jumps n the hybrid matrix column vector that estimation obtains

M element.

6-2) utilize formula (7) judge l (l=2,3 ...) and jump the source signal and first of estimating and jump corresponding relation between the source signal of estimation, as follows

${m_n}^{\left(l\right)}=\underset{m}{\arg \min }|{\widehat{\mathrm{\&theta;}}}_m^{\left(l\right)}-{\widehat{\mathrm{\&theta;}}}_n^{\left(1\right)}|,n=\mathrm{1,2},L,\hat{N}---\left(7\right)$

M wherein _n ^(l)Represent that l jumps the m that estimates _n ^(l)Individual signal and first is jumped n the signal of estimating and is belonged to same source signal.

6-3) with different frequency hopping point estimation to the signal that belongs to same source signal be stitched together, estimate as final time-frequency domain source signal, use Y _nN source signal of (p, q) expression the time time-frequency domain estimated value on frequency (p, q), p=0,1,2 ..., P, q=0,1,2 ..., N _Fft-1, namely

(7) root signal time-frequency domain estimated value is recovered the time domain source signal, and concrete steps are as follows:

7-1) to each sampling instant p (p=0,1,2 ...) and frequency domain data Y _n(p, q), q=0,1,2, L, N _Fft-1 is N _FftThe IFFT conversion of point obtains time domain source signal corresponding to p sampling instant, uses y _n(p, q _t) (q _t=0,1,2, L, N _Fft-1) expression.

7-2) to above-mentioned all time domain source signal y that constantly obtain _n(p, q _t) merge processing, obtain final time domain source signal and estimate.Concrete formula is as follows:

$s_n[\mathrm{kC}:(k+1)C-1]=\left\{\begin{array}{cc}\underset{m=0}{\overset{k}{\mathrm{\&Sigma;}}}{y}_n[m,(k-m)C:(k-m+1)C-1]& k<K_c\\ \underset{m=k-K_c+1}{\overset{k}{\mathrm{\&Sigma;}}}{y}_n[m,(k-m)C:(k-m+1)C-1]& k\&GreaterEqual;K_c\end{array}\right.k=\mathrm{0,1,2},L---\left(9\right)$

Here K _c=N _Fft/ C, the sampling number at C windowing interval.

Before method of the present invention was elaborated, at first when adopting even linear antenna arrays to receive Frequency Hopping Signal, the characteristic of hybrid matrix described.

Suppose to have N source signal by evenly linear antenna arrays reception, the reception element number of array in this array is M.The incidence angle of supposing N source signal arrival aerial array is respectively θ ₁, θ ₂, L, θ _N, then evenly the response matrix of line style aerial array is:

$H\left(t\right)=\left[\begin{array}{cccc}1& 1& L& 1\\ {\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="HSA00000819859700021.png,HSA00000819859700022.png"\; state="\{\{state\}\}">e</figure-callout>}}^j& {\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="HSA00000819859700021.png,HSA00000819859700022.png"\; state="\{\{state\}\}">e</figure-callout>}}^j& \mathrm{<figure-callout\; id="2"\; label="L\; e\; j"\; filenames="HSA00000819859700021.png,HSA00000819859700022.png"\; state="\{\{state\}\}">L</figure-callout>}& e^j{\frac{2\mathrm{\&pi;}{f}_n\left(t\right)}{c}\&CenterDot;d\&CenterDot;\sin {\mathrm{\&theta;}}_{\mathrm{<figure-callout\; id="2"\; label="N\; e\; j"\; filenames="HSA00000819859700021.png,HSA00000819859700022.png"\; state="\{\{state\}\}">N</figure-callout>}}}^{}& \\ e^j{\frac{2\mathrm{\&pi;}{f}_1\left(t\right)}{c}\&CenterDot;2\&CenterDot;d\&CenterDot;\sin {\mathrm{\&theta;}}_1}^{}& {\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="HSA00000819859700021.png,HSA00000819859700022.png"\; state="\{\{state\}\}">e</figure-callout>}}^j& \mathrm{<figure-callout\; id="2"\; label="L\; e\; j"\; filenames="HSA00000819859700021.png,HSA00000819859700022.png"\; state="\{\{state\}\}">L</figure-callout>}& e^j{\frac{2\mathrm{\&pi;}{f}_n\left(t\right)}{c}\&CenterDot;2\&CenterDot;d\&CenterDot;\sin {\mathrm{\&theta;}}_N}^{}\\ M& M& L& \mathrm{<figure-callout\; id="2"\; label="M\; e\; j"\; filenames="HSA00000819859700021.png,HSA00000819859700022.png"\; state="\{\{state\}\}">M</figure-callout>}& \\ e^j{\frac{2\mathrm{\&pi;}{f}_1\left(t\right)}{c}\&CenterDot;(M-1)\&CenterDot;d\&CenterDot;\mathrm{din}{\mathrm{\&theta;}}_1}^{}& {\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="HSA00000819859700021.png,HSA00000819859700022.png"\; state="\{\{state\}\}">e</figure-callout>}}^j& \mathrm{<figure-callout\; id="2"\; label="L\; e\; j"\; filenames="HSA00000819859700021.png,HSA00000819859700022.png"\; state="\{\{state\}\}">L</figure-callout>}& e^j{\frac{2\mathrm{\&pi;}{f}_n\left(t\right)}{c}\&CenterDot;(M-1)d\&CenterDot;\sin {\mathrm{\&theta;}}_N}^{}\end{array}\right]---\left(10\right)$

Wherein, f _n(t) be that n source signal is in t carrier frequency constantly, c=3 * 10 ⁸M/s is the light velocity, and d represents array element distance.Can see a certain moment, n source signal to the transmission coefficient between m the reception antenna is

This coefficient is only relevant with this moment signal carrier frequency and incident angle.

M road received signal vector x (t)=[x then ₁(t) x ₂(t) Lx _M(t)] ^TWith original signal N frequency hopping synthesizer signal vector s (t)=[ _s1 (t) s ₂(t) L s _N(t)] ^TBetween the pass be:

x(t)＝H(t)s(t)+n(t) (11)

N (t)=[n wherein ₁(t) n ₂(t) L n _M(t)] ^TBe the noise that M road antenna reception arrives, be generally white Gaussian noise.Since the Frequency Hopping Signal frequency at set intervals can saltus step once, so the hybrid matrix in this system is at each frequency hopping point in the duration, hybrid matrix remains unchanged, and when the Frequency generated saltus step, saltus step also occurs hybrid matrix thereupon.

By (10) as can be known

$\frac{h_{m+1,n}\left(t\right)}{h_{m,n}\left(t\right)}={\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="HSA00000819859700021.png,HSA00000819859700022.png"\; state="\{\{state\}\}">e</figure-callout>}}^{j}m=\mathrm{1,2},L,M,n=\mathrm{1,2},L,N---\left(12\right)$

H wherein _{M, n}(t) (m, n) individual element of expression hybrid matrix H (t) can be seen the arbitrary column vector to hybrid matrix from following formula (12), and the ratio of its adjacent element equates that namely the hybrid matrix of even linear array has the Fan Demeng characteristic.

Embodiment one,

Saltus step characteristic and the Fan Demeng characteristic of Frequency Hopping Signal hybrid matrix when utilizing even linear array to receive, with reference to figure 1, the step of the inventive method is as follows:

Step 1), utilize and to contain the linear array array antenna received of M array element from the signal of a plurality of synchronized orthogonal frequency hopping radio sets, M the signal that receives sampled, sample frequency is f _s, obtain M discrete data, namely

$x_m^{\%}\left(k\right)=x_m(k\&CenterDot;T_s)m=\mathrm{1,2},L,M---\left(13\right)$

Wherein k represents k sampling instant index.T _s=1/f _sThe expression sampling interval.

Step 2), the rear resulting multichannel data of sampling is carried out overlapping windowing Short Time Fourier Transform, wherein windowed function adopts rectangular window, obtains the time-frequency domain matrix of M observation signal, namely

$X_m^{\%}(p,q)=\underset{k=p\&CenterDot;C+1}{\overset{t=p\&CenterDot;C+N_{\mathrm{fft}}}{\mathrm{\&Sigma;}}}{x}_m^{\%}\left(k\right)e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HSA00000819859700021.png,HSA00000819859700022.png"\; state="\{\{state\}\}">j</figure-callout>}\frac{2\mathrm{\&pi;kq}}{N_{\mathrm{fft}}}}p=\mathrm{0,1},\mathrm{L\; P}-1;q=\mathrm{0,1},L,(N_{\mathrm{fft}}-1);m=\mathrm{1,2},L,M---\left(14\right)$

N wherein _FftFourier transform length, N _FftLarger, frequency resolution is lower, and vice versa.C is integer, the sampling number at expression Short Time Fourier Transform windowing interval, and C is less, and temporal resolution is higher, and vice versa.General C≤N _Fft, and K _c=N _Fft/ C is integer.

Represent m road observation signal

At p moment q amplitude-frequency response that Frequency point is corresponding.Frequency index during (p, q) expression, corresponding time-frequency value is

We know that for the frequency hopping synthesizer signal multiple source signals has the probability of value very little simultaneously on synchronization, same Frequency point, especially when adopting the synchronized orthogonal networking mode, at a time on a certain Frequency point, only have at most a non-zero signal.Suppose at p _nConstantly, q _nOn the frequency, only have n signal that value is arranged, when not considering noise, by formula (11), (13)-(14) as can be known:

$b_m(p_n,q_n)@\frac{X_m^{\%}(p_n,q_n)}{{\mathrm{<figure-callout\; id="1"\; label="X"\; filenames="HSA00000819859700021.png,HSA00000819859700022.png"\; state="\{\{state\}\}">X</figure-callout>}}_1^{\%}(p_n,q_n)}=\frac{h_{\mathrm{mn}}\left(p_n\right)}{h_{1n}\left(p_n\right)}m=\mathrm{1,2},...,M---\left(15\right)$

According to the analysis of front as can be known, n source signal is at moment p _nTransmission coefficient relevant with this signal carrier frequency constantly, and the carrier frequency of Frequency Hopping Signal is every T _h(T _hBe the frequency hopping time interval) the time saltus step once, namely at frequency hopping point b in the duration _m(p _n, q _n) be constant, namely

b _n(p _n, q _n)=[b ₁(p _n, q _n), b ₂(p _n, q _n), b _{, M}(p _n, q _n)] ^TIt is constant within a certain jumping duration.Then in a certain jumping duration, the normalized vector on all Frequency points

Mainly concentrate on N the value.

Step 3), to the time-frequency domain data matrix

(m=1,2, L, M) does preliminary treatment and obtains vectorial a (p, q), specifically comprises following two steps:

3.1) right

Go low-yield preliminary treatment, namely at each sampling instant p, will

Amplitude sets to 0 less than the value of thresholding ε, obtains

Here the setting of thresholding can be determined according to the average energy that receives signal.

3.2) find out the constantly time-frequency domain data of (p=0,1,2, L, P-1) non-zero of p, use

Expression, wherein

Constantly time-frequency response of expression p

Corresponding frequency indices when non-zero to these non-zero normalization preliminary treatment, obtains pretreated vectorial b (p, q)=[b ₁(p, q), b ₂(p, q), L, b _M(p, q)] ^T, namely

$b_m(p,q)=\left\{\begin{array}{cc}\frac{{\stackrel{V}{X}}_m^{\%}(p,q)}{{\stackrel{V}{\mathrm{<figure-callout\; id="1"\; label="X\; V"\; filenames="HSA00000819859700021.png,HSA00000819859700022.png"\; state="\{\{state\}\}">X</figure-callout>}}}_1^{\%}(p,q)},& q={\stackrel{V}{\mathrm{<figure-callout\; id="0"\; label="q\; V\; p"\; filenames="HSA00000819859700021.png,HSA00000819859700022.png"\; state="\{\{state\}\}">q</figure-callout>}}}_p\\ 0,& q\&NotEqual;{\stackrel{V}{q}}_p\end{array}\right.,m=\mathrm{1,2},\mathrm{L\; M}---\left(16\right)$

Step 4), utilize clustering algorithm to estimate jumping moment and corresponding normalized hybrid matrix column vector, the frequency hopping frequency of each jumping of each jumping.May further comprise the steps:

4-1) p (p=0,1,2 ..., P-1) constantly, right

The frequency values of expression carries out cluster, the cluster centre number that obtains

The carrier frequency number that expression p exists constantly, Individual cluster centre then represents the size of carrier frequency, uses respectively

Expression;

4-2) to each sampling instant p, utilize clustering algorithm pair

Carry out cluster, can obtain equally Individual cluster centre is used

Expression.

4-3) to all Average and round, obtain the estimation of source signal number

Namely

$\hat{N}=\mathrm{round}\left(\frac{1}{p}\underset{p=0}{\overset{P-1}{\mathrm{\&Sigma;}}}{\hat{N}}_p\right)---\left(17\right)$

4-4) find out

The moment, use p _hExpression is to the p of the continuous value of each section _hAsk intermediate value, use

Represent the l section p that links to each other _hIntermediate value, then

Represent the estimation constantly of l frequency hopping.

4-5) obtain according to estimation in the step (4-2)

P ≠ p _hAnd estimate in the step (4-4) that the frequency hopping obtain constantly estimates each and jumps corresponding

Individual hybrid matrix column vector

Concrete formula is as follows:

${\hat{a}}_n\left(l\right)=\left\{\begin{array}{cc}\frac{1}{{\stackrel{\&OverBar;}{p}}_h\left(1\right)}\&CenterDot;\underset{p=1,p\&NotEqual;p_h}{\overset{{\stackrel{\&OverBar;}{p}}_h\left(1\right)}{\mathrm{\&Sigma;}}}{b}_{n,p}^0& l=1,\\ \frac{1}{{\stackrel{\&OverBar;}{p}}_h\left(l\right)-{\stackrel{\&OverBar;}{p}}_h(l-1)}\&CenterDot;\underset{p={\stackrel{\&OverBar;}{p}}_h(l-1)+1,p\&NotEqual;p_h}{\overset{{\stackrel{\&OverBar;}{p}}_h\left(l\right)}{\mathrm{\&Sigma;}}}{b}_{n,p}^0& l>1,\end{array}\right.n=\mathrm{1,2},...,\hat{N}---\left(18\right)$

Here ${\hat{a}}_n\left(l\right)={[{\hat{a}}_{n,1}\left(l\right),{\hat{a}}_{n,2}\left(l\right),L,{\hat{a}}_{n,M}\left(l\right)]}^T(n=\mathrm{1,2},...,\hat{N})$ It is corresponding to represent that l jumps

Individual hybrid matrix column vector estimated value.

4-6) estimate the carrier frequency frequency that each jumping is corresponding, use

It is corresponding to represent that l jumps Individual frequency estimation, computing formula is as follows:

${\hat{f}}_{c,n}\left(l\right)=\left\{\begin{array}{cc}\frac{1}{{\stackrel{\&OverBar;}{p}}_h\left(1\right)}\&CenterDot;\underset{p=1,p\&NotEqual;p_h}{\overset{{\stackrel{\&OverBar;}{p}}_h\left(1\right)}{\mathrm{\&Sigma;}}}{f}_o^n\left(p\right)& l=1,\\ \frac{1}{{\stackrel{\&OverBar;}{p}}_h\left(l\right)-{\stackrel{\&OverBar;}{p}}_h(l-1)}\&CenterDot;\underset{p={\stackrel{\&OverBar;}{p}}_h(l-1)+1,p\&NotEqual;p_h}{\overset{{\stackrel{\&OverBar;}{p}}_h\left(l\right)}{\mathrm{\&Sigma;}}}{f}_o^n\left(p\right)& l>1,\end{array}\right.n=\mathrm{1,2},...,\hat{N}---\left(19\right)$

Step 5), estimate the time-frequency domain source signal according to the normalization hybrid matrix column vector of estimating in the step (4) to obtain, concrete steps are as follows:

5-1) all sampling instant index p are judged which this moment index belongs to and jump, method is as follows:

If Represent that then p belongs to the l jumping constantly;

If

Represent that then p belongs to the 1st jumping constantly.

5-2) to l (l=1,2, all moment p that L) jump _l, utilize formula (20) to estimate that this jumps the time-frequency domain data of each source signal, computing formula is as follows:

$\left\{\begin{array}{c}{S}_j^{\%}(p_l,q)=\frac{1}{{\left|\right|{\hat{a}}_j\left(l\right)\left|\right|}^2}\&CenterDot;{\hat{a}}_j^H\left(l\right)\&times;\left[\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="X"\; filenames="HSA00000819859700021.png,HSA00000819859700022.png"\; state="\{\{state\}\}">X</figure-callout>}}_1^{\%}(p_l,q)\\ {\mathrm{<figure-callout\; id="2"\; label="X"\; filenames="HSA00000819859700021.png,HSA00000819859700022.png"\; state="\{\{state\}\}">X</figure-callout>}}_2^{\%}(p_l,q)\\ M\\ X_M^{\%}(p_l,q)\end{array}\right]\\ j=\underset{j_{}}{\mathrm{<figure-callout\; id="0"\; label="arg\; max\; j"\; filenames="HSA00000819859700021.png,HSA00000819859700022.png"\; state="\{\{state\}\}">arg</figure-callout>}\max }\left(\right|{[{\mathrm{<figure-callout\; id="1"\; label="X"\; filenames="HSA00000819859700021.png,HSA00000819859700022.png"\; state="\{\{state\}\}">X</figure-callout>}}_1^{\%}(p_l,q),{\mathrm{<figure-callout\; id="2"\; label="X"\; filenames="HSA00000819859700021.png,HSA00000819859700022.png"\; state="\{\{state\}\}">X</figure-callout>}}_2^{\%}(p_l,q),L,X_M^{\%}(p_l,q)]}^H\&times;{\hat{a}}_{j_0}\left(l\right)\left|\right)\\ S_m^{\%}(p_l,q)=0m=\mathrm{1,2},L,M,m\&NotEqual;j\\ q=\mathrm{0,1,2},L,N_{\mathrm{fft}}-1\end{array}\right.---\left(20\right)$

Step 6) splicing of source signal between the different frequency hopping point, concrete steps are as follows:

6-1) estimation l jumps correspondence

Individual incident angle is used

Represent that l jumps n the incident angle that source signal is corresponding,

Computing formula as follows:

${\widehat{\mathrm{\&theta;}}}_n\left(l\right)=\frac{1}{M-1}\underset{m=2}{\overset{M}{\mathrm{\&Sigma;}}}{\sin }^{-1}\left[\frac{\mathrm{angle}({\hat{a}}_{n,m}\left(l\right)/{\hat{a}}_{n,m-1}\left(l\right))*\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="HSA00000819859700021.png,HSA00000819859700022.png"\; state="\{\{state\}\}">c</figure-callout>}}{2\mathrm{\&pi;}{\hat{f}}_{c,n}\left(l\right)d}\right]n=\mathrm{1,2},...,\hat{N}---\left(21\right)$

Here

M the element that represents n the hybrid matrix column vector that l jumping estimation obtains,

6-2) utilize formula (22) judge l (l=2,3 ...) and jump the source signal and first of estimating and jump corresponding relation between the source signal of estimation

${m_n}^{\left(l\right)}=\underset{m}{\arg \min }|{\widehat{\mathrm{\&theta;}}}_m^{\left(l\right)}-{\widehat{\mathrm{\&theta;}}}_n^{\left(1\right)}|,n=\mathrm{1,2},L,\hat{N}--\left(22\right)-$

Here m _n ^(l)Represent that l jumps the m that estimates _n ^(l)Individual signal and first is jumped n the signal of estimating and is belonged to same source signal.

6-3) with different frequency hopping point estimation to the signal that belongs to same source signal be stitched together, estimate as final time-frequency domain source signal, use Y _nN source signal of (p, q) expression the time time-frequency domain estimated value on frequency (p, q), p=1,2 ...., q=1,2 ..., N _Fft, namely

Step 7) root signal time-frequency domain estimated value is recovered the time domain source signal.Concrete steps are as follows

7-1) to each sampling instant p (p=0,1,2 ..., frequency domain data Y P-1) _n(p, q), q=0,1,2, L, N _Fft-1 is N _FftThe IFFT conversion of point obtains time domain source signal corresponding to p sampling instant, uses y _n(p, q _t) (q _t=0,1,2, L, N _Fft-1) expression.

7-2) to above-mentioned all time domain source signal y that constantly obtain _n(p, q _t) merge processing, obtain final time domain source signal and estimate.Concrete formula is as follows:

$s_n[\mathrm{kC}:(k+1)C-1]=\left\{\begin{array}{cc}\underset{m=0}{\overset{k}{\mathrm{\&Sigma;}}}{y}_n[m,(k-m)C:(k-m+1)C-1]& k<K_c\\ \underset{m=k-K_c+1}{\overset{k}{\mathrm{\&Sigma;}}}{y}_n[m,(k-m)C:(k-m+1)C-1]& k\&GreaterEqual;K_c\end{array}\right.k=\mathrm{0,1,2},L---\left(24\right)$

Here K _c=N _Fft/ C, the sampling number at C windowing interval.

Embodiment two:

In order to verify that the present invention estimates the accuracy of the Frequency Hopping Signal that obtains, the Frequency Hopping Signal that the present invention is proposed is owed surely blind separation algorithm and is carried out emulation.Suppose to have 4 frequency hopping synthesizer signals, adopt the even linear array of 2 array elements to receive frequency hopping frequency sets [1:0.5:8] MHz, sample frequency fs=20MHz, the BPSK modulation system, character rate is respectively 20kbps, 40kbps, 25kbps, 50kbps, incident angle is respectively-20 °, and 60 °, 80 °,-40 °, since the restriction of calculator memory, each 3 frequency hopping points of simulation process, FFT counts 4096, at every turn 256 sampled points in sliding window interval.

Fig. 2-5 has provided respectively Frequency Hopping Signal that the present invention estimates and the time domain waveform figure of source signal.The Frequency Hopping Signal time domain waveform that as can be seen from the figure estimates and original Frequency Hopping Signal time domain waveform are basically identical.Owe surely blind separation algorithm performance in order quantitatively to weigh the Frequency Hopping Signal that the present invention provides, Fig. 6 has provided estimation obtains under the different signal to noise ratio conditions Frequency Hopping Signal and the coefficient correlation between the original Frequency Hopping Signal.The signal that estimates of the present invention and source signal are when signal to noise ratio 0dB as can see from Figure 6, and the time domain coefficient correlation reaches more than 0.9.

The invention has the advantages that:

1. the present invention can not know under the condition of any channel information, only according to the mixed signal of a plurality of Frequency Hopping Signals that receive, estimates the frequency hopping synthesizer signal;

2. the present invention can under the condition of reception antenna number less than the source signal number, carry out blind estimation to a plurality of Frequency Hopping Signals;

3. the present invention has only utilized Short Time Fourier Transform, and amount of calculation is little, realizes easily;

4. when the present invention just carries out blind separation to Frequency Hopping Signal, can also estimate partial parameters.

The synchronized orthogonal Frequency Hopping Signal blind source separation method based on cluster that the embodiment of the invention provides, do not knowing under the condition of any channel information, only according to the mixed signal of a plurality of Frequency Hopping Signals of receiving, estimate the frequency hopping synthesizer signal, can be under the condition of reception antenna number less than the source signal number, a plurality of Frequency Hopping Signals are carried out blind estimation, only utilized Short Time Fourier Transform, amount of calculation is little, realize that easily the method can also be estimated partial parameters when Frequency Hopping Signal is carried out blind separation, practical, have stronger propagation and employment and be worth.

The above only is preferred embodiment of the present invention, not in order to limiting the present invention, all any modifications of doing within the spirit and principles in the present invention, is equal to and replaces and improvement etc., all should be included within protection scope of the present invention.

Claims (7)

1. synchronized orthogonal Frequency Hopping Signal blind source separation method based on cluster is characterized in that the method may further comprise the steps:

Step 1 is utilized and is contained the array antenna received of M array element from the Frequency Hopping Signal of a plurality of synchronized orthogonal frequency hopping radio sets, each road is received signal sample the M road discrete time-domain mixed signal after obtaining sampling

M=1,2, L, M;

Step 2 is carried out overlapping windowing Short Time Fourier Transform to M road discrete time-domain mixed signal, obtains the time-frequency domain matrix of M mixed signal

p＝0，1，L P-1，q＝0，1，L N _fft-1；

Step 3 is to the frequency-hopping mixing signal time-frequency domain matrix that obtains in the step 2

Carry out preliminary treatment;

Step 4 utilizes clustering algorithm to estimate jumping moment and corresponding normalized hybrid matrix column vector, the frequency hopping frequency of each jumping of each jumping;

Step 5, the normalization hybrid matrix column vector that estimation obtains according to step 4 is estimated time-frequency domain frequency hopping synthesizer signal;

Step 6 is spliced the time-frequency domain frequency hopping synthesizer signal between the different frequency hopping points;

Step 7 according to source signal time-frequency domain estimated value, is recovered the time domain source signal.

2. the method for claim 1 is characterized in that, in step 2, and (p, q) expression time-frequency index, concrete time-frequency value is Here Nfft represents the length of FFT conversion, and P represents the windowing number of times, and C is integer, the sampling number at expression Short Time Fourier Transform windowing interval, general C＜N _Fft, and K _c=N _Fft/ C is integer, and what that is to say employing is the Short Time Fourier Transform of overlapping windowing.

3. the method for claim 1 is characterized in that, in step 3, to frequency-hopping mixing signal time-frequency domain matrix

Carry out preliminary treatment, specifically comprise following two steps:

The first step is right

Go low-yield preliminary treatment, namely at each sampling instant p, will

Amplitude sets to 0 less than the value of thresholding ε, obtains

The setting of thresholding ε can be determined according to the average energy that receives signal;

Second step is found out the constantly time-frequency domain data of (p=0,1,2, L P-1) non-zero of p, uses

Expression, wherein

Constantly time-frequency response of expression p Corresponding frequency indices when non-zero to these non-zero normalization preliminary treatment, obtains pretreated vectorial b (p, q)=[b ₁(p, q), b ₂(p, q), L, b _M(p, q)] ^T, wherein

$b_m(p,q)=\left\{\begin{array}{cc}\frac{{\stackrel{V}{X}}_m^{\%}(p,q)}{{\stackrel{V}{X}}_1^{\%}(p,q)},& q={\stackrel{V}{q}}_p\\ 0,& q\&NotEqual;{\stackrel{V}{q}}_p\end{array}\right.,m=\mathrm{1,2},\mathrm{L\; M}.$

4. the method for claim 1 is characterized in that, in step 4, when utilizing clustering algorithm to estimate that the jumping moment of each jumping and each are jumped corresponding normalized hybrid matrix column vector, frequency hopping frequency, may further comprise the steps:

The first step, p (p=0,1,2 ... P-1) constantly, right

The frequency values of expression carries out cluster, the cluster centre number that obtains The carrier frequency number that expression p exists constantly,

Individual cluster centre then represents the size of carrier frequency, uses respectively

Expression;

Second step, to each sampling instant p (p=0,1,2 ... P-1), utilize clustering algorithm pair

Carry out cluster, can obtain equally

Individual cluster centre is used

Expression;

The 3rd step is to all

Average and round, obtain the estimation of source signal number

Namely

$\hat{N}=\mathrm{round}\left(\frac{1}{p}\underset{p=0}{\overset{P-1}{\mathrm{\&Sigma;}}}{\hat{N}}_p\right);$

In the 4th step, find out

The moment, use p _hExpression is to the p of the continuous value of each section _hAsk intermediate value, use

Represent the l section p that links to each other _hIntermediate value, then Represent the estimation constantly of l frequency hopping;

The 5th step is according to what estimate in the second step to obtain

P ≠ p _hAnd the 4th estimate that the frequency hopping obtain constantly estimates each and jumps corresponding in the step

Individual hybrid matrix column vector

Concrete formula is:

${\hat{a}}_n\left(l\right)=\left\{\begin{array}{cc}\frac{1}{{\stackrel{\&OverBar;}{p}}_h\left(1\right)}\&CenterDot;\underset{p=1,p\&NotEqual;p_h}{\overset{{\stackrel{\&OverBar;}{p}}_h\left(1\right)}{\mathrm{\&Sigma;}}}{b}_{n,p}^0& l=1,\\ \frac{1}{{\stackrel{\&OverBar;}{p}}_h\left(l\right)-{\stackrel{\&OverBar;}{p}}_h(l-1)}\&CenterDot;\underset{p={\stackrel{\&OverBar;}{p}}_h(l-1)+1,p\&NotEqual;p_h}{\overset{{\stackrel{\&OverBar;}{p}}_h\left(l\right)}{\mathrm{\&Sigma;}}}{b}_{n,p}^0& l>1,\end{array}\right.n=\mathrm{1,2},...,\hat{N}$

Here ${\hat{a}}_n\left(l\right)={[{\hat{a}}_{n,1}\left(l\right),{\hat{a}}_{n,2}\left(l\right),L,{\hat{a}}_{n,M}\left(l\right)]}^T(n=\mathrm{1,2},...,\hat{N})$ It is corresponding to represent that l jumps

Individual hybrid matrix column vector estimated value;

The 6th step, estimate the carrier frequency frequency that each jumping is corresponding, use It is corresponding to represent that l jumps

Individual frequency estimation, computing formula is as follows:

${\hat{f}}_{c,n}\left(l\right)=\left\{\begin{array}{cc}\frac{1}{{\stackrel{\&OverBar;}{p}}_h\left(1\right)}\&CenterDot;\underset{p=1,p\&NotEqual;p_h}{\overset{{\stackrel{\&OverBar;}{p}}_h\left(1\right)}{\mathrm{\&Sigma;}}}{f}_o^n\left(p\right)& l=1,\\ \frac{1}{{\stackrel{\&OverBar;}{p}}_h\left(l\right)-{\stackrel{\&OverBar;}{p}}_h(l-1)}\&CenterDot;\underset{p={\stackrel{\&OverBar;}{p}}_h(l-1)+1,p\&NotEqual;p_h}{\overset{{\stackrel{\&OverBar;}{p}}_h\left(l\right)}{\mathrm{\&Sigma;}}}{f}_o^n\left(p\right)& l>1,\end{array}\right.n=\mathrm{1,2},...,\hat{N}.$

5. the method for claim 1 is characterized in that, in step 5, estimates time-frequency domain frequency hopping synthesizer signal according to the normalization hybrid matrix column vector of estimating in the step 4 to obtain, and concrete steps are as follows:

The first step judges that to all sampling instant index p which this moment index belongs to and jump, and concrete grammar is: if

Represent that then p belongs to the l jumping constantly; If

Represent that then p belongs to the 1st jumping constantly;

Second step, to l (l=1,2, all of L) jumping are pl constantly, estimate that this jumps the time-frequency domain data of each frequency hopping synthesizer signal, computing formula is as follows:

$\left\{\begin{array}{c}{S}_j^{\%}(p_l,q)=\frac{1}{{\left|\right|{\hat{a}}_j\left(l\right)\left|\right|}^2}\&CenterDot;{\hat{a}}_j^H\left(l\right)\&times;\left[\begin{array}{c}{X}_1^{\%}(p_l,q)\\ X_2^{\%}(p_l,q)\\ M\\ X_M^{\%}(p_l,q)\end{array}\right]\\ j=\underset{j_0=1\hat{N}}{\arg \max }\left(\right|{[X_1^{\%}(p_l,q),X_2^{\%}(p_l,q),L,X_M^{\%}(p_l,q)]}^H\&times;{\hat{a}}_{j_0}\left(l\right)\left|\right)\\ S_m^{\%}(p_l,q)=0m=\mathrm{1,2},L,M,m\&NotEqual;j\\ q=\mathrm{0,1,2},L,N_{\mathrm{fft}}-1\end{array}\right..$

6. the method for claim 1 is characterized in that, in step 6, the time-frequency domain frequency hopping synthesizer signal between the different frequency hopping points is spliced, and concrete steps are as follows:

The first step, it is corresponding to estimate that l jumps Individual incident angle is used

Represent that l jumps n the incident angle that source signal is corresponding,

Computing formula as follows:

${\widehat{\mathrm{\&theta;}}}_n\left(l\right)=\frac{1}{M-1}\underset{m=2}{\overset{M}{\mathrm{\&Sigma;}}}{\sin }^{-1}\left[\frac{\mathrm{angle}({\hat{a}}_{n,m}\left(l\right)/{\hat{a}}_{n,m-1}\left(l\right))*c}{2\mathrm{\&pi;}{\hat{f}}_{c,n}\left(l\right)d}\right]n=\mathrm{1,2},...,\hat{N}$

Represent that l jumps n the hybrid matrix column vector that estimation obtains

M element;

Second step, judge l (l=2,3 ...) and source signal and first that jump to estimate jumps the corresponding relation between the source signal of estimation, judgment formula is as follows:

${m_n}^{\left(l\right)}=\underset{m}{\arg \min }|{\widehat{\mathrm{\&theta;}}}_m^{\left(l\right)}-{\widehat{\mathrm{\&theta;}}}_n^{\left(1\right)}|,n=\mathrm{1,2},L,\hat{N}$

M wherein _n ^(l)Represent that l jumps the m that estimates _n ^(l)Individual signal and first is jumped n the signal of estimating and is belonged to same source signal;

The 3rd step, with different frequency hopping point estimation to the signal that belongs to same source signal be stitched together, estimate as final time-frequency domain source signal, use Y _nN source signal of (p, q) expression the time time-frequency domain estimated value on frequency (p, q), p=0,1,2 ...., P, q=0,1,2 ..., N _Fft-1, namely

7. the method for claim 1 is characterized in that, in step 7, when recovering the time domain source signal according to source signal time-frequency domain estimated value, concrete steps are as follows:

The first step, to each sampling instant p (p=0,1,2 ...) and frequency domain data Y _n(p, q), q=0,1,2, L, N _Fft-1 is N _FftThe IFFT conversion of point obtains time domain source signal corresponding to p sampling instant, uses y _n(p, q _t) (qt=0,1,2, L, N _Fft-1) expression;

Second step is to above-mentioned all time domain source signal y that constantly obtain _n(p, q _t) merge processing, obtain final time domain source signal and estimate, concrete formula is as follows:

$s_n[\mathrm{kC}:(k+1)C-1]=\left\{\begin{array}{cc}\underset{m=0}{\overset{k}{\mathrm{\&Sigma;}}}{y}_n[m,(k-m)C:(k-m+1)C-1]& k<K_c\\ \underset{m=k-K_c+1}{\overset{k}{\mathrm{\&Sigma;}}}{y}_n[m,(k-m)C:(k-m+1)C-1]& k\&GreaterEqual;K_c\end{array}\right.k=\mathrm{0,1,2},L$

Here K _c=N _Fft/ C, the sampling number at C windowing interval.

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