CN109344754A - A kind of improvement type shortest path is deficient to determine source signal restoration methods - Google Patents
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Abstract
The invention belongs to radar-reconnaissance technical field, a kind of disclosed improvement type shortest path is deficient to determine source signal restoration methods.Under the conditions of being known to the observation signal, using the hybrid matrix of estimation as condition, it is converted into according to Sparse Component Analysis recovery resource signal problem and solves following optimization problems, it is greater than 2 or the source signal recovery situation equal to 2 in observation signal number, 1st and m-th of observation signal are formed a two-dimensional observation signal combination by the step of by step 1 to 10；For each combination, corresponding source signal is recovered using classical critical path method (CPM), then always there are m two-dimensional observation signal combination；A new matrix, the final estimation for obtaining n source signal are formed by isolated signal is combined by m two-dimensional observation signalSource signal as to be restored.The present invention can be handled radar signal, signal of communication, biomedicine signals etc., realize the deficient recovery for determining blind source separating source signal in the case where hybrid matrix estimated completion.
Description
Technical field
The invention belongs to radar-reconnaissance technical fields, further relate to one of Radar Signal Sorting Technology field and change
It owes to determine source signal restoration methods into formula shortest path.Technical solution of the present invention can be to radar signal, signal of communication, biomedicine
Signal etc. is handled, and realizes the deficient recovery for determining blind source separating source signal in the case where hybrid matrix estimated completion.
Background technique
It owes to determine blind source separating to be in emitter Signals prior information and propagation channel unknown parameters, and the number of observation signal
In the case where less than source signal number, the signal processing technology that estimates source signal merely with observation signal.In view of its tool
Standby exclusive ability owes to determine the research hotspot that blind source separating has become the circle of international signal processing in recent years.Currently, solving to owe fixed blind
Separation problem usual base in source uses two-step method thinking, i.e., first with observation signal estimated mixing matrix, recycles what is estimated to mix
It closes matrix and observation signal recovers source signal.Since hybrid matrix owes fixed, cannot directly finding the inverse matrix with realize source believe
Number recovery, the recovery of source signal also relates to the algorithm of a series of complex.It is blind that source signal recovery effects are directly related to signal
The success or failure of separating treatment, therefore source signal Restoration Algorithm Research has important theoretical value and practical significance.
There is document to assume that source signal has stringent orthogonality or quasi- orthogonality in time-frequency domain, i.e., it is complete in each time frequency point
It is not overlapped or is hardly overlapped entirely, source signal separation is realized by time-frequency mask.The degeneration separation estimation skill of the propositions such as Yilmaz
Art (Degenerate unmixing estimation technique, DUET) is a kind of typical time-frequency masking method,
Cobos etc. improves the accuracy of Signal separator to the improvement of DUET, but it is 2 that both methods, which is all only applicable to observation signal,
A situation.There is document to relax the assumed condition of orthogonality, only requires and be less than in the simultaneous source signal number of time frequency point
Observation signal number.Time-frequency masking method has been extended to the situation of observation signal more than two by Araki etc..Time-frequency masking method pair
The sparsity of signal requires very high.It is overlapped in certain time frequency points if the degree of rarefication of source signal is inadequate, under separating effect is serious
Drop.Document further relaxes assumed condition, and the simultaneous source signal of time frequency point is allowed to be not more than number of probes.
P.Bofill etc. proposes the shortest path source signal recovery algorithms based on source signal sparsity[1], method effect is good
It is good, but this method is only applicable to the situation that observation signal is 2 dimensions.M.Zibulevsky etc. is directed to abundant sparse signal, proposes
A kind of L1 norm source signal based on maximum a posteriori probability (Maximum Aposteriori Probability, MPA) restores
Algorithm.Under conditions of source signal is sufficiently sparse, L1 norm method can obtain good separating effect, and Theis etc. is demonstrated most
Smallization L1 norm method is equivalent to critical path method (CPM).Electronic information complex electromagnetic environment effect National Key Laboratory declares
National inventing patent " based on improve critical path method (CPM) it is deficient determine blind source separating source signal restoration methods (number of accepting:
2017102051088) ", classical shortest path source signal restoring method is improved, enables the algorithm to be suitable for observation letter
Source signal under number number more than two situation restores problem, but classical critical path method (CPM) still has room for improvement, owes to determine source to improve
The effect that signal restores.
M.Xiao etc. proposes a kind of source signal recovery algorithms (Statistically based on statistics sparse decomposition
Sparse Decomposition Principle, SSDP), the algorithm is by minimizing source signal in interval at a fixed time
Related coefficient estimate source signal, but the algorithm requires the non-zero source signal in each Fixed Time Interval to be no more than 2,
It is not suitable for non-sufficiently sparse deficient determine source signal recovery problem.Zhao Min etc. extends SSDP algorithm, has obtained one
For non-sparse decomposition principle (the Statistically Non-Sparse Decomposition of 2 observation signals
Principle,SNSDP)。
Compressive sensing theory, which also be used to realize, to be owed to determine source signal recovery.Under conditions of hybrid matrix is completed to estimate, owe
It is similar with compressed sensing reconstruction model to determine blind separation source signal recovery problem, difference is that compressed sensing requires very sparsity
It is high and mainly for big data quantity problem.Yan Xin improves complementary matching pursuit algorithm, and the time for reducing algorithm is multiple
Miscellaneous degree.W.H.Fu etc. is owing to determine source signal recovery side to greedy algorithm, L1 norm algorithm and smooth L0 norm algorithm three classes method
The effect in face is compared, and proposes a kind of SCMP algorithm, is improved signal recovery effects and is reduced the calculating time.Pressure
Contracting perception theory is applied to owe to determine blind source separating source signal to restore existing main problem to be the sparsity requirement for source signal
It is high, data sampling point requirement is more, and calculate the time it is longer.Bibliography:
[1]P.Bofill,M.Zibulevsky.Underdeterminedblind source separation using
sparse representations[J].Signal Process.,2001(81):2353-2362。
[2] Chen Jie tiger is compressed sensing based owes to determine the Xi'an blind separation source signal Restoration Algorithm Research [D]: Xi'an electronics
University of Science and Technology, 2015.
[3] Fu Weihong, agriculture is refined, Chen Jiehu, and is waited to determine recovery [J] the Beijing postal of blind separation source signal based on the deficient of RBF network
Electric college journal, 2017,40 (1): 94-98.
Summary of the invention
For the source signal restoration methods based on critical path method (CPM), it is an object of the invention to overcome above-mentioned prior art
Deficiency proposes a kind of improvement type shortest path and owes determine source signal restoration methods, with realization in observation signal number more than two
In the case of source signal Exact recovery.
For achieving the above object, the present invention adopts the following technical scheme:
A kind of improvement type shortest path is owed determine source signal restoration methods, under the conditions of being known to the observation signal, to estimate
Hybrid matrix be condition, according to Sparse Component Analysis theory, recovery resource signal problem be converted into solve it is following optimization ask
Topic:
In formula, x (t) is observation signal, and observation signal number is m, and A is the hybrid matrix of estimation, and source signal number is n,
aiFor the i-th column of hybrid matrix, si(t) it is i-th of source signal, minimizes at this timeBe exactly to observation signal along
Linear decomposition is done in the direction that hybrid matrix two arranges, and finds out the shortest path from origin to observation signal.For observation signal number
The situation that mesh is 2, the solution thought of the above problem as indicated with 1, will minimize at this timeIt can be seen from the figure that from
The shortest path of origin to observation signal x be with the angle of x closest to two vectors a and b；
When observation signal number is greater than 2 or the source signal recovery situation equal to 2 takes phase for m observation signal every time
Two adjacent observation signals, might as well be expressed as i-th and j-th of observation signal, i=1,2 ..., m-1, j=i+1 locate every time
The observation signal of reason is the combination of two adjacent observation signals, is obtainedKind combination；Realize that specific step is as follows for this method:
Step 1: in the m observation signal x (t) that one-shot measurement obtains, x (t)=[x1(t),x2(t),…,xm(t)]T；
Subscript T in formula is that roman then indicates transposition, and similarly hereinafter, sampling instant t=1,2 ..., T choose adjacent two observations letter every time
Number xi(t) and xj(t), i=1,2 ..., m-1, j=i+1；
Step 2: x is combined to each of step 1 observation signalk(t), k=1,2 ..., m are pre-processed, and removal is seen
The column vector that signal is all zero is surveyed, then direction unitizes；
Step 3: calculate the angle of each base vector of hybrid matrix A: the angle of base vector is defined as
AjIndicate j-th of column vector of hybrid matrix, j=1,2 ..., n, n is source signal number, and subscript 2 and 1 respectively indicates the column vector
The 2nd row and the 1st row；
Step 4: at each observation moment, for the combination of m only 2 observation signals, using classical critical path method (CPM),
Calculate separately the observation signal vector x in each combinationtAngle；
Step 5: finding out the moment closest to observation signal vector angle, θtTwo basal orientation measuring angles, and record corresponding
Two column vector a of hybrid matrixiAnd bi, wherein ai,biI-th of combined serial number in ∈ A, i m combination of expression, i=1,
2,…,m；
Step 6: assuming that Ar=[ai bi], ArFor a of hybrid matrix AiAnd biOne 2 × 2 submatrix that two column are constituted,
aiAnd biIt is in t moment closest to xtTwo vectors, enable
Step 7: the source signal of moment t restores as the following formula:
Wherein,It is x along vector aiAnd biThe component of both direction；
It is greater than 2 or the source signal recovery situation equal to 2 in observation signal number, is two in observation signal per treatment
After the combination of a adjacent observation signal；
1st and m-th of observation signal are formed into a two-dimensional observation signal combination, then always there are m two-dimensional observation letter
Number combination；For each combination, corresponding source signal is recovered using classical critical path method (CPM), then the source signal recovered has m
Group, if source signal number is n, then after carrying out signal recovery by the m observation signal two-dimensional combination that former observation signal combines,
N separation signal can be obtained respectively, if the isolated signal of each combination is expressed asWherein i=1,2 ..., m indicates every
A two-dimensional observation signal combines serial number, and k=1,2 ..., n indicate the isolated signal serial number of each two-dimensional combination: expression is adopted
Number of samples；The isolated signal of this m group is formed into a new matrix, is expressed as
ThenFor the vector combinatorial matrix of m × n dimension；Wherein, subscriptTIndicate transposition；
For matrixThe vector angle between its row and row is sought, the square matrix Q of mn × mn dimension is obtained；For this
The preceding n row of square matrix × mn column, by detecting whether matrix element is greater than 0, and less than 20 °, this representing matrixMiddle signal
The angle of vector less than 20 °, average respectively by the signal for these angles less than 20 °, and one as source signal estimates
Meter, the final estimation for obtaining n source signalSource signal as to be restored；
Wherein step 1 is choosing two adjacent observation signal x every timei(t) and xj(t), i=1,2 ..., m-1, j=i+
After 1；1st and m-th of observation signal are formed into a two-dimensional observation signal combination, then can generate m only 2 observation signals
Signal combination, be expressed as xk(t)=[xi(t),xj(t)]T, k=1,2 ..., m；
The step 8 of use: for each combination, corresponding source signal is recovered using classical critical path method (CPM), then is restored
Source signal out has m group, uses source signal number for n, then after carrying out signal recovery by m observation signal two-dimensional combination, respectively
N signal, combine isolated signal if each and be expressed asWherein i=1,2 ..., m indicates each two-dimensional observation
Signal combination, k=1,2 ..., n indicate the isolated signal of each two-dimensional combination: indicate sampling number；
The step 9 of use: a new matrix, table are formed by isolated signal is combined by m two-dimensional observation signal
It is shown as Vector for m × n dimension combines square
Battle array, each vector indicate a signal, sampling number T；
Step 10: being directed to matrixThe vector angle between its row and row is sought, the square matrix Q of mn × mn dimension is obtained；
For preceding n row × mn column of the square matrix, by detecting whether matrix element is greater than 0, and less than 20 °, this representing matrix
The angle of middle signal vector is less than 20 °, and the signal for these angles less than 20 ° is averaged respectively, as source signal
One estimation, the final estimation for obtaining n source signalSource signal as to be restored.
Technical solution of the present invention bring superiority is as follows:
First, owing determine source signal recovery algorithms the present invention overcomes existing critical path method (CPM), can not to be suitable for observation signal a
Number the deficient of more than two determines blind source separating signal recovery problems.
Second, the principle of the invention is more clear, and algorithm steps are more succinct, and signal recovery effects are more preferable, calculates time cost
It is smaller.
Detailed description of the invention
Critical path method (CPM) schematic diagram when Fig. 1 observation signal is 2；
Fig. 2-4 is m=2 of the present invention, the simulation result diagram of n=5 ... ... signal-to-noise ratio and existing method signal-to-noise ratio.
Specific embodiment
Below with reference to attached drawing and example in detail embodiments of the present invention, attached drawing described herein is used to provide
A further understanding of the present invention constitutes part of this application, and illustrative embodiments and their description of the invention are for explaining
The present invention, and do not constitute a limitation of the invention.
As shown in Figure 1,2,3, 4, a kind of improvement type shortest path is owed to determine source signal restoration methods, is known to observation signal
Under conditions of, using the hybrid matrix of estimation as condition, according to Sparse Component Analysis theory, recovery resource signal problem can be converted into
Solve following optimization problems:
In formula, x (t) is observation signal, and observation signal number is m, and A is the hybrid matrix of estimation, and source signal number is n,
aiFor the i-th column of hybrid matrix, si(t) it is i-th of source signal, minimizes at this timeBe exactly to observation signal along
Linear decomposition is done in the direction that hybrid matrix two arranges, and finds out the shortest path from origin to observation signal.For observation signal number
The situation that mesh is 2, the solution thought of the above problem as indicated with 1, will minimize at this timeIt can be seen from the figure that from
The shortest path of origin to observation signal x be with the angle of x closest to two vectors a and b.
It is greater than 2 or the source signal recovery problem equal to 2 for observation signal number.Improved though is for m observation
Signal takes two adjacent observation signals every time, might as well be expressed as i-th and j-th of observation signal, i=1,2 ..., m-1, j
=i+1, i.e., observation signal per treatment are the combinations of two adjacent observation signals, can be obtainedKind combination, by the 1st and m
A observation signal forms a two-dimensional observation signal combination, then can obtain m two-dimensional observation signal combination in total.For each group
It closes, recovers corresponding source signal using classical critical path method (CPM), then the source signal recovered has m group, as source signal number is
N after then carrying out signal recovery by the m observation signal two-dimensional combination that former observation signal combines, can obtain n separation letter respectively
Number, if the isolated signal of each combination is expressed asWherein i=1,2 ..., m indicates each two-dimensional observation signal group
Serial number is closed, k=1,2 ..., n indicate the isolated signal serial number of each two-dimensional combination: indicate sampling number.By this m component
A new matrix is formed from obtained signal, is represented by
ThenFor the vector combinatorial matrix of m × n dimension.Wherein, subscriptTIndicate transposition.
For matrixThe vector angle between its row and row is sought, the square matrix Q of mn × mn dimension can be obtained.For
The preceding n row of the square matrix × mn column, by detecting whether matrix element is greater than 0, and less than 20 °, this representing matrixMiddle letter
The angle of number vector is less than 20 °, and the signal for these angles less than 20 ° is averaged respectively, one as source signal
Estimation, can finally obtain the estimation of n source signalSource signal as to be restored.
Realizing this algorithm, specific step is as follows:
Step 1: in the m observation signal x (t) that one-shot measurement obtains, x (t)=[x1(t),x2(t),…,xm(t)]T
(the subscript T in formula is that roman then indicates transposition, similarly hereinafter), sampling instant t=1,2 ..., T choose two adjacent observations every time
Signal xi(t) and xj(t), the 1st and m-th of observation signal are formed a two-dimensional observation letter by i=1,2 ..., m-1, j=i+1
Number combination, then can generate the signal combination of only 2 observation signals of m, be expressed as xk(t)=[xi(t),xj(t)]T, k=1,
2,…,m；
Step 2: x is combined to each of step 1 observation signalk(t), k=1,2 ..., m are pre-processed, and removal is seen
The column vector that signal is all zero is surveyed, then direction unitizes；
Step 3: calculate the angle of each base vector of hybrid matrix A: the angle of base vector is defined as
AjIndicate j-th of column vector of hybrid matrix, j=1,2 ..., n, n is source signal number, and subscript 2 and 1 respectively indicates the column vector
The 2nd row and the 1st row；
Step 4: at each observation moment, for the combination of m only 2 observation signals, using classical critical path method (CPM),
Calculate separately the observation signal vector x in each combinationtAngle；
Step 5: finding out the moment closest to observation signal vector angle, θtTwo basal orientation measuring angles, and record corresponding
Two column vector a of hybrid matrixiAnd bi, wherein ai,biI-th of combined serial number in ∈ A, i m combination of expression, i=1,
2,…,m；
Step 6: assuming that Ar=[ai bi], ArFor a of hybrid matrix AiAnd biOne 2 × 2 submatrix that two column are constituted,
aiAnd biIt is in t moment closest to xtTwo vectors, enable
Step 7: the source signal of moment t restores as the following formula:
Wherein,It is x along vector aiAnd biThe component of both direction；
Step 8: for each combination, recovering corresponding source signal using classical critical path method (CPM), then the source recovered
Signal has m group, such as source signal number is n, then after carrying out signal recovery by m observation signal two-dimensional combination, can obtain n respectively
Signal, if the isolated signal of each combination is expressed asWherein i=1,2 ..., m indicates each two-dimensional observation signal
Combination, k=1,2 ..., n indicate the isolated signal of each two-dimensional combination: indicate sampling number；
Step 9: forming a new matrix for isolated signal is combined by m two-dimensional observation signal, be represented by For a m × n dimension vector combinatorial matrix, often
A vector indicates a signal, sampling number T；
Step 10: being directed to matrixThe vector angle between its row and row is sought, the square matrix of mn × mn dimension can be obtained
Q.For preceding n row × mn column of the square matrix, by detecting whether matrix element is greater than 0, and less than 20 °, this representing matrixThe angle of middle signal vector is less than 20 °, and the signal for these angles less than 20 ° is averaged respectively, as source
One estimation of signal, can finally obtain the estimation of n source signalSource signal as to be restored.
The specific implementation step of this method is as follows:
Step 1: in the m observation signal x (t) that one-shot measurement obtains, x (t)=[x1(t),x2(t),…,xm(t)]T
(the subscript T in formula is that roman then indicates transposition, similarly hereinafter), sampling instant t=1,2 ..., T choose two adjacent observations every time
Signal xi(t) and xj(t), the 1st and m-th of observation signal are formed a two-dimensional observation letter by i=1,2 ..., m-1, j=i+1
Number combination, then can generate the signal combination of only 2 observation signals of m, be expressed as xk(t)=[xi(t),xj(t)]T, k=1,
2,…,m；
Step 2: x is combined to each of step 1 observation signalk(t), k=1,2 ..., m are pre-processed, and removal is seen
The column vector that signal is all zero is surveyed, then direction unitizes；
Step 3: calculate the angle of each base vector of hybrid matrix A: the angle of base vector is defined as
AjIndicate j-th of column vector of hybrid matrix, j=1,2 ..., n, n is source signal number, and subscript 2 and 1 respectively indicates the column vector
The 2nd row and the 1st row；
Step 4: at each observation moment, for the combination of m only 2 observation signals, using classical critical path method (CPM),
Calculate separately the observation signal vector x in each combinationtAngle；
Step 5: finding out the moment closest to observation signal vector angle, θtTwo basal orientation measuring angles, and record corresponding
Two column vector a of hybrid matrixiAnd bi, wherein ai,biI-th of combined serial number in ∈ A, i m combination of expression, i=1,
2,…,m；
Step 6: assuming that Ar=[ai bi], ArFor a of hybrid matrix AiAnd biOne 2 × 2 submatrix that two column are constituted,
aiAnd biIt is in t moment closest to xtTwo vectors, enable
Step 7: the source signal of moment t restores as the following formula:
Wherein,It is x along vector aiAnd biThe component of both direction；
Step 8: for each combination, recovering corresponding source signal using classical critical path method (CPM), then the source recovered
Signal has m group, such as source signal number is n, then after carrying out signal recovery by m observation signal two-dimensional combination, can obtain n respectively
Signal, if the isolated signal of each combination is expressed asWherein i=1,2 ..., m indicates each two-dimensional observation signal
Combination, k=1,2 ..., n indicate the isolated signal of each two-dimensional combination: indicate sampling number；
Step 9: forming a new matrix for isolated signal is combined by m two-dimensional observation signal, be represented by For a m × n dimension vector combinatorial matrix, often
A vector indicates a signal, sampling number T；
Step 10: being directed to matrixThe vector angle between its row and row is sought, the square matrix of mn × mn dimension can be obtained
Q.For preceding n row × mn column of the square matrix, by detecting whether matrix element is greater than 0, and less than 20 °, this representing matrixThe angle of middle signal vector is less than 20 °, and the signal for these angles less than 20 ° is averaged respectively, as source
One estimation of signal, can finally obtain the estimation of n source signalSource signal as to be restored.
1. simulated conditions:
Experimental verification of the invention is in DELL9020MT type personal computer, Intel (R) Core (TM) i7-
4770CPU@3.40GHz is carried out under the simulated conditions of 64 Windows operating systems, and simulation software uses MATLAB
R2010a.The recovery effects of source signal are using separation signal interference ratio and similarity factor index, and the calculation formula of two indices is respectively such as
Shown in formula (4) and (5).Wherein,WithRespectively indicate i-th separated and j-th of signal, si(t) it indicates i-th
Source signal.
In following emulation experiments, mixed signal SNR ranges are 8-20dB, simulation step length 2dB, each signal-to-noise ratio
Locate Monte Carlo to emulate 100 times.In order to sufficiently verify the validity of this paper innovatory algorithm, carry out three for different situations
Group emulation experiment.
Simulation parameter setting:
Experiment one: emitter Signals number is 5, this 5 signals are sufficiently sparse in time domain, and signal pattern and parameter are such as
Under:
s1For general pulse signal, carrier frequency fc1=5MHz, pulsewidth tr1=10 μ s, pulse repetition period Tr1=100 μ s, arteries and veins
Rush initial time t01=0；
s2For general pulse signal, carrier frequency fc2=5MHz, pulsewidth tr2=7 μ s, pulse repetition period Tr2=100 μ s, pulse
Initial time t02=10 μ s；
s3For linear FM signal, carrier frequency fc3=5MHz, pulsewidth tr3=10 μ s, pulse repetition period Tr3=100 μ s, arteries and veins
Rush initial time t03=20 μ s, bandwidth is B in arteries and veins3=10MHz；
s4For linear FM signal, carrier frequency fc4=5MHz, pulsewidth tr4=8 μ s, pulse repetition period Tr4=100 μ s, pulse
Initial time t04=30 μ s, bandwidth B in arteries and veins4=15MHz；
s5For sinusoidal phase-modulated signal, carrier frequency fc5=5MHz, pulsewidth tr5=8 μ s, pulse repetition period Tr5=100 μ s, pulse
Initial time t05=40 μ s, frequency modulating signal fa5=100kHz, modulation index a5=5.
Receiver sample frequency is 50MHz, and signal sampling points are 10000, and observation signal number is 2, and hybrid matrix A is adopted
It is generated with rand function,Work as m=2, when n=5, that is, sees
In the case that survey signal is 2, the method for the present invention substantially becomes classical shortest path source signal restoration methods, uses this hair
Bright match tracing method (CMP) complementary with document[2], the complementary match tracing method (L1CMP) based on L1 norm[2]And diameter
To base network method (RBF network)[3]Source signal is restored, as a result as shown in attached drawing 2 (a)-(c).
Experiment two: with experiment one, receiver sample frequency is 50MHz for emitter Signals and number, and signal sampling points are 10000, are seen
Surveying signal number is 3, and hybrid matrix A is generated using rand function,
Work as m=3, when n=5, i.e., in the case that observation signal is 3, uses the CMP method in context of methods and document, L1CMP method
Source signal is restored with RBF network method, as a result as shown in attached drawing 3 (a)-(c).
Experiment three: emitter Signals number is 7, this 7 signals are sufficiently sparse in time domain, and signal pattern and parameter are such as
Under:
s1For NLFM signal, carrier frequency fc1=10MHz, pulsewidth tr1=16 μ s, pulse repetition period Tr1=200 μ s,
Bandwidth B in arteries and veins1=10MHz, pulse initial time t01=0；
s2For general pulse signal, carrier frequency fc2=8MHz, pulsewidth tr2=15 μ s, pulse repetition period Tr2=180 μ s, arteries and veins
Rush initial time t02=20 μ s；
s3For linear FM signal, carrier frequency fc3=5MHz, pulsewidth tr3=15 μ s, pulse repetition period Tr3=180 μ s, arteries and veins
Rush initial time t03=40 μ s, bandwidth B in arteries and veins3=20MHz；
s4For linear FM signal, carrier frequency fc4=5MHz, pulsewidth tr4=20 μ s, pulse repetition period Tr4=180 μ s, arteries and veins
Rush initial time t04=60 μ s, bandwidth B in arteries and veins4=15MHz；
s5For sinusoidal phase-modulated signal, carrier frequency fc5=5MHz, pulsewidth tr5=20 μ s, pulse repetition period Tr5=200 μ s, arteries and veins
Rush initial time t05=80 μ s, frequency modulating signal fa5=200kHz, modulation index a5=5；
s6For sinusoidal phase-modulated signal, carrier frequency fc6=5MHz, pulsewidth tr6=15 μ s, pulse repetition period Tr6=200 μ s, arteries and veins
Rush initial time t05=100 μ s, frequency modulating signal fa6=200kHz, modulation index a6=2；
s7For NLFM signal, carrier frequency fc7=15MHz, pulsewidth tr7=20 μ s, pulse repetition period Tr7=200 μ s,
Bandwidth B in arteries and veins7=5MHz, pulse initial time t07=115 μ s.
The sample frequency that receiver receives signal is 50MHz, sampling number 10000.Hybrid matrix uses arbitrary function
It generates,Work as m=4, when n=7,
In the case that i.e. observation signal is 4, using the CMP method in the method for the present invention and document, L1CMP method and RBF network side
Method restores source signal, as a result as shown in attached drawing 4 (a)-(c).
2. analysis of simulation result:
Work as m=2, when n=5, i.e., in the case that observation signal is 2, the present invention becomes classical critical path method (CPM), with
The increase of mixed signal signal-to-noise ratio, by Fig. 2 (a) and (b) as it can be seen that being believed using the signal that unlike signal recovery algorithms are restored dry
Than and similarity factor be all in increase tendency, indicate that effect of signal separation turns for the better, coincide with general understanding.But algorithms of different restores letter
Number effect relatively aspect, under the simulated conditions, set forth herein method separating effects to be slightly inferior to CMP method, better than L1CMP and
RBF network method.In terms of computational efficiency, Fig. 2 (c) reflects that set forth herein the calculating times of method far less than other methods
The calculating time.
Work as m=3, when n=5, for this experimental setup condition, can be seen that improvement side herein from Fig. 3 (a), 3 (b) and 3 (c)
The separating effect of method is better than other three kinds of methods, and computational efficiency is higher than CMP method and RBF network method, is slightly inferior to the side L1CMP
Method.
Work as m=4, when n=7, can be seen that context of methods separating effect is compared to other three kinds of methods from Fig. 4 (a) and (b)
It is slightly weaker, but from the point of view of separation signal interference ratio and similarity factor numerical value, such numerical value indicates that this paper innovatory algorithm is enough accurately
Ground separates 7 road source signals from 4 reception signals, and computational efficiency and experiment two results presentation rule are essentially identical.
In summary emulation experiment shows that the method for the present invention can be when observation signal number be 2 or more than two
Using.Under conditions of the method for the present invention can be abundant in source signal time domain and non-sufficiently sparse, with the realization of higher computational efficiency
Comparatively ideal source signal restores.Source signal it is non-sufficiently it is sparse in the case where, can by observation signal carry out rarefaction representation, into
And the method for the present invention is applied to restore source signal.
Claims (1)
1. a kind of improvement type shortest path is owed to determine source signal restoration methods, under the conditions of being known to the observation signal, with estimation
Hybrid matrix is condition, and according to Sparse Component Analysis theory, recovery resource signal problem, which is converted into, solves following optimization problems:
In formula, x (t) is observation signal, and observation signal number is m, and A is the hybrid matrix of estimation, and source signal number is n, aiIt is mixed
Close the i-th column of matrix, si(t) it is i-th of source signal, minimizes at this timeIt is exactly to observation signal along mixed moment
Linear decomposition is done in the direction of certain two column of battle array, finds out the shortest path from origin to observation signal；It is 2 for observation signal number
The case where, it to minimizeFrom origin to the shortest path of observation signal x be with the angle of x closest to two
Vector a and b；
When observation signal number be greater than 2 or the source signal recovery situation equal to 2 take every time adjacent for m observation signal
Two observation signals might as well be expressed as i-th and j-th of observation signal, and i=1,2 ..., m-1, j=i+1 are that is, per treatment
Observation signal is the combination of two adjacent observation signals, is obtainedKind combination；Realize that specific step is as follows for this method:
Step 1: in the m observation signal x (t) that one-shot measurement obtains, x (t)=[x1(t),x2(t),…,xm(t)]T；In formula
Subscript T be roman then indicate transposition, similarly hereinafter, sampling instant t=1,2 ..., T choose two adjacent observation signal x every timei
(t) and xj(t), i=1,2 ..., m-1, j=i+1；
Step 2: x is combined to each of step 1 observation signalk(t), k=1,2 ..., m are pre-processed, removal observation letter
It number is all zero column vector, then direction unitizes；
Step 3: calculate the angle of each base vector of hybrid matrix A: the angle of base vector is defined asAjTable
Show j-th of column vector of hybrid matrix, j=1,2 ..., n, n is source signal number, and subscript 2 and 1 respectively indicates the 2nd of the column vector
Capable and the 1st row；
Step 4: at each observation moment, for the combination of m only 2 observation signals, using classical critical path method (CPM), respectively
Calculate the observation signal vector x in each combinationtAngle；
Step 5: finding out the moment closest to observation signal vector angle, θtTwo basal orientation measuring angles, and record corresponding mixing
Two column vector a of matrixiAnd bi, wherein ai,biI-th of combined serial number in ∈ A, i m combination of expression, i=1,2 ...,
m；
Step 6: assuming that Ar=[ai bi], ArFor a of hybrid matrix AiAnd biOne 2 × 2 submatrix that two column are constituted, aiAnd bi
It is in t moment closest to xtTwo vectors, enable
Step 7: the source signal of moment t restores as the following formula:
Wherein,It is x along vector aiAnd biThe component of both direction；It is characterized in that:
It is greater than 2 or the source signal recovery situation equal to 2 in observation signal number, is two phases in observation signal per treatment
After the combination of adjacent observation signal；
1st and m-th of observation signal are formed into a two-dimensional observation signal combination, then always there are m two-dimensional observation signal group
It closes；For each combination, corresponding source signal is recovered using classical critical path method (CPM), then the source signal recovered has m group, such as
Source signal number is n, then after carrying out signal recovery by the m observation signal two-dimensional combination that former observation signal combines, respectively
N separation signal can be obtained, if the isolated signal of each combination is expressed asWherein i=1,2 ..., m indicates each two
It tieing up observation signal and combines serial number, k=1,2 ..., n indicate the isolated signal serial number of each two-dimensional combination: indicate sampled point
Number；The isolated signal of this m group is formed into a new matrix, is expressed as
ThenFor the vector combinatorial matrix of m × n dimension；Wherein, subscriptTIndicate transposition；
For matrixThe vector angle between its row and row is sought, the square matrix Q of mn × mn dimension is obtained；For the square matrix
Preceding n row × mn column, by detecting whether matrix element is greater than 0, and less than 20 °, this representing matrixMiddle signal vector
Angle less than 20 °, average respectively by the signal for these angles less than 20 °, as an estimation of source signal, finally
Obtain the estimation of n source signalSource signal as to be restored；
Wherein step 1 is choosing two adjacent observation signal x every timei(t) and xj(t), after i=1,2 ..., m-1, j=i+1；
1st and m-th of observation signal are formed into a two-dimensional observation signal combination, then can generate the letter of m only 2 observation signals
Number combination, be expressed as xk(t)=[xi(t),xj(t)]T, k=1,2 ..., m；
The step 8 of use: for each combination, corresponding source signal is recovered using classical critical path method (CPM), then is recovered
Source signal has m group, uses source signal number for n, then after carrying out signal recovery by m observation signal two-dimensional combination, obtains n respectively
Signal, if the isolated signal of each combination is expressed asWherein i=1,2 ..., m indicates each two-dimensional observation signal
Combination, k=1,2 ..., n indicate the isolated signal of each two-dimensional combination: indicate sampling number；
The step 9 of use: a new matrix is formed by isolated signal is combined by m two-dimensional observation signal, is expressed as For a m × n dimension vector combinatorial matrix, often
A vector indicates a signal, sampling number T；
Step 10: being directed to matrixThe vector angle between its row and row is sought, the square matrix Q of mn × mn dimension is obtained；For
The preceding n row of the square matrix × mn column, by detecting whether matrix element is greater than 0, and less than 20 °, this representing matrixMiddle letter
The angle of number vector is less than 20 °, and the signal for these angles less than 20 ° is averaged respectively, one as source signal
Estimation, the final estimation for obtaining n source signalSource signal as to be restored.
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