CN110412499A - Broadband DOA Estimation algorithm based on the RSS algorithm under compressive sensing theory - Google Patents

Broadband DOA Estimation algorithm based on the RSS algorithm under compressive sensing theory Download PDF

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CN110412499A
CN110412499A CN201910638851.1A CN201910638851A CN110412499A CN 110412499 A CN110412499 A CN 110412499A CN 201910638851 A CN201910638851 A CN 201910638851A CN 110412499 A CN110412499 A CN 110412499A
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窦慧晶
梁霄
张文倩
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Beijing University of Technology
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Abstract

Broadband DOA Estimation algorithm based on the RSS algorithm under compressive sensing theory belongs to the related fieldss such as array signal processing, radar detection.The present invention, with the polydispersity index signal required far below Nyquist sampling thheorem, while can restore signal in the case where guaranteeing that information is not lost completely again.Data at data at each frequency point and reference frequency point are realized that " shared " improves the precision of estimation so as to avoid orientation pre-estimation by the present invention.The present invention combines compressive sensing theory with DOA estimation, divides into the narrow band signal such as broadband signal using the thought of focusing, so that the thought using narrowband is solved, greatly reduces the huge calculation amount of original broadband estimation.The precision of estimation is improved under the premise of identical sampling.

Description

Broadband DOA Estimation algorithm based on the RSS algorithm under compressive sensing theory
Technical field
The present invention is a kind of direction of arrival (DOA) algorithm for estimating, is applied in wireless communication, medical imaging, electronic countermeasure etc. Task can be automatically performed the estimation that one-dimensional wave reaches orientation angle.The invention belongs to the correlations such as array signal processing, radar detection Field.
Background technique
Array signal processing is also known as airspace signal processing, is an important branch of modern signal processing, defends in movement Star communication, seismic monitoring and the fields such as radio astronomy and national economy generally use, and have obtained extensive research and hair Exhibition.Array signal processing is mainly by being placed on the different position in space according to fixed mode for one group of sensor, to this A little sensor received signals carry out corresponding data processing and theory analysis, extract the useful signal in electromagnetic signal and suppression Noise processed and interference signal.
Most basic problem is the estimation of spacing wave direction of arrival (DOA) in array signal processing field, and signal source exists Energy distribution in space on all directions can indicate with its spatial spectrum, i.e. the direction of arrival of space spectral representation signal.DOA Estimation is to be determined using array signal processing method more in space in complicated electromagnetic environment according to array antenna received signals The spatial position of a interested signal, and then obtain the deflection that signal reaches array.DOA estimation has highly important grind Study carefully value and application value, be widely used in radar and communication system, it has also become the hot spot of array signal processing area research.
DOA estimation theory have passed through the research and development of many decades, form more perfect theoretical system and classics Algorithm.Currently, high-resolution DOA algorithm for estimating is broadly divided into three kinds: the first is to be in Capon Adaptive beamformer method The linear prediction class algorithm of representative, by the airspace for forming desired beam shape acquisition signal using information for improving signal Spectrum；The subspace for representative that be for second with multiple signal classification (multiple signal classification, MUSIC) be Class algorithm is decomposed, constructs high-resolution space spectral peak according to Subspace Decomposition, crosses the frontier of DOA estimation；The third It is the subspace fitting algorithm with maximum likelihood algorithm (maximum likelihood, ML) for representative, this algorithm needs are searched Suo Duowei spectral peak, statistic property is excellent, but operation complexity needs suitable initial value.These classical DOA algorithm for estimating exist Using when have certain limitation, the limitation of subspace class algorithm can not be broken through, in low signal-to-noise ratio, small snap and information source space Direction of arrival generally can not be accurately estimated when spacing very little, practicability is subject to certain restrictions.
In recent years, it with the appearance of compressive sensing theory system and constantly improve, core theory sparse signal reconfiguring draws Play the concern of domestic and foreign scholars.The appearance of sparse theory and compressed sensing has led the new direction of Estimation of Spatial Spectrum problem, i.e., sharp DOA estimation sparse model is established with the airspace sparse characteristic of signal, restores to receive signal using sparse restructing algorithm, overcomes biography The deficiency of system DOA algorithm for estimating.Compressed sensing is really exactly will be to reconstruction signal rarefaction representation, under certain condition, can be with It is sampled with the frequency lower than signal bandwidth, it is only necessary to a small amount of observation data, it will be able to realize the weight to signal high probability Structure or approximation, have been greatly saved system resource.DOA estimation method based on rarefaction representation is no longer by coherent signal and array junctions The influence of structure reduces the hits of signal, the cost of data transmission, storage and processing, improves the estimation performance of parameter.Using dilute It dredges signal reconstruction algorithm and carries out Estimation of Spatial Spectrum, associative array signal explores sparse restructuring array signal in the sparsity in airspace Method for parameter estimation improves the practicability of algorithm, has important theoretical value and development prospect.
Summary of the invention
Current existing DOA algorithm for estimating is primarily present the drawbacks such as calculation amount is excessive, and solving precision is not high enough, on solving The defect for stating technology, the present invention is based on the RSS algorithms of compressive sensing theory we have proposed a kind of, to reduce algorithm calculating Amount, improves anti-noise jamming ability.
For with reaching above-mentioned mesh, the present invention the following steps are included:
1) arrival bearing of signal is estimated using conventional low resolution algorithm, obtains DOA initial estimation set θ, Reference frequency point f is determined simultaneously0。
2) the array manifold matrix A (f of all sub-bands is constructed according to DOA initial value θj, θ), obtain all sub-bands Focusing transform battle array T (fj)；
3) focusing transform battle array T (f is utilizedj) the array received data X (f in respective frequency sub-bandsj) focusing frequency point is transformed to, Obtain the array output data Y (f under the frequency pointj) and correlation matrix Ry(fj)；
4) pass through frequency domain smoothing for transformed data Correlation Matrix Ry(fj) it is built into the unified array in reference frequency point Correlation matrix RY；
5) the final estimated value of broadband signal DOA is obtained using compressed sensing based L1-SVD algorithm；
Compressive sensing theory is combined the beneficial effect reached with tradition DOA estimation by the present invention the following aspects:
1. traditional Nyquist sampling thheorem is pointed out, in order to avoid distorted signals, the sample frequency of band-limited signal must be big In twice of its bandwidth, however, the increasingly increase signal bandwidth with current information demand is more and more wider, a large amount of numbers adopted According to needing to compress, store and transmit, all these all propose higher challenge to signal processing hardware system；The present invention makes In the case where guaranteeing that information is not lost, with the polydispersity index signal required far below Nyquist sampling thheorem, while again may be used To restore signal completely.The appearance of compressed sensing is sampled so that in the case where guaranteeing that information is not lost with far below Nyquist The polydispersity index signal that theorem requires, while signal can be restored completely again.
2., such as ISSM, TCT and MTLS-CSSM scheduling algorithm, all not can avoid and focusing in focus variations CSSM class algorithm Before first have to obtain discreet value to information source orientation estimation angle, then can just go to calculate necessary focussing matrix in focusing operation. It is easy to cause orientation to estimate mistake when the focussing matrix discreet value and larger true value deviation in our constituencies, and innovatory algorithm will Data realize that " shared " improves the precision of estimation so as to avoid orientation pre-estimation with data at reference frequency point at each frequency point.
3. compressive sensing theory is combined with DOA estimation, into the narrowband is divided such as broadband signal using the thought of focusing and is believed Number, so that the thought using narrowband is solved, greatly reduce the huge calculation amount of original broadband estimation.In identical sampling Under the premise of improve the precision of estimation.
Detailed description of the invention
Fig. 1 is inventive algorithm flow chart
Fig. 2 compressed sensing measurement process 1
Fig. 3 compressed sensing measurement process 2
Success rate change curve when Fig. 4 changes with signal-to-noise ratio
Root-mean-square error change curve when Fig. 5 changes with signal-to-noise ratio
Algorithm success rate change curve when Fig. 6 changes with number of snapshots
Root-mean-square error change curve when Fig. 7 changes with number of snapshots
Specific embodiment
The embodiment of the present invention is described below in detail, examples of the embodiments are shown in the accompanying drawings, wherein from beginning to end Same or similar label indicates same or similar element or element with the same or similar functions.Below with reference to attached The embodiment of figure description is exemplary, and for explaining only the invention, and is not construed as limiting the claims.
As shown in Figure 1 it is flow chart of the invention: the arrival bearing of signal is estimated using conventional low resolution algorithm Meter obtains DOA initial estimation set θ, while determining reference frequency point f0.Specific method: by direction matrix after focusing with Constraint is established between direction matrix on focusing frequency, it is poly- by being removed in bandwidth under the conditions of guaranteeing that focusing instrument error is the smallest Subband signal except burnt frequency focuses in reference frequency, finally carries out spatial spectrum to the whole frequency-region signal after focusing and estimates Meter.Assuming that frequency domain array received signal is as follows, with T (fj) and Y (fj) centre frequency is respectively indicated as fjSubband focussing matrix and Receiving matrix, by the sense matrix A (f of itself and respective frequenciesj, θ) and it is multiplied, so that signal is mapped to focusing frequency f0It is upper:
T(fj)Y(fj)=T (fj)A(fj,θ)S(fj)=A (f0)S(fj) (1)
Wherein A (fj, θ) and A (f0, θ) and it is frequency point f respectivelyjWith reference frequency point f0The array prevalence matrix at place, S (fj) it is fj The information source data at place.
Consider the case where choosing optimal conditions, (1) formula be converted to the fitting form of F- norm:
In focussing matrixIn the case where meeting unitary matrice, it may be assumed thatWherein I is unit matrixForTransposed matrix obtain optimal optimization method group by (2) formula in its simultaneous:
Wherein J is a kind of solution that natural number acquires equation group (3):
T(fj)=V (fj)UH(fj) (4)
V (f in formulaj)、U(fj) it is respectively A (fj,θ)AH(fj, θ) left and right singular vectors UH(fj) it is U (fj) transposition.In Focusing frequency f0Selection on, can from focus accuracy angle, selection possess minimum focusing error on the whole Frequency acquires the focusing error ε of broadband on the whole according to (4) formula as focusing frequency, method:
The wherein sequence on Re { tr } representing matrix border, in above formula | | | |FIt is expressed as Frobenius norm, it can be with abbreviation For constant MK, wherein K is a constant, indicates the constraint to signal degree of rarefication, M is matrix dimensionality.
It is available to bring formula (6) into formula (5):
Wherein J is the number of effective frequency point, λk[A(f0,θ)AH(fj, θ)] it is A (f0,θ)AH(fj, θ) singular value, in formula AH(f0, θ) and it is A (f0, θ) transposition.In the case that first multinomial is constant in formula (7), to guarantee that ε is to go to zero Minimum, then need second multinomial that can set up in the case where obtaining maximum situation.If In the case where K is less than M one thousandth, δ meets inequality (8), wherein λkIndicate characteristic value.
It enablesThen
It is available with the narrow band data in focussing matrix processing respective sub-bands:
Y(fj)=T (fj)X(fj)=A (f0,θ)S(fj)+T(fj)N(fj) (10)
Directly using the focusing transform criterion in formula (10) come to focussing matrix solution, there are two o'clock problems: first is that usual nothing Method is directly acquired without information source data of making an uproarWith S (f0)；Second is that orientation discreet value is needed to come to array manifold matrixWith A (f0, θ) estimated.It, can by the mutual information and self-information using array received data between different frequent points To avoid the above problem.For this purpose, introducing two matrix variables, cross-correlation matrix R (fj,f0) and without the covariance matrix P (f that makes an uproar0), It is respectively used to characterization mutual information and self-information:
R(fj,f0)=A (fj,θ)S(fj)·SH(f0)AH(f0)/L (11)
P(f0)=A (f0,θ)S(f0)SH(f0)AH(f0)/L (12)
Wherein R (fj,f0)∈CM×MIndicate frequency point fjPlace and reference frequency f0Locate data X (fj) and X (f0) between mutual association side Poor matrix；P(f0)∈CM×MThen indicate about reference frequency f0Locate data X (f0) nothing make an uproar covariance matrix.Formula (10) are carried out Transformation, both sides are simultaneously multiplied by SH(f0)AH(f0)/L, obtains:
T(fj)A(fj,θ)S(fj)SH(f0)AH(f0)/L=A (f0,θ)S(f0)SH(f0)AH(f0)/L (13)
Formula (11), (12) are updated in above formula (13), are obtained:
T(fj)·Ρ(fj,f0)=P (f0) (14)
Formula (14) is the focusing transform criterion with formula (10) equivalent, under the focusing criterion, by being connect using array The auto-correlation and cross-correlation information of the collection of letters number can construct focussing matrix without azimuth estimation value.We are by formula (14) matrix is utilized:
P(fj)=A (fj,θ)S(fj)SH(fj)AH(fj, θ) and=A (fj,θ)R(fj)AH(fj,θ) (15)
Focusing transform is solved, the arithmetic mean of instantaneous value of the data cross-correlation matrix after converting on each sub-band is and then solved, It realizes frequency domain smoothing, obtains transformed data correlation matrix RY:
Wherein RY∈CM×MTo focus the array sample covariance matrix after smoothing processing, referred to as population sample covariance square Battle array.It, next should be using the high resolution spatial spectral estimation algorithm of narrowband subspace class come to poly- by the flow diagram in Fig. 1 Defocused population sample covariance matrix RYIt is handled, the sample covariance matrix R that will be obtainedYUsing classical based on compression The L1-SVD algorithm of perception theory obtains the final estimated value of broadband signal DOA；
Compressive sensing theory process is as shown in Figure 2 and Figure 3, ties up observing matrix Φ and the direct phase of signal using M × N (M < < N) It is multiplied to the non-adaptive linear projection measured value y=of M [y (1) ... y (M)]T, M < < N, K indicate that the quantity of measurement sample is remote Much smaller than the dimension (far smaller than indicating hundred times of the two difference or more, be all in full in this way without specified otherwise) of signal, and completely Sufficient K<M, M>=cK log (N/K), c are the constant infinitely to go to zero, mathematic(al) representation are as follows:
Y=Φ x (17)
For a RNThe one-dimensional scattered time signal x in space, it is assumed that there are the base vector of M N-dimensionalConstitute N × N Wiki matrix Ψ, signal x can be indicated are as follows:
Wherein s only contains K (K < < N) a nonzero value, and signal x is claimed to be compressible at this time.Square is observed using M × N (M < < N) Battle array Φ is observed compressible signal, expression formula are as follows:
Y=Φ x=Φ Ψ s=Θ s (19)
Above-mentioned matrix measurement process is as indicated, wherein Φ=RM×NFor calculation matrix, Ψ=RN×NFor the sparse table of signal Show matrix, s=RN×1For rarefaction representation coefficient, y=RM×1For calculation matrix, Θ=RM×NFor by calculation matrix and rarefaction representation square The dictionary that battle array is constituted, Θ must satisfy limited equidistant (Restricted Isometry Property, RIP) property, that is, select One and the incoherent observing matrix Φ of exchange base Ψ.
In order to prove the validity of inventive algorithm, we choose classical MUSIC algorithm, RSS algorithm and inventive algorithm It compares.The success rate variation and root-mean-square error situation of change of three kinds of algorithms algorithm when signal-to-noise ratio changes are compared first, 100 are set by number of snapshots in experiment and keeps constant constant, and signal-to-noise ratio is changed from -10dB to 10dB by interval of 2dB.For The accuracy of guarantee test is 20 experiments, experimental result such as Fig. 4, shown in Fig. 5 under each number of snapshots.We pass through result It can be seen that three kinds of algorithm success rates are all increasing when signal-to-noise ratio increases, root-mean-square error all decreases figure, longitudinal to compare It can be seen that inventive algorithm performance is superior to other two kinds of algorithms in success rate and root-mean-square error.
Secondly comparing will letter in the success rate variation and root-mean-square error variation test when three kinds of algorithms change with number of snapshots It makes an uproar than being set as 10dB and keeping constant constant, number of snapshots are changed from 20 to 200 with 10 intervals.For the standard of guarantee test True property is 20 experiments, experimental result such as Fig. 5, shown in Fig. 6 under each number of snapshots.We can be seen that by result figure fast Three kinds of algorithm success rates are all increasing when umber of beats increases, and root-mean-square error all decreases, and longitudinal comparison is it can be seen that the present invention Algorithm performance is superior to other two kinds of algorithms in success rate and root-mean-square error.

Claims (2)

1. the Broadband DOA Estimation algorithm based on the RSS algorithm under compressive sensing theory, it is characterised in that:
1) estimated using arrival bearing of the low resolution algorithm to signal, obtain DOA initial estimation set θ, while determining ginseng Examine frequency point f0；
2) the array manifold matrix A (f of all sub-bands is constructed according to DOA initial value θj, θ), the focusing for obtaining all sub-bands becomes Change a gust T (fj)；
3) focusing transform battle array T (f is utilizedj) the array received data X (f in respective frequency sub-bandsj) focusing frequency point is transformed to, it obtains Array output data Y (f under the frequency pointj) and correlation matrix Ry(fj)；
4) pass through frequency domain smoothing for transformed data Correlation Matrix Ry(fj) it is built into the unified array correlation in reference frequency point Matrix RY；
5) the final estimated value of broadband signal DOA is obtained using compressed sensing based L1-SVD algorithm.
2. algorithm according to claim 1, it is characterised in that:
Estimated using arrival bearing of the low resolution algorithm to signal, obtains DOA initial estimation set θ, while determining reference Frequency point f0；Specific method: it is constrained, is being protected by being established between the direction matrix on the direction matrix and focusing frequency after focusing Under the conditions of card focusing instrument error is the smallest, the subband signal in bandwidth in addition to focusing frequency is focused in reference frequency, Estimation of Spatial Spectrum finally is carried out to the whole frequency-region signal after focusing；Assuming that frequency domain array received signal is as follows, with T (fj) and Y (fj) centre frequency is respectively indicated as fjSubband focussing matrix and receiving matrix, by the sense matrix A of itself and respective frequencies (fj, θ) and it is multiplied, so that signal is mapped to focusing frequency f0It is upper:
T(fj)Y(fj)=T (fj)A(fj,θ)S(fj)=A (f0)S(fj) (1)
Wherein A (fj, θ) and A (f0, θ) and it is frequency point f respectivelyjWith reference frequency point f0The array prevalence matrix at place, S (fj) it is fjPlace Information source data；
Consider the case where choosing optimal conditions, (1) formula be converted to the fitting form of F- norm:
In focussing matrixIn the case where meeting unitary matrice, it may be assumed thatWherein I is unit matrix ForTransposed matrix obtain optimal optimization method group by (2) formula in its simultaneous:
Wherein J is a kind of solution that natural number acquires equation group (3):
T(fj)=V (fj)UH(fj) (4)
V (f in formulaj)、U(fj) it is respectively A (fj,θ)AH(fj, θ) left and right singular vectors UH(fj) it is U (fj) transposition；It is focusing Frequency f0Selection on, from the angle for focusing accuracy, select to possess on the whole the frequency of minimum focusing error as Focusing frequency, method acquire the focusing error ε of broadband on the whole according to (4) formula:
The wherein sequence on Re { tr } representing matrix border, in above formula | | | |FIt is expressed as Frobenius norm, abbreviation is constant MK, Wherein K is a constant, indicates the constraint to signal degree of rarefication, M is matrix dimensionality；
Formula (6) is brought into formula (5) to obtain:
Wherein J is the number of effective frequency point, λk[A(f0,θ)AH(fj, θ)] it is A (f0,θ)AH(fj, θ) singular value, A in formulaH (f0, θ) and it is A (f0, θ) transposition；In the case that first multinomial is constant in formula (7), to guarantee that ε goes to zero Minimum then needs second multinomial that can set up in the case where obtaining maximum situation；IfIn the case where K is less than M one thousandth, δ meets inequality (8), wherein λkIt indicates Characteristic value；
It enablesThen
With the narrow band data in focussing matrix processing respective sub-bands, obtain:
Y(fj)=T (fj)X(fj)=A (f0,θ)S(fj)+T(fj)N(fj) (10)；；
Introduce two matrix variables, cross-correlation matrix R (fj,f0) and without the covariance matrix P (f that makes an uproar0), it is respectively used to characterization mutual trust Breath and self-information:
R(fj,f0)=A (fj,θ)S(fj)·SH(f0)AH(f0)/L (11)
P(f0)=A (f0,θ)S(f0)SH(f0)AH(f0)/L (12)
Wherein R (fj,f0)∈CM×MIndicate frequency point fjPlace and reference frequency f0Locate data X (fj) and X (f0) between cross covariance square Battle array；P(f0)∈CM×MThen indicate about reference frequency f0Locate data X (f0) nothing make an uproar covariance matrix；Formula (10) is converted, Both sides are simultaneously multiplied by SH(f0)AH(f0)/L, obtains:
T(fj)A(fj,θ)S(fj)SH(f0)AH(f0)/L=A (f0,θ)S(f0)SH(f0)AH(f0)/L (13)
Formula (11), (12) are updated in above formula (13), are obtained:
T(fj)·Ρ(fj,f0)=P (f0) (14)
Formula (14) is the focusing transform criterion with formula (10) equivalent, under the focusing criterion, by being believed using array received Number auto-correlation and cross-correlation information, focussing matrix can be constructed without azimuth estimation value；Formula (14) are utilized into square Battle array:
P(fj)=A (fj,θ)S(fj)SH(fj)AH(fj, θ) and=A (fj,θ)R(fj)AH(fj,θ) (15)
Focusing transform is solved, and then solves the arithmetic mean of instantaneous value of the data cross-correlation matrix after converting on each sub-band, i.e., in fact Existing frequency domain smoothing, obtains transformed data correlation matrix RY:
Wherein RY∈CM×MTo focus the array sample covariance matrix after smoothing processing, referred to as population sample covariance matrix；It connects Get off using the high resolution spatial spectral estimation algorithm of narrowband subspace class come to the population sample covariance matrix R after focusingY It is handled, the sample covariance matrix R that will be obtainedYWidth is obtained using the classical L1-SVD algorithm based on compressive sensing theory The final estimated value of band signal DOA；
It is directly multiplied to obtain M non-adaptive linear projection measured value y=with signal using M × N (M < < N) dimension observing matrix Φ [y(1),...y(M)]T, M<<N, K indicate that the quantity of measurement sample is far smaller than the dimension of signal, and meet K<M, M>=cKlog (N/K), c is the constant infinitely to go to zero, mathematic(al) representation are as follows:
Y=Φ x (17)
For a RNThe one-dimensional scattered time signal x in space, it is assumed that there are the base vector of M N-dimensionalConstitute N × N-dimensional base Matrix Ψ, signal x are indicated are as follows:
Wherein s only contains K (K < < N) a nonzero value, and signal x is claimed to be compressible at this time；Utilize M × N (M < < N) observing matrix Φ Compressible signal is observed, expression formula are as follows:
Y=Φ x=Φ Ψ s=Θ s (19)
Wherein Φ=RM×NFor calculation matrix, Ψ=RN×NFor the rarefaction representation matrix of signal, s=RN×1For rarefaction representation coefficient, y =RM×1For calculation matrix, Θ=RM×NFor the dictionary being made of calculation matrix and rarefaction representation matrix, Θ must satisfy limited etc. Away from, that is, select one with the incoherent observing matrix Φ of exchange base Ψ.
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