CN105974358A - Compression-sensing-based DOA estimation method for intelligent antenna - Google Patents

Abstract

The invention, which belongs to the communication technology, especially relates to a compression-sensing-based direction-of-arrival (DOA) estimation method for an intelligent antenna. According to a sparse characteristic of a target signal in a natural space in an airspace, a CS-theory-based DOA estimation model under single sampling is constructed; on the basis of the constructed DOA estimation model, CS-theory-based DOA estimation is realized, thereby obtaining a DOA of the target signal; and with an orthogonal matching pursuit algorithm, a reconstruction problem of a s spatial sparse signal in the CS-theory-based DOA estimation is solved, and iteration is carried out by multiple times and thus a residual error between an estimation signal and an original signal is reduced continuously, so that the estimation signal is close to the original signal and DOA estimation is completed. The method has the following beneficial effects: relevant information can be estimated accurately based on a little sampling information; and thus novel DOA estimation method is provided.

Description

Smart antenna DOA estimation method based on compressed sensing

Technical field

The invention belongs to communication technology, particularly relate to a kind of smart antenna DOA estimation method based on compressed sensing.

Background technology

Smart antenna has direction finding and Wave beam forming ability, and it is for the availability of frequency spectrum in raising wireless communication system, increase Power system capacity, to improve communication quality etc. significant, wherein direction of arrival (Direction of Arrival, DOA) estimate be One of key technology of antenna system.DOA estimation technique is one and estimates and at the signal of airspace filter based on Time Domain Spectrum Reason technology, it is therefore an objective to utilize the output of aerial array, detects and simultaneously appears in all expectation users' in the range of space Positional information, is i.e. estimated the azimuth information of each subscriber signal by array data.Much about in the problem of signal processing, Being required for array signal is carried out DOA estimation, including serving the positioning function of new generation of wireless communication system, DOA estimates Meter technology is to realize the many multi-functional keys of communication system, is the emphasis of antenna system research.

Traditional array DOA estimation technique is based primarily upon the concept of Wave beam forming, the algorithm of formation be Bartlett beam-forming schemes or Claim conventional beamformer (CBF) algorithm, by forming wave beam and being pointed to the power outbound course of maximum, find the ripple of signal to reach Direction, this algorithm is limited to Rayleigh limit (Rayleigh limit), the i.e. effective aperture of array and determines the resolution of algorithm, and it Exist many not enough in terms of the accuracy and sensitivity of Signal estimation.

Time-domain signal is generalized to spatial processing and once received significant attention, and creates many Estimation of Spatial Spectrum methods, including maximum entropy method (MEM) (MEM), least variance method (MVM), although MEM is higher than the resolution of CBF method, but line splitting may be produced；MVM It is the improvement to CBF algorithm, on direction of arrival interested, not only forms wave beam, be also upwardly formed zero in non-interested parties and fall into, But it is for the close signal source of multiple directions inapplicable, and resolution is limited by very large.

The research that the proposition of subspace method is Estimation of Spatial Spectrum is made that a large amount of contribution, wherein calculates with multiple signal classification (MUSIC) Method and invariable rotary subspace (ESPRIT) algorithm are especially prominent, and this kind of algorithm uses mathematic decomposition method, such as Eigenvalues Decomposition, The covariance matrix of array received signal is decomposed, array data is drawn and is decomposed into two orthogonal subspaces.Subspace method In signal subspace class algorithm mainly include LS-ESPRIT method, TAM method, TLS-ESPRIT method etc., noise subspace class is calculated Method mainly includes that MUSIC method, MNM method, Characteristic Vectors are mensuration etc..MUSIC algorithm and ESPRIT algorithm all have the highest angle Degree resolution, but it is only applicable to uncorrelated signal or low coherent signal, improvement both classic algorithm carried out for this shortcoming, Such as subspace fitting class algorithm, this kind of algorithm can be directly used in coherent signal, and be easily achieved, but amount of calculation is very big, is not suitable for Engineer applied, the algorithm for reduction amount of calculation is also investigated certainly, calculates including rooting MUSIC algorithm and at rooting MUSIC Innovatory algorithm in method, but these method comparison are complicated and also estimated accuracy is relatively low.

Realization to DOA Estimation in Coherent Signal mainly has dimensionality reduction and non-dimension-reduction treatment two class algorithm, and dimension-reduction treatment class algorithm is with space Smooth class algorithm is representative；Rather than dimension-reduction treatment class algorithm mainly has Toeplitz algorithm, virtual array transformation algorithm etc., its spy Point is to need not lose array effective aperture, and these algorithms are all based on space smoothing class algorithm or feature decomposition, it is possible to use maximum Characteristic vector structural matrix thus use a kind of new Toeplitz Decorrelating algorithm, additionally, also have based on matrix reconstruction thought ESPRIT-Like algorithm etc..These algorithms are accomplished that and all signals carry out DOA estimation simultaneously, and whether be correlated with according to signal will Signal is divided into two classes, i.e. space parallax sorting algorithm, such as space parallax sub matrix square or feature decomposition scheduling theory on the basis of change The DOA algorithm for estimating entered, space parallax sorting algorithm is generalized to uniform circular array and has higher estimated accuracy by it.

Generally for obtaining more preferable DOA estimation effect, then need substantial amounts of sampling, the most not only cause signal processing, Transmission and the immense pressure of storage, also add the complexity of hardware, but the introducing of compressed sensing (CS) theory adopted to signal Quadrat method brings revolutionary impact, CS theory show when signal compressible or sparse time, with less than Nyquist rate just Signal can be sampled, thus reduce data and process, transmit and store pressure.Generally echo signal in whole space only Occupy sub-fraction, i.e. echo signal is sparse, so research is significant in estimating based on DOA theoretical for CS, But CS is theoretical as a kind of new data capture method, the most more effectively applies the research in each field to be still left to be desired. In sum, CS is theoretical as a kind of new data capture method, and the application in DOA estimates is also in the exploratory stage.

Summary of the invention

In order to overcome above-mentioned the deficiencies in the prior art, the present invention is directed to the tradition DOA big information processing of algorithm for estimating sampled data output Complicated deficiency, it is provided that a kind of smart antenna DOA estimation method based on compressed sensing, uses the basis of a small amount of sample information On can accurately estimate relevant information, it is provided that a kind of new DOA estimation method.

To achieve these goals, the present invention provides smart antenna DOA estimation method based on compressed sensing, it is characterised in that Carry out as steps described below:

Step 1: according to the echo signal in place, there is in spatial domain sparse characteristic, manage based on CS under structure unitary sampling The DOA of opinion estimates model；

Step 2: estimate that model realization is estimated based on DOA theoretical for CS according to the DOA of above-mentioned structure, obtain echo signal DOA；

Step 3: set M × 1 and tie up array received signal y, M × N-dimensional array manifold matrix A, the degree of rarefication of signal s, initialize Noise residual error r₀, indexed setIterations i=0, threshold value δ=10^-8, use orthogonal matching pursuit algorithm to carry out base In DOA theoretical for CS estimates, the reconstruct of space sparse signal, makes the noise of estimation signal and original signal by successive ignition Residual error is gradually reduced and approaches primary signal, to estimate variance reach set threshold value time, complete DOA estimate.

In described step 1, under unitary sampling, step based on DOA estimation model theoretical for CS is:

(1a) whole spatial domain scope (-90 °～90 °), N number of incoming signal s=[s are set₁ s₂ Λ s_N]^T, N number of incidence The angle of incidence of signal is followed successively by { θ₁ θ₂ Λ θ_N, θ_iWith s_iOne_to_one corresponding；

(1b) set in N number of incoming signal comprise the signal source in likely direction, and N is than the echo signal of necessary being Number K much bigger, in s, only K non-zero value, other N-K position is 0, thus it is dilute to verify that s possesses K- Dredge characteristic；

(1c) DOA is estimated that model constructs, under the unitary sampling of structure, estimate model based on DOA theoretical for CS For:

Y=As+r (1)

In formula, y=[y₁ y₂ Λ y_M]^TFor M array at the reception signal in certain moment, matrix A is M × N-dimensional battle array Row flow pattern matrix, signal s is that matrix is tieed up in N × 1 that the sparse incoming signal in space comprising actual arrival bearing is constituted, and r is array The noise matrix received.

The expression formula of described array manifold matrix A is:

$\begin{array}{c}A=\[a\left({\mathrm{\θ}}_1\right),a\left({\mathrm{\θ}}_2\right),\mathrm{\Λ},a\left({\mathrm{\θ}}_N\right)\]\\ =\left[\begin{array}{cccc}1& 1& \mathrm{\Λ}& 1\\ e^{-j2\mathrm{\π}\frac{d{\mathrm{sin\θ}}_1}{\mathrm{\λ}}}& e^{-j2\mathrm{\π}\frac{d{\mathrm{sin\θ}}_2}{\mathrm{\λ}}}& \mathrm{\Λ}& e^{-j2\mathrm{\π}\frac{d{\mathrm{sin\θ}}_N}{\mathrm{\λ}}}\\ M& M& O& M\\ e^{-j2\mathrm{\π}\frac{(M-1)d{\mathrm{sin\θ}}_1}{\mathrm{\λ}}}& e^{-j2\mathrm{\π}\frac{(M-1)d{\mathrm{sin\θ}}_2}{\mathrm{\λ}}}& \mathrm{\Λ}& e^{-j2\mathrm{\π}\frac{(M-1)d{\mathrm{sin\θ}}_N}{\mathrm{\λ}}}\end{array}\right]\end{array}---\left(2\right)$

In formula, matrix A is M × N-dimensional array manifold matrix or referred to as guiding vector matrix, a (θ_i) be matrix A guiding to Amount, M is antenna array columns, θ_iFor the angle of incidence of incoming signal, d is adjacent array element distance, and λ is carrier wavelength.

In described step 2, first by known array received signal, (title of y wants consistent, can unify as array received signal Or in data) y is by array manifold matrix A reconstruction attractor sparse signal s=[s₁ s₂ Λ s_N]^T, wherein s_iMiddle K Individual bigger signal is exactly in esse echo signal, then according to θ_iWith s_iOne-to-one relationship realizes based on CS theory DOA estimates i.e. to can get the DOA of echo signal, concretely comprises the following steps:

(2a) checking estimates the orthogonality between respectively arranging in array manifold matrix A in model and battle array based on DOA theoretical for CS 2K-submatrix RIP character in row flow pattern matrix A；

(2b) according to waiting sine method to carry out space lattice division:

(1) carry out angularly space lattice to divide: by whole spatial domain scope (-90 °～90 °) by being divided at equal intervals {θ₁ θ₂ Λ θ_N, thenI=1,2, Λ, N, make in modelThen array manifold Matrix A is:

$A=\left[\begin{array}{cccc}1& 1& \mathrm{\Λ}& 1\\ e^{-{\mathrm{j\πsin\θ}}_1}& e^{-{\mathrm{j\πsin\θ}}_2}& \mathrm{\Λ}& e^{-{\mathrm{j\πsin\θ}}_N}\\ M& M& O& M\\ e^{-j\mathrm{\π}(M-1){\mathrm{sin\θ}}_1}& e^{-j\mathrm{\π}(M-1){\mathrm{sin\θ}}_2}& \mathrm{\Λ}& e^{-j\mathrm{\π}(M-1){\mathrm{sin\θ}}_N}\end{array}\right]---\left(3\right)$

(2) the sine space stress and strain model such as: make on the basis of formula (3)I=1,2, Λ, N, Then array manifold A is:

$A=\left[\begin{array}{ccccc}1& \mathrm{\Λ}& 1& \mathrm{\Λ}& 1\\ e^{j\mathrm{\π}}& \mathrm{\Λ}& e^{-j\mathrm{\π}\[-1+(i-1)\frac{2}{N-1}\]}& \mathrm{\Λ}& e^{-j\mathrm{\π}}\\ M& O& M& O& M\\ e^{j(M-1)\mathrm{\π}}& \mathrm{\Λ}& e^{-j\mathrm{\π}(M-1)\[-1+(i-1)\frac{2}{N-1}\]}& \mathrm{\Λ}& e^{-j(M-1)\mathrm{\π}}\end{array}\right]---\left(4\right)$

In formula, A is M × N-dimensional array manifold matrix or referred to as guiding vector matrix, and M is antenna array columns, and N is incident Signal number.

In described step 3, using OMP algorithm to complete DOA and estimate, the process of implementing is:

(1) find row maximally related with noise residual error in array manifold A matrix, will in array manifold matrix A all row to Amount a_jIt is multiplied with noise residual error r, finds out the row λ corresponding to product maximum_i=arg max_{J=1, Λ, N}|<a_j,r^n-1>|；

(2) indexed set Λ is updated_i=Λ_i-1∪{λ_i, and atom set

(3) method of least square approximation signal is utilized

(4) formula r is utilized_i=y-A_is_iUpdate noise residual values；

(5) judge that iteration stopping condition has met threshold value δ=10^-8If being unsatisfactory for, continue cycling through from step (2) Above step, if meeting, then stops iteration；

(6) approximate reconstruction goes out signal s=[s₁ s₂ Λ s_N]^T；

(7) signal s_iMiddle K bigger signal is exactly in esse echo signal, according to θ_iWith s_iOne-to-one relationship is i.e. The direction of arrival of available echo signal.

The invention has the beneficial effects as follows: use orthogonal matching pursuit (OMP) restructing algorithm to realize the weight to sparse signal first Structure, is then applied to CS theory in the DOA estimation of array signal, builds and estimate model based on DOA theoretical for CS, Employings etc. are sinusoidal divides space lattice mode, uses OMP algorithm can realize the signal reconstruction of high probability under unitary sampling, Estimating it is thus possible to realize DOA accurately, accuracy of estimation increased with increasing of signal to noise ratio simultaneously, and uses CS Theory is superior to traditional algorithm on accuracy of estimation and operation time.The present invention has been experimentally confirmed reconstruct smart antenna letter Number far from meet completeness condition in sampled data, or sampled data signal to noise ratio can complete than this method in the case of relatively low DOA estimates.And the algorithm simple possible of the present invention, the smart antenna DOA that can be used for possessing sparse signal characteristic estimates In.

Accompanying drawing explanation

Fig. 1 is signal reconstruction figure based on OMP algorithm；

Fig. 2 is to wait the signal reconstruction figure under sinusoidal dividing mode；

Fig. 3 is to wait the DOA estimated result figure under sinusoidal dividing mode；

Fig. 4 is the curve that DOA based on CS estimates that RMSE changes with SNR；

Fig. 5 is that DOA based on CS estimates and DOA based on MUSIC algorithm estimates spectrogram.

Detailed description of the invention

Below in conjunction with the accompanying drawings a kind of detailed description of the invention of invention is explained.

Present invention DOA based on OMP restructing algorithm estimates that implementing step includes the following:

Step 1: there is in spatial domain sparse characteristic according to the echo signal in place under practical situation, construct based on DOA theoretical for CS estimates model.

1a) set whole spatial domain scope (-90 °～90 °), N number of incoming signal s=[s₁ s₂ Λ s_N]^T, N number of incident letter Number angle of incidence be followed successively by { θ₁ θ₂ Λ θ_N, θ_iWith s_iOne_to_one corresponding；

1b) set in N number of signal comprise the signal source in likely direction, and N is than the echo signal of necessary being Number K is much bigger, so only K non-zero value in s, other N-K position is 0, and it is sparse that checking s possesses K- Characteristic；

1c) based on DOA estimation model theoretical for CS under given unitary sampling:

Y=As+r (1)

In formula, y=[y₁ y₂ Λ y_M]^TFor M array at the reception signal in certain moment, matrix A is M × N-dimensional battle array Row flow pattern matrix, s is sparse signal N × 1, the space dimension matrix comprising actual arrival bearing, and r is the noise square that array received arrives Battle array.

1d) the array manifold matrix A of the most given DOA estimation method:

$\begin{array}{c}A=\&lsqb;a\left({\mathrm{\&theta;}}_1\right),a\left({\mathrm{\&theta;}}_2\right),\mathrm{\&Lambda;},a\left({\mathrm{\&theta;}}_N\right)\&rsqb;\\ =\left[\begin{array}{cccc}1& 1& \mathrm{\&Lambda;}& 1\\ e^{-j2\mathrm{\&pi;}\frac{d{\mathrm{sin\&theta;}}_1}{\mathrm{\&lambda;}}}& e^{-j2\mathrm{\&pi;}\frac{d{\mathrm{sin\&theta;}}_2}{\mathrm{\&lambda;}}}& \mathrm{\&Lambda;}& e^{-j2\mathrm{\&pi;}\frac{d{\mathrm{sin\&theta;}}_N}{\mathrm{\&lambda;}}}\\ M& M& O& M\\ e^{-j2\mathrm{\&pi;}\frac{(M-1)d{\mathrm{sin\&theta;}}_1}{\mathrm{\&lambda;}}}& e^{-j2\mathrm{\&pi;}\frac{(M-1)d{\mathrm{sin\&theta;}}_2}{\mathrm{\&lambda;}}}& \mathrm{\&Lambda;}& e^{-j2\mathrm{\&pi;}\frac{(M-1)d{\mathrm{sin\&theta;}}_N}{\mathrm{\&lambda;}}}\end{array}\right]\end{array}---\left(2\right)$

In traditional DOA estimation method, the every string steering vector in array manifold matrix A and the echo signal in space One_to_one corresponding, needs array manifold matrix A is expanded to whole space, according to given space rarefaction when using CS theory Mode { θ₁ θ₂ Λ θ_NI.e. can determine that matrix A, i.e. A are no longer dependent on K real target signal direction.

Step 2: carried out reconstruction attractor sparse signal by array manifold matrix A by known array received signal y S=[s₁ s₂ Λ s_N]^T, wherein s_iMiddle K bigger signal is exactly in esse echo signal, according to θ_iWith s_iOne a pair Relational implementation is answered to estimate i.e. to can get the DOA of echo signal based on DOA theoretical for CS:

(2a) checking estimates the orthogonality between respectively arranging in array manifold matrix A in model based on DOA theoretical for CS.

Array received signal y is equivalent to the observation data in CS theory, and array manifold matrix A is equivalent to the sight in CS theory Survey matrix Φ (signal x itself is sparse in time-space domain) or perception matrix Θ (x is sparse under transform domain Ψ), perception Matrix Θ needs to meet certain RIP characteristic (limited equidistant character (RIP)), and the 2K i.e. randomly drawed in Θ row must be Linear independence, therefore, estimate that can be reconstructed s by y depends in array manifold matrix A based on DOA theoretical for CS Orthogonality between each row, this part is relevant with space lattice division.

(2b) according to waiting sine method to carry out space lattice division

Generally space lattice divides angularly two ways sinusoidal with grade, enters parameter on the basis of angularly etc. sinusoidal manner One step limits, particularly as follows: the most angularly divide: by whole spatial domain scope (-90 °～90 °) by being divided at equal intervals {θ₁ θ₂ Λ θ_N, thenI=1,2, Λ, N, the most to simplify the analysis；Make in modelSo array manifold matrix A is:

$A=\left[\begin{array}{cccc}1& 1& \mathrm{\&Lambda;}& 1\\ e^{-{\mathrm{j\&pi;sin\&theta;}}_1}& e^{-{\mathrm{j\&pi;sin\&theta;}}_2}& \mathrm{\&Lambda;}& e^{-{\mathrm{j\&pi;sin\&theta;}}_N}\\ M& M& O& M\\ e^{-j\mathrm{\&pi;}(M-1){\mathrm{sin\&theta;}}_1}& e^{-j\mathrm{\&pi;}(M-1){\mathrm{sin\&theta;}}_2}& \mathrm{\&Lambda;}& e^{-j\mathrm{\&pi;}(M-1){\mathrm{sin\&theta;}}_N}\end{array}\right]---\left(3\right)$

The sinusoidal manner such as carry out on the basis of the above to divide, orderI=1,2, Λ, N, then A is:

$A=\left[\begin{array}{ccccc}1& \mathrm{\&Lambda;}& 1& \mathrm{\&Lambda;}& 1\\ e^{j\mathrm{\&pi;}}& \mathrm{\&Lambda;}& e^{-j\mathrm{\&pi;}\&lsqb;-1+(i-1)\frac{2}{N-1}\&rsqb;}& \mathrm{\&Lambda;}& e^{-j\mathrm{\&pi;}}\\ M& O& M& O& M\\ e^{j(M-1)\mathrm{\&pi;}}& \mathrm{\&Lambda;}& e^{-j\mathrm{\&pi;}(M-1)\&lsqb;-1+(i-1)\frac{2}{N-1}\&rsqb;}& \mathrm{\&Lambda;}& e^{-j(M-1)\mathrm{\&pi;}}\end{array}\right]---\left(4\right)$

(2c) the 2K-submatrix RIP character of array manifold is verified

The 2K-submatrix of the array manifold obtained Deng sine space stress and strain model mode is than the submatrix that angularly mode obtains more There is significant orthogonality, there is more significant RIP character.And RIP character is the necessary requirement of signal reconstruction, and RIP The most notable quality reconstruction of matter is the best, and present invention employing etc. on the basis of choosing suitable restructing algorithm is sinusoidal divides space lattice side Formula completes reconstruct.

Step 3: use orthogonal matching pursuit (Orthogonal Matching Pursuit, OMP) algorithm to solve based on CS theory The reconstruction of signal s in DOA estimation.

Orthogonal matching pursuit (OMP) algorithm is more typical method in greedy algorithm.Its thought is that calculation matrix is former as redundancy The linear combination of some atoms in word bank, and to arrange an atom indexed set be empty set, often carries out an iteration and just selects with residual The maximally related atom of difference signal, and update indexed set, atom set and residual error, each time iteration all can make estimation signal with The residual error of original signal is more and more less, thus approaches primary signal.

Smart antenna compressed sensing DOA estimation method based on OMP algorithm is embodied as follows:

(1): initialize following parameter: M × 1 dimension array received signal, M × N-dimensional array manifold matrix, signal s dilute Dredge degree, initialize noise residual error r0=y, indexed setIterations i=0；

(2): find row maximally related with residual error in array manifold matrix A, will all column vectors a in array manifold matrix A_j It is multiplied with noise residual error r, finds out the row λ corresponding to product maximum_i=arg max_{J=1, Λ, N}|<a_j,r^n-1>|；

(3) indexed set Λ is updated_i=Λ_i-1∪{λ_i, and atom set

(4) method of least square approximation signal is utilized

(5) formula r is utilized_i=y-A_is_iUpdate noise residual values；

(6) judge that iteration stopping condition has met threshold value δ=10^-8If being unsatisfactory for, continue cycling through from step (2) Above step, if meeting, then stops iteration；

(7) approximate reconstruction goes out signal s=[s₁ s₂ Λ s_N]^T；

(8) signal s_iMiddle K bigger signal is exactly in esse echo signal, according to θ_iWith s_iOne-to-one relationship is i.e. The direction of arrival of available echo signal.

The method implementation process of the present invention is described with embodiment with reference to the accompanying drawings.

Embodiment 1

According to above theoretical, smart antenna compressed sensing DOA estimation method based on OMP algorithm is emulated reality as follows Test:

(1) the OMP algorithm sparse reconstitution experiments to signal is utilized

The cosine signal x of a length of 256 is sparse under fast Fourier transform territory, chooses gaussian random matrix as observation Matrix, the observation data length of cosine signal x is 64, carries out cosine signal x heavily according to observation data acquisition OMP algorithm Structure is tested, and result is as shown in Figure 1.

In this experiment, cosine signal x itself is not sparse, first chooses fast Fourier transform base by x rarefaction, observation Matrix chooses gaussian random matrix, then observing matrix is multiplied with orthogonal reverse transform matrix and constitutes perception matrix, by observation data Orthogonal matching pursuit (OMP) restructing algorithm is used to recover rarefaction representation coefficient, finally by rarefaction representation by perception matrix Coefficient does inverse Fourier transform and reconstructs time-domain signal x, as seen from Figure 1, reconstruct waveform (Recovery) out with The waveform of original (Original) time domain cosine signal x overlaps, and test result indicate that reconstructed error is only 4.3350 × 10^-15, So can accurately reconstruct primary signal based on OMP algorithm.

(2) etc. sinusoidal when dividing space lattice, DOA based on OMP algorithm estimates emulation experiment

Experiment condition is identical with during angularly division space lattice, and Fig. 2 is under waiting sinusoidal division space lattice mode, based on The OMP algorithm reconstruction result to signal source s, Fig. 3 is the DOA estimated result waiting sine to divide under space lattice mode.

As in figure 2 it is shown, with etc. sinusoidal manner divide space lattice:I=1,2, Λ, 1801, Under this mode, the signal (Recovery) of OMP algorithm reconstruct is used to essentially coincide with original signal (Original), and experiment Result display reconstructed error is 0.6507, and reconstructed error when angularly dividing space lattice is 0.9011, so waiting sine The quality reconstruction divided under space lattice mode is better than angularly mode.Experimental result has absolutely proved and has waited sine space grid to draw Array manifold matrix under point mode is compared to having more significant RIP character, at DOA estimation problem under angularly mode In be more suitable for the reconstruct of sparse signal.

As it is shown on figure 3, because waiting sinusoidal division under space lattice mode, have more significant RIP character, OMP is used to calculate The sparse signal reconfiguring error that method is recovered is relatively low, so the DOA estimated result realized according to reconstruction signal -59.9 ° ,-30 °, 10.1 °, 40 ° and 60.1 °, hence it is evident that close to-60 ° of actual signal source ,-30 °, 10 °, 40 ° and the incidence of 60 ° Angle.This description of test has been capable of accurate DOA and has estimated waiting sinusoidal division under space lattice mode.

(3) DOA estimation effect based on OMP algorithm during different signal to noise ratio

Signal source with on the incident angles of 40 ° to the even linear array of 64 array elements, array element distance d=λ/2, adopt under unitary sampling With waiting sine to divide space lattice, signal to noise ratio (SNR) is spaced 5dB successively and increases to 30dB from-10dB, for every SNR Do 100 experiments, use OMP algorithm signal is reconstructed and carries out DOA estimation, obtain the root-mean-square that DOA estimates Error (RMSE), as shown in Figure 4.

As seen from Figure 4, under unitary sampling, employing etc. are sinusoidal divides space lattice mode, by using OMP algorithm pair Signal reconstruction also carries out the result of DOA estimation according to reconstruction result and shows, along with the increase of SNR, RMSE is gradually reduced, After signal to noise ratio increases to a certain degree, RMSE no longer reduces, so DOA based on OMP algorithm estimates performance with the letter Make an uproar than increase increase, but after SNR increases to certain numerical value, estimate that performance there will be no significantly raising.

(4) theoretical based on compressed sensing (CS) and that DOA based on multiple signal classification (MUSIC) algorithm estimates contrast is real Test

Signal source with-30 °, 10 °, 50 °, on the incident angles of 60 ° to even linear array, array number 32, array element distance d=λ/2, SNR takes 10dB, carries out DOA based on OMP algorithm and estimates emulation experiment, and calculate based on MUSIC under unitary sampling The DOA of method estimates emulation experiment, and the DOA being illustrated in figure 5 two kinds of methods estimates spectrum, and table 1 is the computing of this method Time.

As can be seen from Table 1, CS theory is used to realize the operation time of DOA estimation less than the computing using MUSIC algorithm Time, so the introducing of CS theory reduces operand, improve arithmetic speed, body in terms of the real-time that DOA estimates Show superiority.

As seen from Figure 5, under conditions of unitary sampling, estimate to be capable of DOA accurately based on DOA theoretical for CS Estimate, and DOA based on MUSIC algorithm estimate spectrum P (θ) more secondary lobe occurs and also some amplitudes higher secondary lobe impact The accuracy that DOA estimates, then want the performance improving MUSIC algorithm in DOA estimation problem, need increase to adopt Sample number of times.Thus illustrate that introducing CS theory in DOA estimation problem overcomes lacking of the traditional algorithm a large amount of sampled datas of needs Point.

Table 1 estimates operation time based on the DOA that MUSIC algorithm and CS are theoretical

Above the example of the present invention is described in detail, but described content has been only presently preferred embodiments of the present invention, it is impossible to quilt Think the practical range for limiting the present invention.All impartial changes made according to the present patent application scope and improvement etc., all should be still Within belonging to the patent covering scope of the present invention.

Claims (5)

1. smart antenna DOA estimation method based on compressed sensing, it is characterised in that carry out as steps described below:

Step 1: according to the echo signal in place, there is in spatial domain sparse characteristic, manage based on CS under structure unitary sampling The DOA of opinion estimates model；

Step 2: estimate that model realization is estimated based on DOA theoretical for CS according to the DOA of above-mentioned structure, obtain echo signal DOA；

Step 3: set M × 1 and tie up array received signal y, M × N-dimensional array manifold matrix A, the degree of rarefication of signal s, initialize Residual error r₀, indexed setIterations i=0, threshold value δ=10^-8, use orthogonal matching pursuit algorithm carry out based on DOA theoretical for CS estimate in the reconstruct of space sparse signal, by successive ignition make the residual error of estimation signal and original signal by The least and approach primary signal, to estimate variance reach to set threshold value time, complete DOA and estimate.

Smart antenna DOA estimation method the most according to claim 1, it is characterised in that in described step 1, unitary sampling Under estimate that the step of model is based on DOA theoretical for CS:

(1a) whole spatial domain scope (-90 °～90 °), N number of incoming signal s=[s are set₁ s₂ Λ s_N]^T, N number of enter The angle of incidence penetrating signal is followed successively by { θ₁ θ₂ Λ θ_N, θ_iWith s_iOne_to_one corresponding；

(1b) set in N number of incoming signal comprise the signal source in likely direction, and N is than the echo signal of necessary being Number K much bigger, in s, only K non-zero value, other N-K position is 0, thus it is dilute to verify that s possesses K- Dredge characteristic；

(1c) DOA is estimated that model constructs, under the unitary sampling of structure, estimate model based on DOA theoretical for CS For:

Y=As+r (1)

In formula, y=[y₁ y₂ Λ y_M]^TFor M array at the reception signal in certain moment, matrix A is M × N-dimensional battle array Row flow pattern matrix, signal s is that matrix is tieed up in N × 1 that the sparse incoming signal in space comprising actual arrival bearing is constituted, and r is array The noise matrix received.

Smart antenna DOA estimation method the most according to claim 2, it is characterised in that described array manifold matrix A Expression formula be:

$\begin{array}{c}A=\&lsqb;a\left({\mathrm{\&theta;}}_1\right),a\left({\mathrm{\&theta;}}_2\right),\mathrm{\&Lambda;},a\left({\mathrm{\&theta;}}_N\right)\&rsqb;\\ =\left[\begin{array}{cccc}1& 1& \mathrm{\&Lambda;}& 1\\ e^{-j2\mathrm{\&pi;}\frac{d{\mathrm{sin\&theta;}}_1}{\mathrm{\&lambda;}}}& e^{-j2\mathrm{\&pi;}\frac{d{\mathrm{sin\&theta;}}_2}{\mathrm{\&lambda;}}}& \mathrm{\&Lambda;}& e^{-j2\mathrm{\&pi;}\frac{d{\mathrm{sin\&theta;}}_N}{\mathrm{\&lambda;}}}\\ M& M& O& M\\ e^{-j2\mathrm{\&pi;}\frac{\left(M-1\right)d{\mathrm{sin\&theta;}}_1}{\mathrm{\&lambda;}}}& e^{-j2\mathrm{\&pi;}\frac{\left(M-1\right)d{\mathrm{sin\&theta;}}_2}{\mathrm{\&lambda;}}}& \mathrm{\&Lambda;}& e^{-j2\mathrm{\&pi;}\frac{\left(M-1\right)d{\mathrm{sin\&theta;}}_N}{\mathrm{\&lambda;}}}\end{array}\right]\end{array}---\left(2\right)$

In formula, matrix A is M × N-dimensional array manifold matrix or referred to as guiding vector matrix, a (θ_i) be matrix A guiding to Amount, M is antenna array columns, θ_iFor the angle of incidence of incoming signal, d is adjacent array element distance, and λ is carrier wavelength.

Smart antenna DOA estimation method the most according to claim 3, it is characterised in that in described step 2, first by The array received signal y known passes through array manifold matrix A reconstruction attractor sparse signal s=[s₁ s₂ Λ s_N]^T, wherein s_iMiddle K Individual bigger signal is exactly in esse echo signal, then according to θ_iWith s_iOne-to-one relationship realizes based on CS theory DOA estimates i.e. to can get the DOA of echo signal, concretely comprises the following steps:

(2a) checking estimates the orthogonality between respectively arranging in array manifold matrix A in model and battle array based on DOA theoretical for CS 2K-submatrix RIP character in row flow pattern matrix A；

(2b) according to waiting sine method to carry out space lattice division:

(1) carry out angularly space lattice to divide: by whole spatial domain scope (-90 °～90 °) by being divided at equal intervals {θ₁ θ₂ Λ θ_N, thenI=1,2, Λ, N, make in modelThen array manifold Matrix A is:

$A=\left[\begin{array}{cccc}1& 1& \mathrm{\&Lambda;}& 1\\ e^{-{\mathrm{j\&pi;sin\&theta;}}_1}& e^{-{\mathrm{j\&pi;sin\&theta;}}_2}& \mathrm{\&Lambda;}& e^{-{\mathrm{j\&pi;sin\&theta;}}_N}\\ M& M& O& M\\ e^{-j\mathrm{\&pi;}\left(M-1\right){\mathrm{sin\&theta;}}_1}& e^{-j\mathrm{\&pi;}\left(M-1\right){\mathrm{sin\&theta;}}_2}& \mathrm{\&Lambda;}& e^{-j\mathrm{\&pi;}\left(M-1\right){\mathrm{sin\&theta;}}_N}\end{array}\right]---\left(3\right)$

(2) the sine space stress and strain model such as: make on the basis of formula (3)I=1,2, Λ, N, Then array manifold A is:

$A=\left[\begin{array}{ccccc}1& \mathrm{\&Lambda;}& 1& \mathrm{\&Lambda;}& 1\\ e^{j\mathrm{\&pi;}}& \mathrm{\&Lambda;}& e^{-j\mathrm{\&pi;}\&lsqb;-1+(i-1)\frac{2}{N-1}\&rsqb;}& \mathrm{\&Lambda;}& e^{-j\mathrm{\&pi;}}\\ M& O& M& O& M\\ e^{j(M-1)\mathrm{\&pi;}}& \mathrm{\&Lambda;}& e^{-j\mathrm{\&pi;}\left(M-1\right)\&lsqb;-1+(i-1)\frac{2}{N-1}\&rsqb;}& \mathrm{\&Lambda;}& e^{-j(M-1)\mathrm{\&pi;}}\end{array}\right]---\left(4\right)$

In formula, A is M × N-dimensional array manifold matrix or referred to as guiding vector matrix, and M is antenna array columns, and N is incident Signal number.

Smart antenna DOA estimation method the most according to claim 4, it is characterised in that in described step 3, adopt Completing DOA with OMP algorithm to estimate, the process of implementing is:

(1) row maximally related with residual error in array manifold A matrix are found, will all column vectors a in array manifold matrix A_j It is multiplied with noise residual error r, finds out the row λ corresponding to product maximum_i=arg max_{J=1, Λ, N}|<a_j,r^n-1>|；

(2) indexed set Λ is updated_i=Λ_i-₁∪{λ_i, and atom set

(3) method of least square approximation signal is utilized

(4) formula r is utilized_i=y-A_is_iUpdate noise residual values；

(5) judge that iteration stopping condition has met threshold value δ=10^-8If being unsatisfactory for, continue cycling through from step (2) Above-mentioned steps, if meeting, then stops iteration；

(6) approximate reconstruction goes out signal s=[s₁ s₂ Λ s_N]^T；

(7) signal s_iMiddle K bigger signal is exactly in esse echo signal, according to θ_iWith s_iOne-to-one relationship is i.e. The direction of arrival of available echo signal.