CN103902822A - Signal number detection method applied on condition of incoherent signal and coherent signal mixing - Google Patents

Abstract

The invention discloses a signal number estimation method applied in incidence of incoherent signals and multiple groups of coherent signals on the basis of uniform linear arrays. After an outer-product matrix based on a cross covariance matrix of received signals of two linear arrays is acquired, a first combined matrix is constructed by the cross covariance matrix and a transformation matrix thereof, and an outer-product matrix of the combined matrix is acquired, the number of the incoherent signals and the number of the groups of coherent signals can be acquired according to the rank of the two outer-product matrixes. Further, a new oblique projector is estimated to suppress the incoherent signals of data of the received array, a series of cross covariance matrixes composed of data of one uniform linear array and a series of sub-arrays of the other uniform linear array form a new combined matrix, and the rank of the outer-product matrix of the combined matrix is equal to the number of the coherent signals. According to great quantities of experiments, the signal number estimation method with less snapshots and low signal-to-noise ratio is superior to the MDL/AIC method, the MENSE method and the SRP(smoothed rank profile test) which are subjected to the FBSS (front-rear space smooth) preprocess.

Description

Sources number detection method in incoherent and coherent signal mixing situation

Technical field

The invention belongs to array signal process technique field, be specifically related to a kind of sources number detection method in incoherent and coherent signal mixing situation.

Background technology

Two mains direction of studying of Array Signal Processing are that number estimation of signal and sense are estimated, wherein number estimation of signal is again the basis that direction is estimated, in the time that number estimation of signal is inaccurate, sense is estimated to be had a strong impact on, therefore research is a kind of efficient, and accurate number estimation of signal algorithm has great Research Significance.

In sources number detection algorithm, the most classical is the algorithm based on information theory criterion, comprises based on AIC criterion and MDL criterion algorithm.But due to the existence of multipath transmi, incoming signal is often (relevant) of complete dependence, thereby causes traditional AIC/MDL method serious degradation in practice.Nonparametric technique MENSE is (referring to J.Xin, N.Zheng, and A.Sano, " Simple and efficient nonparametric method for estimating the number of signals without eigendecomposition; " IEEE Trans.Signal Process., vol.55, no.4, pp.1405-1420,2007.) can estimate coherent signal number.

In the recent period the signal direction of arrival in incoherent and coherent signal mixing situation is estimated to have obtained paying attention to widely, and the one dimension DOA of mixed signal estimates conventionally to adopt even linear array, two-dimentional DOA to estimate conventionally to adopt Z-shaped or parallel linear array.But in these methods, noncoherent signal number and coherent signal number be considered to through estimate in advance or as priori.Although for example space smoothing of preconditioning technique (SS) or front-rear space smooth (FBSS) can be estimated the total number of mixed signal in conjunction with being applied to parallel linear array with MENSE method with AIC/MDL method, but noncoherent signal number and coherent signal number can not obtain respectively, and can estimated signal number be limited to the array aperture being reduced.Although level and smooth order profile (SRP) method is (referring to T.-J.Shan, A.Paulraj, and T.Kailath, " On smoothed rank profile tests in eigenstructure methods for direction-of-arrival estimation; " IEEE Trans.Acoust., Speech, Signal Process., vol.35, no.10, pp.1377-1385,1987.) can estimate uncorrelated and coherent signal number, but in the time that signal to noise ratio (snr) is very low or fast umber of beats is very little, the detection effect of the method can be degenerated.

Although H.Tao in 2012 etc. have proposed a kind of new mixed signal number detection algorithm (referring to H.Tao, J.Xin, J.Wang, N.Zheng, and A.Sano " Estimation of the number of narrowband signals in the presence of multipath propagation, " in Proc.IEEE7th Sens.Array and Multichannel Signal Process.Workshop, pp.497-500, Hoboken, NJ, 2012.), this algorithm only can solve the number estimation problem in uncorrelated signal and one group of coherent signal mixing situation.The present invention therefore.

Summary of the invention

The object of the invention is to provide a kind of sources number detection method in incoherent and coherent signal mixing situation, confirm through a large amount of emulation experiments, this method is better than through the pretreated MDL/AIC method of FBSS, MENSE and SRP under fast umber of beats still less and low signal-to-noise ratio.

In order to solve these problems of the prior art, technical scheme provided by the invention is:

A sources number detection method in incoherent and coherent signal mixing situation, is characterized in that said method comprising the steps of:

(1) obtain the Cross-covariance of incoming signal and the outer product matrix of Cross-covariance based on even linear array, construct the first confederate matrix and obtain the outer product matrix of the first confederate matrix by Cross-covariance and its transformation matrix;

(2) the ratio criterion of decomposing based on QR according to the apposition rank of matrix of the outer product matrix of Cross-covariance and the first confederate matrix obtains noncoherent signal number and coherent signal group number;

(3) the incoherent part to matrix according to the orthogonality differentiate of subspace, carries out QR decomposition to the Cross-covariance that projects to noncoherent signal space; Estimate oblique projection operator according to the incoherent part of guiding matrix and the result that QR decomposes; Described oblique projection operator is realized signal separation for suppressing the noncoherent signal of receiving array data;

(4) adopt oblique projection operator to carry out project to Cross-covariance, according to the Cross-covariance after projection, be divided into 2L forward direction stack submatrix and 2L backward stack submatrix; Generate the second confederate matrix according to forward direction stack matrix and backward stack matrix; Construct the outer product matrix of the second confederate matrix according to the second confederate matrix; The ratio criterion of decomposing based on QR according to the apposition rank of matrix of the second confederate matrix is tried to achieve coherent signal number.

In preferred technical scheme: the ratio criterion of decomposing based on QR according to the apposition rank of matrix of the first confederate matrix in described method step (2) obtains noncoherent signal number.

In preferred technical scheme: in described method, incoming signal is two kinds or the two or more any mixing that is selected from unrelated signal, part coherent signal, coherent signal and additive noise.

In preferred technical scheme: in described method, incoming signal is the mixing of part coherent signal, coherent signal and additive noise; Or incoming signal is the mixing of unrelated signal, coherent signal and additive noise; Or incoming signal is the mixing of part coherent signal, coherent signal and additive noise; Or incoming signal is the mixing of unrelated signal, part coherent signal and additive noise; Or incoming signal is the mixing of unrelated signal and additive noise; Or incoming signal is the mixing of part coherent signal and additive noise; Or incoming signal is the mixing of coherent signal and additive noise.

In preferred technical scheme: in described method, the array structure of even linear array is two parallel linear arrays or L-type linear array.

In preferred technical scheme: in described method, suppose that even linear array sensor array is placed on x-y plane, and formed by two row even linear arrays, the sensor that every row even linear array comprises M omnidirectional, spacing is d _y, between row, spacing is d _x; K narrow band signal { s _k(t) } by K _nindividual noncoherent signal

and K _hindividual coherent signal composition, by far field from the different elevations angle and position angle { (α _k, β _k) incide on array K=K _n+ K _h; Coherent signal has P group, and every group by independent source s _hpform through multipath transmisstion, p group has K _pindividual coherent signal,

be expressed as s _{p, k}(t)=η _{p, k}s _hp(t), s wherein _p,k(t) be k signal in p coherent signal group, η _{p, k}for multiple attenuation coefficient, the signal that two row even linear arrays receive is:

y(t)＝AΓs(t)+w _y(t) (1)；

x(t)＝SDΓs(t)+w _x(t) (2);

Wherein s (t) is by K _nindividual noncoherent signal (is s _n(t)) and P coherent source signal (be s _h(t)) composition, A=[A _n, A _h], A _nk _nthe guiding matrix of individual noncoherent signal,

a _hthe guiding matrix of coherent signal, $A_h=[a\left(a_{\mathrm{1,1}}\right),...,a\left(a_{{1,}_{K_1}}\right),...,a\left({\mathrm{\α}}_{P,K_P}\right)],$ $a\left({\mathrm{\α}}_{p,k}\right)=[1,e^{\mathrm{j\τ}\left({\mathrm{\α}}_{p,k}\right)},...,e^{j(M-1)\mathrm{\τ}\left({\mathrm{\α}}_{p.k}\right)}{]}^T,$ τ(α _k)＝2πd _ycosα _k/λ，τ(α _p,k)＝2πd _ycosα _p,k/λ，

Λ＝blkdiag(η ₁，η ₂，…，η _p)，

D＝blkdiag(D _n,D _h)，

$D_n=\mathrm{diag}(e^{\mathrm{j\γ}\left({\mathrm{\β}}_1\right)},e^{\mathrm{j\γ}\left({\mathrm{\β}}_2\right)},...,e^{\mathrm{j\γ}\left({\mathrm{\β}}_{K_n}\right)})$ D _h＝blkdiag(D ₁，D ₂，…，D _P)， $D_P=$ $\mathrm{diag}(e^{\mathrm{j\γ}\left({\mathrm{\β}}_{p,1}\right)},e^{\mathrm{j\γ}\left({\mathrm{\β}}_{p,2}\right)},...,e^{\mathrm{j\γ}\left({\mathrm{\β}}_{p,K_n}\right)}),$ γ (β _k)=2 π d _xcos β _k/ λ, γ (β _p,k)=2 π d _xcos β _p,k/ λ; s _nand s (t) _h(t) be zero-mean time domain white Gaussian random process again, coherent signal is on the same group not uncorrelated mutually, and irrelevant mutually with noncoherent signal, additive noise

with zero-mean space-time white Gaussian random process again, and uncorrelated with incoming signal;

Describedly specifically carry out in accordance with the following steps:

1) can obtain array Cross-covariance by (1) (2):

R _yx=E{y(t)x ^H(t)}＝AΓR _sΓ ^HD ^HS ^H (3);

Wherein R _s=E{s (t) s ^h(t) }=blkdiag (R _n, R _h), R _nwith R _yxdefine the Cross-covariance of similar noncoherent signal, R _hbe and R _yxdefine the Cross-covariance of similar coherent signal, α _k≠ α _i, β _k≠ β _i, η _p,k≠ 0, and K _h>=2P, ρ (A)=ρ (D)=K, ρ (R _s)=K _n+ P, ρ (Γ)=K _n+ P; R _yxorder be:

ρ(R _yx)＝min{K,K _n+P}＝K _n+P；

2) noncoherent signal number detects

Obtain R by (3) _yxouter product matrix Ψ ₁:

${\mathrm{\Ψ}}_1=R_{\mathrm{yx}}{R}_{\mathrm{yx}}^H=\mathrm{A\Γ}{R}_s{\mathrm{\Γ}}^H{D}^H{A}^H\mathrm{AD\Γ}{R}_s{\mathrm{\Γ}}^H{A}^H---\left(4\right);$

Wherein ρ (Ψ ₁)=ρ (R _yx)=K _n+ P, according to the confederate matrix of a M × 2M of (3) structure

for:

${\stackrel{\‾}{R}}_{\mathrm{yx}}=[R_{\mathrm{yx}},J_M{R}_{\mathrm{yx}}^{*}]=\mathrm{ACB}---\left(5\right);$

Wherein $C=[\mathrm{\Γ},{\stackrel{\‾}{D}}^{-(M-1)}{\mathrm{\Γ}}^{*}],$ $\stackrel{\‾}{D}=\mathrm{blkdiag}({\stackrel{\‾}{D}}_n,{\stackrel{\‾}{D}}_h),$

with

definition except γ (β _k) and γ (β _p,k) by τ (α _k) and τ (α _p,k) substitute outside with D, D _nand D _hit is similar, $B=\mathrm{blkdiag}(R_s{\mathrm{\Γ}}^H{D}^H{A}^H,R_s^{*}{\mathrm{\Γ}}^T{\mathrm{DA}}^T);$ If M > is K _n+ P, ρ (B)=2 ρ (R _sΓ ^hd ^hsH)=2min{K _n+ P, M}=2 (K _n+ P);

The order of C is:

$\mathrm{\ρ}\left(C\right)=\mathrm{\ρ}\left(\mathrm{blkdiag}\left(\right[I_{K_n},{{\stackrel{\‾}{D}}_n}^{-(M-1)}],[\mathrm{\Λ},{{\stackrel{\‾}{D}}_h}^{-(M-1)}\left]\right)\right)=\mathrm{\ρ}\left(\right[I_{K_n},{{\stackrel{\‾}{D}}_n}^{-(M-1)}\left]\right)+\mathrm{\ρ}\left(\right[\mathrm{\Λ},{{\stackrel{\‾}{D}}_h}^{-(M-1)}{\mathrm{\Λ}}^{*}\left]\right)---\left(6\right);$

Wherein $\mathrm{\ρ}\left(\right[\mathrm{\Λ},{{\stackrel{\‾}{D}}_h}^{-(M-1)}{\mathrm{\Λ}}^{*}\left]\right)=2P,$ $\mathrm{\ρ}\left(\right[I_{K_n},{{\stackrel{\‾}{D}}_n}^{-(M-1)}\left]\right)=K_n;$ ρ(C)＝K _n+2P， $\mathrm{\ρ}\left({\stackrel{\‾}{R}}_{\mathrm{yx}}\right)=\min \{K,K_n+2P,2(K_n+P),M\}=K_n+2P,$ M > K _n+ K _h>=K _n+ 2P; Build new

outer product matrix Ψ ₂:

${\mathrm{\Ψ}}_2={\stackrel{\‾}{R}}_{\mathrm{yx}}{\stackrel{\‾}{R}}_{\mathrm{yx}}^H=\mathrm{ACB}{B}^H{C}^H{A}^H---\left(7\right);$

Wherein

m > K _n+ 2P, K _n=2 ρ (Ψ ₁)-ρ (Ψ ₂);

Utilize QRRC method, matrix Ψ ₁and Ψ ₂order be: ρ (Ψ ₁)=QRRC (Ψ ₁)=K _n+ P, ρ (Ψ ₂)=QRRC (Ψ ₂)=K _n+ 2P; In the time that fast umber of beats is limited, noncoherent signal number is defined as:

${\hat{K}}_n=2\mathrm{QRRC}\left({\widehat{\mathrm{\Ψ}}}_1\right)-\mathrm{QRRC}\left({\widehat{\mathrm{\Ψ}}}_2\right)---\left(13\right);$

Coherent signal group number is determined by (14) formula:

$\hat{P}=\mathrm{QRRC}\left({\widehat{\mathrm{\Ψ}}}_1\right)-{\hat{K}}_n---\left(14\right);$

3) coherent signal number detects

I) calculate oblique projection operator

There is respectively a K by what even linear array y (t) is divided into two non-overlapping copies _n+ P and M-K _nthe forward direction submatrix of-P sensor, the signal receiving accordingly

with

for:

${\stackrel{\‾}{y}}_1\left(t\right)=A_1\mathrm{\Γs}\left(t\right)+w_{{\stackrel{\‾}{y}}_1}\left(t\right)---\left(15\right);$

${\stackrel{\‾}{y}}_2\left(t\right)=A_2\mathrm{\Γs}\left(t\right)+w_{{\stackrel{\‾}{y}}_2}\left(t\right)---\left(16\right);$

Obtain from (3)

with

and the Cross-covariance between x (t)

$R_{{\stackrel{\‾}{y}}_{1}x}=E\left\{{\stackrel{\‾}{y}}_1\left(t\right)x^H\left(t\right)\right\}={\stackrel{\‾}{A}}_1{R}_s{\mathrm{\Γ}}^H{D}^H{A}^H---\left(17\right);$

$R_{{\stackrel{\‾}{y}}_{2}x}=E\left\{{\stackrel{\‾}{y}}_2\left(t\right)x^H\left(t\right)\right\}={\stackrel{\‾}{A}}_2{R}_s{\mathrm{\Γ}}^H{D}^H{A}^H---\left(18\right);$

Wherein

reversible, with

with

between there is (a K _n+ P) × (M-K _n-P) linear operator P _{α n}:

$P_{\mathrm{\αn}}^H{\stackrel{\‾}{A}}_1={\stackrel{\‾}{A}}_2---\left(19\right);$

Then P _{α n}can be tried to achieve by (20) formula:

$P_{\mathrm{\αn}}={\left({\stackrel{\‾}{A}}_1\right)}^{-H}{\stackrel{\‾}{A}}_2^{-H}={\left(R_{{\stackrel{\‾}{y}}_{1}x}{R}_{{\stackrel{\‾}{y}}_{1}x}^H\right)}^{-1}{R}_{{\stackrel{\‾}{y}}_{1}x}{R}_{{\stackrel{\‾}{y}}_{2}x}---\left(20\right);$

Meet: ${\mathrm{\Π}}_{\mathrm{\αn}}{A}_n=O_{M\×K_n}---\left(23\right);$ ${\mathrm{\Π}}_{\mathrm{\αn}}{A}_h\mathrm{\Λ}=O_{M\×P}---\left(24\right);$

And $Q_{\mathrm{\αn}}^H\stackrel{\‾}{A}=O_{(M-K_n-P)\×(K_n+P)}---\left(21\right);$ Wherein $Q_{\mathrm{\αn}}=[P_{\mathrm{\αn}}^T,{-I}_{M-K_n-P}^T{]}^T;$ Project to

the rectangular projection operator in space is ${\mathrm{\Π}}_{\mathrm{\αn}}=Q_{\mathrm{\αn}}{(Q_{\mathrm{\αn}}^H\·Q_{\mathrm{\αn}})}^{-1}{Q}_{\mathrm{\αn}}^H;$ : ${\mathrm{\Π}}_{\mathrm{\αn}}\stackrel{\‾}{A}=O_{M\×(K_n+P)}---\left(22\right);$

In the time that the fast umber of beats of array data is limited, the elevation angle of noncoherent signal

can obtain by the parameter of asking the cost function minimum that makes following formula:

$f_n\left(\mathrm{\α}\right)=a^H\left(\mathrm{\α}\right){\widehat{\mathrm{\Π}}}_{\mathrm{\αn}}\mathrm{\α}\left(\mathrm{\α}\right)---\left(25\right)$

Wherein a (α)=[1, e ^{j τ (α)}..., ej ^{(M-1) r (α)}] ^t, τ (α)=2 π d _ycos α/λ;

By will be along being parallel to space projection is to R (A _n) the oblique projection operator representation in space is

its expression formula is:

$E_{A_n{\stackrel{\‾}{A}}_h}=A_n{\left(A_n^H{\mathrm{\Π}}_{{\stackrel{\‾}{A}}_h}^{\⊥}{A}_n\right)}^{-1}{A}_n^H{\mathrm{\Π}}_{A_h---\left(26\right);}^{\⊥}$

Wherein

to project to the rectangular projection operator in space, definition is

and ${\mathrm{\Π}}_{{\stackrel{\‾}{A}}_h}={\stackrel{\‾}{A}}_h{\left({\stackrel{\‾}{A}}_h^H{\stackrel{\‾}{A}}_h\right)}^{-1}{\stackrel{\‾}{A}}_h^H,$ Have $E_{A_n|{\stackrel{\‾}{A}}_h}{A}_n=A_n$ With $E_{A_n|{\stackrel{\‾}{A}}_h}{\stackrel{\‾}{A}}_h=O_{M\×P};$

Project to by definition the rectangular projection operator in space

for $H_{A_n}^{\⊥}=I_M-A_n{\left(A_n^H{A}_n\right)}^{-1}{A}_n^H;$ Can obtain a new matrix from (3):

${\tilde{R}}_{\mathrm{yx}}=R_{\mathrm{yx}}{H}_{A_n}^{\⊥}={\stackrel{\‾}{A}}_h{R}_h{\mathrm{\Λ}}^H{D}_h^H{A}_h^H{\mathrm{\Π}}_{A_n}^{\⊥}---\left(27\right);$

order be its QR decomposes and can be expressed as:

${\tilde{R}}_{\mathrm{yx}}\widetilde{\mathrm{\Π}}=\tilde{Q}\tilde{R}=[{\tilde{q}}_1,{\tilde{q}}_2,...,{\tilde{q}}_M]\left[\begin{array}{c}{\tilde{R}}_1\\ O_{(M-P)\×M}\end{array}\right]\begin{array}{c}\}P\\ \}M-P\end{array}={\tilde{Q}}_1{\tilde{R}}_1---\left(28\right);$

Wherein

the unitary matrix of a M × M, $\tilde{Q}=[{\tilde{Q}}_1,{\tilde{Q}}_2],{\tilde{Q}}_1=[{\tilde{q}}_1,{\tilde{q}}_2,...,{\tilde{q}}_p],{\tilde{Q}}_2=[{\tilde{q}}_{P+1},{\tilde{q}}_{P+2},$ $...,{\tilde{q}}_M],$

the row non-singular matrix of P × M, the permutation matrix of M × M,

do not change

in the correlativity of each row; From (27) and (28), can obtain,

and project to

the rectangular projection operator representation in space is

oblique projection operator ask for by alternate ways below:

$E_{A_n|{\stackrel{\‾}{A}}_h}=A_n{\left(A_n^H{\mathrm{\Π}}_{{\tilde{Q}}_1}^{\⊥}{A}_n\right)}^{-1}{A}_n^H{\mathrm{\Π}}_{{\tilde{Q}}_1}^{\⊥}=A_n{\left({{\tilde{Q}}_2\tilde{Q}}_2^H{A}_n\right)}^{?}---\left(29\right);$

according to the array data R having obtained _yxand A _nask for;

Ii) extract coherence messages and signal decorrelation

First by the ULAx (t) in (2) is divided into forward direction/backward submatrix that L overlapping aperture is m, wherein L=M-m+1 and m>=K _h+ 1, l the forward direction/backward submatrix of signal vector is expressed as:

$x_{\mathrm{fl}}\left(t\right)=A_m{\stackrel{\‾}{D}}^{l-1}\mathrm{D\Γs}\left(t\right)+w_{x_{\mathrm{fl}}}\left(t\right)---\left(30\right);$

$x_{\mathrm{bl}}=A_m{\stackrel{\‾}{D}}^{-(M-l)}{D}^{*}{\mathrm{\Γ}}^{*}{s}^{*}\left(t\right)+w_{x_{\mathrm{bl}}}\left(t\right)=F_l{J}_M{x}^{*}\left(t\right)---\left(31\right);$

Wherein F _lbe the selection matrix of m × M, definition is F _l=[O _{m × (l-1)}, I _m, O _{m × (M-m-l+1)}], w _xfland w (t) _xbl(t) be the vector corresponding to additive noise; Obtain

$\stackrel{\‾}{y}\left(t\right)=(I_m-E_{A_n|{\stackrel{\‾}{A}}_h})y\left(t\right)=A_h\mathrm{\Λ}{s}_h\left(t\right)+(I_M-E_{A_n|{\stackrel{\‾}{A}}_h})w_y\left(t\right)---\left(32\right);$

By cutting apart

for forward direction/backward " virtual " submatrix that L overlapping aperture is m, obtain

${\stackrel{\‾}{y}}_{\mathrm{fl}}\left(t\right)={[{\stackrel{\‾}{y}}_l\left(t\right),{\stackrel{\‾}{y}}_{l+1}\left(t\right),...,{\stackrel{\‾}{y}}_{l+m-1}\left(t\right)]}^T=F_l{\stackrel{\‾}{y}}_l\left(t\right)=A_{\mathrm{mh}}{\stackrel{\‾}{D}}_h^{l-1}\mathrm{\Λ}{s}_h\left(t\right)+F_l(I_M-E_{A_n|{\stackrel{\‾}{A}}_h})w_y\left(t\right)---\left(33\right);$

${\stackrel{\‾}{y}}_{\mathrm{bl}}\left(t\right)={[{\stackrel{\‾}{y}}_{M-l+1}\left(t\right),{\stackrel{\‾}{y}}_{M-l}\left(t\right),...,{\stackrel{\‾}{y}}_{L-l+1}\left(t\right)]}^T=F_l{\stackrel{\‾}{J}}_M{\stackrel{\‾}{y}}^{*}\left(t\right)=A_{\mathrm{mh}}{\stackrel{\‾}{D}}_h^{-(M-l)}{\mathrm{\Λ}}^{*}{s}_h^{*}\left(t\right)+F_l{J}_M{(I_M-E_{A_n|{\stackrel{\‾}{A}}_h})}^{*}{w}_y^{*}\left(t\right)---\left(34\right);$

Obtain a submatrix in (33)

and the Cross-covariance between the reception signal x (t) (2) on a ULA

$R_{{\stackrel{\‾}{y}}_{\mathrm{fl}}x}=E\left\{{\stackrel{\‾}{y}}_{\mathrm{fl}}\left(t\right)x^H\left(t\right)\right\}=F_l(I_M-E_{A_n|{\stackrel{\‾}{A}}_h})R_{\mathrm{yx}}=A_{\mathrm{mh}}{\stackrel{\‾}{D}}_h^{l-1}\mathrm{\Λ}{R}_h{\mathrm{\Λ}}^H{D}_h^H{A}_h^H---\left(35\right);$

And other Cross-covariance

with expression formula:

$R_{{\stackrel{\‾}{y}}_{\mathrm{bl}}x}=E\left\{{\stackrel{\‾}{y}}_{\mathrm{bl}}\left(t\right)x^H\left(t\right)\right\}=F_l{J}_M{(I_M-E_{A_n|{\stackrel{\‾}{A}}_h})}^{*}{R}_{\mathrm{yx}}^{*}=A_{\mathrm{mh}}{\stackrel{\‾}{D}}_h^{-(M-l)}{\mathrm{\Λ}}^{*}{R}_h{\mathrm{\Λ}}^T{D}_h^T{A}_h^T---\left(36\right);$

$R_{x_{\mathrm{fl}}\stackrel{\‾}{y}}=E\left\{x_{\mathrm{fl}}\left(t\right){\stackrel{\‾}{y}}^H\left(t\right)\right\}=F_l{R}_{\mathrm{yx}}^H{(I_M-E_{A_n|{\stackrel{\‾}{A}}_h})}^H=A_{\mathrm{mh}}{\stackrel{\‾}{D}}_h^{l-1}{D}_h\mathrm{\Λ}{R}_h{\mathrm{\Λ}}^H{A}_h^H---\left(37\right);$

$R_{x_{\mathrm{bl}}\stackrel{\‾}{y}}=E\left\{x_{\mathrm{bl}}\left(t\right){\stackrel{\‾}{y}}^H\left(t\right)\right\}=F_l{J}_M{R}_{\mathrm{yx}}^H{(I_M-E_{A_n|{\stackrel{\‾}{A}}_h})}^T=A_{\mathrm{mh}}{\stackrel{\‾}{D}}_h^{-(M-l)}{D}_h^{*}{\mathrm{\Λ}}^{*}{R}_h{\mathrm{\Λ}}^T{A}_h^T---\left(38\right);$

For l=1,2,, the associating covariance matrix Φ of a m × 4LM of L structure is:

Wherein:

If even linear array is made submatrix size m and forward direction/backward submatrix quantity L meet inequality m>=K by classifying rationally _h+ 1,2L>=K _m, and K _m=max{K _pfor p=1,2 ..., order probability 1 ground of P Φ equals coherent signal number, i.e. ρ (Φ)=K _h;

Then obtain the outer product matrix Ψ of Φ ₃

Ψ ₃＝ΦΦ ^H (41)；

Wherein ρ (Ψ ₃)=ρ (Φ)=K _h; In the time obtaining the limited snap of array data, by estimating coherent signal number by QRRC method:

${\hat{K}}_h=\mathrm{QRRC}\left({\widehat{\mathrm{\Ψ}}}_3\right)---\left(42\right);$

Can obtain incoming signal number by (8) and (42) is

In preferred technical scheme: ratio criterion (QRRC) method of decomposing based on QR in described method is:

The square formation that is p to the order of a M × M

wherein p < M, its QR with rank transformation is decomposed into:

$\stackrel{\&OverBar;}{\mathrm{\&Psi;}}\stackrel{\&OverBar;}{\mathrm{\&Pi;}}=\stackrel{\&OverBar;}{Q}\stackrel{\&OverBar;}{R}=\stackrel{\&OverBar;}{Q}\left[\begin{array}{cc}{\stackrel{\&OverBar;}{R}}_{11}& {\stackrel{\&OverBar;}{R}}_{12}\\ O_{(M-P)\&times;M}& \end{array}\right]\begin{array}{c}\}p\\ \}M-p\end{array}---\left(8\right);$

Wherein

the permutation matrix of M × M,

the unitary matrix of M × M, with it is respectively the non-null matrix of the upper triangle nonsingular matrix of p × p and p × (M-p);

by introducing an auxiliary quantity ζ (i) as the factor in QR decomposition

the element that i is capable:

$\mathrm{\&zeta;}\left(i\right)=\underset{k=1}{\overset{M}{\mathrm{\&Sigma;}}}\left|{\stackrel{\&OverBar;}{r}}_{\mathrm{ik}}\right|+\mathrm{\&epsiv;}={\stackrel{\&OverBar;}{\mathrm{\&zeta;}}}_i+\mathrm{\&epsiv;},\mathrm{fori}=\mathrm{1,2},...M---\left(9\right);$

Wherein ε is a positive little constant arbitrarily, defines a ratio criterion (QRRC) of decomposing based on QR to be:

${\mathrm{QRRC}}_{\stackrel{\&OverBar;}{\mathrm{\&Psi;}}}\left(i\right)=\frac{\mathrm{\&zeta;}\left(i\right)}{\mathrm{\&zeta;}(i+1)},\mathrm{fori}=\mathrm{1,2},...M-1---\left(10\right);$

Then ratio criterion

can be expressed as

${\mathrm{QRRC}}_{\stackrel{\&OverBar;}{\mathrm{\&Psi;}}}\left(i\right)=\left\{\begin{array}{cc}\frac{{\stackrel{\&OverBar;}{\mathrm{\&zeta;}}}_i+\mathrm{\&epsiv;}}{{\stackrel{\&OverBar;}{\mathrm{\&zeta;}}}_{i+1}+\mathrm{\&epsiv;}}\&ap;\frac{{\stackrel{\&OverBar;}{\mathrm{\&zeta;}}}_i}{{\mathrm{\&zeta;}}_{i+1}}=c\left(i\right)& \mathrm{for}1\&le;i<p\\ \frac{{\stackrel{\&OverBar;}{\mathrm{\&zeta;}}}_n+\mathrm{\&epsiv;}}{\mathrm{\&epsiv;}}\&RightArrow;\&infin;& \mathrm{fori}=p\\ \frac{\mathrm{\&epsiv;}}{\mathrm{\&epsiv;}}=1& \mathrm{forp}\&le;i<M-1\end{array}\right.---\left(11\right);$

order by ask iE (I, 2 ... M) make in scope

maximum subscript i obtains, that is: $p=\underset{i}{\arg \max }{\mathrm{QRRC}}_{\stackrel{\&OverBar;}{\mathrm{\&Psi;}}}\left(i\right)=\mathrm{QRRC}\left(\stackrel{\&OverBar;}{\mathrm{\&Psi;}}\right)---\left(12\right).$

The invention provides a kind of sources number detection method based in the incoherent of simple flat surface array and coherent signal mixing situation, relate to the estimation of mixed signal number, its method is utilized two parallel even linear arrays, and the noncoherent signal number in mixed signal and coherent signal number are estimated respectively.Specifically, the present invention proposes a kind of number estimation of signal algorithm based in the incoherent of two parallel even linear arrays and coherent signal mixing situation.First from two apposition ranks of matrix, obtain the group number of number and the coherent signal of noncoherent signal, then the noncoherent signal in the array signal that suppresses to receive by a new oblique projection operator, and obtain coherent signal number from a new apposition rank of matrix that only comprises coherent signal information.The method can estimate respectively noncoherent signal and coherent signal number, and can prove by numerical example the performance that little at fast umber of beats of signal to noise ratio (S/N ratio) had the in the situation that of low.

Concrete, the invention provides a kind of sources number detection method based in the incoherent of two parallel even linear arrays and coherent signal mixing situation.This method is utilized oblique projection operator to realize signal and is separated, by the order of ratio criterion estimated matrix of decomposing based on QR to realize sources number detection.This new algorithm comprises the following steps:

1) Cross-covariance and the confederate matrix of calculating sample;

2) according to Cross-covariance and two outer product matrixs of confederate matrix structure;

3) according to the ratio criterion of decomposing based on QR, can try to achieve noncoherent signal number and coherent signal group number;

4) the incoherent part to matrix according to the orthogonality differentiate of subspace;

5) Cross-covariance that projects to noncoherent signal space is carried out to QR decomposition;

6) calculate oblique projection operator according to the incoherent part of guiding matrix and the result that QR decomposes;

7) according to oblique projection operator, Cross-covariance is carried out to project;

8), according to the Cross-covariance after projection, be divided into 2L forward direction stack submatrix and 2L backward stack submatrix;

9) generate a new confederate matrix according to forward direction stack matrix and backward stack matrix;

10) construct new outer product matrix according to confederate matrix;

11) according to the ratio criterion of decomposing based on QR, can try to achieve coherent signal number.

In preferred technical scheme, form confederate matrix by signal covariance matrix, be used for estimating noncoherent signal number.

In preferred technical scheme, calculate oblique projection operator according to the incoherent part of guiding matrix and the result that QR decomposes.

In preferred technical scheme, utilize the noncoherent signal in the array signal that oblique projection operator suppresses to receive, the information of extraction coherent signal.

In preferred technical scheme, the Cross-covariance after projection is cut apart, to coherent signal decorrelation.

In preferred technical scheme, be configured to estimate the new confederate matrix of coherent signal number.

In preferred technical scheme, while being the mixing of unrelated signal, part coherent signal, coherent signal and additive noise for incoming signal, to the estimation of incoming signal number.

In preferred technical scheme, while being the mixing of unrelated signal, coherent signal and additive noise for incoming signal, to the estimation of incoming signal number.

In preferred technical scheme, while being the mixing of part coherent signal, coherent signal and additive noise for incoming signal, for the estimation of incoming signal number.

In preferred technical scheme, while being the mixing of unrelated signal, part coherent signal and additive noise for incoming signal, to the estimation of incoming signal number.

In preferred technical scheme, while only having the mixing of unrelated signal and additive noise for incoming signal, to the estimation of incoming signal number.

In preferred technical scheme, while only having the mixing of part coherent signal and additive noise for incoming signal, to the estimation of incoming signal number.

In preferred technical scheme, while only having the mixing of coherent signal and additive noise for incoming signal, to the estimation of incoming signal number.

In preferred technical scheme, array structure is two parallel linear arrays.

In preferred technical scheme, wherein, array structure is L-type linear array.

Therefore number estimation of signal problem when, the present invention's research is based on incoherent in two parallel linear array situations and the incident of many groups coherent signal.First, obtain an outer product matrix that receives the Cross-covariance of signals based on two linear arrays, then construct the first confederate matrix by Cross-covariance and its transformation matrix and obtain the outer product matrix of confederate matrix.Now can obtain noncoherent signal number and coherent signal group number according to two apposition ranks of matrix.Secondly, estimate a new oblique projection operator for suppressing the noncoherent signal of receiving array data, the a series of Cross-covariances that are made up of a series of submatrixs of even linear array data and another even linear array data have formed a new confederate matrix, and the apposition rank of matrix of this confederate matrix is exactly coherent signal number.Finally, an order decision method decomposing based on QR is introduced into the order for estimated matrix, and noncoherent signal number and coherent signal number obtain from estimative order.Confirm through a large amount of emulation experiments, this method is better than through the pretreated MDL/AIC method of FBSS, MENSE and SRP under fast umber of beats still less and low signal-to-noise ratio.

The present invention proposes a kind of individual number estimation method when incoherent and coherent signal is mixed incident under two parallel linear arrays.First, obtain an outer product matrix that receives the Cross-covariance of signals based on two linear arrays, then construct the first confederate matrix by Cross-covariance and its transformation matrix and obtain the outer product matrix of confederate matrix.Now can obtain noncoherent signal number and coherent signal group number according to two apposition ranks of matrix.Secondly, estimate a new oblique projection operator for suppressing the noncoherent signal of receiving array data, the a series of Cross-covariances that are made up of a series of submatrixs of even linear array data and another even linear array data have formed a new confederate matrix, and the apposition rank of matrix of this confederate matrix is exactly coherent signal number.Finally, an order decision method decomposing based on QR is introduced into the order for estimated matrix, and noncoherent signal number and coherent signal number obtain from estimative order.

Accompanying drawing explanation

Below in conjunction with drawings and Examples, the invention will be further described:

Fig. 1 is the geometry figure that represents two parallel linear arrays of a number estimation method.

Fig. 2 represents to detect outline flowchart according to the compound information number of the embodiment of the present invention.

Fig. 3 shows the estimated performance of algorithm under different signal to noise ratio (S/N ratio)s and fast umber of beats.

Embodiment

Below in conjunction with specific embodiment, such scheme is described further.Should be understood that these embodiment are not limited to limit the scope of the invention for the present invention is described.The implementation condition adopting in embodiment can be done further adjustment according to the condition of concrete producer, and not marked implementation condition is generally the condition in normal experiment.

Embodiment

As depicted in figs. 1 and 2, Fig. 2 represents to detect outline flowchart according to the compound information number of the embodiment of the present invention.Fig. 1 is the geometry figure that represents two parallel linear arrays of a number estimation method.Concrete scheme is described below:

One, data model and problem are described

As shown in Figure 1, two parallel sensor arraies are placed on x-y plane, and are made up of two row even linear arrays, the sensor that every row even linear array comprises M omnidirectional, and spacing is d _y, between row, spacing is d _x.Suppose K narrow band signal { s _k(t) } by K _nindividual noncoherent signal

and K _hindividual coherent signal composition, by far field from the different elevations angle and position angle { (α _k, β _k) incide on array K=K _n+ K _h.Suppose that coherent signal has P group, every group by independent source s _hpform through multipath transmisstion, p group has K _pindividual coherent signal, therefore

can be expressed as s _{p, k}(t)=η _{p, k}s _hp0), s wherein _p,k(t) be k signal in p coherent signal group, η _{p, k}for multiple attenuation coefficient.

Here the signal that two row even linear arrays receive can be expressed as

y(t)＝AΓs(t)+w _y(t) (1)；

x(t)＝SDΓs(t)+w _x(t) (2)；

Wherein s (t) is by K _nindividual noncoherent signal (is s _n(t)) and P coherent source signal (be s _h(t)) composition, A=[A _n, A _h], A _nk _nthe guiding matrix of individual noncoherent signal,

a _hthe guiding matrix of coherent signal, $A_h=[a\left(a_{\mathrm{1,1}}\right),...,a\left(a_{{1,}_{K_1}}\right),...,a\left({\mathrm{\&alpha;}}_{P,K_P}\right)],$ $a\left({\mathrm{\&alpha;}}_{p,k}\right)=[1,e^{\mathrm{j\&tau;}\left({\mathrm{\&alpha;}}_{p,k}\right)},...,e^{j(M-1)\mathrm{\&tau;}\left({\mathrm{\&alpha;}}_{p.k}\right)}{]}^T,$ τ(α _k)＝2πd _ycosα _k/λ，τ(α _p,k)＝2πd _ycosα _p,k/λ，

Λ＝blkdiag(η ₁,η ₂,…,η _P)，

D＝blkdiag(D _n,D _h)， $D_n=\mathrm{diag}(e^{\mathrm{j\&gamma;}\left({\mathrm{\&beta;}}_1\right)},e^{\mathrm{j\&gamma;}\left({\mathrm{\&beta;}}_2\right)},...,e^{\mathrm{j\&gamma;}\left({\mathrm{\&beta;}}_{K_n}\right)})$ D _h＝blkdiag(D ₁,D ₂,…,D _P)，

γ(β _k)＝2πd _xcosβ _k/λ，γ(β _p,k)＝2πd _xcosβ _p,k/λ。

Suppose s _nand s (t) _h(t) be zero-mean time domain white Gaussian random process again, coherent signal is on the same group not uncorrelated mutually, and irrelevant mutually with noncoherent signal, additive noise

with

zero-mean space-time white Gaussian random process again, and uncorrelated with incoming signal.

According to the data model of hypothesis, can obtain array Cross-covariance by (1) (2):

R _yx＝E{y(t)x ^H(t)}＝AΓR _sΓ ^HD ^HA ^H (3)；

Wherein R _s=E{s (t) s ^h(t) }=blkdiag (R _n, R _h), R _nand R _hbe respectively and R _yxdefine the Cross-covariance of similar noncoherent signal and coherent signal, the impact of additive noise is eliminated in (3).Due to α _k≠ α _i, β _k≠ β _i, η _p,k≠ 0, and K _h>=2P, we can obtain ρ (A)=ρ (D)=K, ρ (R _s)=K _n+ P, p (r)=K _n+ PoR _yxorder be ρ (R _yx)=min{K, K _n+ P}=K _n+ P, due to the R that exists of coherent signal _yxorder be less than incoming signal number K.Noncoherent signal number and coherent signal number can not be from R _yxmiddle direct estimation.

A. noncoherent signal number detects

Obtain R by (3) _yxouter product matrix Ψ ₁

${\mathrm{\&Psi;}}_1=R_{\mathrm{yx}}{R}_{\mathrm{yx}}^H=\mathrm{A\&Gamma;}{R}_s{\mathrm{\&Gamma;}}^H{D}^H{A}^H\mathrm{AD\&Gamma;}{R}_s{\mathrm{\&Gamma;}}^H{A}^H---\left(4\right);$

From analysis above, ρ (Ψ ₁)=ρ (R _yx)=K _n+ P.Can define the confederate matrix of a M × 2M according to (3) simultaneously

for

${\stackrel{\&OverBar;}{R}}_{\mathrm{yx}}=[R_{\mathrm{yx}},J_M{R}_{\mathrm{yx}}^{*}]=\mathrm{ACB}---\left(5\right);$

Wherein $C=[\mathrm{\&Gamma;},{\stackrel{\&OverBar;}{D}}^{-(M-1)}{\mathrm{\&Gamma;}}^{*}],$ $\stackrel{\&OverBar;}{D}=\mathrm{blkdiag}({\stackrel{\&OverBar;}{D}}_n,{\stackrel{\&OverBar;}{D}}_h),$

with

definition except γ (β _k) and γ (β _p,k) by τ (α _k) and τ (α _p,k) substitute outside with D, D _nand D _hit is similar, obviously, if M > is K _n+ P, we can obtain ρ (B)=2 ρ (R _sΓ ^hd ^ha ^h)=2min{K _n+ P, M}=2 (K _n+ P).Because the fundamental sequence conversion to matrix can not change rank of matrix, the order of C can be expressed as

$\mathrm{\&rho;}\left(C\right)\begin{array}{c}=\mathrm{\&rho;}\left(\mathrm{blkdiag}\left(\right[I_{K_n},{{\stackrel{\&OverBar;}{D}}_n}^{-(M-1)}],[\mathrm{\&Lambda;},{{\stackrel{\&OverBar;}{D}}_h}^{-(M-1)}{\mathrm{\&Lambda;}}^{*}\left]\right)\right)\\ =\mathrm{\&rho;}\left(\right[I_{K_n},{{\stackrel{\&OverBar;}{D}}_n}^{-(M-1)}\left]\right)+\mathrm{\&rho;}\left(\right[\mathrm{\&Lambda;},{{\stackrel{\&OverBar;}{D}}_h}^{-(M-1)}{\mathrm{\&Lambda;}}^{*}\left]\right)\end{array}---\left(6\right)$

Wherein $\mathrm{\&rho;}\left(\right[\mathrm{\&Lambda;},{{\stackrel{\&OverBar;}{D}}_h}^{-(M-1)}{\mathrm{\&Lambda;}}^{*}\left]\right)=2P,$ $\mathrm{\&rho;}\left(\right[I_{K_n},{{\stackrel{\&OverBar;}{D}}_n}^{-(M-1)}\left]\right)=K_n;$ Therefore ρ (C)=K _n+ 2P, $\mathrm{\&rho;}\left({\stackrel{\&OverBar;}{R}}_{\mathrm{yx}}\right)=\min \{K,K_n+2P,2(K_n+P),M\}=K_n+2P,$ If M > K(is M > K _n+ K _h>=K _n+ 2P).Then new by one of definition

outer product matrix Ψ ₂, we have ${\mathrm{\&Psi;}}_2={\stackrel{\&OverBar;}{R}}_{\mathrm{yx}}{\stackrel{\&OverBar;}{R}}_{\mathrm{yx}}^H=\mathrm{ACB}{B}^H{C}^H{A}^H.---\left(7\right)$

Obviously,

if M > is K _n+ 2P, and we can obtain K _n=2 ρ (Ψ ₁)-ρ (Ψ ₂).

MENSE is (referring to J.Xin, N.Zheng, and A.Sano, " Simple and efficient nonparametric method for estimating the number of signals without eigendecomposition; " IEEE Trans.Signal Process., vol.55, no.4, pp.1405-1420,2007.) ratio criterion (QRRC) method of decomposing based on QR in is expressed as follows:

The square formation that is p to the order of a M × M

wherein p < M, its QR with rank transformation decomposes and can be expressed as

$\stackrel{\&OverBar;}{\mathrm{\&Psi;}}\stackrel{\&OverBar;}{\mathrm{\&Pi;}}=\stackrel{\&OverBar;}{Q}\stackrel{\&OverBar;}{R}=\stackrel{\&OverBar;}{Q}\left[\begin{array}{cc}{\stackrel{\&OverBar;}{R}}_{11}& {\stackrel{\&OverBar;}{R}}_{12}\\ O_{(M-P)\&times;M}& \end{array}\right]\begin{array}{c}\}p\\ \}M-p\end{array}---\left(8\right);$

Wherein the permutation matrix of M × M,

the unitary matrix of M × M,

with it is respectively the non-null matrix of the upper triangle nonsingular matrix of p × p and p × (M-p).Obviously by introducing an auxiliary quantity ζ (i) as the factor in QR decomposition

the element that i is capable

$\mathrm{\&zeta;}\left(i\right)=\underset{k=1}{\overset{M}{\mathrm{\&Sigma;}}}\left|{\stackrel{\&OverBar;}{r}}_{\mathrm{ik}}\right|+\mathrm{\&epsiv;}={\stackrel{\&OverBar;}{\mathrm{\&zeta;}}}_i+\mathrm{\&epsiv;},\mathrm{fori}=\mathrm{1,2},...M---\left(9\right);$

Wherein ε is positive little constant (for example ε=10 arbitrarily ^-6), define one based on QR decompose ratio criterion (QRRC) be

${\mathrm{QRRC}}_{\stackrel{\&OverBar;}{\mathrm{\&Psi;}}}\left(i\right)=\frac{\mathrm{\&zeta;}\left(i\right)}{\mathrm{\&zeta;}(i+1)},\mathrm{fori}=\mathrm{1,2},...M-1.---\left(10\right);$

Then ratio criterion

can be expressed as

${\mathrm{QRRC}}_{\stackrel{\&OverBar;}{\mathrm{\&Psi;}}}\left(i\right)=\left\{\begin{array}{cc}\frac{{\stackrel{\&OverBar;}{\mathrm{\&zeta;}}}_i+\mathrm{\&epsiv;}}{{\stackrel{\&OverBar;}{\mathrm{\&zeta;}}}_{i+1}+\mathrm{\&epsiv;}}\&ap;\frac{{\stackrel{\&OverBar;}{\mathrm{\&zeta;}}}_i}{{\mathrm{\&zeta;}}_{i+1}}=c\left(i\right)& \mathrm{for}1\&le;i<p\\ \frac{{\stackrel{\&OverBar;}{\mathrm{\&zeta;}}}_n+\mathrm{\&epsiv;}}{\mathrm{\&epsiv;}}\&RightArrow;\&infin;& \mathrm{fori}=p\\ \frac{\mathrm{\&epsiv;}}{\mathrm{\&epsiv;}}=1& \mathrm{forp}\&le;i<M-1\end{array}\right.---\left(11\right);$

order can by ask i ∈ (1,2 ... within the scope of M}, make

maximum subscript i obtains,

$p=\underset{i}{\arg \max }{\mathrm{QRRC}}_{\stackrel{\&OverBar;}{\mathrm{\&Psi;}}}\left(i\right)=\mathrm{QRRC}\left(\stackrel{\&OverBar;}{\mathrm{\&Psi;}}\right)---\left(12\right).$

Therefore, utilize above-mentioned QRRC method, matrix Ψ ₁and Ψ ₂order can be determined by following expression, i.e. ρ (Ψ ₁)=QRRC (Ψ ₁)=K _n+ P, ρ (Ψ ₂)=QRRC (Ψ ₂)=K _n+ 2P.Therefore in the time that fast umber of beats is limited, noncoherent signal number can be defined as

${\hat{K}}_n=2\mathrm{QRRC}\left({\widehat{\mathrm{\&Psi;}}}_1\right)-\mathrm{QRRC}\left({\widehat{\mathrm{\&Psi;}}}_2\right).---\left(13\right);$

Further, coherent signal group number (being coherent signal source number) is determined by following formula

$\hat{P}=\mathrm{QRRC}\left({\widehat{\mathrm{\&Psi;}}}_1\right)-{\hat{K}}_n.---\left(14\right);$

B. coherent signal number detects

Due to noncoherent signal and codomain corresponding to coherent signal not overlapping and non-orthogonal, rectangular projection operator can not be eliminated the impact of known DOA in unknown DOA estimates, we adopt oblique projection Operator Method to solve coherent signal number and detect.

1) calculate oblique projection operator

There is respectively a K by what even linear array y (t) is divided into two non-overlapping copies _n+ P and M-K _nthe forward direction submatrix of-P sensor, the signal receiving accordingly

with

can write

${\stackrel{\&OverBar;}{y}}_1\left(t\right)=A_1\mathrm{\&Gamma;s}\left(t\right)+w_{{\stackrel{\&OverBar;}{y}}_1}\left(t\right)---\left(15\right);$

${\stackrel{\&OverBar;}{y}}_2\left(t\right)=A_2\mathrm{\&Gamma;s}\left(t\right)+w_{{\stackrel{\&OverBar;}{y}}_2}\left(t\right)---\left(16\right);$

Obtain from (3) with

and the Cross-covariance between x (t)

$R_{{\stackrel{\&OverBar;}{y}}_{1}x}=E\left\{{\stackrel{\&OverBar;}{y}}_1\left(t\right)x^H\left(t\right)\right\}={\stackrel{\&OverBar;}{A}}_1{R}_s{\mathrm{\&Gamma;}}^H{D}^H{A}^H---\left(17\right);$

$R_{{\stackrel{\&OverBar;}{y}}_{2}x}=E\left\{{\stackrel{\&OverBar;}{y}}_2\left(t\right)x^H\left(t\right)\right\}={\stackrel{\&OverBar;}{A}}_2{R}_s{\mathrm{\&Gamma;}}^H{D}^H{A}^H---\left(18\right);$

Wherein

reversible, so

with between there is (a K _n+ P) × (M-K _n-P) linear operator P _{α n}

$P_{\mathrm{\&alpha;n}}^H{\stackrel{\&OverBar;}{A}}_1={\stackrel{\&OverBar;}{A}}_2.---\left(19\right);$

Then P _{α n}can be tried to achieve by following formula

$P_{\mathrm{\&alpha;n}}={\left({\stackrel{\&OverBar;}{A}}_1\right)}^{-H}{\stackrel{\&OverBar;}{A}}_2^{-H}={\left(R_{{\stackrel{\&OverBar;}{y}}_{1}x}{R}_{{\stackrel{\&OverBar;}{y}}_{1}x}^H\right)}^{-1}{R}_{{\stackrel{\&OverBar;}{y}}_{1}x}{R}_{{\stackrel{\&OverBar;}{y}}_{2}x}.---\left(20\right);$

Can obtain from (19)

$Q_{\mathrm{\&alpha;n}}^H\stackrel{\&OverBar;}{A}=O_{(M-K_n-P)\&times;(K_n+P)}---\left(21\right);$

Wherein

project to

the rectangular projection operator in space is

this shows

${\mathrm{\&Pi;}}_{\mathrm{\&alpha;n}}\stackrel{\&OverBar;}{A}=O_{M\&times;(K_n+P)}.---\left(22\right);$

From (20), it meets

${\mathrm{\&Pi;}}_{\mathrm{\&alpha;n}}{A}_n=O_{M\&times;K_n}---\left(23\right)$

Π _αnA _hΛ＝O _M×P。(24)

So from (23), in the time that the fast umber of beats of array data is limited, the elevation angle of noncoherent signal

can obtain by the parameter of asking the cost function minimum that makes following formula

$f_n\left(\mathrm{\&alpha;}\right)=a^H\left(\mathrm{\&alpha;}\right){\widehat{\mathrm{\&Pi;}}}_{\mathrm{\&alpha;n}}\mathrm{\&alpha;}\left(\mathrm{\&alpha;}\right)---\left(25\right)$

Wherein a (α)=[1, e ^{j τ (α)}..., e ^{j (M 1) τ (α)}] ^t, τ (α)=2 π d _ycos α/λ.

By will be along being parallel to space projection is to R (A _n) the oblique projection operator representation in space is

its expression formula is

$E_{A_n{\stackrel{\&OverBar;}{A}}_h}=A_n{\left(A_n^H{\mathrm{\&Pi;}}_{{\stackrel{\&OverBar;}{A}}_h}^{\&perp;}{A}_n\right)}^{-1}{A}_n^H{\mathrm{\&Pi;}}_{A_h---\left(26\right);}^{\&perp;}$

Wherein

to project to

the rectangular projection operator in space, definition is

and

we have $E_{A_n|{\stackrel{\&OverBar;}{A}}_h}{A}_n=A_n$ With $E_{A_n|{\stackrel{\&OverBar;}{A}}_h}{\stackrel{\&OverBar;}{A}}_h=O_{M\&times;P}.$ But, because

(be A _hand Λ) the unknown, cannot directly ask with (26)

therefore need to consider the other oblique projection operator of asking

method.

Project to by definition

the rectangular projection operator in space

for $H_{A_n}^{\&perp;}=I_M-A_n{\left(A_n^H{A}_n\right)}^{-1}{A}_n^H,$ Can obtain a new matrix from (3)

${\tilde{R}}_{\mathrm{yx}}=R_{\mathrm{yx}}{H}_{A_n}^{\&perp;}={\stackrel{\&OverBar;}{A}}_h{R}_h{\mathrm{\&Lambda;}}^H{D}_h^H{A}_h^H{\mathrm{\&Pi;}}_{A_n}^{\&perp;}.---\left(27\right);$

Obviously

order be

its QR decomposes and can be expressed as

${\tilde{R}}_{\mathrm{yx}}\widetilde{\mathrm{\&Pi;}}=\tilde{Q}\tilde{R}=[{\tilde{q}}_1,{\tilde{q}}_2,...,{\tilde{q}}_M]\left[\begin{array}{c}{\tilde{R}}_1\\ O_{(M-P)\&times;M}\end{array}\right]\begin{array}{c}\}P\\ \}M-P\end{array}={\tilde{Q}}_1{\tilde{R}}_1---\left(28\right);$

Wherein

the unitary matrix of a M × M, $\tilde{Q}=[{\tilde{Q}}_1,{\tilde{Q}}_2],{\tilde{Q}}_1=[{\tilde{q}}_1,{\tilde{q}}_2,...,{\tilde{q}}_p],{\tilde{Q}}_2=[{\tilde{q}}_{P+1},{\tilde{q}}_{P+2},$ $...,{\tilde{q}}_M],$ the row non-singular matrix of P × M,

the permutation matrix of M × M,

do not change in the correlativity of each row.From (27) and (28), can obtain,

and project to

the rectangular projection operator in space can be expressed as

therefore we can prove the oblique projection operator in (26)

can ask for by alternate ways below

$E_{A_n|{\stackrel{\&OverBar;}{A}}_h}=A_n{\left(A_n^H{\mathrm{\&Pi;}}_{{\tilde{Q}}_1}^{\&perp;}{A}_n\right)}^{-1}{A}_n^H{\mathrm{\&Pi;}}_{{\tilde{Q}}_1}^{\&perp;}=A_n{\left({{\tilde{Q}}_2\tilde{Q}}_2^H{A}_n\right)}^{?}.---\left(29\right);$

Compared with (26), in (29)

be not subject to unknown projection operator

impact, can be according to the array data R having obtained _yxand A _nask for, and avoided the Eigenvalues Decomposition that calculated amount is heavy.

2) extract coherence messages and signal decorrelation

First by the ULAx (t) in (2) is divided into forward direction/backward submatrix that L overlapping aperture is m, wherein L=M-m+1 and m>=K _h+ 1, l the forward direction/backward submatrix of signal vector can be expressed as

$x_{\mathrm{fl}}\left(t\right)=A_m{\stackrel{\&OverBar;}{D}}^{l-1}\mathrm{D\&Gamma;s}\left(t\right)+w_{x_{\mathrm{fl}}}\left(t\right)---\left(30\right);$

$x_{\mathrm{bl}}=A_m{\stackrel{\&OverBar;}{D}}^{-(M-l)}{D}^{*}{\mathrm{\&Gamma;}}^{*}{s}^{*}\left(t\right)+w_{x_{\mathrm{bl}}}\left(t\right)=F_l{J}_M{x}^{*}\left(t\right)---\left(31\right);$

Wherein F _lbe the selection matrix of m × M, definition is F _l=[O _{m × (l-1)}, I _m, O _{m × (M-m-l+1)}],

with

it is the vector corresponding to additive noise.By application oblique projection operator

and character, according to (1), we can obtain

$\stackrel{\&OverBar;}{y}\left(t\right)=(I_m-E_{A_n|{\stackrel{\&OverBar;}{A}}_h})y\left(t\right)=A_h\mathrm{\&Lambda;}{s}_h\left(t\right)+(I_M-E_{A_n|{\stackrel{\&OverBar;}{A}}_h})w_y\left(t\right)---\left(32\right);$

Similarly, by cutting apart " compression " data

for forward direction/backward " virtual " submatrix that L overlapping aperture is m, we obtain

${\stackrel{\&OverBar;}{y}}_{\mathrm{fl}}\left(t\right)\begin{array}{c}{[{\stackrel{\&OverBar;}{y}}_l\left(t\right),{\stackrel{\&OverBar;}{y}}_{l+1}\left(t\right),...,{\stackrel{\&OverBar;}{y}}_{l+m-1}\left(t\right)]}^T=F_l\stackrel{\&OverBar;}{y}\left(t\right)\\ =A_{\mathrm{mb}}{\stackrel{\&OverBar;}{D}}_h^{l-1}\mathrm{\&Lambda;}{s}_h\left(t\right)+F_l(I_M-E_{A_n|{\stackrel{\&OverBar;}{A}}_h})w_y\left(t\right)\end{array}---\left(33\right)$

${\stackrel{\&OverBar;}{y}}_{\mathrm{bl}}\left(t\right)\begin{array}{c}{[{\stackrel{\&OverBar;}{y}}_{M-l+1}\left(t\right),{\stackrel{\&OverBar;}{y}}_{M-l}\left(t\right),...,{\stackrel{\&OverBar;}{y}}_{L-l+1}\left(t\right)]}^T=F_l{J}_M{\stackrel{\&OverBar;}{y}}^{*}\left(t\right)\\ =A_{\mathrm{mh}}{\stackrel{\&OverBar;}{D}}_h^{-(M-l)}{\mathrm{\&Lambda;}}^{*}{s}_h^{*}\left(t\right)+F_l{J}_M(I_M-E_{A_n|{\stackrel{\&OverBar;}{A}}_h})w_y^{*}\left(t\right)\end{array}.---\left(34\right)$

We can obtain a submatrix in (33) now

and the Cross-covariance between the reception signal x (t) (2) on a ULA

$R_{{\stackrel{\&OverBar;}{y}}_{\mathrm{fl}}x}\begin{array}{c}=E\left\{{\stackrel{\&OverBar;}{y}}_{\mathrm{fl}}\left(t\right)x^H\left(t\right)\right\}=F_l(I_M-E_{A_n|{\stackrel{\&OverBar;}{A}}_h})R_{\mathrm{yx}}\\ =A_{\mathrm{mh}}{\stackrel{\&OverBar;}{D}}_h^{l-1}\mathrm{\&Lambda;}{R}_h{\mathrm{\&Lambda;}}^H{D}_n^H{A}_h^H\end{array}.---\left(35\right)$

The independence of noticing noncoherent signal and coherent signal causes Cross-covariance item

disappear.With (2), (30)-(32) are similar with (34), and we can obtain other Cross-covariance

with

expression formula

$R_{{\stackrel{\&OverBar;}{y}}_{\mathrm{bl}}x}\begin{array}{c}=E\left\{{\stackrel{\&OverBar;}{y}}_{\mathrm{bl}}\left(t\right)x^H\left(t\right)\right\}=F_l{J}_M{(I_M-E_{A_n|{\stackrel{\&OverBar;}{A}}_h})}^{*}{R}_{\mathrm{yx}}^{*}\\ =A_{\mathrm{mh}}{\stackrel{\&OverBar;}{D}}_h^{-l(M-l)}{\mathrm{\&Lambda;}}^{*}{R}_h{\mathrm{\&Lambda;}}^H{D}_n^T{A}_h^T\end{array}---\left(36\right)$

$R_{x_{\mathrm{fl}}\stackrel{\&OverBar;}{y}}\begin{array}{c}=E\left\{x_{\mathrm{fl}}\left(t\right){\stackrel{\&OverBar;}{y}}^H\left(t\right)\right\}=F_l{R}_{\mathrm{yx}}^H{(I_M-E_{A_n|{\stackrel{\&OverBar;}{A}}_h})}^H\\ =A_{\mathrm{mh}}{\stackrel{\&OverBar;}{D}}_h^{l-1}{D}_h\mathrm{\&Lambda;}{R}_h{\mathrm{\&Lambda;}}^H{A}_h^H\end{array}---\left(37\right)$

$R_{x_{\mathrm{bl}}\stackrel{\&OverBar;}{y}}\begin{array}{c}=E\left\{x_{\mathrm{bl}}\left(t\right){\stackrel{\&OverBar;}{y}}^H\left(t\right)\right\}=F_l{J}_M{R}_{\mathrm{yx}}^H{(I_M-E_{A_n|{\stackrel{\&OverBar;}{A}}_h})}^T\\ =A_{\mathrm{mh}}{\stackrel{\&OverBar;}{D}}_h^{-l(M-1)}{D}_h^{*}{\mathrm{\&Lambda;}}^{*}{R}_h{\mathrm{\&Lambda;}}^T{A}_h^T\end{array}.---\left(38\right)$

Obviously the Cross-covariance in (35)-(38) only comprises the information of coherent signal.Therefore, for l=1,2 ..., L we the associating covariance matrix Φ that can construct a m × 4LM be

Wherein

Can prove if even linear array is made submatrix size m and forward direction/backward submatrix quantity L meet inequality m>=K by classifying rationally _h+ 1,2L>=K _m, and K _m=max{K _pfor p=1,2 ..., P, order probability 1 ground of Φ equals coherent signal number, i.e. ρ (Φ)=K _h.

Then we obtain the outer product matrix Ψ of Φ ₃

Ψ ₃＝ΦΦ ^H (41)

Wherein ρ (Ψ ₃)=ρ (Φ)=K _h.Therefore in the time obtaining the limited snap of array data, by estimating coherent signal number with QRRC

${\hat{K}}_h=\mathrm{QRRC}\left({\widehat{\mathrm{\&Psi;}}}_3\right)---\left(42\right)$

So can obtain incoming signal number by (8) and (42) be

therefore, noncoherent signal number, coherent signal number and coherent signal group number can be determined.

Following the present embodiment has carried out Computer Simulation, the number of probes M=12 that simulated conditions is each even linear array, transducer spacing d _y=d _xthe independent experiment of=λ/2 procedure simulation result based on 500 times.

Signal composition in Fig. 3 (a) a: aspect is the unrelated signal of (45 °, 65 °); Two orientation are respectively the part coherent signal of (56 °, 30 °) and (68 °, 48 °), and related coefficient is 0.3e ^{-j π/18}; Two groups of totally four coherent signals, position angle is respectively (80 °, 115 °), (97 °, 108 °), and (116 °, 80 °) and (130 °, 95 °), multiple attenuation coefficient is η ₁=[1, e ^{j π/6}] ^tand η ₂=[1, e ^{-j π/12}] ^t.Submatrix size

fast umber of beats N _t=128, signal to noise ratio (S/N ratio) changes to 20B from-10dB.

In Fig. 3 (b), remove fast umber of beats from 10 ¹to 10 ⁴between change and signal to noise ratio (S/N ratio) be outside 0dB, other is identical with Fig. 3 (a) conditional.

Fig. 3 shows the estimated performance of algorithm under different signal to noise ratio (S/N ratio)s and fast umber of beats.Fig. 3 (a) shows the estimated performance of algorithm under different signal to noise ratio (S/N ratio)s, and signal to noise ratio (S/N ratio) is from-10dB when changing 20B, and algorithm of the present invention and Performance Ratio through the pretreated MDL/AIC method of FBSS, MENSE and SRP are; Fig. 3 (b) shows the estimated performance of algorithm under the fast umber of beats of difference, and fast umber of beats is from 10 ¹to 10 ⁴between while changing, algorithm of the present invention and Performance Ratio through the pretreated MDL/AIC method of FBSS, MENSE and SRP are.As can be drawn from Figure 3: this method is better than through the pretreated MDL/AIC method of FBSS, MENSE and SRP under fast umber of beats still less and low signal-to-noise ratio.

Above-described embodiment is only explanation technical conceive of the present invention and feature, and its object is to allow person skilled in the art can understand content of the present invention and implement according to this, can not limit the scope of the invention with this.All equivalent transformations that Spirit Essence does according to the present invention or modification, within all should being encompassed in protection scope of the present invention.

Claims (7)

1. the sources number detection method in incoherent and coherent signal mixing situation, is characterized in that said method comprising the steps of:

(1) obtain the Cross-covariance of incoming signal and the outer product matrix of Cross-covariance based on even linear array, construct the first confederate matrix and obtain the outer product matrix of the first confederate matrix by Cross-covariance and its transformation matrix;

(2) the ratio criterion of decomposing based on QR according to the apposition rank of matrix of the outer product matrix of Cross-covariance and the first confederate matrix obtains noncoherent signal number and coherent signal group number;

(3) the incoherent part to matrix according to the orthogonality differentiate of subspace, carries out QR decomposition to the Cross-covariance that projects to noncoherent signal space; Estimate oblique projection operator according to the incoherent part of guiding matrix and the result that QR decomposes; Described oblique projection operator is realized signal separation for suppressing the noncoherent signal of receiving array data;

(4) adopt oblique projection operator to carry out project to Cross-covariance, according to the Cross-covariance after projection, be divided into 2L forward direction stack submatrix and 2L backward stack submatrix; Generate the second confederate matrix according to forward direction stack matrix and backward stack matrix; Construct the outer product matrix of the second confederate matrix according to the second confederate matrix; The ratio criterion of decomposing based on QR according to the apposition rank of matrix of the second confederate matrix is tried to achieve coherent signal number.

2. sources number detection method according to claim 1, is characterized in that the ratio criterion of decomposing based on QR according to the apposition rank of matrix of the first confederate matrix in described method step (2) obtains noncoherent signal number.

3. sources number detection method according to claim 1, is characterized in that in described method, incoming signal is two kinds or the two or more any mixing that is selected from unrelated signal, part coherent signal, coherent signal and additive noise.

4. sources number detection method according to claim 1, is characterized in that in described method, incoming signal is the mixing of part coherent signal, coherent signal and additive noise; Or incoming signal is the mixing of unrelated signal, coherent signal and additive noise; Or incoming signal is the mixing of part coherent signal, coherent signal and additive noise; Or incoming signal is the mixing of unrelated signal, part coherent signal and additive noise; Or incoming signal is the mixing of unrelated signal and additive noise; Or incoming signal is the mixing of part coherent signal and additive noise; Or incoming signal is the mixing of coherent signal and additive noise.

5. sources number detection method according to claim 1, the array structure that it is characterized in that even linear array in described method is two parallel linear arrays or L-type linear array.

6. sources number detection method according to claim 1, is characterized in that supposing that even linear array sensor array is placed on x-y plane in described method, and is made up of two row even linear arrays, the sensor that every row even linear array comprises M omnidirectional, and spacing is d _y, between row, spacing is d _x; K narrow band signal { s _k(t) } by K _nindividual noncoherent signal

and K _hindividual coherent signal composition, by far field from the different elevations angle and position angle { (α _k, β _k) incide on array K=K _n+ K _h; Coherent signal has P group, and every group by independent source s _hpform through multipath transmisstion, p group has K _pindividual coherent signal,

be expressed as s _p,k(t)=η _p,ks _hp(t), s wherein _p,k(t) be k signal in p coherent signal group, η _{p, k}for multiple attenuation coefficient, the signal that two row even linear arrays receive is:

y(t)＝ＡΓs(t)+w _y(t) (1)；

x(t)＝ADΓs(t)+w _x(t) (2);

Wherein s (t) is by K _nindividual noncoherent signal (is s _n(t)) and P coherent source signal (be s _h(t)) composition, A=[A _n, A _h], A _nk _nthe guiding matrix of individual noncoherent signal,

a _hthe guiding matrix of coherent signal, $A_h=[a\left(a_{\mathrm{1,1}}\right),...,a\left(a_{{1,}_{K_1}}\right),...,a\left({\mathrm{\&alpha;}}_{P,K_P}\right)],$ $a\left({\mathrm{\&alpha;}}_{p,k}\right)=[1,e^{\mathrm{j\&tau;}\left({\mathrm{\&alpha;}}_{p,k}\right)},...,e^{j(M-1)\mathrm{\&tau;}\left({\mathrm{\&alpha;}}_{p.k}\right)}{]}^T,$ τ(α _k)＝2πd _ycosα _k/λ，τ(α _p,k)＝2πd _ycosα _p,k/λ，

Λ＝blkdiag(η ₁，η ₂，…，η _P) D＝blkdiag(D _n,D _h)， $D_n=\mathrm{diag}(e^{\mathrm{j\&gamma;}\left({\mathrm{\&beta;}}_1\right)},e^{\mathrm{j\&gamma;}\left({\mathrm{\&beta;}}_2\right)},...,e^{\mathrm{j\&gamma;}\left({\mathrm{\&beta;}}_{K_n}\right)})$ D _h＝blkdiag(D ₁,D ₂,…,D _P)， $D_P=$ $\mathrm{diag}(e^{\mathrm{j\&gamma;}\left({\mathrm{\&beta;}}_{p,1}\right)},e^{\mathrm{j\&gamma;}\left({\mathrm{\&beta;}}_{p,2}\right)},...,e^{\mathrm{j\&gamma;}\left({\mathrm{\&beta;}}_{p,K_n}\right)}),$ γ (β _k)=2 π d _xcos β _k/ λ, γ (β _p,k)=2 π d _xcos β _p,k/ λ; s _nand s (t) _h(t) be zero-mean time domain white Gaussian random process again, coherent signal is on the same group not uncorrelated mutually, and irrelevant mutually with noncoherent signal, additive noise

with

zero-mean space-time white Gaussian random process again, and uncorrelated with incoming signal;

Describedly specifically carry out in accordance with the following steps:

1) can obtain array Cross-covariance by (1) (2):

R _yx=E{y(t)x ^H(t)}＝AΓR _sΓ ^HD ^HA ^H (3);

Wherein R _s=E{s (t) s ^h(t) }=blkdiag (R _n, R _h), R _nwith R _yxdefine the Cross-covariance of similar noncoherent signal, R _hbe and R _yxdefine the Cross-covariance of similar coherent signal, α _k≠ α _i, β _k≠ β _i, η _p,k≠ 0, and K _h>=2P, ρ (A)=ρ (D)=K, ρ (R _s)=K _n+ P, p (r)=K _n+ p; R _yxorder be:

ρ(R _yx)＝min{K,K _n+P}＝K _n+P；

2) noncoherent signal number detects

Obtain R by (3) _yxouter product matrix Ψ ₁:

${\mathrm{\&Psi;}}_1=R_{\mathrm{yx}}{R}_{\mathrm{yx}}^H=\mathrm{A\&Gamma;}{R}_s{\mathrm{\&Gamma;}}^H{D}^H{A}^H\mathrm{AD\&Gamma;}{R}_s{\mathrm{\&Gamma;}}^H{A}^H---\left(4\right);$

Wherein ρ (Ψ ₁)=ρ (R _yx)=K _n+ P, according to the confederate matrix of a M × 2M of (3) structure

for:

${\stackrel{\&OverBar;}{R}}_{\mathrm{yx}}=[R_{\mathrm{yx}},J_M{R}_{\mathrm{yx}}^{*}]=\mathrm{ACB}---\left(5\right);$

Wherein $C=[\mathrm{\&Gamma;},{\stackrel{\&OverBar;}{D}}^{-(M-1)}{\mathrm{\&Gamma;}}^{*}],$ $\stackrel{\&OverBar;}{D}=\mathrm{blkdiag}({\stackrel{\&OverBar;}{D}}_n,{\stackrel{\&OverBar;}{D}}_h),$

with definition except γ (β _k) and γ (β _p,k) by τ (α _k) and τ (α _p,k) substitute outside with D, D _nand D _hit is similar, $B=\mathrm{blkdiag}(R_s{\mathrm{\&Gamma;}}^H{D}^H{A}^H,R_s^{*}{\mathrm{\&Gamma;}}^T{\mathrm{DA}}^T);$ If M > is K _n+ P, ρ (B)=2 ρ (R _sΓ ^hd ^ha ^h)=2min{K _n+ P, M}=2 (K _n+ P);

The order of C is:

$\mathrm{\&rho;}\left(C\right)=\mathrm{\&rho;}\left(\mathrm{blkdiag}\left(\right[I_{K_n},{{\stackrel{\&OverBar;}{D}}_n}^{-(M-1)}],[\mathrm{\&Lambda;},{{\stackrel{\&OverBar;}{D}}_h}^{-(M-1)}\left]\right)\right)=\mathrm{\&rho;}\left(\right[I_{K_n},{{\stackrel{\&OverBar;}{D}}_n}^{-(M-1)}\left]\right)+\mathrm{\&rho;}\left(\right[\mathrm{\&Lambda;},{{\stackrel{\&OverBar;}{D}}_h}^{-(M-1)}{\mathrm{\&Lambda;}}^{*}\left]\right)---\left(6\right);$

Wherein $\mathrm{\&rho;}\left(\right[\mathrm{\&Lambda;},{{\stackrel{\&OverBar;}{D}}_h}^{-(M-1)}{\mathrm{\&Lambda;}}^{*}\left]\right)=2P,$ $\mathrm{\&rho;}\left(\right[I_{K_n},{{\stackrel{\&OverBar;}{D}}_n}^{-(M-1)}\left]\right)=K_n;$ ρ(C)＝K _n+2P， $\mathrm{\&rho;}\left({\stackrel{\&OverBar;}{R}}_{\mathrm{yx}}\right)=\min \{K,K_n+2P,2(K_n+P),M\}=K_n+2P,$ M > K _n+ K _h>=K _n+ 2P; Build new

outer product matrix Ψ ₂:

${\mathrm{\&Psi;}}_2={\stackrel{\&OverBar;}{R}}_{\mathrm{yx}}{\stackrel{\&OverBar;}{R}}_{\mathrm{yx}}^H=\mathrm{ACB}{B}^H{C}^H{A}^H---\left(7\right);$

Wherein

m > K _n+ 2P, K _n=2 ρ (Ψ ₁)-ρ (Ψ ₂);

Utilize QRRC method, matrix Ψ ₁and Ψ ₂order be: ρ (Ψ ₁)=QRRC (Ψ ₁)=K _n+ P, ρ (Ψ ₂)=QRRC (Ψ ₂)=K _n+ 2P; In the time that fast umber of beats is limited, noncoherent signal number is defined as:

${\hat{K}}_n=2\mathrm{QRRC}\left({\widehat{\mathrm{\&Psi;}}}_1\right)-\mathrm{QRRC}\left({\widehat{\mathrm{\&Psi;}}}_2\right)---\left(13\right);$

Coherent signal group number is determined by (14) formula:

$\hat{P}=\mathrm{QRRC}\left({\widehat{\mathrm{\&Psi;}}}_1\right)-{\hat{K}}_n---\left(14\right);$

3) coherent signal number detects

I) calculate oblique projection operator

There is respectively a K by what even linear array y (t) is divided into two non-overlapping copies _n+ P and M-K _nthe forward direction submatrix of-P sensor, the signal receiving accordingly

with

for:

${\stackrel{\&OverBar;}{y}}_1\left(t\right)=A_1\mathrm{\&Gamma;s}\left(t\right)+w_{{\stackrel{\&OverBar;}{y}}_1}\left(t\right)---\left(15\right);$

${\stackrel{\&OverBar;}{y}}_2\left(t\right)=A_2\mathrm{\&Gamma;s}\left(t\right)+w_{{\stackrel{\&OverBar;}{y}}_2}\left(t\right)---\left(16\right);$

Obtain from (3)

with

and the Cross-covariance between x (t)

$R_{{\stackrel{\&OverBar;}{y}}_{1}x}=E\left\{{\stackrel{\&OverBar;}{y}}_1\left(t\right)x^H\left(t\right)\right\}={\stackrel{\&OverBar;}{A}}_1{R}_s{\mathrm{\&Gamma;}}^H{D}^H{A}^H---\left(17\right);$

$R_{{\stackrel{\&OverBar;}{y}}_{2}x}=E\left\{{\stackrel{\&OverBar;}{y}}_2\left(t\right)x^H\left(t\right)\right\}={\stackrel{\&OverBar;}{A}}_2{R}_s{\mathrm{\&Gamma;}}^H{D}^H{A}^H---\left(18\right);$

Wherein

reversible, with

with

between there is (a K _n+ P) × (M-K _n-P) linear operator P _{α n}:

$P_{\mathrm{\&alpha;n}}^H{\stackrel{\&OverBar;}{A}}_1={\stackrel{\&OverBar;}{A}}_2---\left(19\right);$

Then P _{α n}can be tried to achieve by (20) formula:

$P_{\mathrm{\&alpha;n}}={\left({\stackrel{\&OverBar;}{A}}_1\right)}^{-H}{\stackrel{\&OverBar;}{A}}_2^{-H}={\left(R_{{\stackrel{\&OverBar;}{y}}_{1}x}{R}_{{\stackrel{\&OverBar;}{y}}_{1}x}^H\right)}^{-1}{R}_{{\stackrel{\&OverBar;}{y}}_{1}x}{R}_{{\stackrel{\&OverBar;}{y}}_{2}x}---\left(20\right);$

Meet: ${\mathrm{\&Pi;}}_{\mathrm{\&alpha;n}}{A}_n=O_{M\&times;K_n}---\left(23\right);$ ${\mathrm{\&Pi;}}_{\mathrm{\&alpha;n}}{A}_h\mathrm{\&Lambda;}=O_{M\&times;P}---\left(24\right);$

And $Q_{\mathrm{\&alpha;n}}^H\stackrel{\&OverBar;}{A}=O_{(M-K_n-P)\&times;(K_n+P)}---\left(21\right);$ Wherein $Q_{\mathrm{\&alpha;n}}=[P_{\mathrm{\&alpha;n}}^T,{-I}_{M-K_n-P}^T{]}^T;$ Project to

the rectangular projection operator in space is ${\mathrm{\&Pi;}}_{\mathrm{\&alpha;n}}=Q_{\mathrm{\&alpha;n}}{(Q_{\mathrm{\&alpha;n}}^H\&CenterDot;Q_{\mathrm{\&alpha;n}})}^{-1}{Q}_{\mathrm{\&alpha;n}}^H;$ : ${\mathrm{\&Pi;}}_{\mathrm{\&alpha;n}}\stackrel{\&OverBar;}{A}=O_{M\&times;(K_n+P)}---\left(22\right);$

In the time that the fast umber of beats of array data is limited, the elevation angle of noncoherent signal can obtain by the parameter of asking the cost function minimum that makes following formula:

$f_n\left(\mathrm{\&alpha;}\right)=a^H\left(\mathrm{\&alpha;}\right){\widehat{\mathrm{\&Pi;}}}_{\mathrm{\&alpha;n}}\mathrm{\&alpha;}\left(\mathrm{\&alpha;}\right)---\left(25\right)$

Wherein a (α)=[1, e ^{j τ (α)}..., e ^{j (M-1) τ (α)}] ^t, τ (α)=2 π d _ycos α/λ;

By will be along being parallel to

space projection is to R (A _n) the oblique projection operator representation in space is

its expression formula is

$E_{A_n{\stackrel{\&OverBar;}{A}}_h}=A_n{\left(A_n^H{\mathrm{\&Pi;}}_{{\stackrel{\&OverBar;}{A}}_h}^{\&perp;}{A}_n\right)}^{-1}{A}_n^H{\mathrm{\&Pi;}}_{A_h---\left(26\right);}^{\&perp;}$

Wherein

to project to

the rectangular projection operator in space, definition is

and ${\mathrm{\&Pi;}}_{{\stackrel{\&OverBar;}{A}}_h}={\stackrel{\&OverBar;}{A}}_h{\left({\stackrel{\&OverBar;}{A}}_h^H{\stackrel{\&OverBar;}{A}}_h\right)}^{-1}{\stackrel{\&OverBar;}{A}}_h^H,$ Have $E_{A_n|{\stackrel{\&OverBar;}{A}}_h}{A}_n=A_n$ With $E_{A_n|{\stackrel{\&OverBar;}{A}}_h}{\stackrel{\&OverBar;}{A}}_h=O_{M\&times;P};$

Project to by definition

the rectangular projection operator in space for $H_{A_n}^{\&perp;}=I_M-A_n{\left(A_n^H{A}_n\right)}^{-1}{A}_n^H;$ Can obtain a new matrix from (3):

${\tilde{R}}_{\mathrm{yx}}=R_{\mathrm{yx}}{H}_{A_n}^{\&perp;}={\stackrel{\&OverBar;}{A}}_h{R}_h{\mathrm{\&Lambda;}}^H{D}_h^H{A}_h^H{\mathrm{\&Pi;}}_{A_n}^{\&perp;}---\left(27\right);$

order be

its QR decomposes and can be expressed as:

${\tilde{R}}_{\mathrm{yx}}\widetilde{\mathrm{\&Pi;}}=\tilde{Q}\tilde{R}=[{\tilde{q}}_1,{\tilde{q}}_2,...,{\tilde{q}}_M]\left[\begin{array}{c}{\tilde{R}}_1\\ O_{(M-P)\&times;M}\end{array}\right]\begin{array}{c}\}P\\ \}M-P\end{array}={\tilde{Q}}_1{\tilde{R}}_1---\left(28\right);$

Wherein

the unitary matrix of a M × M, $\tilde{Q}=[{\tilde{Q}}_1,{\tilde{Q}}_2],{\tilde{Q}}_1=[{\tilde{q}}_1,{\tilde{q}}_2,...,{\tilde{q}}_p],{\tilde{Q}}_2=[{\tilde{q}}_{P+1},{\tilde{q}}_{P+2},$ $...,{\tilde{q}}_m],$ the row non-singular matrix of P × M,

the permutation matrix of M × M,

do not change in the correlativity of each row; From (27) and (28), can obtain,

and project to

the rectangular projection operator representation in space is

oblique projection operator

ask for by alternate ways below:

$E_{A_n|{\stackrel{\&OverBar;}{A}}_h}=A_n{\left(A_n^H{\mathrm{\&Pi;}}_{{\tilde{Q}}_1}^{\&perp;}{A}_n\right)}^{-1}{A}_n^H{\mathrm{\&Pi;}}_{{\tilde{Q}}_1}^{\&perp;}=A_n{\left({{\tilde{Q}}_2\tilde{Q}}_2^H{A}_n\right)}^{?}---\left(29\right);$

according to the array data R having obtained _yxand A _nask for;

Ii) extract coherence messages and signal decorrelation

First by the ULAx (t) in (2) is divided into forward direction/backward submatrix that L overlapping aperture is m, wherein L=M-m+1 and m>=K _h+ 1, l the forward direction/backward submatrix of signal vector is expressed as:

$x_{\mathrm{fl}}\left(t\right)=A_m{\stackrel{\&OverBar;}{D}}^{l-1}\mathrm{D\&Gamma;s}\left(t\right)+w_{x_{\mathrm{fl}}}\left(t\right)---\left(30\right);$

$x_{\mathrm{bl}}=A_m{\stackrel{\&OverBar;}{D}}^{-(M-l)}{D}^{*}{\mathrm{\&Gamma;}}^{*}{s}^{*}\left(t\right)+w_{x_{\mathrm{bl}}}\left(t\right)=F_l{J}_M{x}^{*}\left(t\right)---\left(31\right);$

Wherein F _lbe the selection matrix of m × M, definition is F _l=[O _{m × (l-1)}, I _m, O _{m × (M-m-l+1)}],

with

it is the vector corresponding to additive noise; Obtain

$\stackrel{\&OverBar;}{y}\left(t\right)=(I_m-E_{A_n|{\stackrel{\&OverBar;}{A}}_h})y\left(t\right)=A_h\mathrm{\&Lambda;}{s}_h\left(t\right)+(I_M-E_{A_n|{\stackrel{\&OverBar;}{A}}_h})w_y\left(t\right)---\left(32\right);$

By cutting apart

for forward direction/backward " virtual " submatrix that L overlapping aperture is m, obtain

${\stackrel{\&OverBar;}{y}}_{\mathrm{fl}}\left(t\right)={[{\stackrel{\&OverBar;}{y}}_l\left(t\right),{\stackrel{\&OverBar;}{y}}_{l+1}\left(t\right),...,{\stackrel{\&OverBar;}{y}}_{l+m-1}\left(t\right)]}^T=F_l{\stackrel{\&OverBar;}{y}}_l\left(t\right)=A_{\mathrm{mh}}{\stackrel{\&OverBar;}{D}}_h^{l-1}\mathrm{\&Lambda;}{s}_h\left(t\right)+F_l(I_M-E_{A_n|{\stackrel{\&OverBar;}{A}}_h})w_y\left(t\right)---\left(33\right);$

${\stackrel{\&OverBar;}{y}}_{\mathrm{bl}}\left(t\right)={[{\stackrel{\&OverBar;}{y}}_{M-l+1}\left(t\right),{\stackrel{\&OverBar;}{y}}_{M-l}\left(t\right),...,{\stackrel{\&OverBar;}{y}}_{L-l+1}\left(t\right)]}^T=F_l{\stackrel{\&OverBar;}{J}}_M{\stackrel{\&OverBar;}{y}}^{*}\left(t\right)=A_{\mathrm{mh}}{\stackrel{\&OverBar;}{D}}_h^{-(M-l)}{\mathrm{\&Lambda;}}^{*}{s}_h^{*}\left(t\right)+F_l{J}_M{(I_M-E_{A_n|{\stackrel{\&OverBar;}{A}}_h})}^{*}{w}_y^{*}\left(t\right)---\left(34\right);$

Obtain a submatrix in (33)

and the Cross-covariance between the reception signal x (t) (2) on a ULA

$R_{{\stackrel{\&OverBar;}{y}}_{\mathrm{fl}}x}=E\left\{{\stackrel{\&OverBar;}{y}}_{\mathrm{fl}}\left(t\right)x^H\left(t\right)\right\}=F_l(I_M-E_{A_n|{\stackrel{\&OverBar;}{A}}_h})R_{\mathrm{yx}}=A_{\mathrm{mh}}{\stackrel{\&OverBar;}{D}}_h^{l-1}\mathrm{\&Lambda;}{R}_h{\mathrm{\&Lambda;}}^H{D}_h^H{A}_h^H---\left(35\right);$

And other Cross-covariance

with

expression formula:

$R_{{\stackrel{\&OverBar;}{y}}_{\mathrm{bl}}x}=E\left\{{\stackrel{\&OverBar;}{y}}_{\mathrm{bl}}\left(t\right)x^H\left(t\right)\right\}=F_l{J}_M{(I_M-E_{A_n|{\stackrel{\&OverBar;}{A}}_h})}^{*}{R}_{\mathrm{yx}}^{*}=A_{\mathrm{mh}}{\stackrel{\&OverBar;}{D}}_h^{-(M-l)}{\mathrm{\&Lambda;}}^{*}{R}_h{\mathrm{\&Lambda;}}^T{D}_h^T{A}_h^T---\left(36\right);$

$R_{x_{\mathrm{fl}}\stackrel{\&OverBar;}{y}}=E\left\{x_{\mathrm{fl}}\left(t\right){\stackrel{\&OverBar;}{y}}^H\left(t\right)\right\}=F_l{R}_{\mathrm{yx}}^H{(I_M-E_{A_n|{\stackrel{\&OverBar;}{A}}_h})}^H=A_{\mathrm{mh}}{\stackrel{\&OverBar;}{D}}_h^{l-1}{D}_h\mathrm{\&Lambda;}{R}_h{\mathrm{\&Lambda;}}^H{A}_h^H---\left(37\right);$

$R_{x_{\mathrm{bl}}\stackrel{\&OverBar;}{y}}=E\left\{x_{\mathrm{bl}}\left(t\right){\stackrel{\&OverBar;}{y}}^H\left(t\right)\right\}=F_l{J}_M{R}_{\mathrm{yx}}^H{(I_M-E_{A_n|{\stackrel{\&OverBar;}{A}}_h})}^T=A_{\mathrm{mh}}{\stackrel{\&OverBar;}{D}}_h^{-(M-l)}{D}_h^{*}{\mathrm{\&Lambda;}}^{*}{R}_h{\mathrm{\&Lambda;}}^T{A}_h^T---\left(38\right);$

For l=1,2 ..., the associating covariance matrix Φ of a m × 4LM of L structure is:

Wherein:

If even linear array is made submatrix size m and forward direction/backward submatrix quantity L meet inequality m>=K by classifying rationally _h+ 1,2L>=K _m, and K _m=max{K _pfor p=1,2 ..., order probability 1 ground of P Φ equals coherent signal number, i.e. ρ (Φ)=K _h;

Then obtain the outer product matrix Ψ of Φ ₃

Ψ ₃＝ΦΦ ^H (41)；

Wherein ρ (Ψ ₃)=ρ (Φ)=K _h; In the time obtaining the limited snap of array data, by estimating coherent signal number by QRRC method:

${\hat{K}}_h=\mathrm{QRRC}\left({\widehat{\mathrm{\&Psi;}}}_3\right)---\left(42\right);$

Can obtain incoming signal number by (8) and (42) is

7. sources number detection method according to claim 6, is characterized in that ratio criterion (QRRC) method of decomposing based on QR in described method is:

The square formation that is p to the order of a M × M

wherein p < M, its QR with rank transformation is decomposed into:

$\stackrel{\&OverBar;}{\mathrm{\&Psi;}}\stackrel{\&OverBar;}{\mathrm{\&Pi;}}=\stackrel{\&OverBar;}{Q}\stackrel{\&OverBar;}{R}=\stackrel{\&OverBar;}{Q}\left[\begin{array}{cc}{\stackrel{\&OverBar;}{R}}_{11}& {\stackrel{\&OverBar;}{R}}_{12}\\ O_{(M-P)\&times;M}& \end{array}\right]\begin{array}{c}\}p\\ \}M-p\end{array}---\left(8\right);$

Wherein

the permutation matrix of M × M,

the unitary matrix of M × M, with

it is respectively the non-null matrix of the upper triangle nonsingular matrix of p × p and p × (M-p);

by introducing an auxiliary quantity ζ (i) as the factor in QR decomposition

the element that i is capable:

$\mathrm{\&zeta;}\left(i\right)=\underset{k=1}{\overset{M}{\mathrm{\&Sigma;}}}\left|{\stackrel{\&OverBar;}{r}}_{\mathrm{ik}}\right|+\mathrm{\&epsiv;}={\stackrel{\&OverBar;}{\mathrm{\&zeta;}}}_i+\mathrm{\&epsiv;},\mathrm{fori}=\mathrm{1,2},...M---\left(9\right);$

Wherein ε is a positive little constant arbitrarily, defines a ratio criterion (QRRC) of decomposing based on QR to be:

${\mathrm{QRRC}}_{\stackrel{\&OverBar;}{\mathrm{\&Psi;}}}\left(i\right)=\frac{\mathrm{\&zeta;}\left(i\right)}{\mathrm{\&zeta;}(i+1)},\mathrm{fori}=\mathrm{1,2},...M-1---\left(10\right);$

Then ratio criterion

can be expressed as

${\mathrm{QRRC}}_{\stackrel{\&OverBar;}{\mathrm{\&Psi;}}}\left(i\right)=\left\{\begin{array}{cc}\frac{{\stackrel{\&OverBar;}{\mathrm{\&zeta;}}}_i+\mathrm{\&epsiv;}}{{\stackrel{\&OverBar;}{\mathrm{\&zeta;}}}_{i+1}+\mathrm{\&epsiv;}}\&ap;\frac{{\stackrel{\&OverBar;}{\mathrm{\&zeta;}}}_i}{{\mathrm{\&zeta;}}_{i+1}}=c\left(i\right)& \mathrm{for}1\&le;i<p\\ \frac{{\stackrel{\&OverBar;}{\mathrm{\&zeta;}}}_n+\mathrm{\&epsiv;}}{\mathrm{\&epsiv;}}\&RightArrow;\&infin;& \mathrm{fori}=p\\ \frac{\mathrm{\&epsiv;}}{\mathrm{\&epsiv;}}=1& \mathrm{forp}\&le;i<M-1\end{array}\right.---\left(11\right);$

order by ask i ∈ 1,2 ... within the scope of M}, make

maximum subscript i obtains, that is: $p=\underset{i}{\arg \max }{\mathrm{QRRC}}_{\stackrel{\&OverBar;}{\mathrm{\&Psi;}}}\left(i\right)=\mathrm{QRRC}\left(\stackrel{\&OverBar;}{\mathrm{\&Psi;}}\right)---\left(12\right).$

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