CN104142445A - Method for measuring uniform linear array phase response parameters under multi-path propagation environment - Google Patents

Abstract

The invention belongs to a method for measuring antenna array phase response parameters in the technical field of electronic information. The method comprises the steps that initializing is carried out, a multi-path signal direction difference matrix of a first direction and other set directions is established, the direction difference of direct wave signals and indirect wave signals of set direction correcting signal sources is determined, and the uniform linear array phase response parameters are determined. The correcting signal sources are arranged on different known directions respectively and emit signals in sequence, after a uniform linear array receives the various signals emitted by the signal sources, various multi-path signals are respectively processed, an all-direction difference matrix is established, the direction difference between the multi-path signals of the correcting signal sources is determined, and the conjugate vector of the uniform linear array phase response parameter vector and the normalization average vector is determined. The method has the advantages that under the propagation environment where the multi-path and indirect wave signal directions are unknown, the uniform linear array phase response parameters are accurately measured, the error between the measured parameters and the actual parameters is small, and the similarity is high.

Description

The assay method of even linear array phase response parameter in a kind of multipath propagation environment

Technical field

The invention belongs to the assay method of aerial array phase response parameter in electronic information technical field, particularly in multipath propagation environment the unknown of multipath indirect wave sense in the situation that, utilize the direction of direct-path signal and even linear array received signal vector to measure the method for phase response parameter.

Background technology

Be one of gordian technique of antenna array signals processing to signal direction-finding, be extensively studied and apply in fields such as radar, communication, sonars.One-to-one relationship between actual direction vector and the signal arrival bearing (abbreviation sense) of known antenna array is to realize the prerequisite of high-resolution direction finding, and the actual direction vector of aerial array equals the direction vector definite according to sense vector model and the product vector (corresponding element multiplies each other) of aerial array phase response parameter vector.In actual applications, the one-to-one relationship between direction vector and the sense of aerial array is subject to the impact of unknown aerial array phase response parameter, causes high-resolution Measure direction performance to worsen.Therefore, measure aerial array phase response parameter and move towards significant in practical evolution at high-resolution direction finding technology.

In the environment that there is no multipath transmisstion, can a correction signal be set in known direction, first measure aerial array received signal vector, then it is normalized to average treatment, determine actual direction vector, finally utilize the direction vector definite according to sense vector model and actual direction vector to determine aerial array phase response parameter vector.But, in actual applications, except there is direct-path signal, have multipath indirect wave signal toward contact, and multipath indirect wave sense being unknown, corresponding actual direction vector is also unknown.Existing in the environment of multipath indirect wave signal, because aerial array received signal vector is the linear combination of actual direction vector with the actual direction vector of multipath indirect wave signal of direct-path signal, cause directly utilizing aerial array received signal vector and determine that according to the direction vector of the definite through wave-wave signal of sense vector model the method for aerial array phase response parameter vector lost efficacy.

In addition,, owing to being subject to the impact of unknown aerial array phase response parameter, utilize the submatrix of even linear array received signal vector or the multipath signal processing method of Subspace smoothing also no longer applicable.

Summary of the invention

The object of the invention is the mensuration problem for the even linear array phase response parameter in the multipath propagation environment existing in background technology, the assay method of even linear array phase response parameter in a kind of multipath propagation environment of development research, the method is placed in 1 correction signal source successively and is no less than in 2 different directions, timesharing transmits, in the situation that there is multipath indirect wave signal (direction the unknown), realize the object of Accurate Determining even linear array phase response parameter in multipath propagation environment.

Solution thinking of the present invention is: first correction signal source is placed in to the direction of first known (setting) and transmits, even linear array receives by the signal (direct-path signal and indirect wave signal) of this correction signal source transmitting, after multipath signal, treated, to determine even linear array received signal vector and normalization average vector thereof, and the Hadamard product (corresponding element multiplies each other) of definite normalization average vector and conjugate vector thereof, thereby determine with even linear array phase response cache oblivious without phase vector; Then to carrying out Subarray partition without phase vector, set up the poor matrix of direction; Secondly, change the placement direction in correction signal source, repeat said process, the placement direction in corresponding each correction signal source is set up the poor matrix of corresponding direction respectively; Then, utilize the poor matrix of all directions, determine that the direction between direct-path signal and the indirect wave signal in corresponding correction signal source is poor; Then, utilize the direction between its corresponding indirect wave signal of all direct-path signal directions poor, determine the conjugate vector of even linear array phase response parameter vector and normalization average vector thereof, thereby in the case of there is the indirect wave signal of multipath and direction the unknown, realize the object of Accurate Determining even linear array phase response parameter in multipath propagation environment.

Thereby the inventive method comprises:

Step 1. initialization process: by the antenna number M of even linear array, divide the antenna number J of submatrix, the aerial position coordinate x of even linear array _m=(m-1) d, d is the interval between even linear array adjacent antenna, m=1,2 ..., M, correction signal source setting party to number K, correction signal source place different directions θ _k, k=1,2 ..., K, the judgement thresholding η of the large singular value of matrix, and the number L initialization of even linear array received signal vector deposits internal memory in;

Step 2. is set up the poor matrix of direction of first direction: first adopt I/Q dual channel receiver method or Hilbert transform method to be positioned over first direction θ to what receive ₁the signal containing direct-path signal and indirect wave signal that sends of correction signal source process, to determine even linear array received signal vector; Then determine the normalization average vector of even linear array received signal vector, and the Hadamard product (corresponding element multiplies each other) of definite normalization average vector and conjugate vector thereof, thus determine with even linear array phase response cache oblivious without phase vector; Then to carrying out Subarray partition without phase vector, thereby set up the poor matrix (U of multipath signal direction of this direction ₁);

Step 3. is set up the poor matrix of multipath signal direction of all the other direction initializations: after step 2 completes, correction signal source is placed in the direction of all the other settings successively, thereby the signal sending by correction signal source respectively repeats steps the 2 poor matrixes of multipath signal direction of setting up successively all the other directions;

Direction between direct-path signal and the indirect wave signal in the definite each direction initialization correction signal of step 4. source is poor: first step 2, the poor matrix of the each multipath signal direction of step 3 gained are carried out respectively svd, determine that the number of large singular value (is designated as N _k), and then utilize respectively each (N _k) singular vector corresponding to individual large singular value determine signal subspace; Then utilize signal subspace, determine that respectively when correction signal source is positioned over each direction initialization, the direction between the direct-path signal in each correction signal source and its indirect wave signal is poor; (k=1,2 ..., K, n=1,2 ..., N _k);

Step 5. is determined even linear array phase response parameter: the different directions (θ that utilizes correction signal source to place _k) and the corresponding direction of all directions of step 4 gained poor set up phase bit recovery matrix and from this recovery matrix, determine the submatrix of the phase bit recovery matrix identical with direction number; Then phase bit recovery matrix is carried out to svd, determine the right singular vector corresponding to minimum singular value of phase bit recovery matrix; Again right the singular vector corresponding minimum singular value of phase bit recovery matrix is divided into (K) subvector identical with direction number by order of elements, and then each (K) individual submatrix of phase bit recovery matrix and corresponding subvector are carried out to the processing of (work) product, and definite its normalization average vector, the conjugate vector that finally even linear array phase response parameter vector is converted to normalization average vector, in conjugate vector, each element is even linear array phase response parameter.

Described in step 2, first adopting I/Q dual channel receiver method or Hilbert transform method to be positioned over first direction (θ to what receive ₁) the signal that sends of correction signal source process, to determine even linear array received signal vector, its received signal vector is:

$x^{\left(1\right)}\left(t\right)={\left[\begin{array}{cccc}{x}_1^{\left(1\right)}\left(t\right)& x_2^{\left(1\right)}\left(t\right)& \·\·\·& x_M^{\left(1\right)}\left(t\right)\end{array}\right]}^T$

Wherein: x ⁽¹⁾(t) for correction signal source is positioned over first direction θ ₁time even linear array received signal vector, t is sampling instant, t=1,2 ..., L, L represents total sampling instant number, represent even linear array received signal vector x ⁽¹⁾(t) m element, m=1,2 ..., M, M is the antenna number of even linear array.

At the normalization average vector of determining even linear array received signal vector described in step 2, for:

$r^{\left(1\right)}=\frac{1}{L}\underset{t=1}{\overset{L}{\mathrm{\Σ}}}{x}^{\left(1\right)}\left(t\right)/x_1^{\left(1\right)}\left(t\right)$

Wherein, even linear array received signal vector x ⁽¹⁾(t) first element, L is the number of even linear array received signal vector; The Hadamard product (corresponding element multiplies each other) of described definite normalization average vector and conjugate vector thereof, thus determine with even linear array phase response cache oblivious without phase vector, for:

u ₁＝r ⁽¹⁾⊙r ^(1)*

Wherein r ^{(1) *}average vector r ⁽¹⁾conjugate vector, ⊙ represents Hadamard product (corresponding element multiplies each other); Described to carrying out Subarray partition without phase vector, thus the poor matrix of multipath signal direction of this direction set up, and the poor matrix of its direction is:

$U_1=\left[\begin{array}{cccc}{r}_1^{\left(1\right)}& r_2^{\left(1\right)}& \·\·\·& r_{M-J+1}^{\left(1\right)}\\ r_2^{\left(1\right)}& r_3^{\left(1\right)}& \·\·\·& r_{M-J+2}^{\left(1\right)}\\ \·& \·& \·& \·\\ \·& \·& \·& \·\\ \·& \·& \·& \·\\ r_J^{\left(1\right)}& r_{J+1}^{\left(1\right)}& \·\·\·& r_M^{\left(1\right)}\end{array}\right]{\left[\begin{array}{cccc}{r}_1^{\left(1\right)}& r_2^{\left(1\right)}& \·\·\·& r_{M-J+1}^{\left(1\right)}\\ r_2^{\left(1\right)}& r_3^{\left(1\right)}& \·\·\·& r_{M-J+2}^{\left(1\right)}\\ \·& \·& \·& \·\\ \·& \·& \·& \·\\ \·& \·& \·& \·\\ r_J^{\left(1\right)}& r_{J+1}^{\left(1\right)}& \·\·\·& r_M^{\left(1\right)}\end{array}\right]}^H$

Wherein: average vector r ⁽¹⁾m element, m=1,2 ..., M, the antenna number that M is even linear array, J is the antenna number of submatrix.

Described in step 3, correction signal source is being placed in the direction of all the other settings successively, thereby the signal sending by correction signal source respectively repeats steps the 2 poor matrixes of multipath signal direction of setting up successively all the other directions, the poor matrix of all the other each multipath signal directions is:

$U_k=\left[\begin{array}{cccc}{r}_1^{\left(k\right)}& r_2^{\left(k\right)}& \·\·\·& r_{M-J+1}^{\left(k\right)}\\ r_2^{\left(k\right)}& r_3^{\left(k\right)}& \·\·\·& r_{M-J+2}^{\left(k\right)}\\ \·& \·& \·& \·\\ \·& \·& \·& \·\\ \·& \·& \·& \·\\ r_J^{\left(k\right)}& r_{J+1}^{\left(k\right)}& \·\·\·& r_M^{\left(k\right)}\end{array}\right]{\left[\begin{array}{cccc}{r}_1^{\left(k\right)}& r_2^{\left(k\right)}& \·\·\·& r_{M-J+1}^{\left(k\right)}\\ r_2^{\left(k\right)}& r_3^{\left(k\right)}& \·\·\·& r_{M-J+2}^{\left(k\right)}\\ \·& \·& \·& \·\\ \·& \·& \·& \·\\ \·& \·& \·& \·\\ r_J^{\left(k\right)}& r_{J+1}^{\left(k\right)}& \·\·\·& r_M^{\left(k\right)}\end{array}\right]}^H$

Wherein: θ _kfor the direction that place in correction signal source, U _kfor the poor matrix of direction, average vector r ^(k)m element, k=2 ..., K, m=1,2 ..., M, the antenna number that M is even linear array, J is the antenna number of submatrix, r ^(k)that correction signal source is positioned over to direction θ _ktime definite even linear array received signal vector normalization average vector.

Described in step 4, step 2, the poor matrix of the each multipath signal direction of step 3 gained are being carried out respectively to svd, svd is undertaken by following formula:

$U_k=W_k{\mathrm{\Λ}}_k{W}_k^H$

Wherein: matrix Λ _kbe diagonal matrix, diagonal element is the poor matrix U of corresponding multipath signal direction respectively _ksingular value, by descending sort, matrix W _kby the poor matrix U of multipath signal direction _ksingular vector the matrix forming, corresponding one by one with singular value, representing matrix U _kassociate matrix, k=1,2 ..., K;

(be designated as N in the number of determining large singular value described in step 4 _k), the number N of large singular value _kdetermined by following formula: $N_k=\arg \underset{D}{\min }D,s.t.\underset{n=1}{\overset{D}{\mathrm{\Σ}}}{\mathrm{\λ}}_n^{\left(k\right)}>\mathrm{\η}\underset{n=1}{\overset{J}{\mathrm{\Σ}}}{\mathrm{\λ}}_n^{\left(k\right)},$ Be N _kto meet inequality $\underset{n=1}{\overset{D}{\mathrm{\Σ}}}{\mathrm{\λ}}_n^{\left(k\right)}>\mathrm{\η}\underset{n=1}{\overset{J}{\mathrm{\Σ}}}{\mathrm{\λ}}_N^{\left(K\right)}$ Minimum D value, wherein, J is the antenna number of submatrix, η is the judgement thresholding of large singular value, k=1,2 ..., K, D is positive integer.

Described in step 4, utilizing respectively each (N _k) singular vector corresponding to individual large singular value determine signal subspace, for: wherein N _kfor the poor matrix U of direction _kthe number of large singular value, k=1,2 ..., K;

Described in step 4, utilizing signal subspace, determining that respectively when correction signal source is positioned over the direction of each setting, the direction between the direct-path signal in each correction signal source and its indirect wave signal is poor, for:

${\widehat{\mathrm{\θ}}}_{\mathrm{kn}}=\mathrm{angle}\left({\mathrm{\β}}_{\mathrm{kn}}\right)$

Wherein β _knfor matrix eigenwert, with be respectively signal subspace j-1 row vector above and the matrix that J-1 row vector forms below, it is matrix generalized inverse matrix, angle (β _kn) representing matrix eigenwert β _knphase place, n=1,2 ..., N _k, k=1,2 ..., K;

At the different directions (θ that utilizes correction signal source to place described in step 5 _k) and the corresponding direction of all directions of step 4 gained poor set up phase bit recovery matrix, represent by the form of partitioned matrix, for:

Q＝[Q ₁?Q ₂?…?Q _K]

Wherein: $Q_k={\mathrm{diag}}^{-1}\left(u_k\right)\left[\begin{array}{cccc}a({\mathrm{\θ}}_k+{\widehat{\mathrm{\θ}}}_{k1})& a({\mathrm{\θ}}_k+{\widehat{\mathrm{\θ}}}_{k2})& \·\·\·& a({\mathrm{\θ}}_k+{\widehat{\mathrm{\θ}}}_{k{N}_k})\end{array}\right],$ K the submatrix of phase bit recovery matrix Q, $a({\mathrm{\θ}}_k+{\widehat{\mathrm{\θ}}}_{\mathrm{kn}})={\left[\begin{array}{cccc}1& e^{-j2\mathrm{\π}\frac{d}{\mathrm{\λ}}\sin ({\mathrm{\θ}}_k+{\widehat{\mathrm{\θ}}}_{\mathrm{kn}})}& \·\·\·& e^{-j2\mathrm{\π}\frac{(M-1)d}{\mathrm{\λ}}\sin ({\mathrm{\θ}}_k+{\widehat{\mathrm{\θ}}}_{\mathrm{kn}})}\end{array}\right]}^T,$ λ is signal wavelength, diag ^-1(u _k) be matrix diag (u _k) inverse matrix, diag (u _k) be with without phase vector u _kthe element diagonal matrix that is diagonal element, n=1,2 ..., N _k, k=1,2 ..., K, [] ^trepresent vectorial transposition;

Described in step 5, phase bit recovery matrix is being carried out to svd, svd is undertaken by following formula:

Q＝SYG ^H

Wherein: matrix Y is diagonal matrix, diagonal element is the singular value of phase bit recovery matrix Q, by descending sort, matrix S and G are respectively the matrix being made up of left singular vector and the right singular vector of phase bit recovery matrix Q, corresponding one by one with the singular value of phase bit recovery matrix Q;

At right singular vector corresponding to minimum singular value of determining phase bit recovery matrix described in step 5, for the rightmost column vector of matrix G, be designated as g; Described right the singular vector corresponding minimum singular value of phase bit recovery matrix is divided into identical with direction number (K) subvector by order of elements, is respectively:

g ^(k)＝[g(N ₁+...+N _k-1+1)?g(N ₁+...+N _k-1+2)?...?g(N ₁+...+N _k-1+N _k)] ^T

Wherein, [] ^trepresent vectorial transposition, g (i) is i the element of vectorial g, described each (K) individual submatrix of setting up by this recovery matrix and subvector are accordingly carried out to the processing of (work) product, its result is:

f ^(k)＝Q _kg ^(k)

Wherein, Q _kk the submatrix of phase bit recovery matrix Q, k=1,2 ..., K; Described definite its normalization average vector, its average vector is:

$f=\frac{1}{K}\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{f}^{\left(k\right)}/{f_1}^{\left(k\right)}$

Wherein: f ₁ ^kfor vector f ^(k)the 1st element; The described conjugate vector that even linear array phase response parameter vector is converted to normalization average vector, its conjugate vector is:

$\hat{p}=f^{*}$

Wherein: f ^*for the conjugate vector of vector f, in conjugate vector, each element is even linear array phase response parameter.

The present invention is placed in correction signal source respectively in different known direction and transmits successively owing to adopting, even linear array is received after each signal of this signal source transmitting, respectively each the multipath signal receiving processed, set up the poor matrix of direction of all directions, and utilize the poor matrix of its direction to determine that the direction between the multipath signal in each corresponding correction signal source is poor, and then the conjugate vector of definite even linear array phase response parameter vector and normalization average vector thereof.Thereby in the case of there is the indirect wave signal of multipath and direction the unknown, realize the object of Accurate Determining even linear array phase response parameter in multipath propagation environment.The inventive method through embodiment measure even linear array phase response parameter vector phase error and and actual phase response parameter between correlation test, adopt the specific embodiment of the invention, the direction number of placing in correction signal source equals 2, while all there is the multipath indirect wave signal of 1 direction the unknown in each direction that place in corresponding correction signal source, the phase error of the each element of even linear array phase response parameter vector of measuring is all in 1.4 degree, and related coefficient between the each element of actual phase response parameter vector is greater than 0.999.Thereby there is multipath indirect wave signal in the present invention, and in the multipath propagation environment of multipath indirect wave sense the unknown, can effectively measure even linear array phase response parameter, error between phase response parameter and the actual phase response parameter of mensuration is little, similarity is high.

Embodiment

The even linear array that present embodiment equals half times of wavelength, 8 antennas composition taking the interval d between adjacent antenna is as example, i.e. M=8; The direction number K=2 that in this example, place in correction signal source, the direction θ that place in correction signal source ₁=10.28 when spend, and unknown multipath indirect wave sense is 33.52 degree; The direction that place in correction signal source is θ ₂=-12.07 when spend, and unknown multipath indirect wave sense is 19.36 degree; Signal to noise ratio (S/N ratio) is all set to 15dB; The number of even linear array received signal vector equals 100, i.e. L=100.Even linear array phase response parameter vector is set as: wherein: unit: degree, [] ^tfor vectorial transposition.In the present embodiment, implementing object of the present invention is exactly to utilize the correction signal source timesharing that is positioned over 2 different directions to transmit, in the situation that there is multipath indirect wave signal (direction the unknown), realize the object of Accurate Determining even linear array phase response parameter in multipath propagation environment.

The flow process of the specific embodiment of the present invention is as follows:

Step 1. initialization process: by receiving the antenna number M=8 of even linear array, divide the antenna number J=5 of submatrix, the position coordinates x of antenna _m=(m-1)/2, m=1,2 ..., 8, the direction number K=2 that place in correction signal source, the direction θ that place in correction signal source ₁=10.28 degree, θ ₂=-12.07 degree, judgement thresholding η=0.95 of the large singular value of matrix, and the number of even linear array received signal vector (L=100) initialization deposits internal memory in;

Correction signal source is positioned over direction θ by step 2. ₁=10.28 spend, and determine the normalization average vector r of even linear array received signal vector ⁽¹⁾for:

[1.00，3.36-1.09i，-2.09-4.61i，4.36-2.46i，-1.99-2.56i，0.98-0.22i，-2.38-1.10i，3.10-3.56i] ^T，

Wherein: [] ^trepresent vectorial transposition;

Determine normalization average vector r ⁽¹⁾and the Hadamard product of conjugate vector, thereby determine even linear array received signal vector without phase vector u ₁for:

[1.000，12.4447，25.6243，25.0308，10.5358，1.0094，6.8495，22.2493] ^T；

To without phase vector u ₁carry out Subarray partition, determine the poor matrix U of direction ₁, its column vector is respectively:

$\begin{array}{ccccc}1.0e+003x& & & & \\ 1.4390& 1.2364& 0.6324& 0.3535& 0.7555\\ 1.2364& 1.5490& 1.2346& 0.6789& 0.5628\\ 0.6324& 1.2346& 1.3952& 0.9227& 0.3899\\ 0.3535& 0.6789& 0.9227& 0.7855& 0.4337\\ 0.7555& 0.5628& 0.3899& 0.4337& 0.6540\end{array}$

Step 3., for k=2, is positioned over direction θ by correction signal source ₂=-12.07 degree, repeating step 2, determine that the normalization average vector r (2) of even linear array received signal vector is:

[1.00，-0.14-0.23i，0.99+0.50i，0.87+1.07i，-0.26-0.68i，-0.29-0.43i，-0.50+1.21i，-1.18+0.38i] ^T，

Wherein: [] ^trepresent vectorial transposition;

Determine normalization average vector r ⁽²⁾and the Hadamard product of conjugate vector, thereby determine even linear array received signal vector without phase vector u ₂for:

[1.0000，0.0729，1.2239，1.8975，0.5324，0.2638，1.7154，1.5399] ^T；

To without phase vector u ₂carry out Subarray partition, determine the poor matrix U of direction ₂, the poor matrix column vector of its direction is respectively:

$\begin{array}{ccccc}6.1037& 3.4946& 2.5143& 5.5141& 5.5731\\ 3.4946& 5.3871& 3.5621& 2.2036& 4.4364\\ 2.5143& 3.5621& 5.4514& 3.9254& 2.4715\\ 5.5141& 2.2036& 3.9254& 6.8961& 4.2447\\ 5.5731& 4.4364& 2.4715& 4.2447& 5.6670\end{array}$

Step 4. is to step 2, the poor matrix U of step 3 gained direction ₁and U ₂carry out respectively svd, determine that the number of large singular value is respectively N ₁=3, N ₂=3, definite signal subspace is respectively:

$\begin{array}{ccc}-0.4790& 0.6509& 0.0417\\ -0.5808& 0.0523& 0.4690\\ -0.4963& -0.5540& 0.1472\\ -0.3273& -0.4394& -0.5053\\ -0.2824& 0.2714& -0.7080\end{array}$

With

$\begin{array}{ccc}-0.5003& 0.3483& 0.2482\\ -0.3903& -0.6440& 0.3023\\ -0.3614& -0.4773& -0.6608\\ -0.4887& 0.4853& -0.4512\\ -0.4774& 0.0261& 0.4548\end{array}$

Then utilize signal subspace, determine that correction signal source is positioned over direction θ ₁=10.28 when spend, and the poor estimation of direction between the direct-path signal in correction signal source and indirect wave signal is respectively: 0 degree, 23.31 degree and-21.60 degree; Determine that correction signal source is positioned over direction θ ₂=12.07 when spend, and the poor estimation of direction between the direct-path signal in correction signal source and indirect wave signal is respectively: 0 degree, 31.71 degree and-36.90 degree;

The direction θ that step 5. utilizes the poor estimation of the direction of step 4 gained and correction signal source to place ₁=10.28 degree and θ ₂=12.07 degree, determine phase bit recovery matrix, and before it, the submatrix of 3 column vector compositions is:

$\begin{array}{ccc}1.0000& 1.0000& 1.0000\\ 0.1821+0.2173i& -0.1309+0.2515i& 0.2705-0.0849i\\ -0.1975+0.0048i& 0.1360-0.1433i& 0.1429+0.1364i\\ -0.1169+0.1621i& 0.1698-0.1054i& 0.0465-0.1944i\\ -0.0724-0.2994i& -0.2992+0.0733i& 0.2997-0.0715i\\ -0.9885+0.1163i& -0.8669+0.4890i& -0.9567-0.2745i\\ 0.3736-0.0800i& 0.3217+0.2061i& 0.2091-0.3198i\\ 0.0140+0.2115i& 0.1906+0.0929i& -0.2012+0.0669i\end{array}$

The submatrix of 3 column vectors composition next is:

$\begin{array}{ccc}-2.8715+0.0000i& -2.8715+0.0000i& -2.8715+0.0000i\\ -1.1006-10.5775i& 10.6268+0.4078i& -10.3152+2.5868i\\ 0.5550+2.5356i& 0.1779-2.5895i& -1.2434-2.2785i\\ 2.0031+0.5771i& 1.3535+1.5855i& 0.3024+2.0626i\\ -3.0156+2.5289i& -3.9026+0.5091i& -1.1812+3.7542i\\ -2.4394+5.0310i& -2.2243-5.1297i& 5.4051-1.4303i\\ -2.0399-0.8034i& 0.7382+2.0645i& 1.9477-1.0066i\\ -0.9607+2.1051i& 0.3422+2.2886i& -1.9530+1.2411i\end{array}$

Phase bit recovery matrix is carried out to svd, determine the right singular vector corresponding to minimum singular value of phase bit recovery matrix, for: [0.8091,0.5642+0.1347i, 0.0088+0.0109i ,-0.0353+0.0687i,-0.0471-0.0199i, 0.0016+0.0019i] ^t;

Right the singular vector corresponding minimum singular value of phase bit recovery matrix is divided into 2 subvectors by order of elements, is respectively:

[-0.8091，0.5642+0.1347i，0.0088+0.0109i] ^T

With

[-0.0353+0.0687i，-0.0471-0.0199i，0.0016+0.0019i] ^T

Determine 2 corresponding submatrixs of phase bit recovery matrix and the product of corresponding subvector, and determine that its normalization average vector is:

[1，0.70-0.63i，-0.91+0.24i，-0.93-0.15i，0.82+0.52i，-0.67+0.62i，0.84+0.45i，0.19+0.93i] ^T；

Finally, determine (being designated as of even linear array phase response parameter vector ) be the conjugate vector of normalization average vector, that is: [1,0.70+0.63i ,-0.91-0.24i ,-0.93+0.15i, 0.82-0.52i ,-0.67-0.62i, 0.84-0.45i, 0.19-0.93i] ^t;

The phase place of each element in even linear array phase response parameter vector is respectively:

0，-41.97，165.06，-170.90，32.77，137.50，28.14，78.08

Unit: degree; And the error between the phase place of each element of the even linear array phase response parameter vector of setting is respectively:

0，-1.36，1.38，0.30，-0.11，-0.87，-1.34，0.21

Unit: degree.As can be seen here, the phase error of the each element of even linear array phase response parameter vector of mensuration is all in 1.4 degree.

Related coefficient between the estimation of even linear array phase response parameter vector and actual even linear array phase response parameter vector is defined as: wherein [] ^hrepresent vectorial conjugate transpose, || represent to take absolute value; Related coefficient more approaches 1, represents the even linear array phase response parameter vector of measuring more approaching with actual even linear array phase response parameter vector p, adopt the specific embodiment of the invention, the direction number of placing in correction signal source equals 2, each direction that place in corresponding correction signal source, while there is respectively the multipath indirect wave signal of 1 direction the unknown, the related coefficient between each element of the even linear array phase response parameter vector of mensuration and each element of actual even linear array phase response parameter vector is greater than 0.999.

Claims (10)

1. an assay method for even linear array phase response parameter in multipath propagation environment, comprising:

Step 1. initialization process: by the antenna number M of even linear array, divide the antenna number J of submatrix, the aerial position coordinate x of even linear array _m=(m-1) d, d is the interval between even linear array adjacent antenna, m=1,2 ..., M, correction signal source setting party to number K, correction signal source place different directions θ _k, k=1,2 ..., K, the judgement thresholding η of the large singular value of matrix, and the number L initialization of even linear array received signal vector deposits internal memory in;

Step 2. is set up the poor matrix of direction of first direction: first adopt I/Q dual channel receiver method or Hilbert transform method to be positioned over first direction θ to what receive ₁the signal containing direct-path signal and indirect wave signal that sends of correction signal source process, to determine even linear array received signal vector; Then determine the normalization average vector of even linear array received signal vector, and the Hadamard product of definite normalization average vector and conjugate vector thereof, thus determine with even linear array phase response cache oblivious without phase vector; Then to carrying out Subarray partition without phase vector, thereby set up the poor matrix of multipath signal direction of this direction;

Step 3. is set up the poor matrix of multipath signal direction of all the other direction initializations: after step 2 completes, correction signal source is placed in the direction of all the other settings successively, thereby the signal sending by correction signal source respectively repeats steps the 2 poor matrixes of multipath signal direction of setting up successively all the other directions;

Direction between direct-path signal and the indirect wave signal in the definite each direction initialization correction signal of step 4. source is poor: first step 2, the poor matrix of the each multipath signal direction of step 3 gained are carried out respectively svd, determine the number of large singular value, and then utilize respectively singular vector corresponding to each large singular value to determine signal subspace; Then utilize signal subspace, determine that respectively when correction signal source is positioned over each direction initialization, the direction between the direct-path signal in each correction signal source and its indirect wave signal is poor;

Step 5. is determined even linear array phase response parameter: utilize the different directions of correction signal source placement and the poor submatrix of setting up phase bit recovery matrix and determine the phase bit recovery matrix identical with direction number from this recovery matrix of the corresponding direction of all directions of step 4 gained; Then phase bit recovery matrix is carried out to svd, determine the right singular vector corresponding to minimum singular value of phase bit recovery matrix; Again right the singular vector corresponding minimum singular value of phase bit recovery matrix is divided into the subvector identical with direction number by order of elements, and then each submatrix of phase bit recovery matrix and corresponding subvector are carried out to product processing, and definite its normalization average vector, the conjugate vector that finally even linear array phase response parameter vector is converted to normalization average vector, in conjugate vector, each element is even linear array phase response parameter.

2. by the assay method of even linear array phase response parameter in multipath propagation environment described in claim 1, it is characterized in that described in step 2 being positioned over first direction θ to what receive ₁the signal that sends of correction signal source process, to determine even linear array received signal vector, its received signal vector is:

Wherein: x ⁽¹⁾(t) for correction signal source is positioned over first direction θ ₁time even linear array received signal vector, t is sampling instant, t=1,2 ..., L, L represents total sampling instant number, represent even linear array received signal vector x ⁽¹⁾(t) m element, m=1,2 ..., M, M is the antenna number of even linear array;

And the normalization average vector of described definite even linear array received signal vector, for:

Wherein, even linear array received signal vector x ⁽¹⁾(t) first element, L is the number of even linear array received signal vector;

The Hadamard product of described definite normalization average vector and conjugate vector thereof, thus determine and even linear array phase response ginseng

Number irrelevant without phase vector, for:

u ₁＝r ⁽¹⁾⊙r ^(1)*

Wherein: r ^{(1) *}average vector r ⁽¹⁾conjugate vector, ⊙ represents Hadamard product (corresponding element multiplies each other).

3. by the assay method of even linear array phase response parameter in multipath propagation environment described in claim 1, it is characterized in that described in step 2 carrying out Subarray partition without phase vector, thereby set up the poor matrix of multipath signal direction of this direction, the poor matrix of its direction is:

Wherein: average vector r ⁽¹⁾m element, m=1,2 ..., M, the antenna number that M is even linear array, J is the antenna number of submatrix.

4. by the assay method of even linear array phase response parameter in multipath propagation environment described in claim 1, it is characterized in that setting up successively described in step 3 the poor matrix of multipath signal direction of all the other directions, the poor matrix of all the other each multipath signal directions is:

Wherein: θ _kfor the direction that place in correction signal source, U _kfor the poor matrix of direction, average vector r ^(k)m element, k=2 ..., K, m=1,2 ..., M, the antenna number that M is even linear array, J is the antenna number of submatrix, r ^(k)that correction signal source is positioned over to direction θ _ktime definite even linear array received signal vector normalization average vector.

5. by the assay method of even linear array phase response parameter in multipath propagation environment described in claim 1, it is characterized in that, described in step 4, the poor matrix of the each multipath signal direction of gained is carried out respectively to svd, svd is undertaken by following formula:

Wherein: matrix Λ _kbe diagonal matrix, diagonal element is the poor matrix U of corresponding multipath signal direction respectively _ksingular value, by descending sort, matrix W _kby the poor matrix U of multipath signal direction _ksingular vector the matrix forming, corresponding one by one with singular value, representing matrix U _kassociate matrix, k=1,2 ..., K;

And the described number of determining large singular value, the number N of large singular value _kdetermined by following formula:

be that Nk meets inequality minimum D value,

Wherein, J is the antenna number of submatrix, and η is the judgement thresholding of large singular value, k=1, and 2 ..., K, D is positive integer.

6. by the assay method of even linear array phase response parameter in multipath propagation environment described in claim 1, it is characterized in that utilizing respectively singular vector corresponding to each large singular value to determine signal subspace described in step 4, signal subspace is:

Wherein: for singular vector, N _kfor the poor matrix U of multipath signal direction _kthe number of large singular value, k=1,2 ..., K;

And direction between direct-path signal and its indirect wave signal in described each correction signal source is poor, for:

Wherein: β _knfor matrix eigenwert, with be respectively signal subspace j-1 row vector above and the matrix that J-1 row vector forms below, it is matrix generalized inverse matrix, angle (β _kn) representing matrix eigenwert β _knphase place, n=1,2 ..., N _k, k=1,2 ..., K.

7. by the assay method of even linear array phase response parameter in multipath propagation environment described in claim 1, it is characterized in that utilizing described in step 5 the corresponding direction of all directions of gained poor set up phase bit recovery matrix, phase bit recovery matrix is expressed as by the form of partitioned matrix:

Q＝[Q ₁?Q ₂?…?Q _K]

Wherein: k the submatrix of phase bit recovery matrix Q, λ is signal wavelength, diag ^-1(u _k) be matrix diag (u _k) inverse matrix, diag (u _k) be with without phase vector u _kthe element diagonal matrix that is diagonal element, n=1,2 ..., N _k, k=1,2 ..., K, [] ^trepresent vectorial transposition.

8. by the assay method of even linear array phase response parameter in multipath propagation environment described in claim 1, it is characterized in that, described in step 5, phase bit recovery matrix is carried out to svd, svd is undertaken by following formula:

Q＝SYG ^H

Wherein: matrix Y is diagonal matrix, diagonal element is the singular value of phase bit recovery matrix Q, by descending sort, matrix S and G are respectively the matrix being made up of left singular vector and the right singular vector of phase bit recovery matrix Q, corresponding one by one with the singular value of phase bit recovery matrix Q.

9. by the assay method of even linear array phase response parameter in multipath propagation environment described in claim 1, it is characterized in that determining described in step 5 the right singular vector corresponding to minimum singular value of phase bit recovery matrix, for the rightmost column vector of matrix G, be designated as g; Described right the singular vector corresponding minimum singular value of phase bit recovery matrix is divided into the subvector identical with direction number by order of elements, subvector is respectively:

g ^(k)＝[g(N ₁+...+N _k-1+1)?g(N ₁+...+N _k-1+2)?...?g(N ₁+...+N _k-1+N _k)] ^T

Wherein, [] ^trepresent vectorial transposition, g (i) is i the element of vectorial g,

And described each submatrix of setting up by this recovery matrix and corresponding subvector are carried out to product processing, its result is:

f ^(k)＝Q _kg ^(k)

Wherein, Q _kk the submatrix of phase bit recovery matrix Q, k=1,2 ..., K.

10. by the assay method of even linear array phase response parameter in multipath propagation environment described in claim 1, it is characterized in that determining that its normalization average vector is described in step 5:

Wherein: f ₁ ^kfor vector f ^(k)the 1st element;

And the described conjugate vector that even linear array phase response parameter vector is converted to normalization average vector, conjugate vector is:

Wherein: f ^*for the conjugate vector of vector f, in conjugate vector, each element is even linear array phase response parameter.