CN103017728B - Method for determining direction vector of antenna array in interference environment - Google Patents

Abstract

The invention discloses a method for determining a direction vector of an antenna array and belongs to the field of electronic information technologies. The method comprises the steps of carrying out initialization processing, establishing a sample autocorrelation matrix for received signal vectors, determining noise subspaces and signal subspaces in current and all discrete directions, establishing noise subspace correlated matrixes and determining the minimum singular value of all the matrixes, obtaining an angle difference between an interference signal direction and a test signal source direction, and determining the direction vector of the antenna array. According to the method, on the basis that the antenna array receives signal vector samples, a constraint relation that a first element of the noise subspaces, signal subspaces, noise subspace correlated matrixes, signal subspace correlated matrixes and direction vector of the sample autocorrelation matrix is equal to 1 is adopted, and then, the determination of the direction vector of the antenna array in an interference environment is realized. The method has the characteristics that correlation coefficients between the determined direction vector and an actual direction vector are all higher than 97%, 95% of the correlation coefficients are higher than 99%, the similarity is very high, and the like.

Description

The assay method of aerial array direction vector under interference environment

Technical field

The invention belongs to the assay method of the aerial array direction vector in electronic information technical field, particularly a kind of assay method of the aerial array direction vector under interference environment.

Background technology

Along with more and more higher to the detection of spatial domain signal and parameter estimation requirement, as the antenna array signals of spatial processing Main Means, process and be widely used in the numerous areas such as electronic reconnaissance, radar, communication, sonar, earthquake, radio astronomy.Aerial array has the outstanding advantages such as signal gain is high, wave beam is controlled flexibly, spatial resolution is high, is for many years constantly subject to domestic and international researcher and pays close attention to.Yet, no matter be the beam scanning aerial array in World War II later stage, or current digital antenna array or the intelligent antenna array of moving communicating field, the error of aerial array is always ubiquitous, causes the direction vector of aerial array very large with the result difference that adopts theoretical analytic formula to calculate.The corresponding different aerial array direction vector of each direction, it is accurately known in advance that existing high-resolution direction finding technology all requires aerial array direction vector, when there is larger error between known aerial array direction vector and actual aerial array direction vector, inevitably can cause the Measure direction performance degradation of aerial array.Therefore, obtain aerial array direction vector is accurately study hotspot and the difficult point of antenna array signals process field always, can be bring into play the prerequisite that antenna array signals is processed many advantages, be also to restrict one of key factor that can antenna array signals treatment technology practical.

Existing aerial array direction vector assay method is first by discrete--direction, then test is placed in a discrete direction and is transmitted by signal source, aerial array is determined the mean value of the received signal vector of aerial array by repeatedly receiving this signal, and using the mean value of this aerial array received signal vector as aerial array direction vector.But, the prerequisite that adopts this aerial array direction vector assay method is not have undesired signal in supposition working environment, otherwise, when aerial array is determined the received signal vector of aerial array by receiving signal, in the received signal vector of aerial array, not only comprise test the transmitting by signal source in a discrete direction that is placed on setting, also comprise the undesired signal from other direction, and the direction of undesired signal is unknown in advance.Now, if will adopt the measured aerial array direction vector of the method as the received signal vector of this aerial array now, its result will cause and between gained aerial array direction vector and actual aerial array direction vector, have larger error, thereby causes the defects such as Measure direction performance degradation of aerial array.

Summary of the invention

The object of the invention is the problem existing for background technology, research and develop the assay method of aerial array direction vector under a kind of interference environment, with from measure containing rejecting its undesired signal the aerial array received signal vector of undesired signal, recover direction that test transmits by signal source the direction vector of corresponding array antenna, and then for the direction finding of aerial array, provide accurately the objects such as parameter.

Solution of the present invention is on the expression basis of the aerial array received signal vector sample of background technology, the problem of the disturbed signal corruption of one-to-one relationship between the corresponding array antenna direction vector of sense of launching by signal source for received signal vector and the test of aerial array, the noise subspace of the sample autocorrelation matrix of the received signal vector of employing aerial array, signal subspace, correlated noise subspace matrix, first element of correlation signal subspace matrix and direction vector equals the restriction relation such as 1, realization recovers the corresponding array antenna direction vector of sense of signal source transmitting for test from the received signal vector of the aerial array that is interfered.

The sample of the received signal vector of the aerial array that the present invention adopts is typically expressed as:

x(t,θ _k)=a(θ _k)s ₁(t)+a(θ _k+η)s ₂(t)+v(t)

X (t, θ wherein _k) be the received signal vector of aerial array, vectorial dimension equals the antenna number M of aerial array, and t is sampling instant, s ₁(t), s ₂(t) and v (t) to be respectively test vectorial with the receiver noise of the transmitting of signal source, undesired signal and aerial array, θ _kfor test uses signal source with respect to the direction of aerial array, need to measure the discrete direction of aerial array direction vector, k=1,2,, K, K is for needing the number of the corresponding discrete direction of aerial array direction vector of mensuration, η is direction and the differential seat angle of test between the direction of signal source of undesired signal, a (θ _k) and a (θ _k+ η) be respectively the direction θ of signal source for test _kcorresponding aerial array direction vector and the direction θ of undesired signal _kthe aerial array direction vector that+η is corresponding.

Due to the direction θ of test by signal source _kcorresponding aerial array direction vector a (θ _k) and test the s emission signal s by signal source ₁(t) multiply each other together, for avoiding amplitude fuzzy, without loss of generality, all suppose a (θ _k) first element equal 1.

When the signal that does not exist undesired signal and test with signal source transmitting is better than the receiver noise of aerial array far away, received signal vector x (t, the θ of aerial array _k) approximate a (θ _k) s ₁(t), therefore can measure the direction θ of signal source for test _kcorresponding aerial array direction vector a (θ _k) be vector x (t, θ _k) divided by vector x (t, θ _k) first element; And definite aerial array direction vector a (θ by this way _k) first element equal 1.

But, when there is undesired signal, received signal vector x (t, the θ of aerial array _k) equal the direction θ of signal source for test _kcorresponding aerial array direction vector a (θ _k) and the direction θ of undesired signal _kthe aerial array direction vector a (θ that+η is corresponding _k+ η) linear combination, therefore, can not be again with vector x (t, θ _k) divided by vector x (t, θ _k) first element as the direction θ of signal source for test _kcorresponding aerial array direction vector a (θ _k), otherwise by causing aerial array to occur obvious angle measurement error in the practical application of direction finding, even cannot obtain direction finding result.

The sample autocorrelation matrix of the inventive method aerial array received signal vector used is:

$R\left({\mathrm{\θ}}_k\right)=\frac{1}{T}\underset{t=1}{\overset{T}{\mathrm{\Σ}}}x(t,{\mathrm{\θ}}_k)x^H(t,{\mathrm{\θ}}_k)$

R (θ wherein _k) represent to test by signal source at direction θ _ksample autocorrelation matrix while transmitting, ∑ represents summation, t is sampling instant, and each sampling instant samples to a received signal vector, t=1,2 ..., T, T represents the number of the aerial array received signal vector corresponding with sampling instant number, [] ^hthe conjugate transpose that represents vector or matrix.

Test uses signal source at direction θ _kwhile transmitting, the svd of sample autocorrelation matrix is:

R(θ _k)=U(θ _k)Λ(θ _k)U ^H(θ _k)

Matrix Λ (θ wherein _k) be diagonal matrix, the element that diagonal angle makes progress is corresponding sample autocorrelation matrix R (θ respectively _k) singular value, by descending sort, be λ ₁(θ _k)>=λ ₂(θ _k) > λ ₃(θ _k)>=...>=λ _m(θ _k), matrix U (θ _k) be by sample autocorrelation matrix R (θ _k) singular vector u ₁(θ _k), u ₂(θ _k), u ₃(θ _k) ..., u _m(θ _k) matrix that forms, corresponding one by one with singular value, [] ^hthe conjugate transpose that represents vector or matrix.

Test uses signal source at direction θ _kwhile transmitting, the noise subspace of the sample autocorrelation matrix of aerial array is:

Q _n(θ _k)=[u ₃(θ _k) u ₄(θ _k) … u _M(θ _k)]

The signal subspace of the sample autocorrelation matrix of aerial array is:

Q _s(θ _k)=[u ₁(θ _k) u ₂(θ _k)]

The present invention utilizes first element of noise subspace, signal subspace and direction vector of sample autocorrelation matrix of the received signal vector of aerial array to equal the restriction relation such as 1, from the received signal vector of the aerial array that is interfered, recover thus the array antenna direction vector corresponding to sense of signal source transmitting for test, thereby realize its goal of the invention.Thereby the inventive method comprises:

Step 1. initialization process: by the antenna number of receiving antenna array, the number and all discrete directions that need the corresponding discrete direction of aerial array direction vector of mensuration, received signal vector number on each discrete direction, test deposits internal memory with the setting party of signal source in to initialization

Step 2. is set up the sample autocorrelation matrix of received signal vector: first by aerial array over against test with the setting party of signal source to or the 1st discrete direction receive the signal of signal source for test, and process to determine through conventional method the signal vector that aerial array receives, then set up the sample autocorrelation matrix of received signal vector;

Step 3. is determined noise subspace and the signal subspace in current direction: sample autocorrelation matrix is carried out to its svd, determine noise subspace and the signal subspace of sample autocorrelation matrix;

Step 4: determine signal subspace and noise subspace on all discrete directions: aerial array is gone to next discrete direction and receives signal the repeating step 2,3 of signal source for test, thereby determine signal subspace and the noise subspace on this discrete direction; Then determine successively as stated above signal subspace and the noise subspace on all discrete directions;

Step 5. is set up correlated noise subspace matrix and is determined each subspace Smallest Singular Value of Matrices: first utilize noise subspace and the noise subspace on another one discrete direction on first discrete direction to set up correlated noise subspace matrix, and to this correlated noise subspace matrix carry out svd, to determine minimum singular value; By above method, set up respectively noise subspace on first discrete direction and the correlated noise subspace matrix of the noise subspace on all the other each (respectively) discrete directions, and determine the minimum singular value of each correlated noise subspace matrix, go to step 6;

Step 6. is obtained undesired signal direction and the differential seat angle between signal source direction for test: first the minimum singular value of the whole correlated noises of step 5 gained subspace matrix is searched for, to find out minimum value wherein, gained minimum value is the minimum singular value in the minimum singular value of whole correlated noises subspace matrix; Discrete direction angle corresponding to this minimum singular value is the deflection of undesired signal, then determines and is somebody's turn to do (undesired signal) deflection and tests with after the differential seat angle between signal source direction angle, goes to step 7;

The mensuration of step 7. aerial array direction vector: first using the direction of measurement of arbitrary discrete direction as aerial array direction vector, utilize signal subspace on this arbitrary discrete direction and differential seat angle apart from this discrete direction to set up correlation signal subspace matrix for the signal subspace on another discrete direction of step 6 gained differential seat angle, then the restriction relation of utilizing first element of direction vector to equal 1, thus measure the aerial array direction vector on this arbitrary discrete direction; Aerial array direction vector on last according to said method sequentially determining all the other each discrete directions except above-mentioned arbitrary discrete direction, completes the mensuration to aerial array direction vector under interference environment.

Sample at the received signal vector of aerial array described in step 2 is typically expressed as:

x(t,θ _k)=a(θ _k)s ₁(t)+a(θ _k+η)s ₂(t)+v(t)

Wherein: x (t, θ _k) be the received signal vector of aerial array, vectorial dimension equals the antenna number M of aerial array, and t is sampling instant, s ₁(t), s ₂(t) and v (t) to be respectively test vectorial with the receiver noise of the transmitting of signal source, undesired signal and aerial array, θ _kfor direction, the k=1 of test by signal source, 2 ..., K, the number that K is discrete direction, the direction that η is undesired signal and the differential seat angle of test between signal source direction, a (θ _k), a (θ _k+ η) be respectively the direction θ of signal source for test _kcorresponding aerial array direction vector and the direction θ of undesired signal _kthe aerial array direction vector that+η is corresponding, and a (θ _k) first element equal 1.

And at the sample autocorrelation matrix of the received signal vector of aerial array described in step 2 be:

$R\left({\mathrm{\θ}}_k\right)=\frac{1}{T}\underset{t=1}{\overset{T}{\mathrm{\Σ}}}x(t,{\mathrm{\θ}}_k)x^H(t,{\mathrm{\θ}}_k)$

Wherein, R (θ _k) represent to test by signal source at direction θ _ksample autocorrelation matrix while transmitting, ∑ represents summation, t is sampling instant, and each sampling instant samples to a received signal vector, t=1,2 ..., T, T represents the number of the aerial array received signal vector corresponding with sampling instant number, [] ^hthe conjugate transpose that represents vector or matrix.

Described in step 2, through conventional method, processing the signal vector of determining that aerial array receives, its disposal route is I/Q dual channel receiver method or Hilbert transform disposal route.

Described in step 3, sample autocorrelation matrix is being carried out to its svd, the svd of sample autocorrelation matrix is:

R(θ _k)=U(θ _k)Λ(θ _k)U ^H(θ _k)

Wherein: matrix Λ (θ _k) be diagonal matrix, the element on diagonal line is corresponding sample autocorrelation matrix R (θ respectively _k) singular value, by descending sort, be λ ₁(θ _k)>=λ ₂(θ _k) > λ ₃(θ _k)>=...>=λ _m(θ _k), matrix U (θ _k) be by sample autocorrelation matrix R (θ _k) singular vector u ₁(θ _k), u ₂(θ _k), u ₃(θ _k) ..., u _m(θ _k) matrix that forms, corresponding one by one with singular value, [] ^hthe conjugate transpose that represents vector or matrix.

Described in step 3, determine noise subspace and the signal subspace of sample autocorrelation matrix, wherein:

The noise subspace of sample autocorrelation matrix is:

Q _n(θ _k)=[u ₃(θ _k) u ₄(θ _k) … u _M(θ _k)]

The signal subspace of sample autocorrelation matrix is:

Q _s(θ _k)=[u ₁(θ _k) u ₂(θ _k)]

In above-mentioned two formulas: u ₁(θ _k), u ₂(θ _k), u ₃(θ _k) ..., u _m(θ _k) sample autocorrelation matrix R (θ _k) in singular vector, corresponding one by one with singular value, k=1,2 ..., the number that K, K are discrete direction, M is the number of antenna in aerial array.

Described in step 5, utilize noise subspace on first discrete direction and the noise subspace on another one discrete direction to set up correlated noise subspace matrix to be:

$G\left({\mathrm{\θ}}_k\right)={\left[\begin{array}{c}{Q}_n\left(0\right)\\ Q_n\left({\mathrm{\θ}}_k\right)\end{array}\right]}^H\left[\begin{array}{c}{Q}_n\left(0\right)\\ Q_n\left({\mathrm{\θ}}_k\right)\end{array}\right]$

Wherein: Q _n(θ _k) for testing by signal source at direction θ _kthe signal subspace of the sample autocorrelation matrix of aerial array and noise subspace while transmitting, k=2,3 ..., 360;

Described in step 5, this correlated noise subspace matrix being carried out to svd is:

G(θ _k)=W(θ _k)Ω(θ _k)W ^H(θ _k)

Wherein: matrix Ω (θ _k) be diagonal matrix, the element that diagonal angle makes progress is corresponding correlated noise subspace matrix G (θ respectively _f) singular value, by descending sort, be β ₁(θ _k)>=β ₂(θ _k) > β ₃(θ _k)>=...>=β _m-2(θ _k), minimum singular value is β _m-2(θ _k), k=2 wherein, 3 ..., 360, matrix W (θ _f) be by correlated noise subspace matrix G (θ _f) the matrix that forms of singular vector, corresponding one by one with singular value, W ^h(θ _k) be W (θ _f) associate matrix;

Setting up correlation signal subspace matrix described in step 7 be:

$D\left({\mathrm{\θ}}_k\right)=\left[\begin{array}{c}{q}_s\left({\mathrm{\θ}}_k\right)\\ q_s\left({\mathrm{\θ}}_{k+k_0-1}\right)Q_s^H\left({\mathrm{\θ}}_{k+k_0-1}\right)Q_s\left({\mathrm{\θ}}_k\right)\end{array}\right]$

Q wherein _s(θ _k) and be respectively signal subspace Q _s(θ _k) and the first row vector, Q _s(θ _k) with being respectively test uses signal source at direction θ _kwith the signal subspace of the sample autocorrelation matrix of aerial array while transmitting, be conjugate transpose, k=1,2 ..., 360, k ₀for the definite β of step 6 _m-2(θ _k) k value corresponding to minimum singular value.

At first element that utilizes direction vector described in step 7, equaling 1 restriction relation is:

$D\left({\mathrm{\θ}}_k\right)g\left({\mathrm{\θ}}_k\right)=\left[\begin{array}{c}1\\ 1\end{array}\right]$

Aerial array direction vector on arbitrary discrete direction of measuring is:

b(θ _k)=Q _s(θ _k)g(θ _k)

Wherein: g (θ _k) expression discrete direction θ _kon the coordinate coefficient of aerial array direction vector in signal subspace, by first element of direction vector, equaled 1 restriction relation and be defined as:

$g\left({\mathrm{\θ}}_k\right)=D^{-1}\left({\mathrm{\θ}}_k\right)\left[\begin{array}{c}1\\ 1\end{array}\right]$

In various above: b (θ _k) be discrete direction θ _kthe measurement result of upper aerial array direction vector, Q _s(θ _k) for testing by signal source at direction θ _kthe signal subspace of the sample autocorrelation matrix of aerial array while transmitting, D ^-1(θ _k) expression correlation signal subspace matrix D (θ _k) contrary.

On the basis of the present invention due to the aerial array received signal vector sample in background technology, adopt first element of noise subspace, signal subspace, correlated noise subspace matrix, correlation signal subspace matrix and direction vector of sample autocorrelation matrix of the received signal vector of aerial array to equal the restriction relation such as 1, thereby realize the corresponding array antenna direction vector of sense that recovers signal source transmitting for test the received signal vector of the aerial array from being interfered.Through correlation test, the direction vector that employing the inventive method records is all greater than 97% with the related coefficient between corresponding actual direction vector, and the related coefficient between the direction vector recording on 95% discrete direction and actual direction vector is all greater than 99%, the correlativity between itself and actual direction vector is all less than 90% apparently higher than the direction vector of measuring in 90% above direction of background technology and the related coefficient between actual direction vector.Thereby the present invention has the impact that the electromagnetic interference (EMI) that can effectively eliminate in environment is measured the array antenna direction vector of measuring, error between measured aerial array direction vector and actual aerial array direction vector is little, similarity is high, is subject to the features such as the impact of ambient electromagnetic field undesired signal is little in mensuration process.

Accompanying drawing explanation

Fig. 1 is for adopting the minimum singular value of correlated noise subspace matrix corresponding to instantiation mode of the present invention different angles in the situation that there is undesired signal, and ordinate is minimum singular value, is designated as β _m-2(θ _k), horizontal ordinate is direction θ _k=k-1 degree, k=2 ..., 360.

Fig. 2 is the direction vector that adopts instantiation mode of the present invention and measure in the situation that there is undesired signal and the related coefficient between actual direction vector, and ordinate is related coefficient, is designated as ρ (θ _k), horizontal ordinate is direction θ _k=k-1 degree, k=1,2 ..., 360.

Embodiment

It is example, i.e. M=9 that present embodiment be take the uniform circular array that radius is that 2 times of wavelength, 9 antennas form; The received signal vector number T=48 that needs the aerial array of reception; Discrete direction θ is set in this example _k=k-1, k=1,2 ..., 360, need the number K=360 of the corresponding discrete direction of aerial array direction vector measured.Test is set and by signal source, is located at 0 degree direction, signal to noise ratio (S/N ratio) is 13dB; Undesired signal direction is unknown, is set to 32.2 degree in this example, and receiver signal to noise ratio (S/N ratio) is 16dB; Uniform circular array is placed on a turntable, controls turntable and rotates with the interval of 1 degree, turn to respectively 0 degree, 1 degree ..., 359 degree, be equivalent to change test by signal source the direction with respect to aerial array; Turntable moves in the direction of the clock, and every rotation 1 degree, all will receive signal by aerial array, determines 48 received signal vectors of this antenna capable of adjusting angle array.

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

Step 1. initialization process: by the antenna number of receiving antenna array (9), need number (360) and all discrete direction θ of the corresponding discrete direction of aerial array direction vector of mensuration _k=k-1, k=1,2 ..., 360, received signal vector number on each discrete direction (48), test deposits internal memory with the setting party of signal source in to (0 degree) initialization;

Step 2. is set up the sample autocorrelation matrix of received signal vector: first by aerial array over against test with the setting party of signal source to or the 1st discrete direction (θ ₁=0 degree) receive the signal of signal source for test, then adopt the conventional disposal route I/Q dual channel receiver method (or Hilbert transform disposal route) in this area to determine the signal vector x (t that aerial array receives, 0), t is sampling instant, and each sampling instant is sampled to a received signal vector, and present embodiment is t=1,2,, 48, then set up the sample autocorrelation matrix of received signal vector:

$R\left(0\right)=\frac{1}{48}\underset{t=1}{\overset{48}{\mathrm{\Σ}}}x(t,0)x^H(t,0)$

Wherein, ∑ represents summation, and t is sampling instant, [] ^hthe conjugate transpose that represents vector or matrix;

Step 3. pair sample autocorrelation matrix carries out its svd:

R(0)=U(0)Λ(0)U ^H(0)

Wherein: matrix Λ (0) is diagonal matrix, the element that diagonal angle makes progress is the singular value of corresponding sample autocorrelation matrix R (0) respectively, by descending sort, be 1.2124>=0.4863>0.0071>=0.0061>=0.0053>=0.0040>=0.0033>=0.0028>=0.0021, matrix U (0) is the singular vector u by sample autocorrelation matrix R (0) ₁(0), u ₂(0), u ₃(0) ..., u ₉(0) matrix forming is corresponding one by one with singular value; Note Q _sand Q (0) _n(0) being respectively test uses signal source at direction θ ₁=0 spends signal subspace and the noise subspace of the sample autocorrelation matrix of aerial array while transmitting, and determines the signal subspace of sample autocorrelation matrix:

$Q_s\left(0\right)=\left[\begin{array}{cc}{u}_1\left(0\right)& u_2\left(0\right)\end{array}\right]$

$=\left[\begin{array}{cc}-0.3442+0.0000i& 0.3666+0.0000i\\ 0.0556-0.1184i& -0.4924+0.2269i\\ 0.3863+0.0787i& 0.1315+0.0583i\\ -0.0419-0.3350i& -0.0235-0.2852i\\ -0.2710-0.1907i& 0.3221+0.2558i\\ 0.0253-0.4068i& 0.0702-0.0017i\\ 0.1081-0.1747i& 0.1517-0.4410i\\ 0.4064-0.0860i& -0.0280+0.0726i\\ -0.0403+0.3205i& -0.0422+0.2641i\end{array}\right]$

And noise subspace:

$Q_n\left(0\right)=\left[\begin{array}{cccc}{u}_3\left(0\right)& u_4\left(0\right)& \·\·\·& u_9\left(0\right)\end{array}\right]$

$=\left[\begin{array}{ccccccc}-0.4071-0.0000i& 0.2990-0.0000i& -0.4089+0.0000i& 0.2269-0.0000i& -0.1766+0.0000i& -0.4794-0.0000i& 0.1106+0.0000i\\ -0.0962+0.2386i& 0.3207-0.1160i& -0.1841+0.1922i& 0.1531-0.2395i& 0.1854-0.0127i& 0.1268-0.2317i& 0.4346+0.2484i\\ -0.4339+0.1768i& -0.1463-0.1185i& 0.3809-0.0171i& -0.0210-0.1826i& -0.3881-0.2674i& -0.1014-0.1228i& -0.0429+0.3748i\\ 0.4426+0.0441i& 0.2269+0.0421i& 0.3228+0.2706i& 0.2910-0.0553i& -0.0104-0.0815i& -0.4095-0.1767i& -0.2314+0.1691i\\ -0.1821+0.2764i& 0.0397+0.0719i& 0.3628-0.0155i& 0.1094+0.1669i& 0.5031+0.0391i& 0.1686+0.2813i& -0.0375+0.2637i\\ -0.0551-0.1880i& 0.1144+0.1501i& 0.0559+0.2797i& 0.2309+0.0239i& -0.4125-0.2453i& 0.4150+0.3573i& 0.2067-0.2164i\\ -0.2091-0.2525i& 0.2853-0.2433i& 0.1423+0.1283i& -0.5019+0.2318i& 0.2186-0.0095i& 0.0201-0.1433i& 0.2847+0.0089i\\ -0.0746+0.1054i& 0.5364-0.0888i& 0.0615-0.4240i& 0.0564-0.1716i& 0.1496-0.0701i& -0.0567+0.1866i& -0.2619-0.3987i\\ 0.2557+0.1152i& 0.4623-0.1151i& 0.0722+0.0211i& -0.1358+0.5439i& -0.3772+0.0552i& 0.0714+0.0685i& -0.0415+0.2043i\end{array}\right]$

Step 4: rotary antenna array is to next discrete direction and receive the signal of signal source for test, repeating step 2,3, thus determine signal subspace and the noise subspace on this discrete direction; By above method, determine signal subspace and the noise subspace on all discrete directions, 0 degree, 1 degree, 2 degree ..., the 359 signal subspace Qs of degree in directions _s(0), Q _s(1), Q _s(2) ..., Q _sand noise subspace Q (359) _n(0), Q _n(1), Q _n(2) ..., Q _n(359);

Step 5. utilizes noise subspace and the noise subspace on another one discrete direction on first discrete direction to set up correlated noise subspace matrix, that is:

$G\left({\mathrm{\θ}}_k\right)={\left[\begin{array}{c}{Q}_n\left(0\right)\\ Q_n\left({\mathrm{\θ}}_k\right)\end{array}\right]}^H\left[\begin{array}{c}{Q}_n\left(0\right)\\ Q_n\left({\mathrm{\θ}}_k\right)\end{array}\right]$

Wherein: Q _n(θ _k) for testing by signal source at direction θ _kthe signal subspace of the sample autocorrelation matrix of aerial array and noise subspace while transmitting, k=2,3 ..., 360, and correlated noise subspace matrix is carried out to svd:

G(θ _k)=W(θ _k)Ω(θ _k)W ^H(θ _k)

Wherein: matrix Ω (θ _k) be diagonal matrix, the element that diagonal angle makes progress is corresponding correlated noise subspace matrix G (θ respectively _f) singular value, by descending sort, be β ₁(θ _k)>=β ₂(θ _k) > β ₃(θ _k)>=...>=β _m-2(θ _k), matrix W (θ _f) be by correlated noise subspace matrix G (θ _f) the matrix that forms of singular vector, corresponding one by one with singular value; Determine that minimum singular value is β _m-2(θ _k) (concrete value is shown in Fig. 1); By above method, set up respectively noise subspace on first discrete direction and the correlated noise subspace matrix of the noise subspace on all the other each discrete directions, then determine that the minimum singular value of each correlated noise subspace matrix is β _m-2(θ _k), k=2,3 ..., 360, go to step 6;

First step 6. search for minimum value in the Smallest Singular Value of Matrices of all correlated noises subspace, be minimum singular value, and search for k=2 by the mode increasing progressively, 4 ..., 360, determine β _m-2(θ _k) k corresponding to minimum singular value be k ₀; Then determine discrete direction corresponding to this minimum singular value, this discrete direction θ _k0be the deflection of undesired signal, the deflection of then determining this undesired signal is poor with first discrete direction angle, and this difference is the direction and the differential seat angle of testing between the use direction of signal source of undesired signal; As seen from Figure 1, β _m-2(θ _k) k corresponding to minimum singular value be k ₀=33, corresponding differential seat angle is 32 degree;

Step 7. is for a discrete direction θ _k, determine another one with it angle differ the discrete direction that equals the definite differential seat angle of step 6 on signal subspace with for this discrete direction θ _kon signal subspace Q _s(θ _k) jointly set up together correlation signal subspace matrix:

$D\left({\mathrm{\θ}}_k\right)=\left[\begin{array}{c}{q}_s\left({\mathrm{\θ}}_k\right)\\ q_s\left({\mathrm{\θ}}_{k+k_0-1}\right)Q_s^H\left({\mathrm{\θ}}_{k+k_0-1}\right)Q_s\left({\mathrm{\θ}}_k\right)\end{array}\right]$

Q wherein _s(θ _k) and be respectively signal subspace Q _s(θ _k) and the first row vector, Q _s(θ _k) with being respectively test uses signal source at direction θ _kwith the signal subspace of the sample autocorrelation matrix of aerial array while transmitting, k=1,2 ..., 360, k ₀for the definite minimum singular value β of step 6 _m-2(θ _k) k corresponding to minimum singular value; Then, utilize first element of direction vector to equal 1 restriction relation to be:

$D\left({\mathrm{\θ}}_k\right)g\left({\mathrm{\θ}}_k\right)=\left[\begin{array}{c}1\\ 1\end{array}\right]$

The aerial array direction vector of measuring on this discrete direction is:

b(θ _k)=Q _s(θ _k)g(θ _k)

B (θ wherein _k) be discrete direction θ _kthe measurement result of upper aerial array direction vector, g (θ _k) aerial array direction vector on this discrete direction of represent the measuring coordinate coefficient in signal subspace, g (θ _k) by first element of direction vector, equal 1 restriction relation and be defined as:

$g\left({\mathrm{\θ}}_k\right)=D^{-1}\left({\mathrm{\θ}}_k\right)\left[\begin{array}{c}1\\ 1\end{array}\right]$

D ^-1(θ _k) expression correlation signal subspace matrix D (θ _k) contrary; Make k=1,2 ..., K, determines the measurement result of aerial array direction vector on all discrete directions by above method, the final measurement result of aerial array direction vector is:

B=[b(θ ₁) b(θ ₂) … b(θ ₃₆₀)]。

For check, measure the degree of approximation between present embodiment gained direction vector and actual direction vector, the related coefficient defining between the two is ρ (θ _k), the direction vector that note is measured is b (θ _k), actual direction vector is a (θ _k); Pass through following formula:

$\mathrm{\ρ}\left({\mathrm{\θ}}_k\right)=\frac{\left|a^H\left({\mathrm{\θ}}_k\right)b\left({\mathrm{\θ}}_k\right)\right|}{\sqrt{\left|a^H\left({\mathrm{\θ}}_k\right)a\left({\mathrm{\θ}}_k\right)\right|\left|b^H\left({\mathrm{\θ}}_k\right)b\left({\mathrm{\θ}}_k\right)\right|}}$

Check its approximate (being correlated with) degree and contrast with background technology, in formula: [] ^hthe conjugate transpose that represents vector or matrix, || represent to take absolute value; It is 100% that related coefficient more approaches 1(), the direction vector b (θ that explanation is measured _k) more approach actual direction vector a (θ _k).

Fig. 2 is the direction vector that adopts instantiation mode of the present invention and measure in the situation that there is undesired signal and the related coefficient between actual direction vector, and ordinate is correlation coefficient ρ (θ _k), horizontal ordinate is direction θ _k=k-1 degree, k=1,2 ..., 360.

Visible in figure, the direction vector of all mensuration is all greater than 97% with the related coefficient between corresponding actual direction vector, and the related coefficient between the direction vector of measuring and actual direction vector is all greater than 99%, the direction vector and the vectorial no significant difference of actual direction measured are described in 95% direction.

In contrast, if directly measure the aerial array direction vector of each direction and be the mean value of the received signal vector of corresponding aerial array, the direction vector of measuring in more than 90% direction and the related coefficient between actual direction vector are all less than 90%, illustrate that the direction vector of measuring obviously departs from actual direction vector.

Claims (10)

1. an assay method for aerial array direction vector under interference environment, comprising:

Step 1. initialization process: by the antenna number of receiving antenna array, the number and all discrete directions that need the corresponding discrete direction of aerial array direction vector of mensuration, received signal vector number on each discrete direction, test deposits internal memory with the setting party of signal source in to initialization;

Step 2. is set up the sample autocorrelation matrix of received signal vector: first by aerial array over against test with the setting party of signal source to or the 1st discrete direction receive the signal of signal source for test, and process to determine through conventional method the signal vector that aerial array receives, then set up the sample autocorrelation matrix of received signal vector;

Step 3. is determined noise subspace and the signal subspace in current direction: sample autocorrelation matrix is carried out to its svd, determine noise subspace and the signal subspace of sample autocorrelation matrix;

Step 4: determine signal subspace and noise subspace on all discrete directions: aerial array is gone to next discrete direction and receives signal the repeating step 2,3 of signal source for test, thereby determine signal subspace and the noise subspace on this discrete direction; Then determine successively as stated above signal subspace and the noise subspace on all discrete directions;

Step 5. is set up correlated noise subspace matrix and is determined each correlated noise subspace Smallest Singular Value of Matrices: first utilize noise subspace and the noise subspace on another one discrete direction on first discrete direction to set up correlated noise subspace matrix, and to this correlated noise subspace matrix carry out svd, to determine minimum singular value; By above method, set up respectively noise subspace on first discrete direction and the correlated noise subspace matrix of the noise subspace on all the other each discrete directions, and determine the minimum singular value of each correlated noise subspace matrix, go to step 6;

Step 6. is obtained undesired signal direction and the differential seat angle between signal source direction for test: first the minimum singular value of the whole correlated noises of step 5 gained subspace matrix is searched for, to find out minimum value wherein, gained minimum value is the minimum singular value in the minimum singular value of whole correlated noises subspace matrix; Discrete direction angle corresponding to this minimum singular value is the deflection of undesired signal, then determines that this deflection and test, with after the differential seat angle between signal source direction angle, go to step 7;

The mensuration of step 7. aerial array direction vector: first using the direction of measurement of arbitrary discrete direction as aerial array direction vector, utilize signal subspace on this arbitrary discrete direction and differential seat angle apart from this discrete direction to set up correlation signal subspace matrix for the signal subspace on another discrete direction of step 6 gained differential seat angle, then the restriction relation of utilizing first element of direction vector to equal 1, thus measure the aerial array direction vector on this arbitrary discrete direction; Aerial array direction vector on last according to said method sequentially determining all the other each discrete directions except above-mentioned arbitrary discrete direction, completes the mensuration to aerial array direction vector under interference environment.

2. by the assay method of aerial array direction vector under interference environment described in claim 1, it is characterized in that at the sample of the received signal vector of aerial array described in step 2 being:

x(t,θ _k)＝a(θ _k)s ₁(t)+a(θ _k+η)s ₂(t)+v(t)

Wherein: x (t, θ _k) be the received signal vector of aerial array, vectorial dimension equals the antenna number M of aerial array, and t is sampling instant, s ₁(t), s ₂(t) and v (t) to be respectively test vectorial with the receiver noise of the transmitting of signal source, undesired signal and aerial array, θ _kfor direction, the k=1 of test by signal source, 2 ..., K, the number that K is discrete direction, the direction that η is undesired signal and the differential seat angle of test between signal source direction, a (θ _k), a (θ _k+ η) be respectively the direction θ of signal source for test _kcorresponding aerial array direction vector and the direction θ of undesired signal _kthe aerial array direction vector that+η is corresponding, and a (θ _k) first element equal 1.

3. by the assay method of aerial array direction vector under interference environment described in claim 1, it is characterized in that at the sample autocorrelation matrix of the received signal vector of aerial array described in step 2 being:

Wherein, R (θ _k) represent to test by signal source at direction θ _ksample autocorrelation matrix while transmitting, ∑ represents summation, t is sampling instant, and each sampling instant samples to a received signal vector, t=1,2 ..., T, T represents the number of the aerial array received signal vector corresponding with sampling instant number, [] ^hthe conjugate transpose that represents vector or matrix.

4. by the assay method of aerial array direction vector under interference environment described in claim 1, it is characterized in that through conventional method, processing the signal vector of determining that aerial array receives described in step 2, its disposal route is I/Q dual channel receiver method or Hilbert transform disposal route.

5. by the assay method of aerial array direction vector under interference environment described in claim 1, it is characterized in that in the svd of sample autocorrelation matrix described in step 3 being:

R(θ _k)＝U(θ _k)Λ(θ _k)U ^H(θ _k)

Wherein: matrix Λ (θ _k) be diagonal matrix, the element on diagonal line is corresponding sample autocorrelation matrix R (θ respectively _k) singular value, by descending sort, be λ ₁(θ _k)>=λ ₂(θ _k) > λ ₃(θ _k)>=...>=λ _m(θ _k), matrix U (θ _k) be by sample autocorrelation matrix R (θ _k) singular vector u ₁(θ _k), u ₂(θ _k), u ₃(θ _k) ..., u _m(θ _k) matrix that forms, θ _kfor the direction of test by signal source, k=1,2 ..., K, the number that K is discrete direction, [] ^hthe conjugate transpose that represents vector or matrix.

6. by the assay method of aerial array direction vector under interference environment described in claim 1, it is characterized in that described in step 3, determining noise subspace and the signal subspace of sample autocorrelation matrix, wherein:

The noise subspace of sample autocorrelation matrix is:

Q _n(θ _k)＝[u ₃(θ _k) u ₄(θ _k) … u _M(θ _k)]

The signal subspace of sample autocorrelation matrix is:

Q _s(θ _k)＝[u ₁(θ _k) u ₂(θ _k)]

In above-mentioned two formulas: u ₁(θ _k), u ₂(θ _k), u ₃(θ _k) ..., u _m(θ _k) sample autocorrelation matrix R (θ _k) in singular vector, θ _kfor the direction k=1 of test by signal source, 2 ..., the number that K, K are discrete direction, M is the number of antenna in aerial array.

7. by the assay method of aerial array direction vector under interference environment described in claim 1, it is characterized in that at the subspace of correlated noise described in step 5 matrix being:

Wherein: Q _n(0) for discrete direction, be the noise subspace of 0 degree, Q _n(θ _k) for testing by signal source at direction θ _kthe signal subspace of the sample autocorrelation matrix of aerial array and noise subspace while transmitting, k=2,3 ..., 360.

8. by the assay method of aerial array direction vector under interference environment described in claim 1, it is characterized in that in the svd of the subspace of correlated noise described in step 5 matrix being:

G(θ _k)＝W(θ _k)Ω(θ _k)W ^H(θ _k)

Wherein: matrix Ω (θ _k) be diagonal matrix, the element that diagonal angle makes progress is corresponding correlated noise subspace matrix G (θ respectively _k) singular value, by descending sort, be β ₁(θ _k)>=β ₂(θ _k) > β ₃(θ _k)>=...>=β _m-2(θ _k), minimum singular value is β _m-2(θ _k), k=2 wherein, 3 ..., 360 matrix W (θ _k) be by correlated noise subspace matrix G (θ _k) the matrix that forms of singular vector, W ^h(θ _k) be W (θ _k) associate matrix.

9. by the assay method of aerial array direction vector under interference environment described in claim 1, it is characterized in that at the subspace of correlation signal described in step 7 matrix being:

Wherein: q _s(θ _k) and be respectively signal subspace Q _s(θ _k) and the first row vector, Q _s(θ _k) with being respectively test uses signal source at direction θ _kwith the signal subspace of the sample autocorrelation matrix of aerial array while transmitting, be conjugate transpose, k=1,2 ..., 360, k0 is the definite β of step 6 _m-2(θ _k) k value corresponding to minimum singular value.

10. by the assay method of aerial array direction vector under interference environment described in claim 1, it is characterized in that at first element that utilizes direction vector described in step 7, equaling 1 restriction relation is:

Aerial array direction vector on arbitrary discrete direction of measuring is:

b(θ _k)＝Q _s(θ _k)g(θ _k)

Wherein: g (θ _k) expression discrete direction θ _kon the coordinate coefficient of aerial array direction vector in signal subspace, by first element of direction vector, equaled 1 restriction relation and be defined as:

In various above: b (θ _k) be discrete direction θ _kthe measurement result of upper aerial array direction vector, Q _s(θ _k) for testing by signal source at direction θ _kthe signal subspace of the sample autocorrelation matrix of aerial array while transmitting, D ^-1(θ _k) expression correlation signal subspace matrix D (θ _k) contrary.