CN104049234A - Method for adopting uniform circular arrays to quickly determine spatial spectrums - Google Patents

Abstract

The invention belongs to a method for adopting uniform circular arrays to quickly determine spatial spectrums. The method comprises the steps of performing initialization treatment, confirming dual vectors of vectors in all of directions, confirming dual vectors of column vectors in signal subspaces, performing quick discrete Fourier transformation to confirm vectors of all of spectrums and finally confirming the spatial spectrums corresponding to all of searching angles. The method utilizes cyclic shift relation of direction vectors of the uniform circular arrays, a mode that spatial spectrum values corresponding to the searching angles are calculated to form the spatial spectrums in the prior art is changed into a mode that the spatial spectrums are determined through the direction vectors in direction vector subsets of the uniform circular arrays, the required time for determining the spatial spectrums is less than one fourth of the time required in the prior art. Therefore, the method has the advantages of being capable of remarkably reducing the calculation amount required by spatial spectrum determination, performing quick determination on the spatial spectrums of the uniform circular arrays, being used for high-accuracy and high-definition angle searching under the same time condition, obtaining high-accuracy and high-definition spatial spectrums and the like.

Description

Adopt the method for uniform circular array Fast Measurement spatial spectrum

Technical field

The invention belongs to the assay method of aerial array spatial spectrum in electronic information technical field, particularly a kind of method that adopts uniform circular array Fast Measurement spatial spectrum.

Background technology

The technology of utilizing aerial array to measure spatial spectrum is widely used in the numerous areas such as electronic reconnaissance, radar, communication, sonar, earthquake, radio astronomy, the important evidence that spatial spectrum is measured signal arrival bearing, carry out wave beam formation.Measure spatial spectrum and need in certain angular range, determine according to certain angle intervals the spatial spectrum value corresponding to angle of each search, all spatial spectrum value Special composition spectrums.Therefore, need the number of the spatial spectrum value of mensuration to equal the angle number that will search for.In order to obtain high precision, high-resolution spatial spectrum measurement result, need the angle intervals of setting very little, a lot of in requisition for the angle number of search, thereby cause measuring the required time increase of spatial spectrum; When array number becomes large, the calculating quantitative change required due to the angle of each search is large, causes again measuring the required time of spatial spectrum along with the angle intervals of searching for diminishes and huge increasing.

Spatial spectrum assay method based on subspace principle, for example, on March 26th, 2008 disclosed application number be 200610113171, name is called < < and is applicable to the array mutual coupling calibration of uniform circular array and the patent documentation of source direction estimation method > >, the angle of corresponding each search of this source direction estimation method, all needs to measure its spatial spectrum value (being spatial spectrum Direct Determination) by following formula:

$f\left({\mathrm{\&theta;}}_p\right)=\frac{1}{M-\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}{\left|u_k^{H}a\left({\mathrm{\&theta;}}_p\right)\right|}^2}$

In formula: θ _pbe the angle of p search, p=1,2 ..., P, the number of the angle that P is all search; F (θ _p) be p search angle θ _pcorresponding spatial spectrum value, all spatial spectrum values form spatial spectrum, the arrival bearing of the peak respective signal of spatial spectrum; M is the antenna number of uniform circular array; u _krepresent k vector in signal subspace, k=1,2 ..., K, the dimension that K is signal subspace, is also the number of signal, represent vectorial u _kconjugate transpose; A (θ _p) be p search angle θ _pcorresponding uniform circular array direction vector; Σ represents summation, || ²represent to take absolute value square.For uniform circular array direction finding, generally need to search for 360 orientation angles, if the interval of the angle of search equals d degree, P=[360/d], [] represents round; For example, when d=1 spends, need to measure P=[360/d]=360 spatial spectrum values, and when d=0.5 spends, need to measure P=[360/d]=720 spatial spectrum values, the required calculated amount of direction finding doubles.

Thereby, in spatial spectrum Direct Determination, take direction finding as example, calculation of complex, calculated amount become greatly high precision, high-resolution uniform circular array direction finding technology moves towards one of practical bottleneck, and mensuration spatial spectrum has wherein occupied the major part in the required calculated amount of uniform circular array direction finding; Therefore, reducing spatial spectrum measures required calculated amount and becomes uniform circular array direction finding technology and be able to one of practical key.

Summary of the invention

The object of the invention is the defect existing for background technology, a kind of method that adopts uniform circular array Fast Measurement spatial spectrum of research and design, to reach, reduce the speed that spatial spectrum is measured required calculated amount, effectively improved spatial spectrum mensuration, and can be used for the more angle searching of high precision and resolution, obtain the objects such as high precision, high-resolution spatial spectrum.

Solution of the present invention is first to utilize the ring shift relation existing between uniform circular array direction vector, sets up uniform circular array direction vector subset; Then each direction vector that antithetical phrase is concentrated carries out fast discrete Fourier conversion, obtains the dual vector of each direction vector in subset; Again each column vector in the signal subspace of the sample autocorrelation matrix of uniform circular array is carried out to fast discrete Fourier conversion, and get conjugation, obtain the dual vector of each column vector in signal subspace; Secondly the corresponding element of the dual vector of each column vector in the dual vector of each direction vector in subset and signal subspace is multiplied each other, and gained vector is carried out to fast contrary discrete Fourier transform (DFT); Finally by fast contrary discrete Fourier transform (DFT) result, obtain the corresponding spatial spectrum of all angles, thereby realize the object of the method that adopts uniform circular array Fast Measurement spatial spectrum.

In above-mentioned solution:

For the existing disadvantage of spatial spectrum assay method based on subspace principle in background technology, in order to save computing time when obtaining high precision, high-resolution spatial spectrum measurement result, the present invention first sets up uniform circular array direction vector subset:

{a(θ _q)} _{q＝1,2，…,Q}

In formula, a (θ _q) be q search angle θ _qcorresponding uniform circular array direction vector, θ _q=(q-1) d, d is the interval of the angle of search, q=1,2,, Q, Q=[P/M] and be the direction vector number in uniform circular array direction vector subset, P=[360/d], the number of the angle of all search, the antenna number that M is uniform circular array, [] represents round.

Utilize the ring shift relation existing between the uniform circular array direction vector of angle intervals 360/M degree, can obtain p search angle θ by the direction vector in uniform circular array direction vector subset _pcorresponding uniform circular array direction vector a (θ _p), θ wherein _pbe the angle of p search, p=1,2 ..., P, the number of the angle that P is all search.Therefore, the present invention adopts Q direction vector in uniform circular array direction vector subset to measure spatial spectrum, due to the number P of the direction vector number Q in uniform circular array direction vector subset much smaller than the angle of all search, thereby can significantly reduce spatial spectrum compared with spatial spectrum Direct Determination, measure required calculated amount.

Each direction vector that antithetical phrase is concentrated again carries out fast discrete Fourier conversion, obtains the dual vector of each direction vector in subset:

{b(θ _q)} _{q＝1,2,…,Q}

In formula, b (θ _q)=FFT (a (θ _q)), FFT (a (θ _q)) represent direction vector a (θ _q) carry out fast discrete Fourier conversion, q=1,2 ..., Q, Q is the direction vector number in uniform circular array direction vector subset.

Secondly each column vector in the signal subspace of the sample autocorrelation matrix of uniform circular array is carried out to fast discrete Fourier conversion, and gets conjugation, obtain the dual vector of each column vector in signal subspace:

{v _k} _{k＝1,2,…,K}

In formula, v _k=(FFT (u _k)) ^*, FFT (u _k) represent direction vector u _kcarry out fast discrete Fourier conversion, (FFT (u _k)) ^*expression is to FFT (u _k) get conjugation, k=1,2 ..., K, the dimension that K is signal subspace, is also the number of signal.

The present invention and then the corresponding element of the dual vector of each column vector in the dual vector of each direction vector in subset and signal subspace is multiplied each other, and gained vector is carried out to fast contrary discrete Fourier transform (DFT):

{w _k(θ _q)} _{k＝1,2,…,K;q＝1，2,…,Q}

In formula, expression is to direction vector carry out fast contrary discrete Fourier transform (DFT), dual vector b (the θ that represents direction vector _q) with signal subspace in the dual vector v of each column vector _kthe multiply each other vector of gained of corresponding element, k=1,2 ..., K, the dimension that K is signal subspace, the namely number of signal.

Spatial spectrum value corresponding to angle that the present invention finally obtains all search by fast contrary discrete Fourier transform (DFT) is:

$f({\mathrm{\&theta;}}_q+(m-1)\mathrm{Qd})=\frac{1}{M-\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}{\left|w_k^m\left({\mathrm{\&theta;}}_q\right)\right|}^2}$

In formula, θ _q=(q-1) d, d is the interval of the angle of search, q=1,2 ..., Q, Q is the direction vector number in uniform circular array direction vector subset, m=1,2 ..., M, the antenna number that M is uniform circular array, represent vectorial w _k(θ _q) m element, k=1,2 ..., K, the dimension that K is signal subspace, is also the number of signal.

Thereby the inventive method comprises:

Step 1. initialization process: the number P of the angle of the footpath Bob (α) of uniform circular array, antenna number (M), signal number (K), the angular range of search, the interval angle (d) between adjacency search angle, all search is carried out to initialization process and deposits internal memory in;

Step 2. is determined the dual vector of all directions vector: first determine the direction vector number (Q) in uniform circular array direction vector subset, determine again uniform circular array direction vector subset, then each direction vector in uniform circular array direction vector subset is carried out to fast discrete Fourier conversion, thereby determine the dual vector of each direction vector in uniform circular array direction vector subset;

Step 3. is determined the dual vector of each column vector in signal subspace: all column vectors that are first identified for representing the sample autocorrelation matrix signal subspace of uniform circular array, again each column vector in the signal subspace of the sample autocorrelation matrix of uniform circular array is carried out to fast discrete Fourier conversion, and get conjugation, thereby determine the dual vector of each column vector in signal subspace;

Step 4. fast contrary discrete Fourier transform (DFT) processes to determine each spectrum vector: by the dual vector of the 1st direction vector in direction vector subset respectively with signal subspace in the 1st corresponding element to the dual vector of last (i.e. K) individual column vector multiply each other, obtain equating with signal number (K) individual long-pending vector; Again each long-pending vector is carried out respectively to fast contrary discrete Fourier transform (DFT) and process, obtain that one group of number equates with signal number (K), the spectrum of its element number identical with antenna number (M) (be K each contain M element) is vectorial; And then successively by the 2nd dual vector to last (Q) individual direction vector in direction vector subset respectively with signal subspace in the 1st corresponding element to the dual vector of last (i.e. K) individual column vector multiply each other, again each long-pending vector of gained being carried out respectively to fast contrary discrete Fourier transform (DFT) processes, obtain, after corresponding all the other each groups (being Q-1 group) spectrum vector, going to step in the lump 5;

Step 5. is determined the spatial spectrum corresponding with all search angles: each group spectrum vector of step 4 gained is all pressed: each (M) element in each (K) spectrum vector of this group is taken absolute value respectively also square, and then the corresponding element after in each spectrum vector square is added respectively, gained each be respectively the spatial spectrum value corresponding with corresponding search angle with value; Then by same procedure, obtain the spatial spectrum value that all the other each group spectrum vectors are corresponding with each search angle; Thereby the spatial spectrum that the individual spatial spectrum value of product (MQ) that obtains direction vector number (Q) in antenna number (M) and direction vector subset forms.

The number P=[360 °/d in the angle of all search described in step 1], 360 ° is the angular range of search, d is the interval angle between adjacency search angle;

Described in step 2, determining the direction vector number Q=[P/M in uniform circular array direction vector subset], described definite uniform circular array direction vector subset is { a (θ _q) _{q=1,2 ..., Q}, wherein,

$a\left({\mathrm{\&theta;}}_q\right)={\left[\begin{array}{cccc}{e}^{j2\mathrm{\&pi;\&alpha;}\cos \left({\mathrm{\&theta;}}_q\right)}& e^{j2\mathrm{\&pi;\&alpha;}\cos ({\mathrm{\&theta;}}_q-\frac{1}{M}2\mathrm{\&pi;})}& ...& e^{j2\mathrm{\&pi;\&alpha;}\cos ({\mathrm{\&theta;}}_q-\frac{M-1}{M}2\mathrm{\&pi;})}\end{array}\right]}^T,$

α represents the footpath Bob of uniform circular array, [] ^trepresent vectorial transposition, θ _q=(q-1) d, q=1,2 ..., Q;

In all column vectors that are identified for representing the sample autocorrelation matrix signal subspace of uniform circular array described in step 3, be u _k, k=1,2 ..., K, K is the number of signal;

Described in step 3, each column vector in the signal subspace of the sample autocorrelation matrix of uniform circular array is being carried out to fast discrete Fourier conversion, and getting conjugation, the dual vector that obtains each column vector in signal subspace is v _kfor: v _k=(FFT (u _k)) ^*, wherein, FFT (u _k) represent direction vector u _kcarry out fast discrete Fourier conversion, (FFT (u _k)) ^*expression is to FFT (u _k) get conjugation, k=1,2 ..., K, the number that K is signal;

Described in step 4, the corresponding element of the dual vector of each column vector in the dual vector of each direction vector in subset and signal subspace is being multiplied each other, and gained vector is carried out to fast contrary discrete Fourier transform (DFT), result is: wherein, expression is to direction vector carry out fast contrary discrete Fourier transform (DFT), dual vector b (the θ that represents direction vector _q) with signal subspace in the dual vector v of each column vector _kthe multiply each other vector of gained of corresponding element, k=1,2 ..., K, the number that K is signal.

At spatial spectrum corresponding to angle that obtains all search by fast contrary discrete Fourier transform (DFT) described in step 5, be:

$f({\mathrm{\&theta;}}_q+(m-1)\mathrm{Qd})=\frac{1}{M-\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}{\left|w_k^m\left({\mathrm{\&theta;}}_q\right)\right|}^2}$

Wherein, θ _q=(q-1) d, d is the interval angle between adjacency search angle, q=1,2 ..., Q, Q is the direction vector number in uniform circular array direction vector subset, m=1,2 ..., M, the antenna number that M is uniform circular array, represent vectorial w _k(θ _q) m element, k=1,2 ..., K, the number that K is signal.

The method of uniform circular array Fast Measurement spatial spectrum of the present invention due to do not need by directly to the mensuration of all search angle direction vectors, measure its spatial spectrum, but only search for angle corresponding to direction vector in uniform circular array direction vector subset, direction vector number (Q) in uniform circular array direction vector subset is much smaller than the number (P) of the angle of all search, so the present invention can carry out Fast Measurement to the spatial spectrum of uniform circular array.Compare with background technology spatial spectrum Direct Determination: when the certain and array number in the interval of the angle of search is identical, the array number times more, the required mensuration spatial spectrum of the relative background technology of the present invention shorter (referring to embodiment table 1) of uniform circular array; When the interval of the angle of and search identical when the array number of uniform circular array is different, the present invention measures spatial spectrum required time all less than 1/4th (referring to embodiment tables 2) of background technology.Thereby the present invention has and can significantly reduce spatial spectrum and measure required calculated amount, the spatial spectrum of uniform circular array is carried out to Fast Measurement, effectively improved the speed that spatial spectrum is measured, and under the restriction of identical time conditions, can be used for the more angle searching of high precision and resolution, obtain high precision, high-resolution spatial spectrum.

Embodiment

It is example that present embodiment be take the uniform circular array of Bob α=4, footpath, signal number K=3 in this example, and the arrival bearing of 3 signals is respectively θ ₁=-15.2 °, θ ₂=0.4 ° and θ ₃=24.7 °, signal to noise ratio (S/N ratio) is all 6.0dB, the interval d=1 of the angle of search ° (degree), the angular range of corresponding 360 ° of degree search, the number P=[360 of the angle of all search °/d]=360.

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

Step 1. initialization process: to the footpath Bob α of uniform circular array, antenna number M, signal number K, the angular range of search, the interval d(unit of the angle of search: degree), the number P of the angle of all search carries out initialization setting, that is: α=4, K=3; The angular range of search is 360 °, in the time of the interval d=1 of the angle of search °, 0.5 °, 0.25 °, 0.1 °, and the number P=[360 of the angle of all search °/d]=360,720,1440,3600;

The antenna number M of the uniform circular array that step 2. is corresponding different, determines the direction vector number Q=[P/M in uniform circular array direction vector subset accordingly], for example work as: M=9,18,36,72 o'clock, corresponding Q=40,20,10,5; Determine uniform circular array direction vector subset { a (θ _q) _{q=1,2 ..., Q}; Each direction vector in uniform circular array direction vector subset is carried out to fast discrete Fourier conversion, determine the dual vector of each direction vector in uniform circular array direction vector subset, when M=9, the direction vector of 0 ° of degree is:

1.0000+0.0000i

0.9198-0.3924i

-0.3411+0.9400i

1.0000-0.0000i

0.0551-0.9985i

0.0551-0.9985i

1.0000+0.0000i

-0.3411+0.9400i

0.9198-0.3924i

Corresponding dual vector is: 4.2675-0.9017i

1.1872+1.6018i

1.0450-3.4327i

2.3663+0.4509i

-2.2322+1.8309i

-2.2322+1.8309i

2.3663+0.4509i

1.0450-3.4327i

1.1872+1.6018i

Step 3. is determined the column vector in the signal subspace of sample autocorrelation matrix of uniform circular array: when M=9, during signal number K=3, once the column vector of the signal subspace in experiment has 3, is respectively:

-0.3588-0.0000i0.2719+0.0000i0.1962+0.0000i

-0.2046-0.2828i-0.2192+0.1083i-0.3557-0.1322i

0.1401+0.2872i0.1170-0.2914i-0.1388-0.2640i

-0.3582+0.0178i-0.1261+0.2832i-0.0169-0.0713i

0.2440-0.1632i0.2349+0.3444i0.0806-0.2762i

0.1179-0.3557i0.2924-0.2069i0.1716-0.1995i

-0.3305-0.0917i0.2322+0.1566i-0.1654+0.2430i

0.1414-0.0372i0.2133-0.3568i-0.4250+0.4495i

-0.3578-0.1585i0.0425-0.3412i0.2551-0.1924i

Each column vector in the signal subspace of the sample autocorrelation matrix of uniform circular array is carried out to fast discrete Fourier conversion, and get conjugation, determine the dual vector of each column vector in signal subspace, M=9 for example, during signal number K=3, once the column vector of the signal subspace in experiment has 3, and the dual vector of all column vectors is respectively:

-0.9737+0.6134i1.1011+0.3255i-0.3388+0.3743i

-0.4109-0.1453i0.3066+0.0715i-1.0751-0.4468i

-0.3462+0.8483i0.2549-0.3052i1.1764+0.2402i

-1.5992+0.2483i0.2304-0.7666i0.9382-1.3010i

0.3029-0.7411i0.3194-0.1155i0.3547-0.4341i

0.9198-0.9394i1.2868+0.0949i-0.0895-0.1819i

-0.8020-0.1189i-1.0642-0.2810i-0.3402+0.4043i

0.0397+0.6107i0.3463-0.5754i0.7219+1.2611i

-0.6959-0.3760i-0.9658+1.5518i0.7887+0.0840i

Step 4. multiplies each other the corresponding element of the dual vector of each column vector in the dual vector of each direction vector in direction vector subset and signal subspace, then carries out fast contrary discrete Fourier transform (DFT) and process; Work as M=9, during signal number K=3, once in experiment, the dual vector of first direction vector in direction vector subset and the corresponding element of the dual vector of each column vector in signal subspace multiply each other:

-3.6022+3.4959i4.9924+0.3963i-1.1083+1.9028i

-0.2552-0.8307i0.2495+0.5759i-0.5606-2.2525i

2.5501+2.0747i-0.7813-1.1941i2.0538-3.7872i

-3.8962-0.1334i0.8907-1.7101i2.8067-2.6555i

0.6807+2.2089i-0.5015+0.8427i0.0030+1.6186i

-0.3332+3.7808i-3.0462+2.1443i0.5328+0.2422i

-1.8442-0.6431i-2.3915-1.1447i-0.9873+0.8033i

2.1378+0.5018i-1.6132-1.7900i5.0832-1.1604i

-0.2239-1.5612i-3.6323+0.2952i0.8017+1.3631i

Again above-mentioned column vector is carried out to fast contrary discrete Fourier transform (DFT) and process:

-0.5318+0.9882i-0.6481-0.1761i0.9583-0.4362i

-0.2815-0.4637i0.6930+0.6881i0.7043-0.1350i

-0.7534+0.7635i0.3201+0.7440i-0.6582+0.3807i

-1.0589+0.0140i1.0616+0.2166i-0.3979+0.3360i

0.2379+0.6771i0.6629+0.0408i0.8016+0.6096i

0.5109+1.3552i0.7752-0.2102i-0.0648-0.5657i

-1.5235-0.0957i0.7504-0.8601i-0.3234+0.1171i

-0.3475+0.4889i0.7216+0.8265i-1.1801+1.5635i

0.1456-0.2317i0.6558-0.8735i-0.9481+0.0327i

Then successively the second corresponding element to the dual vector of Q direction vector and the dual vector of each column vector in signal subspace in all the other direction vector subsets multiplied each other and carry out, after corresponding fast contrary discrete Fourier transform (DFT) processing, going to step 5;

Step 5. first takes absolute value contrary discrete Fourier transform (DFT) result corresponding to all directions vector in the direction vector subset of step 4 gained respectively, and square, then be added in row and separately, obtain altogether M spatial spectrum value, all direction vectors in direction vector subset obtain MQ spatial spectrum value altogether; For example, during M=9, once in experiment, contrary discrete Fourier transform (DFT) result corresponding to first direction vector in direction vector subset obtains 1,41,81,121,161,201,241, the 281 and 321 spatial spectrum values of spending, during Q=40, altogether obtain the spatial spectrum that comprises all search angles that 360 spatial spectrum values form; In present embodiment in the situation that search interval d=1 ° of angle and array number equal 9,0 °, 1 ° ..., the measurement result of 358 °, 359 ° spatial spectrum values is respectively 0.4840,0.4743 ..., 0.4978,0.4920, totally 360 spatial spectrum values; Thereby obtain the spatial spectrum that comprises all search angles being formed by these 360 spatial spectrum values.

Adopt the specific embodiment of the invention: table 1 be in the situation that the interval d=1 of the angle of search for ° measure spatial spectrum with different array numbers, present embodiment required time and spatial spectrum Direct Determination (that is: the method for the spatial spectrum value of goniometry by a corresponding search obtains all spatial spectrum values) required time contrast table; Table 2 is at array number and is equal to 9 and adopt different angles IV interval in the situation that, the time contrast table that present embodiment required time and spatial spectrum value Direct Determination are required.

When equaling 1 ° (degree), the interval of the angle of table 1 search measures the comparison of spatial spectrum required time

Table 2 array number equals to measure the comparison of spatial spectrum required time at 9 o'clock

From above two contrast tables, can find out: array number is more, the ratio multiple between the time that background technology spatial spectrum Direct Determination is required and rapid assay methods required time of the present invention is just larger, and the effect that the inventive method is saved is in time more obvious; And when array number equates, when the interval of the angle of search equals 0.25 °, the spatial spectrum rapid assay methods required time of employing uniform circular array of the present invention is 2.3036 milliseconds, than the interval of angle of search, equal 2.5424 milliseconds required of the times of 1 ° of time space spectrum Direct Determination also few, illustrate that spatial spectrum rapid assay methods of the present invention is under identical time restriction, can be used for the more angle searching of high precision and resolution.

Claims (7)

1. adopt the method for uniform circular array Fast Measurement spatial spectrum, comprising:

Step 1. initialization process: the number P of the angle of the interval angle between the angular range of the footpath Bob of uniform circular array, antenna number, signal number, search, adjacency search angle, all search is carried out to initialization process and deposits internal memory in;

Step 2. is determined the dual vector of all directions vector: first determine the direction vector number in uniform circular array direction vector subset, determine again uniform circular array direction vector subset, then each direction vector in uniform circular array direction vector subset is carried out to fast discrete Fourier conversion, thereby determine the dual vector of each direction vector in uniform circular array direction vector subset;

Step 3. is determined the dual vector of each column vector in signal subspace: all column vectors that are first identified for representing the sample autocorrelation matrix signal subspace of uniform circular array, again each column vector in the signal subspace of the sample autocorrelation matrix of uniform circular array is carried out to fast discrete Fourier conversion, and get conjugation, thereby determine the dual vector of each column vector in signal subspace;

Step 4. fast contrary discrete Fourier transform (DFT) processes to determine each spectrum vector: by the dual vector of the 1st direction vector in direction vector subset respectively with signal subspace in the corresponding element of the 1st dual vector to last column vector multiply each other, obtain equating with signal number long-pending vectorial; Again each long-pending vector is carried out respectively to fast contrary discrete Fourier transform (DFT) and process, obtain one group of number vectorial with the spectrum that signal number equates, its element number is identical with antenna number; And then successively by the 2nd in direction vector subset to last each and every one direction vector dual vector respectively with signal subspace in the corresponding element of the 1st dual vector to last column vector multiply each other, again each long-pending vector of gained being carried out respectively to fast contrary discrete Fourier transform (DFT) processes, obtain, after corresponding all the other each group spectrum vectors, going to step in the lump 5;

Step 5. is determined the spatial spectrum corresponding with all search angles: each group spectrum vector of step 4 gained is all pressed: this group is respectively composed to each element in vector and take absolute value respectively also square, and then the corresponding element after in each spectrum vector square is added respectively, gained each be respectively the spatial spectrum value corresponding with corresponding search angle with value; Then by same procedure, obtain the spatial spectrum value that all the other each group spectrum vectors are corresponding with each search angle; Thereby obtain a product spatial spectrum that spatial spectrum value forms of direction vector number in antenna number and direction vector subset.

2. by the method that adopts uniform circular array Fast Measurement spatial spectrum described in claim 1, it is characterized in that the number P=[360 °/d in the angle of all search described in step 1], 360 ° is the angular range of search, d is the interval angle between adjacency search angle.

3. by the method that adopts uniform circular array Fast Measurement spatial spectrum described in claim 1, it is characterized in that described in step 2, determining the direction vector number Q=[P/M in uniform circular array direction vector subset], described definite uniform circular array direction vector subset is { a (θ _q) _q=1,2,, _q, wherein,

$a\left({\mathrm{\&theta;}}_q\right)={\left[\begin{array}{cccc}{e}^{j2\mathrm{\&pi;\&alpha;}\cos \left({\mathrm{\&theta;}}_q\right)}& e^{j2\mathrm{\&pi;\&alpha;}\cos ({\mathrm{\&theta;}}_q-\frac{1}{M}2\mathrm{\&pi;})}& ...& e^{j2\mathrm{\&pi;\&alpha;}\cos ({\mathrm{\&theta;}}_q-\frac{M-1}{M}2\mathrm{\&pi;})}\end{array}\right]}^T,$

α represents the footpath Bob of uniform circular array, [] ^trepresent vectorial transposition, θ _q=(q-1) d, q=1,2 ..., Q.

4. by the method that adopts uniform circular array Fast Measurement spatial spectrum described in claim 1, it is characterized in that in all column vectors that are identified for representing the sample autocorrelation matrix signal subspace of uniform circular array described in step 3 be u _k, k=1,2 ..., K, K is the number of signal.

5. by the method that adopts uniform circular array Fast Measurement spatial spectrum described in claim 1, it is characterized in that at the dual vector that obtains each column vector in signal subspace described in step 3 be v _kfor: v _k=(FFT (u _k)) ^*, wherein, FFT (u _k) represent direction vector u _kcarry out fast discrete Fourier conversion, (FFT (u _k)) ^*expression is to FFT (u _k) get conjugation, k=1,2 ..., K, the number that K is signal.

6. by the method that adopts uniform circular array Fast Measurement spatial spectrum described in claim 1, it is characterized in that, described in step 4, gained vector is being carried out to fast contrary discrete Fourier transform (DFT), result is: wherein, expression is to direction vector carry out fast contrary discrete Fourier transform (DFT), dual vector b (the θ that represents direction vector _q) with signal subspace in the dual vector v of each column vector _kthe multiply each other vector of gained of corresponding element, k=1,2 ..., K, the number that K is signal.

7. by the method that adopts uniform circular array Fast Measurement spatial spectrum described in claim 1, it is characterized in that described in step 5 by obtaining spatial spectrum corresponding to all search angles against discrete Fourier transform (DFT) fast, being:

$f({\mathrm{\&theta;}}_q+(m-1)\mathrm{Qd})=\frac{1}{M-\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}{\left|w_k^m\left({\mathrm{\&theta;}}_q\right)\right|}^2}$

Wherein, θ _q=(q-1) d, d is the interval angle between adjacency search angle, q=1,2 ..., Q, Q is the direction vector number in uniform circular array direction vector subset, m=1,2 ..., M, the antenna number that M is uniform circular array, represent vectorial w _k(θ _q) m element, k=1,2 ..., K, the number that K is signal.