CN1773307A - Small size antenna array aperture expanding and space signal processing method - Google Patents
Small size antenna array aperture expanding and space signal processing method Download PDFInfo
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Abstract
The present invention relates to a small type antenna array aperture expanding and space signal processing method. Said method includes the following steps: making antenna array into any array form: dividing scanning area of whole antenna into several subregions, finely-dividing any one subregion of said several subregions; in the finely-divided subregion constructing actual array flow form of antenna array and array flow form of expanded array so as to further obtain the array expansion conversion matrix; utilizing the obtained array expansion conversion matrix to reconstitute the signal of expanded antenna array; then making said signal undergo the process of digital beam formation or adaptive beam formation or utilizing space high resolution algorithm to obtain space arrival angle of signal.
Description
Technical Field
The invention relates to a method for aperture expansion and space signal processing of a small antenna array.
Background
According to classical antenna theory, the angular resolution of the radar is related to the antenna beam width, which is approximately inversely proportional to the antenna electrical length, i.e.
Wherein, theta3dBIs the antenna beam half power width, λ is the radar operating wavelength, and L is the antenna array length. When the spacing between the antenna elements is about half of the radar operating wavelength, a large phased array antenna and a large number of receive channels are required to achieve high angular resolution. However, in the case of a radar antenna with a limited location, for example, for a high-frequency ground wave or high-frequency sky wave over-the-horizon radar, in order to obtain high-resolution ocean surface current and sea surface target azimuth information, a high-resolution algorithm such as a multiple signal classification algorithm (MUSIC) is generally adopted, and in order to obtain high-resolution sea surface wind wave information, a DBF technology is generally adopted. For example, if a high frequency radar is operated at a frequency of 5MHz, to achieve an angular resolution of 1 °, the radar array length would be up to 3000 meters. Moreover, in order to effectively excite the surface waves propagating along the sea surface, the radar antenna array should be arranged as close to the sea as possible, and the distance usually requires 1-2 radar wavelengths, so that under the actual coastal condition, an antenna site which can be matched with a large antenna array is difficult to find, and the radar station building cost and the daily maintenance cost are greatly increased. Meanwhile, because the radar antenna array is too large, the far field range of the radar antenna array reaches thousands of meters, and the radar system is extremely difficult to calibrate. All of these will limit the widespread use of many radars, including high frequency surface wave radars.
Disclosure of Invention
Aiming at the limitation of the existing multi-channel large phased array radar, the invention aims to provide a method for expanding the aperture of a small antenna array and processing a space signal, which realizes the function only realized by the large phased array radar by utilizing an array expansion technology.
In order to achieve the above object, the present invention provides a method for aperture expansion and spatial signal processing of a small antenna array, which sets the antenna array in any array form; dividing the whole antenna scanning area into a plurality of areas, and then subdividing any one of the sub-areas: constructing an antenna array in subdivided sub-regionsExtreme manifold a ═ a (θ)1)，a(θ1+Δθ)，a(θ2+2Δθ)，…，a(θr)]And an array manifold a ═ a (θ) of the extended array1)， a(θ1+Δθ)， a(θ2+2Δθ)，…， a(θr)]And further obtaining an array expansion transformation matrix B ═ AA-1Wherein, theta1，θrThe left and right boundaries of the sub-region are respectively, and delta theta is the step length of sub-region subdivision; reconstructing a signal Z ═ BX of an extended array antenna by using the obtained array extended transformation matrix, wherein X is a signal received by the original antenna array; and performing digital beam forming or adaptive beam forming on the reconstructed signal Z of the extended array antenna or solving the spatial arrival angle of the signal by using a spatial high-resolution algorithm.
According to the invention, when the actual matrix manifold a is a non-square matrix, the matrix a is loaded diagonally.
In addition, the present invention may utilize a norm minimum of | A-BA |, to determine the number of cells of the extended array.
The invention has the advantages of excellent practical performance: (1) the aperture and the antenna array element number of the antenna array are greatly expanded by the method; (2) by using the unique advantages of software, the signals of the extended antenna units are reconstructed, so that the modern digital signal processing technology can be flexibly applied to digital beam forming, beam shape change, spatial super-resolution direction finding and antenna self-adaptive anti-interference; (3) because the antenna aperture expansion is established on the basis of software, the number of antenna units and receiving channels can be greatly reduced, and the research and development cost and the station establishment cost are greatly reduced; (4) by implementing extension transformation on a small arbitrary antenna array, compared with an original array, the method not only increases the number of detectable information sources and improves the overload capacity of the antenna array, but also can overcome the signal fuzzy problem possibly occurring in the array and improve the decorrelation capacity of the array.
The invention provides a method for increasing the aperture of an antenna array by implementing extension transformation on a small dense phased array antenna aiming at the special occasion that the array arrangement of a radar antenna is limited, breaking through the old program of the design of a general phased array radar, and providing a new way for reducing antenna units and receiving channels of the phased array radar, reducing the cost, and being simple and easy to build. The invention is not only suitable for uniform arrays, but also suitable for any non-uniform arrays, and the expanded antenna aperture is equivalent to the performance achieved by more than three times of the original antenna aperture. The antenna array is applied to a high-frequency ground wave over-the-horizon radar, and through the expanded antenna array, not only can the azimuth information of high-resolution ocean surface currents and sea surface targets be obtained, but also relatively narrow wave beams can be formed, and the storm information meeting the ocean engineering requirements can be obtained. The invention provides theoretical and engineering basis for the miniaturization of the radar antenna array.
The invention is applied to engineering practice, has relatively low research and development and equipment maintenance cost, and has the functions which are not possessed by the traditional large phased array radar under the flexible cooperation of software. The invention has important theoretical value and engineering significance for using the phased array in the occasions with limited antenna array places and electromagnetic compatibility, and for national defense construction and economic construction of aviation, aerospace, air defense, sea defense and the like, and miniaturizing the phased array radar and reducing the cost.
A large number of theoretical analyses and radar tests show that effective extension of the antenna array element number is realized through array extension provided by the invention, namely, the extended array has more array element numbers through array extension transformation, the advantages are obvious, the detectable signal source number is increased, namely, the overload capacity of the array is improved, the possible signal fuzzy problem of the array can be overcome, the coherent resolving capacity of the array is improved, the actual antenna aperture and the receiving channel number are greatly reduced, the radar development cost is reduced, and the requirement of realizing spatial super-resolution by using the array extension technology provided by the invention is met.
Drawings
FIGS. 1, 2 and 3 are Doppler spectra of a primary array, an extended array and a conventional large array, respectively, at a scan angle of 40 °;
FIGS. 4, 5 and 6 are Doppler spectra of the original array, extended array and conventional macroarray, respectively, at a scan angle of 60 °;
FIGS. 7, 8 and 9 are Doppler spectra of the original array, extended array and conventional large array, respectively, at a scan angle of 80 deg.;
FIGS. 10, 11 and 12 are Doppler spectra of the original array, the extended array and the conventional large array, respectively, at a scan angle of 100 deg.;
FIGS. 13, 14 and 15 are Doppler spectra of the original array, extended array and conventional large array, respectively, at a scan angle of 120 deg.;
FIGS. 16, 17 and 18 are Doppler spectra of the original array, extended array and conventional macroarray at a scan angle of 140 deg., respectively;
FIG. 19, FIG. 20 and FIG. 21 are Doppler spectra of the original array, extended array and conventional macroarray at a signal-to-noise ratio of 25dB and a scan angle of 40 degrees, respectively;
FIG. 22, FIG. 23 and FIG. 24 are Doppler spectra of the original array, extended array and conventional macroarray, respectively, at a signal-to-noise ratio of 25dB and a scan angle of 60 °;
FIGS. 25, 26 and 27 are Doppler spectra of the original array, extended array and conventional macroarray at a signal-to-noise ratio of 25dB and a scan angle of 80 degrees, respectively;
FIG. 28, FIG. 29 and FIG. 30 are Doppler spectra of the original array, extended array and conventional macroarray at a signal-to-noise ratio of 25dB and a scan angle of 100 degrees, respectively;
FIG. 31, FIG. 32 and FIG. 33 are Doppler spectra of the original array, extended array and conventional macroarray at a signal-to-noise ratio of 25dB and a scan angle of 120 degrees, respectively;
FIG. 34, FIG. 35 and FIG. 36 are Doppler spectra of the original array, extended array and conventional macroarray at a signal-to-noise ratio of 25dB and a scan angle of 140 degrees, respectively;
FIG. 37 is a Doppler spectrum with the primary beam pointed at 60 °;
FIG. 38 is a echo spectrum with beams pointing 60 after array expansion;
FIG. 39 is a Doppler spectrum with 120 ° beam orientation of the primary array;
FIG. 40 is a echo spectrum with beams pointing 120 after array expansion;
FIG. 41 is a MUSIC spectrum before array expansion;
figure 42 is the MUSIC spectrum after array expansion.
Detailed Description
The present invention will be described in more detail with reference to the accompanying drawings and examples.
In order to achieve the purpose, the invention adopts a method for expanding the aperture of any antenna array and realizing spatial super-resolution, and the antenna array is set to be in any array form; dividing the whole antenna scanning area into a plurality of areas, and subdividing a certain sub-area; obtaining an array expansion transformation matrix B (AA) through the relation between the actual array manifold A and the expansion array manifold A-1(ii) a Reconstructing a signal Z ═ BX of the extended array antenna by using the obtained array extension matrix (wherein X is a signal received by the original antenna array); and (3) carrying out beam forming on the data Z received by the reconstruction expansion array, or solving a spatial super-resolution arrival angle of the signal by using a spatial high-resolution algorithm.
1. Original array signal model
Without loss of generality, it is assumed that the spatial array is composed of m array elements, there are d signal sources, and signals are incident on the array in the form of plane waves. The data received by the ith array element is:
then the output snapshot data of m array elements at time t form a vector as follows:
X(t)＝[x1(t)，x2(t)，...，xm(t)]T (2)
a is an array manifold
A＝[a(θ1)，a(θ2)，...，a(θd)] (3)
Wherein theta iskAngle of direction of k-th incident signal, a (θ)i) Represented by the following formula:
τki＝(xkcos(θi)+yksin(θi) C is the delay of the ith signal on the kth array element, (x)k，yk) For the position coordinates of the array element, c is the speed of light.
I.e. the data matrix received by the array:
X＝AS (5)
2. design of extended arrays
2.1 array extension transformation method
For irregular dense arrays or non-uniform arrays, the original array data is converted into the output of an extended uniform linear array by a digital conversion method.
Setting the signal direction vector of the expanded uniform linear array as
and a (theta) is [1, exp (-jkd cos theta),., exp (-jk (N-1) dcos theta) ] (6), wherein d is the array element spacing of the extended antenna array. An NxN order nonsingular matrix T (theta) is arranged to satisfy the following relation
B(Θ)A(Θ)＝[ a(θ1)， a(θ2)，...， a(θP)]The matrix B (theta) converts the direction matrix of the original array into the direction matrix of a new uniform array by the function of the above formula transformation, the new uniform array obtained in the way is called an extended array, and once the matrix B (theta) is obtained, the output vector of the extended uniform linear array can be obtained
z(t)＝B(Θ)x(t) (8)
2.2 obtaining array transformation matrix
The processing idea of array expansion is to divide the whole antenna scanning area into a plurality of sub-areas and then subdivide a certain sub-area. Assuming that the signal lies within the region Θ, the region Θ is averaged into
Θ＝[θ1，θ1+Δθ，θ1+2Δθ，...，θr] (9)
θ1，θrLet Θ be the left and right boundaries and Δ θ be the step size, then the array manifold matrix of the actual array is
A＝[a(θ1)，a(θ1+Δθ)，a(θ2+2Δθ)，...，a(θr)] (10)
And the array manifold matrix A of the extended uniform linear arrays in the same region theta is
A＝[ a(θ1)， a(θ1+Δθ)， a(θ2+2Δθ)，…， a(θr)] (11)
a(θi) Represented by the following formula:
wherein n is the number of array elements of the extended array, and delta ki＝(xxk cos(θi)+yyk sin(θi) C is the delay of the ith signal in the kth element of the spreading array, (xx)k，yyk) For this purpose, the position coordinates of the array elements are extended, and c is the speed of light.
A fixed transformation relationship B (t) exists between the expanded array and the real array, so that BA _ a _ B _ AA-1 (13)
In the above formula, inversion of a is involved. In general, the matrix a is not a square matrix and cannot be directly inverted, so that a diagonal loading technique is adopted, and a is a loading coefficient.
C＝A′*A
A-1≈(C+a*eye(size(C，1)))-1*A′ (14)
Assuming that a certain matrix Z satisfies Z ═ BX,
Z＝BX＝ AA-1X＝ AA-1AS＝ AS (15)
z may be considered as data received by the extended array.
2.3 determination of initial Angle and array expansion Unit
From the above analysis, the first problem faced by the transformation method of the extended array is the determination of the initial angle and the number of antenna units, and the azimuth angle of the signal source is the parameter to be estimated, so that the azimuth angle needs to be estimated before constructing the transformation matrix, and the quality of the estimation directly affects the quality of the transformation matrix and finally affects the estimation result. In practical applications, a simple method is to process each range bin space signalIn the method, the whole antenna scanning area is divided into a plurality of radar elements according to the expanded array beam width, signals are assumed to be located in the digital beam area where the digital antenna array is located, and then calculation is carried out <math> <msub> <mrow> <mo>|</mo> <mo>|</mo> <mover> <mi>A</mi> <mo>‾</mo> </mover> <mrow> <mo>(</mo> <mover> <mi>Θ</mi> <mo>^</mo> </mover> <mo>)</mo> </mrow> <mo>-</mo> <mi>B</mi> <mrow> <mo>(</mo> <mover> <mi>Θ</mi> <mo>^</mo> </mover> <mo>)</mo> </mrow> <mi>A</mi> <mrow> <mo>(</mo> <mover> <mi>Θ</mi> <mo>^</mo> </mover> <mo>)</mo> </mrow> <mo>|</mo> <mo>|</mo> </mrow> <mi>F</mi> </msub> </math> If the value is not small enough, the number of elements of the extension antenna can be adjusted, the proper lobe width and signal initial angle are selected, and then the extension transformation matrix is recalculated
So that <math><msub> <mrow> <mo>|</mo> <mo>|</mo> <mover> <mi>A</mi> <mo>‾</mo> </mover> <mrow> <mo>(</mo> <mover> <mi>Θ</mi> <mo>^</mo> </mover> <mo>)</mo> </mrow> <mo>-</mo> <mi>B</mi> <mrow> <mo>(</mo> <mover> <mi>Θ</mi> <mo>^</mo> </mover> <mo>)</mo> </mrow> <mi>A</mi> <mrow> <mo>(</mo> <mover> <mi>Θ</mi> <mo>^</mo> </mover> <mo>)</mo> </mrow> <mo>|</mo> <mo>|</mo> </mrow><mi>F</mi></msub> </math> The norm reaches a minimum.
2.4 determination of antenna element spacing
The array expansion is carried out by firstly knowing the initial direction of the signal and estimating the initial angle
There are errors, so when designing an extended uniform linear array, the array which is least sensitive to the error of the initial angle estimation and forms the smallest transformation error should be selected as an extended array as possible. In practical applications, we are concerned with matrices
And
whether the column spaces of (a) are consistent. In the sense of column space, vectorsThe distance from a (theta) can be defined by the angle between the two
Represents:
In general doptTo theta andnot very sensitive and so for simplicity θ can be chosen as the beamformer maximum output direction. Nevertheless, doptThe calculation of (a) is still inconvenient. In light of the foregoing discussion, the amplitude and phase characteristics of the main beam of the original array and the main beam of the extended uniform line array should be as close to unity as possible in order to reduce the transformation error. Therefore, if the 3dB main beam width of the original array is W, a simple choice for uniform linear array element spacing is[7]
Where λ is the wavelength. Thus, the 3dB main beam widths of the original array and the extended uniform linear array are equal. Computer simulations indicate that d is generally close to dopt。
2.5 extended transform error analysis
To examine the error of unitary transformation matrix, the following steps are carried out <math> <mrow> <mover> <mi>Θ</mi> <mo>^</mo> </mover> <mo>=</mo> <mo>{</mo> <msub> <mover> <mi>θ</mi> <mo>^</mo> </mover> <mn>1</mn> </msub> <mo>,</mo> <msub> <mover> <mi>θ</mi> <mo>^</mo> </mover> <mn>2</mn> </msub> <mo>}</mo> </mrow> </math> A simple case of (2) is an example. When the array element is an omnidirectional array element, it is easy to prove
Wherein,
when the formula (18) is studied, it can be found thata→_bOr whena→ 0 and \ ubOn a scale of → 0, (19) the left side of the equation approaches zero. That is to say, when
And
when the wave beam width is within one wave beam width, the amplitude characteristic and the phase characteristic of the main wave beam of the original array and the expanded array are close to each other as much as possible to minimize the error of the transformation matrix; when in
And
the lower the side lobes of the two arrays, the smaller the transform matrix error, when the interval of (a) exceeds one beam width. When the unitary transformation matrix (15) is selected, the conclusion not only indicates the requirements of the array data transformation method on the original array, but also indicates the direction of the design of the extended uniform linear array.
2.6 Effect of extended transforms on noise
Assuming that the data covariance matrix of the actual array is R and the noise covariance matrix is RNThen the data covariance matrix of the extended array is
RT＝NRBH＝B(ARsAH+RN)TH
＝BARsAHTH+BRNTH (21)
When the environmental noise is white noise, then
BRNBH＝σ2BBH (22)
From the above equation, the white noise received by the original array becomes color noise after the array expansion transformation.
3. Super-resolution algorithm of extended array
From the above analysis, since white noise received by the original array becomes color noise after the array is transformed by the extended array, when the noise received by each array element is independent of each other, the covariance matrix can be estimated by the following method:
wherein M is the time domain smoothing times, L is the fast beat number, and x (i: j) represents the data from the ith fast beat to the jth fast beat. Obviously, when the array element noises are independent of each other, the noise term of the estimated covariance matrix should be 0. To RTAnd performing characteristic decomposition, and then obtaining super-resolution estimation of the signal DOA by using the MUSIC spatial spectrum estimator.
4. Algorithm performance simulation
Simulation test 1: uniform linear array caliber expansion
The omnidirectional array elements with N-8 are uniformly distributed on a straight line with the length of lambda. The existing 6 signals move away from the radar direction, and the radial speed and the moving direction are {4, 8, 12, 16, 20, 24} m/s and {40 °, 60 °, 80 °, 100 °, 120 °, 140 ° }. Data sample points 256. The echo Doppler spectra with beam pointing 40 °, 60 °, 80 °, 100 °, 120 ° and 140 ° before array expansion (original array) are shown in fig. 1, 4, 7, 10, 13 and 16, respectively. The original array is now extended to an array with an antenna spacing d of 0.5 λ. Fig. 2, 5, 8, 11, 14 and 17 show echo Doppler spectrums of array beam pointing 40 °, 60 °, 80 °, 100 °, 120 ° and 140 ° after array expansion, respectively. Fig. 3, 6, 9, 12, 15 and 18 show an 8-element uniform linear array with half-wavelength spacing between array elements. From this result, it is clear that the original array cannot distinguish several signal directions existing in one beam before the array is expanded, but after the array is expanded by the scheme proposed herein, the directions and Doppler of the signals can be clearly distinguished, and the resolution effect of the expanded array is almost the same as that of the actual array with equal aperture. Further analysis of the reason can show that the beam width of the original array is about 60 degrees before the array is expanded, and the beam width of the array is reduced to about 15 degrees after the array is expanded, namely the resolution of the dense array is equivalent to three times of the aperture of the original array.
Simulation test 2: influence of signal-to-noise ratio on uniform linear array aperture expansion
The N-8 omnidirectional array elements are uniformly distributed on a straight line with the length of lambda, and incident wave signals are the same as those in the simulation test 1, except that the signal-to-noise ratio of each signal is 25 dB. The echo Doppler spectra for beam pointing 40 °, 60 °, 80 °, 100 °, 120 ° and 140 ° before array expansion (original array) are shown in fig. 19, 22, 25, 28, 31 and 34, respectively. The original array is now extended to an array with an antenna spacing d of 0.5 λ. Fig. 20, 23, 26, 29, 32 and 35 show echo Doppler spectrums of array beam pointing 40 °, 60 °, 80 °, 100 °, 120 ° and 140 ° after array expansion, respectively. Fig. 21, 24, 27, 30, 33 and 36 show large uniform linear arrays with half-wavelength spacing between array elements. As the conclusion obtained in the simulation test 1, the original array cannot distinguish several signal directions existing in one beam before the array is expanded, but after the array is expanded by using the scheme provided herein, the directions and Doppler of each signal can be clearly distinguished, and further analysis shows that the distinguishing effect is greatly improved along with the increase of the signal-to-noise ratio or the increase of the antenna spacing of the original array unit.
Simulation test 3: large-spacing uniform linear array caliber expansion
The N-8 omnidirectional array elements are uniformly distributed on a straight line with the length of 10 lambda (obviously, the antenna spacing is far larger than a half wavelength, and the original array directional diagram has grating lobes). The signal-to-noise ratio is 25 dB. The incident wave signal is the same as that in simulation 1. Typical simulation results are: figure 37 shows the echo Doppler spectrum with the beam pointing 60 ° before array expansion. The original array is now extended to an array with an antenna spacing d of 0.5 λ. Fig. 38 shows the echo spectrum with the beam pointing 60 ° after array expansion. From this result, it is obvious that multiple angles of arrival appear in one beam before the array is expanded, which is apparently due to the ambiguity of direction finding caused by the grating lobe of the antenna pattern due to the too large distance between the original antenna arrays. However, after the array is expanded by the scheme provided by the invention, the antenna spacing is greatly reduced, and grating lobes appearing in an antenna directional diagram are eliminated, so that the direction and Doppler of signals in a wave beam can be clearly distinguished.
Simulation test 4: expanding the number of redundant actual array elements
The N-8 omnidirectional array elements are uniformly distributed on a straight line with the length of lambda, and incident wave signals are the same as those in the simulation test 1, except that the signal-to-noise ratio of each signal is 20 dB. Typical simulation results are: figure 39 shows the echo Doppler spectrum with the beam pointing 120 before array expansion. The original array is expanded into a 12-element array line array with an antenna spacing d equal to 0.5 lambda. Fig. 40 shows a 120 ° echo spectrum with the beam pointing after array expansion. A large number of random mode experiments show that the original array cannot distinguish a plurality of signal directions existing in a beam before the array is expanded, but the directions and Doppler of all signals can be clearly distinguished after the array is expanded by the scheme provided by the invention. Further analysis can also show that the beam width of the antenna array is narrower than that of an 8-uniform linear array, but the result is more influenced by the signal-to-noise ratio, and the effect is better as the signal-to-noise ratio is higher.
Simulation test 5: non-uniform array aperture expansion
N-8 omnidirectional array elements are randomly distributed on a straight line with the length of lambda (or uniformly distributed on a semicircle with the radius of r-0.5 lambda). The incident wave signal is the same as that in simulation 1. The original array is now extended to an array with an antenna spacing d of 0.5 λ. A large number of random simulation experiments show that the original array cannot distinguish a plurality of signal directions existing in a wave beam before the array is expanded, but the direction and Doppler of each signal can be clearly distinguished after the array is expanded by using the technical scheme of the invention.
Simulation test 6: high-resolution algorithm of extended array
N-8 omnidirectional array elements are uniformly distributed on a straight line with the length of 5 lambda. The signal-to-noise ratio of the incident wave signal is 25dB as in simulation test 1. The original array is now extended to an array with an antenna spacing d of 0.5 λ. FIG. 41 shows the super-resolved spatial spectrum obtained using the MUSIC algorithm before array expansion. FIG. 42 shows the super-resolved spatial spectrum obtained using the MUSIC algorithm after array expansion. From the results, the antenna array has direction-finding ambiguity before the antenna array is expanded, but the original array is expanded by the method provided by the text, so that the resolution of the antenna is high, and the direction-finding ambiguity is eliminated.
5. Discussion of the related Art
The aperture expanding method based on the small antenna array has the following characteristics:
(a) in the transformation process, the accurate direction of the signal is not needed to be known, and the array manifold matrix of the original array and the expanded array can be obtained only by assuming the initial incident angle of the signal, so that the transformation array of the array is realized. In practical application, the transformation array T can be stored in advance, and the expansion of the array can be realized.
(b) The spacing of the array antennas is required to be smaller than half wavelength, direction-finding fuzzy occurs if the spacing exceeds the half wavelength, and the non-equidistant antenna array can be changed into the antenna array with the array element spacing smaller than the half wavelength through array expansion and transformation, so that the signal fuzzy of the array can be solved.
(c) The flexibility of the array is increased, because the array element number (degree of freedom) is increased by the expansion array, the number of the digital array elements of the expansion array can be flexibly selected according to the actual environment when DOA estimation is carried out, if the number of signals is less, the expansion array with small aperture can be selected, and the array element number can be properly increased to increase the aperture of the antenna array on the occasion with high precision requirement.
(d) Since the extended array can have a larger number of array elements than the actual array, the extended array can estimate a larger number of signal sources.
(e) The number of the extended array units cannot be infinite, and the selection of the array element number can only be effective within a certain range. This is because: in terms of energy, the energy and the information quantity received by the antenna are conserved, and any mathematical transformation can only improve the traditional algorithm to a certain extent without increasing the energy and the useful information quantity; mathematically speaking, the number of array elements is increased, the condition number of the expansion transformation matrix is increased, the error of the amplitude phase of the unit of the reconstructed expansion array antenna is increased, and finally, a larger error is brought to the result. And as the number of extended array elements increases, their signal-to-noise ratio requirements increase dramatically in order to achieve an engineering-usable result. In practical application, the number of the spread array elements should be a compromise between factors such as signal-to-noise ratio, actual signal number, and condition number of the spread transformation matrix.
(f) The small array antenna array has smaller aperture, which is favorable for reducing the calibration distance of the antenna array.
(g) The invention is combined with a modern high-resolution algorithm, and the array space super-resolution direction finding can be realized.
Claims (3)
1. A method for aperture expansion and spatial signal processing of a small antenna array is characterized in that: setting the antenna array into any array form; dividing the whole antenna scanning area into a plurality of areas, and then subdividing any one of the sub-areas; constructing the actual array manifold a ═ a (θ) of the antenna array in subdivided sub-regions1)，a(θ1+Δθ)，a(θ2+2Δθ)，...，a(θr)]And an array manifold a ═ a (θ) of the extended array1)， a(θ1+Δθ)， a(θ2+2Δθ)，...， a(θr)]And further obtaining an array expansion transformation matrix B ═ AA-1Wherein, theta1，θrThe left and right boundaries of the sub-region are respectively, and delta theta is the step length of sub-region subdivision; reconstructing a signal Z ═ BX of an extended array antenna by using the obtained array extended transformation matrix, wherein X is a signal received by the original antenna array; and performing digital beam forming or adaptive beam forming on the reconstructed signal Z of the extended array antenna or solving the spatial arrival angle of the signal by using a spatial high-resolution algorithm.
2. The method of claim 1, wherein: and when the actual matrix manifold A is a non-square matrix, carrying out diagonal loading on the matrix A.
3. The method according to claim 1 or 2, characterized in that: the number of cells of the extended array is determined using a norm minimum of | a-BA |.
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101520507B (en) * | 2007-07-20 | 2012-03-21 | 通用汽车环球科技运作公司 | Ow cost short range radar |
| CN101272168B (en) * | 2007-03-23 | 2012-08-15 | 中国科学院声学研究所 | Signal sources estimation method and its DOA estimation method |
| CN104134354A (en) * | 2013-04-30 | 2014-11-05 | 业纳遥控设备有限公司 | Traffic monitoring system for speed measurement and assignment of moving vehicles in a multi-target recording module |
| CN108089147A (en) * | 2017-12-07 | 2018-05-29 | 西南电子技术研究所（中国电子科技集团公司第十研究所） | Improved shortwave unit localization method |
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| SE518207C2 (en) * | 1999-09-10 | 2002-09-10 | Ericsson Telefon Ab L M | Large group antenna |
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101272168B (en) * | 2007-03-23 | 2012-08-15 | 中国科学院声学研究所 | Signal sources estimation method and its DOA estimation method |
| CN101520507B (en) * | 2007-07-20 | 2012-03-21 | 通用汽车环球科技运作公司 | Ow cost short range radar |
| CN104134354A (en) * | 2013-04-30 | 2014-11-05 | 业纳遥控设备有限公司 | Traffic monitoring system for speed measurement and assignment of moving vehicles in a multi-target recording module |
| CN108089147A (en) * | 2017-12-07 | 2018-05-29 | 西南电子技术研究所（中国电子科技集团公司第十研究所） | Improved shortwave unit localization method |
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