CN105022268A - Linear constraint virtual antenna beam forming method - Google Patents

Abstract

The invention discloses a linear constraint virtual antenna beam forming method. The method comprises the following steps: to begin with, carrying out pre-estimation on rough orientations of M interferences reaching an array antenna; determining a transformation region theta, and carrying out interpolation transformation according to manifold relationship of an actual array and a virtual array to obtain a transformation matrix; obtaining a covariance matrix of the virtual array by utilizing the transformation matrix; carrying out forward-backward spatial smoothing treatment on the covariance matrix of the virtual array; constructing a correlation matrix of steering vectors in an interpolation transformation region, extracting feature vectors corresponding to larger characteristic values in the correlation matrix and carrying out linear zero-setting constraint on the extracted feature vectors; and calculating the optimal weight vector and forming a wave beam. The method can greatly deepen nulling depth of the wave beam formed by the virtual array, reduce side lobe level, improve output SINR(signal to interference plus noise ratio), effectively suppress interference of super array freedom degree and improve anti-interference performance of the virtual antenna array.

Description

A kind of linear restriction virtual antenna beam formation method

Technical field

The invention belongs to the control field of adaptive array antenna, particularly relate to a kind of linear restriction virtual antenna beam formation method that antijamming capability is strong.

Background technology

Along with the development of electronic information technology, electromagnetic environment becomes increasingly complex, electromagnetic interference (EMI) gets more and more, also more and more serious, especially in the occasion of some electronic warfare, need the amount of interference of suppression a lot, this just needs the quantity increasing antenna element, but in a lot of applied environment, limit by practical factor, it is very large that antenna array size can not do.Therefore, people wish to reduce antenna amount in the finite space, reduce the basic matrix size of aerial array while, numerous interference can be resisted again.Virtual array antenna technology is exactly produce in this case, the virtual array transformation technology that Friedlander proposes mainly studies the degree of freedom how increasing array antenna, to suppress numerous interference, or process the interference of identical number with less antenna element.

Interpolation conversion virtual-antenna technology is by realizing the conversion between actual array and virtual array in interested REGION INTERPOLATION, current research mainly concentrates on virtual array in direction of arrival (DOA) estimation, and the applied research in Adaptive beamformer is relatively less.Su Baowei is at document (Su Baowei.Robust adaptive beam forming via arraytransformation [C] .2005IEEE AP-S International Symposium on Antennas and Propagation.Washington, DC, USA, July 2005, the impact chosen virtual array Wave beam forming performance of interpolation domain transformation is analyzed 1B:331-334), if research shows that domain transformation is selected excessive, Wave beam forming performance can be caused sharply to decline.Although sometimes can zero point be formed, main lobe can be caused to drift about and secondary lobe distortion simultaneously.Zhang Xue the people such as to respect at document (Zhang Xuejing, Yang Zhiwei, Liao Guisheng. two kinds of virtual mapping mode performance comparison [J] of the conformal array of hemisphere. Xian Electronics Science and Technology University's journal, 2014,41 (3): 33-40) compare in by semisphere array respectively interpolation be transformed to the performance of Wave beam forming after virtual uniform planar array and virtual cross array.But above document does not all provide the method improving virtual array Wave beam forming interference free performance.Document (Wenxing Li, Yipeng Li, Wenhua Yu.On adaptive beamforming for coherent interferencesuppression via virtual antenna array [J] .Progress in Electromagnetics Research-PIER, 2012, have studied 125:165-184) and utilize the method for Interference subspace projection to improve the performance that virtual array suppresses coherent interference, but the method needs the arrival bearing accurately knowing each interference, this is difficult to accomplish in actual applications.

Although conventional virtual array beams can increase array freedom, but owing to there is mapping fault, the wave beam formed, the zero sunken degree of depth is more shallow, export Signal to Interference plus Noise Ratio (SINR) lower, especially when suppressing the interference of super actual array degree of freedom, minor level raises, even occur that zero falls into skew, array output performance can not meet system requirements.

Summary of the invention

The object of this invention is to provide a kind of virtual antenna beam that can improve and form interference free performance, linear restriction virtual antenna beam formation method.

A kind of linear restriction virtual antenna beam formation method, comprises following step:

Step one: pre-estimation is carried out to the orientation of M the interference arriving array antenna;

Step 2: according to upper step and estimated result determination interpolation domain transformation Θ,

In domain transformation, evenly mark off L interpolation point, determine actual array and the virtual array steering vector at each interpolation point, and obtain actual array stream shape matrix A and virtual array stream shape matrix obtain transformation matrix

The Covariance Matrix Transform of actual array is the covariance matrix of virtual array by step 3: utilize transformation matrix B: again to matrix carry out space smoothing process, obtain the covariance matrix of a new virtual array $\widehat{\stackrel{\‾}{R}}=\frac{\stackrel{\‾}{R}+J{\stackrel{\‾}{R}}^{*}J}{2};$

Wherein:

B: the transformation matrix representing actual array and virtual array;

: the covariance matrix representing actual array;

: the covariance matrix representing virtual array;

J: represent a transition matrix,

Step 4: Θ in interpolation domain transformation, builds the steering vector correlation matrix Q of virtual array, feature decomposition is carried out to Q, obtains: there is M interference in domain transformation, extract M large eigenwert characteristic of correspondence vector in Q structural matrix step 5: the wanted signal steering vector of virtual array is the virtual array Wave beam forming criterion obtained based on linear restriction is:

$\left\{\begin{array}{c}\underset{w}{\min }{w}^H\widehat{\stackrel{\‾}{R}}w\\ \begin{array}{cc}st.& w^{H}U=f\end{array}\end{array}\right.$

Wherein: f=[1,0 ..., 0] ^h, f is the matrix that (M+1) × 1 is tieed up,

: the element number of array representing virtual array;

: represent and the kth eigenwert that feature decomposition obtains is carried out to Q;

: represent the proper vector of carrying out corresponding to a kth eigenwert that feature decomposition obtains to Q;

W: represent optimal weighting vector;

Step 6: utilize Lagrange product method, tries to achieve optimal weighting vector carry out Wave beam forming, obtain virtual array and export data.

A kind of linear restriction virtual antenna beam of the present invention formation method, can also comprise

1, this method is not only applicable to the formation of single user virtual antenna beam, is also applicable to multi-user virtual antenna beam and is formed.

2, this method is not only applicable to the formation of single beam virtual antenna beam, is also applicable to multi-beam virtual antenna beam and is formed.

Beneficial effect:

For in actual array antenna applications, when amount of interference is more, when exceeding actual array degree of freedom, the situation that actual array cannot suppress ultra-thin 3-freedom degree to disturb, the present invention, by virtual conversion, increases the degree of freedom of array antenna, can ultra-thin 3-freedom degree be suppressed preferably to disturb; And in amount of interference one timing, compare with existing smart antenna or adaptive antenna, need less actual array number, and pass through Adaptive beamformer, main lobe can be made to aim at wanted signal direction, fall in the adaptive formation zero of the interference radiating way in space, the effective suppression is disturbed and noise, to improving the output performance of adaptive array antenna and improving the Electro Magnetic Compatibility important in inhibiting of crowded platform and integrally.

To convert for common virtual in the beam pattern formed zero fall into more shallow, export the problem that SINR is lower, the present invention utilizes Search Space Smoothing to carry out front and back to smoothing processing to virtual array covariance matrix, construct the correlation matrix of interpolation domain transformation steering vector again, extract larger eigenwert characteristic of correspondence vector in correlation matrix, and linear zero setting constraint is applied to this proper vector, greatly can deepen wave beam zero falls into the degree of depth, reduce minor level, improve and export SINR, improve the jamproof performance of virtual array Wave beam forming.

For this problem, the virtual array Beamforming Method of linear restriction is proposed, the method utilizes Search Space Smoothing to carry out front and back to smoothing processing to virtual array covariance matrix, construct the correlation matrix of interpolation domain transformation steering vector again, extract larger eigenwert characteristic of correspondence vector in correlation matrix, linear zero setting constraint is applied to this proper vector.The method is compared with conventional interpolation virtual array Beamforming Method, does not need to increase any prior imformation.Emulation experiment shows, the method can greatly deepen virtual array formed wave beam zero fall into the degree of depth, reduce minor level, improve export SINR.When disturbing incoming wave number to exceed array freedom, also can form dark zero in interference position accurately and falling into, effectively suppressing the interference of super array freedom, improve the robustness of virtual antenna array.

Accompanying drawing explanation

Fig. 1 is performing step schematic diagram of the present invention;

Fig. 2 is Adaptive beamformer figure;

Fig. 3 is that array exports Signal to Interference plus Noise Ratio figure;

Fig. 4 is Adaptive beamformer figure;

Fig. 5 is that array exports Signal to Interference plus Noise Ratio figure.

Embodiment

Below in conjunction with accompanying drawing, the present invention is described in further details.

A kind of linear restriction virtual antenna beam formation method, comprises the steps:

(1) pre-estimation is carried out to the general orientation of M the interference arriving array antenna;

(2) interpolation domain transformation Θ is determined, according to the stream shape relation of actual array and virtual array, carry out interpolation conversion, obtain transformation matrix: in domain transformation, evenly mark off L interpolation point, determine actual array and the virtual array steering vector at each interpolation point, and obtain actual and virtual array stream shape matrix A with by formula obtain transformation matrix B;

(3) utilizing transformation matrix B, is the covariance matrix of virtual array by the Covariance Matrix Transform of actual array: again to matrix carry out space smoothing process, obtain the covariance matrix of a new virtual array $\widehat{\stackrel{\‾}{R}}=\frac{\stackrel{\‾}{R}+J{\stackrel{\‾}{R}}^{*}J}{2};$

Wherein:

Θ: represent the space angle region of carrying out interpolation conversion, i.e. the arrival bearing of undesired signal;

A: the stream shape matrix representing actual array antenna in domain transformation;

: the stream shape matrix representing virtual array antenna in domain transformation;

B: the transformation matrix representing actual antennas array and virtual antenna array;

: the covariance matrix representing actual array;

: the covariance matrix representing virtual array;

J: represent a transition matrix,

(4) Θ in interpolation domain transformation, builds the steering vector correlation matrix Q of virtual antenna array, feature decomposition is carried out to Q, obtains: if there be M interference in domain transformation, extract M large eigenwert characteristic of correspondence vector in Q structural matrix

(5) set the wanted signal steering vector of virtual array as the virtual array Wave beam forming criterion obtained based on linear restriction is:

$\left\{\begin{array}{c}\underset{w}{\min }{w}^H\widehat{\stackrel{\‾}{R}}w\\ \begin{array}{cc}st.& w^{H}U=f\end{array}\end{array}\right.$

Wherein: f=[1,0 ..., 0] ^h, f is the matrix that (M+1) × 1 is tieed up.

: the element number of array representing virtual antenna array;

: represent and the kth eigenwert that feature decomposition obtains is carried out to Q;

: represent the proper vector of carrying out corresponding to a kth eigenwert that feature decomposition obtains to Q;

W: represent optimal weighting vector;

(6) utilize Lagrange product method, try to achieve optimal weighting vector carry out Wave beam forming, obtain virtual array and export data.

With reference to Fig. 1, specific embodiment of the invention step is as follows:

Step 1: first interested viewing area is divided, suppose that interference drops in the Θ of region, region Θ is evenly divided into:

Θ＝[θ _l,θ _l+Δθ,θ _l+2Δθ,…,θ _r-Δθ,θ _r] (1)

Wherein, θ _l, θ _rfor the right boundary of Θ, Δ θ is interpolation step-length.

In this region, the stream shape matrix of actual array antenna is:

A＝[a(θ _l),a(θ _l+Δθ),a(θ _l+2Δθ),…,a(θ _r-Δθ),a(θ _r)] (2)

Wherein, a (θ _l) for actual array antenna is at θ _lthe steering vector in direction.

If the array manifold matrix of virtual array antenna is in the same area then have:

$\stackrel{\‾}{A}=\[\stackrel{\‾}{a}\left({\mathrm{\θ}}_l\right),\stackrel{\‾}{a}({\mathrm{\θ}}_l+\mathrm{\Δ}\mathrm{\θ}),\stackrel{\‾}{a}({\mathrm{\θ}}_l+2\mathrm{\Δ}\mathrm{\θ}),\mathrm{...},\stackrel{\‾}{a}({\mathrm{\θ}}_r-\mathrm{\Δ}\mathrm{\θ}),\stackrel{\‾}{a}\left({\mathrm{\θ}}_r\right)\]---\left(3\right)$

Wherein, for virtual array antenna is at θ _lthe steering vector in direction.

Step 2: the transformation relation that between the array manifold matrix of true array antenna and the stream shape matrix of virtual array antenna, existence one is fixing, makes: here || || _ffor Frobenius mould.

Transformation matrix B make true and virtual array antenna steering vector matrix A with between meet:

$B^{H}A\left(\mathrm{\θ}\right)=\stackrel{\‾}{A}\left(\mathrm{\θ}\right)\mathrm{\θ}\∈\mathrm{\Θ}---\left(4\right)$

Step 3: when conversion count be greater than actual array bay number and when for full rank, utilize least square method, can solve virtual transformation matrix is:

$B=\stackrel{\‾}{A}{A}^H{\left({\mathrm{AA}}^H\right)}^{-1}---\left(5\right)$

The calculating of transformation matrix is the process of a calculated off-line, is stored in system and can directly calls.

Step 4: suppose that the data covariance matrix of true array antenna is noise covariance matrix is then after virtual conversion, data covariance matrix is:

$\stackrel{\‾}{R}=B\hat{R}{B}^H=B(A{\hat{R}}_s{A}^H+{\hat{R}}_N)B^H=BA{\hat{R}}_s{A}^H{B}^H+B{\hat{R}}_N{B}^H---\left(6\right)$

In formula, R _sfor the autocorrelation matrix of signal, when neighbourhood noise is white noise, noise power is

Known by formula (5), BB ^h≠ I, as seen after virtual conversion, array antenna white noise is originally contaminated is coloured noise.In order to numerous method can be applied on virtual array antenna, need albefaction coloured noise again.Transformation matrix is made to be:

$T={\left(B^{H}B\right)}^{-1/2}{B}^H---\left(7\right)$

Step 5: the data covariance matrix of virtual-antenna can be expressed as:

Step 6: under normal circumstances, after interpolation conversion the virtual array that obtains be one symmetrical, therefore, the virtual-antenna covariance matrix obtained in formula (8) be Hermitian symmetric matrix, have and:

Wherein () ^*represent and get conjugate operation, J is a transition matrix, definition

Step 7: utilize front-rear space smooth technology to obtain a new virtual-antenna covariance matrix be defined as:

Step 8: mark off L interpolation point in domain transformation Θ, the steering vector that virtual antenna arrays is listed in these interpolation points is expressed as the correlation matrix Q building steering vector is:

$Q={\∫}_{\mathrm{\Θ}}\stackrel{\‾}{a}\left(\mathrm{\θ}\right){\stackrel{\‾}{a}}^H\left(\mathrm{\θ}\right)d\mathrm{\θ}---\left(12\right)$

Step 9: feature decomposition is carried out to Q, obtains:

$Q=\underset{k=1}{\overset{\hat{N}}{\Σ}}{\mathrm{\μ}}_{{\mathrm{\θ}}_k}{\stackrel{\‾}{\mathrm{\υ}}}_{{\mathrm{\θ}}_k}{\stackrel{\‾}{\mathrm{\υ}}}_{{\mathrm{\θ}}_k}^H,{\mathrm{\μ}}_{{\mathrm{\θ}}_1}\≥{\mathrm{\μ}}_{{\mathrm{\θ}}_2}\≥\mathrm{...}\≥{\mathrm{\μ}}_{{\mathrm{\θ}}_N}---\left(13\right)$

Wherein μ _θrepresentation feature value, represent and eigenwert corresponding proper vector.? in individual eigenwert ( array number for virtual array), extract wherein M large eigenwert characteristic of correspondence vector wherein M is the number of interference in domain transformation Θ, structural matrix

Step 10: utilize the virtual-antenna covariance matrix newly obtained in formula (11) the linear restriction zero setting of the proper vector extracted is obtained:

$\left\{\begin{array}{c}\underset{w}{\min }{w}^H\widehat{\stackrel{\‾}{R}}w\\ \begin{array}{cc}st.& w^{H}U=f\end{array}\end{array}\right.---\left(14\right)$

Wherein, w represents optimal weighting vector, f=[1,0 ..., 0] ^h, f is the matrix that (M+1) × 1 is tieed up.

Step 11: utilize Lagrange product method, structure cost function:

make its derivative equal zero to w differentiate, have:

Then have:

$w={\widehat{\stackrel{\‾}{R}}}^{-1}U\mathrm{\λ}---\left(17\right)$

Be updated to w ^hin U=f, can solve:

$\mathrm{\λ}={\left(U^H{\widehat{\stackrel{\‾}{R}}}^{-1}U\right)}^{-1}f---\left(18\right)$

Step 12: formula (18) is updated to formula (17), can obtain the direct form of the adaptive weighted vector of virtual-antenna based on linear restriction:

$w={\widehat{\stackrel{\‾}{R}}}^{-1}U{\left(U^H{\widehat{\stackrel{\‾}{R}}}^{-1}U\right)}^{-1}f---\left(19\right)$

Step 13: Wave beam forming, utilizes optimal weighting vector w to be weighted antenna array receiver data, obtains virtual antenna array and exports data.

What the present invention relates to is a kind of control method of adaptive array antenna, it is more shallow that the wave beam zero specifically formed for conventional virtual aerial array falls into the degree of depth, export Signal to Interference plus Noise Ratio lower, especially in the super actual array degree of freedom interference of suppression, occur that zero falls into the problem offset, invent a kind of virtual antenna beam formation method of linear restriction.

The present invention includes following steps: first pre-estimation is carried out to the general orientation of M the interference arriving array antenna; Determine domain transformation Θ, according to the stream shape relation of actual array and virtual array, carry out interpolation conversion, obtain transformation matrix; Transformation matrix is utilized to obtain the covariance matrix of virtual array; Front-rear space smooth process is carried out to virtual array covariance matrix; Construct the correlation matrix of interpolation domain transformation steering vector again, extract larger eigenwert characteristic of correspondence vector in correlation matrix, and linear zero setting constraint is applied to the proper vector extracted; Try to achieve optimal weighting vector and form wave beam.The present invention can greatly deepen virtual array formed wave beam zero fall into the degree of depth, reduce minor level, improve export Signal to Interference plus Noise Ratio.When disturbing incoming wave quantity to exceed actual antennas array freedom, also can form dark zero at interference radiating way accurately and falling into, effectively suppressing the interference of super array freedom, improve the interference free performance of virtual antenna array.

Below in conjunction with accompanying drawing, the present invention is described further:

Method of the present invention adopts following emulation to verify:

Simulated conditions: actual 4 array element ULA battle arrays, array element distance is λ, and wanted signal is from 0 ° of incidence, and SNR=0dB, 3 independent interference lay respectively at-55 ° ,-35 °, 40 ° of directions, INR=30dB, and virtual-antenna is 8 array elements, spacing uLA battle array, interpolation domain transformation is [-60 ° ,-50 °] ∪ [-40 ° ,-30 °] ∪ [35 °, 45 °], and step-length is 0.1 °, and fast umber of beats is 200.Fig. 2 is 4 array element actual array, the beam pattern of 8 array element conventional algorithm virtual arrays and 8 array element the inventive method virtual arrays compares.

As can see from Figure 2, when disturbing incoming wave number to be no more than the degree of freedom of actual array antenna, 3 kinds of algorithms can both form zero point adaptively at interference radiating way.4 array element actual array antennas cross greatly 1 wavelength due to array element distance, have occurred graing lobe, and secondary lobe rises, and zero falls into the degree of depth about-50dB; Zero of conventional algorithm virtual array falls into the degree of depth about-40dB, and minor level is higher, and the skew of 3 ° has appearred in main lobe; The virtual array beam pattern that the inventive method is formed, zero falls into the degree of depth all reaches more than-60dB, and average zero falls into the degree of depth reaches-80dB, better can suppress interference, also at-20dB once, main lobe width is conventional interpolation virtual array algorithm broadening to some extent comparatively for minor level.

Fig. 3 is that 3 kinds of algorithms export the comparison of SINR with input SNR, and as can see from Figure 3, when disturbing number not exceed actual array degree of freedom, the output SINR of 4 array element actual array is slightly better than 8 array element conventional algorithm virtual arrays; The inventive method falls into the degree of depth owing to having deepened zero, and inhibit interference better, its SINR, far above other algorithm, has and exports SINR preferably within the scope of whole input SNR.

Simulated conditions: actual 4 array element ULA battle arrays, array element distance is λ, wanted signal from 0 ° of incidence, SNR=0dB, 4 independent interference lay respectively at-50 ° ,-35 °, 30 °, 60 ° of directions, INR=30dB, virtual-antenna is 8 array elements, spacing uLA battle array, interpolation domain transformation is [-55 ° ,-45 °] ∪ [-40 ° ,-30 °] ∪ [25 °, 35 °] ∪ [55 °, 65 °], and step-length is 0.1 °, and fast umber of beats is 200.Fig. 4 is 4 array element actual array, the beam pattern of 8 array element conventional algorithm virtual arrays and 8 array element the inventive method virtual arrays compares.

As can see from Figure 4, when disturbing incoming wave number to exceed the degree of freedom of actual array, 4 array element actual array antennas can not form zero at all interference radiating way and fall into, and can not effectively work; Conventional algorithm virtual array owing to adding array freedom, can at-50 ° ,-35 °, 30 ° of interference radiating way form zero and fall into, but the zero sunken degree of depth is more shallow, about-30dB, at 60 ° of interference radiating way, occurred that zero falls into skew, minor level is higher, and the skew of 5 ° has appearred in main lobe; The beam pattern that the inventive method virtual array is formed, zero falls into the degree of depth all reaches more than-50dB, and average zero falls into the degree of depth reaches-65dB, better can suppress interference, minor level is also about-30dB, and main lobe width is conventional interpolation virtual array algorithm broadening to some extent comparatively.

Fig. 5 is that 3 kinds of algorithms export the comparison of SINR with input SNR.As can see from Figure 5, when disturbing number to exceed actual array degree of freedom, the output SINR of 8 array element conventional algorithm virtual arrays is better than 4 array element actual array, and this falls into because 4 array element actual array can not form zero at all interference radiating way; The inventive method falls into the degree of depth owing to having deepened zero, and inhibit interference better, its SINR, far above other algorithm, has and exports SINR preferably within the scope of whole input SNR.

Claims (3)

1. a linear restriction virtual antenna beam formation method, is characterized in that: comprise following step:

Step one: pre-estimation is carried out to the orientation of M the interference arriving array antenna;

Step 2: according to upper step and estimated result determination interpolation domain transformation Θ,

In domain transformation, evenly mark off L interpolation point, determine actual array and the virtual array steering vector at each interpolation point, and obtain actual array stream shape matrix A and virtual array stream shape matrix obtain transformation matrix

The Covariance Matrix Transform of actual array is the covariance matrix of virtual array by step 3: utilize transformation matrix B: again to matrix carry out space smoothing process, obtain the covariance matrix of a new virtual array $\widehat{\stackrel{\‾}{R}}=\frac{\stackrel{\‾}{R}+J{\stackrel{\‾}{R}}^{*}J}{2};$

Wherein:

B: the transformation matrix representing actual array and virtual array;

represent the covariance matrix of actual array;

represent the covariance matrix of virtual array;

J: represent a transition matrix,

Step 4: Θ in interpolation domain transformation, builds the steering vector correlation matrix Q of virtual array, feature decomposition is carried out to Q, obtains: there is M interference in domain transformation, extract M large eigenwert characteristic of correspondence vector in Q structural matrix step 5: the wanted signal steering vector of virtual array is the virtual array Wave beam forming criterion obtained based on linear restriction is:

$\left\{\begin{array}{c}\underset{w}{\min }{w}^H\widehat{\stackrel{\‾}{R}}w\\ \begin{array}{cc}st.& w^{H}U=f\end{array}\end{array}\right.$

Wherein: f=[1,0 ..., 0] ^h, f is the matrix that (M+1) × 1 is tieed up,

represent the element number of array of virtual array;

represent and the kth eigenwert that feature decomposition obtains is carried out to Q;

represent the proper vector of carrying out corresponding to a kth eigenwert that feature decomposition obtains to Q;

W: represent optimal weighting vector;

Step 6: utilize Lagrange product method, tries to achieve optimal weighting vector carry out Wave beam forming, obtain virtual array and export data.

2. a kind of linear restriction virtual antenna beam formation method according to claim 1, is characterized in that: this method is not only applicable to single user virtual antenna beam and is formed, and is also applicable to multi-user virtual antenna beam and is formed.

3. a kind of linear restriction virtual antenna beam formation method according to claim 1, is characterized in that: this method is not only applicable to single beam virtual antenna beam and is formed, and is also applicable to multi-beam virtual antenna beam and is formed.