CN105785347A - Vector antenna array robust adaptive wave beam formation method - Google Patents

Abstract

The invention discloses a vector antenna array robust adaptive wave beam formation method. The method comprises steps that firstly, multiple snapshot values of an array output signal tensor are utilized to estimate an array output covariance tensor R<^>, contraction operation for the array output covariance tensor R<^> is carried out, and an array output space smoothing covariance matrix R(b) and an array output polarization smoothing covariance matrix R(a) are respectively acquired; according to design criteria, a beam former weight tensor W<^>WCC1 is solved, an expression as described in the specifications is further acquired, and an optimization problem is further solved; similarly, the W<^>WCC2 and another expression as described in the specifications are further acquired, and output yw(t) of a tensor domain beam former is acquired. According to the method, problems of vector mismatch and signal cancellation caused by error factors such as antenna pointing errors, antenna position errors, polarized disturbance and channel inconsistency during vector antenna array adaptive wave beam formation are solved.

Description

A kind of vector sensor battle array robust adaptive beamforming method

Technical field

The invention belongs to array signal process technique field, be specifically related to a kind of vector sensor battle array robust adaptive beamforming method.

Background technology

At present, existing vector sensor array adaptive beam former, though the space between available signal and interference, polarization associating difference, but do not take into full account by antenna pointing error, Antenna position error, polarization disturbance, steering vector mismatch that difference between channels error factors causes and caused signal cancellation problem thereof.The present invention considers by array spatial domain steering vector mismatch and polarizing field steering vector mismatch are carried out uncertain intensive bundle respectively, introduce polarizing field and the dual worst case optimized design criterion in spatial domain, to realizing the vector sensor battle array robust adaptive beamforming that steering vector mismatch is insensitive.

Summary of the invention

In view of this, the invention provides a kind of vector sensor battle array robust adaptive beamforming method, it is possible to solve in vector sensor array Adaptive beamformer by antenna pointing error, Antenna position error, polarization disturbance, steering vector mismatch that difference between channels error factors causes and caused signal cancellation problem thereof.

Realize technical scheme as follows:

A kind of vector sensor battle array robust adaptive beamforming method, it is achieved the step of the method is as follows:

Step one, a Wave beam forming array being made up of vector sensor, its output signal tensor X (t) is:

In formula (1),For desired signal s₀The guiding matrix of (t), wherein a₀And b₀Respectively desired signal s₀The spatial domain steering vector of (t) and polarizing field steering vector, subscript " T " represents transposition,Desired signal s is disturbed for m-th_mThe guiding matrix of (t), wherein a_mAnd b_mRespectively desired signal s_mT the spatial domain steering vector of () and polarizing field steering vector, N (t) is noise tensor, and M is interference number；

Step 2, the X (t) obtained based on step one, array output covariance tensor R is as follows in definition:

In formula (2), symbol " ο " is tensor product symbol, and " E " represents that mathematic expectaion, K represent fast umber of beats,For the estimated value of covariance tensor R, subscript " * " represents conjugation；Make C=A ο B

C (k, l, m, n)=A (k, l) B (m, n) (3)

In formula (3), C is guiding matrix；A, B respectively spatial domain guiding matrix and polarizing field guiding matrix；K, l, m, n are the index to C；

Carry out shrinking computing to R on k and m index and l and n index respectively, respectively obtain array output space smoothing covariance matrix R^(b)And array output polarization smoothed covariance matrix R^(a):

In formula (5), L is the dimension of vector sensor, and its value is between 2 and 6, and N is the number of vector sensor；

Step 3, based on step oneWithAccording to the array output space smoothing covariance matrix R that step 2 obtains^(b)And array output polarization smoothed covariance matrix R^(a), the power tensor of robust tensor adaptive beam former has following form:

In formula (6) and formula (7),WithRespectively a₀And b₀Nominal value,WithThe respectively weight vectors of the weight vectors in spatial domain and polarizing field,WithTwo kinds of form estimated values of tensor W are weighed for Beam-former；W is weight vectors；A is obtained according to different antennas₀And b₀Nominal value, andWithDesign criteria be respectively as follows:

WhereinWithRespectively a₀And b₀Affiliated spherical uncertain collection；ε_aAnd ε_bRespectively A_aAnd A_bThe upper bound of error；

Step 4, based on step 3, the optimization problem shown in formula (8) and formula (9) is solved, it is thus achieved that Beam-former power tensor W two kinds of form estimated values；

Step 5, output y according to tensor territory Beam-former_WT () weighs the scalar product between tensor W for array output signal tensor X (t) and Wave beam forming: y_W(t)=<X (t), W>；Obtain the output y of two kinds of forms corresponding to tensor territory Beam-former_W(t)。

Beneficial effect:

The present invention contrasts prior art, it is possible to substantially reduces the vector sensor battle array adaptive beam former sensitivity to steering vector mismatch, has the effect utilizing polarized area calibration effectively to suppress major lobe suppression and noise.

Accompanying drawing explanation

Fig. 1 is the flow chart of a kind of vector sensor battle array robust adaptive beamforming method；

Fig. 2 is the performance simulation figure (fast umber of beats is 50) that Beam-former output Signal to Interference plus Noise Ratio changes with input signal-to-noise ratio；

Fig. 3 is the performance simulation figure (input signal-to-noise ratio is 6dB) that Beam-former output Signal to Interference plus Noise Ratio changes with fast umber of beats；

The performance simulation figure (fast umber of beats is 50) that when Fig. 4 is there is major lobe suppression, Beam-former output Signal to Interference plus Noise Ratio changes with input signal-to-noise ratio；

The performance simulation figure (input signal-to-noise ratio is 6dB) that when Fig. 5 is there is major lobe suppression, Beam-former output Signal to Interference plus Noise Ratio changes with fast umber of beats；.

Detailed description of the invention

Develop simultaneously embodiment below in conjunction with accompanying drawing, describe the present invention.

The invention provides a kind of vector sensor battle array robust adaptive beamforming method, its flow chart is as shown in Figure 1；Its concrete steps include:

A kind of vector sensor battle array robust adaptive beamforming method, it is achieved the step of the method is as follows:

Step one, a Wave beam forming array being made up of vector sensor, its output signal tensor X (t) is:

In formula (1),For desired signal s₀The guiding matrix of (t), wherein a₀And b₀Respectively desired signal s₀The spatial domain steering vector of (t) and polarizing field steering vector, subscript " T " represents transposition,Desired signal s is disturbed for m-th_mThe guiding matrix of (t), wherein a_mAnd b_mRespectively desired signal s_mT the spatial domain steering vector of () and polarizing field steering vector, N (t) is noise tensor, and M is interference number；

Step 2, the X (t) obtained based on step one, array output covariance tensor R is as follows in definition:

In formula (2), symbol " ο " is tensor product symbol, and " E " represents that mathematic expectaion, K represent fast umber of beats,For the estimated value of covariance tensor R, subscript " * " represents conjugation；Make C=A ο B

C (k, l, m, n)=A (k, l) B (m, n) (3)

In formula (3), C is guiding matrix；A, B respectively spatial domain guiding matrix and polarizing field guiding matrix；K, l, m, n are the index to C；

Carry out shrinking computing to R on k and m index and l and n index respectively, respectively obtain array output space smoothing covariance matrix R^(b)And array output polarization smoothed covariance matrix R^(a):

In formula (5), L is the dimension of vector sensor, and its value is between 2 and 6, and N is the number of vector sensor；

Step 3, based on step oneWithAccording to the array output space smoothing covariance matrix R that step 2 obtains^(b)And array output polarization smoothed covariance matrix R^(a), the power tensor of robust tensor adaptive beam former has following form:

In formula (6) and formula (7),WithRespectively a₀And b₀Nominal value,WithThe respectively weight vectors of the weight vectors in spatial domain and polarizing field,WithTwo kinds of form estimated values of tensor W are weighed for Beam-former；W is weight vectors；A is obtained according to different antennas₀And b₀Nominal value, andWithDesign criteria be respectively as follows:

WhereinWithRespectively a₀And b₀Affiliated spherical uncertain collection；ε_aAnd ε_bRespectively A_aAnd A_bThe upper bound of error；

Step 4, based on step 3, the optimization problem shown in formula (8) and formula (9) is solved, it is thus achieved that Beam-former power tensor W two kinds of form estimated values；

Step 5, output y according to tensor territory Beam-former_WT () weighs the scalar product between tensor W for array output signal tensor X (t) and Wave beam forming: y_W(t)=<X (t), W>；Obtain the output y of two kinds of forms corresponding to tensor territory Beam-former_W(t)。

Based on above-mentioned steps it can be seen that first with the array output covariance tensor in repeatedly snap value estimator (2) of array output signal tensor X (t)Secondly rightCarry out shrinking computing, respectively obtain the array output space smoothing covariance matrix R in formula (4)^(b)And the array output polarization smoothed covariance matrix R in formula (5)^(a)；Thirdly, according to design criteria (8), solve Beam-former power tensorFirst to R^(b)Carry out Cholesky decomposition: R^(b)=U^HU, wherein U is the upper triangular matrix of L × L dimension, further problem (9) is converted into following problems:

In formula,Wherein " Re " and " Im " represents real part and imaginary part respectively；WhereinRecycling Second-order cone programming method can solve weight vectorCan obtain furtherFinally, optimization problem shown in formula (9) is solved.The method similar with step 3 is utilized to obtainAnd；Since then, it is achieved that robust adaptive beamforming method, is illustrated in figure 2 the performance simulation figure that the Beam-former output Signal to Interference plus Noise Ratio that snap number of times is 50 changes with input signal-to-noise ratio；It is illustrated in figure 3 the performance simulation figure that the Beam-former output Signal to Interference plus Noise Ratio that input signal-to-noise ratio is 6dB changes with fast umber of beats；Being illustrated in figure 4 fast umber of beats is the 50 performance simulation figure having that when major lobe suppression, Beam-former output Signal to Interference plus Noise Ratio changes with input signal-to-noise ratio；The performance simulation figure that when being illustrated in figure 5 the existence major lobe suppression that input signal-to-noise ratio is 6dB, Beam-former output Signal to Interference plus Noise Ratio changes with fast umber of beats.

In sum, these are only presently preferred embodiments of the present invention, be not intended to limit protection scope of the present invention.All within the spirit and principles in the present invention, any amendment of making, equivalent replacement, improvement etc., should be included within protection scope of the present invention.

Claims (1)

1. a vector sensor battle array robust adaptive beamforming method, it is characterised in that the step realizing the method is as follows:

Step one, a Wave beam forming array being made up of vector sensor, its output signal tensor X (t) is:

$X\left(t\right)=C_0{s}_0\left(t\right)+\underset{m=1}{\overset{M}{\&Sigma;}}{C}_m{s}_m\left(t\right)+N\left(t\right)---\left(1\right)$

In formula (1),For desired signal s₀The guiding matrix of (t), wherein a₀And b₀Respectively desired signal s₀The spatial domain steering vector of (t) and polarizing field steering vector, subscript " T " represents transposition,Desired signal s is disturbed for m-th_mThe guiding matrix of (t), wherein a_mAnd b_mRespectively desired signal s_mT the spatial domain steering vector of () and polarizing field steering vector, N (t) is noise tensor, and M is interference number；

Step 2, the X (t) obtained based on step one, array output covariance tensor R is as follows in definition:

In formula (2), symbol " o " is tensor product symbol, and " E " represents that mathematic expectaion, K represent fast umber of beats,For the estimated value of covariance tensor R, subscript " * " represents conjugation；Make C=A o B

C (k, l, m, n)=A (k, l) B (m, n) (3)

In formula (3), C is guiding matrix；A, B respectively spatial domain guiding matrix and polarizing field guiding matrix；K, l, m, n are the index to C；

Carry out shrinking computing to R on k and m index and l and n index respectively, respectively obtain array output space smoothing covariance matrix R^(b)And array output polarization smoothed covariance matrix R^(a):

$R^{\left(b\right)}=<R{>}_{(k,m)}=\underset{n_1=1}{\overset{N}{\&Sigma;}}R(n_1,:,n_1,:)\&ap;\underset{n_1=1}{\overset{N}{\&Sigma;}}\hat{R}(n_1,:,n_1,:)={\hat{R}}^{\left(b\right)}---\left(4\right)$

$R^{\left(a\right)}=<R{>}_{(l,n)}=\underset{l_1=1}{\overset{L}{\&Sigma;}}R(:,l_1,:,l_1)\&ap;\underset{l=1}{\overset{L}{\&Sigma;}}\hat{R}(:,l_1,:,l_1)={\hat{R}}^{\left(a\right)}---\left(5\right)$

In formula (5), L is the dimension of vector sensor, and its value is between 2 and 6, and N is the number of vector sensor；

Step 3, based on step oneWithAccording to the array output space smoothing covariance matrix R that step 2 obtains^(b)And array output polarization smoothed covariance matrix R^(a), the power tensor of robust tensor adaptive beam former has following form:

${\hat{W}}_{WCC-ATB1}={\hat{a}}_0{\hat{w}}_{WCC1}^H---\left(6\right)$

${\hat{W}}_{WCC-ATB2}={\hat{w}}_{WCC2}{\hat{b}}_0^H---\left(7\right)$

In formula (6) and formula (7),WithRespectively a₀And b₀Nominal value,WithThe respectively weight vectors of the weight vectors in spatial domain and polarizing field,WithTwo kinds of form estimated values of tensor W are weighed for Beam-former；W is weight vectors；A is obtained according to different antennas₀And b₀Nominal value, andWithDesign criteria be respectively as follows:

$\begin{array}{ccc}{\hat{w}}_{WCC1}=\arg \underset{w}{min}{w}^H{\hat{R}}^{\left(b\right)}w& s.t.& \underset{b\&Element;A_b}{\min }\left|w^{H}b\right|\&GreaterEqual;1\end{array}---\left(8\right)$

$\begin{array}{ccc}{\hat{w}}_{WCC2}=\arg \underset{w}{min}{w}^H{\hat{R}}^{\left(a\right)}w& s.t.& \underset{a\&Element;A_a}{\min }\left|w^{H}a\right|\&GreaterEqual;1\end{array}---\left(9\right)$

WhereinWithRespectively a₀And b₀Affiliated spherical uncertain collection；ε_aAnd ε_bRespectively A_aAnd A_bThe upper bound of error；

Step 4, based on step 3, the optimization problem shown in formula (8) and formula (9) is solved, it is thus achieved that Beam-former power tensor W two kinds of form estimated values；

Step 5, output y according to tensor territory Beam-former_WT () weighs the scalar product between tensor W for array output signal tensor X (t) and Wave beam forming: y_W(t)=< X (t), W >；Obtain the output y of two kinds of forms corresponding to tensor territory Beam-former_W(t)。