CN103885045B - Based on the circulation associating Adaptive beamformer method of Subarray partition - Google Patents

Abstract

The present invention discloses a kind of circulation based on Subarray partition associating Adaptive beamformer method, large to independent same distribution sample requirement amount when solving extensive radar antenna array Wave beam forming, computation complexity is high and the problem of interference number filter effect of many times difference.Performing step of the present invention is: (1) Subarray partition; (2) steering vector is obtained; (3) the direct product decomposition of steering vector; (4) cost function is set up; (5) weight vector is solved; (6) Wave beam forming.The present invention carries out the method for Wave beam forming compared to existing technology, have the advantage few to good, the required sample number of interference suppressioning effect, iteration convergence is fast, the present invention can be used for that radar antenna array scale is large, number of training is few and radar beam under the susceptible condition of interference number is formed.

Description

Based on the circulation associating Adaptive beamformer method of Subarray partition

Technical field

The invention belongs to Radar Technology field, further relate to a kind of associating of the circulation based on the Subarray partition Adaptive beamformer method in array signal process technique field.The present invention can be used for solving that radar antenna array scale is large, number of training is few and Wave beam forming problem under the susceptible condition of interference number.

Background technology

Array signal process technique, in the development of nearly 50 years, is widely used in numerous military affairs and the national economy fields such as radar, communication, navigation, sonar, speech processes, geologic prospecting.Particularly in recent years, along with the fast development of radio digital communication technology, the application of array signal process technique in mobile communication system causes extensive attention and the research interest of people, and this accelerates the development of this technology further.Adaptive beamformer, also referred to as Spatially adaptive filtering, namely by being weighted addition process at receiving end to space array element, suppressing space interference and noise, strengthening useful signal, to obtain the Output rusults of expectation.The method that self-adaptation solves array element optimum power is called Beamforming Method.At present, the beam-forming technology often used is sample matrix inversion method.The method according to linearly constrained minimum variance (namely when ensure expect sense gain constant, array element is made to receive the energy of data minimum) to set up cost function and use method of Lagrange multipliers to solve wave filter weight vector, the covariance matrix that array element receives data is estimated to obtain by multiple independent identically distributed sampled data.Scientific research shows, in order to make sample matrix inversion method play optimum performance, the independent same distribution sample number of needs should be greater than the twice of covariance matrix dimension, and in actual applications, the usual Rapid Variable Design of interference environment, available independent same distribution sample number is limited.In addition, sample matrix inversion method needs to invert to covariance matrix, and computational complexity is high.And in order to improve the ability of array manifold resolution and detection Weak target signal, the array number of modern massive phased array may reach hundreds and thousands of even up to ten thousand, if take sample matrix inversion method, the independent same distribution sample number not only needed and computation complexity huge, and the equipment amount needed, memory space are also very big, it is also unnecessary that engineering cannot realize.Equally, existing some other Beamforming Method, when for large scale array, is also faced with similar problem.

Patent " digital array ultralow side lobe self-adaptive numerical integration algorithm the method " (number of patent application: 201210002661 of Hohai University's application, publication No.: CN102608580A), disclose a kind of digital array ultralow side lobe self-adaptive numerical integration algorithm method.First the method estimates interference radiating way, then builds interference secondary beam and carries out spatial domain dimension-reduction treatment, last calculating beamforming device weights.The method has good ultralow side lobe wave beam conformal ability, and training sample demand is little, but the deficiency that the method still exists is, need to estimate interference radiating way in advance, in time disturbing number more, estimate that multiple interference needs larger calculated amount, and the dimension of covariance matrix is still higher after dimension-reduction treatment, required number of training is more, and filter effect is also undesirable, now, the performance of the method has larger decline.

Summary of the invention

The object of the invention is to overcome above-mentioned the deficiencies in the prior art, propose a kind of circulation based on Subarray partition associating Adaptive beamformer method.The method can reduce the demand of independent same distribution sample effectively, and reduces computation complexity, effectively can suppress interference simultaneously, thus solve the Wave beam forming problem of extensive radar antenna array.

Realization approach of the present invention is: first, and radar antenna array is divided into multiple subarray; Then, radar target signal guide vector, outer aerial array steering vector and internal layer aerial array steering vector is calculated; Then, radar target signal guide vector is carried out the direct product decomposition, and adopts linearly constrained minimum variance, set up cost function; Finally, adopt circulation Method for minimization to solve cost function, obtain wave filter weight vector, carry out Wave beam forming.

Concrete steps of the present invention are as follows:

(1) Subarray partition:

To multiple radar antenna array element, p array element is wherein chosen as a submatrix according to the divided dose order of element number of array N, form M=N/p submatrix, the outer arrays obtaining being made up of M the submatrix aerial array that form nested with the inner array that p array element is formed, wherein, N represents radar antenna element number of array, and p represents that the array number that the submatrix of radar antenna array comprises, M represent the submatrix number of radar antenna array.

(2) steering vector is obtained:

Adopt steering vector formula, calculate radar target signal guide vector, outer aerial array steering vector and internal layer aerial array steering vector respectively.

(3) the direct product decomposition of steering vector:

By radar target signal guide vector, be decomposed into the direct product of outer aerial array steering vector and internal layer aerial array steering vector.

(4) cost function is set up:

According to linearly constrained minimum variance, set up the cost function of outer aerial array weight vector corresponding to outer aerial array steering vector and internal layer aerial array weight vector corresponding to internal layer aerial array steering vector.

(5) weight vector is solved:

(5a) the iterative initial value vector of outer aerial array weight vector according to the following formula, is set:

$v_0=a_m^{*}/\left|\right|a_m^{*}\left|\right|$

Wherein, v ₀represent the iterative initial value vector of outer aerial array weight vector, a _mrepresent outer aerial array steering vector, * represents conjugate operation, || || represent and get two norm operations;

(5b) set ε as stopping iteration parameter, the span of ε be 0 < ε < < 1, < < represent much smaller than;

(5c) the iterative initial value vector of internal layer aerial array weight vector according to the following formula, is calculated:

$u_0=\frac{R_0^{-1}{s}_0}{s_0^H{R}_0^{-1}{s}_0}$

Wherein, u ₀represent the iterative initial value vector of internal layer aerial array weight vector, R ₀represent the sample estimated matrix of internal layer antenna array receiver data covariance matrix, s ₀represent the coefficient vector of internal layer aerial array, H represents conjugate transposition operation, () ^-1represent and get inverse operation;

(5d) the iteration vector of outer aerial array weight vector according to the following formula, is calculated:

$v_1=\frac{R_1^{-1}{s}_1}{s_1^H{R}_1^{-1}{s}_1}/\left|\right|\frac{R_1^{-1}{s}_1}{s_1^H{R}_1^{-1}{s}_1}\left|\right|$

Wherein, v ₁represent the iteration vector of outer aerial array weight vector, R ₁represent the sample estimated matrix of outer antenna array receiver data covariance matrix, s ₁represent the coefficient vector of outer aerial array, H represents conjugate transposition operation, () ^-1represent and get inverse operation, || || represent and get two norm operations;

(5e) the iteration vector v of outer aerial array weight vector is judged ₁with the iterative initial value vector v of outer aerial array weight vector ₀difference v ₁-v ₀, whether meet the stopping iterated conditional of following formula, if meet, iteration ends, obtain the iteration vector of outer aerial array weight vector as outer aerial array weight vector, the iterative initial value vector of internal layer aerial array weight vector is as internal layer aerial array weight vector; If do not meet, by the iteration vector v of outer aerial array weight vector ₁as the iterative initial value vector v of new outer aerial array weight vector ₀perform step (5c), stop iterated conditional until meet, iteration ends, obtain the iteration vector of outer aerial array weight vector as outer aerial array weight vector, the iterative initial value vector of internal layer aerial array weight vector is as internal layer aerial array weight vector;

||v ₁-v ₀||≤ε

Wherein, v ₁and v ₀represent the iteration vector iterative initial value vector of outer aerial array weight vector respectively, ε represents stopping iteration parameter, and the span of ε is 0 < _ε< < 1, || || represent get two norms operation, < < represent much smaller than.

(6) Wave beam forming:

Outer aerial array weight vector and internal layer aerial array weight vector are done operation of direct product, obtain wave filter weight vector, with wave filter weight vector, summation is weighted to the data vector that radar receives, make the output power of radar antenna array minimum, form main beam in expectation target direction, complete Wave beam forming.

The present invention has the following advantages compared with prior art:

First, owing to present invention employs the method for Subarray partition, original radar antenna array is divided into the nested form of outer arrays and inner array, overcome the problem that prior art is large to independent same distribution sample requirement amount, the present invention is had and effectively reduces sample requirement amount, under condition of small sample, still can obtain the advantage of premium properties.

Second, owing to present invention employs Subarray partition and circulation Method for minimization, overcome the problem that prior art is large, the present invention is had and can obtain wave filter weight vector fast, greatly reduce computation complexity, be more conducive to the advantage of process in real time.

3rd, owing to present invention employs circulation Method for minimization, circulation associating self-adaptive processing outer arrays and inner array, overcome the problem of prior art and interference number many time filter effect difference large in radar antenna array scale, radar antenna array beam pattern the present invention being had obtain has lower secondary lobe and better wave beam conformal ability, is more conducive to the advantage of filtering.

Accompanying drawing explanation

Fig. 1 is process flow diagram of the present invention;

Fig. 2 is the iteration convergence curve map that the present invention adopts circulation Method for minimization to obtain;

Fig. 3 is that the present invention and prior art sample matrix inversion method export Signal to Interference plus Noise Ratio with input signal-to-noise ratio change curve;

Fig. 4 is that the present invention and prior art sample matrix inversion method export Signal to Interference plus Noise Ratio with sample number change curve;

Fig. 5 is that the wave filter weight vector that the present invention and prior art sample matrix inversion method are tried to achieve is spent to the beam pattern within the scope of 90 degree-90.

Embodiment

Below in conjunction with accompanying drawing, the present invention will be further described.

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

Step 1, Subarray partition.

To multiple radar antenna array element, p array element is wherein chosen as a submatrix according to the divided dose order of element number of array N, form M=N/p submatrix, the outer arrays obtaining being made up of M the submatrix aerial array that form nested with the inner array that p array element is formed, wherein, N represents radar antenna element number of array, and p represents that the array number that the submatrix of radar antenna array comprises, M represent the submatrix number of radar antenna array.

Step 2, obtains steering vector.

Adopt steering vector formula, calculate radar target signal guide vector, outer aerial array steering vector and internal layer aerial array steering vector respectively.

Radar target signal guide vector formulas is as follows:

$a_n={[1,e^{j\frac{2\mathrm{\&pi;}d\sin \mathrm{\&theta;}}{\mathrm{\&lambda;}}},e^{j\frac{2\mathrm{\&pi;}2d\sin \mathrm{\&theta;}}{\mathrm{\&lambda;}}},...,e^{j\frac{2\mathrm{\&pi;}(N-1)d\sin \mathrm{\&theta;}}{\mathrm{\&lambda;}}}]}^T$

Wherein, a _nrepresent radar target signal guide vector, j represents imaginary unit, and d represents radar antenna array array element distance, θ represents radar target direction, and sin represents and does sinusoidal operation, and λ represents the operation wavelength of radar, N represents the number of radar antenna array element, and T represents matrix transpose operation.

Outer aerial array steering vector formula is as follows:

$a_m={[1,e^{j\frac{2\mathrm{\&pi;pd}\sin \mathrm{\&theta;}}{\mathrm{\&lambda;}}},e^{j\frac{2\mathrm{\&pi;}2\mathrm{pd}\sin \mathrm{\&theta;}}{\mathrm{\&lambda;}}},...,e^{j\frac{2\mathrm{\&pi;}(M-1)\mathrm{pd}\sin \mathrm{\&theta;}}{\mathrm{\&lambda;}}}]}^T$

Wherein, a _mrepresent outer aerial array steering vector, j represents imaginary unit, d represents radar antenna array array element distance, θ represents radar target direction, sin represents and does sinusoidal operation, and λ represents the operation wavelength of radar, and p represents the array number that the submatrix of radar antenna array comprises, M represents the submatrix number of radar antenna array, and T represents matrix transpose operation.

Internal layer aerial array steering vector formula is as follows:

$a_p={[1,e^{j\frac{2\mathrm{\&pi;}d\sin \mathrm{\&theta;}}{\mathrm{\&lambda;}}},e^{j\frac{2\mathrm{\&pi;}2d\sin \mathrm{\&theta;}}{\mathrm{\&lambda;}}},...,e^{j\frac{2\mathrm{\&pi;}(p-1)d\sin \mathrm{\&theta;}}{\mathrm{\&lambda;}}}]}^T$

Wherein, a _prepresent internal layer aerial array steering vector, j represents imaginary unit, and d represents radar antenna array array element distance, θ represents radar target direction, and sin represents and does sinusoidal operation, and λ represents the operation wavelength of radar, p represents the array number that the submatrix of radar antenna array comprises, and T represents matrix transpose operation.

Step 3, the direct product decomposition of steering vector.

By radar target signal guide vector, be decomposed into the direct product of outer aerial array steering vector and internal layer aerial array steering vector.

According in matrix theory to the definition of direct product, directly by radar target signal guide vector a _n, be decomposed into outer aerial array steering vector a _mwith internal layer aerial array steering vector a _pdirect product, obtain represent direct product.

Step 4, sets up cost function.

According to linearly constrained minimum variance (when ensureing to expect target signal direction gain constant, make the output power of radar antenna array minimum), set up the cost function of outer aerial array weight vector corresponding to outer aerial array steering vector and internal layer aerial array weight vector corresponding to internal layer aerial array steering vector.

Suppose that radar antenna array is the even linear array be made up of N number of array element, array element distance is half wavelength, and there are 1 echo signal and J undesired signal in space, then radar antenna array receives data and can be expressed as following formula:

x(t)＝As(t)+n(t)

Wherein, x (t) represents that radar antenna array receives data vector, A represents the matrix that N × (1+J) that the steering vector of echo signal and undesired signal is formed ties up, s (t) represents t Received signal strength amplitude vector, and n (t) represents the white Gaussian noise vector that t receives.After sampling to radar antenna array reception data, the sample data vector of the actual output of radar antenna array is x _i(i=1 ..., L), L represents number of samples.

According to linearly constrained minimum variance, set up cost function as follows:

$\left\{\begin{array}{c}\min f(u,v)=E{\left|\right|{(v^{*}\&CircleTimes;u)}^{H}x\left|\right|}^2\\ s.t.{(v^{*}\&CircleTimes;u)}^H(a_m\&CircleTimes;a_p)=1\end{array}\right.$

Wherein, when min represents that target signal direction gain constant is expected in guarantee, make radar antenna array output power minimize operation, f (u, v) represents radar antenna array output power, u represents internal layer aerial array weight vector, v represents outer aerial array weight vector, and E represents and asks expectation computing, || || represent and get two norms operations, * conjugate operation is represented represent direct product, H represents conjugate transposition operation, and x represents radar antenna array sample data vector, and s.t. represents and gets constraint manipulation, a _mrepresent outer aerial array steering vector, a _prepresent internal layer aerial array steering vector.

By x being lined up the data matrix X of the capable M row of p, and then above formula can be converted into following cost function formula:

$\left\{\begin{array}{c}\min f(u,v)=E{\left|\right|u^H\mathrm{Xv}\left|\right|}^2\\ s.t.u^H{a}_p{a}_m^{T}v=1\end{array}\right.$

Wherein, when min represents that target signal direction gain constant is expected in guarantee, radar antenna array output power is made to minimize operation, f (u, v) represent radar antenna array output power, u represents internal layer aerial array weight vector, and v represents outer aerial array weight vector, E represents and asks expectation computing, || || represent and get two norm operations, H represents conjugate transposition operation, and X represents radar antenna array sampled data matrix, s.t. represent and get constraint manipulation, a _prepresent internal layer aerial array steering vector, a _mrepresent outer aerial array steering vector, T represents matrix transpose operation.

Step 5, solves weight vector.

Adopt circulation Method for minimization, solve cost function, obtain outer aerial array weight vector and internal layer aerial array weight vector.

Lower mask body introduces solution procedure.

Suppose that outer aerial array weight vector v is known, utilize method of Lagrange multipliers to obtain following formula:

$J(u,\mathrm{\&lambda;})=u^H{R}_{0}u+\mathrm{\&lambda;}(1-u^H{a}_p{a}_m^{T}v)$

Wherein, u represents internal layer aerial array weight vector, and λ represents Lagrange multiplier, and v represents outer aerial array weight vector, represent the sample estimated matrix of internal layer antenna array receiver data covariance matrix, L represents number of samples, X _irepresent i-th radar antenna array sampled data matrix, a _prepresent internal layer aerial array steering vector, a _mrepresent outer aerial array steering vector.

Order can obtain internal layer aerial array weight vector is:

$u=\frac{R_0^{-1}{s}_0}{s_0^H{R}_0^{-1}{s}_0}$

Wherein, u represents internal layer aerial array weight vector, represent the coefficient vector of internal layer aerial array, H represents conjugate transposition operation, () ^-1represent and get inverse operation.

Suppose that internal layer aerial array weight vector u is known again, utilize method of Lagrange multipliers to obtain:

$g(v,\mathrm{\&gamma;})=v^H{R}_{1}v+\mathrm{\&gamma;}(1-v^T{a}_m{a}_p^T{u}^{*})$

Wherein, v represents outer aerial array weight vector, and γ represents Lagrange multiplier, and u represents internal layer aerial array weight vector, represent the sample estimated matrix of outer antenna array receiver data covariance matrix, * represents conjugate operation, and H represents conjugate transposition operation, and T represents matrix transpose operation.

Order can obtain outer aerial array weight vector is:

$v=\frac{R_1^{-1}{s}_1}{s_1^H{R}_1^{-1}{s}_1}$

Wherein, v represents outer aerial array weight vector, represent the coefficient vector of outer aerial array.Because cost function exists yardstick fuzzy problem, namely for any non-zero constant there is following relation:

$f({\&PartialD;}^{*}u,{\&PartialD;}^{-1}v)=f(u,v)$

For solving yardstick fuzzy problem, need in an iterative process, be normalized by v, by the modulus value of v divided by it, the modulus value making v is 1, is formulated as: v=v/||v||, || || represent and get two norm operations.

Described circulation Method for minimization, carry out as follows:

(5a) the iterative initial value vector of outer aerial array weight vector according to the following formula, is set:

$v_0=a_m^{*}/\left|\right|a_m^{*}\left|\right|$

Wherein, v ₀represent the iterative initial value vector of outer aerial array weight vector, a _mrepresent outer aerial array steering vector, * represents conjugate operation, || || represent and get two norm operations;

(5b) set ε as stopping iteration parameter, the span of ε be 0 < ε < < 1, < < represent much smaller than;

(5c) the iterative initial value vector of internal layer aerial array weight vector according to the following formula, is calculated:

$u_0=\frac{R_0^{-1}{s}_0}{s_0^H{R}_0^{-1}{s}_0}$

Wherein, u ₀represent the iterative initial value vector of internal layer aerial array weight vector, R ₀represent the sample estimated matrix of internal layer antenna array receiver data covariance matrix, s ₀represent the coefficient vector of internal layer aerial array, H represents conjugate transposition operation, () ^-1represent and get inverse operation;

(5d) the iteration vector of outer aerial array weight vector according to the following formula, is calculated:

$v_1=\frac{R_1^{-1}{s}_1}{s_1^H{R}_1^{-1}{s}_1}/\left|\right|\frac{R_1^{-1}{s}_1}{s_1^H{R}_1^{-1}{s}_1}\left|\right|$

Wherein, v ₁represent the iteration vector of outer aerial array weight vector, R ₁represent the sample estimated matrix of outer antenna array receiver data covariance matrix, s ₁represent the coefficient vector of outer aerial array, H represents conjugate transposition operation, () ^-1represent and get inverse operation, || || represent and get two norm operations;

(5e) the iteration vector v of outer aerial array weight vector is judged ₁with the iterative initial value vector v of outer aerial array weight vector ₀difference v ₁-v ₀, whether meet the stopping iterated conditional of following formula, if meet, iteration ends, obtain the iteration vector of outer aerial array weight vector as outer aerial array weight vector, the iterative initial value vector of internal layer aerial array weight vector is as internal layer aerial array weight vector; If do not meet, by the iteration vector v of outer aerial array weight vector ₁as the iterative initial value vector v of new outer aerial array weight vector ₀perform step (5c), stop iterated conditional until meet, iteration ends, obtain the iteration vector of outer aerial array weight vector as outer aerial array weight vector, the iterative initial value vector of internal layer aerial array weight vector is as internal layer aerial array weight vector;

||v ₁-v ₀||≤ε

Wherein, v ₁and v ₀represent the iteration vector iterative initial value vector of outer aerial array weight vector respectively, ε represents stopping iteration parameter, the span of ε is 0 < ε < < 1, || || represent get two norms operation, < < represent much smaller than.

Step 6, Wave beam forming.

Outer aerial array weight vector and internal layer aerial array weight vector do operation of direct product, obtain wave filter weight vector, with wave filter weight vector, summation is weighted to the data vector that radar receives, make the output power of radar antenna array minimum, form main beam in expectation target direction, complete Wave beam forming.

Effect of the present invention can be verified by following emulation experiment:

1. simulated conditions:

The even linear array that emulation experiment of the present invention adopts 400 array elements to form, array element distance is half wavelength, and target direction is 0 degree, and 16 interference radiating way be that [-80-70-60-50-40-30-20-101020304050607080] spends, and dryly makes an uproar than being 40dB.During Subarray partition, choose 20 array elements successively as a submatrix.

2. emulate content

Emulation 1: the present invention chooses 800 samples, uses the circulation Method for minimization adopted when solving weight vector in the present invention to emulate, and adds up, finally obtain an iteration convergence curve of circulation Method for minimization, as shown in Figure 2 to output Signal to Interference plus Noise Ratio.

Emulation 2: the present invention chooses 800 samples, the sample matrix inversion method of prior art and the present invention's two kinds of methods are used to emulate respectively, output Signal to Interference plus Noise Ratio under two kinds of methods is added up, finally obtain two curves that output Signal to Interference plus Noise Ratio changes with input signal-to-noise ratio, as indicated two curves of the present invention and sample matrix inversion in Fig. 3.

Emulation 3: the present invention is when input Signal to Interference plus Noise Ratio is 40dB, the sample matrix inversion method of prior art and the present invention's two kinds of methods are used to emulate respectively, output Signal to Interference plus Noise Ratio under two kinds of methods is added up, finally obtain two curves that output Signal to Interference plus Noise Ratio changes with sample number, as indicated two curves of the present invention and sample matrix inversion in Fig. 4.

Emulation 4: the present invention is 800 at sample number, when signal to noise ratio (S/N ratio) is-20dB, the sample matrix inversion method of prior art and the present invention's two kinds of methods are used to emulate respectively, export normalized power to the radar antenna array under two kinds of methods to add up, finally obtain the beam pattern under two kinds of methods, as shown in Figure 5.

3. interpretation of result:

Fig. 2 is the iteration convergence curve map that the present invention adopts circulation Method for minimization to obtain, and horizontal ordinate represents iterations, and ordinate represents output Signal to Interference plus Noise Ratio, and physical unit is dB.As seen from Figure 2, when sample number is 800, the iterative process that the present invention adopts circulation Method for minimization to solve wave filter weight vector only needs 1 step to restrain, and the computation complexity carrying out inversion operation owing to tieing up covariance matrix to N is O (N ³), therefore the present invention is O (20 to the computation complexity that the outer arrays covariance matrix of 20 dimensions and the 20 inner array covariance matrixes tieed up carry out inversion operation ³), then total computation complexity is O (20 ³+ 20 ³)=O (2 (20) ³), and the sample matrix inversion method of prior art needs to carry out inversion operation to the covariance matrix of 400 dimensions, its computation complexity is O (400 ³).Obviously O (2 (20) is had ³) < < O (400 ³), namely computation complexity of the present invention is well below the computation complexity of the sample matrix inversion method of prior art, greatly saves calculated amount.

Fig. 3 is that the present invention and prior art sample matrix inversion method export Signal to Interference plus Noise Ratio with input signal-to-noise ratio change curve, and horizontal ordinate represents input signal-to-noise ratio, and ordinate represents output Signal to Interference plus Noise Ratio, and physical unit is dB.As seen from Figure 3, along with the increase of input signal-to-noise ratio, more higher than sample matrix inversion method of output Signal to Interference plus Noise Ratio of the present invention, performance improvement is more obvious.Along with the increasing of signal energy, sample matrix inversion method directly calculates with the covariance matrix of full dimension, echo signal can be caused to offset, serious reduction exports Signal to Interference plus Noise Ratio, and the present invention adopts the decomposed form of wave filter weight vector to approach optimum solution, when signal energy is larger, still can obtains higher output Signal to Interference plus Noise Ratio, exceed about 15dB than sample matrix inversion method.

Fig. 4 is the curve map that the sample matrix inversion method of the present invention and prior art exports Signal to Interference plus Noise Ratio and changes with sample number, and horizontal ordinate represents sample number, and ordinate represents output Signal to Interference plus Noise Ratio, and physical unit is dB.As seen from Figure 4, the present invention starts when sample number is 100 close to convergence, and sample matrix inversion method is when sample number reaches 1000, just starts close to convergence.In actual applications, the usual Rapid Variable Design of interference environment, thousands of independent same distribution samples are difficult to obtain usually, and therefore the application of sample matrix inversion method is restricted, and the present invention only needs up to a hundred independent same distribution samples can obtain premium properties, be more suitable for applying in practice.

Fig. 5 is that the wave filter weight vector that the sample matrix inversion method of the present invention and prior art is tried to achieve is spent to the beam pattern within the scope of 90 degree-90, horizontal ordinate represents angle, physical unit is degree, ordinate represents that radar antenna array exports normalized power, physical unit is dB, solid line represents the present invention, and dotted line represents the sample matrix inversion method of prior art, and arrow represents interference radiating way.As seen from Figure 5, because the present invention adopts circulation associating self-adaptive processing, beam pattern forms lower secondary lobe, reaches about-30dB, is conducive to the suppression to interference and noise.And sample matrix inversion method adopts full dimension covariance matrix to calculate, echo signal can be caused to offset, and therefore the beam pattern secondary lobe of sample matrix inversion method is higher, is about-15dB, is unfavorable for the suppression to interference and noise.

Shown by above simulation result: the present invention is owing to have employed Antenna Subarray Division and circulation Method for minimization, original radar antenna array is divided into the nested form of outer arrays and inner array, and circulation associating self-adaptive processing outer arrays and inner array, thus effectively reduce the demand of independent same distribution sample, substantially reduce computation complexity, effectively can suppress interference, filter effect is better simultaneously.

Claims (3)

1., based on a circulation associating Adaptive beamformer method for Subarray partition, comprise the steps:

(1) Subarray partition:

To multiple radar antenna array element, p array element is wherein chosen as a submatrix according to the divided dose order of element number of array N, form M=N/p submatrix, the outer arrays obtaining being made up of M the submatrix aerial array that form nested with the inner array that p array element is formed, wherein, N represents radar antenna element number of array, and p represents that the array number that the submatrix of radar antenna array comprises, M represent the submatrix number of radar antenna array;

(2) steering vector is obtained:

Adopt steering vector formula, calculate radar target signal guide vector, outer aerial array steering vector and internal layer aerial array steering vector respectively;

(3) the direct product decomposition of steering vector:

By radar target signal guide vector, be decomposed into the direct product of outer aerial array steering vector and internal layer aerial array steering vector;

(4) cost function is set up:

According to linearly constrained minimum variance, set up the cost function of outer aerial array weight vector corresponding to outer aerial array steering vector and internal layer aerial array weight vector corresponding to internal layer aerial array steering vector;

(5) weight vector is solved:

(5a) the iterative initial value vector of outer aerial array weight vector according to the following formula, is set:

$v_0=a_m^{*}/\left|\right|a_m^{*}\left|\right|$

Wherein, v ₀represent the iterative initial value vector of outer aerial array weight vector, a _mrepresent outer aerial array steering vector, * represents conjugate operation, || || represent and get two norm operations;

(5b) set ε as stopping iteration parameter, the span of ε be 0 < ε < < 1, < < represent much smaller than;

(5c) the iterative initial value vector of internal layer aerial array weight vector according to the following formula, is calculated:

$u_0=\frac{R_0^{-1}{s}_0}{s_0^H{R}_0^{-1}{s}_0}$

Wherein, u ₀represent the iterative initial value vector of internal layer aerial array weight vector, represent the sample estimated matrix of internal layer antenna array receiver data covariance matrix, v represents outer aerial array weight vector, and L represents sample number, X _irepresent i-th sample, represent the coefficient vector of internal layer aerial array, a _prepresent internal layer aerial array steering vector, a _mrepresent outer aerial array steering vector, H represents conjugate transposition operation, () ^-1represent and get inverse operation;

(5d) the iteration vector of outer aerial array weight vector according to the following formula, is calculated:

$v_1=\frac{R_1^{-1}{s}_1}{s_1^H{R}_1^{-1}{s}_1}/\left|\right|\frac{R_1^{-1}{s}_1}{s_1^H{R}_1^{-1}{s}_1}\left|\right|$

Wherein, v ₁represent the iteration vector of outer aerial array weight vector, represent the sample estimated matrix of outer antenna array receiver data covariance matrix, u represents internal layer aerial array weight vector, represent the coefficient vector of outer aerial array, H represents conjugate transposition operation, () ^-1represent and get inverse operation, || || represent and get two norm operations;

(5e) the iteration vector v of outer aerial array weight vector is judged ₁with the iterative initial value vector v of outer aerial array weight vector ₀difference v ₁-v ₀, whether meet the stopping iterated conditional of following formula, if meet, iteration ends, obtain the iteration vector of outer aerial array weight vector as outer aerial array weight vector, the iterative initial value vector of internal layer aerial array weight vector is as internal layer aerial array weight vector; If do not meet, by the iteration vector v of outer aerial array weight vector ₁as the iterative initial value vector v of new outer aerial array weight vector ₀perform step (5c), stop iterated conditional until meet, iteration ends, obtain the iteration vector of outer aerial array weight vector as outer aerial array weight vector, the iterative initial value vector of internal layer aerial array weight vector is as internal layer aerial array weight vector;

||v ₁-v ₀||≤ε

Wherein, v ₁and v ₀represent the iteration vector iterative initial value vector of outer aerial array weight vector respectively, ε represents stopping iteration parameter, the span of ε is 0 < ε < < 1, || || represent get two norms operation, < < represent much smaller than;

(6) Wave beam forming:

Outer aerial array weight vector and internal layer aerial array weight vector are done operation of direct product, obtain wave filter weight vector, with wave filter weight vector, summation is weighted to the data vector that radar receives, make the output power of radar antenna array minimum, form main beam in expectation target direction, complete Wave beam forming.

2. the associating of the circulation based on Subarray partition Adaptive beamformer method according to claim 1, it is characterized in that, the steering vector formula described in step (2) is as follows:

Radar target signal guide vector formulas is as follows:

$a_n={\&lsqb;1,e^{j\frac{2\mathrm{\&pi;}dsin\mathrm{\&theta;}}{\mathrm{\&lambda;}}},e^{j\frac{2\mathrm{\&pi;}2dsin\mathrm{\&theta;}}{\mathrm{\&lambda;}}},...,e^{j\frac{2\mathrm{\&pi;}(N-1)dsin\mathrm{\&theta;}}{\mathrm{\&lambda;}}}\&rsqb;}^T$

Wherein, a _nrepresent radar target signal guide vector, j represents imaginary unit, and d represents radar antenna array array element distance, θ represents radar target direction, and sin represents and does sinusoidal operation, and λ represents the operation wavelength of radar, N represents radar antenna element number of array, and T represents matrix transpose operation;

Outer aerial array steering vector formula is as follows:

$a_m={\&lsqb;1,e^{j\frac{2\mathrm{\&pi;}pdsin\mathrm{\&theta;}}{\mathrm{\&lambda;}}},e^{j\frac{2\mathrm{\&pi;}2pdsin\mathrm{\&theta;}}{\mathrm{\&lambda;}}},...,e^{j\frac{2\mathrm{\&pi;}\left(M-1\right)pdsin\mathrm{\&theta;}}{\mathrm{\&lambda;}}}\&rsqb;}^T$

Wherein, a _mrepresent outer aerial array steering vector, j represents imaginary unit, d represents radar antenna array array element distance, θ represents radar target direction, sin represents and does sinusoidal operation, and λ represents the operation wavelength of radar, and p represents the array number that the submatrix of radar antenna array comprises, M represents the submatrix number of radar antenna array, and T represents matrix transpose operation;

Internal layer aerial array steering vector formula is as follows:

$a_p={\&lsqb;1,e^{j\frac{2\mathrm{\&pi;}dsin\mathrm{\&theta;}}{\mathrm{\&lambda;}}},e^{j\frac{2\mathrm{\&pi;}2dsin\mathrm{\&theta;}}{\mathrm{\&lambda;}}},...,e^{j\frac{2\mathrm{\&pi;}(p-1)dsin\mathrm{\&theta;}}{\mathrm{\&lambda;}}}\&rsqb;}^T$

Wherein, a _prepresent internal layer aerial array steering vector, j represents imaginary unit, and d represents radar antenna array array element distance, θ represents radar target direction, and sin represents and does sinusoidal operation, and λ represents the operation wavelength of radar, p represents the array number that the submatrix of radar antenna array comprises, and T represents matrix transpose operation.

3. the associating of the circulation based on Subarray partition Adaptive beamformer method according to claim 1, it is characterized in that, the cost function described in step (4) is as follows:

$\left\{\begin{array}{cc}\min & f\left(u,v\right)=E\left|\right|u^{H}Xv|{|}^2\\ s.t.& u^H{a}_p{a}_m^{T}v=1\end{array}\right.$

Wherein, when min represents that target signal direction gain constant is expected in guarantee, radar antenna array output power is made to minimize operation, f (u, v) represent radar antenna array output power, u represents internal layer aerial array weight vector, and v represents outer aerial array weight vector, E represents and asks desired operation, || || represent and get two norm operations, H represents conjugate transposition operation, and X represents radar antenna array data matrix, s.t. represent and get constraint manipulation, a _prepresent internal layer aerial array steering vector, a _mrepresent outer aerial array steering vector, T represents matrix transpose operation.