CN103885045A - Sub-array division based circulation combined adaptive beam forming method - Google Patents

Abstract

The invention discloses a sub-array division based circulation combined adaptive beam forming method and solves the problems of the large independent identically distributed sample demanded quantity, the high calculation complexity and the poor filter effect during a large amount of interference during large-scale radar antenna array beam forming. The method is implemented through the steps of (1) sub-array division; (2) steering vector obtaining; (3) direct product decomposition of steering vectors; (4) cost function establishing; (5) weight vector solving; (6) beam forming. Compared with the beam forming method in the prior art, the forming method has the advantages of being good in inhibitory effect on interference, small in required sample number and fast in iteration convergence. The forming method can be applied to radar beam forming in the situation that the radar antenna array scale is large, the number of training samples is small and the amount of interference is large.

Description

Circulation associating adaptive beam formation method based on 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 beam formation 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 disturb the wave beam under the susceptible condition of number to form problem.

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 caused people's extensive attention and research interest, and this has further accelerated the development of this technology.Adaptive beam forms, and also referred to as Spatially adaptive filtering, processes by space array element being weighted to be added at receiving end, suppresses space and disturbs and noise, strengthens useful signal, with the Output rusults that obtains expecting.The method that self-adaptation solves the optimum power of array element is called Beamforming Method.At present, the beam-forming technology often using is the sampling matrix method of inverting.The method according to linearly constrained minimum variance (in the situation that guaranteeing to expect sense gain constant, make array element receive the energy minimum of data) to set up cost function and use method of Lagrange multipliers to solve wave filter weight vector, array element receives the covariance matrix of data and is estimated to obtain by multiple independent identically distributed sampled datas.Scientific research shows, in order to make the sampling matrix method of inverting bring into play optimum performance, the independent same distribution sample number needing should be greater than the twice of covariance matrix dimension, and in actual applications, interference environment changes conventionally fast, and available independent same distribution sample number is limited.In addition, the sampling matrix method of inverting need to be inverted 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 large-scale phased array may reach hundreds and thousands of even up to ten thousand, if take the sampling matrix method of inverting, the independent same distribution sample number and the computation complexity that not only need are huge, and the equipment amount, the memory space that need are also very big, and it is also unnecessary in engineering, cannot to realize.Equally, existing some other Beamforming Method, when for large scale array, is also faced with similar problem.

Patent " the ultralow secondary lobe adaptive digital of digital array the Beamforming Method " (number of patent application: 201210002661 of Hohai University's application, publication No.: CN102608580A), the ultralow secondary lobe adaptive digital of a kind of digital array Beamforming Method is disclosed.First the method estimates interference radiating way, then builds and disturbs secondary beam to carry out spatial domain dimension-reduction treatment, last calculating beamforming device weights.The method has good ultralow secondary lobe wave beam conformal ability, and training sample demand is little, but the deficiency that the method still exists is need to estimate in advance interference radiating way, in the time disturbing number more, estimate that multiple interference need 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 associating of the circulation based on Subarray partition adaptive beam formation method.The method can reduce the demand of independent same distribution sample effectively, and reduces computation complexity, can effectively suppress interference simultaneously, thereby solves the wave beam formation problem of extensive radar antenna array.

Realization approach of the present invention is: first, radar antenna array is divided into multiple subarrays; Then, calculate radar target signal guide vector, outer aerial array steering vector and internal layer aerial array steering vector; Then, radar target signal guide vector is carried out to the direct product decomposition, and adopt 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 formation.

Concrete steps of the present invention are as follows:

(1) Subarray partition:

To multiple radar antenna array element, choose p array element wherein as a submatrix according to the divided dose order of element number of array N, form M=N/p submatrix, the nested aerial array forming of internal layer array that the outer array that obtains being made up of M submatrix forms with p array element, wherein, N represents radar antenna element number of array, and p represents the array number that the submatrix of radar antenna array comprises, and M represents the submatrix number of radar antenna array.

(2) obtain steering vector:

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

(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) set up cost function:

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

(5) solve weight vector:

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

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

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 to get two norm operations;

(5b) establish ε for stopping iteration parameter, the span of ε is 0 < ε < < 1, < < represent much smaller than;

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

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

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

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

$v_1=\frac{R_1^{-1}{s}_1}{s_1^H{R}_1^{-1}{s}_1}/\left|\right|\frac{R_1^{-1}{s}_1}{s_1^H{R}_1^{-1}{\mathrm{<figure-callout\; id="1"\; label="s"\; filenames="HDA0000488707560000021.png"\; state="\{\{state\}\}">s</figure-callout>}}_1}\left|\right|$

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

(5e) judge the iteration vector v of outer aerial array weight vector ₁iterative initial value vector v with outer aerial array weight vector ₀difference v ₁-v ₀, whether meet the iterated conditional that stops of following formula, if meet, iteration stops, and obtains 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 ₀execution step (5c), stops iterated conditional until meet, and iteration stops, 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 ₀the iteration vector iterative initial value vector that represents respectively outer aerial array weight vector, ε represents to stop iteration parameter, and the span of ε is 0 < _ε< < 1, || || represent to get two norms operations, < < represent much smaller than.

(6) wave beam forms:

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

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

First, because the present invention has adopted the method for Subarray partition, original radar antenna array is divided into the nested form of outer array and internal layer array, overcome prior art to the large problem of independent same distribution sample demand, make the present invention there is effective reduction sample demand, under condition of small sample, still can obtain the advantage of premium properties.

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

The 3rd, because the present invention has adopted circulation Method for minimization, the outer array of circulation associating self-adaptive processing and internal layer array, overcome prior art large and disturb the poor problem of number filter effect of many times in radar antenna array scale, the radar antenna array beam pattern that the present invention is 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 sampling matrix are inverted method output Signal to Interference plus Noise Ratio with input signal-to-noise ratio change curve;

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

Fig. 5 is the present invention and the prior art sampling matrix method of the inverting wave filter weight vector of trying to achieve at-90 degree to the beam pattern within the scope of 90 degree.

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, choose p array element wherein as a submatrix according to the divided dose order of element number of array N, form M=N/p submatrix, the nested aerial array forming of internal layer array that the outer array that obtains being made up of M submatrix forms with p array element, wherein, N represents radar antenna element number of array, and p represents the array number that the submatrix of radar antenna array comprises, and M represents the submatrix number of radar antenna array.

Step 2, obtains steering vector.

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

Radar target signal guide vector formulas is as follows:

$a_n={[1,e^{\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000488707560000021.png"\; state="\{\{state\}\}">j</figure-callout>}\frac{2\mathrm{\&pi;}d\sin \mathrm{\&theta;}}{\mathrm{\&lambda;}}},e^{\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000488707560000021.png"\; state="\{\{state\}\}">j</figure-callout>}\frac{2\mathrm{\&pi;}2d\sin \mathrm{\&theta;}}{\mathrm{\&lambda;}}},...,e^{\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000488707560000021.png"\; state="\{\{state\}\}">j</figure-callout>}\frac{2\mathrm{\&pi;}(N-1)d\sin \mathrm{\&theta;}}{\mathrm{\&lambda;}}}]}^T$

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 to do 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:

$a_m={[1,{\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="HDA0000488707560000021.png"\; state="\{\{state\}\}">e</figure-callout>}}^j,e^{\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000488707560000021.png"\; state="\{\{state\}\}">j</figure-callout>}\frac{2\mathrm{\&pi;}2\mathrm{pd}\sin \mathrm{\&theta;}}{\mathrm{\&lambda;}}},...,{\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="HDA0000488707560000021.png"\; state="\{\{state\}\}">e</figure-callout>}}^j]}^T$

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 to do 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:

$a_p={[1,e^{\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000488707560000021.png"\; state="\{\{state\}\}">j</figure-callout>}\frac{2\mathrm{\&pi;}d\sin \mathrm{\&theta;}}{\mathrm{\&lambda;}}},e^{\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000488707560000021.png"\; state="\{\{state\}\}">j</figure-callout>}\frac{2\mathrm{\&pi;}2d\sin \mathrm{\&theta;}}{\mathrm{\&lambda;}}},...,e^{\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000488707560000021.png"\; state="\{\{state\}\}">j</figure-callout>}\frac{2\mathrm{\&pi;}(p-1)d\sin \mathrm{\&theta;}}{\mathrm{\&lambda;}}}]}^T$

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 to do 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 to the definition to direct product in matrix theory, 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 (in the situation that guaranteeing to expect target signal direction gain constant, make the output power minimum of radar antenna array), set up the cost function of the internal layer aerial array weight vector that outer aerial array weight vector that outer aerial array steering vector is corresponding and internal layer aerial array steering vector are corresponding.

Suppose that radar antenna array is the even linear array being made up of N array element, array element distance is half wavelength, and there are 1 echo signal and J undesired signal in space, and 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 N × (1+J) matrix of dimension that the steering vector of echo signal and undesired signal forms, s (t) represents that the t moment receives signal amplitude vector, the white Gaussian noise vector that n (t) the expression t moment receives.After radar antenna array reception data are sampled, the sampled 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, min represents to guarantee to expect in the situation of target signal direction gain constant, 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 to ask expectation computing, || || represent to get two norm operations, * represent conjugate operation

represent direct product, H represents conjugate transpose operation, and x represents radar antenna array sampled data vector, and s.t. represents to get constraint manipulation, a _mrepresent outer aerial array steering vector, a _prepresent internal layer aerial array steering vector.

By x being lined up to 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, min represents to guarantee to expect, in the situation of target signal direction gain constant, to make radar antenna array output power 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 to ask expectation computing, || || represent to get two norm operations, H represents conjugate transpose operation, and X represents radar antenna array sampled data matrix, s.t. represent to 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 is introduced 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 that internal layer aerial array receives the sample estimated matrix of data covariance matrix, L represents number of samples, X _irepresent i 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:

$u=\frac{R_0^{-1}{s}_0}{s_0^H{R}_0^{-1}{\mathrm{<figure-callout\; id="0"\; label="s"\; filenames="HDA0000488707560000022.png,HDA0000488707560000032.png"\; state="\{\{state\}\}">s</figure-callout>}}_0}$

Wherein, u represents internal layer aerial array weight vector,

represent the coefficient vector of internal layer aerial array, H represents conjugate transpose operation, () ^-1represent to get inverse operation.

Suppose that again internal layer aerial array weight vector u is known, 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 that outer aerial array receives the sample estimated matrix of data covariance matrix, * represents conjugate operation, and H represents conjugate transpose operation, and T represents matrix transpose operation.

Order can obtain outer aerial array weight vector is:

$v=\frac{R_1^{-1}{s}_1}{s_1^H{R}_1^{-1}{\mathrm{<figure-callout\; id="1"\; label="s"\; filenames="HDA0000488707560000021.png"\; state="\{\{state\}\}">s</figure-callout>}}_1}$

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

there is following relation:

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

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

Described circulation Method for minimization, carry out as follows:

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

${\mathrm{<figure-callout\; id="0"\; label="v"\; filenames="HDA0000488707560000022.png,HDA0000488707560000032.png"\; state="\{\{state\}\}">v</figure-callout>}}_0=a_m^{*}/\left|\right|a_m^{*}\left|\right|$

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 to get two norm operations;

(5b) establish ε for stopping iteration parameter, the span of ε is 0 < ε < < 1, < < represent much smaller than;

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

${\mathrm{<figure-callout\; id="0"\; label="u"\; filenames="HDA0000488707560000022.png,HDA0000488707560000032.png"\; state="\{\{state\}\}">u</figure-callout>}}_0=\frac{R_0^{-1}{s}_0}{s_0^H{R}_0^{-1}{\mathrm{<figure-callout\; id="0"\; label="s"\; filenames="HDA0000488707560000022.png,HDA0000488707560000032.png"\; state="\{\{state\}\}">s</figure-callout>}}_0}$

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

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

${\mathrm{<figure-callout\; id="1"\; label="v"\; filenames="HDA0000488707560000021.png"\; state="\{\{state\}\}">v</figure-callout>}}_1=\frac{R_1^{-1}{s}_1}{s_1^H{R}_1^{-1}{\mathrm{<figure-callout\; id="1"\; label="s"\; filenames="HDA0000488707560000021.png"\; state="\{\{state\}\}">s</figure-callout>}}_1}/\left|\right|\frac{R_1^{-1}{s}_1}{s_1^H{R}_1^{-1}{\mathrm{<figure-callout\; id="1"\; label="s"\; filenames="HDA0000488707560000021.png"\; state="\{\{state\}\}">s</figure-callout>}}_1}\left|\right|$

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

(5e) judge the iteration vector v of outer aerial array weight vector ₁iterative initial value vector v with outer aerial array weight vector ₀difference v ₁-v ₀, whether meet the iterated conditional that stops of following formula, if meet, iteration stops, and obtains 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 ₀execution step (5c), stops iterated conditional until meet, and iteration stops, 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 respectively the iteration vector iterative initial value vector of outer aerial array weight vector, ε represents to stop iteration parameter, the span of ε is 0 < ε < < 1, || || represent to get two norms operations, < < represent much smaller than.

Step 6, wave beam forms.

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

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 are [80-70-60-50-40-30-20-101020304050607080] degree, dry making an uproar than being 40dB.When Subarray partition, choose successively 20 array elements as a submatrix.

2. emulation content

Emulation 1: the present invention chooses 800 samples, is used the circulation Method for minimization adopting while solving weight vector in the present invention to carry out emulation, and output Signal to Interference plus Noise Ratio is added up, an iteration convergence curve of the Method for minimization that finally obtains circulating, as shown in Figure 2.

Emulation 2: the present invention chooses 800 samples, use respectively invert method and two kinds of methods of the present invention of the sampling matrix of prior art to carry out emulation, output Signal to Interference plus Noise Ratio under two kinds of methods is added up, finally obtain exporting two curves that Signal to Interference plus Noise Ratio changes with input signal-to-noise ratio, two curves of inverting as indicated the present invention and sampling matrix in Fig. 3.

Emulation 3: the present invention is in the time that input Signal to Interference plus Noise Ratio is 40dB, use respectively invert method and two kinds of methods of the present invention of the sampling matrix of prior art to carry out emulation, output Signal to Interference plus Noise Ratio under two kinds of methods is added up, finally obtain exporting two curves that Signal to Interference plus Noise Ratio changes with sample number, two curves of inverting as indicated the present invention and sampling matrix in Fig. 4.

Emulation 4: the present invention is 800 at sample number, signal to noise ratio (S/N ratio) is-when 20dB, use respectively invert method and two kinds of methods of the present invention of the sampling matrix of prior art to carry out emulation, radar antenna array output normalized power under two kinds of methods is added up, finally obtain two kinds of beam patterns under method, 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 to export Signal to Interference plus Noise Ratio, and physical unit is dB.As seen from Figure 2, in the time that 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, because the computation complexity that N dimension covariance matrix is carried out to inversion operation is O (N ³), the computation complexity that therefore the internal layer array covariance matrixes of the outer array covariance matrix of the present invention to 20 dimensions and 20 dimensions carry out inversion operation is O (20 ³), total computation complexity is O (20 ³+ 20 ³)=O (2 (20) ³), and the sampling matrix method of inverting of prior art need to be carried out inversion operation to the covariance matrix of 400 dimensions, its computation complexity is O (400 ³).Obviously there is O (2 (20) ³) < < O (400 ³), computation complexity of the present invention, well below the invert computation complexity of method of the sampling matrix of prior art, has been saved calculated amount greatly.

Fig. 3 is that the present invention and prior art sampling matrix are inverted method output 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 to export 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, output Signal to Interference plus Noise Ratio of the present invention is than sampling matrix high more of method that invert, and performance improvement is more obvious.Along with the increasing of signal energy, the sampling matrix method of inverting is directly calculated with the covariance matrix of full dimension, can cause echo signal to offset, the serious output Signal to Interference plus Noise Ratio that reduces, and the present invention adopts the decomposed form of wave filter weight vector to approach optimum solution, in the time that signal energy is larger, still can obtain higher output Signal to Interference plus Noise Ratio, exceed 15dB left and right than the sampling matrix method of inverting.

Fig. 4 is that the sampling matrix of the present invention and the prior art method of inverting is exported the curve map that Signal to Interference plus Noise Ratio changes with sample number, and horizontal ordinate represents sample number, and ordinate represents to export Signal to Interference plus Noise Ratio, and physical unit is dB.As seen from Figure 4, the present invention is within 100 o'clock, to start to approach convergence at sample number, and the sampling matrix method of inverting reaches at 1000 o'clock at sample number, just starts to approach convergence.In actual applications, interference environment conventionally fast changes, and thousands of independent same distribution samples are difficult to obtain conventionally, and therefore the invert application of method of sampling matrix 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 the sampling matrix method of inverting of the present invention and the prior art wave filter weight vector of trying to achieve at-90 degree to the beam pattern within the scope of 90 degree, horizontal ordinate represents angle, physical unit is degree, ordinate represents radar antenna array output normalized power, physical unit is dB, solid line represents the present invention, and dotted line represents the sampling matrix of the prior art method of inverting, 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 approximately-30dB, is conducive to the inhibition to interference and noise.And the sampling matrix method of inverting adopts full dimension covariance matrix to calculate, can cause echo signal to offset, therefore the invert beam pattern secondary lobe of method of sampling matrix is higher, is about-15dB, is unfavorable for disturbing and the inhibition of noise.

Shown by above simulation result: the present invention is owing to having adopted Antenna Subarray Division and circulation Method for minimization, original radar antenna array is divided into the nested form of outer array and internal layer array, and the outer array of circulation associating self-adaptive processing and internal layer array, thereby effectively reduce the demand of independent same distribution sample, greatly reduce computation complexity, can effectively suppress to disturb, filter effect is better simultaneously.

Claims (3)

1. the associating of the circulation based on a Subarray partition adaptive beam formation method, comprises the steps:

(1) Subarray partition:

To multiple radar antenna array element, choose p array element wherein as a submatrix according to the divided dose order of element number of array N, form M=N/p submatrix, the nested aerial array forming of internal layer array that the outer array that obtains being made up of M submatrix forms with p array element, wherein, N represents radar antenna element number of array, and p represents the array number that the submatrix of radar antenna array comprises, and M represents the submatrix number of radar antenna array;

(2) obtain steering vector:

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

(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) set up cost function:

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

(5) solve weight vector:

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

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

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 to get two norm operations;

(5b) establish ε for stopping iteration parameter, the span of ε is 0 < ε < < 1, < < represent much smaller than;

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

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

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

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

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

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

(5e) judge the iteration vector v of outer aerial array weight vector ₁iterative initial value vector v with outer aerial array weight vector ₀difference v ₁-v ₀, whether meet the iterated conditional that stops of following formula, if meet, iteration stops, and obtains 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 ₀execution step (5c), stops iterated conditional until meet, and iteration stops, 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 respectively the iteration vector iterative initial value vector of outer aerial array weight vector, ε represents to stop iteration parameter, the span of ε is 0 < ε < < 1, || || represent to get two norms operations, < < represent much smaller than;

(6) wave beam forms:

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

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

Radar target signal guide vector formulas is as follows:

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

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 to do 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:

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

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 to do 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 to do 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 circulation based on the Subarray partition according to claim 1 associating adaptive beam method of formationing, is characterized in that, the cost function described in step (4) is as follows:

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

Wherein, min represents to guarantee to expect, in the situation of target signal direction gain constant, to make radar antenna array output power 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 to ask desired operation, || || represent to get two norm operations, H represents conjugate transpose operation, and X represents radar antenna array data matrix, s.t. represent to get constraint manipulation, a _prepresent internal layer aerial array steering vector, a _mrepresent outer aerial array steering vector, T represents matrix transpose operation.

Images