CN104270178A - Broadband adaptive array cross-coupling compensation method - Google Patents

Abstract

The invention discloses a broadband adaptive array cross-coupling compensation method. According to the method, the relation between two directional diagrams is set up, and the directional diagrams in an array when all array elements exist are changed into isolated directional diagrams when the signal array element exists; data of multiple angles are extracted from the directional diagrams, and it is supposed that M directions are selected; polynomials related to frequency are selected, and then polynomial functions are constructed and fitted; by calculating cross-coupling compensation matrixes on multiple frequency points, a plurality of sampling values, on the frequency, of the cross-coupling compensation matrixes are obtained; by means of a compound curve fitting method, change functions or curves of all elements of the cross-coupling compensation matrixes along with the frequency are fitted; a frequency band is divided, and then compound curve fitting is carried out on the elements of the cross-coupling compensation matrixes on each frequency band section. According to the method, only a small number of polynomial coefficients need to be stored, the requirement for the system storage capacity is reduced, and a good cross-coupling compensation effect can be obtained on any frequency point in the frequency band.

Description

The compensation method of a kind of wideband adaptive array mutual coupling

Technical field

The invention belongs to adaptive antenna array scheme field, be specially the compensation method of a kind of wideband adaptive array mutual coupling.

Background technology

At present, Wide band array antenna obtains increasing utilization in adaptive array signal process.But some factors limit the lifting of wideband adaptive array performance, as the mutual coupling problem of array.Array mutual coupling is particularly evident in the low-frequency range performance of wideband adaptive array, and this is mainly in low-frequency range, and array element distance is less relative to wavelength, and mutual coupling effect is more obvious.The adverse effect caused thus comprises: weighting vector estimated bias increases, Adaptive beamformer departs from actual direction, adaptive nulling departs from actual direction or adaptive nulling level is raised.

Under above background, the present invention proposes a kind of mutual coupling calibration steps of wideband adaptive array.In the method, the all elements multinomial analytical expression of the mutual coupling compensation matrix of wideband adaptive array is showed, the mutual coupling compensation matrix of frequency arbitrarily in frequency band can be obtained easily, reduce the requirement to system memory size, good mutual coupling compensation effect can be obtained simultaneously on any frequency.The thinking proposing the method is as follows: first, in given directions, the amplitude of Received signal strength and the directional diagram of antenna are directly proportional; Secondly, single array element isolates the impact not having mutual coupling when existing, and when array element is arranged in aerial array, will there is mutual coupling, in the change of the present antenna pattern of body of mutual coupling; Directional diagram converter technique adopts transformation matrix (or mutual coupling compensation matrix) by directional diagram when directional diagram is transformed to isolated in the battle array of antenna, and now, the signal after conversion is just equivalent to the Received signal strength of isolated antenna; Then, for the reception of broadband signal, adopt compound curve fitting process that all elements in transformation matrix is carried out matching on frequency band, obtain the analytical function of matrix element about frequency, so just can obtain the transformation matrix on any frequency.If frequency band is wider, adopts the multinomial of higher-order number still can not obtain good fitting effect, then frequency range can be divided, then in each frequency range, respectively compound curve matching be carried out to mutual coupling compensation entry of a matrix element.

Summary of the invention

In order to solve mutual coupling compensation in wideband adaptive array or calibration problem, the invention provides the compensation method of a kind of wideband adaptive array mutual coupling, for any operating frequency, the value on corresponding frequency can be calculated according to each element of mutual coupling compensation matrix with the change function of frequency, thus obtains the mutual coupling compensation matrix on corresponding frequency.Its technical scheme and step are:

(1) set up antenna element and isolate relation in directional diagram and battle array between directional diagram namely:

In formula, with directional diagram in isolated directional diagram respectively during representative antennas unit individualism and the battle array of antenna element, Matrix C represents mutual coupling compensation matrix, carrys out the mutual coupling of compensated array with it.In equation, the amplitude of electric field and phase place all will be considered;

(2) in order to calculate mutual coupling compensation Matrix C accurately, needing to extract pattern data from different perspectives, supposing to have chosen M direction, having

By least-mean-square-error criterion,

$\underset{\left|\right|\mathrm{CE}-E^i\left|\right|}{\min }\left|\right|C\left|\right|---\left(3\right)$

The least square solution of above equation can be obtained, namely

C＝E ⁱE ^H(EE ^H) ^-1 (4)

In formula, E ⁱrepresent electric field during array element individualism, E represents electric field when array element all exists, symbol || || the 2-norm of representing matrix; Mutual coupling compensation Matrix C can be tried to achieve by above formula, obtains mutual coupling compensation matrix, and just it can be applied in array mutual coupling compensation, suppose that the sampling matrix of Received signal strength is X ', the array signal sampling matrix so after mutual coupling compensation can be expressed as

X＝CX； (5)

(3) multinomial with frequency dependence is chosen, namely

$G\left(\mathrm{jw}\right)=\frac{A_0+A_1\left(\mathrm{jw}\right)+A_2{\left(\mathrm{jw}\right)}^2+A_3{\left(\mathrm{jw}\right)}^3+...}{B_0+B_1\left(\mathrm{jw}\right)+B_2{\left(\mathrm{jw}\right)}^2+B_3{\left(\mathrm{jw}\right)}^3+...}---\left(6\right)$

And then structure fit polynomial function.

(4) for wideband array, by calculating the mutual coupling compensation matrix on multiple frequency, the multiple sampled values of mutual coupling compensation matrix in frequency are obtained

(5) by compound curve approximating method, each element of mutual coupling compensation matrix is simulated with the change function of frequency or curve.

(6) if frequency band is wider, adopt the multinomial of higher-order number still can not obtain good fitting effect, then frequency range can be divided, then in each frequency range, respectively compound curve matching be carried out to mutual coupling compensation entry of a matrix element.

Compared with prior art, beneficial effect of the present invention is:

The first, decrease the requirement of wideband adaptive array mutual coupling compensation to memory capacity.Because mutual coupling compensation matrix is with frequency change, so the mutual coupling compensation matrix of wideband array needs to store a large amount of data, high to the storage capacity requirement of system.Mutual Coupling Compensation Method proposed by the invention, the form of the mutual coupling compensation matrix element analytical expression of wideband adaptive array is showed, what need storage is only a small amount of multinomial coefficient, decrease the requirement to capacity, and the acquisition of mutual coupling compensation matrix is very simple, only need the frequency of Received signal strength to substitute into formula.

The second, good mutual coupling compensation can be obtained in broadband.According to the function of matching each element out with frequency change, obtain the calibration matrix on corresponding frequency, the directional diagram of the mutual coupling compensation matrix correction array then obtained, directional diagram when isolating with array element contrasts, in the groundwork angular range of array, the directional diagram when directional diagram after compensation and array individualism coincide good, that is can carry out good mutual coupling compensation to received signal by mutual coupling compensation matrix from the signal of the groundwork angular range incidence of array.

Accompanying drawing explanation

Fig. 1 is flow chart of the present invention;

Fig. 2 is circle ring array array element schematic diagram;

Fig. 3 is circle ring array array element voltage standing wave ratio figure;

Fig. 4 is for being uniformly distributed eight yuan of circle ring array schematic diagrames;

Fig. 5 is ring array array element voltage standing wave ratio figure in an array;

Fig. 6 is that the present invention is to the amplitude curve fitted figure of equally distributed eight yuan of circle ring array mutual coupling compensation matrix element C11 at 200M ~ 343MHZ;

Fig. 7 be the present invention to equally distributed eight yuan of circle ring array mutual coupling compensation matrix element C11 in 200M ~ 343MHZ phase curve fitted figure;

Fig. 8 be the present invention to equally distributed eight yuan of circle ring array mutual coupling compensation matrix element C11 in 343M ~ 500MHZ amplitude curve fitted figure;

Fig. 9 be the present invention to equally distributed eight yuan of circle ring array mutual coupling compensation matrix element C11 in 343M ~ 500MHZ phase curve fitted figure;

Figure 10 is that the present invention is to the amplitude curve fitted figure of equally distributed eight yuan of circle ring array mutual coupling compensation matrix element C12 at 200M ~ 343MHZ;

Figure 11 be the present invention to equally distributed eight yuan of circle ring array mutual coupling compensation matrix element C12 in 200M ~ 343MHZ phase curve fitted figure;

Figure 12 be the present invention to equally distributed eight yuan of circle ring array mutual coupling compensation matrix element C12 in 343M ~ 500MHZ amplitude curve fitted figure;

Figure 13 be the present invention to equally distributed eight yuan of circle ring array mutual coupling compensation matrix element C12 in 343M ~ 500MHZ phase curve fitted figure;

Figure 14 is that the present invention is to the amplitude curve fitted figure of equally distributed eight yuan of circle ring array mutual coupling compensation matrix element C13 at 200M ~ 343MHZ;

Figure 15 be the present invention to equally distributed eight yuan of circle ring array mutual coupling compensation matrix element C13 in 200M ~ 343MHZ phase curve fitted figure;

Figure 16 be the present invention to equally distributed eight yuan of circle ring array mutual coupling compensation matrix element C13 in 343M ~ 500MHZ amplitude curve fitted figure;

Figure 17 be the present invention to equally distributed eight yuan of circle ring array mutual coupling compensation matrix element C13 in 343M ~ 500MHZ phase curve fitted figure;

Figure 18 is that the present invention is to the amplitude curve fitted figure of equally distributed eight yuan of circle ring array mutual coupling compensation matrix element C14 at 200M ~ 343MHZ;

Figure 19 be the present invention to equally distributed eight yuan of circle ring array mutual coupling compensation matrix element C14 in 200M ~ 343MHZ phase curve fitted figure;

Figure 20 be the present invention to equally distributed eight yuan of circle ring array mutual coupling compensation matrix element C14 in 343M ~ 500MHZ amplitude curve fitted figure;

Figure 21 be the present invention to equally distributed eight yuan of circle ring array mutual coupling compensation matrix element C14 in 343M ~ 500MHZ phase curve fitted figure;

Figure 22 be the present invention to equally distributed eight yuan of circle ring arrays when 200MHz to mutual coupling compensation matrix fitting curve with without the Estimation of Spatial Spectrum figure in mutual coupling compensation situation.

Figure 23 be the present invention to equally distributed eight yuan of circle ring arrays when 350MHz to mutual coupling compensation matrix fitting curve with without the Estimation of Spatial Spectrum figure in mutual coupling compensation situation.

Figure 24 be the present invention to equally distributed eight yuan of circle ring arrays when 500MHz to mutual coupling compensation matrix fitting curve with without the Estimation of Spatial Spectrum figure in mutual coupling compensation situation.

Embodiment:

Below in conjunction with the drawings and specific embodiments, technical scheme of the present invention is described further.

The basic ideas realizing the object of the invention are: first, and in given directions, the amplitude of Received signal strength and the directional diagram of antenna are directly proportional.Secondly, single array element isolates the impact not having mutual coupling when existing, and when array element is arranged in aerial array, will there is mutual coupling, in the change of the present antenna pattern of body of mutual coupling.Therefore, adopt mutual coupling compensation matrix by directional diagram when directional diagram is transformed to isolated in the battle array of antenna, now, the signal after conversion is just equivalent to the Received signal strength of isolated antenna.Then, for the reception of broadband signal, adopt compound curve fitting process that all elements in mutual coupling compensation matrix is carried out matching on frequency band, obtain the analytical function of matrix element about frequency, so just can obtain the mutual coupling compensation matrix on any frequency.If frequency band is wider, adopts the multinomial of higher-order number still can not obtain good fitting effect, then frequency range can be divided, then in each frequency range, respectively compound curve matching be carried out to mutual coupling compensation entry of a matrix element.

The present invention proposes the compensation method of a kind of wideband adaptive array mutual coupling, the mutual coupling compensation entry of a matrix element analytical expression of wideband adaptive array is showed, the requirement to system memory size can be reduced, can obtain the mutual coupling compensation matrix of frequency arbitrarily in frequency band easily, the present invention simultaneously can provide accurate mutual coupling compensation in frequency band.

Step one, sets up Array Model and parameters.

The aerial array of a N unit, each array element terminal meets Z _lload, in directional diagram transform method, two kinds of directional diagrams are that we relate to, a kind of is array element in the array directional diagram (in battle array directional diagram) when all existing, another kind is that (other array elements remove the directional diagram of single array element when existing from array, i.e. isolated directional diagram), set up the relation between this both direction figure, that is:

In formula, with directional diagram when representing array element individualism respectively and the directional diagram of array, Matrix C represents mutual coupling compensation matrix, carrys out the mutual coupling of compensated array with it.In equation, the amplitude of electric field and phase place all will be considered.

Step 2, frequency band extracts certain frequency, calculates the mutual coupling compensation matrix of all sampling frequencies.

In order to calculate mutual coupling compensation Matrix C accurately, the data of multiple angle that needs to sample from directional diagram, the groundwork angular range of cover antenna.Suppose that we have chosen M direction by each sampling frequency on frequency band, have

By solving criterion

$\underset{\left|\right|\mathrm{CE}-E^i\left|\right|}{\min }\left|\right|C\left|\right|---\left(9\right)$

The least square solution of equation can be obtained:

C＝E ⁱE ^H(EE ^H) ^-1 (10)

In formula, E ⁱrepresent electric field during array element individualism, E represents electric field when array element all exists, symbol || || 2 norms of representing matrix.The dimension of Matrix C is that the norm of N × M, C can be written as

$\left|\right|C\left|\right|={\left\{{\mathrm{\Σ}}_{n=1}^N{\mathrm{\Σ}}_{m=1}^M{\left|c_{\mathrm{nm}}\right|}^2\right\}}^{1/2}---\left(11\right)$

Wherein c _nmit is the element of Matrix C.Mutual coupling compensation Matrix C can be tried to achieve by above formula.

Step 3, structure fit polynomial function.

If fit polynomial function is

$G\left(\mathrm{jw}\right)=\frac{A_0+A_1\left(\mathrm{jw}\right)+A_2{\left(\mathrm{jw}\right)}^2+A_3{\left(\mathrm{jw}\right)}^3+...}{B_0+B_1\left(\mathrm{jw}\right)+B_2{\left(\mathrm{jw}\right)}^2+B_3{\left(\mathrm{jw}\right)}^3+...}---\left(12\right)$

Conveniently calculate, (12) formula can be deformed into the formula of following form:

$G\left(\mathrm{jw}\right)=\frac{(A_0-A_2{w}^2+A_4{w}^4-...)+\mathrm{jw}(A_1-A_3{w}^2+A_5{w}^4-...)}{(B_0-B_2{w}^2+B_4{w}^4-...)+\mathrm{jw}(B_1-B_3{w}^2+B_5{w}^4-...)}---\left(13a\right)$

$=\frac{\mathrm{\α}+\mathrm{jw\β}}{\mathrm{\σ}+\mathrm{jw\τ}}---\left(13b\right)$

$=\frac{N\left(w\right)}{D\left(w\right)}---\left(13c\right)$

Wherein w is angular frequency, gets B ₀be 1.

Suppose to have now the function F (jw) that is desirable, F (jw) is plural number, so by test the function G (jw) that obtains should sum functions F (jw) very close.Therefore have:

F(jw)＝R(w)+jI(w) (14)

ε(w)＝F(jw)-G(jw) (15a)

$=F\left(\mathrm{jw}\right)-\frac{N\left(w\right)}{D\left(w\right)}---\left(15b\right)$

Be multiplied by D (w) to (15b) both sides

D(w)ε(w)＝D(w)F(jw)-N(w) (16)

(16) the right of formula is also complex function, so can be expressed as:

D(w)ε(w)＝a(w)+jb(w) (17)

Wherein a (w) and b (w) is not only the function of frequency, also with unknowm coefficient A _iand B _irelevant, the amplitude of function or absolute value are:

|D(w)ε(w)|＝|a(w)+b(w)| (18a)

$=\sqrt{a^2\left(w\right)+b^2\left(w\right)}---\left(18b\right)$

Then determine that the value of frequency is any

|D(w _k)ε(w _k)| ²＝a ²(w _k)+b ²(w _k) (19)

Present definition E is the function defined in (19) formula, and at sampling frequency w _kupper summation, has

$E=\underset{k=0}{\overset{m}{\mathrm{\Σ}}}[a^2\left(w_k\right)+b^2\left(w_k\right)]---\left(20\right)$

In order to obtain multinomial coefficient A _iand B _i, make the value of E minimum, the expression formula from below formula (13b) ~ (17) can obtain:

$E=\underset{k=0}{\overset{m}{\mathrm{\Σ}}}[{(R_k{\mathrm{\σ}}_k-w_k{\mathrm{\τ}}_k{I}_k-{\mathrm{\α}}_k)}^2+{(w_k{\mathrm{\τ}}_k{R}_k+{\mathrm{\σ}}_k{I}_k-w_k{\mathrm{\β}}_k)}^2]---\left(21\right)$

Respectively A is asked to formula (21) below _iand B _ipartial derivative after, and make it be 0.

In equation (20), include unknowm coefficient, can be obtained by linear transformation below:

α _k＝A ₀-α _k (23a)

β _k＝A ₁-β _k (23b)

Due to B ₀=1, σ _k=B ₀-σ _k'=1-σ ' (23c)

τ _k＝B ₁-τ _k (23d)

Formula (23a) ~ (23d) is brought in formula (22) and can obtain:

$\begin{array}{c}\underset{k=0}{\overset{m}{\mathrm{\Σ}}}+A_0-{{\mathrm{\α}}_k}^{\′}+R_k{{\mathrm{\σ}}_k}^{\′}+w_k{I}_k{B}_1-w_k{I}_k{{\mathrm{\τ}}_k}^{\′}=\underset{k=0}{\overset{m}{\mathrm{\Σ}}}{R}_k\\ \underset{k=0}{\overset{m}{\mathrm{\Σ}}}{w_k}^2(A_1-{{\mathrm{\β}}_k}^{\′})+w_k{I}_k{{\mathrm{\σ}}_k}^{\′}-{w_k}^2{R}_k(B_1-{{\mathrm{\τ}}_k}^{\′})=\underset{k=0}{\overset{m}{\mathrm{\Σ}}}{w}_k{I}_k\\ \underset{k=0}{\overset{m}{\mathrm{\Σ}}}{w_k}^2{R}_k{{\mathrm{\σ}}_k}^{\′}+{w_k}^3{I}_k(B_1-{{\mathrm{\τ}}_k}^{\′})+{w_k}^2(A_0-{{\mathrm{\α}}_k}^{\′})=\underset{k=0}{\overset{m}{\mathrm{\Σ}}}{w_k}^2{R}_k\\ \underset{k=0}{\overset{m}{\mathrm{\Σ}}}-{w_k}^4{R}_k(B_1-{{\mathrm{\τ}}_k}^{\′})+{w_k}^3{I}_k{{\mathrm{\σ}}_k}^{\′}+{w_k}^4(A_1-{{\mathrm{\β}}_k}^{\′})=\underset{k=0}{\overset{m}{\mathrm{\Σ}}}{w_k}^3{I}_k\\ .\\ .\\ .\\ \underset{k=0}{\overset{m}{\mathrm{\Σ}}}{w}_k{I}_k(A_0-{{\mathrm{\α}}_k}^{\′})-{w_k}^2{R}_k(A_1-{{\mathrm{\β}}_k}^{\′})+{w_k}^2({R_k}^2+{I_k}^2)(B_1-{{\mathrm{\τ}}_k}^{\′})=0\\ \underset{k=0}{\overset{m}{\mathrm{\Σ}}}{w_k}^2{R}_k(A_0-{{\mathrm{\α}}_k}^{\′})+{w_k}^3{I}_k(A_1-{{\mathrm{\β}}_k}^{\′})+{w_k}^2({R_k}^2+{I_k}^2){{\mathrm{\σ}}_k}^{\′}=\underset{k=0}{\overset{m}{\mathrm{\Σ}}}{w_k}^2({R_k}^2+{I_k}^2)\\ \underset{k=0}{\overset{m}{\mathrm{\Σ}}}{w_k}^3{I}_k(A_0-{{\mathrm{\α}}_k}^{\′})-{w_k}^4{R}_k(A_1-{{\mathrm{\β}}_k}^{\′})+{w_k}^4({R_k}^2+{I_k}^2)(B_1-{{\mathrm{\τ}}_k}^{\′})=0\end{array}---\left(24\right)$

${\mathrm{\λ}}_h=\underset{k=0}{\overset{m}{\mathrm{\Σ}}}{w_k}^h---\left(25\right)$

$S_h=\underset{k=0}{\overset{m}{\mathrm{\Σ}}}{w_k}^h{R}_k---\left(26\right)$

$T_h=\underset{k=0}{\overset{m}{\mathrm{\Σ}}}{w_k}^h{I}_k---\left(27\right)$

$U_h=\underset{k=0}{\overset{m}{\mathrm{\Σ}}}{w_k}^h({R_k}^2+{I_k}^2)---\left(28\right)$

Bring relational expression (25) ~ (28) into formula (24) to be separated by coefficient, we can obtain relational expression below simultaneously:

A ₀λ ₀-A ₂λ ₂+A ₄λ ₄-A ₆λ ₆+…+B ₁T ₁+B ₂S ₂-B ₃T ₃-B ₄S ₄+B ₅T ₅+…＝S ₀

A ₁λ ₂-A ₃λ ₄+A ₅λ ₆-A ₇λ ₈+…-B ₁S ₂+B ₂T ₃+B ₃S ₄-B ₄T ₅-B ₅S ₆+…＝T ₁

A ₀λ ₂-A ₂λ ₄+A ₄λ ₆-A ₆λ ₈+…+B ₁T ₃+B ₂S ₄-B ₃T ₅-B ₄S ₆+B ₅T ₇+…＝S ₂

A ₁λ ₄-A ₃λ ₆+A ₅λ ₈-A ₇λ ₁₀+…-B ₁S ₄+B ₂T ₅+B ₃S ₆-B ₄T ₇-B ₅S ₈+…＝T ₃

.

.

.

A ₀T ₁-A ₁S ₂-A ₂T ₃+A ₃S ₄+A ₄T ₅-…+B ₁U ₂-B ₃U ₄+B ₅U ₆-B ₇U ₈+…＝0

A ₀S ₂+A ₁T ₃-A ₂S ₄-A ₃T ₅+A ₄S ₆+…+B ₂U ₄-B ₄U ₆+B ₆U ₈-B ₈U ₁₀+…＝U ₂

A ₀T ₃-A ₁S ₄-A ₂T ₅+A ₃S ₆+A ₄T ₇-…+B ₁U ₄-B ₃U ₆+B ₅U ₈-B ₇U ₁₀+…＝0

.

.

. (29) are expressed as matrix form and are:

MN＝C (30)

Wherein

$M=\left[\begin{array}{cccccccccccc}{\mathrm{\λ}}_0& 0& -{\mathrm{\λ}}_2& 0& {\mathrm{\λ}}_4& ...& T_1& S_2& -T_3& -S_4& T_5& ...\\ 0& {\mathrm{\λ}}_2& 0& -{\mathrm{\λ}}_4& 0& ...& -S_2& T_3& S_4& -T_5& -S_6& ...\\ {\mathrm{\λ}}_2& 0& -{\mathrm{\λ}}_4& 0& {\mathrm{\λ}}_6& ...& T_3& S_4& -T_5& -S_6& T_7& ...\\ 0& {\mathrm{\λ}}_4& 0& -{\mathrm{\λ}}_6& 0& ...& -S_4& T_5& S_6& -T_7& -S_8& ...\\ .& .& .& .& .& & .& .& .& .& .& \\ .& .& .& .& .& & .& .& .& .& .& \\ .& .& .& .& .& & .& .& .& .& .& \\ T_1& -S_2& -T_3& S_4& T_5& ...& U_2& 0& -U_4& 0& U_6& ...\\ S_2& T_3& -S_4& -T_5& S_6& ...& 0& U_4& 0& -U_6& 0& ...\\ T_3& -S_4& -T_5& S_6& T_7& ...& U_4& 0& -U_6& 0& U_8& ...\\ .& .& .& .& .& & .& .& .& .& .& \\ .& .& .& .& .& & .& .& .& .& .& \\ .& .& .& .& .& & .& .& .& .& .& \end{array}\right]---\left(31a\right)$

N＝[A ₀ A ₁ A ₂ A ₃ … B ₁ B ₂ B ₃ …] ^T (31b)

C＝[S ₀ T ₁ S ₂ T ₃ … 0 U ₂ 0 …] ^T (31c)

Step 4, carries out compound curve matching to all elements of mutual coupling compensation Matrix C according to above step and formula.

For wideband array, by calculating the calibration matrix on multiple frequency, being formed in the multiple sampled points in frequency, by compound curve approximating method, simulating each element of calibration matrix with the change function of frequency or curve.Suppose c in whole frequency range _nm(jk) expression formula, by curve formula, has

${\hat{c}}_{\mathrm{nm}}\left(\mathrm{jk}\right)=\frac{A_0^{\mathrm{nm}}+A_1^{\mathrm{nm}}\left(\mathrm{jk}\right)+A_2^{\mathrm{nm}}{\left(\mathrm{jk}\right)}^2+A_3^{\mathrm{nm}}{\left(\mathrm{jk}\right)}^3+...}{B_0^{\mathrm{nm}}+B_1^{\mathrm{nm}}\left(\mathrm{jk}\right)+B_2^{\mathrm{nm}}{\left(\mathrm{jk}\right)}^2+B_3^{\mathrm{nm}}{\left(\mathrm{jk}\right)}^3+...}---\left(32\right)$

In formula, represent wave number or propagation constant, in formula, polynomial coefficient determines curve with the variation relation of frequency, as long as so obtain polynomial coefficient, just curve formula can be obtained, and then to calculate the value on corresponding frequency with the change function of frequency according to each element, thus obtain the calibration matrix on corresponding frequency.The elements A in N is obtained in through type (18)-(19) _iand B _i, all mutual coupling compensation entry of a matrix elements can be calculated by expression formula below.

$C_{\mathrm{mn}}=\frac{A_0+A_1\left(\mathrm{jk}\right)+A_2{\left(\mathrm{jk}\right)}^2+...+A_p{\left(\mathrm{jk}\right)}^p}{1+B_1\left(\mathrm{jk}\right)+B_2{\left(\mathrm{jk}\right)}^2+...+B_p{\left(\mathrm{jk}\right)}^p}---\left(33\right)$

Wherein, p represents polynomial exponent number.

Step 5, draws the function expression of mutual coupling compensation matrix element

By adjusting the exponent number of polynomial fitting, finding the curve minimum with the mutual coupling compensation matrix element curve error directly calculated, drawing calibration matrix function expression.

Step 6, if frequency band is wider, adopt the multinomial of higher-order number still can not obtain good fitting effect, then frequency range can be divided, then in each frequency range, respectively compound curve matching is carried out to mutual coupling compensation entry of a matrix element according to step 3 to the explanation of step 5.

1. emulation experiment environment

Emulation experiment environment is: FEKO, Windows 7 Professional, Matlab

2. emulation experiment content

In Fig. 6 ~ 21, compensate to implement wideband adaptive array mutual coupling, getting frequency interval is 15MHz, and angular range is that 361 points of [0 °, 360 °] calculate mutual coupling compensation matrix, calculates can obtain 21 mutual coupling compensation matrixes at 200MHz ~ 500MHz.Owing to adopting the multinomial of higher-order number still can not obtain good fitting effect, frequency range is carried out in centre be divided into 2 sections, then in two frequency ranges, respectively compound curve matching is carried out to mutual coupling compensation entry of a matrix element.

In Figure 22 ~ 24, in order to verify the validity of this Mutual Coupling Compensation Method on adaptive array mutual coupling compensation, for 200MHz, 350MHz and 500MHz tri-frequencies, arrival bearing's estimation is carried out to the signal of four different directions incidences, correspond respectively to Figure 22 ~ 24, compared in figure use this method carry out mutual coupling compensation and without in mutual coupling compensation situation simulation result.

In eight yuan of circular antenna array mutual coupling compensation matrix curve-fitting methods in the present invention, the expression formula of mutual coupling compensation matrix element is as follows, wherein C _{ij_1}represent mutual coupling compensation matrix element C on first half band frequency _ijfitting function, C _{ij_2}represent mutual coupling compensation matrix element C in second half section frequency _ijfitting function.Because this mutual coupling compensation matrix has the appropriate Puli of multiple symmetry hereby structure, therefore, other element of mutual coupling compensation matrix directly can be obtained by following several elements.

C _{11_1}(jk)＝{1.0052+0.34(jk)+0.0698(jk) ²+0.0019(jk) ³+0.0015(jk) ⁴

2.5066e ^-5(jk) ⁵+9.2316e ^-6(jk) ⁶}/{1+0.0351(jk)+0.0695(jk) ² (34)

+0.0019(jk) ³+0.0147(jk) ⁴+2.5895e ^-5(jk) ⁵+9.19e ^-6(jk) ⁶}

C _{11_2}(jk)＝{1.007+0.0709(jk)+0.0338(jk) ²+0.0018(jk) ³+0.0004(jk) ⁴

1.1586e ^-5(jk) ⁵+1.2575e ^-6(jk) ⁶}/{1+0.0718(jk)+0.0337(jk) ² (35)

+0.0018(jk) ³+0.0004(jk) ⁴+1.17265e ^-5(jk) ⁵+1.2708e ^-6(jk) ⁶}

C _{12_1}(jk)＝{-0.0455+0.0306(jk)-0.0078(jk) ²+0.0017(jk) ³-0.0003(jk) ⁴

+2.0572e ^-5(jk) ⁵-3.0074e ^-6(jk) ⁶}/{1+0.1087(jk)+0.0963(jk) ² (36)

+0.0053(jk) ³+0.0029(jk) ⁴+5.2559e ^-5(jk) ⁵+2.7618e ^-5(jk) ⁶}

C _{12_2}(jk)＝{0.0645-0.0113(jk)+0.0021(jk) ²-0.0004(jk) ³+2.1755e ^-5(jk) ⁴

-2.5065e ^-6(jk) ⁵+7.2e ^-8(jk) ⁶}/{1+0.0531(jk)+0.0378(jk) ² (37)

+0.0147(jk) ³+0.0005(jk) ⁴+1.009e ^-5(jk) ⁵+1.6704e ^-6(jk) ⁶}

C _{13_1}(jk)＝{0.0617+0.0035(jk)+0.002(jk) ⁵+0.0003(jk) ³+4.1712e ^-6(jk) ⁴

+7.2495e ^-6(jk) ⁵+2.698e ^-7(jk) ⁶}/{1+0.1544(jk)+0.085(jk) ² (38)

+0.0084(jk) ³+0.002(jk) ⁴+0.0001(jk) ⁵+9.05e ^-6(jk) ⁶}

C _{13_2}(jk)＝{-6.8845e ^-8+0.0053(jk)-0.0003(jk) ²+0.0002(jk) ³-2.1234e ^-6(jk) ⁴

+1.266e ^-6(jk) ⁵+2.317e ^-8(jk) ⁶}/{1+0.0204(jk)+0.045(jk) ² (39)

+0.0009(jk) ³+0.0006(jk) ⁴+7.5571e ^-6(jk) ⁵+2.6036e ^-6(jk) ⁶}

C _{14_1}(jk)＝{0.1509-0.0266(jk)+0.0143(jk) ²-0.0015(jk) ³-0.0004(jk) ⁴

-2.1248e ^-5(jk) ⁵+3.2755e ^-6(jk) ⁶}/{1+0.022(jk)+0.0768(jk) ² (40)

-0.001(jk) ³+0.0019(jk) ⁴-5.9283e ^-5(jk) ⁵+1.705e ^-5(jk) ⁶}

C _{14_2}(jk)＝{-0.0846+0.0054(jk)-0.0025(jk) ²+9.3368e ^-5(jk) ³-2.4234e ^-5(jk) ⁴

+2.8285e ^-7(jk) ⁵-7.106e ^-8(jk) ⁶}/{1-0.0937(jk)+0.0318(jk) ² (41)

+0.002(jk) ³+0.0003(jk) ⁴+1.0218e ^-5(jk) ⁵+9.2602e ^-7(jk) ⁶}

3. the simulation experiment result analysis:

As can be seen from Fig. 6 ~ 21, after piecewise fitting, fitting effect is fine, and error is very little, and error substantially all, in given threshold range, reaches expected result.

As can be seen from Figure 22 ~ 24, the mutual coupling compensation matrix using this method to obtain can well compensate by pair array, the successful of Mutual coupling is better than the situation without mutual coupling compensation, the error that curve exists can be ignored the impact of Mutual coupling, curve-fitting method is stable in whole frequency band, can ensure that the arbitrary frequency in frequency band calculates mutual coupling compensation matrix in real time.

Comprehensive analysis, can find out that the distinct advantage of the present invention is: first, in order to obtain the mutual coupling compensation matrix on whole frequency band, what need storage is only a small amount of multinomial coefficient, decrease the requirement of wideband adaptive array mutual coupling compensation to memory capacity, and the acquisition of mutual coupling compensation matrix is very simple, only need the frequency of Received signal strength to substitute into formula;

The second, good mutual coupling compensation can be obtained in broadband, good mutual coupling compensation can be carried out to received signal by mutual coupling compensation matrix from the signal of the groundwork angular range incidence of array.

The above; be only the present invention's preferably embodiment; protection scope of the present invention is not limited thereto; anyly be familiar with those skilled in the art; in the technical scope that the present invention discloses, the simple transformation of the technical scheme that can obtain apparently or equivalence are replaced and are all fallen within the scope of protection of the present invention.

Claims (1)

1. a wideband adaptive array signal calibration steps, is characterized in that, comprises the following steps:

(1) set up the relation between both direction figure, in battle array when array element all being existed, directional diagram is changed to isolated directional diagram when single array element exists;

In formula, with directional diagram in isolated directional diagram when representing array element individualism respectively and the battle array of array element, Matrix C represents mutual coupling compensation matrix, carrys out the mutual coupling of compensated array with it; In equation, the amplitude of electric field and phase place all will be considered;

(2) in order to accurately calculate mutual coupling compensation Matrix C, needing the data extracting multiple angle from directional diagram, supposing to have chosen M direction, then having

According to solving criterion

$\underset{\left|\right|\mathrm{CE}-E^i\left|\right|}{\min }\left|\right|C\left|\right|$

The least square solution of above equation can be obtained, namely

C＝E ⁱE ^H(EE ^H) ^-1

In formula, E ⁱrepresent electric field during array element individualism, E represents electric field when array element all exists, symbol || || the 2-norm of representing matrix; Mutual coupling compensation Matrix C can be tried to achieve by above formula, obtains mutual coupling compensation matrix, and just it can be applied in array mutual coupling compensation, suppose that the sampling matrix of Received signal strength is X ', the sampling matrix of the signal so after mutual coupling compensation can be expressed as

X＝CX′；

(3) multinomial with frequency dependence is chosen, namely

$G\left(\mathrm{jw}\right)=\frac{A_0+A_1\left(\mathrm{jw}\right)+A_2{\left(\mathrm{jw}\right)}^2+A_3{\left(\mathrm{jw}\right)}^3+...}{B_0+B_1\left(\mathrm{jw}\right)+B_2{\left(\mathrm{jw}\right)}^2+B_3{\left(\mathrm{jw}\right)}^3+...}$

And then structure fit polynomial function, with all elements of above Polynomial curve-fit mutual coupling compensation matrix;

(4) for wideband array, by calculating the mutual coupling compensation matrix on multiple frequency, the multiple sampled values of mutual coupling compensation matrix in frequency are obtained

(5) by compound curve approximating method, each element of mutual coupling compensation matrix is simulated with the change function of frequency or curve;

(6) if frequency band is wider, adopt the multinomial of higher-order number still can not obtain good fitting effect, then frequency range can be divided, then in each frequency range, respectively compound curve matching be carried out to mutual coupling compensation entry of a matrix element.