CN103020363A - Method for designing antenna by improving side lobe characteristics of array wave beam directivity diagram - Google Patents

Abstract

The method relates to a method for designing an antenna by improving the side lobe characteristics of an array wave beam directivity diagram, belonging to the technical field of array antennae. The method comprises the following steps of: setting an expected response directivity diagram A; under the unrestraint condition, determining a array wave directivity diagram B according to a minimum mean square error criterion; selecting a side lobe S to be optimized to determine an interval Omega; under the condition of taking a principle that the directivity diagram amplitude at a k equal division point is zero in the Omega as a constrict condition, calculating an optimal weighting vector Wopt(k) of an array, approaching to the directivity diagram A, according to the minimum mean square error criterion under the corresponding constraint condition to obtain a directivity diagram Ck, and searching the peak value p1(k) and a peak value p2(k) of side lobes at the left side and the right side of the k equal division point in the Ck; and marking Mr (k)=max{pr2(k), pr1 (k)}, searching a maximum value Mr (krm) in all Mr(k), determining the corresponding Wopt (krm) and a wave beam directivity diagram D, and carrying out array antenna design according to the Wopt (krm) and D. The method disclosed by the invention is used for designing the array antenna by improving the characteristics of the side lobes at the single side or both sides without carrying out hardware improvement on the original array and has the advantages of good flexibility, low cost and good effect.

Description

A kind of by improving the method for array beams directional diagram sidelobe performance designing antenna

Technical field

The inventive method relates to the array antenna technical field.The invention provides a kind of by improving the method for array beams directional diagram sidelobe performance designing antenna.

Background technology

Array antenna has in a plurality of fields such as radar, radio communication, direction finding, radioastronomys widely to be used.Array antenna can utilize the spatial feature of signal, and the signal during to sky in the field domain carries out filtering to be processed.

Carry out array antenna when design, having two aspects to determine the performance of this array antenna airspace filter, the one, the geometry of array antenna has consisted of the basic restriction of this array antenna serviceability, and the 2nd, design the complex weighting that each array element is exported data.Under the condition of given array antenna geometry, the selection of these weights has determined array antenna beam direction Graph Character, has also namely determined the feature of array antenna airspace filter.Because the array antenna beam directional diagram has determined the feature of array antenna airspace filter, therefore, the research of array aerial direction figure is one of key problem of array antenna design field with design.

In technical fields such as radar, radio communication, direction findings, usually expectation obtains one and has the space narrow beam that sharp-pointed directivity is pointed to, in two dimensional surface, desirable expectation beam pattern as shown in Figure 1, its model is shown in equation (1).

Equation (1):

$F_0\left(\mathrm{\η}\right)=\left\{\begin{array}{cc}\frac{1}{{\mathrm{\η}}_0}({\mathrm{\η}}_0-|\mathrm{\η}\left|\right),& \left|\mathrm{\η}\right|\≤{\mathrm{\η}}_0\\ 0,& \left|\mathrm{\η}\right|>{\mathrm{\η}}_0\end{array}\right.$

In the formula, η is horizontal azimuth

Or pitching angle theta.

Equation (1) and desirable expectation beam pattern shown in Figure 1 can not physics realizations, can only to a certain degree approach.Usually one of the criterion of approaching that adopts is minimum mean square error criterion.Equation (2) is depicted as the directional diagram error under the square error meaning.

Equation (2):

$\mathrm{\ξ}={\left|\right|F\left(\mathrm{\η}\right)-F_0\left(\mathrm{\η}\right)\left|\right|}^2={\∫}_{-\mathrm{\π}}^{\mathrm{\π}}{|F\left(\mathrm{\η}\right)-F_0\left(\mathrm{\η}\right)|}^2\mathrm{d\η}$

In the formula, the actual normalized beam pattern function of F (η) expression, F ₀(η) the desirable normalized expectation beam pattern function of expression.

Physically realizable beam pattern must have beam side lobe, as shown in Figure 2.

Owing to the inevitable secondary lobe that occurs in the beam pattern, had a strong impact on the application performance of array antenna, therefore, how to reduce the key problem that beam side lobe becomes the array antenna design.

Because linear array can only provide 180 ° azimuth sweep, and circular array also can well scan angle of pitch direction except realizing 360 ° azimuth sweep.Circle battle array just can easily realize comprehensive scanning to the space by simple in turn mobile array stimulating.Far Field Pattern and the frequency-independent of circle battle array adopt broadband, ultra-broadband signal can obtain High Range Resolution, because these advantage circle battle arrays have obtained paying attention to more and more widely and using.Have higher sidelobe level but circular array is compared with linear array, this means that its interference to the secondary lobe zone can not well suppress.

Because the paraxial characteristic of the first secondary lobe of circle battle array is directly connected to the noiseproof feature of array antenna, therefore, the secondary lobe that how to reduce circular array antenna particularly the first secondary lobe has been subject to paying attention to widely.

The method of traditional reduction the first secondary lobe that is used widely is: adopt at the first side lobe peak place constraint at zero point (ZFC) is set, the side lobe peak after the division is minimized.As document " the phased array antenna handbook (and Mailloux R.J. work. Nanjing electronic technology research institute, translate. Beijing: the Electronic Industry Press, 2005:130-134) discussed this kind method.Be illustrated in figure 3 as ZFC method synoptic diagram, be to be taken at directional diagram F zero point ₁₁Angle corresponding to the first side lobe peak level (η)

The place is improved as shown in Figure 4 in the hope of the sidelobe performance after the division.But this method performance is unsatisfactory, and reason is that the constraint of fixed zero can not provide effective improvement of sidelobe performance.

The ZFC method is a kind of method that still lacks checking based on intuition to add the method that reduces sidelobe level zero point.ZFC constraint condition is the position η at zero point _L1, η _R1, to the sidelobe level p after the division _L1, p _L2, p _R1, p _R2And no requirement (NR).So the directional diagram after optimizing can not guarantee to make corresponding secondary lobe peak level can reach our requirement.

The limitation of ZFC method manifests comparatively obvious when it is applied in circular array antenna.Show 16 equally distributed circular array antennas of array element in the xoy plane such as Fig. 5, establish this array array element pattern function and be

Circle battle array radius R=1.2815 λ, λ is signal wavelength, establishes the desirable expectation beam pattern of this array antenna as shown in Figure 6, adopts minimum mean square error criterion to be optimized weighting, definite 16 are added with weights and are:

W ₁=-0.0360+0.1359i,W ₂=0.0689+0.1710i,W ₃=0.0989-0.0784i,

W ₄=-0.0706+0.0129i,W ₅=0.0287-0.0006i,W ₆=-0.0138+0.0009i,

W ₇=0.0050+0.0006i,W ₈=-0.0019+0.0008i,W ₉=0.0015-0.0015i,

W ₁₀=-0.0019+0.0008i,W ₁₁=0.0050+0.0006i,W ₁₂=-0.0138+0.0009i,

W ₁₃=0.0287-0.0006i,W ₁₄=-0.0706+0.0129i,W ₁₅=0.0989-0.0784i,

W ₁₆=0.0689+0.1710i;

Fig. 7 shows its corresponding directional diagram, and the first side lobe peak is reduced to-20.3dB, and the second side lobe peak is-26.25dB.

Keep the frontal array situation constant, still with shown in Figure 6

For design expectation responder to figure, adopt 16 of retraining that the ZFC method utilizes minimum mean square error criterion to determine zero point to be added with weights to be:

W ₁＝-0.0007+0.0373i,W ₂=0.0138+0.0477i,W ₃=0.0282-0.0186i,

W ₄=-0.0181+0.0089i,W ₅=0.0071-0.0057i,W ₆＝-0.0038+0.0032i,

W ₇=0.0013-0.0011i,W ₈＝-0.0006+0.0008i,W ₉＝0.0005-0.0007i,

W ₁₀＝-0.0006+0.0008i,W ₁₁=0.0013-0.0011i,W ₁₂＝-0.0038+0.0032i,

W ₁₃=0.0071-0.0057i,W ₁₄=-0.0181+0.0089i,W ₁₅=0.0282-0.0186i,

W ₁₆0.0138+0.0477i;

The directional diagram of this array as shown in Figure 8.Fig. 8 shows the first side lobe peak p that the main lobe arranged on left and right sides forms respectively _L1, p _R1Decay is about-47dB, but at-50 °, 50 ° the second side lobe peak p that locate to produce _L2, p _R2Only be-22.63dB that these two second secondary lobes are than the second sidelobe level of Fig. 7-taller about 3.62dB of 26.25dB.

It is unsatisfactory to retrain ZFC method performance zero point, reason is that the constraint of ZFC fixed zero can not provide effective improvement of sidelobe performance, what ZFC constraint condition retrained is the position at zero point, to side lobe peak and the no requirement (NR) after the division, thereby can not guarantee to make corresponding side lobe peak can reach requirement.

Summary of the invention

The present invention is a kind of by improving the method for array beams directional diagram sidelobe performance designing antenna, may further comprise the steps:

The first step, setting array antenna expectation beam pattern A;

Second step, according to minimum mean square error criterion, the directional diagram B that directional diagram A approached of computing array antenna under unconfined condition;

In the 3rd step, secondary lobe S to be optimized among the choice direction figure B determines the interval Δ in position angle of S, and then determines the interval Ω in position angle by the peak point of the interval Δ in described position angle and S;

When S is single-lobe, Ω is carried out the M five equilibrium; When S is two secondary lobe to the main lobe symmetry, Ω is carried out the 2M five equilibrium; The Along ent of Ω is corresponding with integer variable k; Be specially:

When S is the single secondary lobe in main lobe right side, Δ=[α, β], the peak point position angle of establishing S is γ, then Ω=(alpha, gamma], and make k=1,2 ..., M, and k=1 is corresponding to first Along ent of α value point right side, k=M correspondence γ value point position angle; Perhaps, when S is the single secondary lobe in main lobe left side, Δ=[α, β], the peak point position angle of establishing S is γ, then Ω=[γ, β), and make k=1,2 ..., M, and k=1 is corresponding to first Along ent of β value point left side, the corresponding γ value point of k=M position angle; Perhaps, when S is two secondary lobe to the main lobe symmetry, note Δ=[β,-α] ∪ [α, β], establish S peak point position angle and be ± γ, then Ω=[γ ,-β) ∪ (alpha, gamma], and make k=± 1, ± 2 ..., ± M, and first Along ent of the corresponding α value point of k=1 right side, k=-1 correspondence-first Along ent of β value point left side, k=± M is correspondence ± γ value point position angle respectively.

In the 4th step, when S was single secondary lobe, " k Along ent prescription is zero to the figure amplitude " was as constraint condition in Ω; Perhaps, when S was two secondary lobe for the main lobe symmetry, " ± k Along ent prescription is zero to the figure amplitude " was as constraint condition in Ω; According to minimum mean square error criterion, the optimum weight vectors W that directional diagram A approached of computing array under corresponding constraint condition _Opt(k), obtain directional diagram C _k, direction of search figure C _kIn be positioned at the peak value p of secondary lobe of the arranged on left and right sides at k Along ent place ₁(k) and p ₂(k);

The 5th step, note M _r(k)=max{p ₁(k), p ₂(k) }, M _r(k) and W _Opt(k) combination is designated as array I _k

The 6th step, to k=1,2 ... M finished for the 5th step to the 6th step, carried out for the 7th step;

In the 7th step, search for all array I _kMiddle M _r(k) minimum M _r(k _Rm), determine and M _r(k _Rm) W in the same array _Opt(k _Rm) and corresponding beam pattern D, and according to described W _Opt(k _Rm) and beam pattern D carry out array antenna design.

Figure 9 shows that the inventive method implementation flow chart of steps.

The inventive method is characterized in that:

1. described array antenna is uniform linear array of antennas or uniform circular array antenna, and array center is placed on the initial point of coordinate system, and array array element is omnidirectional's array element or is oriented array element;

2. pattern function is one dimension function F (η), and η is horizontal azimuth

Or pitching angle theta;

3. the number at simultaneously set zero point must be less than the array element number of array in directional diagram;

4. the inventive method is limited to the single secondary lobe of optimizing directional diagram or with respect to two secondary lobes of main lobe symmetry;

5. expect that beam pattern A is the triangle wave beam, it is zero place that triangular apex is positioned at the position angle, and its model is equation (1).

Describe spatial beams and relate to two position angles: horizontal azimuth With pitching angle theta.When research array antenna design problem, linear array and circular array are two kinds of array formats commonly used.For linear linear array, can only differentiate an angle component, therefore, its array beams directional diagram is two dimensional form; For face battle arrays such as circular array, form the spatial beams of three dimensional form, two angles of distinguishable level and pitching are taked that usually it is decomposed into two two-dimensional function problems and are analyzed.Therefore, the inventive method is carried out calculation Design at two dimensional surface pair array antenna beam pattern.

The inventive method proposes the optimisation strategy of new constraint secondary lobe (SLC).SLC arranges zero point in the nearly main lobe side zero sunken position of directional diagram right side (or left side) secondary lobe to the zone of side lobe peak position, Figure 10 shows that the beam pattern that the expectation after SLC retrains forms.

The SLC strategy is not the position of determining ZF, but requires two secondary lobes obtaining after the ZF all lower, i.e. side lobe peak p among Figure 10 _L1, p _L2, p _R1, p _R2All lower.Because can't determine what direction of optimizing directional diagram at unconfined condition the condition that can satisfy the SLC constraint zero point is set with resolving, calculates M thereby SLC will carry out point by point scanning to the zone near between zero sunken position to the side lobe peak position of main lobe side of secondary lobe _rAnd find out and make M (k), _r(k) reach minimum k _RmLike this, obtain corresponding to M _r(k) W _Opt(k _Rm) be under certain constraint condition, to make the corresponding minimum global optimum's weight vectors of secondary lobe amplitude, the W of optimizing _Opt(k _Rm) corresponding beam pattern D also is the global optimum's directional diagram under this constraint condition, and then according to W _Opt(k _Rm) and corresponding beam pattern D carry out the array antenna design.

Increase the constraint at zero point, can further reduce this secondary lobe amplitude, the thought of its thought and the inventive method---determine that by searching optimum is similar; Therefore, the inventive method has only provided in nearly main lobe side zero and has fallen into the method that a constraint at zero point is set in position to the zone of side lobe peak position; Simultaneously, the number of constraint at zero point is subjected to the constraint of array array element number, zero point, the number of constraint must be less than the number of array array element, and the number increase of constraint at zero point means that antenna array control forms the minimizing of the degree of freedom of directional diagram integral body, causes the other parts hydraulic performance decline.

Description of drawings

Fig. 1 shows the desirable expectation beam pattern F of two dimensional form ₀(η)

Fig. 2 shows physically realizable beam pattern F with secondary lobe ₁(η).

Fig. 3 shows that the ZFC method is at directional diagram F ₁₁(η) the first side lobe peak place arranges the synoptic diagram at zero point.

Fig. 4 shows that the ZFC method arranges zero point at the first side lobe peak point place, with two sidelobe performance synoptic diagram after the division of Ji.

Fig. 5 shows 16 equally distributed circular array antennas of oriented array element in the xoy plane, array element pattern function

Circle battle array radius R=1.2815 λ, λ is signal wavelength.

Fig. 6 shows desirable expectation beam pattern

Fig. 7 shows the directional diagram B that obtains that circular array antenna employing minimum mean square error criterion shown in Figure 5 is optimized weighting.

Fig. 8 shows the directional diagram that adopts the ZFC method to obtain to circular array antenna shown in Figure 5.

Fig. 9 shows the inventive method implementation steps flow chart.

Figure 10 shows that the inventive method falls into the position in nearly main lobe side zero and to the zone of side lobe peak position is set zero point, with two sidelobe performance synoptic diagram after the division of Ji.

Figure 11 shows M _r(k) and the graph of a relation between the null position.

Figure 12 shows that the inventive method is to the optimization directional diagram of circular array antenna shown in Figure 5.

Embodiment

In instructions and claims, used 16 equally distributed circular array antennas of oriented array element as the embodiment accompanying drawings method for designing proposed by the invention.The scope of application of this method for designing is not limited to circular array antenna, also is applicable to uniform linear array of antennas.In instructions, used the specific computation process of some vocabulary and symbols and mathematical function, it will be appreciated by those skilled in the art that.

The method is by as follows to the detailed process of being carried out Array Design by the improvement of 16 equally distributed circular array antenna secondary lobes of oriented array element:

The first step, setting array antenna beam Expected Response directional diagram A.

If Expected Response directional diagram A is For the uniform circular array of as shown in Figure 5 16 array elements, circle battle array radius R=1.2815 λ, wherein λ is signal wavelength, the Expected Response directional diagram

Be made as equation (3).

Equation (3):

In the formula,

Be horizontal azimuth.

Figure 6 shows that the design expectation responder of this embodiment is to figure

Second step, according to minimum mean square error criterion, computing array antenna unconfined condition to directional diagram A approximation computation, obtain beam pattern B.

As shown in Figure 5, a uniform circular array is positioned at the xoy plane, and the center of circle is true origin, and the radius of circle battle array is R, wherein

Be and the angle of x positive axis, be the position angle; θ is and the angle of z positive axis, is the angle of pitch.If the heavy coefficient of the restore one's right of each array element is W _n, n=1,2 ..., N, first array element is positioned on the x positive axis, and the position angle of n array element is

Equation (4) is the pattern function of uniform circular array.

Equation (4):

In the formula, subscript " * " expression conjugate operation,

For to the space arrival bearing being

Plane wave illumination to circular array antenna, n array element is with respect to the relative phase of array center, λ is wavelength,

It is the pattern function of n array element.

Equation (5) is equation (4) array aerial direction figure of only considering circle battle array plane, place (θ=90 °), supposes that each array element has identical pattern function.

Equation (5):

In the formula, subscript " * " expression conjugate operation, the computing of subscript " H " expression conjugate transpose,

Be the pattern function of n array element this moment, W=[W ₁W ₂W _N] for being added with weighted vector,

Be steering vector.

Equation (6) is the optimal direction figure of oriented array element array antenna under the mean square meaning.

Equation (6):

Equation (7) is for when equation (6) being the equation that hour is satisfied.

Equation (7):

$\frac{\∂\mathrm{\ξ}}{\∂W^H}=0$

The solution of equation (7) is the optimum weight vectors W of array antenna _Opt, W _OptDetermined by equation (8).

Equation (8):

$W_{\mathrm{opt}}=R_s^{-1}P$

Wherein,

Note R _s=[R _Mn], m, n=1,2 ..., N,

Wherein,

Note P=[P _n], n=1,2 ..., N,

Wherein

Expected Response directional diagram to the setting of equation (3) expression

Under unconfined condition, utilize equation (5) and formula (8) to carry out beam pattern and calculate the optimum weight vectors W that determines _OptBe following 16 complex values:

W ₁=-0.0360+0.1359i,W ₂=0.0689+0.1710i,W ₃=0.0989-0.0784i,

W ₄=-0.0706+0.0129i,W ₅=0.0287-0.0006i,W ₆=-0.0138+0.0009i,

W ₇=0.0050+0.0006i,W ₈=-0.0019+0.0008i,W ₉=0.0015-0.0015i,

W ₁₀=-0.0019+0.0008i,W ₁₁=0.0050+0.0006i,W ₁₂=-0.0138+0.0009i,

W ₁₃=0.0287-0.0006i,W ₁₄=-0.0706+0.0129i,W ₁₅=0.0989-0.0784i,

W ₁₆=0.0689+0.1710i;

Fig. 7 shows its corresponding directional diagram B.

In the 3rd step, secondary lobe S to be optimized among the choice direction figure B determines the interval Δ in position angle of S, and then determines the interval Ω in position angle by the peak point of the interval Δ in described position angle and S; When S is single-lobe, Ω is carried out the M five equilibrium; When S is two secondary lobe to the main lobe symmetry, Ω is carried out the 2M five equilibrium; The Along ent of Ω is corresponding with integer variable k; Be specially:

When S is the single secondary lobe in main lobe right side, Δ=[α, β], the peak point position angle of establishing S is γ, then Ω=(alpha, gamma], and make k=1,2 ..., M, and k=1 is corresponding to first Along ent of α value point right side, k=M correspondence γ value point position angle; Perhaps, when S is the single secondary lobe in main lobe left side, Δ=[α, β], the peak point position angle of establishing S is γ, then Ω=[γ, β), and make k=1,2 ..., M, and k=1 is corresponding to first Along ent of β value point left side, the corresponding γ value point of k=M position angle; Perhaps, when S is two secondary lobe to the main lobe symmetry, note Δ=[β,-α] ∪ [α, β], establish S peak point position angle and be ± γ, then Ω=[γ ,-β) ∪ (alpha, gamma], and make k=± 1, ± 2 ... ± M, and first Along ent of the corresponding α value point of k=1 right side, k=-1 correspondence-first Along ent of β value point left side, k=± M is correspondence ± γ value point position angle respectively.

This step determines that the principle of Ω is: intercept secondary lobe to be optimized near secondary lobe zero trapping spot of main lobe one side to the interval, position angle of side lobe peak point correspondence as Ω, and Ω carried out five equilibrium.Single-lobe is made the M five equilibrium, and symmetrical bivalve is made the 2M five equilibrium; Because symmetry, the Along ent of bivalve also is symmetrical.

The inventive method is applicable to the improvement of general sidelobe performance, and the improvement of the first secondary lobe is more common demand, and particularly to circular array antenna, the improvement of main lobe bilateral the first secondary lobe has special value.Therefore, the below is to improve circular array antenna bilateral the first secondary lobe as the follow-up implementation step of example explanation.

The first secondary lobe interval of directional diagram B shown in Figure 7 is [47.1 ° ,-26.7 °] and [26.7 °, 47.1 °], α=26.7 °, and β=47.1 °, the first side lobe peak point is ± 34.6 °.Be Δ=[47.1 ° ,-26.7 °] ∪ [26.7 °, 47.1 °], Ω=[34.6 ° ,-26.7 °) and ∪ (26.7 °, 34.6 °], get M=40, Ω is carried out 80 five equilibriums.

In the 4th step, when S was single secondary lobe, " k Along ent prescription is zero to the figure amplitude " was as constraint condition in Ω; Perhaps, when S was two secondary lobe for the main lobe symmetry, " ± k Along ent prescription is zero to the figure amplitude " was as constraint condition in Ω; According to minimum mean square error criterion, the optimum weight vectors W that directional diagram A approached of computing array under corresponding constraint condition _Opt(k), obtain directional diagram C _k, direction of search figure C _kIn be positioned at the peak value p of secondary lobe of the arranged on left and right sides at k Along ent place ₁(k) and p ₂(k).

When the expectation responder still is shown in the equation (3) to figure A Need to

(during Q＜N), optimal direction figure optimization problem becomes the Solve problems under the constrained lowest mean square meaning Deng be set on Q the angle zero point.Be expressed as equation (9) zero point on Q angle.

Equation (9):

i＝1,2，...,Q

Equation (9) becomes equation (10).

Equation (10):

W ^HC＝0

Wherein,

Retrain composite demand zero point and satisfy simultaneously equation (7) and equation (10).Adopt lagrange's method of multipliers, equation (11) is arranged.

Equation (11)

In the formula, L is the k n dimensional vector n that Lagrange's multiplier forms, L=[l ₁l ₂L _Q] ^T, order

Obtain equation (12).

Equation (12):

R _sW _opt-P+CL＝0

Push away to get equation (13) by above-mentioned equation

Equation (13):

$\left\{\begin{array}{c}{C}^H{W}_{\mathrm{opt}}=0\\ C^H\left(R_s^{-1}{R}_s\right)W_{\mathrm{opt}}=0\end{array}\right.$

Associating equation (12), equation (13) obtain at the optimum weight vectors W that the oriented array element array antenna under the constraint condition at zero point is arranged _OptBe equation (14).

Equation (14):

$W_{\mathrm{opt}}=R_s^{-1}P-R_s^{-1}C{\left(C^H{R}_s^{-1}C\right)}^{-1}{C}^H{R}_s^{-1}P$

Symmetrical bivalve situation occurring, k gets a value in 1 to M, must be positioned at applying respectively between the left and right region of the Ω that the first secondary lobe is corresponding about directional diagram ± constraint at zero point at k Along ent place, calculates W according to equation (14) _Opt(k), obtain directional diagram C _k, C _kIn ± secondary lobe can respectively appear in the left and right sides at k Along ent place, and in fact, the first secondary lobe divided respectively two secondary lobes about this was original, and as schematically shown in Figure 10, its peak value is p _L1, p _L2, p _R1, p _R2, because symmetry has p _L1=p _R1, p _L2=p _R2, therefore, only need determine that two secondary lobes that the division of a side goes out get final product, the peak value meter of two secondary lobes is shown p ₁(k) and p ₂(k).

The 5th step, note M _r(k)=max{p ₁(k), p ₂(k) }, M _r(k) and W _Opt(k) combination is designated as array I _k

The 6th step, to k=1,2 ... M finished for the 5th step to the 6th step, carried out for the 7th step;

Equation (15) is illustrated in two side lobe peak p ₁(k) and p ₂(k) in, determine the greater, remember into M _r(k).

Equation (15):

M _r(k)=max{p ₂(k),p ₁(k)}

With M _r(k) with corresponding W _Opt(k) be recorded as an array, purpose is to be convenient to the subsequent step search.

The inventive method proposes the optimisation strategy of new constraint secondary lobe (SLC).The SLC strategy arranges zero point in the zone of side lobe peak position, first zero position to the first, directional diagram right side (or left side), Figure 10 shows that the desired orientation figure behind the SLC constrained optimization.The SLC strategy is not the position of determining ZF, but requires two secondary lobes obtaining after the ZF all lower, i.e. p among Figure 10 _L1, p _L2, p _R1, p _R2All lower.

In what direction of unconstrained optimization directional diagram the condition that can satisfy the SLC constraint zero point is set because can't determine with resolving, thereby SLC will carry out point by point scanning calculation equation (15) to the zone of side lobe peak position, first zero position to the first, and finds out and make M _r(k) reach minimum k _Rm

This example is carried out M=40 suboptimization calculating altogether, and the M of calculation equation (15) is all wanted in each time computing _r(k).

Calculate k by optimization _Rm=11.Figure 11 shows that M _r(k) with the relation curve of null position, be the graph of a relation between the maximal value in the null position that arranges in the interval, side lobe peak point place, paraxial first zero place to the first that the inventive method seeks out circular array antenna shown in Figure 5 and corresponding paraxial two side lobe peaks.Corresponding 26.7 ° of horizontal ordinate " 0 ".

In the 7th step, search for all array I _kMiddle M _r(k) minimum M _r(k _Rm), determine and M _r(k _Rm) W in the same array _Opt(k _Rm) and corresponding beam pattern D, and according to described W _Opt(k _Rm) and beam pattern D carry out array antenna design.

With k _RmAs the zero point that arranges, calculate one group of optimum weights W _Opt(k _Rm) and corresponding directional diagram D, be directional diagram B the first side lobe peak applied and retrain corresponding optimal result of overall importance a zero point.This example is improved the most obvious null position of effect and is approximately appeared at 28.9 ° of 26.7 °+11 (34.6 °-26.7 °)/40 ≈ and locate.

The inventive method to the optimization weighting complex coefficient that the even distribution circular array antenna that is made of 16 oriented array elements shown in Figure 5 designs is:

W ₁＝-0.0050+0.0389i,W ₂=0.0164+0.0462i,W ₃=0.0276-0.0189i,

W ₄=-0.0180+0.0059i,W ₅=0.0056-0.0031i,W ₆=-0.0029+0.0015i,

W ₇=0.0010-0.0004i,W ₈=-0.0004+0.0005i,W ₉0.0003-0.0005i,

W ₁₀-0.0004+0.0005i,W ₁₁=0.0010-0.0004i,W ₁₂=-0.0029+0.0015i,

W ₁₃=0.0056-0.0031i,W ₁₄=-0.0180+0.0059i,W ₁₅=0.0276-0.0189i,

W ₁₆0.0164+0.0462i;

Figure 12 is its directional diagram.Null position is chosen as 28.9 °, and secondary lobe originally splits into two almost contour secondary secondary lobes, and its highest paraxial side lobe peak is-27.64dB.Compare with Fig. 7 and to have improved 7.34dB, effect is fairly obvious.

The advantage of the inventive method is: at the first side lobe peak place the method for designing that retrains ZFC zero point is set and compares with traditional, adopt the array antenna performance of the inventive method design better.

The inventive method can be used for improving single, double side side lobe performance, can the peak value of a plurality of secondary lobes be suppressed in principle, and is equally also effective to the Array Design of omnidirectional's array element, has the very wide scope of application.

The inventive method does not need to carry out hardware modifications to original array antenna, and dirigibility is good, and cost is low, and is simple, effective, is adapted at using in the phased array antenna.For the Phased Circular array antenna, because its symmetry of space, in case determined the position at zero point, then just can realize easily hanging down the secondary lobe spacescan by mobile array antenna weighting in turn.

Above embodiment has done comparatively detailed description to the present invention is a kind of by the method for improving array beams directional diagram sidelobe performance designing antenna, and has provided the design result by 16 equally distributed circular array antennas of oriented array element.

Claims (8)

1. one kind by improving the method for array beams directional diagram sidelobe performance designing antenna, may further comprise the steps:

The first step, setting array antenna expectation beam pattern A;

Second step, according to minimum mean square error criterion, the directional diagram B that directional diagram A approached of computing array antenna under unconfined condition;

In the 3rd step, secondary lobe S to be optimized among the choice direction figure B determines the interval Δ in position angle of S, and then determines the interval Ω in position angle by the peak point of the interval Δ in described position angle and S; When S is single-lobe, Ω is carried out the M five equilibrium; When S is two secondary lobe to the main lobe symmetry, Ω is carried out the 2M five equilibrium; The Along ent of Ω is corresponding with integer variable k;

In the 4th step, when S was single secondary lobe, " k Along ent prescription is zero to the figure amplitude " was as constraint condition in Ω; Perhaps, when S was two secondary lobe for the main lobe symmetry, " ± k Along ent prescription is zero to the figure amplitude " was as constraint condition in Ω; According to minimum mean square error criterion, the optimum weight vectors W that directional diagram A approached of computing array under corresponding constraint condition _Opt(k), obtain directional diagram C _k, direction of search figure C _kIn be positioned at the peak value p of secondary lobe of the arranged on left and right sides at k Along ent place ₁(k) and p ₂(k);

The 5th step, note M _r(k)=max{p ₁(k), p ₂(k) }, M _r(k) and W _Opt(k) combination is designated as array I _k

The 6th step, to k=1,2 ... M finished for the 5th step to the 6th step, carried out for the 7th step;

In the 7th step, search for all array I _kMiddle M _r(k) minimum M _r(k _Rm), determine and M _r(k _Rm) W in the same array _Opt(k _Rm) and corresponding beam pattern D, and according to described W _Opt(k _Rm) and beam pattern D carry out array antenna design.

2. the method for claim 1, it is characterized in that, described array antenna is uniform linear array of antennas or uniform circular array antenna, and described array antenna center is placed on the initial point of coordinate system, and described array antenna array element is omnidirectional's array element or is oriented array element.

3. the method for claim 1 is characterized in that, described pattern function is one dimension function F (η), and η is horizontal azimuth

Or pitching angle theta.

4. the method for claim 1 is characterized in that, the number at simultaneously set zero point must be less than the array element number of array in described directional diagram.

5. the method for claim 1 is characterized in that, the method be used for to be optimized the single secondary lobe of directional diagram or with respect to two secondary lobes of main lobe symmetry.

6. the method for claim 1 is characterized in that, in the described first step, described expectation beam pattern A is the triangle wave beam, and it is zero place that triangular apex is positioned at the position angle, and its model is:

$F_0\left(\mathrm{\η}\right)=\left\{\begin{array}{cc}\frac{1}{{\mathrm{\η}}_0}({\mathrm{\η}}_0-|\mathrm{\η}\left|\right),& \left|\mathrm{\η}\right|\≤{\mathrm{\η}}_0\\ 0,& \left|\mathrm{\η}\right|>{\mathrm{\η}}_0\end{array}\right.$

In the formula, η is horizontal azimuth

Or pitching angle theta.

7. the method for claim 1 is characterized in that, in described the 3rd step, be specially: when S is the single secondary lobe in main lobe right side, Δ=[α, β], if the peak point position angle of S is γ, then Ω=(alpha, gamma], and make k=1,2 ..., M, and k=1 is corresponding to first Along ent of α value point right side, the corresponding γ value point of k=M position angle; Perhaps, when S is the single secondary lobe in main lobe left side, Δ=[α, β], the peak point position angle of establishing S is γ, then Ω=[γ, β), and make k=1,2 ..., M, and k=1 is corresponding to first Along ent on the left of the β value point, k=M correspondence γ value point position angle; Perhaps, when S is two secondary lobe to the main lobe symmetry, note Δ=[β,-α] ∪ [α, β], establish S peak point position angle and be ± γ, Ω=[γ ,-β ∪ (alpha, gamma] then, and make k=± 1, ± 2 ..., ± M, and first Along ent of the corresponding α value point of k=1 right side, k=-1 correspondence-first Along ent of β value point left side, k=± M is correspondence ± γ value point position angle respectively.

8. the method for claim 1 is characterized in that, the array antenna in described array antenna is 16 Homogeneous Circular array antennas that oriented array element consists of, and the pattern function of described array element is

Circle battle array radius R=1.2815 λ, λ is signal wavelength, with F ₀(η) be expectation directional diagram, η ₀In the time of=20 °, the designed array antenna complex weighting coefficient of the method is:

W ₁＝-0.0050+0.0389i,W ₂=0.0164+0.0462i,W ₃=0.0276-0.0189i,

W ₄=-0.0180+0.0059i,W ₅=0.0056-0.0031i,W ₆=-0.0029+0.0015i,

W ₇=0.0010-0.0004i,W ₈=-0.0004+0.0005i,W ₉=0.0003-0.0005i,

W ₁₀-0.0004+0.0005i,W ₁₁=0.0010-0.0004i,W ₁₂=-0.0029+0.0015i,

W ₁₃=0.0056-0.0031i,W ₁₄=-0.0180+0.0059i,W ₁₅=0.0276-0.0189i,

W ₁₆0.0164+0.0462i。

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