CN102104196B - Module-level error analytic control method for phased array antenna system - Google Patents

Abstract

The invention discloses a module-level error analytic control method for a phased array antenna system, which belongs to the technical field of electronics. The method comprises the following steps of: first, determining initial values of each module error according to a phased array system error analytic control probability model; then, establishing a numerical experiment model according to an amplitude-phase error of each module and an active unit directional diagram; next, generating a numerical test matrix; and finally, outputting a phased array antenna system error analytic control result meeting an expected requirement in a numerical experiment mode. The method finally guides a module design and an overall system design effectively by effectively regulating and controlling various types of errors of a system based on each of module errors and an interconnection mismatch influence among the module errors; and in reverse, the method also can evaluate performance indexes such as an array minor lobe level of the phased array antenna system, a 3dB beam width, the gain loss of an array, beam-pointing accuracy and the like according to actual amplitude-phase errors of modules, and a system error caused by the interconnection mismatch of each of modules.

Description

A kind of module-level error analytic control method for phased array antenna system

Technical field

The invention belongs to electronic technology field, particularly array antenna technology and phased array antenna technology.

Background technology

Phased array antenna system is comprised of core components such as aerial array, TR assembly, radio frequency networks usually.The imperfect element of these that comprise in the system and module can cause multiple at random with the space on relevant error, will cause great impact to phased array antenna system after all these error stacks, may reduce the ability that the anti-electronic jamming of system, anti-antiradiation missile and clutter suppress.

Traditional phased array antenna error analysis control method adopts Probability Principles to analyze, for example, technical report " The Theory of Array Antennas " (MIT Lincoln Lab., 1963) and books " phased array radar system " (National Defense Industry Press, 1993) studied antenna element random magnitude and phase error to the impact on amplitude-phase consistency of the impact of the impact of antenna performance, digital phase shifter quantization error pair array antenna performance and feeder line standing wave.Document " Design of Error Tolerance of a Phased Array " (Electronics Letters, 1985) studied the impact of amplitude phase error on the two-dimensional planar array secondary lobe, provided relevant probability distribution curve according to the Rice random distribution, and the impact of the impact of amplitude phase error pair array directivity and array lobe width.Books " Phased Array Antenna Handbook; Second Edition " (Artech House Inc., 2005) according to average lobe statistical property, studied the impact of the amplitude phase error pair array peak value secondary lobe of cyclic array, and the periodicity width of cloth distributes mutually and the impact of time retardation pair array secondary lobe.Document " random error is on the impact of modular array antenna side lobe " (electric wave science journal, Vol.21, No.6,2006) the derived span of phase error, cell position error and submatrix site error and the relation of modular array antenna side lobe cumulative probability and the relation of cell position error, submatrix site error and integral position error.Books " Phased Array Radar Antenna " (National Defense Industry Press, 2007) with Probability Principles the statistical property of planar phased array antenna has been done analysis, array gain loss and the minor level studied in array element excitation amplitude phase error, site error and the element failure situation worsen situation.Generally speaking, traditional phase array error analysis and secondary lobe performance estimating method adopt Probability Principles to carry out modeling analysis, its shortcoming is that said method can not obtain accurately result when array antenna is structure Weighting Matrices, aperiodic structure battle array, curved surface conformal array structure.In addition, traditional analytical method do not analyze from the conceptive error to modules of module level, the systematic error that the module interconnects mismatch causes does not consider that therefore traditional analytical method is difficult to the accurately Discrepancy Control Area of control modules yet.

Generally speaking, for phased array antenna system, how exactly the irregularity degree of analytical system (comprising the front distortion that the factors such as mismachining tolerance, location tolerance, wind-force, gravity of device cause), modules amplitude phase error, phase shifter quantization error, array mutual coupling impact and module interconnects mismatch also not have definite technical scheme at present to the impact of systematic function.

Summary of the invention

The invention provides a kind of module-level error analytic control method for phased array antenna system.The present invention can calculate the error range that modules need to be controlled in the phased array antenna system, thereby effectively instruct modular design according to the expectation requirement of the overall secondary lobe performance of phased array antenna system, finishes the phased array antenna system master-plan; The present invention can also be according to the amplitude phase error of modules reality in the phased array antenna system, and the systematic error that causes of modules interconnection mismatch, assesses conversely the overall secondary lobe performance of phased array antenna system.

Because the error of all modules has stochastic behaviour in the phased array antenna system, can set up according to Probability Principles the probabilistic model of phased array antenna system error analysis and secondary lobe Performance Evaluation, obtain the roughly approximation of phased array antenna system modules error; Then, analyze according to the systematic error that module amplitude phase error, the irregularity degree of system, array mutual coupling impact, phase shifter quantization error, the module interconnects mismatch of phased array antenna system causes, set up the numerical experiment model of phased array antenna system error analysis; Again with the approximation of the phased array antenna system modules error that obtains the at first initial input as the numerical experiment model, according to the algorithmic rule that arranges all kinds of errors of system are regulated and control, pass through iteration optimization algorithms, adopt the mode of numerical experiment, accurately draw the error control and systematic function assessment of full spatial domain arbitrary structures phased array antenna system.

Detailed technology scheme of the present invention is as follows:

A kind of module-level error analytic control method for phased array antenna system as shown in Figure 2, may further comprise the steps:

Step 1: the variances sigma of tentatively determining phased array antenna system overall error δ ²According to the statistical property of standard array antenna lobe, set up the probability theory model of phased array antenna system error analysis and secondary lobe Performance Evaluation:

$P(S\≤S_L)={\∫}_0^{s_L}\frac{S}{{\mathrm{\σ}}_1^2}\exp \left[\frac{-(S^2+{\stackrel{\‾}{R}}^2)}{{2\mathrm{\σ}}_1^2}\right]I_0\left(\frac{S\stackrel{\‾}{R}}{{\mathrm{\σ}}_1^2}\right)\mathrm{dS}---\left(1\right)$

Wherein, P is that the actual minor level S of phased array antenna system is no more than (being better than) expectation minor level S _LProbability, S is the actual minor level of phased array antenna system, S _LBe the expectation minor level of phased array antenna system,

Be the mean value of secondary lobe and main lobe ratio,

Be the variance of phased array antenna system overall error, I ₀Be Rayleigh Distribution Function; Minor level S according to the phased array antenna system expectation _LAnd probability P, can obtain a path channels error delta in the phased array antenna system by (1) formula ₁Variance

And then can get the variances sigma of phased array antenna system overall error δ ²:

${\mathrm{\σ}}^2;{2\mathrm{\σ}}_1^2\mathrm{\ηP}\left(\mathrm{\Γ}\right)W---\left(2\right)$

Wherein, η is the efficient of phased array antenna system; W is phased array antenna system array element sum; P (Γ) is effective work probability of phased array antenna system array element; Γ represents the stochastic variable distribution matrix whether array element damages, and the element among the matrix Γ is " 1 " or " 0 ", and the array element of " 1 " expression correspondence position is intact, and the array element of " 0 " expression correspondence position damages.

Step 2: determine

With

Initial value.

Because the variances sigma of the phased array antenna system overall error δ that step 1 draws ²Satisfy following relation:

$\left\{\begin{array}{c}{\mathrm{\σ}}^2={\mathrm{\σ}}_A^2+{\mathrm{\σ}}_{\mathrm{\φ}}^2\\ {\mathrm{\σ}}_A^2={\mathrm{\σ}}_{A,\mathrm{TR}}^2+{\mathrm{\σ}}_{A,\mathrm{BF}}^2\\ {\mathrm{\σ}}_{\mathrm{\φ}}^2={\mathrm{\σ}}_{\mathrm{AN}}^2+{\mathrm{\σ}}_{\mathrm{\φ},\mathrm{TR}}^2+{\mathrm{\σ}}_{\mathrm{\φ},\mathrm{BF}}^2+{\mathrm{\σ}}_P^2+{\mathrm{\σ}}_c^2\end{array}\right.---\left(3\right)$

Wherein

Be the total range error δ of phased array antenna system _AVariance, be generally σ ²20%～40%;

Be the total phase error δ of phased array antenna system _φVariance, be generally σ ²60%～80%;

Be TR assembly range error δ in the phased array antenna system _{A, TR}Variance, be generally

60%～80%;

Be phased array antenna system medium wave l network range error δ _{A, BF}Variance, be generally

20%～40%;

Irregularity degree error delta for phased array antenna system _ANVariance, be generally

5%～15%;

Be TR assembly phase error δ in the phased array antenna system _{φ, TR}Variance, be generally

35%～65%;

The δ of phased array antenna system medium wave l network phase error _{φ, BF}Variance is generally

10%～30%;

The variance of digital phase shifter quantization error is generally in the phased array antenna system

5%～10%;

The error delta that the module interconnects mismatch causes in the phased array antenna system _cVariance, be generally

15%～30%.

According to formula (3), determine the initial input parameter of the variance of various errors in the numerical experiment model.

Step 3: determine the active cell directional diagram in the phased array antenna system

Adopt the method for theoretical calculating, Electromagnetic Simulation or experiment test, obtain the active cell directional diagram of considering element mutual coupling, mounting plate, array environmental impact

Step 4: make up the numerical experiment model.

Make up the numerical experiment model F of the phased array antenna system in any array structure arbitrary scan zone, full spatial domain _N(θ, φ):

$F_N(\mathrm{\θ},\mathrm{\φ})=\underset{m=1}{\overset{M}{\mathrm{\Σ}}}\underset{n=1}{\overset{N}{\mathrm{\Σ}}}\mathrm{\Γ}\·I_{\mathrm{mn}}\·(1+{\mathrm{\δ}}_A)\exp \left({\mathrm{j\δ}}_{\mathrm{\φ}}\right)f_{\mathrm{mn}}^a(\mathrm{\θ},\mathrm{\φ})\exp (\mathrm{jk}\hat{r}\·R_{\mathrm{mn}})\exp (\mathrm{jk}\hat{r}\·R_0)---\left(4\right)$

(4) in the formula,

The unit radiation vector of from the origin of coordinates to the point of observation (θ, φ), R _MnThe position coordinates of antenna element in the phased array antenna system, I _MnBe that m is capable, the current value of n row radiating element, k is wave number, j unit imaginary number, R ₀Main lobe pointing direction when being array pattern scanning; δ _ASatisfying average is zero, and variance is

Normal distribution; δ _φSatisfying average is zero, and variance is

Normal distribution.

Step 5: according to the determined numerical experiment model of step 4, produce the numerical value test matrix.Wherein the numerical value test comprises Γ matrix, δ with matrix _AMatrix and δ _φMatrix.Described Γ matrix is the stochastic variable distribution matrix whether array element damages, and its producing method is: for effective work probability P (Γ) of a given phased array antenna system array element, adopt the Discrete Stochastic location mode to determine.Described δ _AMatrix is that to satisfy average be zero, and variance is

The normal distribution matrix; Described δ _φMatrix is that to satisfy average be zero, and variance is

The normal distribution matrix.

Step 6: with the numerical value test matrix substitution formula (4) that step 5 produces, calculate the numerical experiment results of a phased array antenna system.

Step 7: execution in step 5～6 is total to T repeatedly ₁Inferior, obtain T ₁The numerical experiment results of individual phased array antenna system; To T ₁The numerical experiment results of individual phased array antenna system is carried out statistical analysis, if reach the expectation requirement of phased array antenna system, exports then that step 2 determines

With

Value; Otherwise execution in step 8.

Step 8: right

With

Again assignment is returned step 5.

By technique scheme, can finish phased array antenna system module level error analysis control.

The invention has the beneficial effects as follows:

The invention solves the technical problem that conventional method is not suitable for the error analysis control of phased array antenna system module level and the overall performance assessment of structure Weighting Matrices, aperiodic structure battle array and curved surface conformal array structure.The method based on modules error in the phased array antenna system and between them the interconnection mismatch impact, by all kinds of errors of system are carried out Effective Regulation, phased array antenna system that can arbitrary face arbitrary scan position, the full spatial domain of pair array carries out module level error analysis control.The present invention not only can calculate the error range that modules need to be controlled according to the expectation requirement of phased array antenna system secondary lobe performance, thereby can effectively instruct modular design, finishes the phased array antenna system master-plan; Conversely also can be according to the amplitude phase error of module and the actual arrival of device, and the systematic error that causes of modules interconnection mismatch, the performance index such as the gain loss of phased array antenna system array minor level, 3dB beamwidth, array and beam-pointing accuracy are assessed.The present invention combines active cell directional diagram technology, can accurately obtain element pattern data message in the battle array, so that the analysis and Control result accurately and reliably, has very strong engineering adaptability, can be applicable to one dimensional linear array, two dimensional surface battle array, structure Weighting Matrices, Sparse Array, curved surface conformal array, and the phased array antenna system module level error analysis control of other any array structure and overall performance assessment.

Description of drawings

Fig. 1 is phased array antenna system modules cascade schematic diagram of the present invention.This phased array antenna system is comprised of antenna array, TR assembly, radio frequency network, frequency conversion channel, ripple control device, power supply, device end.

Fig. 2 is the workflow diagram of phased array antenna system error analysis of the present invention and Performance Evaluation.Wherein the systematic error approximation that obtains of probability theory model can be decomposed into module amplitude phase error, module-cascade error, system's irregularity degree, quantization error, and the initial parameter input of these errors as the numerical experiment model, calculate the numerical experiment results of phased array antenna system by the numerical experiment model, carry out next step flow process by judging, if index is up to standard, direct Output rusults then is if index is not up to standard, then carry out parameter and upgrade, until export satisfactory result.

Fig. 3 is the octangle structure Weighting Matrices structural representation described in the specific embodiment of the invention.

Fig. 4 is the φ=0 ° of the octangle structure Weighting Matrices phased array antenna system Performance Evaluation actual measurement described in the specific embodiment of the invention, 180 °, and the antenna pattern of θ=0 °～90 ° of faces.

Fig. 5 is the φ=45 ° of the octangle structure Weighting Matrices phased array antenna system Performance Evaluation actual measurement described in the specific embodiment of the invention, 225 °, and the antenna pattern of θ=0 °～90 ° of faces.

Fig. 6 is the φ=90 ° of the octangle structure Weighting Matrices phased array antenna system Performance Evaluation actual measurement described in the specific embodiment of the invention, 270 °, and the antenna pattern of θ=0 °～90 ° of faces.

Fig. 7 is the φ=135 ° of the anistree structure Weighting Matrices phased array antenna system Performance Evaluation actual measurement described in the specific embodiment of the invention, 315 °, and the antenna pattern of θ=0 °～90 ° of faces.

Embodiment

It is as follows to implement principle of the present invention: at first set up the probabilistic model of phased array antenna system error analysis control according to Probability Principles, determine the initial parameter value of phased array antenna system modules error; Then the systematic error that causes according to module amplitude phase error, the irregularity degree of system, phase shifter quantization error, the module interconnects mismatch of phased array antenna system, take the active cell directional diagram information of array mutual coupling impact into consideration, set up the numerical experiment model of phased array antenna system error analysis control; Produce according to the numerical experiment model again and comprise Γ matrix, δ _AMatrix and δ _φThe numerical value test matrix of matrix; At last with the initial parameter value substitution numerical experiment model of modules error, calculate the numerical experiment results of phased array antenna system, and the logarithm value experimental result is carried out statistical analysis: if reach the expectation requirement of phased array antenna system, then export phased array antenna system error analysis control result, otherwise upgrade the parameter value of modules error, recomputate according to the numerical experiment model, until the phased array antenna system error analysis control result that output meets the expectation and requires.

Below in conjunction with an octangle structure Weighting Matrices phased array antenna system, the present invention is further specified.

If the phased array antenna system antenna array is M * N array element, get M=12 in the present embodiment, N=12,6 unit are removed respectively at four angles, form one 120 yuan anistree battle array, as shown in Figure 3.

(1), estimates the variance of phased array antenna system accumulation overall error.According to probabilistic model

$P(S\≤S_L)={\∫}_0^{s_L}\frac{S}{{\mathrm{\σ}}_1^2}\exp \left[\frac{-(S^2+{\stackrel{\‾}{R}}^2)}{{2\mathrm{\σ}}_1^2}\right]I_0\left(\frac{S\stackrel{\‾}{R}}{{\mathrm{\σ}}_1^2}\right)\mathrm{dS}$

Can draw the variances sigma of phased array antenna system accumulation overall error ²In this example, the theoretical minor level of structure Weighting Matrices is-17.8dB, so the average minor level

Very little, when strict departure, desirable average minor level is Get simultaneously expectation minor level S _L=-16dB, probability is taken as 97%, can obtain the systematic error variances sigma ₁=0.0297, consider that the efficiency eta of phased array antenna system is 80%, array element lost efficacy 5%, and the overall error σ of system is then arranged ²0.1614.

(2), determine the initial input parameter of numerical experiment model.

The first, determine the error of modules, the irregularity degree σ of system in this example _AN=3.5 °; The range error σ of TR assembly _{A, TR}=1.5dB, phase error σ _{φ, TR}=18.45 °; The range error σ of radio frequency network _{A, BF}=0.5dB, phase error σ _{φ, BF}=4.5 °; Digital phase shifter is got 6, and its quantization error is σ _P=1.62 °.

The second, computing module interconnection mismatch, the modules mismatch that the reflection standing wave when considering phased array antenna system modules cascade and Insertion Loss cause, getting the antenna array standing wave in this example is that 1.8, TR assembly standing wave is 2, the radio frequency network standing wave is 1.8; Insertion Loss between antenna array and the TR is taken as-1.5dB, and the Insertion Loss between TR assembly and the radio frequency network is taken as-2.5dB; By formula:

${\mathrm{\σ}}_c^2=\frac{1}{2}\underset{j}{\mathrm{\Σ}}{\left\{\frac{\underset{i=1}{\overset{j}{\mathrm{\Π}}}{s}_i{r}_j\left(\underset{i=1}{\overset{j}{\mathrm{\Σ}}}\underset{l=j-i+1}{\overset{j}{\mathrm{\Π}}}{s}_l^{\′}{r}_{j-i}^{\′}\right)}{\underset{i=1}{\overset{n}{\mathrm{\Π}}}{s}_i}\right\}}^2$

The error that draws modules cascade mismatch is σ _c=5.13 °.

Three, extract element pattern information in the battle array that comprises mutual coupling, cell orientation diagram data in the battle array in this example Adopt Electromagnetic Simulation software HFSS Straight simulation to obtain.

(3), the parameter input information numerical experiment model that step (2) is drawn

$F_N(\mathrm{\θ},\mathrm{\φ})=\underset{m=1}{\overset{M}{\mathrm{\Σ}}}\underset{n=1}{\overset{N}{\mathrm{\Σ}}}\mathrm{\Γ}\·I_{\mathrm{mn}}\·(1+{\mathrm{\δ}}_A)\exp \left({\mathrm{j\δ}}_{\mathrm{\φ}}\right)f_{\mathrm{mn}}^a(\mathrm{\θ},\mathrm{\φ})\exp (\mathrm{jk}\hat{r}\·R_{\mathrm{mn}})\exp (\mathrm{jk}\hat{r}\·R_0)$

Obtain accurately information by the test matrix that produces.In this example, the number of times T that each parameter input is calculated ₁=1000, thus when obtaining the input of initial parameter, the phased array antenna system secondary lobe is actual to be arrived-and the probability of 16dB is 82.33%, and be not 97%.

(4), logarithm value experimental model

With

Again assignment, and calculate according to the numerical experiment model satisfying the phased array antenna system minor level and be no more than-when the probability of 16dB is 97%, the irregularity degree σ of system _AN=2.13 °; The range error σ of TR assembly _{A, TR}=1.12dB, phase error σ _{φ, TR}=10.17 °; The range error σ of radio frequency network _{A, BF}=0.42dB, phase error σ _{φ, BF}=3.15 °; Digital phase shifter is got 6, and its quantization error is σ _P=1.62 °.Modules interconnection mismatch error σ _c=2.81 °, namely the antenna array standing wave is that 1.5, TR assembly standing wave is 1.5, and the radio frequency network standing wave is 1.5, and the Insertion Loss between antenna array and the TR is taken as-1dB, and the Insertion Loss between TR assembly and the radio frequency network is taken as-1dB; Array element can lose efficacy 5%.

According to technique scheme, can also draw phased array antenna system is 0.27～0.42dB at the normal direction gain loss; The 3dB beamwidth is 9.54 °～9.67 °; Beam-pointing accuracy is 0.36 °～0.43 °.

(5), the modules index distribution condition that obtains according to step (4) is carried out the material object design, Fig. 4, Fig. 5, Fig. 6, Fig. 7 are phased array antenna system secondary lobe performance object test figure, can find out that from the actual measurement situation the method can accurately draw the array performance situation of each section and arbitrary scan position.

Claims (3)

1. module-level error analytic control method for phased array antenna system may further comprise the steps:

Step 1: the variances sigma of tentatively determining phased array antenna system overall error δ ²

According to the statistical property of standard array antenna lobe, set up the probability theory model of phased array antenna system error analysis and secondary lobe Performance Evaluation:

$P(S\≤S_L)={\∫}_0^{s_L}\frac{S}{{\mathrm{\σ}}_1^2}\exp \left[\frac{-(S^2+{\stackrel{\‾}{R}}^2)}{2{\mathrm{\σ}}_1^2}\right]I_0\left(\frac{S\stackrel{\‾}{R}}{{\mathrm{\σ}}_1^2}\right)\mathrm{dS}---\left(1\right)$

Wherein, P is that the actual minor level S of phased array antenna system is no more than expectation minor level S _LProbability, S is the actual minor level of phased array antenna system, S _LBe the expectation minor level of phased array antenna system,

Be the mean value of secondary lobe and main lobe ratio, I ₀Be Rayleigh Distribution Function; Minor level S according to the phased array antenna system expectation _LAnd probability P, can obtain a path channels error delta in the phased array antenna system by (1) formula ₁Variance

And then can get the variances sigma of phased array antenna system overall error δ ²:

${\mathrm{\σ}}^2\≅2{\mathrm{\σ}}_1^2\mathrm{\ηP}\left(\mathrm{\Γ}\right)W---\left(2\right)$

Wherein, η is the efficient of phased array antenna system; W is phased array antenna system array element sum; P (Γ) is effective work probability of phased array antenna system array element; Γ represents the stochastic variable distribution matrix whether array element damages, and the element among the matrix Γ is " 1 " or " 0 ", and the array element of " 1 " expression correspondence position is intact, and the array element of " 0 " expression correspondence position damages;

Step 2: determine

With

Initial value;

Because the variances sigma of the phased array antenna system overall error δ that step 1 draws ²Satisfy following relation:

$\left\{\begin{array}{c}{\mathrm{\σ}}^2={\mathrm{\σ}}_A^2+{\mathrm{\σ}}_{\mathrm{\φ}}^2\\ {\mathrm{\σ}}_A^2={\mathrm{\σ}}_{A,\mathrm{TR}}^2+{\mathrm{\σ}}_{A,\mathrm{BF}}^2\\ {\mathrm{\σ}}_{\mathrm{\φ}}^2={\mathrm{\σ}}_{\mathrm{AN}}^2+{\mathrm{\σ}}_{\mathrm{\φ},\mathrm{TR}}^2+{\mathrm{\σ}}_{\mathrm{\φ},\mathrm{BF}}^2+{\mathrm{\σ}}_P^2+{\mathrm{\σ}}_c^2\end{array}\right.---\left(3\right)$

Wherein

Be the total range error δ of phased array antenna system _AVariance;

Be the total phase error δ of phased array antenna system _φVariance;

Be TR assembly range error δ in the phased array antenna system _{A, TR}Variance;

Be phased array antenna system medium wave l network range error δ _{A, BF}Variance;

Irregularity degree error delta for phased array antenna system _ANVariance;

Be TR assembly phase error δ in the phased array antenna system _{φ, TR}Variance;

The δ of phased array antenna system medium wave l network phase error _{φ, BF}Variance;

The variance of digital phase shifter quantization error in the phased array antenna system;

The error delta that the module interconnects mismatch causes in the phased array antenna system _cVariance;

According to formula (3), determine the initial input parameter of the variance of various errors in the numerical experiment model;

Step 3: determine the active cell directional diagram in the phased array antenna system

Adopt the method for theoretical calculating, Electromagnetic Simulation or experiment test, obtain the active cell directional diagram of considering element mutual coupling, mounting plate, array environmental impact

Step 4: make up the numerical experiment model;

Make up the numerical experiment model F of the phased array antenna system in any array structure arbitrary scan zone, full spatial domain _N(θ, φ):

$F_N(\mathrm{\θ},\mathrm{\φ})=\underset{m=1}{\overset{M}{\mathrm{\Σ}}}\underset{n=1}{\overset{N}{\mathrm{\Σ}}}\mathrm{\Γ}\·I_{\mathrm{mn}}\·(1+{\mathrm{\δ}}_A)\exp \left({\mathrm{j\δ}}_{\mathrm{\φ}}\right)f_{\mathrm{mn}}^a(\mathrm{\θ},\mathrm{\φ})\exp (\mathrm{jk}\hat{r}\·R_{\mathrm{mn}})\exp (\mathrm{jk}\hat{r}\·R_0)---\left(4\right)$

(4) in the formula, The unit radiation vector of from the origin of coordinates to the point of observation (θ, φ), R _MnThe position coordinates of antenna element in the phased array antenna system, I _MnBe that m is capable, the current value of n row radiating element, k is wave number, j unit imaginary number, R ₀Main lobe pointing direction when being array pattern scanning; δ _ASatisfying average is zero, and variance is Normal distribution; δ _φSatisfying average is zero, and variance is

Normal distribution;

Step 5: according to the determined numerical experiment model of step 4, produce the numerical value test matrix;

Described numerical value test comprises Γ matrix, δ with matrix _AMatrix and δ _φMatrix; Described Γ matrix is the stochastic variable distribution matrix whether array element damages, and its producing method is: for effective work probability P (Γ) of a given phased array antenna system array element, adopt the Discrete Stochastic location mode to determine; Described δ _AMatrix is that to satisfy average be zero, and variance is

The normal distribution matrix; Described δ _φMatrix is that to satisfy average be zero, and variance is

The normal distribution matrix;

Step 6: with the numerical value test matrix substitution formula (4) that step 5 produces, calculate the numerical experiment results of a phased array antenna system;

Step 7: execution in step 5 ~ 6 is total to T repeatedly ₁Inferior, obtain T ₁The numerical experiment results of individual phased array antenna system; To T ₁The numerical experiment results of individual phased array antenna system is carried out statistical analysis, if reach the expectation requirement of phased array antenna system, exports then that step 2 determines

With

Value; Otherwise execution in step 8;

Step 8: right With

Again assignment is returned step 5.

2. module-level error analytic control method for phased array antenna system according to claim 1 is characterized in that, described in the step 2

Be σ ²20% ~ 40%, described

Be σ ²60% ~ 80%; Described

For

60% ~ 80%, described

For

20% ~ 40%, described

For

5% ~ 15%, described

For

35% ~ 65%, described

For

10% ~ 30%, described

For

5% ~ 10%, described

For

15% ~ 30%.

3. module-level error analytic control method for phased array antenna system according to claim 1, it is characterized in that, the array antenna structure of described phased array antenna system is one dimensional linear array, two dimensional surface battle array, structure Weighting Matrices, Sparse Array, curved surface conformal array, and the array of other arbitrary structures.

Images