CN105116241A - Novel on-site equivalent darkroom measurement method - Google Patents

Abstract

Disclosed is a novel on-site equivalent darkroom measurement method. Fourier transforms are performed on signals received by two antennas firstly, a zero point occurs in a directional diagram on a frequency domain by utilizing weight values and through combination with the directional diagram of a binary antenna array, the zero point is aligned with a signal direction of arrival (DOA) of equipment under test (EUT), an array output S<0>(f) only contains an interference component, signals S<1>(f) and S<2>(f) received by single antennas comprise EUT signal components and also comprise interference components, and the interference components in the array output S<0>(f) and the signals S<1>(f) and S<2>(f) are highly relevant, so the interference components in the S<1>(f) and S<2>(f) can be removed by utilizing cancellation processing, and then a signal of the EUT is obtained. Based on an advanced signal processing technology, through adoption of a double-channel system, and through combination of spatial filtering and a signal correlation processing method, when a test is performed on site, an equivalent darkroom environment can be obtained, on-site environment interferences are filtered, and a real radiation characteristic of the EUT is obtained.

Description

A kind of Novel site equivalence darkroom measuring method

Technical field

The present invention relates to Electromagnetic Field and Microwave Technology field, particularly relate to the method for carrying out electromagnetic radiation test in environment at the scene.

Background technology

For large scale electronic equipment, on-the-spot test mode is usually adopted to search electromagnetic interference problem.But the broadcast at scene, TV, mobile phone and other potential radiation source can severe jamming measuring accuracies.Usually, its level sending signal often exceeds standard limited value 30 ~ 40dB, Device under test (EquipmentUnderTset is flooded in this ambient noise level, situation about EUT) transmitting, the test duration can be caused to grow, test error is large, environmental interference is thought by mistake be the adverse consequencess such as EUT signal, the electromagnetic radiation of EUT cannot be accurately measured, cause diagnostic error.Utilize darkroom or screened room to measure and can eliminate these impacts, but some equipments are too huge, can not darkroom be placed on or the standard open area test site of being transported to is tested, can only carry out on-the-spot test.Therefore, need effective on-the-spot test and disposal route, even if when EUT is operated in very big environmental interference, also by the interference filtering in environment, the accurate measurement to EUT electromagnetic radiation can be realized at the scene.

One of environmental interference suppressing method utilizes timesharing to measure.Timesharing measuring method is specially: first, closes EUT in the t1 moment, uses EMI receiver or frequency spectrograph measurement to obtain the power spectrum of environmental interference signal; Then, open EUT in the t2 moment, now record the power spectrum of environmental interference signal and EUT signal, the result that front and back record for twice is subtracted each other, just can offset environmental interference, obtain EUT radiated signal power spectrum.

Within 2005, American scholar Marino.J puies forward the patented technology obtaining virtual darkroom.This patent based on self-adaprive predictive control, the mistiming problem brought when specify that and overcome single channel distribution tests in twin-channel mode, thus improve measuring accuracy and range of application.As shown in Figure 1, antenna A places near EUT its principle, and distance is d, and antenna B then places away from EUT, and distance EUT is at least greater than 10d.Main channel 1 and reference channel 2 are synchronous, wherein main channel 1 receives EUT signal and environmental interference signal by antenna A, and reference channel 2 receives only environmental interference signal by antenna B, the environmental interference signal height arrived due to two channel reception is correlated with, closing property disposal route is wanted in utilization, just can filtering environmental undesired signal.

Also has a kind of measuring method based on Array Signal Processing, as shown in Figure 2, a set of antenna receiving array is placed around radiation source, each antenna element all can receive the mixed signal be made up of EUT radiation signal and background noise, the direction of arrival (directionofarrival, DOA) of each signal of MUSIC Estimation of Spatial Spectrum technical limit spacing can be utilized.According to the Estimation of Spatial Spectrum result of signal, utilize MVDR criterion, optimal weighting is done to each array element Received signal strength, under the distortionless prerequisite of guarantee EUT radiation signal, array beams is formed " zero falls into " the arrival bearing of undesired signal, realize the airspace filter to undesired signal, reflect the true radiation characteristic of EUT comparatively accurately.

, also there is following defect separately in above-mentioned existing three kinds of measuring methods:

The environmental interference power spectrum that the method adopting timesharing to measure proposes moment twice measurement being EUT startup and shutdown is all close to identical, and that is environmental interference belongs to time stationary signal.In fact, undesired signal many times under conventional environment all has feature that is intermittent and amplitude fluctuations, such as when there is short-term burst signal in test environment, the environmental interference signal measured when the environmental interference signal measured during EUT shutdown and EUT start just can not effectively be offset.

The method measured during virtual darkroom method score based on noise cancellation has larger improvement, but effect is unsatisfactory in actual use, be mainly reflected in: 1. in order to reach desirable precision, one of them receiving antenna needs the position be placed on away from EUT, because the inconsistent meeting of two receiving antenna present position environmental interference brings larger test error; 2. antenna is placed at a distance, causes test cable long, infeasible in operation, also have impact on measuring accuracy; 3. when exist in environment with EUT radiation signal with frequently and intensity very large component time, interference suppressioning effect is not obvious.

Disturbance restraining method based on Array Signal Processing have employed hyperchannel system, and its structural system is comparatively complicated, and it is large that design realizes difficulty, and hardware development cost is high, limits its widespread use.

Summary of the invention

In order to more adequately obtain the radiation-emitting characteristic of electronic equipment on Large-Scale Equipment platform under complex electromagnetic environment at the scene, the invention provides a kind of Novel site equivalence darkroom measuring method.

Technical scheme of the present invention is:

As shown in Figure 3, first the signal received two antennas of the present invention does Fourier transform (FFT), and frequency domain utilizes the directional diagram of the comprehensive two-element antenna array of weights, makes it occur a zero point, allow the signal arrival bearing aiming at EUT this zero point, then array exports S ₀f () only comprises interference components, and the signal S that individual antenna receives ₁(f) and S ₂f not only comprise EUT component of signal but also comprise interference components in (), the interference components in three is height correlation, therefore can utilize and offset process, removes S ₁(f) and S ₂interference components in (f), thus the signal obtaining Device under test.

Particularly, a kind of Novel site equivalence of the present invention darkroom measuring method, comprises the following steps:

(1) DOA of EUT signal is first determined, i.e. the angle of EUT sense and aerial array normal direction.Here the existing instruments such as laser angle meter can be utilized to realize;

(2) according to the angle measured, utilize broadband MVDR Beamforming Method, calculate weighted value, exhibition by combination method directional diagram, makes aim at EUT sense the zero point of directional diagram, thus extracts the frequency spectrum of undesired signal; Detailed process is as follows:

1. sampled by the signal that two antennas receive, obtain discrete data x (t), then carry out segmentation respectively, each segment data length is L;

2. the data of two antennas at n-th section are designated as l point quick Fourier conversion (FastFourierTransform, FFT) is done to it, obtains frequency domain narrow band data:

$X_m^{\left(n\right)}\left(k\right)=\underset{l=0}{\overset{L-1}{\&Sigma;}}{x}_m^{\left(n\right)}\left(l\right)e^{-j2\mathrm{\&pi;}kl/L},k=0,1,...,L-1---\left(1\right)$

Wherein j refers to imaginary unit, and e is the nature truth of a matter, and π is circular constant.

3. two antenna arrowband frequency-domain data matrixes are extracted:

$X^{\left(n\right)}\left(k\right)=\&lsqb;X_1^{\left(n\right)}\left(k\right),X_2^{\left(n\right)}\left(k\right)\&rsqb;---\left(2\right)$

If 4. the DOA of EUT radiation signal is θ, assuming that array main beam be oriented to θ ₀, and θ ₀as far as possible away from θ, its steering vector is α (θ ₀) can be expressed as

$\mathrm{\&alpha;}\left({\mathrm{\&theta;}}_0\right)=\left[\begin{array}{c}\exp (-j\mathrm{\&omega;})\\ \exp (-j\mathrm{\&omega;}\mathrm{\&tau;})\end{array}\right]---\left(3\right)$

In formula, $\mathrm{\&omega;}=2\mathrm{\&pi;}f=2\mathrm{\&pi;}\frac{c}{\mathrm{\&lambda;}},\mathrm{\&tau;}=\frac{{\mathrm{dcos\&theta;}}_0}{c},$ C is the light velocity, and λ is wavelength.

5. the beam weight vector that minimum variance undistorted response (MinimumVarianceDistortionlessResponse, MVDR) method design is corresponding is adopted.

If the output power of array signal is expressed as:

P _out＝E{|y| ²}＝E{(w ^Hx)·(w ^Hx) ^H}＝w ^HR _xxw(4)

In formula, y=w ^hx is the output signal after array weight, w=w (f _k)=[w ₁(f _k), w ₂(f _k)], x=[x ₁(t), x ₂(t)], H is the meaning of getting conjugate transpose.The MVDR criterion of optimality can be expressed as:

minP _out＝w ^HR _xxw

s.t.w ^Hα(θ ₀)＝1(5)

This constraint condition is also called wave beam " zero setting condition ", because it forces " zero point " of receiving array beam pattern to point to all EUT sense.Wherein Pout refers to array output power, and the implication of min is the minimized meaning, and namely array output power Pout is minimum, and the implication of s.t. refers to and will satisfy condition simultaneously, R _xxrefer to input signal x=[x ₁(t), x ₂(t)] covariance matrix.

6. Lagrangian function is constructed:

L(w,λ)＝w ^HR _xxw+λ(α(θ ₀) ^Hw-1)+λ ^*(w ^Hα(θ ₀)-1)(6)

Consider w ∈ C ^{m × 1}, make the conjugate gradient of L (w, λ) be 0, namely

$\&part;L(w,\mathrm{\&lambda;})/\&part;w^{*}=0---\left(7\right)$

Obtain

w ^H＝-λα(θ ₀) ^HR _xx ^-1(8)

Substitute into w α (θ ₀)=1, can obtain

λ＝-(α(θ ₀) ^HR _xx ^-1α(θ ₀)) ^-1(9)

Thus can best initial weights be obtained:

w _opt＝R _xx ^-1α(θ ₀)(α ^H(θ ₀)R _xx ^-1α(θ ₀)) ^-1＝R _xx ^-1α(θ ₀)P _omin(10)

P in formula _omin=(α ^h(θ ₀) R _xx ^-1α (θ ₀)) ^-1for minimum output power.

(3) be weighted summation to each narrow band data, the wave beam obtaining each subband exports data:

$Y^{\left(n\right)}\left(k\right)=w^H\left(f_k\right)X^{\left(n\right)}\left(k\right)=\underset{m=1}{\overset{M}{\&Sigma;}}{w}_m^{*}\left(f_k\right)X_m^{\left(n\right)}\left(k\right)---\left(11\right)$

The array of whole test frequency range has been become to export S by the output data groups of each frequency range ₀(f), i.e. S ₀(f)=[Y (1), Y (2) ..., Y (k)].

(4) utilization offsets process and removes environmental interference;

After above-mentioned signal transacting, now array exports S ₀f () is only containing undesired signal, and the output S of individual antenna ₂then both containing EUT signal in (f), also containing undesired signal, now carry out offseting process, can obtain

S _EUT(f)＝S ₂(f)-S ₀(f)。

Beneficial effect of the present invention:

The present invention is based on advanced signal processing technology, adopts binary channels system, in conjunction with airspace filter and signal cancellation disposal route, when testing at the scene, equivalence can go out a dark room conditions, the environmental interference at filtering scene, obtains the true radiation characteristic of EUT.Following unique advantage is had compared with above-mentioned other are invented:

1, the remote discrete placement of antenna and the baroque defect of hyperchannel system is overcome.The present invention only needs two-element antenna array to coordinate two-channel receiver, considerably increases applicability and ease for operation;

2, precision is higher.Relative to macrotype platform, the size of aerial array almost can be ignored, and the signal that bay receives on test position there will not be ground unrest and disturbs inconsistent situation, thus contributes to improving measuring accuracy;

3, co-channel interference inhibition is better.The limitation of the virtual darkroom measuring method of Marino.Jr design causes it to process co-channel interference.And utilize the present invention, as long as the DOA of undesired signal and EUT signal is inconsistent, just effectively co-channel interference can be suppressed;

4, Measuring Time is shorter.The present invention is the mode measured based on time-domain signal, does digital signal processing, do not need to carry out long frequency domain test, thus greatly can promote measuring speed when therefore only needing to test at the scene to the signal in certain hour after sampling.

Accompanying drawing explanation

Fig. 1 is virtual darkroom principle schematic.

Fig. 2 is the anti-interference radiation-emitting in-site measurement schematic diagram based on Array Signal Processing.

Fig. 3 is equivalent virtual darkroom measuring method schematic diagram.

Fig. 4 is the process flow diagram of a kind of Novel site equivalence of the present invention darkroom measuring method.

Fig. 5 is the simulation configurations schematic diagram of the embodiment of the present invention 1

Fig. 6 is the comparison diagram of frequency spectrum and the original signal spectrum utilizing the inventive method to recover in embodiment 1

Fig. 7 is the experimental field arrangement plan of embodiment 2

Fig. 8 is the signal graph that in embodiment 2, dual channel oscilloscope receives

Fig. 9 is the spectral contrast figure in embodiment 2 before and after EUT target signal filter

Figure 10 is the comparison diagram offseting front and back signal spectrum in embodiment 2

Embodiment

Below in conjunction with drawings and Examples, the present invention is described further.

The invention provides a kind of Novel site equivalence darkroom measuring method, comprise the following steps:

(1) DOA of EUT signal is first determined, i.e. the angle of EUT sense and aerial array normal direction.Here the existing instruments such as laser angle meter can be utilized to realize;

(2) according to the angle measured, utilize broadband MVDR Beamforming Method, calculate weighted value, exhibition by combination method directional diagram, makes aim at EUT sense the zero point of directional diagram, thus extracts the frequency spectrum of undesired signal; Detailed process is as follows:

1. sampled by the signal that two antennas receive, obtain discrete data x (t), then carry out segmentation respectively, each segment data length is L;

2. the data of two antennas at n-th section are designated as l point quick Fourier conversion (FastFourierTransform, FFT) is done to it, obtains frequency domain narrow band data:

$X_m^{\left(n\right)}\left(k\right)=\underset{l=0}{\overset{L-1}{\&Sigma;}}{x}_m^{\left(n\right)}\left(l\right)e^{-j2\mathrm{\&pi;}kl/L},k=0,1,...,L-1---\left(1\right)$

Wherein j refers to imaginary unit, and e is the nature truth of a matter, and π is circular constant.

3. two antenna arrowband frequency-domain data matrixes are extracted:

$X^{\left(n\right)}\left(k\right)=\&lsqb;X_1^{\left(n\right)}\left(k\right),X_2^{\left(n\right)}\left(k\right)\&rsqb;---\left(2\right)$

If 4. the DOA of EUT radiation signal is θ, assuming that array main beam be oriented to θ ₀, and θ ₀as far as possible away from θ, its steering vector is α (θ ₀) can be expressed as

$\mathrm{\&alpha;}\left({\mathrm{\&theta;}}_0\right)=\left[\begin{array}{c}\exp (-j\mathrm{\&omega;})\\ \exp (-j\mathrm{\&omega;}\mathrm{\&tau;})\end{array}\right]---\left(3\right)$

In formula, $\mathrm{\&omega;}=2\mathrm{\&pi;}f=2\mathrm{\&pi;}\frac{c}{\mathrm{\&lambda;}},\mathrm{\&tau;}=\frac{{\mathrm{dcos\&theta;}}_0}{c},$ C is the light velocity, and λ is wavelength.

5. the beam weight vector that minimum variance undistorted response (MinimumVarianceDistortionlessResponse, MVDR) method design is corresponding is adopted.If the output power of array signal is expressed as:

P _out＝E{|y| ²}＝E{(w ^Hx)·(w ^Hx) ^H}＝w ^HR _xxw(4)

In formula, y=w ^hx is the output signal after array weight, w=w (f _k)=[w ₁(f _k), w ₂(f _k)], x=[x ₁(t), x ₂(t)], H is the meaning of getting conjugate transpose.The MVDR criterion of optimality can be expressed as:

minP _out＝w ^HR _xxw

s.t.w ^Hα(θ ₀)＝1(5)

This constraint condition is also called wave beam " zero setting condition ", because it forces " zero point " of receiving array beam pattern to point to all EUT sense.Wherein Pout refers to array output power, and the implication of min is the minimized meaning, and namely array output power Pout is minimum, and the implication of s.t. refers to and will satisfy condition simultaneously, R _xxrefer to input signal x=[x ₁(t), x ₂(t)] covariance matrix.

6. Lagrangian function is constructed:

L(w,λ)＝w ^HR _xxw+λ(α(θ ₀) ^Hw- ¹)+λ ^*(w ^Hα(θ ₀)-1)(6)

Consider w ∈ C ^{m × 1}, make the conjugate gradient of L (w, λ) be 0, namely

$\&part;L(w,\mathrm{\&lambda;})/\&part;w^{*}=0---\left(7\right)$

Obtain

w ^H＝-λα(θ ₀) ^HR _xx ^-1(8)

Substitute into w α (θ ₀)=1, can obtain

λ＝-(α(θ ₀) ^HR _xx ^-1α(θ ₀)) ^-1(9)

Thus can best initial weights be obtained:

w _opt＝R _xx ^-1α(θ ₀)(α ^H(θ ₀)R _xx ^-1α(θ ₀)) ^-1＝R _xx ^-1α(θ ₀)P _omin(10)

P in formula _omin=(α ^h(θ ₀) R _xx ^-1α (θ ₀)) ^-1for minimum output power.

(3) be weighted summation to each narrow band data, the wave beam obtaining each subband exports data:

$Y^{\left(n\right)}\left(k\right)=w^H\left(f_k\right)X^{\left(n\right)}\left(k\right)=\underset{m=1}{\overset{M}{\&Sigma;}}{w}_m^{*}\left(f_k\right)X_m^{\left(n\right)}\left(k\right)---\left(11\right)$

The array of whole test frequency range has been become to export S by the output data groups of each frequency range ₀(f), i.e. S ₀(f)=[Y (1), Y (2) ..., Y (k)].

(4) utilization offsets process and removes environmental interference;

After above-mentioned signal transacting, now array exports S ₀f () is only containing undesired signal, and the output S of individual antenna ₂then both containing EUT signal in (f), also containing undesired signal, now carry out offseting process, can obtain

S _EUT(f)＝S ₂(f)-S ₀(f)。

Embodiment 1

The validity of the inventive method is described with a computer simulation example.

As shown in Figure 5, be the simulation configurations schematic diagram of the present embodiment.

Get array element distance d=300mm, if there are four signals in space, one of them is EUT radiation signal (measured signal), and its excess-three is the environmental interference signal that system is different, and mathematical form is as follows:

$\left\{\begin{array}{c}{S}_{EUT}\left(t\right)=A_{0}sin2\mathrm{\&pi;}{f}_{0}t+A_{0}sin2\mathrm{\&pi;}{f}_{1}t+n\left(t\right)\\ S_{jam1}\left(t\right)=A_{1}sin2\mathrm{\&pi;}{f}_{1}t+n\left(t\right)\\ S_{jam2}\left(t\right)=A_2\exp (j2\mathrm{\&pi;}{f}_{2}t+j2\mathrm{\&pi;}k{t}^2)+n\left(t\right),k=band/t_{total}\\ S_{jam3}\left(t\right)=-A_{3}cos\left(j2{\mathrm{\&pi;f}}_{3}t\right)\exp (-4\mathrm{\&pi;}{(t-t_0)}^2/{\mathrm{\&tau;}}^2)+n\left(t\right)\end{array}\right.$

In formula, containing f in EUT radiation signal ₀=300MHz and f ₁two frequency contents of=600MHz, incident angle is θ _eUT=-45 °.Undesired signal 1 simulates mono-tone interference, frequency f ₂=300MHz, incident angle is θ _jam1=-15 °; Undesired signal 2 analog linearity frequency modulation disturbs, frequency modulation initial frequency f ₃=500MHz, modulation band-width band=100MHz, incident angle is θ _jam2=15 °; Undesired signal 3 simulates Gauss's broadband interference of burst, and incident angle is θ _jam3=60 °, centre frequency f ₄=700MHz, time delay t ₀=256ns, modulating time τ=10ns.A ₀＝A ₁＝A ₂＝1，A ₃＝100。Signal to noise ratio snr=20dB, signal length writing time is t _total=512ns.

Utilize the inhibition of the environmental interference after the process of this patent method as shown in Figure 6, from the contrast of constrained input frequency spectrum, the interference at 400MHz place receives the suppression of 80dB, and linear frequency hopping and Gauss's broadband interference receive the compacting of more than 60dB, the more important thing is that the EUT component of signal of 600MHz also obtains recovery from the frequency spectrum of aliasing.

Embodiment 2

Introduce the detailed process of carrying out this method validation verification by experiment below again.As shown in Figure 7, in order to ensure the accuracy of result, testing and carrying out in microwave dark room, object is the interference beyond screening experiment frequency range in experimental field configuration.Place emitting antenna and receiving antenna in calibration position, the working frequency range of antenna is 200MHz-1GHz.The principle of location position is that the antenna allowing simulation EUT launch is on the discovery direction of receiving antenna array, and the emitting antenna of simulation interference source then has a certain degree with receiving antenna array normal direction.Laser range finder and angular instrument is utilized to carry out position correction after antenna places.Signal source 1 and signal source 2 are simulated respectively and are produced EUT signal and undesired signal, and wherein EUT signal setting is pulsed modulation, and the recurrence interval is 240ns, and pulse width is 120ns, and carrier frequency is 400MHz, and output power is 15dBm.And undesired signal is set to the recurrence interval is 400ns, pulse width is 200ns, and carrier frequency is 700MHz, and output power is 15dBm.The center distance d=0.3m of two receiving antennas, the shielded cable respectively by equal length is connected on binary channels sampling oscilloscope, and oscillographic temporal resolution is set to 5ps, and the consistance of two passages is calibrated before testing.

Fig. 8 is the one piece of data display of dual channel oscilloscope sampling, it is 33 degree by the reset of array compound direction figure, Fig. 9 is the contrast of the signal spectrum that the frequency spectrum of only surplus undesired signal after adopting broadband MVDR to carry out filtering out EUT signal after spatial beams is formed and individual antenna receive, can find out, EUT signal by the level of filtering to background noise, only remains undesired signal in frequency spectrum.

As shown in Figure 10, then after offseting process, undesired signal is then suppressed near the end makes an uproar, compared with pure EUT signal spectrum, after this method process, spectrum signature and the former EUT signal spectrum of the EUT signal recovered are basically identical, and EUT signal almost obtains undistorted recovery.

More than contain the explanation of the preferred embodiment of the present invention; this is to describe technical characteristic of the present invention in detail; be not want summary of the invention to be limited in the concrete form described by embodiment, other amendments carried out according to content purport of the present invention and modification are also protected by this patent.The purport of content of the present invention defined by claims, but not defined by the specific descriptions of embodiment.

Claims (1)

1. a Novel site equivalence darkroom measuring method, is characterized in that: comprise the following steps:

(1) DOA of EUT signal is first determined, i.e. the angle of EUT sense and aerial array normal direction;

(2) according to the angle measured, utilize broadband MVDR Beamforming Method, calculate weighted value, exhibition by combination method directional diagram, makes aim at EUT sense the zero point of directional diagram, thus extracts the frequency spectrum of undesired signal; Detailed process is as follows:

1. sampled by the signal that two antennas receive, obtain discrete data x (t), then carry out segmentation respectively, each segment data length is L;

2. the data of two antennas at n-th section are designated as the conversion of L point quick Fourier is done to it, obtains frequency domain narrow band data:

$X_m^{\left(n\right)}\left(k\right)=\underset{l=0}{\overset{L-1}{\&Sigma;}}{x}_m^{\left(n\right)}\left(l\right)e^{-j2\mathrm{\&pi;}kl/L},k=0,1,...,L-1---\left(1\right)$

Wherein j refers to imaginary unit, and e is the nature truth of a matter, and π is circular constant;

3. two antenna arrowband frequency-domain data matrixes are extracted:

$X^{\left(n\right)}\left(k\right)=\&lsqb;X_1^{\left(n\right)}\left(k\right),X_2^{\left(n\right)}\left(k\right)\&rsqb;---\left(2\right)$

If 4. the DOA of EUT radiation signal is θ, assuming that array main beam be oriented to θ ₀, and θ ₀as far as possible away from θ, its steering vector is α (θ ₀) can be expressed as

$\mathrm{\&alpha;}\left({\mathrm{\&theta;}}_0\right)=\left[\begin{array}{c}\exp (-j\mathrm{\&omega;})\\ \exp (-j\mathrm{\&omega;}\mathrm{\&tau;})\end{array}\right]---\left(3\right)$

In formula, $\mathrm{\&omega;}=2\mathrm{\&pi;}f=2\mathrm{\&pi;}\frac{c}{\mathrm{\&lambda;}},\mathrm{\&tau;}=\frac{d{\mathrm{cos\&theta;}}_0}{c},$ C is the light velocity, and λ is wavelength;

5. the beam weight vector that the design of minimum variance undistorted response method is corresponding is adopted;

If the output power of array signal is expressed as:

P _out＝E{|y| ²}＝E{(w ^Hx)·(w ^Hx) ^H}＝w ^HR _xxw（4）

In formula, y=w ^hx is the output signal after array weight, w=w (f _k)=[w ₁(f _k), w ₂(f _k)], x=[x ₁(t), x ₂(t)], H represents the meaning of getting conjugate transpose; The MVDR criterion of optimality can be expressed as:

minP _out＝w ^HR _xxw

s.t.w ^Hα(θ ₀)＝1（5）

This constraint condition is also called wave beam " zero setting condition ", because it forces " zero point " of receiving array beam pattern to point to all EUT sense; Wherein Pout refers to array output power, and the implication of min is the minimized meaning, and namely array output power Pout is minimum, and the implication of s.t. refers to and will satisfy condition simultaneously, R _xxrefer to input signal x=[x ₁(t), x ₂(t)] covariance matrix;

6. Lagrangian function is constructed:

L(w,λ)＝w ^HR _xxw+λ(α(θ ₀) ^Hw-1)+λ ^*(w ^Hα(θ ₀)-1)（6）

Consider w ∈ C ^{m × 1}, make the conjugate gradient of L (w, λ) be 0, namely

$\&part;L(w,\mathrm{\&lambda;})/\&part;w^{*}=0---\left(7\right)$

Obtain

w ^H＝-λα(θ ₀) ^HR _xx ^-1（8）

Substitute into w α (θ ₀)=1, can obtain

λ＝-(α(θ ₀) ^HR _xx ^-1α(θ ₀)) ^-1（9）

Thus can best initial weights be obtained:

w _opt＝R _xx ^-1α(θ ₀)(α ^H(θ ₀)R _xx ^-1α(θ ₀)) ^-1＝R _xx ^-1α(θ ₀)P _omin（10）

P in formula _omin=(α ^h(θ ₀) R _xx ^-1α (θ ₀)) ^-1for minimum output power;

(3) be weighted summation to each narrow band data, the wave beam obtaining each subband exports data;

$Y^{\left(n\right)}\left(k\right)=w^H\left(f_k\right)X^{\left(n\right)}\left(k\right)=\underset{m=1}{\overset{M}{\&Sigma;}}{w}_m^{*}\left(f_k\right)X_m^{\left(n\right)}\left(k\right)---\left(11\right)$

The array of whole test frequency range has been become to export S by the output data groups of each frequency range ₀(f), namely

S ₀(f)＝[Y(1),Y(2),…,Y(k)]；

(4) utilization offsets process and removes environmental interference;

After above-mentioned signal transacting, now array exports S ₀f () is only containing undesired signal, and the output S of individual antenna ₂then both containing EUT signal in (f), also containing undesired signal, now carry out offseting process, can obtain

S _EUT(f)＝S ₂(f)-S ₀(f)。