CN107907880A - One kind is spaceborne to condense polarization SAR fuzziness analysis system, method and memory - Google Patents

One kind is spaceborne to condense polarization SAR fuzziness analysis system, method and memory Download PDF

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CN107907880A
CN107907880A CN201710913798.2A CN201710913798A CN107907880A CN 107907880 A CN107907880 A CN 107907880A CN 201710913798 A CN201710913798 A CN 201710913798A CN 107907880 A CN107907880 A CN 107907880A
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polarization
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CN107907880B (en
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闫伟
高阳
冯帆
谭小敏
王万林
胡继伟
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Xian Institute of Space Radio Technology
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01SRADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/88Radar or analogous systems specially adapted for specific applications
    • G01S13/89Radar or analogous systems specially adapted for specific applications for mapping or imaging
    • G01S13/90Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
    • G01S13/904SAR modes
    • G01S13/9076Polarimetric features in SAR
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01SRADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/88Radar or analogous systems specially adapted for specific applications
    • G01S13/89Radar or analogous systems specially adapted for specific applications for mapping or imaging
    • G01S13/90Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
    • G01S13/904SAR modes

Abstract

One kind is spaceborne to condense polarization SAR fuzziness analysis system, method and memory, spaceborne polarization SAR system of condensing is controlled to generate mapping band, mapping is obtained with the corresponding useful signal energy of interior each point, spaceborne polarization SAR system of condensing is controlled to generate multiple fuzzy regions, the corresponding blurred signal energy of each point in each fuzzy region is obtained, the corresponding fuzziness of current point is obtained according to the corresponding useful signal energy in mapping band midpoint, the corresponding blurred signal energy balane in each fuzzy region midpoint.

Description

One kind is spaceborne to condense polarization SAR fuzziness analysis system, method and memory
Technical field
The present invention relates to Space Microwave remote sensing technology field, particularly a kind of spaceborne polarization SAR fuzziness of condensing analyzes system System, method and memory.
Background technology
In order to meet the SAR quantification applications such as global biomass disturbance monitoring, marine environmental monitoring, satellite-borne SAR load needs Possess multipolarization pattern, including single polarization, dual polarization, complete polarization and condense polarization mode.SAR complete polarizations pattern is in the application Good effect is obtained, but faces the problems such as data transfer rate is big, mapping band is smaller, power consumption is larger.It is a kind of to condense polarization mode Brand-new operating mode, can obtain the quasi- complete polarization information of target, and there is no added due to complete polarization pulse recurrence frequency (PRF) Cause to survey and draw the problem of band halves again.However, due to condensing the polarization factor shadow such as crosstalk and not rounded polar transmitter in polarization mode Ring, the fuzziness index of system is poor, have impact on effectiveness, and lack effective fuzziness analysis means.It is existing to condense pole Changing SAR system method for analyzing ambiguity is divided by establishing the method combination satellite-Earth model of target polarization scattering matrix Analysis, but the influence that the factors such as the not rounded polar transmitter of antenna present in real system and antenna polarization crosstalk are brought is not considered, lead Cause condenses SAR system fuzziness under polarization mode and analyzes distortion, and then have impact on and condense polarization mode SAR system in agricultural and sea The application of foreign aspect.
The content of the invention
Present invention solves the technical problem that it is:Overcome the deficiencies of the prior art and provide and a kind of spaceborne condensed polarization SAR mould Paste degree analysis system, method and memory, solve existing fuzziness analytical technology and do not consider day present in real system The influence that the factor such as the not rounded polar transmitter of line and antenna polarization crosstalk is brought, causes to condense SAR system fuzziness under polarization mode Distortion is analyzed, and then have impact on the application for condensing polarization mode SAR system in terms of agricultural and ocean.
The present invention technical solution be:One kind is spaceborne to condense polarization SAR method for analyzing ambiguity, including following step Suddenly:
(1) the spaceborne mapping band for condensing the generation of polarization SAR system and multiple fuzzy regions are obtained;
(2) according to the corresponding useful signal energy in mapping band midpoint, the corresponding blurred signal energy in each fuzzy region midpoint The corresponding fuzziness of current point is calculated in amount.
One kind is spaceborne to condense polarization SAR fuzziness analysis system, including not rounded polar transmitter analysis module, reception crosstalk point Module, fuzziness computing module are analysed, wherein:
Polarization is condensed in not rounded polar transmitter analysis module, the antenna axial ratio parameter introduced using not rounded polar transmitter, calculating Pattern issues incident polarization vector, and send to fuzziness computing module;
Crosstalk analysis module is received, using the cross-talk parameters that polarize, polarization scattering matrix under polarization mode is condensed in calculating, and is sent To fuzziness computing module;
Fuzziness computing module, issues incident polarization vector, condenses Polarization scattering under polarization mode according to polarization mode is condensed Matrix, useful signal energy of the mapping with midpoint, the blurred signal energy balane at each fuzzy region midpoint obtain current point pair The fuzziness answered.
Useful signal energy P of the mapping with midpointsig(i) computational methods are:
PavFor the spaceborne average emitted power for condensing polarization SAR system,To survey and draw with interior i-th point of corresponding hair Penetrate directivity of antenna,Condensed for mapping with interior i-th point corresponding reception antenna directivity factor, λ to be spaceborne The transmitting signal wavelength of polarization SAR system, c are the light velocity, and L condenses polarization SAR system loss, V to be spacebornesPolarization is condensed to be spaceborne The speed of satellite platform movement, θ where SAR systemi0To survey and draw with interior i-th point corresponding ground incidence angle, MRH、MRVRespectively For the spaceborne Polarization scattering parameter for condensing polarization SAR system;
The corresponding blurred signal energy P in the fuzzy region midpointambThe computational methods of (i, j) are:
Wherein,For i-th point in j-th of fuzzy region corresponding antenna direction of the launch property coefficient,For I-th point of corresponding antenna receiving directivity coefficient, θ in j-th of fuzzy regionijFor i-th point of correspondence of j-th of fuzzy region Ground incidence angle, RijFor i-th point in j-th of fuzzy region oblique distance value formed with satellite.
The spaceborne Polarization scattering parameter M for condensing polarization SAR systemRH、MRVComputational methods be:
Wherein, δ1To receive antenna cross talk during vertically polarized wave, δ2To receive antenna cross talk during horizontal polarized wave, f1 It is the degree of unbalancedness between two-way receiving channel, THLaunch polarization vector, T to condense horizontal direction in polarization modeVTo condense polarization Vertical direction launches polarization vector in pattern.
Described condenses horizontal direction transmitting polarization vector T in polarization modeH, condense in polarization mode vertical direction and launch Polarization vector TVComputational methods be:
Wherein,EmaxFor not rounded polar transmitter when antenna electric field form elliptical major semiaxis, EminTo be not rounded Antenna electric field forms elliptical semi-minor axis during polar transmitter.
A kind of non-transitory memory, is stored with computer program, which makes the requirement of computer perform claim 1st, any means in claim 3, claim 4 or claim 5.
The present invention compared with prior art the advantages of be:
(1) compared with prior art, the present invention by establishing the collision matrix under the polarization crosstalk of SAR antenna systems, by it It is introduced into fuzziness analysis equation, solves the problems, such as the influence that fuzziness is analyzed in antenna polarization crosstalk;
(2) compared with prior art, the present invention by establishing SAR antenna systems since the axis under not rounded polar transmitter is than dissipating Matrix is penetrated, is introduced into fuzziness analysis equation, solves the influence that antenna analyzes fuzziness due to not rounded polar transmitter Problem;
(3) compared with prior art, the present invention by the way that antenna transmit-receive position property coefficient is incorporated into fuzziness accounting equation In, have the advantages that to can be applied to the analysis of digital beam froming SAR system fuzziness.
Brief description of the drawings
Fig. 1 is a kind of spaceborne flow chart for condensing polarization SAR method for analyzing ambiguity;
Fig. 2 (a) is the sequence diagram of complete polarization pattern;
Fig. 2 (b) is the sequence diagram for condensing polarization mode;
Fig. 3 is the satellite-Earth model figure of satellite-borne SAR fuzziness analysis;
Fig. 4 is fuzziness analysis result;
Fig. 5 is spaceborne mapping band and confusion region schematic diagram.
Embodiment
In view of the deficiencies of the prior art, the present invention proposes it is a kind of it is spaceborne condense polarization SAR fuzziness analysis system, method and Memory, solves existing fuzziness analytical technology and does not consider the not rounded polar transmitter of antenna present in real system and antenna The influence that the factors such as polarization crosstalk are brought, causes to condense SAR system fuzziness under polarization mode and analyzes distortion, and then have impact on letter Application of the contracting polarization mode SAR system in terms of agricultural and ocean, below in conjunction with the accompanying drawings carries out the method for the present invention further Explanation and illustration.
It is a kind of spaceborne flow chart for condensing polarization SAR method for analyzing ambiguity as shown in Figure 1, the first step is to be directed to full pole Change system, considers antenna transmit-receive position property coefficient, mapping band geological information, target polarization scattering characteristics and satellite-orbit information, The wave position parameter of SAR system work, and the influence of geometric parameters analysis fuzzy region are established according to star, give fuzziness meter Calculation method, second step are to be directed to condense polarization SAR system performance, consider the mistake introduced after polarization crosstalk and not rounded polar transmitter Difference, just improves polarization scattering matrix, so as to obtain condensing the method for analyzing ambiguity under polarization.It is of the invention a kind of spaceborne Polarization SAR method for analyzing ambiguity is condensed to include the following steps:
First, the fuzziness analytical procedure based on polarization scattering matrix
The fuzzy of satellite-borne SAR image is to be made from the echo-signal surveyed and drawn outside band to surveying and drawing the interference with interior echo-signal Into image quality decrease, or even there is so-called " ghost image " phenomenon, difficulty is caused to SAR image application.Fuzzy problem is SAR works Journey design in the major issue to be solved, particularly borne polarization SAR design in obscure the problem of it is even more important, be star Carry the important indicator of polarization SAR system design.
For Spaceborne SAR System, in radar reception window, since distance is to the side lobe effect of antenna radiation pattern, it is assumed that survey It is useful energy signal to paint the echo-signal with interior target, then survey and draw with several outer preceding exomonental echo-signals or after Several exomonental echo-signals are blurred signal energy, and blurred signal energy weighs in time with useful signal energy It is folded, cause to surveying and drawing the interference with useful signal.
For Spaceborne SAR System, the satellite-Earth model figure that satellite-borne SAR fuzziness is analyzed is illustrated in figure 3.In figure, defend The height of star platform is H, RnFor the corresponding oblique distance of mapping band near-end, RfFor the corresponding oblique distance of mapping band distal end, Ri0For to mapping Band carries out i-th point of corresponding oblique distance after discretization.
Signal in satellite-borne SAR mapping band is useful echo-signal, and the signal surveyed and drawn outside band is fuzzy energy signal, such as Fig. 5 show spaceborne mapping band and confusion region schematic diagram.In figure, 0 represents to survey and draw with corresponding region, and -1 ...,-j ..., - ∞ and 1 ..., j ..., ∞ represents the corresponding region of blurred signal energy.It is R to survey and draw the oblique distance with and satellite at interior i-th pointi0, it is right The ground incidence angle and substar visual angle answered are respectively θi0And γi0.I-th point of j-th of fuzzy region and the oblique distance of satellite are Rij, corresponding ground incidence angle and substar visual angle are respectively θijAnd γij
According to the definition of fuzziness, fuzziness is the ratio of blurred signal energy and useful signal energy, obtains mapping band Interior i-th point of fuzziness RASRmnFor
Wherein, m and n represents transmitting and the polarization received.For complete polarization system, m represents H or V polar transmitters, n Represent H or V polarization receptions.
Psig(i) it is mapping with interior i-th point corresponding useful signal energy, it is related to wave position parameter, it can be expressed as
Wherein, PavFor average emitted power,WithRepresent mapping with interior i-th point corresponding day line-spacing Descriscent direction of the launch property coefficient and receiving directivity coefficient, λ are the wavelength of transmitting signal, and c is the light velocity, and L is system loss, VsFor The speed of satellite platform movement.For polarization SAR system, backscattering cross product of the target under HH, HV, VH and VV polarization can To be expressed asCorresponding Polarization scattering S parameter is respectively SHH、SHV、SVH、SVV
Pamb(i, j) is i-th point of corresponding fuzzy energy in j-th of fuzzy region, can be expressed as
Wherein,WithRepresent i-th point of corresponding antenna direction of the launch property coefficient in j-th of fuzzy region With receiving directivity coefficient.For spaceborne digital beam froming SAR system, since its launching beam is broad beam, covering is whole Band is surveyed and drawn, distance is to directivity factorReception wave beam is narrow beam, and distance is to directivity factorTherefore Directivity of antenna, which is subject to, to be emulated or surveys.Represent i-th point of corresponding off-axis angle in j-th of fuzzy region.
RijRepresent the i-th point of oblique distance value formed with satellite in j-th of fuzzy region, be expressed as
Wherein, Ri0Represent mapping with interior i-th point of corresponding oblique distance;RnAnd RfThe near-end oblique distance in mapping band is represented respectively With distal end oblique distance;ReEarth radius and orbit altitude are represented respectively with h;RmaxRepresent satellite oblique distance corresponding with earth section, fpFor Pulse recurrence frequency, is provided by wave position parameter.
According to satellite-Earth model, the distance definition of satellite to earth center is Rs=Re+h。
γijIt can be expressed as
Wherein off-axis angle calculation formula is
Wherein, r represents the roll angle of satellite,
And then obtain fuzziness and be
Wherein, AjFor FUZZY WEIGHTED coefficient, can be expressed as
2nd, the polarization scattering matrix under polarization is condensed
For condensing polarization SAR system, it is shown with the difference of transmitting sequential such as Fig. 2 (a), Fig. 2 (b) of complete polarization pattern. Polarization mode transmitting circular polarisation is condensed, is represented with CP, and two receiving channels receive H and V polar echos at the same time.
Spaceborne polarization SAR system of condensing usually launches right-handed circular polarization, is represented with R, and uses H and V polarization to be carried out at the same time Receive, its corresponding fuzziness can be expressed as
For condensing polar system, m represents right-handed circular polarization transmitting, and n represents H or V polarization receptions.Condense polar system Fuzziness has two, is respectively RASRRHAnd RASRRV
Psig(i) to survey and draw with interior i-th point corresponding useful signal energy, can be expressed as
Pamb(i, j) is i-th point of corresponding fuzzy energy in j-th of fuzzy region, can be expressed as
In polarization SAR system is condensed, MRHAnd MRVThere is certain correspondence with polarization scattering matrix in formula (2), can be with table It is shown as
Wherein, THAnd TVTo launch polarization vector, can be expressed as
For condensing polarization mode, since receiving polarization isolation is not high, system is caused to there is polarization crosstalk, therefore Formula (12) can be expressed as after considering to receive crosstalk
Wherein, δ1And δ2It is antenna cross talk (i.e. a kind of polarization of reception when receiving vertically polarized wave and horizontal polarized wave respectively The ratio of another polar component is mixed into ripple), f1It is the degree of unbalancedness (including amplitude and phase) between two-way receiving channel, can To be expressed as
For condensing polarization SAR system, it is generally recognized that it meets
Wherein, RHHRepresent the polarization of antenna emission level and be received as the power of horizontal polarization, RVHRepresent that antenna transmitting is vertical Polarize and be received as the power of horizontal polarization, RHVRepresent the polarization of antenna emission level and be received as the power of vertical polarization, RVVTable Show antenna transmitting vertical polarization and be received as the power of vertical polarization.
In polarization SAR system is condensed, since the electromagnetic wave of actual antennas transmitting is unlikely to be preferable circularly polarised wave, lead to Antenna axial ratio is commonly used to weigh circular polarisation degree, can be expressed as
Wherein, EmaxAnd EminFor not rounded polar transmitter when antenna electric field form elliptical major semiaxis and semi-minor axis.
After the not rounded polar transmitter of consideration system, antenna axial ratio can cause transmitting vector distortion, cause formula (13) to represent For
Formula (10), formula (11), formula (14) are brought into formula (9), the spaceborne fuzziness condensed under polarization SAR pattern can be calculated Parameter.
In order to be further illustrated, emulated here with one group of satellite-borne SAR parameter, obtain the mould under wherein RV polarization It is as shown in Figure 4 to paste curve.In emulation, the height of satellite platform is 850km, mapping swath width 25km, and mapping band center corresponds to Incidence angle be 35 degree, receive polarize crosstalk δ be -10dB, the axis ratio of antenna is 2.0dB.It is seen that SAR system exists Condense under polarization mode, fuzziness is superior to -17.5dB, can meet the application requirements such as agricultural and ocean.
The content not being described in detail in description of the invention belongs to the known technology of those skilled in the art.

Claims (6)

1. one kind is spaceborne to condense polarization SAR method for analyzing ambiguity, it is characterised in that includes the following steps:
(1) the spaceborne mapping band for condensing the generation of polarization SAR system and multiple fuzzy regions are obtained;
(2) according to the corresponding useful signal energy in mapping band midpoint, the corresponding blurred signal energy meter in each fuzzy region midpoint Calculation obtains the corresponding fuzziness of current point.
2. one kind is spaceborne to condense polarization SAR fuzziness analysis system, it is characterised in that including not rounded polar transmitter analysis module, connects Crosstalk analysis module, fuzziness computing module are received, wherein:
Polarization mode is condensed in not rounded polar transmitter analysis module, the antenna axial ratio parameter introduced using not rounded polar transmitter, calculating Incident polarization vector is issued, and is sent to fuzziness computing module;
Crosstalk analysis module is received, using the cross-talk parameters that polarize, polarization scattering matrix under polarization mode is condensed in calculating, and is sent to mould Paste degree computing module;
Fuzziness computing module, according to condense polarization mode issue incident polarization vector, condense polarization scattering matrix under polarization mode, Useful signal energy of the mapping with midpoint, the blurred signal energy balane at each fuzzy region midpoint obtain the corresponding mould of current point Paste degree.
3. one kind according to claim 1 is spaceborne to condense polarization SAR method for analyzing ambiguity, it is characterised in that:Described Survey and draw the useful signal energy P with midpointsig(i) computational methods are:
PavFor the spaceborne average emitted power for condensing polarization SAR system,To survey and draw with interior i-th point corresponding transmitting day Line directivity factor,For mapping polarization is condensed to be spaceborne with interior i-th point corresponding reception antenna directivity factor, λ The transmitting signal wavelength of SAR system, c are the light velocity, and L condenses polarization SAR system loss, V to be spacebornesPolarization SAR is condensed to be spaceborne The speed of satellite platform movement, θ where systemi0To survey and draw with interior i-th point corresponding ground incidence angle, MRH、MRVRespectively star Carry the Polarization scattering parameter for condensing polarization SAR system;
The corresponding blurred signal energy P in the fuzzy region midpointambThe computational methods of (i, j) are:
Wherein,For i-th point in j-th of fuzzy region corresponding antenna direction of the launch property coefficient,For j-th I-th point of corresponding antenna receiving directivity coefficient, θ in fuzzy regionijIt is corresponding for i-th point of j-th of fuzzy region Face incidence angle, RijFor i-th point in j-th of fuzzy region oblique distance value formed with satellite.
4. one kind according to claim 3 is spaceborne to condense polarization SAR method for analyzing ambiguity, it is characterised in that:Described The spaceborne Polarization scattering parameter M for condensing polarization SAR systemRH、MRVComputational methods be:
<mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>M</mi> <mrow> <mi>R</mi> <mi>H</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>M</mi> <mrow> <mi>R</mi> <mi>V</mi> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <msub> <mi>&amp;delta;</mi> <mn>2</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>&amp;delta;</mi> <mn>1</mn> </msub> </mtd> <mtd> <msub> <mi>f</mi> <mn>1</mn> </msub> </mtd> </mtr> </mtable> </mfenced> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>S</mi> <mrow> <mi>H</mi> <mi>H</mi> </mrow> </msub> </mtd> <mtd> <msub> <mi>S</mi> <mrow> <mi>H</mi> <mi>V</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>S</mi> <mrow> <mi>V</mi> <mi>H</mi> </mrow> </msub> </mtd> <mtd> <msub> <mi>S</mi> <mrow> <mi>V</mi> <mi>V</mi> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>T</mi> <mi>H</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>T</mi> <mi>V</mi> </msub> </mtd> </mtr> </mtable> </mfenced> </mrow>
Wherein, δ1To receive antenna cross talk during vertically polarized wave, δ2To receive antenna cross talk during horizontal polarized wave, f1It is two Degree of unbalancedness between the receiving channel of road, THLaunch polarization vector, T to condense horizontal direction in polarization modeVTo condense polarization mode Middle vertical direction launches polarization vector.
5. one kind according to claim 4 is spaceborne to condense polarization SAR method for analyzing ambiguity, it is characterised in that:Described Condense horizontal direction transmitting polarization vector T in polarization modeH, condense in polarization mode vertical direction transmitting polarization vector TVMeter Calculation method is:
<mrow> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>T</mi> <mi>H</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>T</mi> <mi>V</mi> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <msqrt> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msqrt> </mtd> </mtr> </mtable> </mfenced> <mo>+</mo> <mfrac> <mrow> <mi>A</mi> <mi>R</mi> <mo>-</mo> <mn>1</mn> </mrow> <mrow> <mi>A</mi> <mi>R</mi> <mo>+</mo> <mn>1</mn> </mrow> </mfrac> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <msqrt> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msqrt> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow>
Wherein,EmaxFor not rounded polar transmitter when antenna electric field form elliptical major semiaxis, EminSent out for non-circular polarisation Antenna electric field forms elliptical semi-minor axis when penetrating.
A kind of 6. non-transitory memory, it is characterised in that:Computer program is stored with, which perform computer Any means in claim 1, claim 3, claim 4 or claim 5.
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