CN107302387A - A kind of high-speed aircraft relays dual polarization mimo channel modeling method - Google Patents
A kind of high-speed aircraft relays dual polarization mimo channel modeling method Download PDFInfo
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Abstract
The invention belongs to TTC＆T Technology field, a kind of high-speed aircraft relaying dual polarization mimo channel modeling method is disclosed, including：Loo channel parameters are determined using plasma sheath Markov state metastasis model；The large scale fading model and multipath fading model for the repeater satellite subchannel set up using Loo models under every plasma sheath, subchannel produce polarization dependence by dual polarization MIMO model；Large scale decline and multipath fading part of the joint per subchannel obtain the polarization mimo channel model under plasma sheath.The present invention, which is adopted, greatly reduces space and launch cost；Consider influence of the dual polarization asymmetry to channel model under plasma sheath.
Description
Technical Field
The invention belongs to the technical field of measurement and control communication, and particularly relates to a modeling method for a relay dual-polarization MIMO channel of a high-speed aircraft.
Background
With the rapid development of aerospace technology, the development and utilization of high-ultrasonic aircrafts become a research hotspot in the aerospace field at home and abroad. When the high-speed aircraft flies at a speed greater than Mach 10, a plasma sheath around the aircraft can seriously attenuate and distort signals, so that the communication interruption (black barrier) phenomenon is caused by the great reduction of the channel capacity, and the flight safety of the aircraft is greatly threatened. In order to overcome or alleviate the black barrier communication interruption problem, researchers have proposed many physical and chemical plasma suppression methods to increase the communication possibilities, which theoretically could reduce the attenuation to some extent, but in practical situations are hardly applicable. For communication, current research on communication for high-speed aircraft is limited to downlink "end-to-end" communication, which is a single-input and single-output transmission channel with relatively small channel capacity. The adoption of uplink relay and diversity transmission is an important means for improving channel capacity and communication quality. In fact, two independent orthogonal sub-channels can be generated in the polarization direction by adopting polarization diversity, and the MIMO system can be formed only by a single relay satellite and a single aircraft, so that the complexity of the system can be greatly reduced. The Dual-polarization MIMO technology applied to satellite is mature, and documents "Konstatinos P.Liois, Jes u s G Lo mez-Vilardeb Lo, Enrico Casini, Ana I.P ez-Neira. statistical Modeling of Dual-Polarized MIMO Land Mobile satellite channels [ J ]. IEEE Transactions on Communications,2010,58(11):3077 and 3083" give a Land Mobile satellite Dual-polarization MIMO channel model, but the high-speed aircraft has a special plasma sheath environment, which causes the following problems in applying the Dual-polarization MIMO technology under the plasma sheath: (1) polarization is generally considered to have symmetry in a satellite dual-polarization MIMO system, and the problem of polarization asymmetry needs to be considered in the design of a dual-polarization MIMO channel model under a plasma sheath, so that the large-scale and small-scale influences on MIMO sub-channels are different. (2) The plasma sheath can affect the large-scale fading and small-scale fading characteristics of the channel, and the plasma sheath environment can affect the independence of the polarized transmission channel, namely, the correlation between the dual-polarized MIMO sub-channels can be changed, so that the independence of the sub-channels is damaged, and the consideration is needed in the modeling process. Aiming at the problem of the reliability of the black obstacle communication of the high-speed aircraft, the method for modeling the relay dual-polarization MIMO channel of the high-speed aircraft is developed for the research of an uplink relay dual-polarization transmission method, and can provide reference for relay diversity communication evaluation and system design.
In summary, the problems of the prior art are as follows: the existing MIMO channel model has the problem that polarization asymmetry needs to be considered in the design of a dual-polarization MIMO channel model under a plasma sheath, so that the large-scale fading and small-scale fading characteristics of a channel are influenced.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a high-speed aircraft relay dual-polarization MIMO channel modeling method.
The invention is realized in such a way that a high-speed aircraft relay dual-polarization MIMO channel modeling method comprises the following steps:
determining a lo channel parameter by using a plasma sheath markov state transition model;
establishing a large-scale fading model and a small-scale fading model of each relay satellite subchannel under each plasma sheath by using a Loo model, wherein the subchannels generate polarization correlation through a dual-polarization MIMO model;
and thirdly, combining the large-scale fading part and the small-scale fading part of each subchannel to obtain a polarization MIMO channel model under the plasma sheath.
Further, the modeling method of the relay dual-polarization MIMO channel of the high-speed aircraft comprises the following steps:
firstly, acquiring a state transition sequence of a Markov channel model according to a state transition matrix P of a Markov channel of a land mobile satellite; determining the lo model channel parameters corresponding to the state sequence according to the land mobile satellite channel test result;
secondly, calculating and obtaining a polarization coupling degree parameter XPC of a left-handed circularly polarized plasma environment according to the electron density and collision frequency of a plasma sheath of the high-speed aircraftenv,LAnd polarization coupling degree parameter and XPC of right-hand circularly polarized plasma environmentenv,R；
Thirdly, using the Loo model channel parameter and parameter XPCenv,L、XPCenv,RRealizing large-scale channel model simulation;
the fourth step, using the channel parameters and the parameter XPC of step S2env,L、XPCenv,RRealizing small-scale channel model simulation;
and fifthly, combining the large-scale fading component and the small-scale fading component to obtain a polarization MIMO channel model under the sheath of the plasma.
Further, the first step specifically includes:
(1) inputting a plasma sheath Markov state transition matrix P, wherein an element P (i, j) in the state transition matrix P represents the probability of jumping from the state i to the state j, P (i, j) is more than 0 and less than or equal to 1, andn denotes that the model simulates n states.
(2) Input status frame LFrame，LFrameExpressed as the minimum distance a state lasts. Given a current state StEach L ofFrameNext state of rice production St+1
A first step of generating a (0, 1) uniformly distributed random number U, and setting k to 1;
second, testing the conditionsIf the test condition is satisfied, the next state St+1K is; if the test condition is not satisfied, k is k +1 and the second step is repeated until the condition is satisfied;
(3) the aircraft moves along its path, every LFrameThe method comprises the steps of judging the state of a terminal once by rice, searching the corresponding Loo model parameters Loo (α, psi and MP) in the state, the Loo model parameters (-1.1045,1.3149 and 16.8763) corresponding to a good state, the Loo model parameters (-13.6829,5.0213 and 22.3256) corresponding to a bad state, and expressing α, psi and MP in a dB form, wherein α and psi respectively express the average value and the variance of the amplitude of large-scale fading, and MP expresses the average energy of the amplitude of small-scale fading.
Further, the second step specifically includes:
1) from the high-speed aircraft electron density and the collision frequency, the electron density profile for the plasma sheath at the aircraft antenna window is approximated using a double gaussian model:
wherein, a1And a2Respectively representing the rising and falling coefficients of the electron density distribution curve, NepeakAnd z0Respectively representing the maximum electron density and the distance from the surface of the aircraft;
2) calculating the transmitted wave of circularly polarized wave after obliquely entering the plasma according to an equivalent wave impedance method:
wherein,andrespectively, parallel polarization and perpendicular polarization unit direction vectors.Andrespectively, into a parallel polarization component and a perpendicular polarization component,andthe parallel polarization component and the vertical polarization component are respectively decomposed into the transmitted wave;andthe transmission coefficients of the parallel polarized wave and the vertical polarized wave are respectively;
3) decomposing the transmitted wave into right-handed circular transmitted wave according to the transmitted wave after the circularly polarized wave is incident into the plasmaAnd transmitted waves of the levogyration
Wherein E is0In order to normalize the field strength of the field,andrespectively the transmission coefficients of the common polarization wave and the cross polarization wave in the transmitted wave after the incidence of the right-handed wave,andtransmission coefficients of common polarization and cross polarization waves in the transmission waves after incidence of the levorotatory waves are respectively;
4) the transmission coefficients of the common polarization and the cross polarization waves in the transmission waves after the left/right spin wave is incident are substituted into the following formula to obtain a parameter XPCenv,LAnd XPCenv,R：
Further, the third step specifically includes:
step one, generating 2 × 2 statistically independent Gaussian random sequence sample matrix with mean value of 0 and variance of 1 for each stateThe sample interval of the samples is T. Then the sample matrixEach element passes through a low-pass IIR filter to realize the time correlation of the signal, and a 2 × 2 matrix with the time correlation is obtained
Step two, inputting a correlation matrix of large-scale fading componentsAnd will beSubstituting into the following, using a correlation matrixGenerating polarization correlation among MIMO sub-channels to obtain 2 × 2 channel matrix of polarization correlation
vec () represents a take column vector operation.
Step three, inputting the channel parameters α and psi of the Loo model according to the condition that the amplitude of the large-scale fading obeys the lognormal distribution, and inputting the channel parametersSubstituting the following formula to generate a channel characteristic matrix of polarization-dependent lognormal distribution
Inputting the polarization discrimination XPD of the polarized antenna positioned in the high-speed aircraft according to the influence of the polarization on the power of the channel sequenceant,rAdjusting the large-scale fading matrix using the following equation
β thereinantIs XPDant,rBy the factor of (a) of (b),
further, the fourth step specifically includes:
1) for each state, a 2 × 2 statistically independent complex gaussian random sequence sample matrix with mean 0 and variance 1 was generated
2) In order to introduce Doppler shift effect, 2 × 2 complex Gaussian random sequence matrixEach element is implemented by a butterworth filter, producing a complex gaussian random sequence matrix with doppler effectThe butterworth filter is represented as:
wherein A ═ exp (-vT/r)c)，v is the flight speed of the aircraft, T is the sample application interval, rcIs a coherence distance, fcIs the cut-off frequency of the k-th order filter;
3) according to the rayleigh distribution obeying the amplitude of small-scale fading, in order to generate a complex rayleigh sequence of 2 × 2, a Loo model channel parameter MP is input, and a complex Gaussian sequence matrix is subjected toEach element multiplied byTo generate a rayleigh 2 × 2 matrixWherein
4) Correlation matrix of input small-scale fading componentAnd will beSubstituting into the following, using a correlation matrixGenerating polarization correlation among MIMO sub-channels to obtain polarization-correlated channel characteristic 2 × 2 matrix
Wherein,denoted Kronecker product, superscript T denotes matrix transpose,and2 × 2 covariance matrices representing the transmit and receive ends, respectively;
wherein,andrespectively representing the cross correlation of the left-hand circular polarization and the right-hand circular polarization of the transmitting terminal;andrespectively representing the cross correlation of the left-hand circular polarization and the right-hand circular polarization of a receiving end;
5) according to the influence of polarization on the channel sequence power, the coupling degree XPC of the input environmentenv,L、XPCenv,RAnd polarization discrimination XPD of polarized antenna located in high-speed aircraftant,rAdjusting the large-scale fading matrix using the following equation
WhereinAnd
another object of the present invention is to provide a high-speed aircraft using the high-speed aircraft relay dual-polarization MIMO channel modeling method.
The invention has the advantages and positive effects that: the multi-state Markov chain is adopted to model the channel, so that the actual channel can be better described, and the limitation that the channel characteristics cannot be accurately described in a single random process is avoided. Based on the uplink dual-polarization transmission of the relay satellite and the high-speed aircraft, compared with the existing aircraft wireless transmission channel research staying at 'end-to-end', the MIMO system can be realized only by one relay satellite and the high-speed aircraft, and the complexity of realizing the system can be greatly reduced compared with a multi-antenna system and a multi-satellite constructed MIMO system;
compared with the polarization symmetry of the existing terrestrial mobile satellite dual-polarization MIMO channel model, the modeling method of the plasma sheath polarized MIMO channel model provided by the invention considers the influence of the dual-polarization asymmetry under the plasma sheath on the channel model, and can accurately describe the large-scale and small-scale fading characteristics of the high-speed aircraft in the plasma sheath environment and the correlation between polarized sub-channels.
The method is suitable for modeling the relay satellite dual-polarization MIMO channel of the near space high-speed aircraft, also can be suitable for modeling the relay satellite dual-polarization MIMO channel of the space reentry aircraft, the established channel model can provide a channel simulation basis and a platform for the communication system design and the adaptability method research of the high-speed aircraft, and can be used for algorithm design and performance evaluation of communication physical layer transmission technologies such as modulation/demodulation, channel coding, channel estimation and equalization.
Drawings
Fig. 1 is a flowchart of a method for modeling a high-speed aircraft relay dual-polarization MIMO channel according to an embodiment of the present invention.
Fig. 2 is a flowchart illustrating a method for modeling and simulating a relay dual-polarization MIMO channel of a high-speed aircraft according to an embodiment of the present invention.
Fig. 3 is a flow chart of a large-scale fading implementation under a plasma sheath provided by an embodiment of the invention.
Fig. 4 is a flow chart of a small-scale fading implementation under a plasma sheath provided by an embodiment of the invention.
Fig. 5 is a diagram comparing the effect of dual polarization MIMO technology in plasma sheath with the effect of dual polarization MIMO technology on channel capacity under certain conditions provided by embodiments of the present invention.
Fig. 6 is a diagram comparing the effect of using dual-polarization MIMO technology and not using dual-polarization MIMO technology on bit error rate under certain conditions provided by an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
The following detailed description of the principles of the invention is provided in connection with the accompanying drawings.
As shown in fig. 1, the method for modeling a high-speed aircraft relay dual-polarization MIMO channel provided by the embodiment of the invention includes the following steps:
s101: determining a lo channel parameter using a plasma sheath markov state transition model;
s102: establishing a large-scale fading model and a small-scale fading model of relay satellite sub-channels under each plasma sheath by using a Loo model, wherein the sub-channels generate polarization correlation through a dual-polarization MIMO model;
s103: and combining the large-scale fading part and the small-scale fading part of each subchannel to obtain a polarization MIMO channel model under the plasma sheath.
The application of the principles of the present invention will now be described in further detail with reference to the accompanying drawings.
As shown in fig. 2, the method for modeling a high-speed aircraft relay dual-polarization MIMO channel according to the embodiment of the present invention includes the following steps:
s1, acquiring a state transition sequence of the Markov channel model according to the state transition matrix P of the Markov channel of the land mobile satellite; and determining the lo model channel parameters corresponding to the state sequence according to the land mobile satellite channel test result.
S1.1 inputting plasma sheath Markov state transition matrixThe element P (i, j) in the state transition matrix P represents the probability of jumping from state i to state j, P (i, j) is greater than 0 and less than 1n denotes that the model simulates n states. According to the actual measurement data of MiLADY, the near space comprehensive channel environment can be modeled into a two-state Markov process, namely a good state and a bad state, so that n is 2;
s1.2: input transition frame LFrame＝5，LFrameExpressed as the minimum distance a state lasts. Given a current state StEach L ofFrameNext state of rice production St+1：
A first step of generating a (0, 1) uniformly distributed random number U, and setting k to 1;
second, testing the conditionsIf the test condition is satisfied, the next state St+1K is; if the test condition is not met, k is k +1 and the second step is repeated until the test condition is met;
s1.3: the aircraft moves along its path, every LFrameThe method comprises the steps of judging the state of a terminal once by rice, searching the corresponding Loo model parameters Loo (α, psi and MP) in the state, the Loo model parameters (-1.1045,1.3149 and 16.8763) corresponding to a good state, the Loo model parameters (-13.6829,5.0213 and 22.3256) corresponding to a bad state, and expressing α, psi and MP in a dB form, wherein α and psi respectively express the average value and the variance of the amplitude of large-scale fading, and MP expresses the average energy of the amplitude of small-scale fading.
S2, calculating and acquiring the polarization coupling degree parameter XPC of the left-handed circularly polarized plasma environment according to the electron density and the collision frequency of the plasma sheath of the high-speed aircraftenv,LAnd polarization coupling degree parameter and XPC of right-hand circularly polarized plasma environmentenv,R。
S2.1: from the high speed aircraft electron density and collision frequency, the electron density profile for the plasma sheath at the aircraft antenna window can be approximated using a double gaussian model:
wherein, a1And a2Respectively representing the rising and falling coefficients of the electron density distribution curve, NepeakAnd z0Representing the electron density maximum and the distance from the aircraft surface, respectively.
S2.2: calculating the transmitted wave of circularly polarized wave after obliquely entering the plasma according to an equivalent wave impedance method:
wherein,andrespectively, parallel polarization and perpendicular polarization unit direction vectors.Andrespectively, into a parallel polarization component and a perpendicular polarization component,andrespectively, into parallel and perpendicular polarization components.Andthe transmission coefficients of the parallel polarized wave and the vertical polarized wave are respectively;
s2.3: the transmitted wave after the circularly polarized wave is incident into the plasma can be decomposed into a right-handed circular (RHCP) transmitted waveAnd Left Hand Circular (LHCP) transmitted waves
Wherein E is0In order to normalize the field strength of the field,andrespectively the transmission coefficients of the common polarization wave and the cross polarization wave in the transmitted wave after the incidence of the right-handed wave,andtransmission coefficients of common polarization and cross polarization waves in the transmission wave after incidence of the levorotatory wave
S2.4: the transmission coefficients of the common polarization and the cross polarization waves in the transmission waves after the left/right spin wave is incident are substituted into the following formula to obtain a parameter XPCenv,LAnd XPCenv,R：
S3 using the Loo model channel parameter of step S1 and the parameter XPC of step S2env,L、XPCenv,RAnd large-scale channel model simulation is realized, as shown in FIG. 3.
S3.1: for theFor each state, a 2 × 2 statistically independent matrix of Gaussian random sequence samples with mean 0 and variance 1 was generatedThe sampling interval of the samples is T-1.2273 × 10-3. Then the sample matrixEach element passes through a low-pass IIR filter to realize the time correlation of the signal, and a 2 × 2 matrix with the time correlation is obtained
S3.2: correlation matrix of input large-scale fading componentAnd will beSubstituting into the following, using a correlation matrixGenerating polarization correlation among MIMO sub-channels to obtain polarization-correlated channel characteristic 2 × 2 matrix
S3.3, according to the condition that the amplitude of large-scale fading obeys log-normal distribution, inputting the channel parameters α and psi of the Loo model, and converting the parameters into a linear formSubstituting the following formula to generate a channel characteristic matrix of polarization-dependent lognormal distribution
S3.4: inputting polarization discrimination XPD of polarized antenna positioned in high-speed aircraft according to influence of polarization on channel sequence powerant,r15dB, the large scale fading matrix is adjusted by the following formula
β thereinantIs XPDant,rBy the factor of (a) of (b),
s4 using the channel parameter of step S1 and the parameter XPC of step S2env,L、XPCenv,RAnd realizing small-scale channel model simulation, as shown in figure 4.
S4.1 for each state, a complex Gaussian random sequence sample matrix with mean 0 and variance 1 is generated 2 × 2 statistically independent
S4.2, in order to introduce the Doppler frequency shift effect, 2 × 2 complex Gaussian random sequence matrix is adoptedEach element is implemented by a butterworth filter, producing a complex gaussian random sequence matrix with doppler effectThe butterworth filter may be expressed as:
wherein A ═ exp (-vT/r)c) The flying speed v of the aircraft is 4080m/s, and the sample application interval T is 1.2273 × 10-3Distance of coherence rc＝2m，fcFor the cut-off frequency of the k-order filter, the Butterworth filter attenuates 3dB to 0.9 × v/lambda and attenuates 100dB to 3 × v/lambda;
s4.3, according to the rayleigh distribution obeying to the amplitude of the small-scale fading, in order to generate a complex rayleigh sequence of 2 × 2, inputting a Loo model channel parameter MP and performing complex Gaussian sequence matrixEach element multiplied byTo generate a rayleigh 2 × 2 matrixWherein
S4.4: correlation matrix of input small-scale fading componentAnd will beSubstituting into the following, using a correlation matrixGenerating polarization correlation among MIMO sub-channels to obtain polarization-correlated channel characteristic 2 × 2 matrix
S4.5: according to the influence of polarization on the channel sequence power, the coupling degree XPC of the input environmentenv,L、XPCenv,RAnd polarization discrimination XPD of polarized antenna located in high-speed aircraftant,rAdjusting the large-scale fading matrix using the following equation
WhereinAnd
it is further noted that in step S4.4, the correlation matrix of the small-scale component needs to be obtained
Wherein,denoted Kronecker product, superscript T denotes matrix transpose,and2 × 2 covariance matrices for transmit and receive ends, respectively:
wherein,andrespectively representing the cross correlation of the left-hand circular polarization and the right-hand circular polarization of the transmitting terminal;andrespectively representing the cross correlation of the left-hand circular polarization and the right-hand circular polarization of a receiving end;
the step S5 is implemented as follows:
combining the large-scale fading component of step S3 and the small-scale fading component of step S4 results in a polarization MIMO channel model under the plasma sheath.
As can be seen from fig. 5, the channel capacity of the close-space high-speed aircraft relay satellite dual-polarized MIMO system and the SISO system increases with the increase of the signal-to-noise ratio, but the channel capacity of the close-space high-speed aircraft relay satellite dual-polarized MIMO system is significantly higher than that of the SISO system. For example, when the signal-to-noise ratio is 20dB, the channel capacity of the near space high speed aircraft relay satellite dual-polarization MIMO system is 5.708bps/Hz, and the channel capacity of the near space high speed aircraft relay satellite SISO system is 2.517 bps/Hz. As can be seen from fig. 6, the bit error rate of the close-space high-speed aircraft relay satellite dual-polarized MIMO system and the SISO system decreases with the increase of the signal-to-noise ratio, but the bit error rate of the close-space high-speed aircraft relay satellite dual-polarized MIMO system is obviously lower than that of the SISO system. For example, when the signal-to-noise ratio is 14dB, the bit error rate of the near space high speed aircraft relay satellite dual-polarization MIMO system is 0.0257, and the bit error rate of the near space high speed aircraft relay satellite SISO system is 0.2319. Therefore, the dual-polarization MIMO technology is adopted on the near space high-speed aircraft and the relay satellite, so that the channel capacity can be greatly increased, the error rate can be improved, and the effectiveness of the invention is demonstrated.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.
Claims (7)
1. A high-speed aircraft relay dual-polarization MIMO channel modeling method is characterized by comprising the following steps:
determining a lo channel parameter by using a plasma sheath markov state transition model;
establishing a large-scale fading model and a small-scale fading model of each relay satellite subchannel under each plasma sheath by using a Loo model, wherein the subchannels generate polarization correlation through a dual-polarization MIMO model;
and thirdly, combining the large-scale fading part and the small-scale fading part of each subchannel to obtain a polarization MIMO channel model under the plasma sheath.
2. A high speed aircraft relay dual polarization MIMO channel modeling method as claimed in claim 1, wherein said high speed aircraft relay dual polarization MIMO channel modeling method comprises the steps of:
firstly, acquiring a state transition sequence of a Markov channel model according to a state transition matrix P of a Markov channel of a land mobile satellite; determining the lo model channel parameters corresponding to the state sequence according to the land mobile satellite channel test result;
secondly, calculating and obtaining a polarization coupling degree parameter XPC of a left-handed circularly polarized plasma environment according to the electron density and collision frequency of a plasma sheath of the high-speed aircraftenv,LAnd polarization coupling degree parameter and XPC of right-hand circularly polarized plasma environmentenv,R；
Thirdly, using the Loo model channel parameter and parameter XPCenv,L、XPCenv,RRealizing large-scale channel model simulation;
the fourth step, using the channel parameters and the parameter XPC of step S2env,L、XPCenv,RRealizing small-scale channel model simulation;
and fifthly, combining the large-scale fading component and the small-scale fading component to obtain a polarization MIMO channel model under the sheath of the plasma.
3. The high-speed aircraft relay dual polarization MIMO channel modeling method of claim 2, wherein the first step specifically comprises:
(1) inputting a plasma sheath Markov state transition matrix P, wherein an element P (i, j) in the state transition matrix P represents the probability of jumping from the state i to the state j, P (i, j) is more than 0 and less than or equal to 1, andn represents that the model simulates n states;
(2) input status frame LFrame，LFrameExpressed as the minimum distance a state lasts; given a current state StEach L ofFrameNext state of rice production St+1
A first step of generating a (0, 1) uniformly distributed random number U, and setting k to 1;
second, testing the conditionsIf the test condition is satisfied, the next state St+1K is; if the test condition is not satisfied, k is k +1 and the second step is repeated until the condition is satisfied;
(3) the aircraft moves along its path, every LFrameAnd judging the state of the terminal once by the meter, and searching for the Loo model parameters Loo (α, psi and MP) in the corresponding state, wherein α, psi and MP are expressed in dB form, wherein α and psi respectively represent the mean value and the variance of the amplitude of large-scale fading, and MP represents the average energy of the amplitude of small-scale fading.
4. The high-speed aircraft relay dual polarization MIMO channel modeling method of claim 2, wherein the second step specifically comprises:
1) from the high-speed aircraft electron density and the collision frequency, the electron density profile for the plasma sheath at the aircraft antenna window is approximated using a double gaussian model:
<mrow> <mi>N</mi> <mi>e</mi> <mrow> <mo>(</mo> <mi>z</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>Ne</mi> <mrow> <mi>p</mi> <mi>e</mi> <mi>a</mi> <mi>k</mi> </mrow> </msub> <mi>exp</mi> <mo>&lsqb;</mo> <mo>-</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <msup> <mrow> <mo>(</mo> <mi>z</mi> <mo>-</mo> <msub> <mi>z</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>&rsqb;</mo> </mrow> </mtd> <mtd> <mrow> <mo>(</mo> <mn>0</mn> <mo>&le;</mo> <mi>z</mi> <mo><</mo> <msub> <mi>z</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>Ne</mi> <mrow> <mi>p</mi> <mi>e</mi> <mi>a</mi> <mi>k</mi> </mrow> </msub> <mi>exp</mi> <mo>&lsqb;</mo> <mo>-</mo> <msub> <mi>a</mi> <mn>2</mn> </msub> <msup> <mrow> <mo>(</mo> <mi>z</mi> <mo>-</mo> <msub> <mi>z</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>&rsqb;</mo> </mrow> </mtd> <mtd> <mrow> <mo>(</mo> <mi>z</mi> <mo>&GreaterEqual;</mo> <msub> <mi>z</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow>
wherein, a1And a2Respectively representing the rising and falling coefficients of the electron density distribution curve, NepeakAnd z0Respectively representing the maximum electron density and the distance from the surface of the aircraft;
2) calculating the transmitted wave of circularly polarized wave after obliquely entering the plasma according to an equivalent wave impedance method:
<mrow> <msup> <mover> <mi>E</mi> <mo>&RightArrow;</mo> </mover> <mi>t</mi> </msup> <mo>=</mo> <msubsup> <mi>E</mi> <mrow> <mo>|</mo> <mo>|</mo> </mrow> <mi>t</mi> </msubsup> <msub> <mover> <mi>v</mi> <mo>&RightArrow;</mo> </mover> <mrow> <mo>|</mo> <mo>|</mo> </mrow> </msub> <mo>+</mo> <msubsup> <mi>E</mi> <mo>&perp;</mo> <mi>t</mi> </msubsup> <msub> <mover> <mi>v</mi> <mo>&RightArrow;</mo> </mover> <mo>&perp;</mo> </msub> <mo>=</mo> <msubsup> <mi>E</mi> <mrow> <mo>|</mo> <mo>|</mo> </mrow> <mi>i</mi> </msubsup> <msub> <mover> <mi>T</mi> <mo>~</mo> </mover> <mrow> <mo>|</mo> <mo>|</mo> </mrow> </msub> <msub> <mover> <mi>v</mi> <mo>&RightArrow;</mo> </mover> <mrow> <mo>|</mo> <mo>|</mo> </mrow> </msub> <mo>+</mo> <msubsup> <mi>E</mi> <mo>&perp;</mo> <mi>i</mi> </msubsup> <msub> <mover> <mi>T</mi> <mo>~</mo> </mover> <mo>&perp;</mo> </msub> <msub> <mover> <mi>v</mi> <mo>&RightArrow;</mo> </mover> <mo>&perp;</mo> </msub> <mo>;</mo> </mrow>
wherein,andrespectively representing unit direction vectors of parallel polarization and vertical polarization;andrespectively, into a parallel polarization component and a perpendicular polarization component,andthe parallel polarization component and the vertical polarization component are respectively decomposed into the transmitted wave;andthe transmission coefficients of the parallel polarized wave and the vertical polarized wave are respectively;
3) decomposing the transmitted wave into right-handed circular transmitted wave according to the transmitted wave after the circularly polarized wave is incident into the plasmaAnd transmitted waves of the levogyration
<mrow> <msubsup> <mover> <mi>E</mi> <mo>&RightArrow;</mo> </mover> <mi>R</mi> <mi>t</mi> </msubsup> <mo>=</mo> <msub> <mi>E</mi> <mn>0</mn> </msub> <msub> <mover> <mi>T</mi> <mo>~</mo> </mover> <mrow> <mo>|</mo> <mo>|</mo> </mrow> </msub> <msub> <mover> <mi>v</mi> <mo>&RightArrow;</mo> </mover> <mrow> <mo>|</mo> <mo>|</mo> </mrow> </msub> <mo>+</mo> <msub> <mi>jE</mi> <mn>0</mn> </msub> <msub> <mover> <mi>T</mi> <mo>~</mo> </mover> <mo>&perp;</mo> </msub> <msub> <mover> <mi>v</mi> <mo>&RightArrow;</mo> </mover> <mo>&perp;</mo> </msub> <mo>=</mo> <msubsup> <mi>T</mi> <mi>R</mi> <mrow> <mi>c</mi> <mi>o</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <msub> <mi>E</mi> <mn>0</mn> </msub> <msub> <mover> <mi>v</mi> <mo>&RightArrow;</mo> </mover> <mo>&perp;</mo> </msub> <mo>+</mo> <mi>j</mi> <mo>&CenterDot;</mo> <msub> <mi>E</mi> <mn>0</mn> </msub> <msub> <mover> <mi>v</mi> <mo>&RightArrow;</mo> </mover> <mrow> <mo>|</mo> <mo>|</mo> </mrow> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msubsup> <mi>T</mi> <mi>R</mi> <mrow> <mi>c</mi> <mi>r</mi> <mi>o</mi> <mi>s</mi> <mi>s</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <msub> <mi>E</mi> <mn>0</mn> </msub> <msub> <mover> <mi>v</mi> <mo>&RightArrow;</mo> </mover> <mo>&perp;</mo> </msub> <mo>-</mo> <mi>j</mi> <mo>&CenterDot;</mo> <msub> <mi>E</mi> <mn>0</mn> </msub> <msub> <mover> <mi>v</mi> <mo>&RightArrow;</mo> </mover> <mrow> <mo>|</mo> <mo>|</mo> </mrow> </msub> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
<mrow> <msubsup> <mover> <mi>E</mi> <mo>&RightArrow;</mo> </mover> <mi>L</mi> <mi>t</mi> </msubsup> <mo>=</mo> <msub> <mi>E</mi> <mn>0</mn> </msub> <msub> <mover> <mi>T</mi> <mo>~</mo> </mover> <mrow> <mo>|</mo> <mo>|</mo> </mrow> </msub> <msub> <mover> <mi>v</mi> <mo>&RightArrow;</mo> </mover> <mrow> <mo>|</mo> <mo>|</mo> </mrow> </msub> <mo>-</mo> <msub> <mi>jE</mi> <mn>0</mn> </msub> <msub> <mover> <mi>T</mi> <mo>~</mo> </mover> <mo>&perp;</mo> </msub> <msub> <mover> <mi>v</mi> <mo>&RightArrow;</mo> </mover> <mo>&perp;</mo> </msub> <mo>=</mo> <msubsup> <mi>T</mi> <mi>L</mi> <mrow> <mi>c</mi> <mi>r</mi> <mi>o</mi> <mi>s</mi> <mi>s</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <msub> <mi>E</mi> <mn>0</mn> </msub> <msub> <mover> <mi>v</mi> <mo>&RightArrow;</mo> </mover> <mo>&perp;</mo> </msub> <mo>+</mo> <mi>j</mi> <mo>&CenterDot;</mo> <msub> <mi>E</mi> <mn>0</mn> </msub> <msub> <mover> <mi>v</mi> <mo>&RightArrow;</mo> </mover> <mrow> <mo>|</mo> <mo>|</mo> </mrow> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msubsup> <mi>T</mi> <mi>L</mi> <mrow> <mi>c</mi> <mi>o</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <msub> <mi>E</mi> <mn>0</mn> </msub> <msub> <mover> <mi>v</mi> <mo>&RightArrow;</mo> </mover> <mo>&perp;</mo> </msub> <mo>-</mo> <mi>j</mi> <mo>&CenterDot;</mo> <msub> <mi>E</mi> <mn>0</mn> </msub> <msub> <mover> <mi>v</mi> <mo>&RightArrow;</mo> </mover> <mrow> <mo>|</mo> <mo>|</mo> </mrow> </msub> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
Wherein E is0In order to normalize the field strength of the field,andrespectively the transmission coefficients of the common polarization wave and the cross polarization wave in the transmitted wave after the incidence of the right-handed wave,andtransmission coefficients of common polarization and cross polarization waves in the transmission waves after incidence of the levorotatory waves are respectively;
4) the transmission coefficients of the common polarization and the cross polarization waves in the transmission waves after the left/right spin wave is incident are substituted into the following formula to obtain a parameter XPCenv,LAnd XPCenv,R：
<mrow> <msub> <mi>XPC</mi> <mrow> <mi>e</mi> <mi>n</mi> <mi>v</mi> <mo>,</mo> <mi>L</mi> </mrow> </msub> <mo>=</mo> <msubsup> <mi>T</mi> <mi>L</mi> <mrow> <mi>c</mi> <mi>o</mi> </mrow> </msubsup> <mo>/</mo> <msubsup> <mi>T</mi> <mi>L</mi> <mrow> <mi>c</mi> <mi>r</mi> <mi>o</mi> <mi>s</mi> <mi>s</mi> </mrow> </msubsup> <mo>;</mo> </mrow>
<mrow> <msub> <mi>XPC</mi> <mrow> <mi>e</mi> <mi>n</mi> <mi>v</mi> <mo>,</mo> <mi>R</mi> </mrow> </msub> <mo>=</mo> <msubsup> <mi>T</mi> <mi>R</mi> <mrow> <mi>c</mi> <mi>o</mi> </mrow> </msubsup> <mo>/</mo> <msubsup> <mi>T</mi> <mi>R</mi> <mrow> <mi>c</mi> <mi>r</mi> <mi>o</mi> <mi>s</mi> <mi>s</mi> </mrow> </msubsup> <mo>.</mo> </mrow>
5. The high-speed aircraft relay dual polarization MIMO channel modeling method of claim 2, wherein the third step specifically comprises:
step one, generating 2 × 2 statistically independent Gaussian random sequence sample matrix with mean value of 0 and variance of 1 for each stateThe sampling interval of the samples is T; then the sample matrixEach element passes through a low-pass IIR filter to realize the time correlation of the signal, and a 2 × 2 matrix with the time correlation is obtained
Step two, inputting a correlation matrix of large-scale fading componentsAnd will beSubstituting into the following, using a correlation matrixGenerating polarization correlation among MIMO sub-channels to obtain 2 × 2 channel matrix of polarization correlation
<mrow> <mi>v</mi> <mi>e</mi> <mi>c</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>H</mi> <mo>&OverBar;</mo> </mover> <mrow> <mi>c</mi> <mi>o</mi> <mi>r</mi> <mi>r</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mover> <mi>C</mi> <mo>&OverBar;</mo> </mover> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msup> <mo>&CenterDot;</mo> <mi>v</mi> <mi>e</mi> <mi>c</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>H</mi> <mo>&OverBar;</mo> </mover> <mrow> <mi>u</mi> <mi>n</mi> <mi>c</mi> <mi>o</mi> <mi>r</mi> <mi>r</mi> </mrow> </msub> <mo>)</mo> </mrow> </mrow>
vec () represents a take column vector operation;
step three, inputting the channel parameters α and psi of the Loo model according to the condition that the amplitude of the large-scale fading obeys the lognormal distribution, and inputting the channel parametersSubstituting the following formula to generate a channel characteristic matrix of polarization-dependent lognormal distribution
<mrow> <mi>v</mi> <mi>e</mi> <mi>c</mi> <mrow> <mo>(</mo> <mover> <mi>H</mi> <mo>&OverBar;</mo> </mover> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mn>10</mn> <mrow> <mo>&lsqb;</mo> <mi>v</mi> <mi>e</mi> <mi>c</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>H</mi> <mo>&OverBar;</mo> </mover> <mrow> <mi>c</mi> <mi>o</mi> <mi>r</mi> <mi>r</mi> </mrow> </msub> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mi>&psi;</mi> <mo>/</mo> <mn>20</mn> <mo>)</mo> </mrow> <mo>+</mo> <mrow> <mo>(</mo> <mi>&alpha;</mi> <mo>/</mo> <mn>20</mn> <mo>)</mo> </mrow> <mo>&rsqb;</mo> </mrow> </msup> <mo>;</mo> </mrow>
Inputting the polarization discrimination XPD of the polarized antenna positioned in the high-speed aircraft according to the influence of the polarization on the power of the channel sequenceant,rAdjusting the large-scale fading matrix using the following equation
<mrow> <mover> <mi>H</mi> <mo>&OverBar;</mo> </mover> <mo>=</mo> <mo>&lsqb;</mo> <msub> <mover> <mi>h</mi> <mo>&OverBar;</mo> </mover> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>&rsqb;</mo> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msqrt> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>&beta;</mi> <mrow> <mi>a</mi> <mi>n</mi> <mi>t</mi> </mrow> </msub> <mo>)</mo> </mrow> </msqrt> <mo>&CenterDot;</mo> <msub> <mover> <mi>h</mi> <mo>&OverBar;</mo> </mover> <mn>11</mn> </msub> </mrow> </mtd> <mtd> <mrow> <msqrt> <msub> <mi>&beta;</mi> <mrow> <mi>a</mi> <mi>n</mi> <mi>t</mi> </mrow> </msub> </msqrt> <mo>&CenterDot;</mo> <msub> <mover> <mi>h</mi> <mo>&OverBar;</mo> </mover> <mn>12</mn> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msqrt> <msub> <mi>&beta;</mi> <mrow> <mi>a</mi> <mi>n</mi> <mi>t</mi> </mrow> </msub> </msqrt> <mo>&CenterDot;</mo> <msub> <mover> <mi>h</mi> <mo>&OverBar;</mo> </mover> <mn>21</mn> </msub> </mrow> </mtd> <mtd> <mrow> <msqrt> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <msub> <mi>&beta;</mi> <mrow> <mi>a</mi> <mi>n</mi> <mi>t</mi> </mrow> </msub> <mo>)</mo> </mrow> </msqrt> <mo>&CenterDot;</mo> <msub> <mover> <mi>h</mi> <mo>&OverBar;</mo> </mover> <mn>22</mn> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow>
β thereinantIs XPDant,rBy the factor of (a) of (b),
6. the high-speed aircraft relay dual polarization MIMO channel modeling method of claim 2, wherein the fourth step specifically comprises:
1) for each state, a 2 × 2 statistically independent complex gaussian random sequence sample matrix with mean 0 and variance 1 was generated
2) In order to introduce Doppler shift effect, 2 × 2 complex Gaussian random sequence matrixEach element is implemented by a Butterworth filter, producing a complex with Doppler effectGaussian random sequence matrixThe butterworth filter is represented as:
<mrow> <mo>|</mo> <msub> <mi>H</mi> <mrow> <mi>B</mi> <mi>u</mi> <mi>t</mi> <mi>t</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>f</mi> <mo>)</mo> </mrow> <msup> <mo>|</mo> <mn>2</mn> </msup> <mo>=</mo> <mfrac> <mi>A</mi> <mrow> <mn>1</mn> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mi>f</mi> <mo>/</mo> <msub> <mi>f</mi> <mi>c</mi> </msub> <mo>)</mo> </mrow> <mrow> <mn>2</mn> <mi>k</mi> </mrow> </msup> </mrow> </mfrac> <mo>;</mo> </mrow>
wherein A ═ exp (-vT/r)c) V is the flight speed of the aircraft, T is the sample application interval, rcIs a coherence distance, fcIs the cut-off frequency of the k-th order filter;
3) according to the rayleigh distribution obeying the amplitude of small-scale fading, in order to generate a complex rayleigh sequence of 2 × 2, a Loo model channel parameter MP is input, and a complex Gaussian sequence matrix is subjected toEach element multiplied byTo generate a rayleigh 2 × 2 matrixWherein
4) Correlation matrix of input small-scale fading componentAnd will beSubstituting into the following, using a correlation matrixGenerating polarization correlation among MIMO sub-channels to obtain polarization-correlated channel characteristic 2 × 2 matrix
<mrow> <mi>v</mi> <mi>e</mi> <mi>c</mi> <mrow> <mo>(</mo> <mover> <mi>H</mi> <mo>~</mo> </mover> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mover> <mi>C</mi> <mo>~</mo> </mover> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msup> <mo>&CenterDot;</mo> <mi>v</mi> <mi>e</mi> <mi>c</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>H</mi> <mo>~</mo> </mover> <mrow> <mi>r</mi> <mi>a</mi> <mi>y</mi> <mi>l</mi> <mi>e</mi> <mi>i</mi> <mi>g</mi> <mi>h</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
<mrow> <mover> <mi>C</mi> <mo>~</mo> </mover> <mo>=</mo> <msubsup> <mover> <mi>R</mi> <mo>~</mo> </mover> <mrow> <mi>t</mi> <mi>x</mi> </mrow> <mi>T</mi> </msubsup> <mo>&CircleTimes;</mo> <msub> <mover> <mi>R</mi> <mo>~</mo> </mover> <mrow> <mi>r</mi> <mi>x</mi> </mrow> </msub> <mo>;</mo> </mrow>
Wherein,denoted Kronecker product, superscript T denotes matrix transpose,and2 × 2 covariance matrices representing the transmit and receive ends, respectively;
<mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mover> <mi>R</mi> <mo>~</mo> </mover> <mrow> <mi>t</mi> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <msub> <mi>&rho;</mi> <mrow> <mi>t</mi> <mo>,</mo> <mi>L</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>&rho;</mi> <mrow> <mi>t</mi> <mo>,</mo> <mi>R</mi> </mrow> </msub> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mover> <mi>R</mi> <mo>~</mo> </mover> <mrow> <mi>r</mi> <mi>x</mi> </mrow> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <msub> <mi>&rho;</mi> <mrow> <mi>r</mi> <mo>,</mo> <mi>L</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>&rho;</mi> <mrow> <mi>r</mi> <mo>,</mo> <mi>R</mi> </mrow> </msub> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> </mrow> </mtd> </mtr> </mtable> <mo>;</mo> </mrow>
wherein,andrespectively representing the cross correlation of the left-hand circular polarization and the right-hand circular polarization of the transmitting terminal;andrespectively representing the cross correlation of the left-hand circular polarization and the right-hand circular polarization of a receiving end;
5) according to the influence of polarization on the channel sequence power, the coupling degree XPC of the input environmentenv,L、XPCenv,RAnd polarization discrimination XPD of polarized antenna located in high-speed aircraftant,rAdjusting the large-scale fading matrix using the following equation
<mrow> <mover> <mi>H</mi> <mo>~</mo> </mover> <mo>=</mo> <mo>&lsqb;</mo> <msub> <mover> <mi>h</mi> <mo>~</mo> </mover> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>&rsqb;</mo> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msqrt> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>&chi;</mi> <mi>L</mi> </msub> </mrow> </msqrt> <msub> <mover> <mi>h</mi> <mo>~</mo> </mover> <mn>11</mn> </msub> </mrow> </mtd> <mtd> <mrow> <msqrt> <msub> <mi>&chi;</mi> <mi>L</mi> </msub> </msqrt> <msub> <mover> <mi>h</mi> <mo>~</mo> </mover> <mn>12</mn> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msqrt> <msub> <mi>&chi;</mi> <mi>R</mi> </msub> </msqrt> <msub> <mover> <mi>h</mi> <mo>~</mo> </mover> <mn>21</mn> </msub> </mrow> </mtd> <mtd> <mrow> <msqrt> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>&chi;</mi> <mi>R</mi> </msub> </mrow> </msqrt> <msub> <mover> <mi>h</mi> <mo>~</mo> </mover> <mn>22</mn> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow>
WhereinAnd
7. a high-speed aircraft using the high-speed aircraft relay dual-polarization MIMO channel modeling method of any one of claims 1-6.
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| CN114465684A (en) * | 2022-03-11 | 2022-05-10 | 南京信息工程大学 | Bi-Gaussian channel simulation method and device |
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| CN114465684B (en) * | 2022-03-11 | 2023-05-09 | 南京信息工程大学 | Simulation method and device for Bi-Gaussian channel |
| CN114826348A (en) * | 2022-04-19 | 2022-07-29 | 电子科技大学 | Polarization filtering method suitable for dual-polarization system |
| CN114826348B (en) * | 2022-04-19 | 2023-03-17 | 电子科技大学 | Polarization filtering method suitable for dual-polarization system |
| CN115378531A (en) * | 2022-10-25 | 2022-11-22 | 中国人民解放军国防科技大学 | Simulation operation method and system for large-scale satellite ground node of aerospace system |
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