TW202002408A - Far-field testing system for antenna - Google Patents

Abstract

Disclosed is a far-field testing system for antenna. The system includes a multi-input multi-output (MIMO) active phased antenna array, a sum testing antenna, a difference testing antenna, a network analyzer, and a processor. The sum and difference testing antennas emit a sum and a difference electromagnetic radiation signals toward an under-test antenna of the MIMO active phased antenna array respectively. The network analyzer measures an electromagnetic mutual coupling parameter. The processor subtracts the difference electromagnetic radiation signal from the sum electromagnetic radiation signal to substantially eliminate noise of the sum and difference electromagnetic radiation signals, and then encodes the remaining parts of the electromagnetic radiation signals to suppress residual noise so as to restore a true electromagnetic mutual coupling parameter.

Description

Antenna far-field test system

The present invention relates to an antenna testing system, and in particular to an antenna far-field testing system that can be used for multi-input multi-output active phased antenna arrays.

With proper operation, any antenna can be successfully measured in the near or far field. However, due to cost, size, and more complex details, the advantages of the far and near field ranges vary. Generally speaking, the far-field range is suitable for lower frequency antennas, which require a single field type measurement; the near-field range is suitable for higher frequency or large antennas, which require a complete field type and polarization measurement. Each measurement has additional subtypes, each of which has certain advantages and disadvantages, which also makes it difficult to compare measurement techniques between the near and far fields. The traditional far-near field measurement technology must exclude weather, electromagnetic interference, safety, etc. when making a complete measurement. Therefore, it is necessary to use microwave anechoic chamber and specifications to ensure the reliability of the measurement signal, which will increase the cost and complexity of the test site construction.

It has been proved that compared with traditional passive antennas, multiple input multiple output (MIMO) antenna array systems require more detailed measurements, require some additional measurement equipment, and complex test methods, resulting in huge expenditures in the system development process. To build complex and expensive test systems and instruments, such as near-field measurement systems or over-the-air (OTA) measurement systems. However, after the MIMO antenna array system is deployed on the antenna base (such as a military radar base or a base station of a wireless communication system), if some transmit/receive modules fail or the signal phase and amplitude settings are incorrect, how to perform Correcting the amplitude and phase of the antenna unit is a very important issue because it is impossible to build a complex and expensive near-field measurement system or OTA measurement system on the field. Therefore, a simple antenna self-calibration system must be developed. This system can detect the failed antenna unit and replace it in time to maintain the MIMO antenna system. In other words, it is the best test method to simplify the strict requirements of the test system on the test environment and at the same time to ensure the reliability of the measurement signal.

In order to solve the lack of conventional technology, the object of the present invention is to provide an exemplary antenna far-field test system, including a multiple input multiple output (MIMO) active phased array antenna array, a test antenna unit, a differential test antenna unit, and a network Analyzer and processing unit. The MIMO active phase alignment antenna array includes multiple antenna elements, and the antenna element located at the center of the multiple antenna elements serves as the antenna element to be tested. Connect the test antenna unit to the antenna unit under test, and the test antenna unit emits electromagnetic radiation signals toward the antenna unit under test to electromagnetically couple with the antenna unit under test, wherein the electromagnetic radiation signal includes the electromagnetic mutual coupling unit and the antenna Noise department. The difference test antenna unit is connected to the antenna unit to be tested, and is set to be coplanar with the antenna unit to be tested and the test antenna unit and adjacent to the antenna unit to be tested, and the distance between the antenna unit to be tested and the antenna unit to be tested is equal to the antenna unit to be tested And the spacing between the antenna units under test, the differential test antenna unit emits a differential electromagnetic radiation signal toward the antenna unit under test to electromagnetically couple with the antenna unit under test, wherein the differential electromagnetic radiation signal includes a differential electromagnetic mutual coupling portion and a differential antenna Noise department. The network analyzer connects and tests the antenna unit, the difference test antenna unit and the antenna unit to be tested, and connects each antenna unit except the antenna unit to be tested to the matched load, and the network analyzer measures and tests the antenna unit and the difference test antenna The electromagnetic mutual coupling between the unit and the antenna unit to be tested to output electromagnetic mutual coupling parameters, wherein the electromagnetic mutual coupling parameters include an electromagnetic mutual coupling part and an interference noise part. The processing unit connects and tests the antenna unit, the difference test antenna unit, and the network analyzer. The processing unit subtracts the sum electromagnetic radiation signal and the difference electromagnetic radiation signal to substantially eliminate the sum antenna noise part and the difference antenna noise part. The part of the unit code and the electromagnetic radiation signal and the difference electromagnetic radiation signal are retained, and the orthogonal rule of the code is used to restore the electromagnetic mutual coupling part from the electromagnetic mutual coupling parameter and suppress the interference noise part.

The antenna far-field test system provided by the present invention is characterized by:

1. Antenna far-field type test in open field test environment

At the test antenna end, it was first proposed to use dual antennas instead of single antennas. In this way, the addition and subtraction of the difference and field pattern of the dual antennas is used to simplify the encoder design. At the same time, it can also eliminate the multiples of open environmental testing. Path interference problem.

2. Applied to multi-input multi-output active antenna array calibration

The excitation coefficient of the antenna unit under test is adjusted according to the radiation pattern of the antenna unit under test so that the radiation pattern of the antenna unit under test conforms to the standard radiation field pattern.

50‧‧‧Multi-input multi-output active phase array antenna array

501‧‧‧ and test antenna unit

502‧‧‧ poor test antenna unit

5031‧‧‧ Antenna unit

503‧‧‧ antenna unit under test

504‧‧‧Network Analyzer

505‧‧‧ matching load

506‧‧‧ processing unit

801‧‧‧Interference noise

802‧‧‧Multipath interference noise

x, y, z, x’, y’, z’ ‧‧‧ coordinate axis

R‧‧‧spacing

h‧‧‧height

d‧‧‧Distance

θ,Φ‧‧‧Azimuth

S ₁₁ ~S ₃₃ ‧‧‧Electromagnetic mutual coupling sampling parameters

FIG. 1 is a first schematic diagram of an antenna far-field testing device according to an embodiment of the present invention.

2 is a second schematic diagram of an antenna far-field testing device according to an embodiment of the present invention.

FIG. 3 is a third schematic diagram of an antenna far-field testing device according to an embodiment of the present invention.

4 is a waveform diagram of electromagnetic mutual coupling parameters measured by a network analyzer of an antenna far-field testing device according to an embodiment of the present invention.

FIG. 5 is a waveform diagram of electromagnetic mutual coupling parameters after the processing unit of the antenna far-field testing device of the embodiment of the present invention eliminates interference noise and ground reflected clutter.

FIG. 6 is a convolution diagram of a processing unit of an antenna far-field test device according to an embodiment of the present invention applying a Gold code to encode an electromagnetic radiation signal.

7 is a first waveform diagram of electromagnetic mutual coupling parameters after the processing unit of the antenna far-field test device of the embodiment of the present invention eliminates interference noise, ground reflection noise, and residual noise.

8 is a second waveform diagram of electromagnetic mutual coupling parameters after the processing unit of the antenna far-field testing device of the embodiment of the present invention eliminates interference noise, ground reflection noise, and residual noise.

Please refer to FIG. 1 to FIG. 8, FIG. 1 to FIG. 3 are first to third schematic diagrams of the antenna far-field test device of the embodiment of the present invention; FIG. 4 is a network analysis of the antenna far-field test device of the embodiment of the present invention FIG. 5 is a waveform diagram of electromagnetic mutual coupling parameters measured by the instrument; FIG. 5 is a waveform diagram of electromagnetic mutual coupling parameters after the processing unit of the antenna far-field test device of the embodiment of the present invention eliminates interference noise and ground reflected clutter; FIG. 6 It is a convolution diagram of the processing unit of the antenna far-field test device of the embodiment of the present invention applying the Guinness code to the electromagnetic radiation signal; FIGS. 7 and 8 are the processing unit of the antenna far-field test device of the embodiment of the present invention to eliminate interference noise The first and second waveform diagrams of the electromagnetic mutual coupling parameters after the signal, ground reflection noise and residual noise.

As shown in FIG. 1, the antenna far-field test system includes a multiple input multiple output (MIMO) active phased array antenna array 50, and a test antenna unit 501, a difference test antenna unit 502, a network analyzer 504, and a processing unit 506, wherein The MIMO active phase alignment antenna array 50 includes a plurality of antenna elements 5031. In this embodiment, the antenna unit located at the center position of the plurality of antenna units 5031 is selected as the antenna unit 503 to be tested.

It is worth noting that, as shown in FIG. 2, in this embodiment, one antenna unit to be tested 503 is not only matched with one test antenna unit, but is paired with dual test antenna units 501 and 502. The center line of the antenna unit 503 to be tested can be aligned with the boundary between the test antenna unit 501 and the difference test antenna unit 502 such that the center line of the test antenna unit 501 and the difference test antenna unit 502 are symmetrical with the center line of the antenna unit 503 to be tested.

The sum test antenna unit 501 and the difference test antenna unit 502 can be arranged in the same plane as the antenna unit 503 to be tested. The distance R between the sum test antenna unit 501 and the antenna unit 503 to be tested may be equal to the distance R between the difference test antenna unit 502 and the antenna unit 503 to be tested. The sum test antenna unit 501 and the difference test antenna unit 502 may be arranged adjacent to each other and juxtaposed. The distance R between the test antenna unit 501 and the antenna unit 503 to be tested may be much larger than the separation distance d between the test antenna unit 501 and the difference test antenna unit 502, which belongs to the far-field range, and The test antenna unit 501 and the difference test antenna unit 502 can be wirelessly connected to the antenna unit to be tested 503 to perform an accurate far-field test as described in detail below.

The sum test antenna unit 501 and the difference test antenna unit 502 can synchronously or asynchronously transmit the sum electromagnetic radiation signal and the difference electromagnetic radiation signal toward the antenna unit 503 to be tested, so as to cause electromagnetic mutual coupling with the antenna unit 503 to be tested. Among them, the sum electromagnetic radiation signal includes the sum electromagnetic mutual coupling part and the antenna noise part, and the difference electromagnetic radiation signal includes the difference electromagnetic mutual coupling part and the difference antenna noise part. That is to say, there are various noises in the electromagnetic radiation signals transmitted between the test antenna unit 501 and the antenna unit 503 to be tested, and between the difference test antenna unit 502 and the antenna unit 503 to be tested.

The network analyzer 504 may be, for example, a 4F network analyzer 504, having four test terminals, respectively connected and tested to the antenna unit 501, the difference test antenna unit 502, the antenna unit to be tested 503, and the matching load 505. The network analyzer 504 may connect a plurality of antenna units 5031 other than the antenna unit 503 to be tested to the matching load 505. With this configuration, the network analyzer 504 measures and tests the electromagnetic mutual coupling between the antenna unit 501 and the difference test antenna unit 502 and the antenna unit 503 to be tested to pass the other three tests except for connection with the matching load 505 End to obtain electromagnetic mutual coupling parameters. As shown in FIG. 4, the electromagnetic mutual coupling parameters measured by the network analyzer 504 include an electromagnetic mutual coupling part and an interference noise part, rather than real electromagnetic mutual coupling parameters (ie, electromagnetic mutual coupling part).

The processing unit 506 is, for example, a processor, which connects and tests the antenna unit 501, the difference test antenna unit 502, and the network analyzer 504. It is worth noting that the processing unit 506 subtracts the sum electromagnetic radiation signal of the sum test antenna unit 501 and the difference electromagnetic radiation signal of the difference test antenna unit 502 to substantially eliminate the sum of the antenna noise part and the difference antenna noise part, such as The electromagnetic radiation signal shown in FIG. 5 has less noise than FIG. 4, that is, the interference noise 801 and the multipath interference noise 802 reflected on the ground have been eliminated. The processing unit 506 then encodes the remaining parts of the electromagnetic radiation signal and the differential electromagnetic radiation signal, and uses the orthogonal rule of the encoding to suppress the electromagnetic mutual coupling parameters according to the remaining parts of the electromagnetic radiation signal and the differential electromagnetic radiation signal The interference noise part is used to restore the electromagnetic mutual coupling part from the electromagnetic mutual coupling parameters. As shown in FIGS. 7 and 8, the noise in the electromagnetic radiation signal is greatly reduced, and only the residual random noise is left.

The operation used in the operation will be described in detail below for the above operation.

When the antenna unit under test 503 is used as the receiving end and the antenna unit 501 and the differential test antenna unit 502 are used as the transmitting end, there are two operating modes: the electromagnetic radiation signal and the differential electromagnetic radiation signal. After the antenna unit 502 is tested, the network analyzer 504 will measure the following electromagnetic mutual coupling parameters:

Among them, [S] represents the electromagnetic mutual coupling parameter, S _ij (n) represents the electromagnetic mutual coupling sampling parameter, S _ij ( n ) = S _ij ( nT ₀ ); t = nT ₀ ; i = 1, 2, 3; j =1,2,3; n=1,2,3,..., T ₀ represents the sampling period of the sum electromagnetic radiation signal and the difference electromagnetic radiation signal.

The sum electromagnetic radiation signal and the difference electromagnetic radiation signal are obtained by the following equation:

代表和電磁輻射訊號，

中的S、cos(ψ)代表和訊號場型(Sum Pattern)，

代表差電磁輻射訊號，

中的D、sin(ψ)代表差訊號場型(Difference Pattern)，Γ代表網路分析儀504的與匹配負載505連接的端口例如第四端口的反射係數，a代表振福，E_s代表地面反射的多重路徑干擾雜訊，λ代表波長，d代表振福峰值，θ _s 代表多重路徑干擾雜訊的入射角度，E_j(θ_j ')代表入射角為 θ_j '的干擾雜訊，N^S(D)(n)代表殘餘隨機雜訊。 among them,

Representatives and electromagnetic radiation signals,

S, cos( ψ ) in the representative and sum pattern (Sum Pattern),

Stands for differential electromagnetic radiation signal,

The D, sin (ψ) representative of the difference signal field pattern (Difference Pattern), Γ network analyzer 504 is representative of the reflection coefficient matched load port 505 connected to the fourth port, for example, a is the representative-fu, E _s behalf ground Reflected multipath interference noise, λ represents the wavelength, d represents the peak of vibration, θ _s represents the incident angle of the multipath interference noise, E _j (θ _j ′ ) represents the interference noise with the incident angle θ _j ′ , N ^S(D) (n) represents residual random noise.

If the configuration and test antenna unit 501 and the difference test antenna unit 502 are symmetrical to each other with the center line of the antenna unit 503 to be tested, the above equation can be simplified as follows due to the geometric symmetry relationship:

The processing unit 506 subtracts the sum electromagnetic radiation signal from the difference electromagnetic radiation signal by the following equation, and can eliminate the sum of the electromagnetic radiation signal and the antenna noise part and the difference electromagnetic radiation signal without complicated circuit design or complicated calculation. The interference noise 801 in the noise portion of the poor antenna is θ ' , that is, E _j (θ _j ' ), and establishes a two-bit bipolar signal:

Among them, r ₁ ( n ) and r _-1 ( n ) represent two-bit bipolar signals, N(n) represents residual random noise, and E _s represents ground-reflected multipath interference noise.

The processing unit 506 can adjust and test the height h of the antenna unit 501 and the difference test antenna unit 502 so that the sum signal field type cos(Ψ) of the test antenna (TA) and the difference signal field type sin(Ψ) of the test antenna (TA) Can cancel each other out. By this, if the multipath interference noise 802/E _s reflected by the ground in the sum of the electromagnetic radiation signal and the antenna noise portion and the difference in the antenna noise portion of the poor electromagnetic radiation signal can be further eliminated by the following equation, the following equation, Therefore, the reliability of the measurement signal can be ensured without the microwave darkroom:

,t=nT The processing unit 506 includes a codec to encode a two-bit bipolar signal. For example, as shown in FIG. 5, after a total of 127 tests, the Gold Code is used to encode 127 times: X(t)= c(t)r(t)

,t=nT

As shown in FIG. 6, the processing unit 506 can use the same code as convolution to eliminate the interference noise part in the electromagnetic mutual coupling parameters, and restore the electromagnetic mutual coupling part in the electromagnetic mutual coupling parameters:

Where c(t) represents coding, R _cc ( τ ) represents the convolution of c(t), R _cn ( τ ) represents the correlation between c(t) and residual random noise, and T represents the integration period, S( τ ) represents the electromagnetic mutual coupling part.

In more detail, the true electromagnetic mutual coupling parameters between the antenna unit under test 503 and the difference test antenna unit 502, and between the antenna unit under test 503 and the test antenna unit 501 (ie, the electromagnetic mutual coupling part of the electromagnetic mutual coupling parameters) (S(τ)) is the steady-state signal, and the noise N(t) is the residual random noise (that is, the interference noise part of the electromagnetic mutual coupling parameter). Since c(t) is a carefully selected known code, the number of autocorrelated connections ( R _cc ( τ )) can be calculated and the number of uncorrelated connections ( R _cn ( τ )) is a very small value. Therefore, the true electromagnetic mutual coupling parameter (S(τ)) can be calculated by the above formula, and at the same time, the residual principle N(n) can be suppressed by using the orthogonal principle of coding. Therefore, as shown in FIGS. 7 and 8, the noise of the electromagnetic radiation signal is minimized. All interference signals such as interference noise 801 with an incident angle of θ ′ , ground reflection noise, and random noise can be processed in two stages. Completely suppressed, without the need for complex encoder design and without the use of reflection-free experimental wave absorption device, can solve the problem of weak electromagnetic signals that are easily affected by noise interference and test errors.

Finally, the electromagnetic mutual coupling part of the decoded electromagnetic mutual coupling parameters can be converted into related antenna performance parameters by the following formula:

代表待測天線單元503的增益場型分布，AUT代表待測天線單元503，(θ',Φ')代表待測天線單元503的方位角，G _TA 代表和測試天線單元501或差測試天線單元502的增益場型分布，TA代表和測試天線單元501以及差測試天線單元502，(θ=0°，Φ=90°)代表和測試天線單元501以及差測試天線單元502的方位角，R代表和測試天線單元501以及待測天線單元503的間距或差測試天線單元502以及待測天線單元503的間距(單位：公尺)，λ代表空中的訊號波長(單位：公尺)。 among them,

Representative test field type distribution gain antenna unit 503, AUT Representative test antenna unit 503, (θ ', Φ' ) representative of the azimuth antenna unit under test, G _TA representative of the antenna unit 503 and the test 501 or test a difference antenna unit 502's gain pattern distribution, TA stands for the test antenna unit 501 and the difference test antenna unit 502, (θ=0°, Φ=90°) stands for the azimuth angle of the test antenna unit 501 and the difference test antenna unit 502, R stands for The distance between the test antenna unit 501 and the antenna unit to be tested 503 or the difference between the test antenna unit 502 and the antenna unit to be tested 503 (unit: m), λ represents the signal wavelength in the air (unit: m).

The azimuth angle (θ ' , Φ ' ) of the antenna unit 503 to be tested is set to (θ ' = 0°, Φ ' = 90°), and the electromagnetic mutual coupling parameters are converted into the relevant antenna performance parameters by the following formula:

The above are only the preferred and feasible embodiments of the present invention, and all changes and modifications made within the scope of the patent application of the present invention shall fall within the scope of the present invention.

50‧‧‧Multi-input multi-output active phase array antenna array

501‧‧‧ and test antenna unit

502‧‧‧ poor test antenna unit

5031‧‧‧ Antenna unit

503‧‧‧ antenna unit under test

504‧‧‧Network Analyzer

505‧‧‧ matching load

506‧‧‧ processing unit

801‧‧‧Interference noise

802‧‧‧Multipath interference noise

x, y, z, x’, y’, z’ ‧‧‧ coordinate axis

R‧‧‧spacing

h‧‧‧height

d‧‧‧Distance

Claims (8)

An antenna far-field test system, including: a multiple input multiple output (MIMO) active phased array antenna, including a plurality of antenna units, one of which is located at the central position of the plurality of antenna units as a test An antenna unit; a test antenna unit connected to the antenna unit under test, and the test antenna unit emits a sum of electromagnetic radiation signals toward the antenna unit under test to electromagnetically couple with the antenna unit under test, wherein the sum electromagnetic The radiated signal includes an electromagnetic mutual coupling part and an antenna noise part; a differential test antenna unit is connected to the antenna unit to be tested, and is disposed coplanar with the antenna unit to be tested and the antenna unit to be tested and is adjacent to the And the test antenna unit, the distance between the difference test antenna unit and the antenna unit under test is equal to the distance between the test antenna unit and the antenna unit under test, and the difference test antenna unit transmits a signal toward the antenna unit under test A differential electromagnetic radiation signal to electromagnetically couple with the antenna unit under test, wherein the differential electromagnetic radiation signal includes a differential electromagnetic mutual coupling unit and a differential antenna noise unit; a network analyzer is connected to the test antenna unit , The difference test antenna unit and the antenna unit to be tested, and connect each antenna unit except the antenna unit to be tested to a matching load, the network analyzer measures the sum test antenna unit and the difference test antenna unit Electromagnetic mutual coupling with the antenna unit to be tested to output an electromagnetic mutual coupling parameter, wherein the electromagnetic mutual coupling parameter includes an electromagnetic mutual coupling part and an interference noise part; and a processing unit, which is connected to the test antenna Unit, the difference test antenna unit and the network analyzer, the processing unit subtracts the sum electromagnetic radiation signal from the difference electromagnetic radiation signal to substantially eliminate the sum antenna noise part and the difference antenna noise part, The processing unit encodes the remaining portion of the sum electromagnetic radiation signal and the differential electromagnetic radiation signal, and uses the orthogonal rule of the code to suppress the interference noise part to restore the electromagnetic mutual coupling from the electromagnetic mutual coupling parameters unit. The antenna far-field test system according to claim 1, wherein the electromagnetic mutual coupling parameters are:

Among them, [S] represents the electromagnetic mutual coupling parameter, S _ij (n) represents the electromagnetic mutual coupling sampling parameter, S _ij ( n ) = S _ij ( nT ₀ ); t = nT ₀ ; i = 1, 2, 3; j=1,2,3; n=1,2,3,..., T ₀ represents the sampling period of the sum electromagnetic radiation signal and the differential electromagnetic radiation signal. The antenna far-field test system according to claim 2, wherein the sum electromagnetic radiation signal and the differential electromagnetic radiation signal are obtained by the following equation:

among them,

Represents the sum electromagnetic radiation signal, cos( ψ ) represents the sum signal field type,

Represents the difference electromagnetic radiation signal, sin( ψ ) represents the difference signal field type, Γ represents the reflection coefficient of the port of the network analyzer connected to the matched load, a represents Zhen Fu, and E _s represents the multipath interference reflected by the ground Noise, λ represents the wavelength, d represents the peak of vibration, θ _s represents the angle of incidence of the multipath interference noise, E _j (θ ' ) represents the interference noise with the angle of incidence θ ' , N ^S(D) (n) Represents residual random noise. The antenna far-field test system according to claim 3, wherein the sum test antenna unit and the difference test antenna unit are symmetrical to each other with the center line of the antenna unit under test, and the following equation is obtained due to the geometric symmetry relationship:

The requested item antenna far-field testing system of claim 4, wherein the processing unit is a subtraction by the following equation and the electromagnetic radiation signal and the difference signal of electromagnetic radiation, to eliminate the interference noise incident angle of θ ', and to obtain Two-digit bipolar signal:

Where r ₁ ( n ) and r _-1 ( n ) represent two-bit bipolar signals, N(n) represents residual random noise, and E _s represents ground-reflected multipath interference noise; the processing unit controls the sum test The height of the antenna unit and the difference test antenna unit to further eliminate the multipath interference noise reflected by the ground in the sum antenna noise part and the difference antenna noise part by the following equation:

The antenna far-field test system according to claim 5, wherein the processing unit includes a codec that encodes a two-bit bipolar signal and uses the same code for convolution to restore the electromagnetic mutual coupling part : X(t)=c(t)r(t)

,t=nT

Where c(t) represents coding, R _cc ( τ ) represents the convolution of c(t), R _cn ( τ ) represents the correlation between c(t) and residual random noise, and T represents the integration period, S( τ ) represents the electromagnetic mutual coupling part. The antenna far-field test system according to claim 6, wherein the electromagnetic mutual coupling part is converted into related antenna performance parameters by the following formula:

among them,

Represents the gain pattern distribution of the antenna unit under test, AUT represents the antenna unit under test, (θ ' , Φ ' ) represents the azimuth of the antenna unit under test, G _TA represents the sum test antenna unit and the difference test antenna The gain field distribution of the unit, TA stands for the sum test antenna unit and the difference test antenna unit, (θ=0°, Φ=90°) stands for the azimuth angle of the sum test antenna unit and the difference test antenna unit, R stands for The distance between the test antenna unit and the antenna unit to be tested, λ represents the signal wavelength in the air. The antenna far-field test system according to claim 7, wherein the azimuth angle (θ ′ , Φ ′ ) of the antenna unit to be tested is set to (θ=0°, Φ=90°), and the electromagnetic mutual coupling part is composed of The formula is converted into related antenna performance parameters:

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