polloss

Polarization loss

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Syntax

rho = polloss(fv_tr,fv_rcv)

rho = polloss(fv_tr,fv_rcv,pos_rcv)

rho = polloss(fv_tr,fv_rcv,pos_rcv,axes_rcv)

rho = polloss(fv_tr,fv_rcv,pos_rcv,axes_rcv,pos_tr)

rho = polloss(fv_tr,fv_rcv,pos_rcv,axes_rcv,pos_tr,axes_tr)

Description

example

rho= polloss(fv_tr,fv_rcv)returns the loss, in decibels, because of mismatch between the polarization of a transmitted field,fv_tr, and the polarization of the receiving antenna,fv_rcv. The field vector lies in a plane orthogonal to the direction of propagation from the transmitter to the receiver. The transmitted field is represented as a 2-by-1 column vector[Eh;Ev]. In this vector,EhandEvare the field’s horizontal and vertical linear polarization components with respect to the transmitter’s local coordinate system. The receiving antenna’s polarization is specified by a 2-by-1 column vector,fv_rcv. You can also specify this polarization in the form of[Eh;Ev]with respect to the receiving antenna’s local coordinate system. In this syntax, both local coordinate axes align with the global coordinate system.

example

rho= polloss(fv_tr,fv_rcv,pos_rcv)specifies, in addition, the position of the receiver. The receiver is defined as a 3-by-1 column vector,[x;y;z], with respect to the global coordinate system (position units are in meters). This syntax can use any of the input arguments in the previous syntax.

example

rho= polloss(fv_tr,fv_rcv,pos_rcv,axes_rcv)specifies, in addition, the orthonormal axes,axes_rcv. These axes define the receiver's local coordinate system as a 3-by-3 matrix. The first column gives thex-axis of the local system with respect to the global coordinate system. The second and third columns give theyandzaxes, respectively. This syntax can use any of the input arguments in the previous syntaxes.

example

rho= polloss(fv_tr,fv_rcv,pos_rcv,axes_rcv,pos_tr)specifies, in addition, the position of the transmitter as a 3-by-1 column vector,[x;y;z], with respect to the global coordinate system (position units are in meters). This syntax can use any of the input arguments in the previous syntaxes.

example

rho= polloss(fv_tr,fv_rcv,pos_rcv,axes_rcv,pos_tr,axes_tr)specifies, in addition, the orthonormal axes,axes_tr. These axes define the transmitter's local coordinate system as a 3-by-3 matrix. The first column gives thex-axis of the local system with respect to the global coordinate system. The second and third columns give theyandzaxes, respectively. This syntax can use any of the input arguments in the previous syntaxes.

Examples

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Mismatch Between 45° Polarized Field and Horizontally Polarized Receiver

Open Live Script

Begin with a 45° polarized transmitted field and a receiver that is horizontally polarized. By default, the transmitter and receiver local axes coincide with the global coordinate system. Compute the polarization loss in dB.

fv_tr = [1;1]; fv_rcv = [1;0]; rho = polloss(fv_tr,fv_rcv)

rho = 3.0103

的loss is 3 dB as expected because only half the power of the field matches to the receive antenna polarization.

Polarization Loss Unaffected by Receiver Position

Open Live Script

Begin with identical transmitter and receiver polarizations. Place the receiver at a position 100 meters along they设在。的transmitter is at the origin (its default position) and both local coordinate axes coincide with the global coordinate system (by default). First, compute the polarization loss. Then, move the receiver 100 meters along the_x_-axis, and compute the polarization loss again.

fv_tr = [1;0]; fv_rcv = [1;0]; pos_rcv = [0;100;0]; rho(1) = polloss(fv_tr,fv_rcv,pos_rcv); pos_rcv = [100;100;0]; rho(2) = polloss(fv_tr,fv_rcv,pos_rcv)

rho =1×20 0

没有极化损失发生在的位置。的spherical basis vectors of each antenna are parallel to other antenna and the polarization vectors are the same.

Loss Due to Receiver Axes Rotation

Open Live Script

Start with identical transmitter and receiver polarizations. Put the receiver at a position 100 meters along they设在。的transmitter is at the origin (default) and both local coordinate axes coincide with the global coordinate system (default). Compute the loss, and then rotate the receiver 30° around they设在。This rotation changes the azimuth and elevation of the transmitter with respect to the receiver and, therefore, the direction of polarization.

fv_tr = [1;0]; fv_rcv = [1;0]; pos_rcv = [0;100;0]; ax_rcv = azelaxes(0,0); rho(1) = polloss(fv_tr,fv_rcv,pos_rcv,ax_rcv); ax_rcv = roty(30)*ax_rcv; rho(2) = polloss(fv_tr,fv_rcv,pos_rcv,ax_rcv)

rho =1×20 1.2494

的receiver polarization vector remains unchanged. However, rotating the local coordinate system changes the direction of the field of the receiving antenna polarization with respect to global coordinates. This change results in a 1.2 dB loss.

Polarization Loss Unaffected by Transmitter Position

Open Live Script

Start with identical transmitter and receiver polarizations. Put the receiver at a position 100 meters along the_y_-axis. The transmitter is at the origin (default) and both local coordinate axes coincide with the global coordinate system (default). First, compute the polarization loss. Then, move the transmitter 100 meters along thex-axis and 100 meters along they-axis, and compute the polarization loss again.

fv_tr = [1;0]; fv_rcv = [1;0]; pos_rcv = [0;100;0]; ax_rcv = azelaxes(0,0); pos_tr = [0;0;0]; rho(1) = polloss(fv_tr,fv_rcv,pos_rcv,ax_rcv,pos_tr); pos_tr = [100;100;0]; rho(2) = polloss(fv_tr,fv_rcv,pos_rcv,ax_rcv,pos_tr)

rho =1×20 0

的re is no polarization loss at either position because the spherical basis vectors of each antenna are parallel to their counterparts and the polarization vectors are the same.

Plot Polarization Loss as Receiving Antenna Rotates

Open Live Script

Specifying identical transmitter and receiver polarizations, plot the loss as the local receiving antenna axes rotate around the设在。

fv_tr = [1;0]; fv_rcv = [1;0];

的position of the transmitting antenna is at the origin and its local axes align with the global coordinate system. The position of the receiving antenna is 100 meters along the global设在。However, its local-axis points towards the transmitting antenna.

pos_tr = [0;0;0]; axes_tr = azelaxes(0,0); pos_rcv = [100;0;0]; axes_rcv0 = rotz(180)*azelaxes(0,0);

Rotate the receiving antenna around its local设在一度在增量。f计算损失or each angle.

angles = [0:1:359]; n = size(angles,2); rho = zeros(1,n);% Initialize spacefork = 1:n axes_rcv = rotx(angles(k))*axes_rcv0; rho(k) = polloss(fv_tr,fv_rcv,pos_tr,axes_tr,...pos_rcv,axes_rcv);end

Plot the polarization loss.

hp = plot(angles,rho); hax = hp.Parent; hax.XLim = [0,360]; xticks = (0:(n-1))*45; hax.XTick = xticks; grid; title('Polarization loss versus receiving antenna rotation') xlabel('Rotation angle (degrees)'); ylabel('Loss (dB)');

的angle-loss plot shows nulls (InfdB) at 90 degrees and 270 degrees where the polarizations are orthogonal.

Input Arguments

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`fv_tr`—Transmitted field vector in linear component representation
2-by-1 complex-valued column vector

的transmitted field vector in linear component representation specified as a 2-by-1, complex-valued column vector[Eh;Ev]. In this vector,EhandEvare the field’s horizontal and vertical linear components.

Example:[1;1]

Data Types:double
Complex Number Support:Yes

`fv_rcv`—Receiver polarization vector in linear component representation
2-by-1 complex-valued column vector

Receiver polarization vector in linear component representation specified as a 2-by-1, complex-valued column vector[Eh;Ev]. In this vector,EhandEvare the polarization vector’s horizontal and vertical linear components.

Example:[0;1]

Data Types:double
Complex Number Support:Yes

`pos_rcv`—Receiving antenna position
[0;0;0](default) |3-by-1 real-valued column vector

Receiving antenna position specified as a 3-by-1, real-valued column vector. The components ofpos_rcvare specified in the global coordinate system as[x;y;z].

Example:[1000;0;0]

Data Types:double

`axes_rcv`—Receiving antenna local coordinate axes
3-by-3 identity matrix(default) |3-by-3 real-valued matrix

Receiving antenna local coordinate axes specified as a 3-by-3, real-valued matrix. Each column is a unit vector specifying the local coordinate system's orthonormalx,y, andzaxes, respectively, with respect to the global coordinate system. Each column is written in[x;y;z]form. Ifaxes_rcvis specified as the identity matrix, the local coordinate system is aligned with the global coordinate system.

Example:[1, 0, 0; 0, 1, 0; 0, 0 ,1]

Data Types:double

`pos_tr`—Transmitter position
[0;0;0](default) |3-by-1 real-valued column vector

Transmitter position specified as a 3-by-1, real-valued column vector. The components ofpos_trare specified in the global coordinate system as[x;y;z].

Example:[0;0;0]

Data Types:double

`axes_tr`—Transmitting antenna local coordinate axes
3-by-3 identity matrix(default) |3-by-3 real-valued matrix

Transmitting antenna local coordinate axes specified as a 3-by-3, real-valued matrix. Each column is a unit vector specifying the local coordinate system's orthonormalx,y, andzaxes, respectively, with respect to the global coordinate system. Each column is written in[x;y;z]form. Ifaxes_tris the identity matrix, the local coordinate system is aligned with the global coordinate system.

Example:[1, 0, 0; 0, 1, 0; 0, 0 ,1]

Data Types:double

Output Arguments

collapse all

`rho`— Polarization loss
scalar

Polarization loss returned as scalar in decibel units. The polarization loss is the projection of the normalized transmitted field vector into the normalized receiving antenna polarization vector. Its value lies between zero and unity. When converted into dB, (and a sign changed to show loss as positive) its value lies between 0 and-Inf.

More About

collapse all

Polarization Loss Due to Field and Receiver Mismatch

Loss occurs when a receiver is not matched to the polarization of an incident electromagnetic field.

In the case of the polarization of a field emitted by a transmitting antenna, first, look at the far zone of the transmitting antenna, as shown in the following figure. At this location―which is the location of the receiving antenna―the electromagnetic field is orthogonal to the direction from transmitter to receiver.

You can represent the transmitted electromagnetic field,fv_tr, by the components of a vector with respect to a spherical basis of the transmitter’s local coordinate system. The orientation of this basis depends on its direction from the origin. The direction is specified by the azimuth and elevation of the receiving antenna with respect to the transmitter’s local coordinate system. Then, the transmitter’s polarization, in terms of the spherical basis vectors of the transmitter’s local coordinate system, is

$E = E_{H} {\hat{e}}_{a z} + E_{V} {\hat{e}}_{e l} = E_{m} P_{i}$

In the same manner, the receiver’s polarization vector,fv_rcv, is defined with respect to a spherical basis in the receiver’s local coordinate system. Now, the azimuth and elevation specify the transmitter’s position with respect to the receiver’s local coordinate system. You can write the receiving antennas polarization in terms of the spherical basis vectors of the receiver’s local coordinate system:

$P = P_{H} {\hat{e}}^{'}_{a z} + P_{V} {\hat{e}}^{'}_{e l}$

This figure shows the construction of the different transmitter and receiver local coordinate systems. It also shows the spherical basis vectors with which to write the field components.

的polarization loss is the projection (or dot product) of the normalized transmitted field vector onto the normalized receiver polarization vector. Notice that the loss occurs because of the mismatch in direction of the two vectors not in their magnitudes. Because the vectors are defined in different coordinate systems, they must be converted to the global coordinate system in order to form the projection. The polarization loss is defined by:

$ρ = \frac{| E_{i} \cdot P |^{2}}{| E_{i} |^{2} | P |^{2}}$

References

[1] Mott, H. Antennas for Radar and Communications.John Wiley & Sons, 1992.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

Does not support variable-size inputs.

Documentation

polloss

Syntax

Description

Examples

Mismatch Between 45° Polarized Field and Horizontally Polarized Receiver

Polarization Loss Unaffected by Receiver Position

Loss Due to Receiver Axes Rotation

Polarization Loss Unaffected by Transmitter Position

Plot Polarization Loss as Receiving Antenna Rotates

Input Arguments

`fv_tr`—Transmitted field vector in linear component representation
2-by-1 complex-valued column vector

`fv_rcv`—Receiver polarization vector in linear component representation
2-by-1 complex-valued column vector

`pos_rcv`—Receiving antenna position
[0;0;0](default) |3-by-1 real-valued column vector

`axes_rcv`—Receiving antenna local coordinate axes
3-by-3 identity matrix(default) |3-by-3 real-valued matrix

`pos_tr`—Transmitter position
[0;0;0](default) |3-by-1 real-valued column vector

`axes_tr`—Transmitting antenna local coordinate axes
3-by-3 identity matrix(default) |3-by-3 real-valued matrix

Output Arguments

`rho`— Polarization loss
scalar

More About

Polarization Loss Due to Field and Receiver Mismatch

References

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

See Also

Introduced in R2013a

Phased Array System Toolbox Documentation

万博1manbetx

Try MATLAB, Simulink, and Other Products

Documentation

polloss

Syntax

Description

Examples

Mismatch Between 45° Polarized Field and Horizontally Polarized Receiver

Polarization Loss Unaffected by Receiver Position

Loss Due to Receiver Axes Rotation

Polarization Loss Unaffected by Transmitter Position

Plot Polarization Loss as Receiving Antenna Rotates

Input Arguments

fv_tr—Transmitted field vector in linear component representation2-by-1 complex-valued column vector

fv_rcv—Receiver polarization vector in linear component representation2-by-1 complex-valued column vector

pos_rcv—Receiving antenna position[0;0;0](default) |3-by-1 real-valued column vector

axes_rcv—Receiving antenna local coordinate axes3-by-3 identity matrix(default) |3-by-3 real-valued matrix

pos_tr—Transmitter position[0;0;0](default) |3-by-1 real-valued column vector

axes_tr—Transmitting antenna local coordinate axes3-by-3 identity matrix(default) |3-by-3 real-valued matrix

Output Arguments

rho— Polarization lossscalar

More About

Polarization Loss Due to Field and Receiver Mismatch

References

Extended Capabilities

C/C++ Code GenerationGenerate C and C++ code using MATLAB® Coder™.

See Also

Introduced in R2013a

Phased Array System Toolbox Documentation

万博1manbetx

Try MATLAB, Simulink, and Other Products

`fv_tr`—Transmitted field vector in linear component representation
2-by-1 complex-valued column vector

`fv_rcv`—Receiver polarization vector in linear component representation
2-by-1 complex-valued column vector

`pos_rcv`—Receiving antenna position
[0;0;0](default) |3-by-1 real-valued column vector

`axes_rcv`—Receiving antenna local coordinate axes
3-by-3 identity matrix(default) |3-by-3 real-valued matrix

`pos_tr`—Transmitter position
[0;0;0](default) |3-by-1 real-valued column vector

`axes_tr`—Transmitting antenna local coordinate axes
3-by-3 identity matrix(default) |3-by-3 real-valued matrix

`rho`— Polarization loss
scalar

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.