# phased.CustomAntennaElement

Custom antenna element

## Description

The `phased.CustomAntennaElement`

System object™ models an antenna element with a custom spatial response pattern. The response
pattern can be defined for polarized or non-polarized fields.

To create a custom antenna element:

Create the

`phased.CustomAntennaElement`

object and set its properties.Call the object with arguments, as if it were a function.

To learn more about how System objects work, see What Are System Objects?

## Creation

### Description

creates a System object, `antenna`

= phased.CustomAntennaElement`antenna`

, with default property values. The default
response pattern is spatially isotropic.

creates a custom antenna object, `antenna`

= phased.CustomAntennaElement(`Name`

,`Value`

)`antenna`

, with each specified
property Name set to the specified Value. You can specify additional name-value pair
arguments in any order as
(`Name1`

,`Value1`

,...,`NameN`

,`ValueN`

).
For example, the output response of the object depends on whether polarization is set or not.

To create a nonpolarized response pattern, set the

`SpecifyPolarizationPattern`

property to`false`

(default). Then, use the`MagnitudePattern`

and`PhasePattern`

properties to define the response pattern.To create a polarized response pattern, set the

`SpecifyPolarizationPattern`

property to`true`

. Then, use any or all of the`HorizontalMagnitudePattern`

,`HorizontalPhasePattern`

,`VerticalMagnitudePattern`

, and`VerticalPhasePattern`

properties to define the response pattern.

## Properties

Unless otherwise indicated, properties are *nontunable*, which means you cannot change their
values after calling the object. Objects lock when you call them, and the
`release`

function unlocks them.

If a property is *tunable*, you can change its value at
any time.

For more information on changing property values, see System Design in MATLAB Using System Objects.

`FrequencyVector`

— Response and pattern frequency vector

`[0 1e20]`

(default) | 1-by-*L* row vector

Frequencies at which the frequency response and antenna patterns are to be returned,
specified as a 1-by-*L* row vector. The elements of the vector must be
in increasing order. The antenna element has no response outside the frequency range
specified by the minimum and maximum elements of the frequency vector. Units are in
Hz.

**Example: **`[200:50:300]*1e6`

**Data Types: **`double`

`FrequencyResponse`

— Frequency responses of antenna element

`[0 0]`

(default) | real-valued 1-by-*L* vector

Frequency responses at the frequencies defined in
`FrequencyVector`

property, specified as a
1-by-*L* row vector. *L* equals the length of the
vector specified in the `FrequencyVector`

property. Units are in
dB.

**Example: **`[0 6 0]`

**Data Types: **`double`

`PatternCoordinateSystem`

— Coordinate system of custom antenna pattern

`'az-el'`

(default) | `'phi-theta'`

Coordinate system of custom antenna pattern, specified `'az-el'`

or
`'phi-theta'`

. When you specify `'az-el'`

, use the
`AzimuthAngles`

and `ElevationAngles`

properties
to specify the pattern coordinates system. When you specify
`'phi-theta'`

, use the `PhiAngles`

and
`ThetaAngles`

properties to specify the pattern coordinates
system.

**Data Types: **`char`

`AzimuthAngles`

— Azimuth angles

`[-180:180]`

(default) | real-valued length-*P* vector

Specify the azimuth angles as a length-*P* vector. These angles are
the azimuth angles where the custom radiation pattern is specified. *P*
must be greater than 2. The azimuth angles must lie between –180° and 180° and be in
strictly increasing order. Units are in degrees.

**Example: **`[30 40 50]`

#### Dependencies

To enable this property, set the `PatternCoordinateSystem`

property to `'az-el'`

.

**Data Types: **`double`

`ElevationAngles`

— Elevation angles

`[-90:90]`

(default) | real-valued length-*Q* vector

Specify the elevation angles as a length-*Q* vector. These angles
are the elevation angles where the custom radiation pattern is specified.
*Q* must be greater than 2. The elevation angles must lie between
–90° and 90° and be in strictly increasing order. Units are in degrees.

**Example: **`[-30 0 +30]`

#### Dependencies

To enable this property, set the `PatternCoordinateSystem`

property to `'az-el'`

.

**Data Types: **`double`

`PhiAngles`

— Phi angles in phi-theta coordinates system

`0:360`

(default) | real-valued *P*-length vector

Phi angles used to represent the element response pattern in phi-theta coordinates,
specified as a real-valued *P*-length vector. Phi angles lie between 0°
and 360°. *P* must be greater than 2. Look here for definitions of
Phi and Theta Angles.

**Example: **`[90:180]`

#### Dependencies

To enable this property, set the `PatternCoordinateSystem`

property to `'phi-theta'`

.

**Data Types: **`double`

`ThetaAngles`

— Theta angles in phi-theta coordinate system

`0:180`

(default) | real-valued *Q*-length vector

Theta angles used to represent the element response pattern in phi-theta
coordinates, specified as a real-valued *Q*-length vector. The theta
angle lies between 0° and 180°. Look here for definitions of Phi and Theta Angles.
*Q* must be greater than 2.

**Example: **`[40:80]`

#### Dependencies

To enable this property, set the `PatternCoordinateSystem`

property to `'phi-theta'`

.

**Data Types: **`double`

`SpecifyPolarizationPattern`

— Polarized array response

`false`

(default) | `true`

Polarized array response, specified as `false`

or
`true`

.

When the

`SpecifyPolarizationPattern`

property is set to`false`

, the antenna element transmits or receives non-polarized radiation. In this case, use the`MagnitudePattern`

property to set the antenna response pattern.When the

`SpecifyPolarizationPattern`

property is set to`true`

, the antenna element transmits or receives polarized radiation. In this case, use the`HorizontalMagnitudePattern`

and`HorizontalPhasePattern`

properties to set the horizontal polarization response pattern and the`VerticalMagnitudePattern`

and`VerticalPhasePattern`

properties to set the vertical polarization response pattern.

**Data Types: **`logical`

`MagnitudePattern`

— Magnitude of combined antenna radiation pattern

`zeros(181,361)`

(default) | real-valued *Q*-by-*P* matrix | real-valued *Q*-by-*P*-by-*L*
array

The magnitude of the combined polarization antenna radiation, pattern specified as a
*Q*-by-*P* matrix or a
*Q*-by-*P*-by-*L* array. This
property is used only when the `SpecifyPolarizationPattern`

property
is set to `false`

. Magnitude units are in dB.

If the value of this property is a

*Q*-by-*P*matrix, the same pattern is applied to*all*frequencies specified in the`FrequencyVector`

property.If the value is a

*Q*-by-*P*-by-*L*array, each*Q*-by-*P*page of the array specifies a pattern for the*corresponding*frequency specified in the`FrequencyVector`

property.

If the pattern contains a `NaN`

at any azimuth and elevation
direction, it is converted to `-Inf`

, indicating zero response in that
direction. The custom antenna object uses interpolation to estimate the response of the
antenna at a given direction. To avoid interpolation errors, the custom response pattern
must contain azimuth angles in the range `[–180,180]`

degrees. Set the
range of elevation angles to `[–90,90]`

degrees.

**Data Types: **`double`

`PhasePattern`

— Phase of combined antenna radiation pattern

`zeros(181,361)`

(default) | real-valued *Q*-by-*P* matrix | real-valued *Q*-by-*P*-by-*L*
array

The phase of the combined polarization antenna radiation pattern, specified as a
*Q*-by-*P* matrix or a
*Q*-by-*P*-by-*L* array. This
property is used only when the `SpecifyPolarizationPattern`

property
is set to `false`

. Units are in degrees.

If the value of this property is a

*Q*-by-*P*matrix, the same pattern is applied to*all*frequencies specified in the`FrequencyVector`

property.If the value is a

*Q*-by-*P*-by-*L*array, each*Q*-by-*P*page of the array specifies a pattern for the*corresponding*frequency specified in the`FrequencyVector`

property.

The custom antenna object uses interpolation to estimate the response of the antenna
at a given direction. To avoid interpolation errors, the custom response pattern must
contain azimuth angles in the range *[–180°,180°]*. Set the
range of elevation angles to *[–90°,90°]*.

**Data Types: **`double`

`HorizontalMagnitudePattern`

— Magnitude of horizontal polarization component of antenna radiation pattern

`zeros(181,361)`

(default) | real-valued *Q*-by-*P* matrix | real-valued *Q*-by-*P*-by-*L*
array

The magnitude of the horizontal polarization component of the antenna radiation
pattern, specified as a real-valued *Q*-by-*P* matrix
or real-valued a *Q*-by-*P*-by-*L*
array. Magnitude units are in dB.

If the value of this property is a

*Q*-by-*P*matrix, the same pattern is applied to*all*frequencies specified in the`FrequencyVector`

property.If the value is a

*Q*-by-*P*-by-*L*array, each*Q*-by-*P*page of the array specifies a pattern for the*corresponding*frequency specified in the`FrequencyVector`

property.

If the magnitude pattern contains a `NaN`

at any azimuth and
elevation direction, it is converted to `-Inf`

, indicating zero
response in that direction. The custom antenna object uses interpolation to estimate the
response of the antenna at a given direction. To avoid interpolation errors, the custom
response pattern must contain azimuth angles in the range
`[–180,180]°`

and elevation angles in the range
`[–90,90]°`

.

#### Dependencies

To enable this property, set the `SpecifyPolarizationPattern`

property to `true`

.

**Data Types: **`double`

`HorizontalPhasePattern`

— Phase of horizontal polarization component of antenna radiation pattern

`zeros(181,361)`

(default) | real-valued *Q*-by-*P* matrix | real-valued *Q*-by-*P*-by-*L*
array

The phase of the horizontal polarization component of the antenna radiation pattern,
specified as a real-valued *Q*-by-*P* matrix or a
real-valued *Q*-by-*P*-by-*L* array.
This property is used only when the `SpecifyPolarizationPattern`

property is set to `true`

. Phase units are in degrees.

*Q*-by-*P*matrix, the same pattern is applied to*all*frequencies specified in the`FrequencyVector`

property.*Q*-by-*P*-by-*L*array, each*Q*-by-*P*page of the array specifies a pattern for the*corresponding*frequency specified in the`FrequencyVector`

property.

The custom antenna object uses interpolation to estimate the response of the antenna
at a given direction. To avoid interpolation errors, the custom response pattern must
contain azimuth angles in the range `[–180,180]°`

and elevation
angles in the range `[–90,90]°`

.

#### Dependencies

To enable this property, set the `SpecifyPolarizationPattern`

property to `true`

.

**Data Types: **`double`

`VerticalMagnitudePattern`

— Magnitude of vertical polarization component of antenna radiation pattern

`zeros(181,361)`

(default) | real-valued *Q*-by-*P* matrix | real-valued *Q*-by-*P*-by-*L*
array

The magnitude of the vertical polarization component of the antenna radiation
pattern specified as a *Q*-by-*P* matrix or a
*Q*-by-*P*-by-*L* array. This
property is used only when the `SpecifyPolarizationPattern`

property
is set to `true`

. Magnitude units are in dB.

*Q*-by-*P*matrix, the same pattern is applied to*all*frequencies specified in the`FrequencyVector`

property.*Q*-by-*P*-by-*L*array, each*Q*-by-*P*page of the array specifies a pattern for the*corresponding*frequency specified in the`FrequencyVector`

property.

If the pattern contains a `NaN`

at any azimuth and elevation
direction, it is converted to `-Inf`

, indicating zero response in that
direction. The custom antenna object uses interpolation to estimate the response of the
antenna at a given direction. To avoid interpolation errors, the custom response pattern
must contain azimuth angles in the range`[–180,180]°`

and
elevation angles in the range `[–90,90]°`

.

#### Dependencies

To enable this property, set the `SpecifyPolarizationPattern`

property to `true`

.

**Data Types: **`double`

`VerticalPhasePattern`

— Phase of vertical polarization component of antenna radiation pattern

`zeros(181,361)`

(default) | real-valued *Q*-by-*P* matrix | real-valued *Q*-by-*P*-by-*L*
array

The phase of the vertical polarization component of the antenna radiation pattern,
specified as a *Q*-by-*P* matrix or a
*Q*-by-*P*-by-*L* array. This
property is used only when the `SpecifyPolarizationPattern`

property
is set to `true`

. Phase units are in degrees.

*Q*-by-*P*matrix, the same pattern is applied to*all*frequencies specified in the`FrequencyVector`

property.*Q*-by-*P*-by-*L*array, each*Q*-by-*P*page of the array specifies a pattern for the*corresponding*frequency specified in the`FrequencyVector`

property.

The custom antenna object uses interpolation to estimate the response of the antenna
at a given direction. To avoid interpolation errors, the custom response pattern must
contain azimuth angles in the range `[–180,180]°`

and elevation
angles in the range `[–90,90]°`

.

#### Dependencies

To enable this property, set the `SpecifyPolarizationPattern`

property to `true`

.

**Data Types: **`double`

`MatchArrayNormal`

— Match element normal to array normal

`true`

(default) | `false`

Set this property to `true`

to align the antenna element to an
array normal. The antenna pattern is rotated so that the *x*-axis of
the element coordinate system points along the array normal. This property is used only
when the antenna element belongs to an array. Use the property in conjunction with the
`ArrayNormal`

property of the `phased.URA`

and `phased.UCA`

System objects. Set this
property to `false`

to use the element pattern without rotation. The
default value is .

**Data Types: **`logical`

## Usage

### Syntax

### Description

returns the antenna’s voltage response `RESP`

= antenna(`FREQ`

,`ANG`

)`RESP`

at operating frequencies
specified in `FREQ`

and directions specified in
`ANG`

. The form of `RESP`

depends upon whether the
antenna element supports polarization as determined by the
`SpecifyPolarizationPattern`

property. If
`SpecifyPolarizationPattern`

is set to `false`

,
`RESP`

is an *M*-by-*L* matrix
containing the antenna response at the *M* angles specified in
`ANG`

and at the *L* frequencies specified in
`FREQ`

. If `SpecifyPolarizationPattern`

is set to
`true`

, `RESP`

is a MATLAB^{®}
`struct`

containing two fields, `RESP.H`

and
`RESP.V`

, representing the antenna's response in horizontal and
vertical polarization, respectively. Each field is an
*M*-by-*L* matrix containing the antenna response at
the *M* angles specified in `ANG`

and at the
*L* frequencies specified in `FREQ`

.

**Note**

The object performs an initialization the first time the object is executed. This
initialization locks nontunable properties
and input specifications, such as dimensions, complexity, and data type of the input data.
If you change a nontunable property or an input specification, the System object issues an error. To change nontunable properties or inputs, you must first
call the `release`

method to unlock the object.

### Input Arguments

`FREQ`

— Operating frequency of antenna element

nonnegative scalar | nonnegative, real-valued 1-by-*L* row vector

Operating frequency of the antenna element, specified as a nonnegative scalar or
nonnegative, real-valued 1-by-*L* row vector. Frequency units are in
Hz.

`FREQ`

must lie within the range of values specified by the
`FrequencyRange`

or the `FrequencyVector`

property of the element. Otherwise, the element produces no response and the response is
returned as `–Inf`

. Element objects use the
`FrequencyRange`

property, except for `phased.CustomAntennaElement`

, which uses the
`FrequencyVector`

property.

**Example: **`[1e8 2e6]`

**Data Types: **`double`

`ANG`

— Azimuth and elevation angles of response directions

real-valued 1-by-*M* row vector | real-valued 2-by-*M* matrix

Azimuth and elevation angles of the response directions, specified as a real-valued
1-by-*M* row vector or a real-valued 2-by-*M*
matrix, where *M* is the number of angular directions. Angle units are
in degrees. The azimuth angle must lie in the range –180° to 180°, inclusive. The
elevation angle must lie in the range –90° to 90°, inclusive.

If

`ANG`

is a 1-by-*M*vector, each element specifies the azimuth angle of the direction. In this case, the corresponding elevation angle is assumed to be zero.If

`ANG`

is a 2-by-*M*matrix, each column of the matrix specifies the direction in the form`[azimuth;elevation]`

.

The azimuth angle is the angle between the *x*-axis and the
projection of the direction vector onto the *xy*-plane. This angle is
positive when measured from the *x*-axis toward the
*y*-axis. The elevation angle is the angle between the direction
vector and *xy*-plane. This angle is positive when measured toward the
*z*-axis. See the definition of Azimuth and Elevation Angles.

**Example: **`[110 125; 15 10]`

**Data Types: **`double`

### Output Arguments

`RESP`

— Voltage response of antenna

complex-valued *M*-by-*L* matrix

Voltage response of antenna element, returned as a complex-valued
*M*-by-*L* matrix. In this matrix,
*M* represents the number of angles specified in
`ANG`

and *L* represents the number of
frequencies specified in `FREQ`

.

**Data Types: **`double`

## Object Functions

To use an object function, specify the
System object as the first input argument. For
example, to release system resources of a System object named `obj`

, use
this syntax:

release(obj)

### Specific to Antenna and Transducer Element System Objects

`beamwidth` | Compute and display beamwidth of sensor element pattern |

`directivity` | Directivity of antenna or transducer element |

`isPolarizationCapable` | Antenna element polarization capability |

`pattern` | Plot antenna or transducer element directivity and patterns |

`patternAzimuth` | Plot antenna or transducer element directivity and pattern versus azimuth |

`patternElevation` | Plot antenna or transducer element directivity and pattern versus elevation |

## Examples

### Response and Directivity of Custom Antenna

Create a user-defined antenna with a cosine pattern. Then, plot an elevation cut of the antenna's power response.

The user-defined pattern is omnidirectional in the azimuth direction and has a cosine pattern in the elevation direction. Assume the antenna operates at 1 GHz. Obtain the response at 20° azimuth and 30° elevation.

fc = 1e9; azang = -180:180; elang = -90:90; magpattern = mag2db(repmat(cosd(elang)',1,numel(azang))); phasepattern = zeros(size(magpattern)); antenna = phased.CustomAntennaElement('AzimuthAngles',azang, ... 'ElevationAngles',elang,'MagnitudePattern',magpattern, ... 'PhasePattern',phasepattern); resp = antenna(fc,[20;30])

resp = 0.8660

Plot an elevation cut of the power response.

pattern(antenna,fc,20,-90:90,'CoordinateSystem','polar','Type','powerdb')

Plot an elevation cut of the directivity.

pattern(antenna,fc,20,-90:90,'CoordinateSystem','polar','Type','directivity')

### Antenna Radiation Pattern in U-V Coordinates

Define a custom antenna in *u-v* space. Then, calculate and plot the response.

Define the radiation pattern (in dB) of an antenna in terms of *u* and *v* coordinates within the unit circle.

u = -1:0.01:1; v = -1:0.01:1; [u_grid,v_grid] = meshgrid(u,v); pat_uv = sqrt(1 - u_grid.^2 - v_grid.^2); pat_uv(hypot(u_grid,v_grid) >= 1) = 0;

Create an antenna with this radiation pattern. Convert *u-v* coordinates to azimuth and elevation coordinates.

[pat_azel,az,el] = uv2azelpat(pat_uv,u,v); array = phased.CustomAntennaElement('AzimuthAngles',az,'ElevationAngles',el, ... 'MagnitudePattern',mag2db(pat_azel),'PhasePattern',45*ones(size(pat_azel)));

Calculate the response in the direction *u = 0.5*, *v = 0*. Assume the antenna operates at 1 GHz. The output of the step method is in linear units.

dir_uv = [0.5;0]; dir_azel = uv2azel(dir_uv); fc = 1e9; resp = array(fc,dir_azel)

resp = 0.6124 + 0.6124i

Plot the 3D response in *u-v* coordinates.

pattern(array,fc,[-1:.01:1],[-1:.01:1],'CoordinateSystem','uv','Type','powerdb')

Display the antenna response as a line plot in *u-v* coordinates.

pattern(array,fc,[-1:.01:1],0,'CoordinateSystem','uv','Type','powerdb')

### Polarized Antenna Radiation Patterns

Model a short dipole antenna oriented along the $$x$$-axis of the local antenna coordinate system. For this type of antenna, the horizontal and vertical components of the electric field are given by $${E}_{H}=\frac{j\omega \mu IL}{4\pi r}\mathrm{sin}(az)$$ and $${E}_{V}=-\frac{j\omega \mu IL}{4\pi r}\mathrm{sin}(el)\mathrm{cos}(az)$$.

Specify a normalized radiation pattern of a short dipole antenna terms of azimuth, $$az$$, and elevation, $$el$$, coordinates. The vertical and horizontal radiation patterns are normalized to a maximum of unity.

az = [-180:180]; el = [-90:90]; [az_grid,el_grid] = meshgrid(az,el); horz_pat_azel = ... mag2db(abs(sind(az_grid))); vert_pat_azel = ... mag2db(abs(sind(el_grid).*cosd(az_grid)));

Set up the antenna. Specify the `SpecifyPolarizationPattern`

property to produce polarized radiation. In addition, use the `HorizontalMagnitudePattern`

and `VerticalMagnitudePattern`

properties to specify the pattern magnitude values. The `HorizontalPhasePattern`

and `VerticalPhasePattern`

properties take default values of zero.

antenna = phased.CustomAntennaElement(... 'AzimuthAngles',az,'ElevationAngles',el,... 'SpecifyPolarizationPattern',true,... 'HorizontalMagnitudePattern',horz_pat_azel,... 'VerticalMagnitudePattern',vert_pat_azel);

Assume the antenna operates at 1 GHz.

fc = 1e9;

Display the vertical response pattern.

pattern(antenna,fc,[-180:180],[-90:90],... 'CoordinateSystem','polar',... 'Type','powerdb',... 'Polarization','V')

Display the horizontal response pattern.

pattern(antenna,fc,[-180:180],[-90:90],... 'CoordinateSystem','polar',... 'Type','powerdb',... 'Polarization','H')

The combined polarization response, shown below, illustrates the $$x$$-axis null of the dipole.

pattern(antenna,fc,[-180:180],[-90:90],... 'CoordinateSystem','polar',... 'Type','powerdb',... 'Polarization','combined')

### Match Custom Antenna Normal to Array Normal

Define a custom antenna in *u-v* space. Show how the array response pattern is affected by the choice of the `MatchArrayNormal`

property of the `phased.CustomAntennaElement`

.

Define the response pattern (in dB) of an antenna as a function of *u* and *v* coordinates within the unit circle. The antenna operates at 1 GHz.

```
fc = 1e9;
c = physconst('LightSpeed');
u = -1:0.01:1;
v = -1:0.01:1;
[u_grid,v_grid] = meshgrid(u,v);
pat_uv = sqrt(1 - u_grid.^2 - v_grid.^2);
pat_uv(hypot(u_grid,v_grid) >= 1) = 0;
```

Create a custom antenna with this pattern. Convert *u-v* coordinates to azimuth and elevation coordinates. Set `MatchArrayNormal`

to `false`

.

[pat_azel,az,el] = uv2azelpat(pat_uv,u,v); antenna = phased.CustomAntennaElement('AzimuthAngles',az,'ElevationAngles',el, ... 'MagnitudePattern',mag2db(pat_azel),'PhasePattern',45*ones(size(pat_azel)), ... "MatchArrayNormal",false);

Construct a 3-by-3 URA with this element and display the antenna pattern in 3-D polar coordinates. The element spacing is one-half wavelength. The array normal points along the *y*-axis.

lam = c/fc; array = phased.URA('Element',antenna,'Size',[3 3],'ElementSpacing', ... [lam/2 lam/2],'ArrayNormal','y'); pattern(array,fc,-180:180,-90:90,'PropagationSpeed',c, ... 'CoordinateSystem','polar','Type','powerdb','Normalize',true)

The pattern shows the interplay between the element pattern pointing along the *x*-axis and the array pattern pointing along the *y*-axis.

Create another custom antenna with the same radiation pattern. Set `MatchArrayNormal`

to true. Then create another array with this element.

antenna2 = phased.CustomAntennaElement('AzimuthAngles',az,'ElevationAngles',el, ... 'MagnitudePattern',mag2db(pat_azel),'PhasePattern',45*ones(size(pat_azel)), ... "MatchArrayNormal",true); array2 = phased.URA('Element',antenna2,'Size',[3 3],'ElementSpacing', ... [lam/2 lam/2],'ArrayNormal','y'); pattern(array2,fc,-180:180,-90:90,'PropagationSpeed',c, ... 'CoordinateSystem','polar','Type','powerdb','Normalize',true)

This pattern shows the aligned element and array patterns pointing along the *y*-axis.

### Custom Antenna Element Response at 30° Elevation

Construct a user-defined antenna with an omnidirectional response in azimuth and a cosine pattern in elevation. The antenna operates at 1 GHz. Plot the response pattern. Then, find the antenna response at 30°.

```
antenna = phased.CustomAntennaElement;
antenna.AzimuthAngles = -180:180;
antenna.ElevationAngles = -90:90;
antenna.MagnitudePattern = mag2db(repmat(cosd(antenna.ElevationAngles)',...
1,numel(antenna.AzimuthAngles)));
```

Find the response at 30° elevation for an operating frequency of 1 GHz.

fc = 1.0e9; resp = antenna(fc,[0;30])

resp = 0.8660

### Antenna with Custom Radiation Pattern

Create a custom antenna element object. The radiation pattern has a cosine dependence on elevation angle but is independent of azimuth angle.

az = -180:90:180; el = -90:45:90; elresp = cosd(el); magpattern = mag2db(repmat(elresp',1,numel(az))); phasepattern = zeros(size(magpattern)); antenna = phased.CustomAntennaElement('AzimuthAngles',az,... 'ElevationAngles',el,'MagnitudePattern',magpattern, ... 'PhasePattern',phasepattern);

Display the radiation pattern.

disp(antenna.MagnitudePattern)

-Inf -Inf -Inf -Inf -Inf -3.0103 -3.0103 -3.0103 -3.0103 -3.0103 0 0 0 0 0 -3.0103 -3.0103 -3.0103 -3.0103 -3.0103 -Inf -Inf -Inf -Inf -Inf

Calculate the antenna response at the azimuth-elevation pairs *(-30,0)* and *(-45,0)* at 500 MHz.

ang = [-30 0; -45 0]; resp = antenna(500.0e6,ang); disp(resp)

0.7071 1.0000

The following code illustrates how nearest-neighbor interpolation is used to find the antenna voltage response in the two directions. The total response is the product of the angular response and the frequency response.

g = interp2(deg2rad(antenna.AzimuthAngles),... deg2rad(antenna.ElevationAngles),... db2mag(antenna.MagnitudePattern),... deg2rad(ang(1,:))', deg2rad(ang(2,:))','nearest',0); h = interp1(antenna.FrequencyVector,... db2mag(antenna.FrequencyResponse),500e6,'nearest',0); antresp = h.*g;

Compare the value of `antresp`

to the response of the antenna.

disp(mag2db(antresp))

-3.0103 0

### Directivity of Custom Antenna

Compute the directivity of a custom antenna element.

Define an antenna pattern for a custom antenna element in azimuth-elevation space. The pattern is omnidirectional in the azimuth direction and has a cosine pattern in the elevation direction. Assume the antenna operates at 1 GHz. Get the response at zero degrees azimuth and from -30 to 30 degrees elevation.

fc = 1e9; azang = [-180:180]; elang = [-90:90]; magpattern = mag2db(repmat(cosd(elang)',1,numel(azang))); phasepattern = zeros(size(magpattern)); antenna = phased.CustomAntennaElement('AzimuthAngles',azang, ... 'ElevationAngles',elang,'MagnitudePattern',magpattern, ... 'PhasePattern',phasepattern);

Calculate the directivities as a function of elevation for 0° azimuth angle.

angs = [0,0,0,0,0,0,0;-30,-20,-10,0,10,20,30]; freq = 1e9; d = directivity(antenna,freq,angs)

`d = `*7×1*
0.5115
1.2206
1.6279
1.7609
1.6279
1.2206
0.5115

The directivity is maximum at $${0}^{\circ}$$ elevation.

### Custom Antenna Element Supports Polarization

Show that the `CustomAntennaElement`

antenna element supports polarization when the `SpecifyPolarizationPattern`

property is set to `true`

.

```
antenna = phased.CustomAntennaElement('SpecifyPolarizationPattern',true);
isPolarizationCapable(antenna)
```

`ans = `*logical*
1

The returned value `1`

shows that this antenna element supports polarization.

### Power and Directivity Patterns of Custom Antenna

Create a custom antenna with a cosine pattern. Show the response at boresight. Then, plot the antenna's field and directivity patterns.

Create the antenna and calculate the response. The user-defined pattern is omnidirectional in the azimuth direction and has a cosine pattern in the elevation direction. Assume the antenna works at 1 GHz.

```
fc = 1e9;
antenna = phased.CustomAntennaElement;
antenna.AzimuthAngles = -180:180;
antenna.ElevationAngles = -90:90;
antenna.MagnitudePattern = mag2db(repmat(cosd(antenna.ElevationAngles)', ...
1,numel(antenna.AzimuthAngles)));
resp = antenna(fc,[0;0])
```

resp = 1

Plot an elevation cut of the magnitude response as a line plot.

pattern(antenna,fc,0,[-90:90],'CoordinateSystem','rectangular', ... 'Type','efield')

Plot an elevation cut of the directivity as a line plot, showing that the maximum directivity is approximately 2 dB.

pattern(antenna,fc,0,[-90:90],'CoordinateSystem','rectangular', ... 'Type','directivity')

### Pattern of Custom Antenna over Selected Range of Angles

Create a custom antenna System object™. The user-defined pattern is omnidirectional in the azimuth direction and has a cosine pattern in the elevation direction. Assume the antenna operates at a frequency of 1 GHz. First show the response at boresight. Display the 3-D pattern for a 60 degree range of azimuth and elevation angles centered at 0 degrees azimuth and 0 degrees elevation in 0.1 degree increments.

fc = 1e9; azang = -180:180; elang = -90:90; magpattern = mag2db(repmat(cosd(elang)',1,numel(azang))); antenna = phased.CustomAntennaElement('AzimuthAngles',azang, ... 'ElevationAngles',elang,'MagnitudePattern',magpattern); resp = antenna(fc,[0;0])

resp = 1

Plot the power pattern for a range of angles.

pattern(antenna,fc,[-30:0.1:30],[-30:0.1:30],'CoordinateSystem','polar', ... 'Type','power')

### Reduced Azimuth Pattern of Custom Antenna Element

Create an antenna with a custom response. The user-defined pattern has a sine pattern in the azimuth direction and a cosine pattern in the elevation direction. Assume the antenna operates at a frequency of 500 MHz. Plot an azimuth cut of the power pattern of the custom antenna element at 0 and 30 degrees elevation. Assume the operating frequency is 500 MHz.

Create the antenna element.

fc = 500e6; antenna = phased.CustomAntennaElement; antenna.AzimuthAngles = -180:180; antenna.ElevationAngles = -90:90; antenna.MagnitudePattern = mag2db(abs(cosd(antenna.ElevationAngles)'*sind(antenna.AzimuthAngles))); patternAzimuth(antenna,fc,[0 30],'Type','powerdb')

Plot a reduced range of azimuth angles using the `Azimuth`

parameter.

patternAzimuth(antenna,fc,[0 30],'Azimuth',[-45:45],'Type','powerdb')

### Reduced Elevation Pattern of Custom Antenna Element

Create an antenna with a custom response. The user-defined pattern has a sine pattern in the azimuth direction and a cosine pattern in the elevation direction. Assume the antenna operates at a frequency of 500 MHz. Plot an elevation cut of the power of the custom antenna element at 0 and 30 degrees elevation. Assume the operating frequency is 500 MHz.

Create the antenna element.

fc = 500e6; antenna = phased.CustomAntennaElement; antenna.AzimuthAngles = -180:180; antenna.ElevationAngles = -90:90; antenna.MagnitudePattern = mag2db(abs(cosd(antenna.ElevationAngles)'*sind(antenna.AzimuthAngles))); patternElevation(antenna,fc,[0 30],'Type','powerdb')

Plot a reduced range of elevation angles using the `Azimuth`

parameter.

patternElevation(antenna,fc,[0 30],'Elevation',[-45:45],'Type','powerdb')

## Algorithms

The total response of a custom antenna element is a combination
of its frequency response and spatial response. `phased.CustomAntennaElement`

calculates
both responses using nearest neighbor interpolation, and then multiplies
the responses to form the total response.

## Extended Capabilities

### C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

`pattern`

,`patternAzimuth`

,`patternElevation`

, and`plotResponse`

methods are not supported.See System Objects in MATLAB Code Generation (MATLAB Coder).

## Version History

**Introduced in R2011a**

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