# pattern

**System object: **phased.UCA

**Namespace: **phased

Plot UCA array pattern

## Syntax

`pattern(sArray,FREQ)`

pattern(sArray,FREQ,AZ)

pattern(sArray,FREQ,AZ,EL)

pattern(___,Name,Value)

[PAT,AZ_ANG,EL_ANG] = pattern(___)

## Description

`pattern(`

plots
the 3-D array directivity pattern (in dBi) for the array specified
in `sArray`

,`FREQ`

)`sArray`

. The operating frequency is specified
in `FREQ`

.

The integration used when computing array directivity has a minimum sampling grid of 0.1 degrees. If an array pattern has a beamwidth smaller than this, the directivity value will be inaccurate.

`pattern(`

plots
the array directivity pattern at the specified azimuth angle.`sArray`

,`FREQ`

,`AZ`

)

`pattern(`

plots
the array directivity pattern at specified azimuth and elevation angles.`sArray`

,`FREQ`

,`AZ`

,`EL`

)

`pattern(___,`

plots the array pattern with additional options specified by one or
more `Name,Value`

)`Name,Value`

pair arguments.

returns the array pattern in `[PAT,AZ_ANG,EL_ANG]`

= pattern(___)`PAT`

. The `AZ_ANG`

output
contains the coordinate values corresponding to the rows of `PAT`

.
The `EL_ANG`

output contains the coordinate values
corresponding to the columns of `PAT`

. If the `'CoordinateSystem'`

parameter
is set to `'uv'`

, then `AZ_ANG`

contains
the *U* coordinates of the pattern and `EL_ANG`

contains
the *V* coordinates of the pattern. Otherwise, they
are in angular units in degrees. *UV* units are dimensionless.

## Input Arguments

`sArray`

— Uniform circular array

System object™

Uniform circular array, specified as a `phased.UCA`

System object.

**Example: **`sArray= phased.UCA;`

`FREQ`

— Frequency for computing directivity and patterns

positive scalar | 1-by-*L* real-valued row vector

Frequencies for computing directivity and patterns, specified
as a positive scalar or 1-by-*L* real-valued row
vector. Frequency units are in hertz.

For an antenna, microphone, or sonar hydrophone or projector element,

`FREQ`

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

or`FrequencyVector`

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

. Most elements use the`FrequencyRange`

property except for`phased.CustomAntennaElement`

and`phased.CustomMicrophoneElement`

, which use the`FrequencyVector`

property.For an array of elements,

`FREQ`

must lie within the frequency range of the elements that make up the array. Otherwise, the array produces no response and the directivity is returned as`–Inf`

.

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

**Data Types: **`double`

`AZ`

— Azimuth angles

`[-180:180]`

(default) | 1-by-*N* real-valued row vector

Azimuth angles for computing directivity and pattern, specified as a 1-by-*N*
real-valued row vector where *N* is the number of azimuth angles. Angle
units are in degrees. Azimuth angles must lie between –180° and 180°.

The azimuth angle is the angle between the *x*-axis
and the projection of the direction vector onto the *xy* plane.
When measured from the *x*-axis toward the *y*-axis,
this angle is positive.

**Example: **`[-45:2:45]`

**Data Types: **`double`

`EL`

— Elevation angles

`[-90:90]`

(default) | 1-by-*M* real-valued row vector

Elevation angles for computing directivity and pattern, specified as a
1-by-*M* real-valued row vector where *M* is the
number of desired elevation directions. Angle units are in degrees. The elevation angle
must lie between –90° and 90°.

The elevation angle is the angle between the direction vector and *xy*-plane.
The elevation angle is positive when measured towards the
*z*-axis.

**Example: **`[-75:1:70]`

**Data Types: **`double`

### Name-Value Arguments

Specify optional pairs of arguments as
`Name1=Value1,...,NameN=ValueN`

, where `Name`

is
the argument name and `Value`

is the corresponding value.
Name-value arguments must appear after other arguments, but the order of the
pairs does not matter.

*
Before R2021a, use commas to separate each name and value, and enclose*
`Name`

*in quotes.*

`CoordinateSystem`

— Plotting coordinate system

`'polar'`

(default) | `'rectangular'`

| `'uv'`

Plotting coordinate system of the pattern, specified as the
comma-separated pair consisting of `'CoordinateSystem'`

and
one of `'polar'`

, `'rectangular'`

,
or `'uv'`

. When `'CoordinateSystem'`

is
set to `'polar'`

or `'rectangular'`

,
the `AZ`

and `EL`

arguments
specify the pattern azimuth and elevation, respectively. `AZ`

values
must lie between –180° and 180°. `EL`

values
must lie between –90° and 90°. If `'CoordinateSystem'`

is
set to `'uv'`

, `AZ`

and `EL`

then
specify *U* and *V* coordinates,
respectively. `AZ`

and `EL`

must
lie between -1 and 1.

**Example: **`'uv'`

**Data Types: **`char`

`Type`

— Displayed pattern type

`'directivity'`

(default) | `'efield'`

| `'power'`

| `'powerdb'`

Displayed pattern type, specified as the comma-separated pair
consisting of `'Type'`

and one of

`'directivity'`

— directivity pattern measured in dBi.`'efield'`

— field pattern of the sensor or array. For acoustic sensors, the displayed pattern is for the scalar sound field.`'power'`

— power pattern of the sensor or array defined as the square of the field pattern.`'powerdb'`

— power pattern converted to dB.

**Example: **`'powerdb'`

**Data Types: **`char`

`Orientation`

— Array orientation

`[0;0;0]`

. (default) | 3-by-1 real-valued column vector

Array orientation, specified as a 3-by-1 real-valued column vector containing three
rotation angles. The three angles define orthogonal rotations with respect to the
*x*-, *y*-, and *z*-axes of the
local coordinate system. To create the full orientation matrix, the orthogonal
rotations are applied in this order:

a rotation around the positive

*x*-axis by the angle*θ*._{x}a rotation around the positive

*y*-axis by the angle*θ*._{y}a rotation around the positive

*z*-axis by the angle*θ*._{z}

Positive angles are defined using the right-handed rule. A positive angle defines a rotation that appears clockwise when looking towards the positive direction of the axis, and negative values when the rotation appears counter-clockwise. The right-hand rule is invoked by pointing the right-hand thumb along an axis. Then the other fingers of the right hand curl in the positive direction,

`Normalize`

— Display normalize pattern

`true`

(default) | `false`

Display normalized pattern, specified as the comma-separated pair consisting of
`'Normalize`

' and a Boolean. Set this parameter to
`true`

to display a normalized pattern. This parameter does not
apply when you set `'Type'`

to `'directivity'`

.
Directivity patterns are already normalized.

**Data Types: **`logical`

`ShowArray`

— View array geometry

`false`

(default) | `true`

View the array geometry along with the 3D radiation pattern, specified as
`false`

or `true`

.

**Data Types: **`logical`

`ShowLocalCoordinates`

— Show local coordinate axes

`true`

(default) | `false`

Show the local coordinate axes, specified as `true`

or `false`

.

**Data Types: **`logical`

`ShowColorbar`

— Show colorbar

`true`

(default) | `false`

Show the colorbar, specified as `true`

or `false`

.

**Data Types: **`logical`

`Parent`

— Handle to axis

scalar

Handle to the axes along which the array geometry is displayed specified as a scalar.

`PlotStyle`

— Plotting style

`'overlay'`

(default) | `'waterfall'`

`Polarization`

— Polarized field component

`'combined'`

(default) | `'H'`

| `'V'`

Polarized field component to display, specified as the comma-separated pair consisting of
'Polarization' and `'combined'`

, `'H'`

, or
`'V'`

. This parameter applies only when the sensors are
polarization-capable and when the `'Type'`

parameter is not set to
`'directivity'`

. This table shows the meaning of the display
options.

`'Polarization'` | Display |
---|---|

`'combined'` | Combined H and V
polarization components |

`'H'` | H polarization component |

`'V'` | V polarization component |

**Example: **`'V'`

**Data Types: **`char`

`PropagationSpeed`

— Signal propagation speed

speed of light (default) | positive scalar

Signal propagation speed, specified as the comma-separated pair
consisting of `'PropagationSpeed'`

and a positive
scalar in meters per second.

**Example: **`'PropagationSpeed',physconst('LightSpeed')`

**Data Types: **`double`

`Weights`

— Array weights

1 (default) | *N*-by-1 complex-valued column vector | *N*-by-*L* complex-valued
matrix

Array weights, specified as the comma-separated pair consisting
of `'Weights`

' and an *N*-by-1 complex-valued
column vector or *N*-by-*L* complex-valued
matrix. Array weights are applied to the elements of the array to
produce array steering, tapering, or both. The dimension *N* is
the number of elements in the array. The dimension *L* is
the number of frequencies specified by `FREQ`

.

Weights Dimension | FREQ Dimension | Purpose |
---|---|---|

N-by-1 complex-valued column vector | Scalar or 1-by-L row vector | Applies a set of weights for the single frequency or for all L frequencies. |

N-by-L complex-valued
matrix | 1-by-L row vector | Applies each of the L columns of `'Weights'` for
the corresponding frequency in `FREQ` . |

**Note**

Use complex weights to steer the array response toward different
directions. You can create weights using the `phased.SteeringVector`

System object or
you can compute your own weights. In general, you apply Hermitian
conjugation before using weights in any Phased Array System Toolbox™ function
or System object such as `phased.Radiator`

or `phased.Collector`

. However, for the `directivity`

, `pattern`

, `patternAzimuth`

,
and `patternElevation`

methods of any array System object use
the steering vector without conjugation.

**Example: **`'Weights',ones(N,M)`

**Data Types: **`double`

**Complex Number Support: **Yes

## Output Arguments

## Examples

### Pattern of 11-Element UCA Antenna Array

Create an 11-element uniform circular array (UCA) having a 1.5 m radius and operating at 500 MHz. The array consists of short-dipole antenna elements. First, display the vertical component of the response at 45 degrees azimuth and 0 degrees elevation. Then plot the azimuth and elevation directivities.

antenna = phased.ShortDipoleAntennaElement(... 'FrequencyRange',[50e6,1000e6],... 'AxisDirection','Z'); array = phased.UCA('NumElements',11,'Radius',1.5,'Element',antenna); fc = 500e6; ang = [45;0]; resp = array(fc,ang); disp(resp.V)

-1.2247 -1.2247 -1.2247 -1.2247 -1.2247 -1.2247 -1.2247 -1.2247 -1.2247 -1.2247 -1.2247

Display the azimuth directivity pattern at 500 MHz for azimuth angles between -180 and 180 degrees.

c = physconst('LightSpeed'); pattern(array,fc,[-180:180],0,'Type','directivity','PropagationSpeed',c)

Display the elevation directivity pattern at 500 MHz for elevation angles between -90 and 90 degrees.

pattern(array,fc,[0],[-90:90],'Type','directivity','PropagationSpeed',c)

### Pattern of 10-Element UCA Antenna Array in UV Space

Create a 10-element UCA antenna array consisting of cosine antenna elements. Display the 3-D power pattern in UV space.

sCos = phased.CosineAntennaElement('FrequencyRange',[100e6 1e9],... 'CosinePower',[2.5,2.5]); sUCA = phased.UCA('NumElements',10,... 'Radius',1.5,... 'Element',sCos); c = physconst('LightSpeed'); fc = 500e6; pattern(sUCA,fc,[-1:.01:1],[-1:.01:1],... 'CoordinateSystem','uv',... 'Type','powerdb',... 'PropagationSpeed',c)

## More About

### Directivity

Directivity describes the directionality of the radiation pattern of a sensor element or array of sensor elements.

Higher directivity is desired when you want to transmit more radiation in a specific direction. Directivity is the ratio of the transmitted radiant intensity in a specified direction to the radiant intensity transmitted by an isotropic radiator with the same total transmitted power

$$D=4\pi \frac{{U}_{\text{rad}}\left(\theta ,\phi \right)}{{P}_{\text{total}}}$$

where
*U*_{rad}*(θ,φ)* is the radiant
intensity of a transmitter in the direction *(θ,φ)* and
*P*_{total} is the total power transmitted by an
isotropic radiator. For a receiving element or array, directivity measures the sensitivity
toward radiation arriving from a specific direction. The principle of reciprocity shows that
the directivity of an element or array used for reception equals the directivity of the same
element or array used for transmission. When converted to decibels, the directivity is
denoted as *dBi*. For information on directivity, read the notes on Element Directivity and Array Directivity.

### Array axes and normals

The U/V coordinate system is determined by the array type and the array orientation. The Phased Array System Toolbox offers four basic array shapes: ULA, URA, UCA, and Conformal.

For the

`phased.ULA`

System object use the`ArrayAxis`

property to select the array orientation as`"x"`

,`"y"`

, or`"z"`

. The`ArrayAxis`

property determines the elements layout, the normal direction of the array, and the orientation of the U/V space as shown in the table here:**ULA Array**ArrayAxis property value Array element positions Array normal U/V space for ULA U/V positive hemisphere for ULA Plot of U/V space for ULA in 3D space `"x"`

*x*-axispositive *y*-axis*xz*-plane*y≥0*`"y"`

*y*-axispositive *x*-axis*yz*-plane*x≥0*`"z"`

*z*-axispositive *x*-axis*yz*-plane*x≥0*For the

`phased.URA`

or`phased.UCA`

System objects use the`ArrayNormal`

property to select the array orientation as`"x"`

,`"y"`

, or`"z"`

. The`ArrayNormal`

property determines the elements layout, the normal direction of the array, and the orientation of the U/V space as shown in the table here:**URA and UCA Arrays**ArrayNormal property value Array element positions Array normal U/V space for URA/UCA U/V positive hemisphere for URA/UCA Plot of U/V space for URA/UCA in 3D space `"z"`

*xy*-planepositive *z*-axis*xy*-plane*z≥0*`"y"`

*xz*-planepositive *y*-axis*xz*-plane*y≥0*`"x"`

*yz*-planepositive *x*-axis*yz*-plane*x≥0*For the

`phased.ConformalArray`

System object, uses the`ElementPosition`

property to determine the elements layout, the normal direction of the array, and the orientation of the U/V space as shown in the table here:**Conformal Array**Array element positions Array normal U/V space for conformal array U/V positive hemisphere for conformal array Plot of U/V space for conformal array in 3D space Arbitrary in 3D space ElementPosition positive *x*-axis*yz*-plane*x≥0*

## Version History

**Introduced in R2015a**

### R2024b: Array axis definitions

Enhanced definitions of array axes and normals.

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