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(sArray,FREQ) plots the 3-D array directivity pattern (in dBi) for the array specified in 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(sArray,FREQ,AZ) plots the array directivity pattern at the specified azimuth angle.

pattern(sArray,FREQ,AZ,EL) plots the array directivity pattern at specified azimuth and elevation angles.

pattern(___,Name,Value) plots the array pattern with additional options specified by one or more Name,Value pair arguments.

[PAT,AZ_ANG,EL_ANG] = pattern(___) returns the array pattern in 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

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`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'`

Plotting style, specified as the comma-separated pair consisting of 'Plotstyle' and either 'overlay' or 'waterfall'. This parameter applies when you specify multiple frequencies in FREQ in 2-D plots. You can draw 2-D plots by setting one of the arguments AZ or EL to a scalar.

Data Types: char

`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

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`PAT` — Array pattern
M-by-N real-valued matrix

Array pattern, returned as an M-by-N real-valued matrix. The dimensions of PAT correspond to the dimensions of the output arguments AZ_ANG and EL_ANG.

`AZ_ANG` — Azimuth angles
scalar | 1-by-N real-valued row vector

Azimuth angles for displaying directivity or response pattern, returned as a scalar or 1-by-N real-valued row vector corresponding to the dimension set in AZ. The columns of PAT correspond to the values in AZ_ANG. Units are in degrees.

`EL_ANG` — Elevation angles
scalar | 1-by-M real-valued row vector

Elevation angles for displaying directivity or response, returned as a scalar or 1-by-M real-valued row vector corresponding to the dimension set in EL. The rows of PAT correspond to the values in EL_ANG. Units are in degrees.

Examples

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Pattern of 11-Element UCA Antenna Array

Open Live Script

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)

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)

Figure contains an axes object. The hidden axes object contains 3 objects of type line, text. This object represents 500 MHz .

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)

Figure contains an axes object. The hidden axes object contains 3 objects of type line, text. This object represents 500 MHz .

Pattern of 10-Element UCA Antenna Array in UV Space

Open Live Script

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)

Figure contains an axes object. The axes object with title 3D Response Pattern in U/V Space, xlabel U, ylabel V contains an object of type surface.

More About

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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

$D = 4 π \frac{U_{rad} (θ, φ)}{P_{total}}$

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
`"x"`	x-axis	positive y-axis	xz-plane	y≥0
`"y"`	y-axis	positive x-axis	yz-plane	x≥0
`"z"`	z-axis	positive 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
`"z"`	xy-plane	positive z-axis	xy-plane	z≥0
`"y"`	xz-plane	positive y-axis	xz-plane	y≥0
`"x"`	yz-plane	positive 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

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R2024b: Array axis definitions

Enhanced definitions of array axes and normals.

pattern

Syntax

Description

Input Arguments

sArray — Uniform circular array System object™

FREQ — Frequency for computing directivity and patterns positive scalar | 1-by-L real-valued row vector

AZ — Azimuth angles [-180:180] (default) | 1-by-N real-valued row vector

EL — Elevation angles [-90:90] (default) | 1-by-M real-valued row vector

Name-Value Arguments

CoordinateSystem — Plotting coordinate system 'polar' (default) | 'rectangular' | 'uv'

Type — Displayed pattern type 'directivity' (default) | 'efield' | 'power' | 'powerdb'

Orientation — Array orientation [0;0;0]. (default) | 3-by-1 real-valued column vector

Normalize — Display normalize pattern true (default) | false

ShowArray — View array geometry false (default) | true

ShowLocalCoordinates — Show local coordinate axes true (default) | false

ShowColorbar — Show colorbar true (default) | false

Parent — Handle to axis scalar

PlotStyle — Plotting style 'overlay' (default) | 'waterfall'

Polarization — Polarized field component 'combined' (default) | 'H' | 'V'

PropagationSpeed — Signal propagation speed speed of light (default) | positive scalar

Weights — Array weights 1 (default) | N-by-1 complex-valued column vector | N-by-L complex-valued matrix

Output Arguments

PAT — Array pattern M-by-N real-valued matrix

AZ_ANG — Azimuth angles scalar | 1-by-N real-valued row vector

EL_ANG — Elevation angles scalar | 1-by-M real-valued row vector

Examples

Pattern of 11-Element UCA Antenna Array

Pattern of 10-Element UCA Antenna Array in UV Space

More About

Directivity

Array axes and normals

Version History

R2024b: Array axis definitions

See Also

`sArray` — Uniform circular array
System object™

`FREQ` — Frequency for computing directivity and patterns
positive scalar | 1-by-L real-valued row vector

`AZ` — Azimuth angles
`[-180:180]` (default) | 1-by-N real-valued row vector

`EL` — Elevation angles
`[-90:90]` (default) | 1-by-M real-valued row vector

`CoordinateSystem` — Plotting coordinate system
`'polar'` (default) | `'rectangular'` | `'uv'`

`Type` — Displayed pattern type
`'directivity'` (default) | `'efield'` | `'power'` | `'powerdb'`

`Orientation` — Array orientation
`[0;0;0]`. (default) | 3-by-1 real-valued column vector

`Normalize` — Display normalize pattern
`true` (default) | `false`

`ShowArray` — View array geometry
`false` (default) | `true`

`ShowLocalCoordinates` — Show local coordinate axes
`true` (default) | `false`

`ShowColorbar` — Show colorbar
`true` (default) | `false`

`Parent` — Handle to axis
scalar

`PlotStyle` — Plotting style
`'overlay'` (default) | `'waterfall'`

`Polarization` — Polarized field component
`'combined'` (default) | `'H'` | `'V'`

`PropagationSpeed` — Signal propagation speed
speed of light (default) | positive scalar

`Weights` — Array weights
1 (default) | N-by-1 complex-valued column vector | N-by-L complex-valued matrix

`PAT` — Array pattern
M-by-N real-valued matrix

`AZ_ANG` — Azimuth angles
scalar | 1-by-N real-valued row vector

`EL_ANG` — Elevation angles
scalar | 1-by-M real-valued row vector