pattern

System object: phased.PartitionedArray
Namespace: phased

Plot partitioned array directivity, field, and power patterns

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.

Note

This method replaces the plotResponse method. See Convert plotResponse to pattern for guidelines on how to use pattern in place of plotResponse.

Input Arguments

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`sArray` — Partitioned array
System object™

Partitioned array, specified as a phased.PartitionedArray System object.

Example: sArray= phased.PartitionedArray;

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

Subarray weights, specified as the comma-separated pair consisting of 'Weights' and an N-by-1 complex-valued column vector or N-by-M complex-valued matrix. The dimension N is the number of subarrays in the array. The dimension L is the number of frequencies specified by the FREQ argument.

`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 the `FREQ` argument.

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

Data Types: double

`SteerAngle` — Subarray steering angle
`[0;0]` (default) | scalar | 2-element column vector

Subarray steering angle, specified as the comma-separated pair consisting of 'SteerAngle' and a scalar or a 2-by-1 column vector.

If 'SteerAngle' is a 2-by-1 column vector, it has the form [azimuth; elevation]. The azimuth angle must be between –180° and 180°, inclusive. The elevation angle must be between –90° and 90°, inclusive.

If 'SteerAngle' is a scalar, it specifies the azimuth angle only. In this case, the elevation angle is assumed to be 0.

This option applies only when the 'SubarraySteering' property of the System object is set to 'Phase' or 'Time'.

Example: 'SteerAngle',[20;30]

Data Types: double

`ElementWeights` — Weights applied to elements within subarray
`1` (default) | complex-valued N_SE-by-N matrix | 1-by-N cell array

Subarray element weights, specified as complex-valued N_SE-by-N matrix or 1-by-N cell array. Weights are applied to the individual elements within a subarray. Subarrays can have different dimensions and sizes.

If ElementWeights is a complex-valued N_SE-by-N matrix, N_SE is the number of elements in the largest subarray and N is the number of subarrays. Each column of the matrix specifies the weights for the corresponding subarray. Only the first K entries in each column are applied as weights where K is the number of elements in the corresponding subarray.

If ElementWeights is a 1-by-N cell array. Each cell contains a complex-valued column vector of weights for the corresponding subarray. The column vectors have lengths equal to the number of elements in the corresponding subarray.

Dependencies

To enable this name-value pair, set the SubarraySteering property of the array to 'Custom'.

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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Azimuth Response of Partitioned ULA

Open Live Script

Plot the azimuth response of a 4-element ULA partitioned into two 2-element ULA's. The element spacing is one-half wavelength.

Create the ULA, and partition it into two 2-element ULA's.

sULA = phased.ULA('NumElements',4,'ElementSpacing',0.5);
sPA = phased.PartitionedArray('Array',sULA,...
    'SubarraySelection',[1 1 0 0;0 0 1 1]);

Plot the azimuth response of the array. Assume the operating frequency is 1 GHz and the propagation speed is the speed of light.

fc = 1e9;
pattern(sPA,fc,[-180:180],0,'Type','powerdb',...
    'CoordinateSystem','polar',...
    'Normalize',true)

Figure contains an axes object. The hidden axes object contains 3 objects of type line, text. This object represents 1 GHz .

Plot Pattern and Directivity of Partitioned URA Over Restricted Range of Angles

Open Live Script

Convert a 2-by-6 URA of isotropic antenna elements into a 1-by-3 partitioned array so that each subarray of the partitioned array is a 2-by-2 URA. Assume that the frequency response of the elements lies between 1 and 6 GHz. The elements are spaced one-half wavelength apart corresponding to the highest frequency of the element response. Plot an azimuth cut from -50 to 50 degrees for different two sets of weights. For partitioned arrays, weights are applied to the subarrays instead of the elements.

Create partitioned array

fmin = 1e9;
fmax = 6e9;
c = physconst('LightSpeed');
lam = c/fmax;
sIso = phased.IsotropicAntennaElement(...
    'FrequencyRange',[fmin,fmax],...
    'BackBaffled',false);
sURA = phased.URA('Element',sIso,'Size',[2,6],...
    'ElementSpacing',[lam/2,lam/2]);
subarraymap = [[1,1,1,1,0,0,0,0,0,0,0,0];...
    [0,0,0,0,1,1,1,1,0,0,0,0];...
    [0,0,0,0,0,0,0,0,1,1,1,1]];
sPA = phased.PartitionedArray('Array',sURA,...
    'SubarraySelection',subarraymap);

Plot power pattern

Plot the response of the array at 5 GHz over the restricted range of azimuth angles.

fc = 5e9;
wts = [[1,1,1]',[.862,1.23,.862]'];
pattern(sPA,fc,[-50:0.1:50],0,...
    'Type','powerdb',...
    'CoordinateSystem','polar',...
    'Weights',wts)

Figure contains an axes object. The hidden axes object contains 4 objects of type line, text. These objects represent Weights 1 Ⓐ , Weights 2 .

The plot of the response shows the broadening of the main lobe and the reduction of the strength of the sidelobes caused by the weight tapering.

Plot directivity

Plot an azimuth cut of the directivity of the array at 5 GHz over the restricted range of azimuth angles for the two different sets of weights.

fc = 5e9;
wts = [[1,1,1]',[.862,1.23,.862]'];
pattern(sPA,fc,[-50:0.1:50],0,...
    'Type','directivity',...
    'CoordinateSystem','rectangular',...
    'Weights',wts)

Figure contains an axes object. The axes object with title Azimuth Cut (elevation angle = 0.0°), xlabel Azimuth Angle (degrees), ylabel Directivity (dBi) contains 2 objects of type line. These objects represent Weights 1, Weights 2.

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.

Convert plotResponse to pattern

For antenna, microphone, and array System objects, the pattern method replaces the plotResponse method. In addition, two new simplified methods exist just to draw 2-D azimuth and elevation pattern plots. These methods are patternAzimuth and patternElevation.

The following table is a guide for converting your code from using plotResponse to pattern. Notice that some of the inputs have changed from input arguments to Name-Value pairs and conversely. The general pattern method syntax is

pattern(H,FREQ,AZ,EL,'Name1','Value1',...,'NameN','ValueN')

plotResponse Inputs plotResponse Description pattern Inputs

H argument Antenna, microphone, or array System object. H argument (no change)

FREQ argument Operating frequency. FREQ argument (no change)

V argument Propagation speed. This argument is used only for arrays. 'PropagationSpeed' name-value pair. This parameter is only used for arrays.

'Format' and 'RespCut' name-value pairs

These options work together to let you create a plot in angle space (line or polar style) or UV space. They also determine whether the plot is 2-D or 3-D. This table shows you how to create different types of plots using plotResponse.

Display space
Angle space (2D)	Set `'RespCut' to 'Az' or 'El'`. Set `'Format'` to `'line'` or `'polar'`. Set the display axis using either the `'AzimuthAngles'` or `'ElevationAngles'` name-value pairs.
Angle space (3D)	Set `'RespCut'` to `'3D'`. Set `'Format'` to `'line'` or `'polar'`. Set the display axis using both the `'AzimuthAngles'` and`'ElevationAngles'` name-value pairs.
UV space (2D)	Set `'RespCut'` to`'U'`. Set `'Format'` to `'UV'`. Set the display range using the `'UGrid'` name-value pair.
UV space (3D)	Set `'RespCut'` to`'3D'`. Set `'Format'` to `'UV'`. Set the display range using both the `'UGrid'` and `'VGrid'` name-value pairs.

'CoordinateSystem' name-value pair used together with the AZ and EL input arguments.

'CoordinateSystem' has the same options as the plotResponse method 'Format'name-value pair, except that 'line' is now named 'rectangular'. The table shows how to create different types of plots using pattern.

Display space
Angle space (2D)	Set `'Coordinate System'` to `'rectangular'` or `'polar'`. Specify either `AZ` or `EL` as a scalar.
Angle space (3D)	Set `'Coordinate System'` to `'rectangular'` or `'polar'`. Specify both `AZ` and `EL` as vectors.
UV space (2D)	Set `'Coordinate System'` to `'uv'`. Use `AZ` to specify a U-space vector. Use `EL` to specify a V-space scalar.
UV space (3D)	Set `'Coordinate System'` to `'uv'`. Use `AZ` to specify a U-space vector. Use `EL` to specify a V-space vector.

If you set CoordinateSystem to 'uv', enter the UV grid values using AZ and EL.

'CutAngle' name-value pair Constant angle at to take an azimuth or elevation cut. When producing a 2-D plot and when 'RespCut' is set to 'Az' or 'El', use 'CutAngle' to set the slice across which to view the plot. No equivalent name-value pair. To create a cut, specify either AZ or EL as a scalar, not a vector.

'NormalizeResponse' name-value pair

Normalizes the plot. When 'Unit' is set to 'dbi', you cannot specify 'NormalizeResponse'.

Use the 'Normalize' name-value pair. When 'Type' is set to 'directivity' you cannot specify 'Normalize'.

'OverlayFreq' name-value pair

Plot multiple frequencies on the same 2-D plot. Available only when 'Format' is set to 'line' or 'uv' and 'RespCut' is not set to '3D'. The value true produces an overlay plot and the value false produces a waterfall plot.

'PlotStyle' name-value pair plots multiple frequencies on the same 2-D plot.

The values 'overlay' and 'waterfall' correspond to 'OverlayFreq' values of true and false. The option 'waterfall' is allowed only when 'CoordinateSystem' is set to 'rectangular' or 'uv'.

'Polarization' name-value pair Determines how to plot polarized fields. Options are 'None', 'Combined', 'H', or 'V'. 'Polarization' name-value pair determines how to plot polarized fields. The 'None' option is removed. The options 'Combined', 'H', or 'V' are unchanged.

'Unit' name-value pair

Determines the plot units. Choose 'db', 'mag', 'pow', or 'dbi', where the default is 'db'.

'Type' name-value pair, uses equivalent options with different names

`plotResponse`	`pattern`
`'db'`	`'powerdb'`
`'mag'`	`'efield'`
`'pow'`	`'power'`
`'dbi'`	`'directivity'`

'Weights' name-value pair Array element tapers (or weights). 'Weights' name-value pair (no change).

'AzimuthAngles' name-value pair

Azimuth angles used to display the antenna or array response.

AZ argument

'ElevationAngles' name-value pair

Elevation angles used to display the antenna or array response.

EL argument

'UGrid' name-value pair

Contains U coordinates in UV-space.

AZ argument when 'CoordinateSystem' name-value pair is set to 'uv'

'VGrid' name-value pair

Contains V-coordinates in UV-space.

EL argument when 'CoordinateSystem' name-value pair is set to 'uv'

Version History

Introduced in R2015a

pattern

Syntax

Description

Input Arguments

sArray — Partitioned 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 — Subarray weights 1 (default) | N-by-1 complex-valued column vector | N-by-L complex-valued matrix

SteerAngle — Subarray steering angle [0;0] (default) | scalar | 2-element column vector

ElementWeights — Weights applied to elements within subarray 1 (default) | complex-valued NSE-by-N matrix | 1-by-N cell array

Dependencies

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

Azimuth Response of Partitioned ULA

Plot Pattern and Directivity of Partitioned URA Over Restricted Range of Angles

More About

Directivity

Convert plotResponse to pattern

Version History

See Also

`sArray` — Partitioned 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` — Subarray weights
1 (default) | N-by-1 complex-valued column vector | N-by-L complex-valued matrix

`SteerAngle` — Subarray steering angle
`[0;0]` (default) | scalar | 2-element column vector

`ElementWeights` — Weights applied to elements within subarray
`1` (default) | complex-valued N_SE-by-N matrix | 1-by-N cell array

`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