# patternAzimuth

System object: phased.ReplicatedSubarray
Package: phased

Plot replicated subarray directivity or pattern versus azimuth

## Syntax

patternAzimuth(sArray,FREQ)
patternAzimuth(sArray,FREQ,EL)
patternAzimuth(sArray,FREQ,EL,Name,Value)
PAT = patternAzimuth(___)

## Description

patternAzimuth(sArray,FREQ) plots the 2-D array directivity pattern versus azimuth (in dBi) for the array sArray at zero degrees elevation angle. The argument FREQ specifies the operating frequency.

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.

patternAzimuth(sArray,FREQ,EL), in addition, plots the 2-D array directivity pattern versus azimuth (in dBi) for the array sArray at the elevation angle specified by EL. When EL is a vector, multiple overlaid plots are created.

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

PAT = patternAzimuth(___) returns the array pattern. PAT is a matrix whose entries represent the pattern at corresponding sampling points specified by the 'Azimuth' parameter and the EL input argument.

## Input Arguments

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Replicated subarray, specified as a phased.ReplicatedSubarray System object.

Example: sArray= phased.ReplicatedSubarray;

Frequency for computing directivity and pattern, specified as a positive scalar. Frequency units are in hertz.

• For an antenna or microphone element, 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 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

Data Types: double

Elevation angles for computing sensor or array directivities and patterns, specified as a 1-by-N real-valued row vector. The quantity N is the number of requested 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 the xy plane. When measured toward the z-axis, this angle is positive.

Example: [0,10,20]

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.

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

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

Subarray weights, specified as the comma-separated pair consisting of 'Weights' and an M-by-1 complex-valued column vector. Subarray weights are applied to the subarrays of the array to produce array steering, tapering, or both. The dimension M is the number of subarrays in the array.

Example: 'Weights',ones(10,1)

Data Types: double
Complex Number Support: Yes

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

Subarray element weights, specified as complex-valued NSE-by-N matrix. Weights are applied to the individual elements within a subarray. All subarrays have the same dimensions and sizes. NSE is the number of elements in each subarray and N is the number of subarrays. Each column of the matrix specifies the weights for 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

Azimuth angles, specified as the comma-separated pair consisting of 'Azimuth' and a 1-by-P real-valued row vector. Azimuth angles define where the array pattern is calculated.

Example: 'Azimuth',[-90:2:90]

Data Types: double

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

## Output Arguments

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Array directivity or pattern, returned as an L-by-N real-valued matrix. The dimension L is the number of azimuth values determined by the 'Azimuth' name-value pair argument. The dimension N is the number of elevation angles, as determined by the EL input argument.

## Examples

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Create a 2-element ULA of isotropic antenna elements, and arrange three copies to form a 6-element ULA. Plot the directivity azimuth pattern within a restricted range of azimuth angles from -30 to 30 degrees in 0.1 degree increments. Plot directivity for 0 degrees and 45 degrees elevation.

Create the array

fmin = 1e9;
fmax = 6e9;
c = physconst('LightSpeed');
lam = c/fmax;
sIso = phased.IsotropicAntennaElement(...
'FrequencyRange',[fmin,fmax],...
'BackBaffled',false);
sULA = phased.ULA('Element',sIso,...
'NumElements',2,'ElementSpacing',0.5);
sRS = phased.ReplicatedSubarray('Subarray',sULA,...
'Layout','Rectangular','GridSize',[1 3],...
'GridSpacing','Auto');

Plot azimuth directivity pattern

fc = 1e9;
wts = [0.862,1.23,0.862]';
patternAzimuth(sRS,fc,[0,45],'PropagationSpeed',physconst('LightSpeed'),...
'Azimuth',[-30:0.1:30],...
'Type','directivity',...
'Weights',wts);