# patternElevation

System object: phased.PartitionedArray
Package: phased

Plot partitioned array directivity or pattern versus elevation

## Syntax

patternElevation(sArray,FREQ)
patternElevation(sArray,FREQ,AZ)
patternElevation(sArray,FREQ,AZ,Name,Value)
PAT = patternElevation(___)

## Description

patternElevation(sArray,FREQ) plots the 2-D array directivity pattern versus elevation (in dBi) for the array sArray at zero degrees azimuth angle. When AZ is a vector, multiple overlaid plots are created. 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.

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

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

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

## Input Arguments

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

Example: sArray= phased.PartitionedArray;

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

Azimuth angles for computing sensor or array directivities and patterns, specified as a 1-by-N real-valued row vector where N is the number of desired azimuth directions. Angle units are in degrees. The azimuth angle 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. This angle is positive when measured from the x-axis toward the y-axis.

Example: [0,10,20]

Data Types: double

### Name-Value Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

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 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 NSE-by-N matrix, NSE 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

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

Example: 'Elevation',[-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 elevation angles determined by the 'Elevation' name-value pair argument. The dimension N is the number of azimuth angles determined by the AZ argument.

## Examples

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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 the directivity for elevation angles from -45 to 45 degrees. 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 elevation directivity pattern

Plot the response of the array at 5 GHz

fc = 5e9;
wts = [0.862,1.23,0.862]';
azimangle = 0;
patternElevation(sPA,fc,azimangle,...
'Type','directivity',...
'PropagationSpeed',physconst('LightSpeed'),...
'Elevation',[-45:45],...
'Weights',wts)

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