# patternAzimuth

System object: phased.PartitionedArray
Package: phased

Plot partitioned array 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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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`

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 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

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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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 azimuth directivity. 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 azimuth directivity pattern

Plot the response of the array at 5 GHz

```fc = 5e9; wts = [0.862,1.23,0.862]'; patternAzimuth(sPA,fc,0,... 'Type','directivity',... 'PropagationSpeed',physconst('LightSpeed'),... 'Weights',wts)```