# patternAzimuth

**System object: **phased.ReplicatedSubarray

**Namespace: **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(`

plots
the 2-D array directivity pattern versus azimuth (in dBi) for the
array `sArray`

,`FREQ`

)`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(`

,
in addition, plots the 2-D array directivity pattern versus azimuth (in dBi) for the array
`sArray`

,`FREQ`

,`EL`

)`sArray`

at the elevation angle specified by `EL`

.
When `EL`

is a vector, multiple overlaid plots are created.

`patternAzimuth(`

plots the array pattern with additional options specified by one or
more `sArray`

,`FREQ`

,`EL`

,`Name,Value`

)`Name,Value`

pair arguments.

returns
the array pattern. `PAT`

= patternAzimuth(___)`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

`sArray`

— Replicated subarray

System object™

Replicated subarray, specified as a `phased.ReplicatedSubarray`

System object.

**Example: **`sArray= phased.ReplicatedSubarray;`

`FREQ`

— Frequency for computing directivity and pattern

positive scalar

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`

`EL`

— Elevation angles

1-by-*N* real-valued row vector

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.*

`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`

`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

*M*-by-1 complex-valued column vector

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

`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

_{SE}

Subarray element weights, specified as complex-valued *N _{SE}*-by-

*N*matrix. Weights are applied to the individual elements within a subarray. All subarrays have the same dimensions and sizes.

*N*is the number of elements in each subarray and

_{SE}*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`

— Azimuth angles

`[-180:180]`

(default) | 1-by-*P* real-valued row vector

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`

`Parent`

— Handle to axis

scalar

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

## Output Arguments

`PAT`

— Array directivity or pattern

*L*-by-*N* real-valued matrix

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

### Azimuth Pattern of Array with Subarrays

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);

## More About

### 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

$$D=4\pi \frac{{U}_{\text{rad}}\left(\theta ,\phi \right)}{{P}_{\text{total}}}$$

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.

## Version History

**Introduced in R2015a**

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