# beamwidth

Compute and display beamwidth of a subarray

## Description

`beamwidth(`

plots the 2-D power pattern (in dB) of the `subarray`

,`freq`

)`subarray`

for all azimuth
angles at a fixed elevation angle of zero degrees. The plot displays the half-power
beamwidth (in degrees) at the frequency specified in `freq`

(in Hz) and
the angles (in degrees) in azimuth at which the magnitude of the power pattern decreases by
3 dB from the peak of the main beam.

`beamwidth(`

computes and plots the beamwidth with the specified parameter `subarray`

,`freq`

,`Name,Value`

)`Name`

set
to the specified `Value`

. You can specify additional name-value pair
arguments in any order as (`Name1,Value1,...,NameN,ValueN`

).

**Example: **`beamwidth(subarray,5e8,'Cut','Elevation')`

## Examples

### Plot Beamwidth of Rectangular Lattice Array

Plot the beamwidth of a rectangular lattice array composed of two uniform rectangular arrays. Consider the antenna elements of the array to be cosine antenna elements.

First, construct a `phased.CosineAntennaElement`

object.

myAnt = phased.CosineAntennaElement

myAnt = phased.CosineAntennaElement with properties: FrequencyRange: [0 1.0000e+20] CosinePower: [1.5000 1.5000]

Next, construct a 5-by-5 uniform rectangular array by creating a `phased.URA`

object.

myArray = phased.URA([5 5],[0.5 0.5],'Element',myAnt,... 'ElementSpacing',[0.15 0.15])

myArray = phased.URA with properties: Element: [1x1 phased.CosineAntennaElement] Size: [5 5] ElementSpacing: [0.1500 0.1500] Lattice: 'Rectangular' ArrayNormal: 'x' Taper: 1

Use two of these 5-by-5 uniform rectangular arrays to construct a 5-by-10 rectangular lattice. Construct the lattice using the `phased.ReplicatedSubarray`

object.

myRSA = phased.ReplicatedSubarray('Subarray',myArray,... 'Layout','Rectangular','GridSize',[1 2],... 'GridSpacing','Auto','SubarraySteering','Phase')

myRSA = phased.ReplicatedSubarray with properties: Subarray: [1x1 phased.URA] Layout: 'Rectangular' GridSize: [1 2] GridSpacing: 'Auto' SubarraySteering: 'Phase' PhaseShifterFrequency: 300000000 NumPhaseShifterBits: 0

Now visualize the 10dB beamwidth of the obtained lattice across the azimuth plane (0 degrees elevation). The subarray is phase steered toward 24 degrees azimuth. Assume the operating frequency of the array to be 1 GHz.

stv = phased.SteeringVector('SensorArray',myRSA); beamwidth(myRSA,1e9,'dBDown',10,'SteerAngle',24,'Weights',stv(1e9,24))

ans = 16.4600

### Calculate Beamwidth and Angles of Two ULAs

Calculate the 3 dB beamwidth of a 10-element uniform linear array (ULA) composed of two 5-element ULAs across the azimuth plane and at 0 degrees elevation. By default, the antenna elements are isotropic. Assume the operating frequency of the array to be 500MHz.

`myArray = phased.ULA('NumElements',5)`

myArray = phased.ULA with properties: Element: [1x1 phased.IsotropicAntennaElement] NumElements: 5 ElementSpacing: 0.5000 ArrayAxis: 'y' Taper: 1

myRSA = phased.ReplicatedSubarray('Subarray',myArray,... 'GridSize',[1 2])

myRSA = phased.ReplicatedSubarray with properties: Subarray: [1x1 phased.ULA] Layout: 'Rectangular' GridSize: [1 2] GridSpacing: 'Auto' SubarraySteering: 'None'

[BW,Ang] = beamwidth(myRSA,5e8)

BW = 6.1200

`Ang = `*1×2*
-3.0600 3.0600

## Input Arguments

`subarray`

— Subarray of sensor elements

Phased Array System Toolbox™
System object™

Subarray of sensor elements, specified as one of the following System objects:

`freq`

— Frequency used to calculate beamwidth

scalar in Hz

Frequency used to calculate the beamwidth, specified as a scalar in Hz.

**Example: **`5e8`

**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.*

**Example: **`beamwidth(subarray,5e8,'Cut','Azimuth','CutAngle',45)`

plots
the beamwidth of the subarray that is operating at a frequency of 0.5 GHz, with the slice
direction set to `'Azimuth'`

, and the cut angle set to 45
degrees.

`Cut`

— Slice direction in azimuth-elevation space

`'Azimuth'`

(default) | `'Elevation'`

The slice direction in azimuth-elevation space along which the beamwidth is
computed, specified as the comma-separated pair consisting of
`'Cut'`

and `'Azimuth'`

for the azimuth plane,
and `'Cut'`

and `'Elevation'`

for the elevation
plane.

`CutAngle`

— Angle for plane to get required 2-D cut

`0`

(default) | scalar

Corresponding angle (in degrees) for the plane to get the required 2-D cut,
specified as the comma-separated pair consisting of `'CutAngle'`

and a scalar. If `'Cut'`

is specified as
`'Azimuth'`

, then `'CutAngle'`

(Elevation)
should lie between [−90, 90] degrees. If `'Cut'`

is specified as
`'Elevation'`

, then `'CutAngle'`

(Azimuth)
should lie between [−180, 180] degrees.

**Data Types: **`double`

`dBDown`

— Power value from peak of main lobe

`3`

(default) | `Inf`

| positive scalar

Power value (in dB) from the peak of the main lobe, specified as the
comma-separated pair consisting of `'dBDown'`

and a positive
scalar. The default value is 3 dB, which translates to half-power beamwidth. To
calculate the first-null beamwidth, specify the `'dBDown'`

value as
`Inf`

.

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

`PropagationSpeed`

— Propagation speed

`3×10^8`

m/s (speed of light) (default) | positive scalar

Propagation speed, specified as the comma-separated pair consisting of
`'PropagationSpeed'`

and a positive scalar (in m/s).

**Data Types: **`double`

`Weights`

— Weights applied to array

length-*N* column vector

Weights applied to the array of sensor elements, specified as the comma-separated
pair consisting of `'Weights'`

and a length-*N*
column vector, where *N* is the number of elements in the
array.

**Data Types: **`double`

`SteerAngle`

— Subarray steering angle

[`0`

; `0`

] (default) | scalar | length-2 column vector

Subarray steering angle (in degrees), specified as the comma-separated pair
consisting of `'SteerAngle'`

and a scalar or a length-2 column
vector. If the steering angle is a scalar, the value represents the azimuth angle and
the elevation angle is assumed to be 0. If the steering angle is a vector, the angle
is specified in the form of [AzimuthAngle; ElevationAngle].

#### Dependencies

This parameter is applicable when you set the
`SubarraySteering`

property of `subarray`

object
to either `'Phase'`

or `'Time'`

.

**Data Types: **`double`

`ElementWeights`

— Weights applied to each element in subarray

matrix of all ones (default) | matrix | cell array

Weights applied to each element in the subarray, specified as the comma-separated
pair consisting of `'ElementWeights'`

and a matrix or a cell
array.

For a `ReplicatedSubarray`

object,
`ElementWeights`

must be a
*NSE*-by-*N* matrix, where *NSE*
is the number of elements in each individual subarray and *N* is the
number of subarrays. Each column in `ElementWeights`

specifies the
weights for the elements in the corresponding subarray.

For a `PartitionedArray`

object, if the individual subarrays have
the same number of elements, `ElementWeights`

must be an
*NSE*-by-*N* matrix, where *NSE*
is the number of elements in each individual subarray and *N* is the
number of subarrays.

Each column in the `WS`

property of the
`subarray`

object specifies the weights for the elements in the
corresponding subarray. If subarrays in the `PartitionedArray`

object
have different number of elements, `ElementWeights`

can be one of
the following:

*NSE*-by-*N*matrix ––*NSE*indicates the number of elements in the largest subarray and*N*is the number of subarrays.1-by-

*N*cell array ––*N*is the number of subarrays and each cell contains a column vector whose length is the same as the number of elements of the corresponding subarray.

If `WS`

is a matrix, the first *K* entries in
each column specify the weights for the elements in the corresponding subarray.
*K* is the number of elements in the corresponding subarray. If
`WS`

is a cell array, each cell in the array is a column vector
specifying the weights for the elements in the corresponding subarray.

#### Dependencies

This parameter is applicable when you set the
`SubarraySteering`

property of `subarray`

object
to `'Custom'`

.

**Data Types: **`double`

## Output Arguments

`bw`

— Angular beamwidth

scalar in degrees

Angular beamwidth of the subarray, returned as a scalar in degrees.

**Data Types: **`double`

`angles`

— Angle values of beamwidth

1-by-2 vector in degrees

Angle values of the beamwidth, returned as a 1-by-2 vector. The two elements in the
vector [*a _{min}*,

*a*] define the beamwidth

_{max}`bw`

as
*a*−

_{max}*a*.

_{min}## Version History

**Introduced in R2020b**

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