beamwidth

Compute and display beamwidth of a subarray

Since R2020b

Syntax

beamwidth(subarray,freq)

beamwidth(subarray,freq,Name=Value)

[bw,angles] = beamwidth(___)

Description

beamwidth(subarray,freq) plots the 2-D power pattern (in dB) of the 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(subarray,freq,Name=Value) computes and plots the beamwidth with the specified parameter 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")

[bw,angles] = beamwidth(___) returns the angular beamwidth bw (in degrees). The function also returns the corresponding angle values (in degrees) of the beamwidth.

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: [1×1 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: [1×1 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: [1×1 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: [1×1 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:

• phased.PartitionedArray

• phased.ReplicatedSubarray

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 equal-sign-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 equal-sign-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 equal-sign-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 equal-sign-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 equal-sign-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 equal-sign-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 equal-sign-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_max] define the beamwidth bw as a_max−a_min.

Version History

Introduced in R2020b