pattern
Syntax
Description
pattern(___,
plots the
array pattern with additional options specified by one or more Name,Value
)Name,Value
pair arguments.
[
returns the array pattern in PAT
,AZ_ANG
,EL_ANG
] = pattern(___)PAT
. The AZ_ANG
output
contains the coordinate values corresponding to the rows of PAT
. The
EL_ANG
output contains the coordinate values corresponding to the columns
of PAT
. If the 'CoordinateSystem'
parameter is set to
'uv'
, then AZ_ANG
contains the U
coordinates of the pattern and EL_ANG
contains the V
coordinates of the pattern. Otherwise, they are in angular units in degrees.
UV units are dimensionless.
Examples
Plot Response of NR Rectangular Panel Array
Construct a 5G antenna array where the grid is 2-by-2 and each panel is a 4-by-4 array. Each antenna element consists of two short-dipole antennas with different dipole axis directions. The antenna elements are spaced 1/2 wavelength apart and the panels are spaced 3 wavelengths apart. Plot the response pattern of the array assuming an operating frequency of 6 GHz.
c = physconst('LightSpeed'); fc = 6e9; lambda = c/fc; antenna1 = phased.ShortDipoleAntennaElement('AxisDirection','Z'); antenna2 = phased.ShortDipoleAntennaElement('AxisDirection','X'); array = phased.NRRectangularPanelArray('ElementSet', ... {antenna1, antenna2},'Size',[4, 4, 2, 2],'Spacing', ... [0.5*lambda, 0.5*lambda,3*lambda, 3*lambda]); pattern(array,fc,'ShowArray',true)
Use the Orientation
property of pattern
to change the orientation along the x-axis, along the y-axis and along the z-axis.
pattern(array,fc,'Orientation',[80;30;60],'ShowArray',true)
Disable the display of local coordinates and the colorbar.
pattern(array,fc,'ShowLocalCoordinate',false,'ShowColorBar',false)
Input Arguments
array
— Phased array
Phased Array System Toolbox™
System object™
Phased array, specified as a Phased Array System Toolbox System object.
FREQ
— Frequency for computing directivity and patterns
positive scalar | 1-by-L real-valued row vector
Frequencies for computing directivity and patterns, specified as a positive scalar or 1-by-L real-valued row vector. Frequency units are in hertz.
For an antenna, microphone, or sonar hydrophone or projector element,
FREQ
must lie within the range of values specified by theFrequencyRange
orFrequencyVector
property of the element. Otherwise, the element produces no response and the directivity is returned as–Inf
. Most elements use theFrequencyRange
property except forphased.CustomAntennaElement
andphased.CustomMicrophoneElement
, which use theFrequencyVector
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 2e6]
Data Types: double
AZ
— Azimuth angles
[-180:180]
(default) | 1-by-N real-valued row vector
Azimuth angles for computing directivity and pattern, specified as a 1-by-N real-valued row vector where N is the number of azimuth angles. Angle units are in degrees. Azimuth angles 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. When measured from the x-axis toward the y-axis, this angle is positive.
Example: [-45:2:45]
Data Types: double
EL
— Elevation angles
[-90:90]
(default) | 1-by-M real-valued row vector
Elevation angles for computing directivity and pattern, specified as a 1-by-M real-valued row vector where M is the number of desired 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 xy-plane. The elevation angle is positive when measured towards the z-axis.
Example: [-75:1:70]
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: CoordinateSystem,'polar',Type,'directivity'
CoordinateSystem
— Plotting coordinate system
'polar'
(default) | 'rectangular'
| 'uv'
Plotting coordinate system of the pattern, specified as the
comma-separated pair consisting of 'CoordinateSystem'
and
one of 'polar'
, 'rectangular'
,
or 'uv'
. When 'CoordinateSystem'
is
set to 'polar'
or 'rectangular'
,
the AZ
and EL
arguments
specify the pattern azimuth and elevation, respectively. AZ
values
must lie between –180° and 180°. EL
values
must lie between –90° and 90°. If 'CoordinateSystem'
is
set to 'uv'
, AZ
and EL
then
specify U and V coordinates,
respectively. AZ
and EL
must
lie between -1 and 1.
Example: 'uv'
Data Types: char
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
Orientation
— Array orientation
[0;0;0]
. (default) | 3-by-1 real-valued column vector
Array orientation, specified as a 3-by-1 real-valued column vector containing three rotation angles. The three angles define orthogonal rotations with respect to the x-, y-, and z-axes of the local coordinate system. To create the full orientation matrix, the orthogonal rotations are applied in this order:
a rotation around the positive x-axis by the angle θx.
a rotation around the positive y-axis by the angle θy.
a rotation around the positive z-axis by the angle θz.
Positive angles are defined using the right-handed rule. A positive angle defines a rotation that appears clockwise when looking towards the positive direction of the axis, and negative values when the rotation appears counter-clockwise. The right-hand rule is invoked by pointing the right-hand thumb along an axis. Then the other fingers of the right hand curl in the positive direction,
Normalize
— Display normalize pattern
true
(default) | false
Display normalized pattern, specified as the comma-separated pair consisting of
'Normalize
' and a Boolean. Set this parameter to
true
to display a normalized pattern. This parameter does not
apply when you set 'Type'
to 'directivity'
.
Directivity patterns are already normalized.
Data Types: logical
ShowArray
— View array geometry
false
(default) | true
View the array geometry along with the 3D radiation pattern, specified as
false
or true
.
Data Types: logical
ShowLocalCoordinates
— Show local coordinate axes
true
(default) | false
Show the local coordinate axes, specified as true
or false
.
Data Types: logical
ShowColorbar
— Show colorbar
true
(default) | false
Show the colorbar, specified as true
or false
.
Data Types: logical
Parent
— Handle to axis
scalar
Handle to the axes along which the array geometry is displayed specified as a scalar.
PlotStyle
— Plotting style
'overlay'
(default) | 'waterfall'
Polarization
— Polarization type
'combined'
(default) | 'H'
| 'V'
Polarization type, specified as the comma-separated pair consisting of
'Polarization'
and either 'combined'
,
'H'
, or 'V'
. If Polarization
is
'combined'
, the horizontal and vertical polarization patterns are
combined. If Polarization
is 'H'
, only the horizontal
polarization is displayed. If Polarization
is 'V'
,
only the vertical polarization is displayed.
Dependencies
To enable this property, set the array
argument to an array that
supports polarization and then set the 'Type'
name-value pair to
'efield'
, 'power'
, or
'powerdb'
.
Data Types: char
| string
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
— Array weights
1 (default) | N-by-1 complex-valued column vector | N-by-L complex-valued
matrix
Array weights, specified as the comma-separated pair consisting
of 'Weights
' and an N-by-1 complex-valued
column vector or N-by-L complex-valued
matrix. Array weights are applied to the elements of the array to
produce array steering, tapering, or both. The dimension N is
the number of elements in the array. The dimension L is
the number of frequencies specified by FREQ
.
Weights Dimension | FREQ Dimension | Purpose |
---|---|---|
N-by-1 complex-valued column vector | Scalar or 1-by-L row vector | Applies a set of weights for the single frequency or for all L frequencies. |
N-by-L complex-valued matrix | 1-by-L row vector | Applies each of the L columns of 'Weights' for
the corresponding frequency in FREQ . |
Note
Use complex weights to steer the array response toward different
directions. You can create weights using the phased.SteeringVector
System object or
you can compute your own weights. In general, you apply Hermitian
conjugation before using weights in any Phased Array System Toolbox function
or System object such as phased.Radiator
or phased.Collector
. However, for the directivity
, pattern
, patternAzimuth
,
and patternElevation
methods of any array System object use
the steering vector without conjugation.
Example: 'Weights',ones(N,M)
Data Types: double
Complex Number Support: Yes
Output Arguments
PAT
— array pattern
N-by-M real-valued matrix
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
where Urad(θ,φ) is the radiant intensity of a transmitter in the direction (θ,φ) and Ptotal 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.
Azimuth and Elevation Angles
Define the azimuth and elevation conventions used in the toolbox.
The azimuth angle of a vector is the angle between the x-axis and its orthogonal projection onto the xy-plane. The angle is positive when going from the x-axis toward the y-axis. Azimuth angles lie between –180° and 180° degrees, inclusive. The elevation angle is the angle between the vector and its orthogonal projection onto the xy-plane. The angle is positive when going toward the positive z-axis from the xy-plane. Elevation angles lie between –90° and 90° degrees, inclusive.
Array axes and normals
The U/V coordinate system is determined by the array type and the array orientation. The Phased Array System Toolbox offers four basic array shapes: ULA, URA, UCA, and Conformal.
For the
phased.ULA
System object use theArrayAxis
property to select the array orientation as"x"
,"y"
, or"z"
. TheArrayAxis
property determines the elements layout, the normal direction of the array, and the orientation of the U/V space as shown in the table here:ULA Array
ArrayAxis property value Array element positions Array normal U/V space for ULA U/V positive hemisphere for ULA Plot of U/V space for ULA in 3D space "x"
x-axis positive y-axis xz-plane y≥0 "y"
y-axis positive x-axis yz-plane x≥0 "z"
z-axis positive x-axis yz-plane x≥0 For the
phased.URA
orphased.UCA
System objects use theArrayNormal
property to select the array orientation as"x"
,"y"
, or"z"
. TheArrayNormal
property determines the elements layout, the normal direction of the array, and the orientation of the U/V space as shown in the table here:URA and UCA Arrays
ArrayNormal property value Array element positions Array normal U/V space for URA/UCA U/V positive hemisphere for URA/UCA Plot of U/V space for URA/UCA in 3D space "z"
xy-plane positive z-axis xy-plane z≥0 "y"
xz-plane positive y-axis xz-plane y≥0 "x"
yz-plane positive x-axis yz-plane x≥0 For the
phased.ConformalArray
System object, uses theElementPosition
property to determine the elements layout, the normal direction of the array, and the orientation of the U/V space as shown in the table here:Conformal Array
Array element positions Array normal U/V space for conformal array U/V positive hemisphere for conformal array Plot of U/V space for conformal array in 3D space Arbitrary in 3D space ElementPosition positive x-axis yz-plane x≥0
Version History
Introduced in R2021aR2024b: Array axis definitions
Enhanced definitions of array axes and normals.
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