pattern

System object: phased.ConformalArray
Package: phased

Plot conformal array pattern

Syntax

pattern(sArray,FREQ)
pattern(sArray,FREQ,AZ)
pattern(sArray,FREQ,AZ,EL)
pattern(___,Name,Value)
[PAT,AZ_ANG,EL_ANG] = pattern(___)


Description

pattern(sArray,FREQ) plots the 3-D array directivity pattern (in dBi) for the array specified in sArray. The operating frequency is specified in FREQ.

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.

pattern(sArray,FREQ,AZ) plots the array directivity pattern at the specified azimuth angle.

pattern(sArray,FREQ,AZ,EL) plots the array directivity pattern at specified azimuth and elevation angles.

pattern(___,Name,Value) plots the array pattern with additional options specified by one or more Name,Value pair arguments.

[PAT,AZ_ANG,EL_ANG] = pattern(___) returns the array pattern in 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.

Note

This method replaces the plotResponse method. See Convert plotResponse to pattern for guidelines on how to use pattern in place of plotResponse.

Input Arguments

sArray — Conformal array

System object™

Conformal array, specified as a phased.ConformalArray System object.

Example: sArray= phased.ConformalArray;

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 the FrequencyRange or 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 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 Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

'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

'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

'PlotStyle' — Plotting style

'overlay' (default) | 'waterfall'

Plotting style, specified as the comma-separated pair consisting of 'Plotstyle' and either 'overlay' or 'waterfall'. This parameter applies when you specify multiple frequencies in FREQ in 2-D plots. You can draw 2-D plots by setting one of the arguments AZ or EL to a scalar.

Data Types: char

'Polarization' — Polarized field component

'combined' (default) | 'H' | 'V'

Polarized field component to display, specified as the comma-separated pair consisting of 'Polarization' and 'combined', 'H', or 'V'. This parameter applies only when the sensors are polarization-capable and when the 'Type' parameter is not set to 'directivity'. This table shows the meaning of the display options.

'Polarization'	Display
'combined'	Combined H and V polarization components
'H'	H polarization component
'V'	V polarization component

Example: 'V'

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' — 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

M-by-N real-valued matrix

Array pattern, returned as an M-by-N real-valued matrix. The dimensions of PAT correspond to the dimensions of the output arguments AZ_ANG and EL_ANG.

AZ_ANG — Azimuth angles

scalar | 1-by-N real-valued row vector

Azimuth angles for displaying directivity or response pattern, returned as a scalar or 1-by-N real-valued row vector corresponding to the dimension set in AZ. The columns of PAT correspond to the values in AZ_ANG. Units are in degrees.

EL_ANG — Elevation angles

scalar | 1-by-M real-valued row vector

Elevation angles for displaying directivity or response, returned as a scalar or 1-by-M real-valued row vector corresponding to the dimension set in EL. The rows of PAT correspond to the values in EL_ANG. Units are in degrees.

Examples

Plot Power Pattern of 8-Element Uniform Circular Array

Using the ConformalArray System object, construct an 8-element uniform circular array (UCA) of isotropic antenna elements. Plot a normalized azimuth power pattern at 0 degrees elevation. Assume the operating frequency is 1 GHz and the wave propagation speed is the speed of light.

N = 8;
azang = (0:N-1)*360/N-180;
sCA = phased.ConformalArray(...
    'ElementPosition',[cosd(azang);sind(azang);zeros(1,N)],...
    'ElementNormal',[azang;zeros(1,N)]);
fc = 1e9;
c = physconst('LightSpeed');
pattern(sCA,fc,[-180:180],0,...
    'PropagationSpeed',c,'Type','powerdb',...
    'CoordinateSystem','polar')

Plot Pattern of 31-Element Uniform Circular Sonar Array

Construct a 31-element acoustic uniform circular sonar array (UCA) using the ConformalArray System object. Assume the array is one meter in diameter. Using the ElevationAngles parameter, restrict the display to +/-40 degrees in 0.1 degree increments. Assume the operating frequency is 4 kHz. A typical value for the speed of sound in seawater is 1500.0 m/s.

Construct the array

N = 31;
theta = (0:N-1)*360/N-180;
Radius = 0.5;
sMic = phased.OmnidirectionalMicrophoneElement(...
    'FrequencyRange',[0,10000],'BackBaffled',true);
sArray = phased.ConformalArray('Element',sMic,...
    'ElementPosition',Radius*[zeros(1,N);cosd(theta);sind(theta)],...
    'ElementNormal',[ones(1,N);zeros(1,N)]);

Plot the magnitude pattern

fc = 4000;
c = 1500.0;
pattern(sArray,fc,0,[-40:0.1:40],...
    'PropagationSpeed',c,...
    'CoordinateSystem','polar',...
    'Type','efield')

Plot the directivity pattern

pattern(sArray,fc,0,[-40:0.1:40],...
    'PropagationSpeed',c,...
    'CoordinateSystem','polar',...
    'Type','directivity')

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.

Convert plotResponse to pattern

For antenna, microphone, and array System objects, the pattern method replaces the plotResponse method. In addition, two new simplified methods exist just to draw 2-D azimuth and elevation pattern plots. These methods are azimuthPattern and elevationPattern.

The following table is a guide for converting your code from using plotResponse to pattern. Notice that some of the inputs have changed from input arguments to Name-Value pairs and conversely. The general pattern method syntax is

pattern(H,FREQ,AZ,EL,'Name1','Value1',...,'NameN','ValueN')

plotResponse Inputs	plotResponse Description	pattern Inputs
H argument	Antenna, microphone, or array System object.	H argument (no change)
FREQ argument	Operating frequency.	FREQ argument (no change)
V argument	Propagation speed. This argument is used only for arrays.	'PropagationSpeed' name-value pair. This parameter is only used for arrays.
'Format' and 'RespCut' name-value pairs	These options work together to let you create a plot in angle space (line or polar style) or UV space. They also determine whether the plot is 2-D or 3-D. This table shows you how to create different types of plots using plotResponse. Display space   Angle space (2D) Set 'RespCut' to 'Az' or 'El'. Set 'Format' to 'line' or 'polar'. Set the display axis using either the 'AzimuthAngles' or 'ElevationAngles' name-value pairs. Angle space (3D) Set 'RespCut' to '3D'. Set 'Format' to 'line' or 'polar'. Set the display axis using both the 'AzimuthAngles' and'ElevationAngles' name-value pairs. UV space (2D) Set 'RespCut' to'U'. Set 'Format' to 'UV'. Set the display range using the 'UGrid' name-value pair. UV space (3D) Set 'RespCut' to'3D'. Set 'Format' to 'UV'. Set the display range using both the 'UGrid' and 'VGrid' name-value pairs.	'CoordinateSystem' name-value pair used together with the AZ and EL input arguments. 'CoordinateSystem' has the same options as the plotResponse method 'Format'name-value pair, except that 'line' is now named 'rectangular'. The table shows how to create different types of plots using pattern. Display space   Angle space (2D) Set 'Coordinate System' to 'rectangular' or 'polar'. Specify either AZ or EL as a scalar. Angle space (3D) Set 'Coordinate System' to 'rectangular' or 'polar'. Specify both AZ and EL as vectors. UV space (2D) Set 'Coordinate System' to 'uv'. Use AZ to specify a U-space vector. Use EL to specify a V-space scalar. UV space (3D) Set 'Coordinate System' to 'uv'. Use AZ to specify a U-space vector. Use EL to specify a V-space vector. If you set CoordinateSystem to 'uv', enter the UV grid values using AZ and EL.
'CutAngle' name-value pair	Constant angle at to take an azimuth or elevation cut. When producing a 2-D plot and when 'RespCut' is set to 'Az' or 'El', use 'CutAngle' to set the slice across which to view the plot.	No equivalent name-value pair. To create a cut, specify either AZ or EL as a scalar, not a vector.
'NormalizeResponse' name-value pair	Normalizes the plot. When 'Unit' is set to 'dbi', you cannot specify 'NormalizeResponse'.	Use the 'Normalize' name-value pair. When 'Type' is set to 'directivity' you cannot specify 'Normalize'.
'OverlayFreq' name-value pair	Plot multiple frequencies on the same 2-D plot. Available only when 'Format' is set to 'line' or 'uv' and 'RespCut' is not set to '3D'. The value true produces an overlay plot and the value false produces a waterfall plot.	'PlotStyle' name-value pair plots multiple frequencies on the same 2-D plot. The values 'overlay' and 'waterfall' correspond to 'OverlayFreq' values of true and false. The option 'waterfall' is allowed only when 'CoordinateSystem' is set to 'rectangular' or 'uv'.
'Polarization' name-value pair	Determines how to plot polarized fields. Options are 'None', 'Combined', 'H', or 'V'.	'Polarization' name-value pair determines how to plot polarized fields. The 'None' option is removed. The options 'Combined', 'H', or 'V' are unchanged.
'Unit' name-value pair	Determines the plot units. Choose 'db', 'mag', 'pow', or 'dbi', where the default is 'db'.	'Type' name-value pair, uses equivalent options with different names plotResponse pattern 'db' 'powerdb' 'mag' 'efield' 'pow' 'power' 'dbi' 'directivity'
'Weights' name-value pair	Array element tapers (or weights).	'Weights' name-value pair (no change).
'AzimuthAngles' name-value pair	Azimuth angles used to display the antenna or array response.	AZ argument
'ElevationAngles' name-value pair	Elevation angles used to display the antenna or array response.	EL argument
'UGrid' name-value pair	Contains U coordinates in UV-space.	AZ argument when 'CoordinateSystem' name-value pair is set to 'uv'
'VGrid' name-value pair	Contains V-coordinates in UV-space.	EL argument when 'CoordinateSystem' name-value pair is set to 'uv'