pattern

R2026b

Plot array directivity and patterns from array manifold

Since R2026b

Syntax

pattern(arraymanifold,FREQ)

pattern(arraymanifold,FREQ,AZ)

pattern(arraymanifold,FREQ,AZ,EL)

pattern(___,Name=Value)

[PAT,AZ_ANG,EL_ANG] = pattern(___)

Description

pattern(arraymanifold,FREQ) plots the 3-D array directivity pattern (in dBi) for the array specified in arraymanifold. The operating frequency is specified in FREQ. You can use this function to display the patterns of arrays that support polarization.

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

pattern(arraymanifold,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. UV units are dimensionless. Otherwise, they are in angular units in degrees.

Examples

Create and Evaluate Array Manifold

Create a phased.ArrayManifold System object™ and evaluate the manifold values in multiple directions.

First, set up the azimuth angle, elevation angle, and frequency grids.

az = -180:10:180;
el = -90:10:90;
fc = [0 1e9 2e9];
manval = complex(ones(numel(az),numel(el),numel(fc),8));

Create the array manifold.

man1 = phased.ArrayManifold(manval,az,el,fc);

Evaluate the manifold at two frequencies and two directions.

M1 = man1([0 1e9],[30 40; 0 10])

M1 = 
M1(:,:,1) =

     1     1
     1     1
     1     1
     1     1
     1     1
     1     1
     1     1
     1     1


M1(:,:,2) =

     1     1
     1     1
     1     1
     1     1
     1     1
     1     1
     1     1
     1     1

Create a second frequency-invariant manifold.

man2 = phased.ArrayManifold( ...
    manval(:,:,1,:),az,el,[]);

Frequency query values are ignored for frequency-invariant data.

M2 = man2([0 1e9 2e9],[0;0]);

Use the directivity object function to compute the directivity of the second manifold at az=-90 degrees and el=10 degrees.

[az(10),el(11)]

ans = 1×2

   -90    10

directivity(man2,fc(2),[az(10);el(11)])

ans = 
1.1025e-04

Using the pattern object function, plot the directivity pattern of the array manifold.

pattern(man2,fc(2)) 

Input Arguments

arraymanifold — Phased array manifold

phased.ArrayManifold System object™

Phased array manifold, specified as a phased.ArrayManifold 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 Hz.

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.

Example: CoordinateSystem="polar",Type="directivity"

CoordinateSystem — Plotting coordinate system

"polar" (default) | "rectangular" | "uv"

Plotting coordinate system of the pattern, specified as the equal sign 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 equal-sign-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 equal sign 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 equal-sign-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

Weights — Array weights

1 (default) | N-by-1 complex-valued column vector | N-by-L complex-valued matrix

Array weights, specified as the equal sign 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

Array pattern, returned as an N-by-M real-valued matrix. The pattern is a function of azimuth and elevation. The rows of PAT correspond to the azimuth angles in the vector specified by EL_ANG. The columns correspond to the elevation angles in the vector specified by AZ_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.

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.

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.

Version History

Introduced in R2026b