patternAzimuth

System object: phased.HeterogeneousULA
Namespace: phased

Plot heterogeneous ULA directivity or pattern versus azimuth

Syntax

patternAzimuth(sArray,FREQ)
patternAzimuth(sArray,FREQ,EL)
patternAzimuth(sArray,FREQ,EL,Name,Value)
PAT = patternAzimuth(___)


Description

patternAzimuth(sArray,FREQ) plots the 2-D array directivity pattern versus azimuth (in dBi) for the array sArray at zero degrees elevation angle. The argument FREQ specifies the operating frequency.

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.

patternAzimuth(sArray,FREQ,EL), in addition, plots the 2-D array directivity pattern versus azimuth (in dBi) for the array sArray at the elevation angle specified by EL. When EL is a vector, multiple overlaid plots are created.

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

PAT = patternAzimuth(___) returns the array pattern. PAT is a matrix whose entries represent the pattern at corresponding sampling points specified by the 'Azimuth' parameter and the EL input argument.

Input Arguments

sArray — Heterogeneous ULA

System object™

Heterogeneous ULA, specified as a phased.HeterogeneousULA System object.

Example: sArray= phased.HeterogeneousULA;

FREQ — Frequency for computing directivity and pattern

positive scalar

Frequency for computing directivity and pattern, specified as a positive scalar. Frequency units are in hertz.

• For an antenna or microphone element, FREQ must lie within the range of values specified by the FrequencyRange or the 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

Data Types: double

EL — Elevation angles

1-by-N real-valued row vector

Elevation angles for computing sensor or array directivities and patterns, specified as a 1-by-N real-valued row vector. The quantity N is the number of requested 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 the xy plane. When measured toward the z-axis, this angle is positive.

Example: [0,10,20]

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.

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

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

M-by-1 complex-valued column vector

Array weights, specified as the comma-separated pair consisting of 'Weights' and an M-by-1 complex-valued column vector. Array weights are applied to the elements of the array to produce array steering, tapering, or both. The dimension M is the number of elements in the array.

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(10,1)

Data Types: double
Complex Number Support: Yes

Azimuth — Azimuth angles

[-180:180] (default) | 1-by-P real-valued row vector

Azimuth angles, specified as the comma-separated pair consisting of 'Azimuth' and a 1-by-P real-valued row vector. Azimuth angles define where the array pattern is calculated.

Example: 'Azimuth',[-90:2:90]

Data Types: double

Parent — Handle to axis

scalar

Handle to the axes along which the array geometry is displayed specified as a scalar.

Output Arguments

PAT — Array directivity or pattern

L-by-N real-valued matrix

Array directivity or pattern, returned as an L-by-N real-valued matrix. The dimension L is the number of azimuth values determined by the 'Azimuth' name-value pair argument. The dimension N is the number of elevation angles, as determined by the EL input argument.

Examples

Azimuth Directivity Pattern For Steered Array

Create an 11-element heterogeneous ULA from short-dipole antenna elements with different axis directions. The element spacing is 0.4 meters. Draw the azimuthal directivity pattern for 0 degrees elevation at an operating frequency of 300 MHz. Then, steer the array and draw the azimuthal directivity pattern.

Construct Heterogeneous ULA

Construct the array from z-directed and y-directed short dipole antenna elements.

sElement1 = phased.ShortDipoleAntennaElement(...
    'FrequencyRange',[200e6 500e6],...
    'AxisDirection','Z');
sElement2 = phased.ShortDipoleAntennaElement(...
    'FrequencyRange',[200e6 500e6],...
    'AxisDirection','Y');
sArray = phased.HeterogeneousULA(...
    'ElementSpacing',0.4,...
    'ElementSet',{sElement1,sElement2},...
    'ElementIndices',[1 1 1 2 2 2 2 2 1 1 1]);

Plot Directivity Pattern

fc = 300e6;
c = physconst('LightSpeed');
lam = c/fc;
patternAzimuth(sArray,fc,0,...
    'PropagationSpeed',c,...
    'Type','directivity')

Steer Array and Plot Directivity Pattern

Steer the array to 30 degrees in azimuth by applying weights to achieve a linear phase shift.

theta = 30;
d = [0:10]*0.4;
ph = 2*pi*d'/lam*sind(theta);
wts = exp(1i*ph);
patternAzimuth(sArray,fc,0,...
    'PropagationSpeed',c,...
    'Type','directivity',....
    'Weights',wts)

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.

Version History

Introduced in R2015a