Main Content


System object: phased.ULA
Package: phased

Directivity of uniform linear array


D = directivity(H,FREQ,ANGLE)
D = directivity(H,FREQ,ANGLE,Name,Value)


D = directivity(H,FREQ,ANGLE) computes the Directivity (dBi) of a uniform linear array (ULA) of antenna or microphone elements, H, at frequencies specified by FREQ and in angles of direction specified by ANGLE.

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.

D = directivity(H,FREQ,ANGLE,Name,Value) returns the directivity with additional options specified by one or more Name,Value pair arguments.

Input Arguments

expand all

Uniform linear array specified as a phased.ULA System object.

Example: H = phased.ULA;

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

Angles for computing directivity, specified as a 1-by-M real-valued row vector or a 2-by-M real-valued matrix, where M is the number of angular directions. Angle units are in degrees. If ANGLE is a 2-by-M matrix, then each column specifies a direction in azimuth and elevation, [az;el]. The azimuth angle must lie between –180° and 180°. The elevation angle must lie between –90° and 90°.

If ANGLE is a 1-by-M vector, then each entry represents an azimuth angle, with the elevation angle assumed to be zero.

The azimuth angle is the angle between the x-axis and the projection of the direction vector onto the xy plane. This angle is positive when measured from the x-axis toward the y-axis. The elevation angle is the angle between the direction vector and xy plane. This angle is positive when measured towards the z-axis. See Azimuth and Elevation Angles.

Example: [45 60; 0 10]

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.

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

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 DimensionFREQ DimensionPurpose
N-by-1 complex-valued column vectorScalar or 1-by-L row vectorApplies a set of weights for the single frequency or for all L frequencies.
N-by-L complex-valued matrix1-by-L row vectorApplies each of the L columns of 'Weights' for the corresponding frequency in FREQ.


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

expand all

Directivity, returned as an M-by-L matrix. Each row corresponds to one of the M angles specified by ANGLE. Each column corresponds to one of the L frequency values specified in FREQ. Directivity units are in dBi where dBi is defined as the gain of an element relative to an isotropic radiator.


expand all

Compute the directivities of two different uniform linear arrays (ULA). One array consists of isotropic antenna elements and the second array consists of cosine antenna elements. In addition, compute the directivity when the first array is steered in a specified direction. For each case, calculate the directivities for a set of seven different azimuth directions all at zero degrees elevation. Set the frequency to 800 MHz.

Array of isotropic antenna elements

First, create a 10-element ULA of isotropic antenna elements spaced 1/2-wavelength apart.

c = physconst('LightSpeed');
fc = 3e8;
lambda = c/fc;
ang = [-30,-20,-10,0,10,20,30; 0,0,0,0,0,0,0];
myAnt1 = phased.IsotropicAntennaElement;
myArray1 = phased.ULA(10,lambda/2,'Element',myAnt1);

Compute the directivity.

d = directivity(myArray1,fc,ang,'PropagationSpeed',c)
d = 7×1


Array of cosine antenna elements

Next, create a 10-element ULA of cosine antenna elements spaced 1/2-wavelength apart.

myAnt2 = phased.CosineAntennaElement('CosinePower',[1.8,1.8]);
myArray2 = phased.ULA(10,lambda/2,'Element',myAnt2);

Compute the directivity.

d = directivity(myArray2,fc,ang,'PropagationSpeed',c)
d = 7×1


The directivity of the cosine ULA is greater than the directivity of the isotropic ULA because of the larger directivity of the cosine antenna element.

Steered array of isotropic antenna elements

Finally, steer the isotropic antenna array to 30 degrees in azimuth and compute the directivity.

w = steervec(getElementPosition(myArray1)/lambda,[30;0]);
d = directivity(myArray1,fc,ang,'PropagationSpeed',c,...
d = 7×1


The directivity is greatest in the steered direction.

More About

expand all