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# directivity

System object: phased.HeterogeneousURA
Package: phased

Directivity of heterogeneous uniform rectangular array

## Syntax

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

## Description

`D = directivity(H,FREQ,ANGLE)` computes the Directivity (dBi) of a heterogeneous uniform rectangular array of antenna or microphone elements, `H`, at frequencies specified by the `FREQ` and in angles of direction specified by the `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)` computes the directivity with additional options specified by one or more `Name,Value` pair arguments.

## Input Arguments

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Uniform rectangular array specified as a `phased.HeterogeneousURA` System object.

Example: `H = phased.HeterogeneousURA`

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`.

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

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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.

## Examples

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Compute the directivity of a 9-element 3-by-3 heterogeneous URA consisting of short-dipole antenna elements. The three elements on the middle row are Y-directed while all the remaining elements are Z-directed.

Set the signal frequency to 1 GHz.

```c = physconst('LightSpeed'); freq = 1e9; lambda = c/freq;```

Create the array of short-dipole antenna elements. The elements have frequency ranges from 0 to 10 GHz.

```myElement1 = phased.ShortDipoleAntennaElement(... 'FrequencyRange',[0 10e9],... 'AxisDirection','Z'); myElement2 = phased.ShortDipoleAntennaElement(... 'FrequencyRange',[0 10e9],... 'AxisDirection','Y'); myArray = phased.HeterogeneousURA(... 'ElementSet',{myElement1,myElement2},... 'ElementIndices',[1 1 1; 2 2 2; 1 1 1]);```

Create the steering vector to point to 30 degrees azimuth and compute the directivity in the same direction as the steering vector.

```ang = [30;0]; w = steervec(getElementPosition(myArray)/lambda,ang); d = directivity(myArray,freq,ang,'PropagationSpeed',c,... 'Weights',w)```
```d = 11.1405 ```

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