# phased.SphericalWavefrontArrayResponse

Array response to spherical wavefront

## Description

The phased.SphericalWavefrontArrayResponse System object™ calculates the complex-valued response of a sensor array to a spherical wave.

To compute the response:

1. Create the phased.SphericalWavefrontArrayResponse object and set its properties.

2. Call the object with arguments, as if it were a function.

## Creation

### Description

example

The response = phased.SphericalWaveformArrayResponse creates a phased.SphericalWaveformArrayResponse System object response with default property values.

response = phased.SphericalWaveformArrayResponse(Name,Value) creates a phased.SphericalWaveformArrayResponse object with each property Name set to a specified Value. You can specify additional name-value pair arguments in any order as (Name1,Value1,...,NameN,ValueN). Enclose each property name in single quotes.

Example: response = phased.SphericalWaveformArrayResponse('SensorArray',phased.URA([10,20],'ElementSpacing',[0.25,0.25]),'PropagationSpeed',physconst('LightSpeed')) creates a phased.SphericalWaveformArrayResponse System object for a 10-by-20 uniform rectangular array (URA) with element spacing set to 0.25 meters The propagation speed set to the speed of light.

## Properties

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Unless otherwise indicated, properties are nontunable, which means you cannot change their values after calling the object. Objects lock when you call them, and the release function unlocks them.

If a property is tunable, you can change its value at any time.

Sensor array, specified as a Phased Array System Toolbox array System object.

Example: phased.URA

Signal propagation speed, specified as a positive scalar. Units are in meters per second. The default propagation speed is the value returned by physconst('LightSpeed'). See physconst for more information.

Example: 3e8

Data Types: double

Option to include individual element responses in the steering vector, specified as false or true. If this property is set to true, the steering vector includes individual array element responses. If this property is set to false, the steering vector is computed assuming that the elements are isotropic, regardless of how the elements are specified. Set this property to true when using polarized signals.

When the array specified in the SensorArray property contains subarrays, the steering vector applies to subarrays. If SensorArray does not contain subarrays, the steering vector applies to the array elements.

Data Types: logical

Enable weights input, specified as false or true. When true, use the object input argument W to specify weights. Weights are applied to individual array elements (or at the subarray level when subarrays are supported).

Data Types: logical

Enable polarization simulation, specified as false or true. Set this property to true to enable polarization and to false to ignore polarization. This property applies when the array specified in the SensorArray property is capable of simulating polarization and the IncludeElementResponse property of the array is set to true.

Data Types: logical

## Usage

### Description

example

RESP = response(FREQ,ANG,RNG) returns the array response RESP at operating frequencies specified in FREQ, directions specified in ANG, and at range RNG.

example

RESP = response(FREQ,ANG,RNG,W) applies weights W to the sensor array. To enable this syntax, set the WeightsInputPort to true.

### Input Arguments

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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 response, 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

Range, specified as a positive 1-by-M real-valued vector of positive values. If ANG has more than one column, RNG must be a scalar or have the same number of columns as ANG. Units are in meters.

Data Types: double

Weights applied to sensor array elements, specified as a complex-valued, length-N column vector or a complex-valued, N-by-L matrix. N is the number of array elements and L is the number of frequencies specified in FREQ. If W is a vector, the same weight is applied at all frequencies. If W is a matrix, each column of W represents the weights used at the corresponding frequency specified in FREQ.

#### Dependencies

To enable this argument, set the WeightsInputPort to true.

Data Types: double
Complex Number Support: Yes

### Output Arguments

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Array response, returned as a complex-valued M-by-L complex-valued matrix or struct containing complex values. The response depends on whether the EnablePolarization property is set to true or false.

• If the EnablePolarization property is set to false, the voltage response, RESP, has the dimensions M-by-L. M represents the number of angles specified in the input argument ANG while L represents the number of frequencies specified in FREQ.

• If the EnablePolarization property is set to true, the voltage response, RESP, is a MATLAB® struct containing two complex fields, RESP.H and RESP.V. The RESP.H field represents the array’s horizontal polarization response, while RESP.V represents the array’s vertical polarization response. Each field has the dimensions M-by-L. M represents the number of angles specified in the input argument, ANG, while L represents the number of frequencies specified in FREQ.

Data Types: double
Complex Number Support: Yes

## Object Functions

To use an object function, specify the System object as the first input argument. For example, to release system resources of a System object named obj, use this syntax:

release(obj)

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 step Run System object algorithm release Release resources and allow changes to System object property values and input characteristics reset Reset internal states of System object

## Examples

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Calculate and plot the azimuth response of a 4-by-8 uniform rectangular array at directions between $-9{0}^{\circ }$ and $9{0}^{\circ }$ in azimuth at a range of 1 km. Assume the array operating frequency is 300 MHz.

Create the array and the phased.SphericalWavefrontArrayResponse System object™.

array = phased.URA([4,8]);
response = phased.SphericalWavefrontArrayResponse( ...
'SensorArray',array);
ang = -90:90;
rng = 1000.0;
fc = 300e6;

Compute and plot the response as a function of azimuth angle.

resp = response(fc,ang,rng);
plot(ang,abs(resp))
xlabel('Angle (degrees)')
ylabel('Magnitude')
title('Azimuth Response')

Calculate and plot the azimuth response of an 11-element uniform linear array at directions between $-9{0}^{\circ }$ and $9{0}^{\circ }$ in azimuth at a range of 1 km. Create a polarized field using short-dipole antenna elements. Assume the array operating frequency is 300 MHz.

Create the ULA array and the phased.SphericalWavefrontArrayResponse System object™.

antenna = phased.ShortDipoleAntennaElement;
array = phased.ULA(11,'Element',antenna);
response = phased.SphericalWavefrontArrayResponse( ...
'SensorArray',array,'EnablePolarization', ...
true,'WeightsInputPort',true);
ang = -90:90;
rng = 1000.0;
fc = 300e6;
w = taylorwin(11);

Compute and plot the response as a function of azimuth angle.

resp = response(fc,ang,rng,w);
plot(ang,abs(resp.V))
xlabel('Angle (degrees)')
ylabel('Magnitude')
title('Azimuth Response to Vertical Polarization')

## Version History

Introduced in R2021b