# Beamspace ESPRIT DOA

Beamspace ESPRIT direction of arrival (DOA) estimator for ULA

## Library

Direction of Arrival (DOA)

`phaseddoalib`

## Description

The Beamspace ESPRIT DOA block estimates the direction of arrival of a specified number of narrowband signals incident on a uniform linear array using the estimation of signal parameters via rotational invariance technique (ESPRIT) algorithm in beamspace.

## Parameters

Signal Propagation speed (m/s)

Specify the propagation speed of the signal, in meters per second, as a positive scalar. You can use the function `physconst` to specify the speed of light.

Operating frequency (Hz)

Specify the operating frequency of the system, in hertz, as a positive scalar.

Number of signals

Specify the number of signals as a positive integer scalar.

Spatial smoothing

Specify the amount of averaging, L, used by spatial smoothing to estimate the covariance matrix as a nonnegative integer. Each increase in smoothing handles one extra coherent source, but reduces the effective number of elements by one. The maximum value of this parameter is N – 2, where N is the number of sensors.

Type of least squares method

Specify the least squares method used for ESPRIT as one of `TLS` or `LS` where `TLS` refers to total least squares and `LS`refers to least squares.

Beam fan center direction (deg)

Specify the direction of the center of the beam fan, in degrees, as a real scalar value between –90° and 90°.

Source of number of beams

Specify the source of the number of beams as one of `Auto` or `Property`. If you set this parameter to `Auto`, the number of beams equals N – L, where N is the number of array elements and L is the value of Spatial smoothing.

Number of beams

Specify the number of beams as a positive scalar integer. The lower the number of beams, the greater the reduction in computational cost. This parameter appears when you set Source of number of beams to `Property`.

Simulate using

Block simulation method, specified as `Interpreted Execution` or ```Code Generation```. If you want your block to use the MATLAB® interpreter, choose `Interpreted Execution`. If you want your block to run as compiled code, choose `Code Generation`. Compiled code requires time to compile but usually runs faster.

Interpreted execution is useful when you are developing and tuning a model. The block runs the underlying System object™ in MATLAB. You can change and execute your model quickly. When you are satisfied with your results, you can then run the block using ```Code Generation```. Long simulations run faster than they would in interpreted execution. You can run repeated executions without recompiling. However, if you change any block parameters, then the block automatically recompiles before execution.

When setting this parameter, you must take into account the overall model simulation mode. The table shows how the Simulate using parameter interacts with the overall simulation mode.

When the Simulink® model is in `Accelerator` mode, the block mode specified using Simulate using overrides the simulation mode.

Acceleration Modes

 Block Simulation Simulation Behavior `Normal` `Accelerator` `Rapid Accelerator` `Interpreted Execution` The block executes using the MATLAB interpreter. The block executes using the MATLAB interpreter. Creates a standalone executable from the model. `Code Generation` The block is compiled. All blocks in the model are compiled.

### Array Parameters

Specify sensor array as

Specify a ULA sensor array directly or by using a MATLAB expression.

Types

 `Array (no subarrays)` `MATLAB expression`

Number of elements

Specifies the number of elements in the array as an integer.

Element spacing

Specify the spacing, in meters, between two adjacent elements in the array.

Array axis

This parameter appears when the Geometry parameter is set to `ULA` or when the block only supports a ULA array geometry. Specify the array axis as `x`, `y`, or `z`. All ULA array elements are uniformly spaced along this axis in the local array coordinate system.

Taper

Tapers, also known as element weights, are applied to sensor elements in the array. Tapers are used to modify both the amplitude and phase of the transmitted or received data.

Specify element tapering as a complex-valued scalar or a complex-valued 1-by-N row vector. In this vector, N represents the number of elements in the array. If Taper is a scalar, the same weight is applied to each element. If Taper is a vector, a weight from the vector is applied to the corresponding sensor element. A weight must be applied to each element in the sensor array.

Expression

A valid MATLAB expression containing a constructor for a uniform linear array, for example, `phased.ULA`.

### Sensor Array Tab: Element Parameters

Element type

Specify antenna or microphone type as

• `Isotropic Antenna`

• `Cosine Antenna`

• `Custom Antenna`

• `Omni Microphone`

• `Custom Microphone`

Exponent of cosine pattern

This parameter appears when you set Element type to ```Cosine Antenna```.

Specify the exponent of the cosine pattern as a scalar or a 1-by-2 vector. You must specify all values as non-negative real numbers. When you set Exponent of cosine pattern to a scalar, both the azimuth direction cosine pattern and the elevation direction cosine pattern are raised to the specified value. When you set Exponent of cosine pattern to a 1-by-2 vector, the first element is the exponent for the azimuth direction cosine pattern and the second element is the exponent for the elevation direction cosine pattern.

Operating frequency range (Hz)

This parameter appears when Element type is set to `Isotropic Antenna`, `Cosine Antenna`, or `Omni Microphone`.

Specify the operating frequency range, in hertz, of the antenna element as a 1-by-2 row vector in the form `[LowerBound,UpperBound]`. The antenna element has no response outside the specified frequency range.

Operating frequency vector (Hz)

This parameter appears when Element type is set to `Custom Antenna` or `Custom Microphone`.

Specify the frequencies, in Hz, at which to set the antenna and microphone frequency responses as a 1-by-L row vector of increasing values. Use Frequency responses to set the frequency responses. The antenna or microphone element has no response outside the frequency range specified by the minimum and maximum elements of Operating frequency vector (Hz).

Frequency responses (dB)

This parameter appears when Element type is set to `Custom Antenna` or `Custom Microphone`.

Specify this parameter as the frequency response of an antenna or microphone, in decibels, for the frequencies defined by Operating frequency vector (Hz). Specify Frequency responses (dB) as a 1-by-L vector matching the dimensions of the vector specified in Operating frequency vector (Hz).

Input Pattern Coordinate System

Coordinate system of custom antenna pattern, specified `az-el` or `phi-theta`. When you specify `az-el`, use the Azimuth angles (deg) and Elevations angles (deg) parameters to specify the coordinates of the pattern points. When you specify `phi-theta`, use the Phi angles (deg) and Theta angles (deg) parameters to specify the coordinates of the pattern points.

Azimuth angles (deg)

This parameter appears when Element type is set to `Custom Antenna` and the Input Pattern Coordinate System parameter is set to `az-el`.

Specify the azimuth angles at which to calculate the antenna radiation pattern as a 1-by-P row vector. P must be greater than 2. Angle units are in degrees. Azimuth angles must lie between –180° and 180° and be in strictly increasing order.

Elevation angles (deg)

This parameter appears when Element type is set to `Custom Antenna` and the Input Pattern Coordinate System parameter is set to `az-el`.

Specify the elevation angles at which to compute the radiation pattern as a 1-by-Q vector. Q must be greater than 2. Angle units are in degrees. Elevation angles must lie between –90° and 90° and be in strictly increasing order.

Phi Angles (deg)

This parameter appears when Element type is set to `Custom Antenna` and the Input Pattern Coordinate System parameter is set to `phi-theta`.

Phi angles of points at which to specify the antenna radiation pattern, specify as a 1-by-P row vector. P must be greater than 2. Angle units are in degrees. Phi angles must lie between 0° and 360° and be in strictly increasing order.

Theta Angles (deg)

This parameter appears when Element type is set to `Custom Antenna` and the Input Pattern Coordinate System parameter is set to `phi-theta`.

Theta angles of points at which to specify the antenna radiation pattern, specify as a 1-by-Q row vector. Q must be greater than 2. Angle units are in degrees. Theta angles must lie between 0° and 180° and be in strictly increasing order.

Magnitude pattern (dB)

This parameter appears when the Element type is set to `Custom Antenna`.

Magnitude of the combined antenna radiation pattern, specified as a Q-by-P matrix or a Q-by-P-by-L array.

• When the Input Pattern Coordinate System parameter is set to `az-el`, Q equals the length of the vector specified by the Elevation angles (deg) parameter and P equals the length of the vector specified by the Azimuth angles (deg) parameter.

• When the Input Pattern Coordinate System parameter is set to `phi-theta`, Q equals the length of the vector specified by the Theta Angles (deg) parameter and P equals the length of the vector specified by the Phi Angles (deg) parameter.

The quantity L equals the length of the Operating frequency vector (Hz).

• If this parameter is a Q-by-P matrix, the same pattern is applied to all frequencies specified in the Operating frequency vector (Hz) parameter.

• If the value is a Q-by-P-by-L array, each Q-by-P page of the array specifies a pattern for the corresponding frequency specified in the Operating frequency vector (Hz) parameter.

Phase pattern (dB)

This parameter appears when the Element type is set to `Custom Antenna`.

Phase of the combined antenna radiation pattern, specified as a Q-by-P matrix or a Q-by-P-by-L array.

• When the Input Pattern Coordinate System parameter is set to `az-el`, Q equals the length of the vector specified by the Elevation angles (deg) parameter and P equals the length of the vector specified by the Azimuth angles (deg) parameter.

• When the Input Pattern Coordinate System parameter is set to `phi-theta`, Q equals the length of the vector specified by the Theta Angles (deg) parameter and P equals the length of the vector specified by the Phi Angles (deg) parameter.

The quantity L equals the length of the Operating frequency vector (Hz).

• If this parameter is a Q-by-P matrix, the same pattern is applied to all frequencies specified in the Operating frequency vector (Hz) parameter.

• If the value is a Q-by-P-by-L array, each Q-by-P page of the array specifies a pattern for the corresponding frequency specified in the Operating frequency vector (Hz) parameter.

• If this parameter is a Q-by-P matrix, the same pattern is applied to all frequencies specified in the Operating frequency vector (Hz) parameter.

• If the value is a Q-by-P-by-L array, each Q-by-P page of the array specifies a pattern for the corresponding frequency specified in the Operating frequency vector (Hz) parameter.

MatchArrayNormal

This parameter appears when the Element type is set to `Custom Antenna`.

Select this check box to rotate the antenna element pattern to align with the array normal. When not selected, the element pattern is not rotated.

When the antenna is used in an antenna array and the Input Pattern Coordinate System parameter is `az-el`, selecting this check box rotates the pattern so that the x-axis of the element coordinate system points along the array normal. Not selecting uses the element pattern without the rotation.

When the antenna is used in an antenna array and Input Pattern Coordinate System is set to `phi-theta`, selecting this check box rotates the pattern so that the z-axis of the element coordinate system points along the array normal.

Use the parameter in conjunction with the Array normal parameter of the `URA` and `UCA` arrays.

Polar pattern frequencies (Hz)

This parameter appears when the Element type is set to `Custom Microphone`.

Specify the measuring frequencies of the polar patterns as a 1-by-M vector. The measuring frequencies lie within the frequency range specified by the Operating frequency vector (Hz) parameter. Frequency units are in Hz.

Polar pattern angles (deg)

This parameter appears when Element type is set to `Custom Microphone`.

Specify the measuring angles of the polar patterns, as a 1-by-N vector. The angles are measured from the central pickup axis of the microphone, and must be between –180° and 180°, inclusive.

Polar pattern (dB)

This parameter appears when Element type is set to `Custom Microphone`.

Specify the magnitude of the microphone element polar pattern as an M-by-N matrix. M is the number of measuring frequencies specified in Polar pattern frequencies (Hz). N is the number of measuring angles specified in Polar pattern angles (deg). Each row of the matrix represents the magnitude of the polar pattern measured at the corresponding frequency specified in Polar pattern frequencies (Hz) and all angles specified in Polar pattern angles (deg). Assume that the pattern is measured in the azimuth plane. In the azimuth plane, the elevation angle is 0° and the central pickup axis is 0° degrees azimuth and 0° degrees elevation. Assume that the polar pattern is symmetric around the central axis. You can construct the microphone’s response pattern in 3-D space from the polar pattern.

Baffle the back of the element

This check box appears only when the Element type parameter is set to `Isotropic Antenna` or `Omni Microphone`.

Select this check box to baffle the back of the antenna element. In this case, the antenna responses to all azimuth angles beyond ±90° from broadside are set to zero. Define the broadside direction as 0° azimuth angle and 0° elevation angle.

## Ports

Note

The block input and output ports correspond to the input and output parameters described in the `step` method of the underlying System object. See link at the bottom of this page.

PortDescriptionSupported Data Types
`In`

Input signal.

The size of the first dimension of the input matrix can vary to simulate a changing signal length. A size change can occur, for example, in the case of a pulse waveform with variable pulse repetition frequency.

Double-precision floating point
`Ang`

Estimated DOA angles.

Double-precision floating point