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Beamspace ESPRIT DOA

Beamspace ESPRIT direction of arrival (DOA) estimator for ULA

  • Library:
  • Phased Array System Toolbox / Direction of Arrival

  • Beamspace ESPRIT DOA block

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.

Ports

Input

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Input signal, specified as an N-by-M complex-valued matrix. N corresponds to the number of samples. M corresponds to the number data channels.

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.

Data Types: single | double

Output

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Estimated broadside direction-of-arrival angles, returned as an M-by-1 real-valued vector. Units are in degrees.

Data Types: double

Parameters

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Main Tab

Signal propagation speed, specified as a real-valued positive scalar. The default value of the speed of light is the value returned by physconst('LightSpeed'). Units are in meters per second.

Example: 3e8

Data Types: double

System operating frequency, specified as a positive scalar. Units are in Hz.

Specify the number of signals as a positive integer scalar.

Specify the amount of averaging 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 in the ULA.

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

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

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.

Specify the number of beams as a positive scalar integer. The lower the number of beams, the greater the reduction in computational cost.

Dependencies

This parameter appears when you set Source of number of beams to Property.

Block simulation, 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 with generated code than in interpreted execution. You can run repeated executions without recompiling, but if you change any block parameters, then the block automatically recompiles before execution.

This table shows how the Simulate using parameter affects the overall simulation behavior.

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

Acceleration Modes

Block SimulationSimulation Behavior
NormalAcceleratorRapid Accelerator
Interpreted ExecutionThe block executes using the MATLAB interpreter.The block executes using the MATLAB interpreter.Creates a standalone executable from the model.
Code GenerationThe block is compiled.All blocks in the model are compiled.

For more information, see Choosing a Simulation Mode (Simulink).

Sensor Array Tab

Method to specify array, specified as Array (no subarrays) or MATLAB expression.

  • Array (no subarrays) — use the block parameters to specify the array.

  • MATLAB expression — create the array using a MATLAB expression.

Element Parameters

Antenna or microphone type, specified as one of the following:

  • Isotropic Antenna

  • Cardioid Antenna

  • Cosine Antenna

  • Custom Antenna

  • Gaussian Antenna

  • Sinc Antenna

  • Omni Microphone

  • Custom Microphone

Specify the operating frequency range of the antenna or microphone element as a 1-by-2 row vector in the form [LowerBound,UpperBound]. The element has no response outside this frequency range. Frequency units are in Hz.

Dependencies

To enable this parameter, set Element type to Isotropic Antenna, Cosine Antenna, or Omni Microphone.

Select this check box to baffle the back response of the element. When back baffled, the responses at all azimuth angles beyond ±90° from broadside are set to zero. The broadside direction is defined as 0° azimuth angle and 0° elevation angle.

Dependencies

To enable this check box, set Element type to Isotropic Antenna or Omni Microphone.

Dependencies

To enable this parameter, set Element type to Cardioid Antenna.

Specify the exponents of the cosine pattern as a nonnegative scalar or a real-valued 1-by-2 matrix of nonnegative values. When Exponent of cosine pattern is a 1-by-2 vector, the first element is the exponent in the azimuth direction and the second element is the exponent in the elevation direction. When you set this parameter to a scalar, both the azimuth direction and elevation direction cosine patterns are raised to the same power.

Dependencies

To enable this parameter, set Element type to Cosine Antenna.

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

Dependencies

To enable this parameter, set Element type to Custom Antenna or Custom Microphone. Use Frequency responses (dB) to set the responses at these frequencies.

Frequency response of a custom antenna or custom microphone for the frequencies defined by the Operating frequency vector (Hz) parameter. The dimensions of Frequency responses (dB) must match the dimensions of the vector specified by the Operating frequency vector (Hz) parameter.

Dependencies

To enable this parameter, set Element type to Custom Antenna or Custom Microphone.

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.

Dependencies

To enable this parameter, set Element type to Custom Antenna.

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. Azimuth angles must lie between –180° and 180°, inclusive, and be in strictly increasing order.

Dependencies

To enable this parameter, set the Element type parameter to Custom Antenna and the Input Pattern Coordinate System parameter 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°, inclusive, and be in strictly increasing order.

Dependencies

To enable this parameter, set the Element type parameter to Custom Antenna and the Input Pattern Coordinate System parameter to az-el.

Phi angles of points at which to specify the antenna radiation pattern, specify as a real-valued 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.

Dependencies

To enable this parameter, set the Element type parameter to Custom Antenna and the Input Pattern Coordinate System parameter to phi-theta.

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

Dependencies

To enable this parameter, set the Element type parameter to Custom Antenna and the Input Pattern Coordinate System parameter to phi-theta.

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.

Dependencies

To enable this parameter, set Element type 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 (

Dependencies

To enable this parameter, set Element type to Custom Antenna.

Dependencies

This parameter is enabled when Element type is set to Custom Antenna.

Dependencies

This parameter is enabled when Element type is set to Gaussian Antenna.

Polar pattern microphone response frequencies, specified as a real scalar, or a real-valued, 1-by-L vector. The response frequencies lie within the frequency range specified by the Operating frequency vector (Hz) vector.

Dependencies

To enable this parameter, set Element type set to Custom Microphone.

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

Dependencies

To enable this parameter, set Element type to Custom Microphone.

Specify the magnitude of the custom microphone element polar patterns as an L-by-P matrix. L is the number of frequencies specified in Polar pattern frequencies (Hz). P is the number of 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). 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. The polar pattern is symmetric around the central axis. You can construct the microphone response pattern in 3-D space from the polar pattern.

Dependencies

To enable this parameter, set Element type to Custom Microphone.

ULA Parameters

The number of array elements for ULA arrays, specified as an integer greater than or equal to two.

Example: 11

Data Types: double

Distance between adjacent ULA elements, specified as a positive scalar. Units are in meters.

Example: 1.5

Linear axis direction of ULA, specified as y, x, or z. All ULA array elements are uniformly spaced along this axis in the local array coordinate system.

Dependencies

  • To enable this parameter, set Geometry to ULA.

  • This parameter is also enabled when the block only supports ULA arrays.

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.

Example: [0.5;1;0.5]

Data Types: double
Complex Number Support: Yes

MATLAB expression used to create a ULA array, specified as a valid Phased Array System Toolbox array System object.

Example: phased.ULA('NumElements',13)

Dependencies

To enable this parameter, set Specify sensor array as to MATLAB expression.

Version History

Introduced in R2014b