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MVDR Spectrum

Minimum variation distortionless response (MVDR) spatial spectrum estimator

Library

Direction of Arrival (DOA)

phaseddoalib

Description

The narrowband MVDR Spectrum block estimates the spatial spectrum of incoming narrowband signals by scanning a range of azimuth and elevation angles using an MVDR conventional beamformer. The block optionally calculate the direction of arrival of a specified number of signals by estimating the peaks of the spectrum. This estimator is also referred to as a Capon estimator.

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 bits in phase shifters

The number of bits used to quantize the phase shift component of beamformer or steering vector weights. Specify the number of bits as a non-negative integer. A value of zero indicates that no quantization is performed.

Forward-backward averaging

Select this parameter to use forward-backward averaging to estimate the covariance matrix for sensor arrays with a conjugate symmetric array manifold.

Azimuth scan angles (deg)

Specify the azimuth scan angles, in degrees, as a real vector. The angles must be between –180° and 180°, inclusive. You must specify the angles in ascending order.

Elevation scan angles (deg)

Specify the elevation scan angles, in degrees, as a real vector or scalar. The angles must be between –90° and 90°, inclusive. You must specify the angles in an ascending order.

Enable DOA output

Select this parameter to output the signals directions of arrival (DOA) through the Ang output port. Selecting this parameter enables the Number of signals parameter.

Number of signals

Specify the number of signals for DOA estimation as a positive scalar integer. This parameter appears when you select the Enable DOA output check box.

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 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) from the Simulink documentation.

Array Parameters

Specify sensor array as

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

Types

Array (no subarrays)
MATLAB expression

Geometry

Specify the array geometry as one of the following:

  • ULA — Uniform linear array

  • URA — Uniform rectangular array

  • UCA — Uniform circular array

  • Conformal Array — arbitrary element positions

Number of elements

Number of array elements.

Number of array elements, specified as a positive integer. This parameter appears when the Geometry is set to ULA or UCA. If Sensor Array has a Replicated subarray option, this parameter applies to the sub-array.

Array size

This parameter appears when Geometry is set to URA. When Sensor Array is set to Replicated subarray, this parameter applies to the subarrays.

Specify the size of the array as a positive integer or 1-by-2 vector of positive integers.

  • If Array size is a 1-by-2 vector, the vector has the form [NumberOfArrayRows,NumberOfArrayColumns].

  • If Array size is an integer, the array has the same number of rows and columns.

For a URA, elements are indexed from top to bottom along a column and continuing to the next columns from left to right. In this figure, an Array size of [3,2] produces an array of three rows and two columns.

Element spacing (m)

This parameter appears when Geometry is set to ULA or URA. When Sensor Array has the Replicated subarray option, this parameter applies to the subarrays.

  • For a ULA, specify the spacing, in meters, between two adjacent elements in the array as a scalar.

  • For a URA, specify the element spacing of the array, in meters, as a 1-by-2 vector or a scalar. If Element spacing is a 1-by-2 vector, the vector has the form [SpacingBetweenRows,SpacingBetweenColumns]. For a discussion of these quantities, see phased.URA. If Element spacing is a scalar, the spacings between rows and columns are equal.

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.

Array normal,

This parameter appears when you set Geometryto URA or UCA. Specify the Array normal as x, y, or z. All URA and UCA array elements are placed in the yz, zx, or xyplanes, respectively, of the array coordinate system.

Radius of UCA (m)

Radius of a uniform circular array specified as a positive scalar. Units are meters.

This parameter appears when the Geometry is set to UCA.

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.

This parameter applies to all array types, but when you set Sensor Array to Replicated subarray, this parameter applies to subarrays.

  • For a ULA or UCA, 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.

  • For a URA, specify element tapering as a complex-valued scalar or complex-valued M-by-N matrix. In this matrix, M is the number of elements along the z-axis, and N is the number of elements along the y-axis. M and N correspond to the values of [NumberofArrayRows,NumberOfArrayColumns] in the Array size matrix. If Taper is a scalar, the same weight is applied to each element. If Taper is a matrix, a weight from the matrix is applied to the corresponding sensor element. A weight must be applied to each element in the sensor array.

  • For a Conformal Array, specify element tapering as a complex-valued scalar or complex-valued 1-by-N vector. In this vector, N is the number of elements in the array as determined by the size of the Element positions vector. If Taper is a scalar, the same weight is applied to each element. If the value of 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.

Element lattice

This parameter appears when Geometry is set to URA. When Sensor Array is set to Replicated subarray, this parameter applies to the subarray.

Specify the element lattice as Rectangular or Triangular

  • Rectangular — Aligns all the elements in row and column directions.

  • Triangular— Shifts the even-row elements of a rectangular lattice toward the positive-row axis direction. The displacement is one-half the element spacing along the row dimension.

Element positions (m)

This parameter appears when Geometry is set to Conformal Array. When Sensor Array is set to Replicated subarray, this parameter applies to subarrays.

Specify the positions of conformal array elements as a 3-by-N matrix, where N is the number of elements in the conformal array. Each column of Element positions (m) represents the position of a single element, in the form [x;y;z], in the array’s local coordinate system. The local coordinate system has its origin at an arbitrary point. Units are in meters.

Element normals (deg)

This parameter appears when Geometry is set to Conformal Array. When Sensor Array is set to Replicated subarray, this parameter applies to subarrays.

Specify the normal directions of the elements in a conformal array as a 2-by-N matrix or a 2-by-1 column vector in degrees. The variable N indicates the number of elements in the array. If Element normals (deg) is a matrix, each column specifies the normal direction of the corresponding element in the form [azimuth;elevation], with respect to the local coordinate system. The local coordinate system aligns the positive x-axis with the direction normal to the conformal array. If Element normals (deg) is a 2-by-1 column vector, the vector specifies the same pointing direction for all elements in the array.

You can use the Element positions (m) and Element normals (deg) parameters to represent any arrangement in which pairs of elements differ by certain transformations. You can combine translation, azimuth rotation, and elevation rotation transformations. However, you cannot use transformations that require rotation about the normal.

Expression

A valid MATLAB expression containing an array constructor, for example, phased.URA.

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).

Azimuth angles (deg)

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

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.

Radiation pattern (dB)

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

The magnitude in db of the combined polarized antenna radiation pattern specified as a Q-by-P matrix or a Q-by-P-by-L array. The value of Q must match the value of Q specified by Elevation angles (deg). The value of P must match the value of P specified by Azimuth angles (deg_. The value of L must match the value of L specified by Operating frequency vector (Hz).

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 byOperating frequency vector (Hz). 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 this input matrix can vary to simulate a changing signal length, such as a pulse waveform with variable pulse repetition frequency.

Double-precision floating point
Y

Spatial spectrum.

Double-precision floating point
Ang

Estimated DOA angle.

Double-precision floating point

Introduced in R2014b

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