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MVDR Spectrum

Minimum variation distortionless response (MVDR) spatial spectrum estimator

  • MVDR Spectrum block

Libraries:
Phased Array System Toolbox / Direction of Arrival

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 calculates 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.

Ports

Input

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Input data, specified as a complex-valued matrix whose columns correspond to channels. Rows correspond to samples.

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: double | single

Output

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Spatial spectrum, returned as a real-valued matrix representing the magnitude of the estimated 2-D spatial spectrum. The row dimension of Y is equal to the number of angles in the Elevation scan angles (deg) parameter and the column dimension of Y is equal to the number of angles in the Azimuth scan angles (deg) parameter.

Data Types: double

Estimated direction of arrival, returned as a two-row real-valued matrix where the first row represents estimated azimuth angles and the second row represents estimated elevation angles. Units are in degrees.

Dependencies

To enable this port, select the Enable DOA output check box.

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.

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.

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

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.

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.

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

Specify the expected number of signals for DOA estimation as a positive scalar integer.

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).

Programmatic Use

Block Parameter:SimulateUsing
Type:enum
Values:Interpreted Execution, Code Generation
Default:Interpreted Execution

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

Example: phased.URA('Size',[5,3])

Dependencies

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

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.

Array Parameters

Array geometry, specified as one of

  • ULA — Uniform linear array

  • URA — Uniform rectangular array

  • UCA — Uniform circular array

  • Conformal Array — arbitrary element positions

The number of array elements for ULA or UCA arrays, specified as an integer greater than or equal to 2.

Dependencies

To enable this parameter, set Geometry to ULA or UCA.

Spacing between adjacent array elements:

  • ULA — specify the spacing between two adjacent elements in the array as a positive scalar.

  • URA — specify the spacing as a positive scalar or a 1-by-2 vector of positive values. If Element spacing (m) is a scalar, the row and column spacings are equal. If Element spacing (m) is a vector, the vector has the form [SpacingBetweenArrayRows,SpacingBetweenArrayColumns].

Dependencies

To enable this parameter, set Geometry to ULA or URA.

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.

Dimensions of a URA array, specified 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 elements in each row and column.

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

Dependencies

To enable this parameter, set Geometry to URA.

Lattice of URA element positions, specified 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.

Dependencies

To enable this parameter, set Geometry to URA.

Array normal direction, specified as x, y, or z.

Elements of planar arrays lie in a plane orthogonal to the selected array normal direction. Element boresight directions point along the array normal direction.

Array Normal Parameter ValueElement Positions and Boresight Directions
xArray elements lie in the yz-plane. All element boresight vectors point along the x-axis.
yArray elements lie in the zx-plane. All element boresight vectors point along the y-axis.
zArray elements lie in the xy-plane. All element boresight vectors point along the z-axis.

Dependencies

To enable this parameter, set Geometry to URA or UCA.

Radius of UCA array, specified as a positive scalar.

Dependencies

To enable this parameter, set Geometry to UCA.

Positions of the elements in a conformal array, specified as a 3-by-N matrix of real values, where N is the number of elements in the conformal array. Each column of this matrix represents the position [x;y;z]of an array element in the array local coordinate system. The origin of the local coordinate system is (0,0,0). Units are in meters.

Dependencies

To enable this parameter set Geometry to Conformal Array.

Data Types: double

Direction of element normal vectors in a conformal array, specified as a 2-by-1 column vector or a 2-by-N matrix. N indicates the number of elements in the array. If the parameter value 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 the parameter value is a 2-by-1 column vector, the same pointing direction is used for all array elements.

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. The transformations can combine translation, azimuth rotation, and elevation rotation. However, you cannot use transformations that require rotation about the normal direction.

To enable this parameter, set Geometry to Conformal Array.

Data Types: double

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.

Also known as element weights, tapers multiply the array element responses. Tapers modify both amplitude and phase of the response to reduce side lobes or steer the main response axis.

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. The number of weights must match the number of elements of the array.

Data Types: double

Version History

Introduced in R2014b