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Subband MVDR Beamformer

Subband MVDR (Capon) beamformer

  • Library:
  • Phased Array System Toolbox / Beamforming

Description

The Subband MVDR Beamformer block performs minimum variance distortionless response (MVDR) beamforming on wideband signals. Signals are decomposed into frequency subbands and narrowband MVDR beamforming is performed in each band. The resulting subband signals are summed to form the output signal. MVDR beamforming preserves signal power in a given direction while suppressing interference and noise from other directions. The MVDR beamformer is also called the Capon beamformer.

Ports

Input

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Input signal, specified as an M-by-N matrix, where M is the number of samples in the data, and N is the number of array elements.

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.

Data Types: double
Complex Number Support: Yes

Input signal, specified as an M-by-N matrix, where M is the number of samples in the data, and N is the number of array elements.

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.

Dependencies

To enable this port, select the Enable training data input check box.

Data Types: double
Complex Number Support: Yes

Beamforming direction, specified as a 2-by-L real-valued matrix, where L is the number of beamforming directions. Each column takes the form of [AzimuthAngle;ElevationAngle]. Angle units are in degrees. The azimuth angle must lie between –180° and 180°, inclusive, and the elevation angle must lie between –90° and 90°, inclusive. Angles are defined with respect to the local coordinate system of the array.

Dependencies

To enable this port, set the Source of beamforming direction parameter to Input port.

Data Types: double

Output

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Beamformed output, returned as an M-by-L complex-valued matrix. The quantity M is the number of signal samples and L is the number of desired beamforming directions specified by the Beamforming direction parameter or from the Ang port.

Data Types: double
Complex Number Support: Yes

Subband center frequencies, returned as K-by-1 real-valued column vector. The quantity K is the number of subbands specified by the Number of subbands property.

Dependencies

To enable this port, select the Enable subband center frequencies output checkbox.

Data Types: double

Beamformed weights, returned as an N-by-L complex-valued matrix. The quantity N is the number of array elements. When the Specify sensor array as parameter is set to Partitioned array or Replicated subarray, N represents the number of subarrays. L is the number of desired beamforming directions specified in the Ang port or by the Beamforming direction (deg) property. There is one set of weights for each beamforming direction.

Dependencies

To enable this port, select the Enable weights output checkbox.

Data Types: double
Complex Number Support: Yes

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 return by physconst('LightSpeed').

Specify the operating frequency of the system as a positive scalar. Units are in Hz.

Select this parameter to inherit the sample rate from upstream blocks. Otherwise, specify the sample rate using the Sample rate (Hz) parameter.

Data Types: Boolean

Specify the signal sampling rate as a positive scalar. Units are in Hz.

Dependencies

To enable this parameter, clear the Inherit sample rate parameter.

Data Types: double

Number of processing subbands, specified as a positive integer.

Example: 128

Specify the diagonal loading factor as a nonnegative scalar. Diagonal loading is a technique used to achieve robust beamforming performance, especially when the sample support is small.

Select this check box to specify additional training data via the input port XT. To use the input signal as the training data, clear the check box which removes the port.

Source of beamforming direction, specified as Property or Input port. When you set Source of beamforming direction to Property, you then set the direction using the Beamforming direction (deg) parameter. When you select Input port, the direction is determined by the input to the Ang port.

Beamforming directions, specified as a 2-by-L real-valued matrix, where L is the number of beamforming directions. Each column takes the form [AzimuthAngle;ElevationAngle]. Angle units are in degrees. The azimuth angle must lie between –180° and 180°. The elevation angle must lie between –90° and 90°. Angles are defined with respect to the local coordinate system of the array.

Dependencies

To enable this parameter, set the Source of beamforming direction parameter to Property.

Select this checkbox to obtain the beamformer weights from the output port, W.

Select this check box to obtain the center frequencies of each subband via the output port, Freq.

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 than 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.

Data Types: char

Sensor Arrays Tab

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

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

  • Partitioned array — use the block parameters to specify the array.

  • Replicated subarray — use the block parameters to specify the array.

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

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.

Element Parameters

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

  • Isotropic Antenna

  • Cosine Antenna

  • Custom 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.

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.

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

Dependencies

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

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

Dependencies

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

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.

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 Element type 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°, inclusive, and be in strictly increasing order.

Dependencies

To enable this parameter, set Element type 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. The quantity Q equals the length of the vector specified by Elevation angles (deg). The quantity P equals length of the vector specified by Azimuth angles (deg). The quantity L equal 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. The quantity Q equals the length of the vector specified by Elevation angles (deg). The quantity P equals length of the vector specified by Azimuth angles (deg). The quantity L equal 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.

Response frequencies of the custom microphone of the polar pattern, specified as a real scalar or 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 is 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). 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 also 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.

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.

When you set Specify sensor array as to Replicated subarray, this parameter applies to each subarray.

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].

  • When you set Specify sensor array as to Replicated subarray, this parameter applies to each subarray.

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 supports only 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 rows and columns.

  • When you set Specify sensor array as to Replicated subarray, this parameter applies to each subarray.

For a URA, array elements are indexed from top to bottom along a column, and continues 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 Geometryto 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.

When you set Specify sensor array as to Replicated subarray, this parameter applies to each subarray.

Dependencies

To enable this parameter set Geometry to Conformal Array.

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.

When you set Specify sensor array as to Replicated subarray, this parameter applies to each subarray.

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.

Dependencies

To enable this parameter, set Geometry to Conformal Array.

Element tapering, specified 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 sidelobes 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.

When you set Specify sensor array as to Replicated subarray, this parameter applies to each subarray.

Specify the subarray selection as an M-by-N matrix. M is the number of subarrays and N is the total number of elements in the array. Each row of the matrix corresponds to a subarray and each entry in the row indicates whether or not an element belongs to the subarray. When the entry is zero, the element does not belong the subarray. A nonzero entry represents a complex-valued weight applied to the corresponding element. Each row must contain at least one nonzero entry.

The phase center of each subarray is located at the subarray geometric center. The subarray geometric center depends on the Subarray definition matrix and Geometry parameters.

Dependencies

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

Subarray steering method, specified as one of

  • None

  • Phase

  • Time

  • Custom

Selecting Phase or Time opens the Steer input port on the Narrowband Receive Array, Narrowband Transmit Array, Wideband Receive Array, Wideband Transmit Array blocks, Constant Gamma Clutter, and GPU Constant Gamma Clutter blocks.

Selecting Custom opens the WS input port on the Narrowband Receive Array, Narrowband Transmit Array, Wideband Receive Array, Wideband Transmit Array blocks, Constant Gamma Clutter, and GPU Constant Gamma Clutter blocks.

Dependencies

To enable this parameter, set Specify sensor array as to Partitioned array or Replicated subarray.

Operating frequency of subarray steering phase shifters, specified as a positive real-valued scalar. Units are Hz.

Dependencies

To enable this parameter, set Sensor array to Partitioned array or Replicated subarray and set Subarray steering method to Phase.

Subarray steering phase shift quantization bits, specified as a non-negative integer. A value of zero indicates that no quantization is performed.

Dependencies

To enable this parameter, set Sensor array to Partitioned array or Replicated subarray and set Subarray steering method to Phase.

Specify the layout of replicated subarrays as Rectangular or Custom.

  • When you set this parameter to Rectangular, use the Grid size and Grid spacing parameters to place the subarrays.

  • When you set this parameter to Custom, use the Subarray positions (m) and Subarray normals parameters to place the subarrays.

Dependencies

To enable this parameter, set Sensor array to Replicated subarray

Rectangular subarray grid size, specified as a single positive integer or a positive integer-valued 1-by-2 row vector.

If Grid size is an integer scalar, the array has an equal number of subarrays in each row and column. If Grid size is a 1-by-2 vector of the form [NumberOfRows, NumberOfColumns], the first entry is the number of subarrays along each column. The second entry is the number of subarrays in each row. A row is along the local y-axis, and a column is along the local z-axis. The figure here shows how you can replicate a 3-by-2 URA subarray using a Grid size of [1,2].

Dependencies

To enable this parameter, set Sensor array to Replicated subarray and Subarrays layout to Rectangular.

The rectangular grid spacing of subarrays, specified as a positive, real-valued scalar, a 1-by-2 row vector of positive, real-values, or Auto. Units are in meters.

  • If Grid spacing is a scalar, the spacing along the row and the spacing along the column is the same.

  • If Grid spacing is a 1-by-2 row vector, the vector has the form [SpacingBetweenRows,SpacingBetweenColumn]. The first entry specifies the spacing between rows along a column. The second entry specifies the spacing between columns along a row.

  • If Grid spacing is set to Auto, replication preserves the element spacing of the subarray for both rows and columns while building the full array. This option is available only when you specify Geometry as ULA or URA.

Dependencies

To enable this parameter, set Sensor array to Replicated subarray and Subarrays layout to Rectangular.

Positions of the subarrays in the custom grid, specified as a real 3-by-N matrix, where N is the number of subarrays in the array. Each column of the matrix represents the position of a single subarray in the array local coordinate system. The coordinates are expressed in the form [x; y; z]. Units are in meters.

Dependencies

To enable this parameter, set Sensor array to Replicated subarray and Subarrays layout to Custom.

Specify the normal directions of the subarrays in the array. This parameter value is a 2-by-N matrix, where N is the number of subarrays in the array. Each column of the matrix specifies the normal direction of the corresponding subarray, in the form [azimuth;elevation]. Angle units are in degrees. Angles are defined with respect to the local coordinate system.

You can use the Subarray positions and Subarray normals parameters to represent any arrangement in which pairs of subarrays 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.

Dependencies

To enable this parameter, set the Sensor array parameter to Replicated subarray and the Subarrays layout to Custom.

Introduced in R2015b

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