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SMI Beamformer

Sample matrix inversion (SMI) beamformer

Library

Space-Time Adaptive Processing

phasedstaplib

Description

The SMI Beamformer block implements a sample matrix inversion (SMI) space-time adaptive beamformer employing the sample space-time covariance matrix.

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.

Pulse repetition frequency (Hz)

Specify the pulse repetition frequency, PRF, as a scalar. Units for PRF are Hertz. This parameter should be set to the same value as used in any Waveforms library block.

Specify direction as

Specify whether the targeting direction for this STAP processor block comes from a block parameter or via an input port. Values of this parameter are

Property
  • For the ADPCA Canceller and DPCA Canceller blocks, targeting direction is specified using Receiving mainlobe direction (deg).

  • For the SMI Beamformer block, targeting direction is specified using Targeting direction.

These parameters appear only when the Specify direction as parameter is set to Property.
Input portEnter the targeting directions using the Ang port. This port appears only when Specify direction as is set to Input port.
Targeting direction (deg)

Specify the targeting direction of the SMI processor as a column vector of length 2. The direction is specified in the format of [AzimuthAngle; ElevationAngle] (in degrees). Azimuth angle should be between –180° and 180°. Elevation angle should be between –90° and 90°. This parameter appear only when you set Specify direction as to Property.

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.

Specify targeting Doppler as

Specify whether targeting Doppler values for the STAP processor comes from the Targeting Doppler (Hz) parameter of this block or via an input port. For the ADPCA Cancellerand DPCA Canceller blocks, this parameter appears only when the Output pre-Doppler result check box is cleared. Values of this parameter are

PropertyTargeting Doppler values are specified by the Targeting Doppler parameter of the block. The Targeting Doppler parameter appears only when Specify targeting Doppler as is set to Property.
Input portTargeting Doppler values are entered using the Dop port. This port appears only when Specify targeting Doppler as is set to Input port.
Targeting Doppler (Hz)

Specify the targeting Doppler of the STAP processor as a scalar. This parameter appears only when you set Specify targeting Doppler as to Property and when, for the ADPCA Cancellerand DPCA Canceller blocks only, the Output pre-Doppler result check box is cleared.

Number of guard cells

Specify the number of guard cells used in the training as an even integer. This parameter specifies the total number of cells on both sides of the cell under test.

Number of training cells

Specify the number of training cells used in training as an even integer. Whenever possible, the training cells are equally divided into regions before and after the test cell.

Enable weights output

Select this check box to obtain the beamformer weights from the output port W.

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

Sensor element or sensor array specified. A sensor array can also contain subarrays or as a partitioned array. This parameter can also be expressed as a MATLAB expression.

Types

Array (no subarrays)
Partitioned array
Replicated subarray
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.

Subarray definition matrix

This parameter appears when Specify sensor array as is set to Partitioned array.

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 its geometric center. Subarray definition matrix and Geometry determine the geometric center.

Subarray steering method

This parameter appears when the Specify sensor array as parameter is set to Partitioned array or Replicated subarray.

Specify the subarray steering method as either

  • 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.

Phase shifter frequency (Hz)

This parameter appears when you set Sensor array to Partitioned array or Replicated subarray and you set Subarray steering method to Phase.

Specify the operating frequency, in hertz, of phase shifters to perform subarray steering as a positive scalar.

Number of bits in phase shifters

This parameter appears when you set Sensor array to Partitioned array or Replicated subarray and you set Subarray steering method to Phase.

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.

Subarrays layout

This parameter appears when you set Sensor array to Replicated subarray.

Specify the layout of the replicated subarrays as Rectangular or Custom.

Grid size

This parameter appears when you set Sensor array to Replicated subarray and Subarrays layout to Rectangular.

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].

Grid spacing

This parameter appears when you set Sensor array to Replicated subarray and Subarrays layout to Rectangular.

Specify the rectangular grid spacing of subarrays as a real-valued positive scalar, a 1-by-2 row vector, or Auto. Grid spacing units are expressed 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.

Subarray positions (m)

This parameter appears when you set Sensor array to Replicated subarray and Subarrays layout to Custom.

Specify the positions of the subarrays in the custom grid as a 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 meters, in the array’s local coordinate system. The coordinates are expressed in the form [x; y; z].

Subarray normals

This parameter appears when you set the Sensor array parameter to Replicated subarray and the 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]. Each angle is in degrees and is defined in 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.

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
X

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
Ang

Targeting direction

Double-precision floating point
Dop

Targeting Doppler frequency

Double-precision floating point
Idx

Range cell index

Double-precision floating point
W

Processing weights

Double-precision floating point
Y

Doppler output

Double-precision floating point

Introduced in R2014b

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