Frost Beamformer

Frost beamformer

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Libraries:
Phased Array System Toolbox / Beamforming

Description

The Frost Beamformer block implements a Frost beamformer. A Frost beamformer consists of a time-domain MVDR beamformer followed by a bank of FIR filters. The MVDR beamformer steers the beam towards a given direction while the FIR filters preserve the input signal power.

Ports

Input

X — Input signal

M-by-N complex-valued matrix

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 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
Complex Number Support: Yes

XT — Training signal

M-by-N complex-valued matrix

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 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.

Dependencies

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

Data Types: double
Complex Number Support: Yes

Ang — Beamforming direction

2-by-1 real-valued vector

Beamforming direction, specified as a 2-by-1 real-valued vector taking 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

Y — Beamformed output

M-by-1 complex-valued vector

Beamformed output, returned as an M-by-1 complex-valued vector. The quantity M is the number of signal samples.

Data Types: double
Complex Number Support: Yes

W — Beamforming weights

N-by-1 complex-valued vector

Beamformed weights, returned as an N-by-1 complex-valued vector. 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.

Dependencies

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

Data Types: double
Complex Number Support: Yes

Parameters

Main Tab

Signal propagation speed (m/s) — Signal propagation speed

physconst('LightSpeed') (default) | real-valued positive scalar

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

Inherit sample rate — Inherit sample rate from upstream blocks

on (default) | off

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

Sample rate (Hz) — Sampling rate of signal

1e6 (default) | positive real-valued scalar

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

Dependencies

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

Data Types: double

FIR filter length — FIR filter length

1 (default) | positive integer

The length of the FIR filter used to process each sensor element data, specified as a positive integer.

Data Types: double

Diagonal loading factor — Diagonal loading factor for stability

nonnegative scalar

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.

Enable training data input — Enable the use of training data

off (default) | on

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 — Source of beamforming direction

Property (default) | Input 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 direction (deg) — Beamforming direction

2-by-1 real-valued vector

Beamforming direction, specified as a 2-by-1 real-valued vector taking 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.

Enable weights output — Option to output beamformer weights

off (default) | on

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

Simulate using — Block simulation method

Interpreted Execution (default) | Code Generation

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 Simulation	Simulation Behavior
	Normal	Accelerator	Rapid Accelerator
Interpreted Execution	The block executes using the MATLAB interpreter.	The block executes using the MATLAB interpreter.	Creates a standalone executable from the model.
Code Generation	The 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

Sensor Arrays Tab

Specify sensor array as — Method to specify array

Array (no subarrays) (default) | MATLAB expression

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.

Expression — MATLAB expression used to create an array

Phased Array System Toolbox™ array System object

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 type — Array element types

Isotropic Antenna (default) | Cosine Antenna | Custom Antenna | Omni Microphone | Custom Microphone

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

• Isotropic Antenna

• Cosine Antenna

• Custom Antenna

• Omni Microphone

• Custom Microphone

Operating frequency range (Hz) — Operating frequency range of the antenna or microphone element

[0,1e20] (default) | real-valued 1-by-2 row vector

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.

Operating frequency vector (Hz) — Operating frequency range of custom antenna or microphone elements

[0,1e20] (default) | real-valued row vector

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.

Baffle the back of the element — Set back response of an Isotropic Antenna element or an Omni Microphone element to zero

off (default) | on

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.

Exponent of cosine pattern — Exponents of azimuth and elevation cosine patterns

[1.5 1.5] (default) | nonnegative scalar | real-valued 1-by-2 matrix of nonnegative values

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.

Frequency responses (dB) — Antenna and microphone frequency response

[0,0] (default) | real-valued row vector

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.

Input Pattern Coordinate System — Coordinate system of custom antenna pattern

az-el (default) | phi-theta

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.

Azimuth angles (deg) — Azimuth angles of antenna radiation pattern

[-180:180] (default) | real-valued row vector

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.

Elevation angles (deg) — Elevation angles of antenna radiation pattern

[-90:90] (default) | real-valued row vector

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 (deg) — Phi angle coordinates of custom antenna radiation pattern

0:360 | real-valued 1-by-P row vector

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 (deg) — Theta angle coordinates of custom antenna radiation pattern

0:180 | real-valued 1-by-Q row vector

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 pattern (dB) — Magnitude of combined antenna radiation pattern

zeros(181,361) (default) | real-valued Q-by-P matrix | real-valued Q-by-P-by-L array

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 pattern (deg) — Custom antenna radiation phase pattern

zeros(181,361) (default) | real-valued Q-by-P matrix | real-valued Q-by-P-by-L array

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.

MatchArrayNormal — Rotate antenna element to array normal

on (default) | off

Select this check box to rotate the antenna element pattern to align with the array normal. When not selected, the element pattern is not rotated.

When the antenna is used in an antenna array and the Input Pattern Coordinate System parameter is az-el, selecting this check box rotates the pattern so that the x-axis of the element coordinate system points along the array normal. Not selecting uses the element pattern without the rotation.

When the antenna is used in an antenna array and Input Pattern Coordinate System is set to phi-theta, selecting this check box rotates the pattern so that the z-axis of the element coordinate system points along the array normal.

Use the parameter in conjunction with the Array normal parameter of the URA and UCA arrays.

Dependencies

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

Polar pattern frequencies (Hz) — Polar pattern microphone response frequencies

1e3 (default) | real scalar | real-valued 1-by-L row vector

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.

Polar pattern angles (deg) — Polar pattern response angles

[-180:180] (default) | real-valued -by-P row vector

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.

Polar pattern (dB) — Custom microphone polar response

zeros(1,361) (default) | real-valued L-by-P matrix

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

Geometry — Array geometry

ULA (default) | URA | UCA | Conformal Array

Array geometry, specified as one of

• ULA — Uniform linear array

• URA — Uniform rectangular array

• UCA — Uniform circular array

• Conformal Array — arbitrary element positions

Number of elements — Number of array elements

2 for ULA arrays and 5 for UCA arrays (default) | integer greater than or equal to 2

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.

Element spacing (m) — Spacing between array elements

0.5 for ULA arrays and [0.5,0.5] for URA arrays (default) | positive scalar for ULA or URA arrays | 2-element vector of positive values for URA arrays

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.

Array axis — Linear axis direction of ULA

y (default) | x | z

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.

Array size — Dimensions of URA array

[2,2] (default) | positive integer | 1-by-2 vector of positive integers

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.

Element lattice — Lattice of URA element positions

Rectangular (default) | Triangular

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 — Array normal direction

x for URA arrays or z for UCA arrays (default) | y

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 Value	Element Positions and Boresight Directions
x	Array elements lie in the yz-plane. All element boresight vectors point along the x-axis.
y	Array elements lie in the zx-plane. All element boresight vectors point along the y-axis.
z	Array 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 (m) — UCA array radius

0.5 (default) | positive scalar

Radius of UCA array, specified as a positive scalar.

Dependencies

To enable this parameter, set Geometry to UCA.

Element positions (m) — Positions of conformal array elements

[0;0;0] (default) | 3-by-Nmatrix of real values

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

Element normals (deg) — Direction of conformal array element normal vectors

[0;0] | 2-by-1 column vector | 2-by-N matrix

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

Taper — Array element tapers

1 (default) | complex scalar | complex-valued row vector

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