Engee documentation

MVDR Beamformer

Narrowband beamformer by MVDR (Capon) method.

mvdr beamformer

Description

The MVDR Beamformer performs minimum variance distortionless response (MVDR) beamforming. The unit maintains signal power in a given direction while suppressing interference and noise from other directions. The MVDR beamformer is also called a Capon beamformer.

Ports

Input

X - input signal
complex matrix M by N

An input signal given as an M by N matrix, where M is the number of samples of the signal and N is the number of signals.

Data types: Float16, Float32, Float64, Int8, Int16, Int32, Int64, UInt8, UInt16, UInt32, UInt64, Bool.

Support for complex numbers: Yes

XT - training signal
complex matrix M by N.

A reference signal given as an M by N matrix, where M is the number of samples of the signal and N is the number of signals.

Dependencies

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

Data types: Float16, Float32, Float64, Int8, Int16, Int32, Int64, UInt8, UInt16, UInt32, UInt64, Bool.

Support for complex numbers: Yes

Ang - beam shaping directions of the beam pattern
real matrix 2 by L | real vector-column 2 by 1

The beam directions given as a 2 by L real matrix, where L is the number of beam shaping directions. Each column specifies a beam direction in the form of [AzimuthAngle;ElevationAngle]. The azimuth angle must lie in the range of -180° to 180° inclusive. The elevation angle shall lie in the range of -90° to 90° inclusive. Angles are specified relative to the local coordinate system of the array. The units of measurement are degrees.

Dependencies

To use this port, set the Source of beamforming direction parameters to Input port.

Data types: Float16, Float32, Float64, Int8, Int16, Int32, Int64, UInt8, UInt16, UInt32, UInt64, Bool.

Output

Y - output signal generated by the beam
`complex matrix M on L

Beamformed signal returned as a complex matrix M on L. M is the number of samples of the signal, and L is the number of desired beamforming directions set by the Beamforming direction parameters or from the Ang port.

Data types: Float16, Float32, Float64, Int8, Int16, Int32, Int64, UInt8, UInt16, UInt32, UInt64, Bool.

Support for complex numbers: Yes.

W - beamforming weights
`complex matrix N on L

Complex conjugate beamforming weights returned as a complex matrix N by L, where N is the number of array elements. If the Specify sensor array as parameters are set to Partitioned array or Replicated subarray, then 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) parameters. There is one set of weights for each beamforming direction.

Dependencies

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

Data types: Float16, Float32, Float64, Int8, Int16, Int32, Int64, UInt8, UInt16, UInt32, UInt64, Bool.

Support for complex numbers: Yes.

Parameters

Main

Signal propagation speed - speed of signal propagation, m/c
3e8 (by default) | positive scalar

Signal propagation speed as a real positive scalar. By default, the value of the speed of light is 3e8 m/c.

The unit of measurement is metres per second.

Operating frequency (Hz) - operating frequency of the system
3e8 (By default) | Positive scalar

The operating frequency of the system specified as a positive scalar. The unit of measurement is hertz.

Diagonal loading factor - diagonal loading factor for stability
`non-negative scalar

A diagonal loading factor specified as a non-negative scalar. Diagonal loading is a technique used to achieve stable beamforming, especially when the specimen support is small.

Enable training data input - use of training data
Off (By default)| `On

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

Source of beamforming direction - source of beamforming direction
Property (By default) | Input port.

Source of beamforming direction, set as Property or Input port.

  • Property - the direction is specified using the Beamforming direction (deg) parameters.

  • Input port - the direction is defined by the Ang port input.

Beamforming direction (deg) - beamforming directions
real matrix 2 by L

Beamforming directions given as a real matrix 2 by L, where L is the number of beamforming directions. Each column is of the form [AzimuthAngle;ElevationAngle]. The units of the angle are degrees. The azimuth angle must lie in the range from -180° to 180°. Elevation angle shall lie in the range of -90° to 90°. The angles are specified relative to the local coordinate system of the array.

Dependencies

To use this parameter, set the Source of beamforming direction parameter to `Property'.

Number of bits in phase shifters - number of bits of phase shift quantisation
0 (by default) | non-negative integer.

Number of bits used to quantise the phase shift component of the beamformer or control vector weights. Specify the number of bits as a non-negative integer. A value equal to zero means that quantisation is not performed.

Enable weights output - output of beamformer weights
` disabled (by default)` | enabled

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

Sensor Array

Specify sensor array as - method of array specification
Array (no subarrays) (by default) | Partitioned array | Replicated subarray

Antenna array assignment method. The antenna array may also contain subarrays or be partitioned.

Available values:

  • Array (no subarrays).

  • Partitioned array

  • Replicated subarray

Element

Element type - types of antenna array elements
Isotropic Antenna (By default) | Cardioid Antenna | Cosine Antenna | Custom Antenna | Gaussian Antenna | Sinc Antenna | Omni Microphone | Custom Microphone

Type of antenna array element.

Available values:

  • Isotropic Antenna.

  • Cardioid Antenna

  • `Cosine Antenna

  • `Custom Antenna

  • `Gaussian Antenna

  • `Sinc Antenna

  • `Omni Microphone

  • `Custom Microphone

Operating frequency range (Hz) - operating frequency range of the antenna array element
[0,1e20] (by default) | ` real vector-string 1 by 2`

The operating frequency range of the antenna array element as a 1-by-2 string-vector in the form of [LowerBound,UpperBound]. The element has no response outside this frequency range. Frequency measurement units are Hz.

Dependencies

To use this parameter, set the Element type parameters to Isotropic Antenna, Cosine Antenna or Omni Microphone.

Baffle the back of the element - consider radiation through the rear beam of the pattern to the rear hemisphere of the Isotropic Antenna element or Omni Microphone.
Off (By default) | `on

Set this flag to exclude radiation to the rear hemisphere. The response from the rear hemisphere at all azimuth angles outside the ±90° interval from the broadside are set to zero. The broadside direction is defined as an azimuth angle of 0° and a place angle of 0°.

Dependencies

To use this parameter, set the Element type parameters to Isotropic Antenna or Omni Microphone.

Null axis direction - the direction of the axis along the null radiation.
-x (By default) | +x | +y | -y | +z | -z.

Axis direction along the null radiation.

Dependencies

To use this parameter, set the Element type parameters to Cardioid Antenna.

Exponent of cosine pattern - exponent of exponent degree when specifying the shape of cosine pattern
[1.5, 1.5] (By default) | non-negative scalar | real matrix of non-negative values 1 by 2.

The exponent of the degree of the exponent of cosine model as a non-negative scalar or a 1-by-2 real matrix of non-negative values. If the Exponent of cosine pattern is a 1 by 2 vector, the first element is the exponent of the exponent degree in the azimuth direction and the second element is the exponent of the exponent degree in the angle-of-place direction. When this parameters is scalar, the cosines in the azimuth and elevation directions are raised to the same degree.

Dependencies

To use this parameter, set the Element type parameter to Cosine Antenna.

Operating frequency vector (Hz) - array of operating frequencies of the antenna array element
[0,1e20] (by default) | real string vector

The array of operating frequencies of the antenna array element as a string vector 1 on of increasing real values. The element has no response outside the frequency range given by the minimum and maximum elements of this vector. The units of frequency measurement are Hz.

Dependencies

To use this parameter, set the Element type parameters to Custom Antenna or Custom Microphone. To set the response at these frequencies, use the Frequency responses (dB) parameters.

Frequency responses (dB) - frequency responses of the antenna array element
[0,0] (by default)| real vector-string.

The frequency response of custom antenna array elements is determined by the Operating frequency vector (Hz) parameters. The dimensions of the Frequency responses (dB) vector must match the dimensions of the vector defined by the Operating frequency vector (Hz) parameters.

Dependencies

To use this parameter, set the Element type parameters to Custom Antenna or Custom Microphone.

Input Pattern Coordinate System - selects the coordinate system of the custom antenna pattern
az-el (by default) | phi-theta.

Selects the user antenna pattern coordinate system, either az-el or phi-theta is specified. When az-el is selected, the Azimuth angles (deg) and Elevations angles (deg) parameters are used to specify the coordinates of the directional pattern points. When the `phi-theta parameter is specified, the Phi angle (deg) and Theta angles (deg) parameters are used to specify the coordinates of the pattern points.

Dependencies

To use this parameter, set the Element type parameters to Custom Antenna.

Azimuth angles (deg) - azimuth angles of the antenna radiation pattern
[-180:180] (By default) | real vector-string

The azimuth angle values for which the antenna radiation pattern will be calculated as vector-string 1 at . must be greater than 2. The values of the azimuth angles must lie in the range from −180° to 180° inclusive and be in strictly ascending order.

Dependencies

To use this parameter, set the Element type parameter to Custom Antenna and the Input Pattern Coordinate System parameter to az-el.

Elevation angles (deg) - values of antenna pattern location angles
[-90:90] (by default) | real vector-string

The values of the place angles at which you want to calculate the radiation pattern as vector 1 at . must be greater than 2. The units of measurement of the angles are degrees. The elevation angles must lie in the range from −90° up to and including 90° and be in strictly ascending order.

Dependencies

To use this parameter, set the Element type parameter to Custom Antenna and the Input Pattern Coordinate System parameter to az-el.

Phi Angles (deg) - values of Phi angles of the antenna pattern
[0:360] (by default) | ` real vector-line 1 on P`

Angular coordinates Phi of the points at which the antenna radiation pattern is specified. Defined as a real vector-string 1 on . must be greater than 2. The units of measurement of the angles are degrees. The values of the angles Phi must lie in the range from 0° to 360° and be arranged in strictly ascending order.

Dependencies

To use this parameter, set the Element type parameter to Custom Antenna and the Input Pattern Coordinate System parameter to phi-theta.

Theta Angles (deg) - Theta angles of the antenna radiation pattern
[0:180] (by default) | ` real vector-line 1 on Q`

Theta angular coordinates of the points where the antenna radiation pattern is specified. Defined as a real vector-string 1 on . must be greater than 2. The units of measurement of the angles are degrees. Values of the angles Theta must lie in the range from 0° to 180° and be arranged in strictly ascending order.

Dependencies

To use this parameter, set the Element type parameter to Custom Antenna and the Input Pattern Coordinate System parameter to phi-theta.

Magnitude pattern (dB) is the magnitude of the antenna pattern
zeros(181,361) (by default) | real matrix Q on P | real array Q on P on L

Antenna pattern magnitude given as a matrix by or an array by by .

  • If the Input Pattern Coordinate System parameter is set to az-el, then is equal to the length of the vector defined by the Elevation angles (deg) parameter, in turn, is equal to the length of the vector defined by the Azimuth angles (deg) parameter.

  • If the Input Pattern Coordinate System parameter is set to phi-theta, then is equal to the length of the vector defined by the Theta Angles (deg) parameter, in turn, is equal to the length of the vector defined by the Phi Angles (deg) parameter.

The value of is equal to the value of the Operating frequency vector (Hz) parameters.

  • If the value of this parameter is a matrix to , then the same scheme is applied for all frequencies specified in the Operating frequency vector (Hz) parameter.

  • If the value is an array to to , each element to of the array specifies a pattern for the corresponding frequency specified in the Operating frequency vector (Hz) parameters.

Dependencies

To use this parameter, set the Element type parameters to Custom Antenna.

Phase pattern (deg) - the phase of the radiation pattern of the custom antenna
zeros(181,361) (By default) | real matrix Q on P | real array Q on P on L

The phase radiation pattern of the combined antenna, given as a matrix on or an array on on .

  • If the Input Pattern Coordinate System parameter is set to az-el, then is equal to the length of the vector defined by the Elevation angles (deg) parameter, in turn, is equal to the length of the vector defined by the Azimuth angles (deg) parameter.

  • If the Input Pattern Coordinate System parameter is set to phi-theta, then is equal to the length of the vector defined by the Theta Angles (deg) parameter, in turn, is equal to the length of the vector defined by the Phi Angles (deg) parameter.

The value of is equal to the value of the Operating frequency vector (Hz) parameters.

  • If the value of this parameter is a matrix to , then the same scheme is applied for all frequencies specified in the Operating frequency vector (Hz) parameter.

  • If the value is an array to to , each element to of the array specifies a pattern for the corresponding frequency specified in the Operating frequency vector (Hz) parameters.

Dependencies

To use this parameter, set the Element type parameters to Custom Antenna.

Align element normal with array normal - align the normal of the antenna array element with the array normal
On (By default) | Off.

If the parameters value is on, the pattern of the antenna element is rotated to align with the array normal. If off, the pattern of the element is not rotated.

If the antenna is used in an antenna array and the Input Pattern Coordinate System parameters is set to az-el, checking this checkbox rotates the pattern so that the x-axis of the element coordinate system points along the array normal. If no selection is made, the element pattern without rotation is used.

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

Use this parameter together with the Array Normal parameter of the URA and UCA arrays.

Dependencies

To use this parameter, set the Element type parameters to Custom Antenna.

Radiation pattern beamwidth (deg) - width of the antenna pattern beamwidth
[10, 10] (by default) | real scalar | real vector-string 1 by 2

Antenna pattern beamwidth in degrees.

Dependencies

To use this parameter, set the Element type parameters to Gaussian Antenna.

Polar pattern frequencies (Hz) - values of frequencies for polar pattern of the microphone
1e3 (By default) | real scalar | real vector-string 1 by L.

The frequency values for the polar radiation pattern are given as a real scalar or real vector-string 1 on . The frequencies lie within the frequency range specified by the parameter Operating frequency vector (Hz).

Dependencies

To use this parameter, set the Element type parameters to Custom Microphone.

Polar pattern angles (deg) - angle values for the polar pattern of the microphone
[-180:180] (by default) | real vector string 1 on P.

The angle values for the microphone’s polar pattern are specified as a vector . The angles are measured from the centre axis of the microphone and should range from −180° to 180° inclusive.

Dependencies

To use this parameter, set the Element type parameters to Custom Microphone.

Polar pattern (dB) - polar pattern of the microphone
zeros(1,361) (by default) | `real vector string 1 to L'.

Set the polar pattern magnitude of the user microphone element as a real vector-string 1 by , where is the number of frequencies specified in the Polar pattern frequencies (Hz) parameters. The string represents the polar pattern magnitude measured at the corresponding frequency specified in Polar pattern frequencies (Hz). The directional pattern is measured in the azimuth plane. In the azimuth plane, the angle of place is 0° and the centre axis is 0° in azimuth and 0° in elevation. The polar pattern is symmetrical around the centre axis. Based on the polar diagram, you can construct the microphone’s radiation pattern in three-dimensional space.

Dependencies

To use this parameter, set the Element type parameters to Custom Microphone.

Array

Geometry - array geometry
ULA (by default) | URA | UCA | Conformal Array

The geometry of the array, specified as:

  • ULA is a uniform linear array.

  • URA - uniform rectangular array.

  • UCA - uniform circular array.

  • Conformal Array - arbitrary arrangement of elements.

Number of elements - number of array elements
2 for ULA arrays and 5 for UCA arrays (by default) | ` an 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.

When the Specify sensor array as parameter is set to Replicated subarray, this parameter is applied to each subarray.

Dependencies

To use this parameter, set the Geometry parameters to ULA or UCA.

Element spacing (m) - the distance between array elements
` 0.5 for ULA arrays and [0.5,0.5] for URA arrays (by default)` | ` positive scalar for ULA or URA arrays | ` two-element vector of positive values for URA arrays`.

The distance between neighbouring elements of an array:

  • ULA - specifies the distance between two neighbouring array elements as a positive scalar.

  • URA - the distance is specified as a positive scalar or a vector of positive values 1 by 2. If Element spacing (m) is a scalar, the distances between rows and columns are equal. If Element spacing (m) is a vector, the vector is [SpacingBetweenArrayRows,SpacingBetweenArrayColumns].

  • When the Specify sensor array as parameter is set to Replicated subarray, this parameter is applied to each subarray.

Dependencies

To use this parameter, set the Geometry parameters to ULA or URA.

Array axis - direction of the linear axis of ULA
y (By default) | x | z

The direction of the ULA linear axis specified as y, x or z. All elements of the ULA array are uniformly distributed along this axis in the local array coordinate system.

Dependencies

  • To use this parameter, set the Geometry parameter to ULA.

  • This parameter is also used if the block only supports ULA arrays.

Array size - URA array size
[2,2] (by default) | ` positive integer` | ` vector of positive integers 1 by 2`

URA array sizes specified as a positive integer or a vector of positive integers 1 by 2.

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

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

  • When the Specify sensor array as parameter is set to Replicated subarray, this parameter is applied to each subarray.

For URA, the array elements are indexed from top to bottom of the leftmost column and then proceed to the next columns from left to right. The figure shows an array for which the Array size parameter is [3,2], that is, it has three rows and two columns.

mvdr beamformer 1

Dependencies

To use this parameter, set the Geometry parameter to URA.

Element lattice is a grid of URA element positions
Rectangular (by default) | Triangular.

Lattice of URA element positions specified as rectangular or triangular.

  • Rectangular - aligns all elements by rows and columns.

  • Triangular - shifts elements of the even row of the rectangular lattice towards the positive direction of the row axis. The offset is half the distance between the elements by the row size.

Dependencies

  • To use this parameter, set the Geometry parameter to URA.

Array normal - the direction of the array normal
x for URA arrays or z for UCA arrays (by default) | y

Array normal direction specified as x, y or z.

The elements of planar arrays lie in a plane orthogonal to the selected array normal direction. The angular coordinate directions of the elements are directed along the array normal direction.

  • x - array elements lie in the yz-plane. The angular coordinate vectors of all elements are directed along the x-axis.

  • y - array elements lie in the zx-plane. The vectors of angular coordinates of all elements are directed along the y-axis.

  • z - array elements lie in the xy-plane. The vectors of angular coordinates of all elements are directed along the z-axis.

Dependencies

To use this parameter, set the Geometry parameter to URA or UCA.

Radius of UCA (m) - radius of UCA array
0.5 (by default) | positive scalar

Radius of UCA array, positive scalar.

Dependencies

To use this parameter, set the Geometry parameters to UCA.

Element positions (m) - positions of conformal array elements
[0;0;0] (by default) | ` real matrix 3 by N`

The positions of the elements of a conformal array given 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’s local coordinate system. The origin of the local coordinate system is (0,0,0). The units of measurement are metres.

When the Specify sensor array as parameter is set to Replicated subarray, this parameter is applied to each subarray.

Dependencies

To use this parameter, set the Geometry parameter to Conformal Array.

Element normals (deg) - direction of normal vectors of elements of the conformal array
[0;0] | `vector-column 2 by 1 | matrix 2 by N

The direction of the vectors of normals of the elements of a conformal array, given as a 2-by-1 column vector or a 2-by-N matrix. N denotes the number of elements in the array. For a matrix, each column specifies the direction of the normal of the corresponding element in the form [azimuth;elevation] with respect to the local coordinate system. In the local coordinate system, the positive x-axis coincides with the normal direction of 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 the Specify sensor array as parameter is set to Replicated subarray, this parameter is applied to each subarray.

The Element positions (m) and Element normals (deg) parameters can be used to represent any arrangement in which pairs of elements differ from each other by certain transformations. These transformations may include translation, azimuth rotation, and elevation rotation. However, you cannot use transformations that require rotation with respect to the direction of the normal.

Dependencies

To use this parameter, set the Geometry parameters to Conformal Array.

Taper - change of directional pattern of antenna array elements
1 (by default) | complex scalar | complex vector.

The change of the directivity diagram of the antenna array elements is specified as a complex scalar or complex vector 1 at , where is the number of antenna array elements.

The coefficients that change the directivity pattern, also called element weights, multiply the responses of the antenna array elements. The coefficients change both the amplitude and phase of the response to reduce side lobes or the direction of the main response axis.

If the value of the Taper parameters is a scalar, the same weight is applied to each element. If Taper is a vector, then the weight from the vector is applied to the corresponding antenna array element. The number of weights must correspond to the number of antenna array elements.

When the Specify sensor array as parameter is set to Replicated subarray, this parameter is applied to each subarray.

Subarray definition matrix - determining whether elements belong to subarrays
`logical matrix

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

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

Dependencies

To use this parameter, set the Specify sensor array as parameters to Partitioned Array.

Subarray steering method - subarray steering method
None (by default) | Phase | Time | Custom

Subarray steering method, specified as:

  • None.

  • Phase

  • Time

  • Custom

Selecting Phase or Time allows the Steer input port to be used for the block.

Selecting Custom allows the unit to use the WS input port.

Dependencies

To use this parameter, set the Specify sensor array as parameters to Partitioned Array or Replicated subarray.

Phase shifter frequency (Hz) - frequency of phase shift of the subarray
3.0e8 (By default) | Positive scalar

The operating frequency of the subarray phase shift, specified as a positive real scalar. The units of measurement are hertz.

Dependencies

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

Number of bits in phase shifters - phase shift quantisation bits
0 (by default) | non-negative integer.

Subarray phase shift quantisation bits specified as a non-negative integer. A value equal to zero means that quantisation is not performed.

Dependencies

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

Subarrays layout - subarray layout
Rectangular (by default).

Specify the layout of replicated subarrays.

When Rectangular is set, Grid size and Grid spacing parameters are used for subarray placement.

When Custom is set, the Subarray positions (m) and Subarray normals parameters are used for subarray placement.

Dependencies

To use this parameter, set the Sensor array parameters to Replicated subarray.

Grid size - dimensions of the rectangular grid of the subarray
[1,2] (by default)

Rectangular subarray grid size specified as a single positive integer or a vector-string of positive integers 1 by 2.

  • If Grid size is an integer scalar, the array has an equal number of subarrays in each row and each column.

  • If Grid size is a 1-by-2 row vector of the form [NumberOfRows, NumberOfColumns], then the first variable is the number of subarrays in each column. The second variable 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 shows how a URA 3 by 2 subarray can be reproduced when the Grid size parameters is set to [1,2].

mvdr beamformer 2

Dependencies

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

Grid spacing (m) - spacing between subarrays on a rectangular grid
Auto (by default) | positive scalar | positive real vector 1 by 2

The distance between subarrays in a rectangular grid, given as a positive real scalar or vector 1 by 2 or Auto. The units of measure are metres.

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

If Grid spacing is a 1 by 2 row vector, the vector is of the form [SpacingBetweenRows,SpacingBetweenColumn], the first variable specifies the row spacing along the column. The second variable is the spacing between columns along the row.

If the Grid spacing parameters are set to Auto, replication preserves the spacing between subarray elements for both rows and columns when building a full array. This option is available only if ULA or URA is selected for the Geometry parameters.

Dependencies

To use this option, set the Sensor array parameters to Replicated subarray and the Subarrays layout parameters to Rectangular.

Subarray positions (m) - subarray positions
[0,0;0.5,0.5;0,0] (by default) | real matrix 3 by N

The positions of subarrays in the user grid, given as a 3-by-N real matrix, where N is the number of subarrays in the array. Each column of the matrix represents the position of one subarray in the local coordinate system of the array. The coordinates are expressed as [x; y; z]. The units of measurement are metres.

Dependencies

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

Subarray normals - direction of subarray normals
[0,0;0,0] (by default) | ` real matrix 2 by N`

The direction of the array subarray normals. The value of this parameters 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]. The units of angles are degrees. Angles are defined relative to the local coordinate system.

The Subarray positions and Subarray normals parameters can be used to represent any arrangement in which pairs of subarrays are distinguished by certain transformations. These transformations may include translation, azimuth rotation, and elevation rotation. However, you cannot use transformations that require rotation with respect to a normal.

Dependencies

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