Subband MVDR Beamformer
A broadband beam shaper using the MVDR (Capon) method.
blockType: SubbandMVDRBeamformer
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Description
Block Subband MVDR Beamformer performs beam shaping with minimum variance distortion-free response (MVDR) for broadband signals. The signals are decomposed into frequency sub-bands, and in each of them a narrow-band MVDR beam is formed. The received subband signals are combined to form an output signal. MVDR beamforming preserves signal power in a given direction by suppressing interference and noise from other directions. The MVDR beam shaper is also called a Capon shaper.
Ports
Entrance
X — input signal
complex matrix M by N
The input signal, specified as a matrix on , where — the number of signal samples, and — the number of antenna array elements.
Data types: Float16, Float32, Float64, Int8, Int16, Int32, Int64, UInt8, UInt16, UInt32, UInt64
Support for complex numbers: Yes
XT — training signal
complex matrix M by N
A reference signal defined as a matrix on , where — the number of signal samples, and — 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 — directions of formation of the output signal
real matrix 2 by L | real vector column 2 by 1
The directions of signal emission, given in the form of a real matrix 2 on , where — the number of beam formation directions. Each column specifies the radiation direction in the form of [AzimuthAngle;ElevationAngle]. The azimuth angle must be in the range from -180° to 180° inclusive. The elevation angle must be in the range from -90° to 90° inclusive. The angles are set relative to the local coordinate system of the array.
Dependencies
To use this port, set the Source of beamforming direction parameter to Input port.
Data types: Float16, Float32, Float64, Int8, Int16, Int32, Int64, UInt8, UInt16, UInt32, UInt64
Output
Y is the output signal generated by the pass beam:q[<br>] complex matrix M on L
The output signal returned as a complex matrix on , where — the number of signal samples, and — the number of desired beamforming directions, set by the Beamforming direction parameter or from the Ang port.
Data types: Float16, Float32, Float64, Int8, Int16, Int32, Int64, UInt8, UInt16, UInt32, UInt64
Support for complex numbers: Yes
Freq — central frequencies of the pass sub-bands:q[<br>] real column vector K by 1
The central frequencies of the sub-bands returned as a column vector with real values on 1, where — this is the number of sub-ranges specified in the Number of subbands parameter.
Dependencies
To use this port, select the Enable subband center frequencies output checkbox.
Data types: Float16, Float32, Float64, Int8, Int16, Int32, Int64, UInt8, UInt16, UInt32, UInt64
W — the weighting coefficients of the pass beam formation:q[<br>] complex matrix N by L
The beamforming weights returned as a complex matrix on , where — the number of array elements. If the Specify sensor array as parameter is set to Partitioned array or `Replicated subarray', then represents the number of subarrays. — the number of desired beamforming directions set in the Ang port or the Beamforming direction (deg) parameter. There is one set of weights for each direction of beam formation.
Dependencies
To use this port, select the Enable weights output checkbox.
Data types: Float16, Float32, Float64, Int8, Int16, Int32, Int64, UInt8, UInt16, UInt32, UInt64
Support for complex numbers: Yes
Parameters
Main
Signal propagation speed (m/s) — signal propagation speed, m/s
3e8 (default) | positive scalar
The propagation velocity of the signal in the form of a real positive scalar. The default value for the speed of light is `3e8 m/s'.
The units of measurement are meters per second.
Data types: Float16, Float32, Float64, Int8, Int16, Int32, Int64, UInt8, UInt16, UInt32, UInt64
Operating frequency (Hz) — operating frequency of the pass sy\$
\$ 3e8 (default) | positive scalar
The operating frequency of the system, set as a positive scalar. The units of measurement are hertz.
Data types: Float16, Float32, Float64, Int8, Int16, Int32, Int64, UInt8, UInt16, UInt32, UInt64
Inherit sample rate — inheriting the sampling rate from higher-level pass:q blocks[<br>] enabled (by default) | disabled
Select this option to inherit the sampling rate from the higher blocks. Otherwise, specify the sampling rate using the Sample rate (Hz) parameter.
Data types: Bool
Sample rate (Hz) — sampling rate of the pass signal:q[<br>] 1e6 (default) | positive scalar
The sampling frequency of the signal, set as a positive scalar. The units of measurement are hertz.
Dependencies
To use this option, uncheck the Inherit sample rate checkbox.
Data types: Float16, Float32, Float64, Int8, Int16, Int32, Int64, UInt8, UInt16, UInt32, UInt64
Number of subbands — number of processed pass subbands:q[<br>] 64 (default) | positive integer
The number of processed sub-ranges, set as a positive integer.
Data types: Int8, Int16, Int32, Int64, UInt8, UInt16, UInt32, UInt64
Source of beamforming direction — source of the beamforming direction
Property (default) | Input port
The source of the beamforming direction is set as Property or `Input port'.
-
Property— the direction is set using the Beamforming direction (deg) parameter. -
`Input port' — the direction is determined by the input to the Ang port.
Beamforming direction (deg) — directions of ray formation
real matrix 2 on L
The directions of ray formation, given in the form of a real matrix 2 on , where — the number of beam formation directions. Each column has the form [AzimuthAngle;ElevationAngle]. The angle measurement units are degrees. The azimuthal angle should be in the range of −180° to 180°. The elevation angle should be in the range of −90° to 90°. The angles are set relative to the local coordinate system of the array.
Dependencies
To use this parameter, set the Source of beamforming direction parameter to Property.
Enable weights output — output of the weights of the pass beam shaper:q[<br>] disabled (by default) | enabled
Check this box to get the beam shaper weights from the output port W.
Enable subband center frequencies output — enable the output of the central frequencies of the pass subbands:q[<br>] disabled (by default) | enabled
Check this box to get the center frequencies of each subband via the Freq output port.
Sensor Array
Specify sensor array as — method for specifying the pass array:q[<br>] Array (no subarrays) (default) | Partitioned array | Replicated subarray
Array assignment method, available values:
-
Array (no subarrays) -
Partitioned array -
Replicated subarray
Element
Element type — types of elements of the pass array:q[<br>] Isotropic Antenna (default) | Cardioid Antenna | Cosine Antenna | Custom Antenna | Gaussian Antenna | Sinc Antenna | Omni Microphone | Custom Microphone
The type of antenna or microphone.
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 or microphone
[0,1e20] (default) | a real vector is a 1 by 2 row
The range of operating frequencies of the antenna or microphone in the form of a vector is a 1 by 2 row in the form [LowerBound, UpperBound]. Outside of this frequency range, the element has no response. The units of frequency measurement are Hz.
Dependencies
To use this parameter, set the Element type parameter to Isotropic Antenna, Cosine Antenna, or 'Omni Microphone'.
Baffle the back of the element — set the response of the Isotropic Antenna element or Omni Microphone' to zero
`disabled (by default) | enabled
`disabled (by default)
Select this option to mute the echo of the element.
When retracting, the echo at all azimuth angles exceeding ± 90° from the wide side is set to zero. The wide side is defined as the azimuth angle of 0° and the elevation angle of 0°.
Dependencies
To use this parameter, set the Element type parameter to Isotropic Antenna or `Omni Microphone'.
Null axis direction — the direction of the zero radiation axis.
-x (default) | +x | +y | -y | +z | -z
The direction of the zero radiation axis.
Dependencies
To use this parameter, set the Element type parameter to Cardioid Antenna.
Exponent of cosine pattern — exponents of azimuthal and altitude cosine radiation patterns
[1.5, 1.5] (default) | non-negative scalar | a real matrix of non-negative values of 1 by 2
Exponentials of the cosine model in the form of 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, then the first element is the exponent in the azimuth direction, and the second is in the elevation direction. With a scalar value of this parameter, the cosines in the azimuthal and elevation directions are raised to one power.
Dependencies
To use this parameter, set the Element type parameter to Cosine Antenna.
Operating frequency vector (Hz) — operating frequency range of the user antenna or microphone
[0,1e20] (default) | real vector is a string
The range of operating frequencies of the antenna or microphone in the form of a vector row 1 on increasing actual values. The element has no response beyond the frequency range specified 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 parameter to Custom Antenna or `Custom Microphone'. To set the responses at these frequencies, use the Frequency responses (dB) parameter.
Frequency responses (dB) — frequency responses of the antenna and microphone
[0,0] (default)| real vector string
The frequency response of the user antenna or user microphone for the frequencies defined by the parameter Operating frequency vector (Hz). The dimensions of the Frequency responses (dB) vector must match the dimensions of the vector specified by the Operating frequency vector (Hz) parameter.
Dependencies
To use this parameter, set the Element type parameter to Custom Antenna or `Custom Microphone'.
Input Pattern Coordinate System — the coordinate system of the radiation pattern of the user antenna
az-el (default) | phi-theta
The coordinate system of the radiation pattern of the user antenna is indicated by az-el or phi-theta'. When specifying `az-el, the Azimuth angles (deg) and Elevations angles (deg) parameters are used to set the coordinates of the points of the directional pattern. When specifying the phi-theta parameter, the Phi angle (deg) and Theta angles (deg) parameters are used to set the coordinates of the part points.
Dependencies
To use this parameter, set the Element type parameter to Custom Antenna.
Azimuth angles (deg) — azimuth angles of the antenna radiation pattern
[-180:180] (default) | real vector is a string
Azimuth angles, which will be used to calculate the radiation pattern of the antenna in the form of a vector row 1 on P. P must be greater than 2. The azimuth angles must be in the range of −180° up to 180° inclusive and 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 az-el.
Elevation angles (deg) — elevation angles of the antenna radiation pattern
[-90:90] (default) | real vector is a string
Elevation angles at which it is necessary to calculate the radiation pattern in the form of a vector 1 on . it must be more than 2. The units of measurement of angles are degrees. Elevation angles should be in the range of −90° to 90° inclusive and 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 az-el.
Phi Angles (deg) — coordinates of the Phi angle of the radiation pattern of the antenna
[0:360] (default) | real vector is row 1 on P
The angular coordinates of the Phi points where the antenna radiation pattern is set. They are defined as a real vector-row 1 on . it must be more than 2. The units of measurement of angles are degrees. The angles of Phi should 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) — coordinates of the angle of the Theta radiation pattern of the antenna
[0:180] (default) | real vector-row 1 on Q
The angular coordinates of the Theta points where the antenna radiation pattern is set. They are defined as a real vector-row 1 on . it must be more than 2. The units of measurement of angles are degrees. The angles of Theta should 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) — the magnitude of the radiation pattern of the combined pass antenna:q[<br>] zeros(181.361) (default) | real matrix Q on P | real array Q on P on L
The value of the radiation pattern of the combined antenna, set as a matrix on or an array on on .
-
If the Input Pattern Coordinate System parameter is set to
az-el, then Q is equal to the length of the vector specified by the Elevation angles (deg) parameter, and P is the length of the vector specified 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 specified by the Theta Angles (deg) parameter, and — the length of the vector specified by the Phi Angles (deg) parameter.
Value is equal to the value of the Operating frequency vector (Hz) parameter.
-
If the value of this parameter is a matrix on , then the same scheme is applied for all frequencies specified in the parameter Operating frequency vector (Hz).
-
If the parameter is an array on on , then each page on The array defines a template for the corresponding frequency specified in the parameter Operating frequency vector (Hz).
Dependencies
To use this parameter, set the Element type parameter to Custom Antenna.
Phase pattern (deg) — phase of the radiation pattern of the user antenna
zeros(181,361) (default) | real matrix Q on P | real array Q on P on L
The phase of the radiation pattern of the combined antenna, set 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 specified by the Elevation angles (deg) parameter, and — the length of the vector specified 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 specified by the Theta Angles (deg) parameter, and — the length of the vector specified by the Phi Angles (deg) parameter.
Value is equal to the value of the Operating frequency vector (Hz) parameter.
-
If the value of this parameter is a matrix on , then the same scheme is used for all frequencies specified in the parameter Operating frequency vector (Hz).
-
If the parameter is an array on on , then each page on The array defines a template for the corresponding frequency specified in the parameter Operating frequency vector (Hz).
Dependencies
To use this parameter, set the Element type parameter to Custom Antenna.
Align element normal with array normal — rotate the antenna element to the normal position of the array
enabled (by default) | disabled
If the parameter value is enabled, the radiation pattern of the antenna element is rotated to align with the normal of the array. If it is off, then the drawing of the element does not rotate.
If the antenna is used in an antenna array and the Input Pattern Coordinate System parameter has the value az-el, checking this box rotates the radiation pattern so that the x-axis of the element coordinate system points along the normal of the array. If there is no selection, the element template is used without rotation.
If the antenna is used in an antenna array and the Input Pattern Coordinate System parameter has the value phi-theta, checking this box rotates the radiation pattern so that the z axis of the element coordinate system points along the normal of the array.
Use this parameter together with the Array Normal parameter of the URA and UCA arrays.
Dependencies
To use this parameter, set the Element type parameter to Custom Antenna.
Radiation pattern beamwidth (deg) — angles of the radiation pattern solution
[10, 10] (default) | real scalar | a real vector is a 1 by 2 row
The angles of the radiation pattern solution in degrees.
Dependencies
To use this parameter, set the Element type parameter to Gaussian Antenna.
Polar pattern frequencies (Hz) — microphone response frequencies of the polar radiation pattern
1e3 (default) | real scalar | real vector-row 1 on L
The response frequencies of a microphone with a polar pattern, set as a real scalar or a real vector, are lines 1 on . The response frequencies are in the frequency range specified by the parameter Operating frequency vector (Hz).
Dependencies
To use this parameter, set the Element type parameter to Custom Microphone.
Polar pattern angles (deg) — response angles of the polar radiation pattern
[-180:180] (default) | real vector is row 1 on P
Set the response angles of the polar radiation pattern as a vector 1 on . The angles are measured from the central axis of the microphone and should be in the range of −180° to 180° inclusive.
Dependencies
To use this parameter, set the Element type parameter to Custom Microphone.
Polar pattern (dB) — polar characteristic of the user microphone
zeros(1,361) (default) | real vector-row 1 on L
Set the value of the polar radiation pattern of the user microphone element in the form of a real vector-row 1 on , where — the number of frequencies specified in the parameter Polar pattern frequencies (Hz). The string represents the value of the polar radiation pattern measured at the corresponding frequency specified in the Polar pattern frequencies (Hz). The radiation pattern is measured in the azimuthal plane. In the azimuthal plane, the elevation angle is 0°, and the central axis is 0° in azimuth and 0° in elevation. The polar radiation pattern is symmetrical around the central axis. Based on the polar diagram, it is possible to construct a microphone directional pattern in three-dimensional space.
Dependencies
To use this parameter, set the Element type parameter to Custom Microphone.
Array
Geometry — geometry of the pass array:q[<br>] ULA (default) | URA | UCA | Conformal Array
The geometry of the array, set as:
-
'ULA' is a uniform linear array.
-
`URA' is a uniform rectangular array.
-
'UCA' is a uniform circular array.
-
`Conformal Array' — arbitrary arrangement of elements.
Number of elements — number of elements of the pass array:q[<br>] 2 for ULA arrays and 5 for UCA arrays (default) | an integer greater than or equal to 2
The number of array elements for ULA or UCA arrays, set as an integer greater than or equal to 2.
When setting the Specify sensor array as parameter to Replicated subarray, this parameter is applied to each subarray.
Dependencies
To use this parameter, set the Geometry parameter to ULA or `UCA'.
Array size — dimensions of the URA pass array:q[<br>] [2,2] (default) | positive integer | vector of positive integers 1 by 2
The dimensions of the URA array, specified as a positive integer or a vector of positive integers 1 by 2.
-
If the size of the array is a 1 by 2 vector, then the vector has the form [NumberOfArrayRows,NumberOfArrayColumns].
-
If the size of the array is an integer, then the array has the same number of rows and columns.
When setting the Specify sensor array as parameter to Replicated subarray, this parameter is applied to each subarray.
To do this, the array elements are indexed from top to bottom in the leftmost column, and then move to the next columns from left to right. The figure shows an array for which the Array size parameter has the value [3,2], that is, it has three rows and two columns.
Dependencies
To use this parameter, set the Geometry parameter to `URA'.
Element spacing (m) — the distance between the elements of the pass array:q[<br>] 0.5 for ULA arrays and [0.5,0.5] for URA arrays (default) | positive scalar for ULA or URA arrays | vector of positive integers 1 by 2 for URA arrays
The distance between adjacent array elements:
-
'ULA` — specify the distance between two adjacent array elements as a positive scalar.
-
URA' — the distance is set as a positive scalar or a vector of positive values 1 by 2. If Element spacing (m) is a scalar, then the distances between rows and columns are equal. If Element spacing(m) is a vector, then the vector has the form `[SpacingBetweenArrayRows,SpacingBetweenArrayColumns].
When setting the Specify sensor array as parameter to Replicated subarray, this parameter is applied to each subarray.
Dependencies
To use this parameter, set the Geometry parameter to ULA or `URA'.
Array axis — direction of the ULA pass linear axis:q[<br>] y (default) | x | z
The direction of the ULA linear axis, set as y, x or z. All elements of the ULA array are evenly distributed along this axis in the local coordinate system of the array.
Dependencies
-
To use this parameter, set the Geometry parameter to
ULA. -
This parameter is also used if the block supports only ULA arrays.
Element lattice — grid of positions of URA pass elements:q[<br>] Rectangular (default) | Triangular
A grid of URA element positions, set as rectangular or triangular.
-
'Rectangular' — aligns all elements in rows and columns.
-
Triangular— shifts the elements of an even row of a rectangular grid towards the positive direction of the row axis. The offset is half the distance between the elements according to the size of the row.
Dependencies
-
To use this parameter, set the Geometry parameter to `URA'.
Array normal — the direction of the normal of the pass array:q[<br>] x for URA arrays or z for UCA arrays (default) | y
The normal direction of the array, specified as x, y, or z.
The elements of flat arrays lie in a plane orthogonal to the selected direction of the array normal. The directions of the angular coordinates of the elements are directed along the direction of the normal of the array.
-
The 'x` elements of the array lie in the yz plane. The angular coordinate vectors of all elements are directed along the x-axis.
-
The 'y` elements of the array lie in the zx plane. The angular coordinate vectors of all elements are directed along the y axis.
-
The 'z` elements of the array lie in the xy plane. The angular coordinate vectors 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 the UCA pass array:q[<br>] 0.5 (default) | positive scalar
The radius of the UCA array, a positive scalar.
Dependencies
To use this parameter, set the Geometry parameter to UCA.
Element positions (m) — positions of elements of the conformal array
[0;0;0] ( by default) | a 3-by-N real matrix
The positions of the elements of the conformal array, given as a matrix of real values 3 on , where — 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 local coordinate system of the array. The origin of the local coordinate system is (0,0,0). The units of measurement are meters.
When setting the Specify sensor array as parameter 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 the normal vectors of the elements of the conformal array
[0;0] | ` column vector 2 by 1 | matrix 2 by N
The direction of the normal vectors of the elements of a conformal array, specified as a 2-by-1 column vector or a 2-by-1 matrix . means the number of elements in the array. For the matrix, each column specifies the direction of the normal of the corresponding element in the form of [azimuth;elevation] relative to the local coordinate system. In the local coordinate system, the positive x-axis coincides with the direction of the normal to the conformal array. If the parameter value is a 2-by-1 column vector, then the same pointing direction is used for all elements of the array.
When setting the Specify sensor array as parameter to Replicated subarray, this parameter is applied to each subarray.
Parameters of Element positions (m) and Element normals (deg) can be used to represent any arrangement in which pairs of elements differ from each other by certain transformations. These transformations can include translation, azimuth rotation, and elevation rotation. However, transformations that require rotation relative to the normal direction cannot be used.
Dependencies
To use this parameter, set the Geometry parameter to `Conformal Array'.
Taper — taper of the elements of the pass array:q[<br>] 1 (default) | complex scalar | complex vector
The taper of an element, defined as a complex scalar or a complex vector 1 on . In this vector — the number of elements in the array.
The narrowing coefficients, also called element weights, multiply the responses of the array elements. The cones change both the amplitude and the phase of the response to reduce the side lobes or the direction of the main axis of the response.
If the value of the Taper parameter is a scalar, then the same weight is applied to each element. If Taper is a vector, then a weight from the vector is applied to the corresponding sensor element. The number of weights must match the number of array elements.
When setting the Specify sensor array as parameter to Replicated subarray, this parameter is applied to each subarray.
Subarray
Subarray definition matrix — determining whether elements belong to subarrays of
logical matrix
Set the selection of the subarray as a matrix on , where — number of subarrays, — the total number of elements in the array. Each row of the matrix represents a subarray, and each entry in the row indicates that an element belongs to this subarray. If the record is zero, then the element does not belong to the subarray. A non-zero entry is a complex weight applied to the corresponding element. Each row must contain at least one non-zero entry.
The phase center of each subarray is located in the geometric center of the subarray. The geometric center of the subarray depends on the matrix of the definition of the subarray and the Geometry parameters.
Dependencies
To use this parameter, set the Specify sensor array as parameter to Partitioned Array.
Subarray steering method — method for controlling the pass subarray:q[<br>] None (default) | Phase | Time
A method for managing a subarray, defined as:
-
None -
Phase -
Time
Dependencies
To use this parameter, set the Specify sensor array as parameter to Partitioned Array or `Replicated subarray'.
Phase shifter frequency (Hz) — the frequency of the phase shift of the pass subarray:q[<br>] 3.0e8 (default) | positive scalar
The operating frequency of the phase shift of the subarray, specified as a positive real scalar. The units of measurement are Hz.
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 — number of phase shift quantization bits
0 (default) | non-negative integer
The quantization bits of the phase shift of the subarray, specified as a non-negative integer. A value of zero means that quantization 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 — the location of the pass subarrays:q[<br>] Rectangular (default) | Custom
Specify the location of the replicated subarrays.
When setting the value to Rectangular, the Grid size and Grid spacing parameters are used to place the subarrays.
When setting the Custom value, the Subarray positions (m) parameters are used to place the subarrays. and Subarray normals.
Dependencies
To use this parameter, set the Sensor array parameter to `Replicated subarray'.
Grid size — dimensions of the rectangular grid of the pass subarray:q[<br>] [1,2] (default)
The grid size of a rectangular subarray, defined as a single positive integer or vector, which is a string of positive integers 1 by 2.
-
If Grid size is an integer scalar, then 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. The row is located along the local y axis, and the column is located along the local z axis. The figure shows how a 3-by-2 URA subarray can be reproduced when the Grid size parameter has the value
[1,2].
Dependencies
To use this parameter, set the Sensor array parameter to Replicated subarray and the Subarrays layout parameter to Rectangular.
Grid spacing (m) — the distance between the subarrays on the rectangular grid
Auto (default) | positive scalar | positive real vector 1 by 2
The distance between the subarrays in a rectangular grid, set as a positive real scalar or a 1 by 2 vector, or `Auto'. The units of measurement are meters.
If Grid spacing is a scalar, then the distance between rows and columns is the same.
If Grid spacing is a row vector 1 by 2, then the vector has the form [SpacingBetweenRows,SpacingBetweenColumn], then the first variable sets the distance between the rows along the column. The second variable is the distance between columns in a row.
If the Grid spacing parameter is set to Auto, then when building a complete array, replication preserves the distance between the elements of the subarray for both rows and columns. This option is only available if the Geometry parameter is set to ULA or `URA'.
Dependencies
To use this parameter, set the Sensor array parameter to Replicated subarray and the Subarrays layout parameter to Rectangular.
Subarray positions (m) — positions of the pass subarrays:q[<br>] [0 0;0.5 0.5;0 0] ( by default) | a 3-by-N real matrix
The positions of the subarrays in the custom grid, defined as a 3-by-3 real matrix , where — 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. Coordinates are expressed as [x; y; z]. The units of measurement are meters.
Dependencies
To use this parameter, set the Sensor array parameter to Replicated subarray and the Subarrays layout parameter to Custom.
Subarray normals — the direction of the normals of the subarrays of
[0 0;0 0] ( by default) | a 2-by-N real matrix
The direction of the normals of the array’s subarrays. The value of this parameter is a matrix of size 2 by , where — the number of subarrays in the array. Each column of the matrix defines the direction of the normal of the corresponding subarray in the form of [azimuth;elevation]. The units of measurement of angles are degrees. The angles are set relative to the local coordinate system.
The Subarray positions and Subarray normals parameters can be used to represent any location in which pairs of subarrays differ by certain transformations. These transformations can include translation, azimuth rotation, and elevation rotation. However, transformations that require rotation relative to the normal cannot be used.
Dependencies
To use this parameter, set the Sensor array parameter to Replicated subarray and the Subarrays layout parameter to Custom.