Engee documentation

GCC DOA and TOA

Generalized cross-correlator with phase transformation.

blockType: GCCDOAandTOA

gcc doa and toa

Path in the library:

/Phased Array Systems/Direction of Arrival/GCC DOA and TOA

Description

Block GCC DOA and TOA evaluates the direction and time of arrival of the signal to the antenna array. The block uses a generalized cross-correlation with phase transform (GCC-PHAT) algorithm.

Ports

Entrance

X — input signal
a complex matrix of size M by N

The input signal is a matrix of size on , where — the number of signal samples, and — the number of antenna array elements.

Data types: Float32, Float64

Support for complex numbers: Yes

Output

Ang — angles determining the arrival directions of the pass signals:q[<br>] a 2-by-1 real vector

The angles defining the arrival directions of the signals returned as a vector with real values in the form of `[azimuth, elevation]'. If the antenna elements are a linear antenna array (ULA), then Ang is a scalar representing the angle of the transverse radiation direction. The angle measurement units are degrees defined relative to the local coordinate system of the antenna array.

Data types: Float64

Tau — time delays of arrival of
real vector is row 1 on P

Arrival time delays displayed as a vector-a string of real values of 1 to , where is the number of pairs of antenna array elements selected from the antenna array.

  • If the Source of sensor pairs parameter is set to `Auto', then , where — the number of antenna array elements in the antenna array.

  • If the Source of sensor pairs parameter has the value `Property', then — this is the number of pairs of antenna array elements set by the Sensor pairs parameter.

The unit of measurement of time is seconds.

Dependencies

To use this port, set the Enable delay output parameter to enabled.

Data types: Float64

Rxy — calculated cross-correlation of
a complex matrix of size (2M+1) on P

The calculated cross-correlation between pairs of antenna array elements is displayed as a complex matrix of the size on , where — the number of pairs of antenna array elements selected from the antenna array, and — the number of time samples in the input signal.

  • If the Source of sensor pairs parameter is set to `Auto', then , where — the number of sublattice elements in the antenna array. The columns in Rxy contain correlations between the first element of the antenna array and all other elements.

  • If the Source of sensor pairs parameter has the value `Property', then — this is the number of pairs of antenna array elements set by the Sensor pairs parameter. Each column in Rxy contains a correlation for the corresponding pair of antenna array elements.

Dependencies

To use this port, set the Enable correlation output parameter to enabled.

Data types: Float64

Support for complex numbers: Yes

Lag — delay time of
real column vector (2M+1) by 1

Delay time values displayed as a real column vector on 1, where — the number of time samples in the input signal. Each lag time value refers to the corresponding row of the cross-correlation matrix.

Dependencies

To use this port, set the Enable correlation output parameter to enabled.

Data types: Float64

Parameters

Main

Signal propagation speed (m/s) — signal propagation speed
299792458 (default) | positive scalar

The propagation velocity of the signal in the form of a real positive scalar. The default value is the speed of light: `299792458 m/s'.

The units of measurement are m/s.

Inherit sample rate — inherit the sample rate of
enabled (by default) | disabled

Check the box to inherit the sampling rate from higher-level blocks. Otherwise, set the sampling rate using the Sample rate (Hz) parameter.

Sample rate (Hz) — pass sampling rate:q[<br>] 1e6 (default) | positive real scalar

The sampling frequency of the signal in the form of a positive scalar. The units of measurement are Hz.

Dependencies

To use this parameter, set the Inherit sample rate parameter to off.

Source of sensor pairs — option for setting pairs of antenna array elements
Auto (default) | Property

Options to choose from:

  • Property — specify the pairs of antenna array elements to calculate the correlation using the Sensor pairs parameter.

  • Auto — correlation is calculated between the first element and all other elements. The first element serves as a reference channel.

Sensor pairs — pairs of pass antenna array elements:q[<br>] [2; 1]

Pairs of antenna array elements defined as a matrix 2 on of positive integers.

Dependencies

To use this parameter, set the Source of sensor pairs parameter to Property.

Enable correlation output — option to enable the pass correlation output port:q[<br>] disabled (by default) | enabled

Select this option to display the correlation values calculated using the GCC-PHAT algorithm, as well as the corresponding delay times between pairs of antenna array elements. Correlation values are output via the Rxy port, and lag time values are output via the Lags port.

Enable delay output — option to enable the output port of the arrival delay time
disabled (by default) | enabled

Select this option to display the delay corresponding to the angle of arrival of the signal between the pairs of antenna array elements. The delay is output to the Tau port.

Sensor Array

Specify sensor array as — pass antenna array setting method:q[<br>] Array (no subarrays) (default) | Partitioned array | Replicated subarray

Specify the antenna element or antenna array. The antenna array may also contain sublattices or be broken into pieces.

Available values:

  • Array (no subarrays)

  • Partitioned array

  • Replicated subarray

Element

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

The 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 pass antenna array element:q[<br>] [0,1e20] (default) | a real vector is a 1 by 2 row

The range of operating frequencies of the antenna array element in the form of a vector row 1 by 2 in the form of [LowerBound, UpperBound]. The element has no response outside this frequency range. 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 — accounting for radiation from the radiation pattern into the rear hemisphere of the Isotropic Antenna element or Omni Microphone
disabled (by default) | enabled

Set this flag to exclude radiation into the rear hemisphere. The response from the rear hemisphere at all azimuth angles outside the ±90° range from the wide side is set to zero. The wide-angle direction 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 axis along the zero radiation.
-x (default) | +x | +y | -y | +z | -z

The direction of the axis is along the zero radiation.

Dependencies

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

Exponent of cosine pattern — exponent exponent when defining the shape of a cosine radiation pattern
[1.5, 1.5] (default) | non-negative scalar | a real matrix of non-negative values of 1 by 2

The exponent of the exponent 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 direction of the azimuth, and the second is in the direction of the angle of the place. 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) — array of operating frequencies of the antenna array element
[0,1e20] (default) | real vector is a string

The array of operating frequencies of the antenna array element 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 array element
[0,0] (default)| real vector string

The frequency response of the user elements of the antenna array is determined 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 — selection of the coordinate system of the radiation pattern of the user antenna
az-el (default) | phi-theta

The choice of the coordinate system of the radiation pattern of the user antenna is indicated by az-el or phi-theta'. When selecting `az-el, the Azimuth angles (deg) and Elevations angles (deg) parameters are used to set the coordinates of the directional pattern points. 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

The values of the azimuth angles, which will be used to calculate the antenna pattern in the form of a vector row 1 on . it must be more than 2. The azimuth angles should 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) — values of the angles of the antenna pattern position
[-90:90] (default) | real vector is a string

The values of the angles of the location 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) — values of the Phi angles of the antenna radiation pattern
[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 values of the Phi angles should be in the range from 0° to 360° 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 phi-theta.

Theta Angles (deg) — values of the angles 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 values of the Theta angles must 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 antenna radiation pattern
zeros(181.361) (default) | real matrix Q on P | real array Q on P on L

The value of the antenna pattern, 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 defined by the Elevation angles (deg) parameter, in turn, — 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 parameter Theta Angles (deg), in turn, — the length of the vector defined 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 value is an array on on , each element 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 radiation pattern of the combined antenna, defined 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, — 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 parameter Theta Angles (deg), in turn, — the length of the vector defined 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 value is an antenna array on on , each element on The grid sets 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 — align the normal of the antenna array element relative to the grid normal
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 antenna 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’s coordinate system points along the antenna array normal. 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 is set to phi-theta, checking this box rotates the radiation pattern so that the z axis of the element’s coordinate system points along the antenna array normal.

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

Dependencies

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

Radiation pattern beamwidth (deg) — the beam width of the antenna pattern
[10, 10] (default) | real scalar | a real vector is a 1 by 2 row

The beam width of the antenna pattern in degrees.

Dependencies

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

Polar pattern frequencies (Hz) — frequency values for the polar pattern of the microphone
1e3 (default) | real scalar | real vector-row 1 on L

The frequency values for the polar radiation pattern are set as a real scalar or a real vector-row 1 on . The 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) — angle values for the polar radiation pattern of the microphone
[-180:180] (default) | real vector-row 1 on P

The angle values for the polar radiation pattern of the microphone are set as a vector . 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 directional pattern of the 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 antenna array
ULA (default) | URA | UCA | Conformal Array

The geometry of the antenna array, defined as:

  • 'ULA' is a uniform linear antenna array.

  • URA is a uniform rectangular antenna array.

  • 'UCA' is a uniform circular antenna array.

  • `Conformal Array' — arbitrary arrangement of elements.

Number of elements — number of pass antenna array elements:q[<br>] 2 for ULA antenna array and 5 for UCA (default) | an integer greater than or equal to 2

The number of antenna array elements for ULA or UCA, 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 sublattice.

Dependencies

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

Array size — URA pass antenna array dimensions:q[<br>] [2,2] (default) | positive integer | vector of positive integers 1 by 2

The dimensions of the URA antenna array, specified as a positive integer or a vector of positive integers 1 by 2.

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

  • If the size of the antenna array is an integer, then 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 antenna array.

For URA, the antenna 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 antenna array for which the Array size parameter has the value [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 spacing (m) — the distance between the elements of the antenna array
0.5 for ULA arrays and [0.5,0.5] for URA arrays (default) | positive scalar for ULA or URA lattices | two-element vector of positive values for URA lattices

The distance between adjacent grid elements:

  • 'ULA` — indicate the distance between two adjacent antenna array elements in the form of 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 the Specify sensor array as parameter is set to Replicated subarray, this parameter is applied to each antenna array.

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 antenna array are evenly distributed along this axis in the local grid coordinate system.

Dependencies

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

  • This parameter is also used if the unit 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 — normal direction of the antenna array
x for URA arrays or z for UCA arrays (default) | y

The direction of the antenna array normal, set as x, y, or z.

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

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

  • The 'y` elements of the antenna array lie in the zx plane. The angular coordinate vectors of all elements are directed along the y axis.

  • The 'z` elements of the antenna 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) — the radius of the UCA pass antenna array:q[<br>] 0.5 (default) | positive scalar

The radius of the UCA antenna array, a positive scalar.

Dependencies

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

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

The positions of the elements of the conformal antenna array, given as a matrix of real values 3 by N, where N is the number of elements in the conformal array. Each column of this matrix represents the position [x;y;z] of an element of the antenna array in the local coordinate system of the antenna 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 sublattice.

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 antenna array
[0;0] | ` column vector 2 by 1 | matrix 2 by N

The direction of the normal vectors of the elements of the conformal antenna array, defined as a 2-by-1 column vector or a 2-by-N matrix. N means the number of elements in the antenna 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 antenna array. If the parameter value is a 2-by-1 column vector, then the same pointing direction is used for all elements of the antenna array.

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

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 — changing the radiation pattern of the elements of the antenna array
1 (default) | complex scalar | complex vector

The change in the radiation pattern of the antenna array elements is set as a complex scalar or a complex vector 1 by , where — the number of antenna array elements.

The coefficients that change the radiation pattern, also called element weights, multiply the responses of the antenna array elements. The coefficients 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 element of the antenna array. The number of scales must correspond to the number of antenna array elements.

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

Subarray

Subarray definition matrix — determination of the elements belonging to the antenna sublattice
logical matrix

Set the choice of the antenna sublattice in the form of a matrix on , where — the number of sublattices, and — the total number of elements in the antenna array. Each row of the matrix represents an antenna sublattice, and each entry in the row indicates that the element belongs to this sublattice. If the entry is zero, then the element does not belong to the sublattice. 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 antenna sublattice is located in the geometric center of the sublattice. The geometric center of the sublattice depends on the sublattice definition matrix and the Geometry parameters.

Dependencies

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

Subarray steering method — pass sublattice beam control method:q[<br>] None (default) | Phase | Time

The sublattice beam control method, 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 antenna sublattice
3.0e8 (default) | positive scalar

The operating frequency of the phase shift of the antenna sublattice, set 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 — phase shift quantization bits
0 (default) | a non-negative integer

The phase shift quantization bits of the antenna sublattice, 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 — pass antenna sublattice location:q[<br>] Rectangular (default) | Custom

Specify the location of the replicated antenna sublattices.

  • When setting the value to Rectangular, the Grid size and Grid spacing parameters are used to place the antenna sublattices.

  • When setting the value to Custom, the Subarray positions (m) parameters are used to place the antenna sublattices. and Subarray normals.

Dependencies

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

Grid size — dimensions of the rectangular grid of antenna sublattices
[1,2] (default)

The size of the grid of rectangular antenna sublattices, specified as a single positive integer or vector-a string of positive integers 1 by 2.

  • If Grid size is an integer scalar, then the antenna array has an equal number of sublattices 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 sublattices in each column. The second variable is the number of sublattices 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 to reproduce 3-by-2 URA sublattices when the Grid size parameter has the value [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) — the distance between antenna sublattices on a rectangular grid
Auto (default) | positive scalar | positive real vector 1 by 2

The distance between the antenna sublattices in a rectangular grid, set as a positive real scalar or vector 1 by 2 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 antenna array, replication preserves the distance between the elements of the sublattices 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 antenna sublattices
[0,0;0.5,0.5;0,0] ( by default) | a 3-by-N real matrix

The positions of the antenna sublattices in the user grid, defined as a real matrix 3 on , where — the number of sublattices in the antenna array. Each column of the matrix represents the position of one sublattice in the local coordinate system of the antenna 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 — direction of the normals of the antenna sublattices
[0,0;0,0] (default) | a 2-by-N real matrix

The direction of the normals of the sublattices of the antenna array. The value of this parameter is a matrix of size 2 by , where — the number of sublattices in the antenna array. Each column of the matrix defines the direction of the normal of the corresponding sublattice 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 arrangement in which pairs of antenna sublattices 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.