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Narrowband MVDR (Capon) beamformer

**Library:**Phased Array System Toolbox / Beamforming

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

`X`

— Input signalInput signal, specified as an *M*-by-*N* matrix,
where *M* is the number of samples in the data, and *N* is
the number of array elements.

The size of the first dimension of the input matrix can vary to simulate a changing signal length. A size change can occur, for example, in the case of a pulse waveform with variable pulse repetition frequency.

**Data Types: **`double`

**Complex Number Support: **Yes

`XT`

— Training signalTraining signal, specified as an *M*-by-*N* matrix, where
*M* is the number of samples in the data, and
*N* is the number of array elements.

The size of the first dimension of the input matrix can vary to simulate a changing signal length. A size change can occur, for example, in the case of a pulse waveform with variable pulse repetition frequency.

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

**Data Types: **`double`

**Complex Number Support: **Yes

`Ang`

— Beamforming direction`2`

-by-`1`

real-valued vector | `2`

-by-Beamforming direction, specified as a `2`

-by-*L* real-valued
matrix, where *L* is the number of beamforming directions.
Each column takes the form of `[AzimuthAngle;ElevationAngle]`

.
Angle units are in degrees. The azimuth angle must lie between –180°
and 180°, inclusive, and the elevation angle must lie between
–90° and 90°, inclusive. Angles are defined with
respect to the local coordinate system of the array.

To enable this port, set the **Source of beamforming
direction** parameter to `Input port`

.

**Data Types: **`double`

`Y`

— Beamformed outputBeamformed output, returned as an *M*-by-*L* complex-valued
matrix. The quantity *M* is the number of signal
samples and *L* is the number of desired beamforming
directions specified by the `Beamforming direction`

parameter
or from the `Ang`

port.

**Data Types: **`double`

**Complex Number Support: **Yes

`W`

— Beamforming weightsBeamformed weights, returned as an *N*-by-*L* complex-valued
matrix. The quantity *N* is the number of array elements.
When the **Specify sensor array as** parameter is
set to `Partitioned array`

or ```
Replicated
subarray
```

, *N* represents the number of
subarrays. *L* is the number of desired beamforming
directions specified in the `Ang`

port or by the ```
Beamforming
direction (deg)
```

property. There is one set of weights for
each beamforming direction.

To enable this port, select the **Enable weights output** checkbox.

**Data Types: **`double`

**Complex Number Support: **Yes

`Signal propagation speed (m/s)`

— Signal propagation speed`physconst('LightSpeed')`

(default) | real-valued positive scalarSignal propagation speed, specified as a real-valued positive scalar. The default value of the
speed of light is the value returned by `physconst('LightSpeed')`

.
Units are in meters per second.

**Example: **`3e8`

**Data Types: **`double`

`Operating frequency (Hz)`

— System operating frequency`3.0e8`

(default) | positive real scalarSystem operating frequency, specified as a positive scalar. Units are in Hz.

`Diagonal loading factor`

— Diagonal loading factor for stabilitynonnegative scalar

Specify the diagonal loading factor as a nonnegative scalar. Diagonal loading is a technique used to achieve robust beamforming performance, especially when the sample support is small.

`Enable training data input`

— Enable the use of training dataoff (default) | on

Select this check box to specify additional training data via
the input port `XT`

. To use the input signal as the
training data, clear the check box which removes the port.

`Source of beamforming direction`

— Source of beamforming direction`Property`

(default) | `Input port`

Source of beamforming direction, specified as `Property`

or ```
Input
port
```

. When you set **Source of beamforming direction** to `Property`

,
you then set the direction using the **Beamforming direction
(deg)** parameter. When you select `Input port`

,
the direction is determined by the input to the `Ang`

port.

`Beamforming direction (deg)`

— Beamforming directionsBeamforming directions, specified as a *2*-by-*L* real-valued
matrix, where *L* is the number of beamforming directions.
Each column takes the form `[AzimuthAngle;ElevationAngle]`

.
Angle units are in degrees. The azimuth angle must lie between –180°
and 180°. The elevation angle must lie between –90°
and 90°. Angles are defined with respect to the local coordinate
system of the array.

To enable this parameter, set the **Source of beamforming
direction** parameter to `Property`

.

`Number of bits in phase shifters`

— Number of phase shift quantization bits`0`

(default) | nonnegative integerThe number of bits used to quantize the phase shift component of beamformer or steering vector weights. Specify the number of bits as a non-negative integer. A value of zero indicates that no quantization is performed.

`Enable weights output`

— Option to output beamformer weightsoff (default) | on

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

.

`Simulate using`

— Block simulation method`Interpreted Execution`

(default) | `Code Generation`

Block simulation, specified as `Interpreted Execution`

or ```
Code
Generation
```

. If you want your block to use the MATLAB^{®} interpreter,
choose `Interpreted Execution`

. If you want
your block to run as compiled code, choose `Code Generation`

.
Compiled code requires time to compile but usually runs faster.

Interpreted execution is useful when you are developing and tuning a model. The block runs the
underlying System
object™ in MATLAB. You can change and execute your model quickly. When you are satisfied
with your results, you can then run the block using ```
Code
Generation
```

. Long simulations run faster than in interpreted execution.
You can run repeated executions without recompiling, but if you change any block
parameters, then the block automatically recompiles before execution.

This table shows how the **Simulate using** parameter affects the overall
simulation behavior.

When the Simulink^{®} model is in `Accelerator`

mode, the block mode specified
using **Simulate using** overrides the simulation mode.

**Acceleration Modes**

Block Simulation | Simulation Behavior | ||

`Normal` | `Accelerator` | `Rapid Accelerator` | |

`Interpreted Execution` | The block executes using the MATLAB interpreter. | The block executes using the MATLAB interpreter. | Creates a standalone executable from the model. |

`Code Generation` | The block is compiled. | All blocks in the model are compiled. |

For more information, see Choosing a Simulation Mode (Simulink).

`Specify sensor array as`

— Method to specify array`Array (no subarrays)`

(default) | `Partitioned array`

| `Replicated subarray`

| `MATLAB expression`

Method to specify array, specified as ```
Array (no
subarrays)
```

or `MATLAB expression`

.

`Array (no subarrays)`

— use the block parameters to specify the array.`Partitioned array`

— use the block parameters to specify the array.`Replicated subarray`

— use the block parameters to specify the array.`MATLAB expression`

— create the array using a MATLAB expression.

`Expression`

— MATLAB expression used to create an arrayPhased Array System Toolbox™ array System object

MATLAB expression used to create an array, specified as a valid Phased Array System Toolbox array System object.

**Example: **`phased.URA('Size',[5,3])`

To enable this parameter, set **Specify sensor array
as** to `MATLAB expression`

.

`Element type`

— Array element types`Isotropic Antenna`

(default) | `Cosine Antenna`

| `Custom Antenna`

| `Omni Microphone`

| `Custom Microphone`

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

`Isotropic Antenna`

`Cosine Antenna`

`Custom Antenna`

`Omni Microphone`

`Custom Microphone`

`Operating frequency range (Hz)`

— Operating frequency range of the antenna or microphone element`[0,1.0e20]`

(default) | real-valued 1-by-2 row vectorSpecify the operating frequency range of the antenna or microphone
element as a 1-by-2 row vector in the form `[LowerBound,UpperBound]`

.
The element has no response outside this frequency range. Frequency
units are in Hz.

To enable this parameter, set **Element type** to ```
Isotropic
Antenna
```

, `Cosine Antenna`

, or ```
Omni
Microphone
```

.

`Operating frequency vector (Hz)`

— Operating frequency range of custom antenna or microphone elements`[0,1.0e20]`

(default) | real-valued row vectorSpecify the frequencies at which to set antenna and microphone
frequency responses as a 1-by-*L* row vector of increasing
real values. The antenna or microphone element has no response outside
the frequency range specified by the minimum and maximum elements
of this vector. Frequency units are in Hz.

To enable this parameter, set **Element type** to ```
Custom
Antenna
```

or `Custom Microphone`

. Use **Frequency
responses (dB)** to set the responses at these frequencies.

`Baffle the back of the element`

— Set back response of an `Isotropic Antenna`

element or an `Omni Microphone`

element to zerooff (default) | on

Select this check box to baffle the back response of the element. When back baffled, the responses at all azimuth angles beyond ±90° from broadside are set to zero. The broadside direction is defined as 0° azimuth angle and 0° elevation angle.

To enable this check box, set **Element type** to ```
Isotropic
Antenna
```

or `Omni Microphone`

.

`Exponent of cosine pattern`

— Exponents of azimuth and elevation cosine patterns`[1.5 1.5]`

(default) | nonnegative scalar | real-valued 1-by-2 matrix of nonnegative valuesSpecify the exponents of the cosine pattern as a nonnegative scalar or a real-valued 1-by-2
matrix of nonnegative values. When **Exponent of cosine pattern** is a
1-by-2 vector, the first element is the exponent in the azimuth direction and the second
element is the exponent in the elevation direction. When you set this parameter to a
scalar, both the azimuth direction and elevation direction cosine patterns are raised to
the same power.

To enable this parameter, set **Element type** to ```
Cosine
Antenna
```

.

`Frequency responses (dB)`

— Antenna and microphone frequency response`[0,0]`

(default) | real-valued row vectorFrequency response of a custom antenna or custom microphone
for the frequencies defined by the **Operating frequency vector
(Hz)** parameter. The dimensions of **Frequency responses
(dB)** must match the dimensions of the vector specified
by the **Operating frequency vector (Hz)** parameter.

To enable this parameter, set **Element type** to ```
Custom
Antenna
```

or `Custom Microphone`

.

`Azimuth angles (deg)`

— Azimuth angles of antenna radiation pattern `[-180:180]`

(default) | real-valued row vectorSpecify the azimuth angles at which to calculate the antenna
radiation pattern as a 1-by-*P* row vector. *P* must
be greater than 2. Azimuth angles must lie between –180°
and 180°, inclusive, and be in strictly increasing order.

To enable this parameter, set **Element type** to ```
Custom
Antenna
```

.

`Elevation angles (deg)`

— Elevation angles of antenna radiation pattern`[-90:90]`

(default) | real-valued row vectorSpecify the elevation angles at which to compute the radiation
pattern as a 1-by-*Q* vector. *Q* must
be greater than 2. Angle units are in degrees. Elevation angles must
lie between –90° and 90°, inclusive, and be in strictly
increasing order.

To enable this parameter, set **Element type** to ```
Custom
Antenna
```

.

`Magnitude pattern (dB)`

— Magnitude of combined antenna radiation pattern`zeros(181,361)`

(default) | real-valued Magnitude of the combined antenna radiation pattern, specified as a
*Q*-by-*P* matrix or a
*Q*-by-*P*-by-*L* array. The quantity
*Q* equals the length of the vector specified by **Elevation angles
(deg)**. The quantity *P* equals length of the vector specified by
**Azimuth angles (deg)**. The quantity *L* equals the length
of the **Operating frequency vector (Hz)**.

If this parameter is a

*Q*-by-*P*matrix, the same pattern is applied to*all*frequencies specified in the**Operating frequency vector (Hz)**parameter.If the value is a

*Q*-by-*P*-by-*L*array, each*Q*-by-*P*page of the array specifies a pattern for the*corresponding*frequency specified in the**Operating frequency vector (Hz)**parameter.

To enable this parameter, set **Element type** to ```
Custom
Antenna
```

.

`Phase pattern (deg)`

— Custom antenna radiation phase pattern`zeros(181,361)`

(default) | real-valued Phase of the combined antenna radiation pattern, specified as a
*Q*-by-*P* matrix or a
*Q*-by-*P*-by-*L* array. The quantity
*Q* equals the length of the vector specified by **Elevation angles
(deg)**. The quantity *P* equals length of the vector specified by
**Azimuth angles (deg)**. The quantity *L* equals the length
of the **Operating frequency vector (Hz)**.

If this parameter is a

*Q*-by-*P*matrix, the same pattern is applied to*all*frequencies specified in the**Operating frequency vector (Hz)**parameter.If the value is a

*Q*-by-*P*-by-*L*array, each*Q*-by-*P*page of the array specifies a pattern for the*corresponding*frequency specified in the**Operating frequency vector (Hz)**parameter.

To enable this parameter, set **Element type** to ```
Custom
Antenna
```

.

`Polar pattern frequencies (Hz)`

— Polar pattern microphone response frequencies1e3 (default) | real scalar | real-valued 1-by-

Polar pattern microphone response frequencies, specified as a real scalar, or a
real-valued, 1-by-*L* vector. The response frequencies lie within the
frequency range specified by the **Operating frequency vector (Hz)**
vector.

To enable this parameter, set **Element type** set to
`Custom Microphone`

.

`Polar pattern angles (deg)`

— Polar pattern response angles`[-180:180]`

(default) | real-valued -by-Specify the polar pattern response angles, as a 1-by-*P* vector.
The angles are measured from the central pickup axis of the microphone
and must be between –180° and 180°, inclusive.

To enable this parameter, set **Element type** to ```
Custom
Microphone
```

.

`Polar pattern (dB)`

— Custom microphone polar response`zeros(1,361)`

(default) | real-valued Specify the magnitude of the custom microphone element polar patterns as an
*L*-by-*P* matrix. *L* is the
number of frequencies specified in **Polar pattern frequencies (Hz)**.
*P* is the number of angles specified in **Polar pattern
angles (deg)**. Each row of the matrix represents the magnitude of the
polar pattern measured at the corresponding frequency specified in **Polar
pattern frequencies (Hz)** and all angles specified in **Polar
pattern angles (deg)**. The pattern is measured in the azimuth plane. In
the azimuth plane, the elevation angle is 0° and the central pickup axis is 0°
degrees azimuth and 0° degrees elevation. The polar pattern is symmetric around the
central axis. You can construct the microphone response pattern in 3-D space from the
polar pattern.

To enable this parameter, set **Element type** to ```
Custom
Microphone
```

.

`Geometry`

— Array geometry`ULA`

(default) | `URA`

| `UCA`

| `Conformal Array`

Array geometry, specified as one of

`ULA`

— Uniform linear array`URA`

— Uniform rectangular array`UCA`

— Uniform circular array`Conformal Array`

— arbitrary element positions

`Number of elements`

— Number of array elements`2`

for ULA arrays and `5`

for
UCA arrays (default) | integer greater than or equal to 2The number of array elements for ULA or UCA arrays, specified as an integer greater than or equal to 2.

When you set **Specify sensor array as** to ```
Replicated
subarray
```

, this parameter applies to each subarray.

To enable this parameter, set **Geometry** to `ULA`

or `UCA`

.

`Element spacing (m)`

— Spacing between array elements`0.5`

for ULA arrays and `[0.5,0.5]`

for
URA arrays (default) | positive scalar for ULA or URA arrays | 2-element vector of positive values for URA arraysSpacing between adjacent array elements:

ULA — specify the spacing between two adjacent elements in the array as a positive scalar.

URA — specify the spacing as a positive scalar or a 1-by-2 vector of positive values. If

**Element spacing (m)**is a scalar, the row and column spacings are equal. If**Element spacing (m)**is a vector, the vector has the form`[SpacingBetweenArrayRows,SpacingBetweenArrayColumns]`

.When you set

**Specify sensor array as**to`Replicated subarray`

, this parameter applies to each subarray.

To enable this parameter, set **Geometry** to `ULA`

or `URA`

.

`Array axis`

— Linear axis direction of ULA`y`

(default) | `x`

| `z`

Linear axis direction of ULA, specified as `y`

, `x`

,
or `z`

. All ULA array elements are uniformly
spaced along this axis in the local array coordinate system.

To enable this parameter, set

**Geometry**to`ULA`

.This parameter is also enabled when the block only supports ULA arrays.

`Array size`

— Dimensions of URA array`[2,2]`

(default) | positive integer | 1-by-2 vector of positive integersDimensions of a URA array, specified as a positive integer or 1-by-2 vector of positive integers.

If

**Array size**is a 1-by-2 vector, the vector has the form`[NumberOfArrayRows,NumberOfArrayColumns]`

.If

**Array size**is an integer, the array has the same number of rows and columns.When you set

**Specify sensor array as**to`Replicated subarray`

, this parameter applies to each subarray.

For a URA, array elements are indexed from top to bottom along the
leftmost column, and then continue to the next columns from left to right. In this
figure, the **Array size** value of `[3,2]`

creates an
array having three rows and two columns.

To enable this parameter, set **Geometry** to `URA`

.

`Element lattice`

— Lattice of URA element positions`Rectangular`

(default) | `Triangular`

Lattice of URA element positions, specified as `Rectangular`

or `Triangular`

.

`Rectangular`

— Aligns all the elements in row and column directions.`Triangular`

— Shifts the even-row elements of a rectangular lattice toward the positive row-axis direction. The displacement is one-half the element spacing along the row dimension.

To enable this parameter, set **Geometry** to `URA`

.

`Array normal`

— Array normal direction`x`

for URA arrays
or `z`

for UCA arrays (default) | `y`

Array normal direction, specified as `x`

, `y`

,
or `z`

.

Elements of planar arrays lie in a plane orthogonal to the selected array normal direction. Element boresight directions point along the array normal direction.

Array Normal Parameter Value | Element Positions and Boresight Directions |
---|---|

`x` | Array elements lie in the yz-plane. All
element boresight vectors point along the x-axis. |

`y` | Array elements lie in the zx-plane. All
element boresight vectors point along the y-axis. |

`z` | Array elements lie in the xy-plane. All
element boresight vectors point along the z-axis. |

To enable this parameter, set **Geometry** to `URA`

or `UCA`

.

`Radius of UCA (m)`

— UCA array radius0.5 (default) | positive scalar

Radius of UCA array, specified as a positive scalar.

To enable this parameter, set **Geometry** to `UCA`

.

`Element positions (m)`

— Positions of conformal array elements`[0;0;0]`

(default) | 3-by-Positions of the elements in a conformal array, specified as
a 3-by-*N* matrix of real values, where *N* is
the number of elements in the conformal array. Each column of this
matrix represents the position `[x;y;z]`

of an array
element in the array local coordinate system. The origin of the local
coordinate system is *(0,0,0)*. Units are in meters.

**Specify sensor array as** to ```
Replicated
subarray
```

, this parameter applies to each subarray.

To enable this parameter set **Geometry** to ```
Conformal
Array
```

.

`Element normals (deg)`

— Direction of conformal array element normal vectors`[0;0]`

| 2-by-1 column vector | 2-by-Direction of element normal vectors in a conformal array, specified as a 2-by-1 column vector
or a 2-by-*N* matrix. *N* indicates the number of
elements in the array. For a matrix, each column specifies the normal direction of the
corresponding element in the form `[azimuth;elevation]`

with respect to
the local coordinate system. The local coordinate system aligns the positive
*x*-axis with the direction normal to the conformal array. If the
parameter value is a 2-by-1 column vector, the same pointing direction is used for all
array elements.

**Specify sensor array as** to ```
Replicated
subarray
```

, this parameter applies to each subarray.

You can use the **Element positions (m)** and **Element
normals (deg)** parameters to represent any arrangement in
which pairs of elements differ by certain transformations. The transformations
can combine translation, azimuth rotation, and elevation rotation.
However, you cannot use transformations that require rotation about
the normal direction.

To enable this parameter, set **Geometry** to ```
Conformal
Array
```

.

`Taper`

— Array element tapers1 (default) | complex-valued scalar | complex-valued row vector

Element tapering, specified as a complex-valued scalar or a
complex-valued 1-by-*N* row vector. In this vector, *N* represents
the number of elements in the array.

Also known as *element weights*, tapers multiply the array element
responses. Tapers modify both amplitude and phase of the response to reduce side lobes
or steer the main response axis.

If **Taper** is a scalar, the same weight is
applied to each element. If **Taper** is a vector,
a weight from the vector is applied to the corresponding sensor element.
The number of weights must match the number of elements of the array.

**Specify sensor array as** to ```
Replicated
subarray
```

, this parameter applies to each subarray.

`Subarray definition matrix`

— Define elements belonging to subarrayslogical matrix

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

The phase center of each subarray lies at the subarray geometric center. The subarray
geometric center depends on the **Subarray definition matrix** and
**Geometry** parameters.

To enable this parameter, set **Specify sensor array as** to
`Partitioned array`

.

`Subarray steering method`

— Specify subarray steering method`None`

(default) | `Phase`

| `Time`

Subarray steering method, specified as one of

`None`

`Phase`

`Time`

`Custom`

Selecting `Phase`

or `Time`

opens the
`Steer`

input port on the Narrowband Receive Array,
Narrowband Transmit Array, Wideband Receive Array,
Wideband Transmit Array blocks, Constant Gamma
Clutter, and GPU Constant Gamma Clutter blocks.

Selecting `Custom`

opens the `WS`

input port on the
Narrowband Receive Array, Narrowband Transmit Array,
Wideband Receive Array, Wideband Transmit Array
blocks, Constant Gamma Clutter, and GPU Constant Gamma
Clutter blocks.

To enable this parameter, set **Specify sensor array as** to
`Partitioned array`

or ```
Replicated
subarray
```

.

`Phase shifter frequency (Hz)`

— Subarray phase shifting frequency`3.0e8`

(default) | positive real-valued scalarOperating frequency of subarray steering phase shifters, specified as a positive real-valued scalar. Units are Hz.

To enable this parameter, set **Sensor array** to ```
Partitioned
array
```

or `Replicated subarray`

and set **Subarray
steering method** to `Phase`

.

`Number of bits in phase shifters`

— Subarray steering phase shift quantization bits`0`

(default) | non-negative integerSubarray steering phase shift quantization bits, specified as a non-negative integer. A value of zero indicates that no quantization is performed.

To enable this parameter, set **Sensor array** to ```
Partitioned
array
```

or `Replicated subarray`

and set **Subarray
steering method** to `Phase`

.

`Subarrays layout`

— Subarray position specification`Rectangular`

(default) | `Custom`

Specify the layout of replicated subarrays as `Rectangular`

or `Custom`

.

When you set this parameter to

`Rectangular`

, use the**Grid size**and**Grid spacing**parameters to place the subarrays.When you set this parameter to

`Custom`

, use the**Subarray positions (m)**and**Subarray normals**parameters to place the subarrays.

To enable this parameter, set **Sensor array** to ```
Replicated
subarray
```

`Grid size`

— Dimensions of rectangular subarray grid`[1,2]`

(default)Rectangular subarray grid size, specified as a single positive integer, or a 1-by-2 row vector of positive integers.

If **Grid size** is an integer scalar, the
array has an equal number of subarrays in each row and column. If **Grid
size** is a 1-by-2 vector of the form ```
[NumberOfRows,
NumberOfColumns]
```

, the first entry is the number of subarrays
along each column. The second entry is the number of subarrays in
each row. A row is along the local *y*-axis, and
a column is along the local *z*-axis. The figure
here shows how you can replicate a 3-by-2 URA subarray using a **Grid
size** of `[1,2]`

.

To enable this parameter, set **Sensor array** to ```
Replicated
subarray
```

and **Subarrays layout** to `Rectangular`

.

`Grid spacing (m)`

— Spacing between subarrays on rectangular grid`Auto`

(default) | positive real-valued scalar | 1-by-2 vector of positive real-valuesThe rectangular grid spacing of subarrays, specified as a positive,
real-valued scalar, a 1-by-2 row vector of positive, real-values,
or `Auto`

. Units are in meters.

If

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

**Grid spacing**is a 1-by-2 row vector, the vector has the form`[SpacingBetweenRows,SpacingBetweenColumn]`

. The first entry specifies the spacing between rows along a column. The second entry specifies the spacing between columns along a row.If

**Grid spacing**is set to`Auto`

, replication preserves the element spacing of the subarray for both rows and columns while building the full array. This option is available only when you specify**Geometry**as`ULA`

or`URA`

.

To enable this parameter, set **Sensor array** to ```
Replicated
subarray
```

and **Subarrays layout** to `Rectangular`

.

`Subarray positions (m)`

— Positions of subarrays`[0,0;0.5,0.5;0,0]`

(default) | 3-by-Positions of the subarrays in the custom grid, specified as
a real 3-by-*N* matrix, where *N* is
the number of subarrays in the array. Each column of the matrix represents
the position of a single subarray in the array local coordinate system.
The coordinates are expressed in the form `[x; y; z]`

.
Units are in meters.

To enable this parameter, set **Sensor array** to ```
Replicated
subarray
```

and **Subarrays layout** to `Custom`

.

`Subarray normals`

— Direction of subarray normal vectors`[0,0;0,0]`

(default) | 2-by-Specify the normal directions of the subarrays in the array.
This parameter value is a 2-by-*N* matrix, where *N* is
the number of subarrays in the array. Each column of the matrix specifies
the normal direction of the corresponding subarray, in the form `[azimuth;elevation]`

.
Angle units are in degrees. Angles are defined with respect to the
local coordinate system.

You can use the **Subarray positions** and **Subarray
normals** parameters to represent any arrangement in which
pairs of subarrays differ by certain transformations. The transformations
can combine translation, azimuth rotation, and elevation rotation.
However, you cannot use transformations that require rotation about
the normal.

To enable this parameter, set the **Sensor array** parameter
to `Replicated subarray`

and the **Subarrays
layout** to `Custom`

.

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