# Documentation

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# GPU Constant Gamma Clutter

Constant gamma clutter simulation using gpu

## Library

Environment and Targets

`phasedenvlib`

## Description

The GPU Constant Gamma Clutter block generates, using a GPU, constant gamma clutter reflected from homogeneous terrain for a monostatic radar transmitting a narrowband signal into free space. The radar is assumed to be at constant altitude moving at constant speed.

## Parameters

Terrain gamma value (dB)

Specify the $\gamma$ value used in the constant $\gamma$ clutter model, as a scalar in dB. The $\gamma$ value depends on both terrain type and the operating frequency.

Earth model

Specify the earth model used in clutter simulation as `Flat` or `Curved`. When you set this parameter to `Flat`, the earth is assumed to be a flat plane. When you set this parameter to `Curved`, the earth is assumed to be a sphere.

Maximum range (m)

Specify the maximum range in meters for the clutter simulation as a positive scalar. The maximum range must be greater than the value specified in the Radar height parameter on the Radar panel.

Azimuth coverage (deg)

Specify the azimuth coverage in degrees as a positive scalar. The clutter simulation covers a region having the specified azimuth span, symmetric to zero degrees azimuth. Typically, all clutter patches have their azimuth centers within the region, but by setting the Clutter patch azimuth span value, you can cause some patches to extend beyond the region.

Clutter patch azimuth span (deg)

Specify the azimuth span of each clutter patch in degrees as a positive scalar.

Clutter coherence time (s)

Specify the coherence time in seconds for the clutter simulation as a positive scalar. After the coherence time elapses, block updates the random numbers it uses for the clutter simulation at the next pulse. A value of `inf` means the random numbers are never updated.

Signal Propagation speed (m/s)

Specify the propagation speed of the signal, in meters per second, as a positive scalar. You can use the function `physconst` to specify the speed of light.

Sample rate (Hz)

Specify the signal sample rate in hertz as a positive scalar. This parameter should be set to the same value as used in any of the Waveforms library blocks.

Pulse repetition frequency (Hz)

Specify the pulse repetition frequency, PRF, as a scalar or a row vector. Units for PRF are hertz. This parameter should be set to the same value as used in any `Waveforms` library block.

Output signal format

Specify the format of the output signal as one of `Pulses` or `Samples`.

This parameter should be set to the same value as used in any Waveforms library blocks.

Number of pulses in output

Specify the number of pulses in the block output as a positive integer. This parameter appears only when you set the Output signal format parameter to `Pulses` and should be set to the same value as used in any Waveforms library blocks.

Number of samples in output

Specify the number of samples in the block output as a positive integer. This parameter appears only when you set the Output signal format parameter to `Samples` and should be set to the same value as used in any Waveforms library blocks.

Simulate using

Block simulation method, 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 they would in interpreted execution. You can run repeated executions without recompiling. However, if you change any block parameters, then the block automatically recompiles before execution.

When setting this parameter, you must take into account the overall model simulation mode. The table shows how the Simulate using parameter interacts with the overall simulation mode.

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.

Operating frequency (Hz)

Specify the operating frequency of the system, in hertz, as a positive scalar.

Effective transmitted power (W)

Specify the transmitted effective radiated power (ERP) of the radar system in watts as a positive scalar.

Specify the radar platform height in meters, measured upward from the surface as a nonnegative scalar.

Specify the radar platform’s speed as a nonnegative scalar in meters per second.

Specify the direction of radar platform motion as a 2-by-1 vector in the form `[AzimuthAngle; ElevationAngle]` in degrees. Both azimuth and elevation angle are measured in the local coordinate system of the radar antenna or antenna array. Azimuth angle must be between –180° and 180°. Elevation angle must be between –90° and 90°.

Specify the depression angle of the radar antenna array in degrees with respect to broadside. This value is a scalar. Broadside is defined as zero degrees azimuth and zero degrees elevation. The depression angle is measured downward from horizontal.

### Array Parameters

Specify sensor array as

Specify sensor element or sensor array. A sensor array can also contain subarrays or be a partitioned array. This parameter can also be expressed as a MATLAB expression.

Types

 `Single element` `Array (no subarrays)` `Partitioned array` `Replicated subarray` `MATLAB expression`

Geometry

Specify the array geometry as one of the following:

• `ULA` — Uniform linear array

• `URA` — Uniform rectangular array

• `UCA` — Uniform circular array

• `Conformal Array` — arbitrary element positions

Number of elements

Number of array elements.

Number of array elements, specified as a positive integer. This parameter appears when the Geometry is set to `ULA` or `UCA`. If Sensor Array has a `Replicated subarray` option, this parameter applies to the sub-array.

Array size

This parameter appears when Geometry is set to `URA`. When Sensor Array is set to `Replicated subarray`, this parameter applies to the subarrays.

Specify the size of the array 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.

For a URA, elements are indexed from top to bottom along a column and continuing to the next columns from left to right. In this figure, an Array size of `[3,2]` produces an array of three rows and two columns.

Element spacing (m)

This parameter appears when Geometry is set to `ULA` or `URA`. When Sensor Array has the `Replicated subarray` option, this parameter applies to the subarrays.

• For a `ULA`, specify the spacing, in meters, between two adjacent elements in the array as a scalar.

• For a `URA`, specify the element spacing of the array, in meters, as a 1-by-2 vector or a scalar. If Element spacing is a 1-by-2 vector, the vector has the form `[SpacingBetweenRows,SpacingBetweenColumns]`. For a discussion of these quantities, see `phased.URA`. If Element spacing is a scalar, the spacings between rows and columns are equal.

Array axis

This parameter appears when the Geometry parameter is set to `ULA` or when the block only supports a ULA array geometry. Specify the array axis as `x`, `y`, or `z`. All ULA array elements are uniformly spaced along this axis in the local array coordinate system.

Array normal,

This parameter appears when you set Geometryto `URA` or `UCA`. Specify the Array normal as `x`, `y`, or `z`. All URA and UCA array elements are placed in the yz, zx, or xyplanes, respectively, of the array coordinate system.

Radius of a uniform circular array specified as a positive scalar. Units are meters.

This parameter appears when the Geometry is set to `UCA`.

Taper

Tapers, also known as element weights, are applied to sensor elements in the array. Tapers are used to modify both the amplitude and phase of the transmitted or received data.

This parameter applies to all array types, but when you set Sensor Array to `Replicated subarray`, this parameter applies to subarrays.

• For a `ULA` or `UCA`, specify element tapering as a complex-valued scalar or a complex-valued 1-by-N row vector. In this vector, N represents the number of elements in the array. 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. A weight must be applied to each element in the sensor array.

• For a `URA`, specify element tapering as a complex-valued scalar or complex-valued M-by-N matrix. In this matrix, M is the number of elements along the z-axis, and N is the number of elements along the y-axis. M and N correspond to the values of `[NumberofArrayRows,NumberOfArrayColumns]` in the Array size matrix. If `Taper` is a scalar, the same weight is applied to each element. If Taper is a matrix, a weight from the matrix is applied to the corresponding sensor element. A weight must be applied to each element in the sensor array.

• For a `Conformal Array`, specify element tapering as a complex-valued scalar or complex-valued 1-by-N vector. In this vector, N is the number of elements in the array as determined by the size of the Element positions vector. If Taper is a scalar, the same weight is applied to each element. If the value of Taper is a vector, a weight from the vector is applied to the corresponding sensor element. A weight must be applied to each element in the sensor array.

Element lattice

This parameter appears when Geometry is set to `URA`. When Sensor Array is set to `Replicated subarray`, this parameter applies to the subarray.

Specify the element lattice 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.

Element positions (m)

This parameter appears when Geometry is set to `Conformal Array`. When Sensor Array is set to `Replicated subarray`, this parameter applies to subarrays.

Specify the positions of conformal array elements as a 3-by-N matrix, where N is the number of elements in the conformal array. Each column of Element positions (m) represents the position of a single element, in the form `[x;y;z]`, in the array’s local coordinate system. The local coordinate system has its origin at an arbitrary point. Units are in meters.

Element normals (deg)

This parameter appears when Geometry is set to `Conformal Array`. When Sensor Array is set to `Replicated subarray`, this parameter applies to subarrays.

Specify the normal directions of the elements in a conformal array as a 2-by-N matrix or a 2-by-1 column vector in degrees. The variable N indicates the number of elements in the array. If Element normals (deg) is a matrix, each column specifies the normal direction of the corresponding element in the form `[azimuth;elevation]`, with respect to the local coordinate system. The local coordinate system aligns the positive x-axis with the direction normal to the conformal array. If Element normals (deg) is a 2-by-1 column vector, the vector specifies the same pointing direction for all elements in the array.

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. You can combine translation, azimuth rotation, and elevation rotation transformations. However, you cannot use transformations that require rotation about the normal.

Subarray definition matrix

This parameter appears when Specify sensor array as is set to `Partitioned array`.

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 corresponds to a subarray and each entry in the row indicates whether or not 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 is its geometric center. Subarray definition matrix and Geometry determine the geometric center.

Subarray steering method

This parameter appears when the Specify sensor array as parameter is set to `Partitioned array` or ```Replicated subarray```.

Specify the subarray steering method as either

• `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.

Phase shifter frequency (Hz)

This parameter appears when you set Sensor array to ```Partitioned array``` or `Replicated subarray` and you set Subarray steering method to `Phase`.

Specify the operating frequency, in hertz, of phase shifters to perform subarray steering as a positive scalar.

Number of bits in phase shifters

This parameter appears when you set Sensor array to ```Partitioned array``` or `Replicated subarray` and you set Subarray steering method to `Phase`.

The 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.

Subarrays layout

This parameter appears when you set Sensor array to ```Replicated subarray```.

Specify the layout of the replicated subarrays as `Rectangular` or `Custom`.

Grid size

This parameter appears when you set Sensor array to ```Replicated subarray``` and Subarrays layout to `Rectangular`.

Rectangular subarray grid size, specified as a single positive integer or a positive integer-valued 1-by-2 row vector.

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]`.

Grid spacing

This parameter appears when you set Sensor array to ```Replicated subarray``` and Subarrays layout to `Rectangular`.

Specify the rectangular grid spacing of subarrays as a real-valued positive scalar, a 1-by-2 row vector, or `Auto`. Grid spacing units are expressed 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`.

Subarray positions (m)

This parameter appears when you set Sensor array to ```Replicated subarray``` and Subarrays layout to `Custom`.

Specify the positions of the subarrays in the custom grid as a 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 meters, in the array’s local coordinate system. The coordinates are expressed in the form ```[x; y; z]```.

Subarray normals

This parameter appears when you set the Sensor array parameter to `Replicated subarray` and the Subarrays layout to `Custom`.

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]```. Each angle is in degrees and is defined in 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.

Expression

A valid MATLAB expression containing an array constructor, for example, `phased.URA`.

### Sensor Array Tab: Element Parameters

Element type

Specify the antenna or microphone type as

• `Isotropic Antenna`

• `Cosine Antenna`

• `Custom Antenna`

Exponent of cosine pattern

This parameter appears when you set Element type to ```Cosine Antenna```.

Specify the exponent of the cosine pattern as a scalar or a 1-by-2 vector. You must specify all values as non-negative real numbers. When you set Exponent of cosine pattern to a scalar, both the azimuth direction cosine pattern and the elevation direction cosine pattern are raised to the specified value. When you set Exponent of cosine pattern to a 1-by-2 vector, the first element is the exponent for the azimuth direction cosine pattern and the second element is the exponent for the elevation direction cosine pattern.

Operating frequency range

This parameter appears when Element type is set to `Isotropic Antenna` or `Cosine Antenna`.

Specify the operating frequency range, in hertz, of the antenna element as a 1-by-2 row vector in the form `[LowerBound,UpperBound]`. The antenna element has no response outside the specified frequency range.

Operating frequency vector (Hz)

This parameter appears when Element type is set to `Custom Antenna` or `Custom Microphone`.

Specify the frequencies, in Hz, at which to set the antenna and microphone frequency responses as a 1-by-L row vector of increasing values. Use Frequency responses to set the frequency responses. The antenna or microphone element has no response outside the frequency range specified by the minimum and maximum elements of Operating frequency vector (Hz).

Frequency responses (dB)

This parameter appears when Element type is set to `Custom Antenna` or `Custom Microphone`.

Specify this parameter as the frequency response of an antenna or microphone, in decibels, for the frequencies defined by Operating frequency vector (Hz). Specify Frequency responses (dB) as a 1-by-L vector matching the dimensions of the vector specified in Operating frequency vector (Hz).

Azimuth angles (deg)

This parameter appears when Element type is set to `Custom Antenna`.

Specify the azimuth angles at which to calculate the antenna radiation pattern as a 1-by-P row vector. P must be greater than 2. Angle units are in degrees. Azimuth angles must lie between –180° and 180° and be in strictly increasing order.

Elevation angles (deg)

This parameter appears when the Element type is set to `Custom Antenna`.

Specify the elevation angles at which to compute the radiation pattern as a 1-by-Q vector. Q must be greater than 2. Angle units are in degrees. Elevation angles must lie between –90° and 90° and be in strictly increasing order.

This parameter appears when the Element type is set to `Custom Antenna`.

The magnitude in db of the combined polarized antenna radiation pattern specified as a Q-by-P matrix or a Q-by-P-by-L array. The value of Q must match the value of Q specified by Elevation angles (deg). The value of P must match the value of P specified by Azimuth angles (deg_. The value of L must match the value of L specified by Operating frequency vector (Hz).

Baffle the back of the element

This check box appears only when the Element type parameter is set to `Isotropic Antenna` or `Omni Microphone`.

Select this check box to baffle the back of the antenna element. In this case, the antenna responses to all azimuth angles beyond ±90° from broadside are set to zero. Define the broadside direction as 0° azimuth angle and 0° elevation angle.

## Ports

### Note

The block input and output ports correspond to the input and output parameters described in the `step` method of the underlying System object. See link at the bottom of this page.

PortData Types
Steer

Steering angle input port. To enable this port, select `Partitioned Array` or `Replicated Subarray` from the Specify sensor array pull-down menu. Then, select `Phase` or `Time` from the Subarray steering method pull-down menu. Data values are double-precision floating point.

WS

Subarray element weights input port. To enable this port, select `Partitioned array` or `Replicated Subarray` from the Specify sensor array pull-down menu. Then, select `Custom` from the Subarray steering method pull-down menu. Data values are double-precision floating point.

• For `Partitioned array`, subarrays may not have the same dimensions and sizes. In this case, you can specify subarray element weights as a complex-valued NSE-by-N matrix, where NSE is the number of elements in the largest subarray. The first Q entries in each column are the element weights for the subarray where Q is the number of elements in the subarray.

• For `Replicated Subarray`, all subarrays have the same dimensions and sizes. Then, you can specify the subarray element weights as a complex-valued NSE-by-N matrix. NSE is the number of elements in each subarray and N is the number of subarrays. Each column of `WS` specifies the weights for the corresponding subarray.

`Out`Double-precision floating point