Steering Vector
Libraries:
Phased Array System Toolbox /
Transmitters and Receivers
Description
Calculate the array steering vector for a given direction and frequency.
Ports
Input
Freq — Array operating frequency
positive scalar
Array operating frequency, specified as a positive scalar. Units are in Hz.
Dependencies
To enable this port, set the Source of operating
frequency parameter to Input port
.
Data Types: double
Ang — steering vector direction
[0;0]
(default) | real-valued length-M vector | real-valued 2-by-M matrix
Steering vector directions, specified as a real-valued, length-M vector, or a real-valued 2-by-M matrix. M is the number of steering directions.
When
Ang
is a 2-by-M matrix, each column of the matrix specifies the steering direction in space in the form[azimuth;elevation]
. The azimuth angle must be between –180° and 180°, and the elevation angle must be between –90° and 90°.When
Ang
is a length-M vector, its values correspond to the azimuth angles of the steering vector direction with elevation angles set to zero.
Angle units are in degrees.
Data Types: double
Output
SV — Steering vector
complex-valued
N-by-M-by-L array | struct
Steering vector, output as a complex-valued
N-by-M-by-L array or a
struct
containing arrays. N is the number of
elements of the phased array. If array contains subarrays, N is the
number of subarrays. M is the number of steering directions
specified in the Ang
argument. L is the number
of frequencies specified in the Freq
argument.
Data Types: double
Complex Number Support: Yes
Parameters
Signal propagation speed (m/s) — Signal propagation speed
physconst('LightSpeed')
(default) | real-valued positive scalar
Signal 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
Source of operating frequency — Source of operating frequency
Input port
(default) | Property
Source of operating frequency, specified as Input Port
or
Property
. When this parameter is set to Input
Port
, the operating frequency is set using the Freq
input port. When this parameter is set to Property
, the
operating frequency is set using the Operating frequency (Hz)
parameter.
Programmatic Use
Block
Parameter:FrequencySource |
Type:char | string |
Values:Input port |
Property |
Default:Input port |
Operating frequency (Hz) — System operating frequency
3e8
(default) | positive real scalar
System operating frequency, specified as a positive scalar. Units are in Hz.
Dependencies
To enable this parameter, set the Source of operating
frequency
parameter to Property
.
Programmatic Use
Block
Parameter:OperatingFrequency |
Type:double | single |
Values:float |
Default:0 |
Output conjugated steering vector — Output conjugated steering vector
on (default) | off
Select this check box to output a conjugated steering vector. Otherwise, the steering vector is not conjugated.
Programmatic Use
Block
Parameter:OutputConjugate |
Type:check box |
Values:0 | 1 |
Default:0 |
Number of bits in phase shifters — Number of phase shift quantization bits
0
(default) | nonnegative integer
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.
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 with generated code 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).
Programmatic Use
Block
Parameter:SimulateUsing |
Type:enum |
Values:Interpreted
Execution , Code Generation |
Default:Interpreted
Execution |
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 array
Phased 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])
Dependencies
To enable this parameter, set Specify sensor array as to
MATLAB expression
.
Specify sensor array as — Method to specify array
Array (no subarrays)
(default) | 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.MATLAB expression
— create the array using a MATLAB expression.
Element type — Array element types
Isotropic Antenna
(default) | Cardioid Antenna
| Cosine Antenna
| Custom Antenna
| Gaussian Antenna
| Sinc Antenna
| Omni Microphone
| Custom Microphone
Antenna or microphone type, specified as one of the following:
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 element
[0,1e20]
(default) | real-valued 1-by-2 row vector
Specify 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.
Dependencies
To enable this parameter, set Element type to
Isotropic Antenna
, Cosine Antenna
, or
Omni Microphone
.
Baffle the back of the element — Set back response of an Isotropic Antenna
element or an Omni Microphone
element to
zero
off (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.
Dependencies
To enable this check box, set
Element type to
Isotropic Antenna
or
Omni Microphone
.
Null axis direction — Null axis direction
-x
(default) | +x
| +y
| -y
| +z
| -z
Dependencies
To enable this parameter, set Element type to Cardioid Antenna
.
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 values
Specify 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.
Dependencies
To enable this parameter, set Element
type to Cosine
Antenna
.
Operating frequency vector (Hz) — Operating frequency range of custom antenna or microphone elements
[0,1e20]
(default) | real-valued row vector
Specify 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.
Dependencies
To enable this parameter, set Element type to Custom
Antenna
or Custom Microphone
. Use
Frequency responses (dB) to set the responses at these
frequencies.
Frequency responses (dB) — Antenna and microphone frequency response
[0,0]
(default) | real-valued row vector
Frequency 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.
Dependencies
To enable this parameter, set
Element type to
Custom Antenna
or
Custom
Microphone
.
Input Pattern Coordinate System — Coordinate system of custom antenna pattern
az-el
(default) | phi-theta
Coordinate system of custom antenna pattern, specified
az-el
or phi-theta
. When you
specify az-el
, use the Azimuth angles
(deg) and Elevations angles (deg) parameters to
specify the coordinates of the pattern points. When you specify
phi-theta
, use the Phi angles (deg)
and Theta angles (deg) parameters to specify the coordinates of the
pattern points.
Dependencies
To enable this parameter, set Element type to
Custom Antenna
.
Azimuth angles (deg) — Azimuth angles of antenna radiation pattern
[-180:180]
(default) | real-valued row vector
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. Azimuth angles must lie between –180° and 180°, inclusive, and be in strictly increasing order.
Dependencies
To enable 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 antenna radiation pattern
[-90:90]
(default) | real-valued row vector
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°, inclusive, and be in strictly increasing order.
Dependencies
To enable this parameter, set the Element type
parameter to Custom Antenna
and the
Input Pattern Coordinate System
parameter to az-el
.
Phi Angles (deg) — Phi angle coordinates of custom antenna radiation pattern
0:360
| real-valued 1-by-P row vector
Phi angles of points at which to specify the antenna radiation pattern, specify as a real-valued 1-by-P row vector. P must be greater than 2. Angle units are in degrees. Phi angles must lie between 0° and 360° and be in strictly increasing order.
Dependencies
To enable this parameter, set the Element type parameter to
Custom Antenna
and the Input Pattern Coordinate
System parameter to phi-theta
.
Theta Angles (deg) — Theta angle coordinates of custom antenna radiation pattern
0:180
| real-valued 1-by-Q row vector
Theta angles of points at which to specify the antenna radiation pattern, specify as a real-valued 1-by-Q row vector. Q must be greater than 2. Angle units are in degrees. Theta angles must lie between 0° and 360° and be in strictly increasing order.
Dependencies
To enable this parameter, set the Element type parameter to
Custom Antenna
and the Input Pattern Coordinate
System parameter to phi-theta
.
Magnitude pattern (dB) — Magnitude of combined antenna radiation pattern
zeros(181,361)
(default) | real-valued Q-by-P matrix | real-valued Q-by-P-by-L
array
Magnitude of the combined antenna radiation pattern, specified as a Q-by-P matrix or a Q-by-P-by-L array.
When the Input Pattern Coordinate System parameter is set to
az-el
, Q equals the length of the vector specified by the Elevation angles (deg) parameter and P equals the length of the vector specified by the Azimuth angles (deg) parameter.When the Input Pattern Coordinate System parameter is set to
phi-theta
, Q equals the length of the vector specified by the Theta Angles (deg) parameter and P equals the length of the vector specified by the Phi Angles (deg) parameter.
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.
Dependencies
To enable this parameter, set Element type to
Custom Antenna
.
Phase pattern (deg) — Custom antenna radiation phase pattern
zeros(181,361)
(default) | real-valued Q-by-P matrix | real-valued Q-by-P-by-L
array
Phase of the combined antenna radiation pattern, specified as a Q-by-P matrix or a Q-by-P-by-L array.
When the Input Pattern Coordinate System parameter is set to
az-el
, Q equals the length of the vector specified by the Elevation angles (deg) parameter and P equals the length of the vector specified by the Azimuth angles (deg) parameter.When the Input Pattern Coordinate System parameter is set to
phi-theta
, Q equals the length of the vector specified by the Theta Angles (deg) parameter and P equals the length of the vector specified by the Phi Angles (deg) parameter.
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 (
Dependencies
To enable this parameter, set Element type to
Custom Antenna
.
Align element normal with array normal — Align element normal with array normal
on (default) | off
Dependencies
This parameter is enabled when Element type is set to
Custom Antenna
.
Radiation pattern beamwidth (deg) — Radiation pattern beamwidth
[10,10]
(default)
Dependencies
This parameter is enabled when Element type is set to Gaussian Antenna
.
Polar pattern frequencies (Hz) — Polar pattern microphone response frequencies
1e3 (default) | real scalar | real-valued 1-by-L row vector
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.
Dependencies
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-P row vector
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.
Dependencies
To enable this parameter, set Element type to
Custom Microphone
.
Polar pattern (dB) — Custom microphone polar response
zeros(1,361)
(default) | real-valued L-by-P matrix
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.
Dependencies
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 arrayURA
— Uniform rectangular arrayUCA
— Uniform circular arrayConformal 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 2
The number of array elements for ULA or UCA arrays, specified as an integer greater than or equal to 2.
Dependencies
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 arrays
Spacing 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]
.
Dependencies
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.
Dependencies
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 integers
Dimensions 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 elements in each row and column.
For a URA, array elements are indexed from top to bottom along the
leftmost array column, and continued 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.
Dependencies
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.
Dependencies
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. |
Dependencies
To enable this parameter, set
Geometry to
URA
or
UCA
.
Radius of UCA (m) — UCA array radius
0.5 (default) | positive scalar
Radius of UCA array, specified as a positive scalar.
Dependencies
To enable this parameter, set Geometry to
UCA
.
Element positions (m) — Positions of conformal array elements
[0;0;0]
(default) | 3-by-Nmatrix of real values
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.
Dependencies
To enable this parameter set Geometry to Conformal
Array
.
Data Types: double
Element normals (deg) — Direction of conformal array element normal vectors
[0;0]
| 2-by-1 column vector | 2-by-N matrix
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. If the parameter value 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 the parameter value is a 2-by-1 column
vector, the same pointing direction is used for all array elements.
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
.
Data Types: double
Taper — Array element tapers
1 (default) | complex scalar | complex-valued row vector
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.
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.
Data Types: double
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.
Version History
Introduced in R2023b
See Also
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