Steering Vector

Array steering vector

Since R2023b

• 

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

Main Tab

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

Sensor Array Tab

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 Parameters

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.

Array Parameters

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 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