phased.ReplicatedSubarray

Phased array formed by replicated subarrays

Description

The ReplicatedSubarray object represents a phased array that contains copies of a subarray created by replicating a single specified array.

To obtain the response of the subarrays:

1. Create the phased.ReplicatedSubarray object and set its properties.

2. Call the object with arguments, as if it were a function.

To learn more about how System objects work, see What Are System Objects?

You can also use a ReplicatedSubarray object as the value of the SensorArray or Sensor property of objects that perform beamforming, steering, and other operations.

Creation

Syntax

array = phased.ReplicatedSubarray

array = phased.ReplicatedSubarray(Name=Value)

Description

array = phased.ReplicatedSubarray creates a replicated subarray System object™, array. This object represents an array that contains copies of a subarray.

array = phased.ReplicatedSubarray(Name=Value) creates a replicated subarray object, array, with each specified property Name set to the specified Value. You can specify additional name-value pair arguments in any order as (Name1=Value1,...,NameN=ValueN).

Properties

Unless otherwise indicated, properties are nontunable, which means you cannot change their values after calling the object. Objects lock when you call them, and the release function unlocks them.

If a property is tunable, you can change its value at any time.

For more information on changing property values, see System Design in MATLAB Using System Objects.

Subarray — Subarray to replicate

phased.ULA with default property values (default) | phased.URA | phased.UCA | phased.ConformalArray

An array type to use to replicate as subarrays, specified as:

• phased.ULA System object

• phased.URA System object

• phased.UCA System object

• phased.ConformalArray System object

You cannot use the phased.HeterogeneousULA, phased.HeterogeneousURA. phased.HeterogeneousConformalArray, or phased.NRRectangularPanelArray System object.

Layout — Layout of subarrays

"Rectangular" (default) | "Custom"

Layout of the replicated subarrays, specified as "Rectangular" or "Custom".

Data Types: char | string

GridSize — Size of rectangular grid

[1 2] (default) | positive integer | 1-by-2 positive integer row vector

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

If GridSize is a scalar, the array has the same number of subarrays in each row and column.

If GridSize is a 1-by-2 vector, the vector has the form [NumberOfRows, NumberOfColumns]. The first entry is the number of subarrays along each column, while 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. This figure shows how a 3-by-2 URA subarray is replicated using a GridSize value of [1,2].

Dependencies

To enable this property, set the Layout property to "Rectangular".

Data Types: double

GridSpacing — Spacing of rectangular grid

"Auto" | positive real-valued scalar | 1-by-2 row vector

The rectangular grid spacing of subarrays, specified as a positive real-valued scalar, a 1-by-2 row vector, or "Auto". Grid spacing units are expressed in meters.

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

If GridSpacing is a length-2 row vector, it 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 GridSpacing is "Auto", the replication preserves the element spacing in both row and column. This option is available only if you use a phased.ULA or phased.URA object as the subarray.

Dependencies

To enable this property, set the Layout property to "Rectangular".

Data Types: char | string | double

SubarrayPosition — Subarray positions in custom grid

[0 0; -0.5 0.5; 0 0] (default) | 3-by-N matrix of real values

The positions of the subarrays in the custom grid, specified as a 3-by-N matrix, where N indicates the number of subarrays in the array. Each column of the matrix represents the position of a single subarray in the array’s local coordinate system, in meters, using the form [x; y; z].

Dependencies

To enable this property, set the Layout property to "Custom".

Data Types: double

SubarrayNormal — Subarray normal directions in custom grid

[0 0; 0 0] (default) | 2-by-N real matrix

The normal directions of the subarrays in the array, specified as 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 SubarrayPosition and SubarrayNormal properties 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.

Dependencies

To enable this property, set the Layout property to "Custom".

Data Types: double

SubarraySteering — Subarray steering method

"None" (default) | "Phase" | "Time" | "Custom"

The method of subarray steering, specified as either "None", "Phase", "Time", or "Custom".

• When you set this property to "Phase", a phase shifter is used to steer the subarray. Use the STEERANG argument of the step method to define the steering direction.

• When you set this property to "Time", subarrays are steered using time delays. Use the STEERANG argument of the step method to define the steering direction.

• When you set this property to "Custom", subarrays are steered by setting independent weights for all elements in each subarray. Use the WS argument of the step method to define the weights for all subarrays.

Data Types: string | char

PhaseShifterFrequency — Subarray phase shifter frequency

3e8 (default) | positive scalar

The operating frequency of phase shifters that perform subarray steering, specified as a positive scalar in Hz.

Dependencies

To enable this property, set the SubarraySteering property to "Phase".

Data Types: double

NumPhaseShifterBits — Number of phase shifter quantization bits

0 (default) | non-negative integer

The number of bits used to quantize the phase shift component of beamformer or steering vector weights, specified as a non-negative integer. A value of zero indicates that no quantization is performed.

Data Types: double

Usage

Syntax

RESP = array(FREQ,ANG,V)

RESP = array(FREQ,ANG,V,STEERANG)

RESP = array(FREQ,ANG,V,WS)

Description

RESP = array(FREQ,ANG,V) returns the responses, RESP, of the subarrays in the array, at operating frequencies specified in FREQ and directions specified in ANG. V is the propagation speed. The elements within each subarray are connected to the subarray phase center using an equal-path feed.

RESP = array(FREQ,ANG,V,STEERANG) uses STEERANG as the steering direction of the subarray. This syntax is available when you set the SubarraySteering property to either "Phase" or "Time".

RESP = array(FREQ,ANG,V,WS) uses WS as the subarray element weights. This syntax is available when you set the SubarraySteering property to "Custom".

Input Arguments

FREQ — Operating frequencies

length L row vector

Operating frequencies of array. FREQ is a row vector of length L. Typical values are within the range specified by a property of H.Subarray.Element. That property is named FrequencyRange or FrequencyVector, depending on the type of element in the array. The element has zero response at frequencies outside that range. Units are in Hz.

Example: [3.0e6 3.2e6]

Data Types: double

ANG — Direction angles

real-valued length-M row vector | real-valued 2-by-M matrix

Directions in degrees. ANG can be either a 2-by-M matrix or a row vector of length M.

If ANG is a 2-by-M matrix, each column of the matrix specifies the direction in the form [azimuth; elevation]. The azimuth angle must be between –180° and 180°, inclusive. The elevation angle must be between –90° and 90°, inclusive.

If ANG is a row vector of length M, each element specifies a direction’s azimuth angle. In this case, the corresponding elevation angle is assumed to be 0.

Example: [10 11 12]

Data Types: double

V — Propagation speed

positive scalar

Propagation speed in meters per second. This value must be a scalar.

Example: physconst("LightSpeed")

Data Types: double

STEERANG — Steer angles

scalar (default) | real-valued 2-element column vector

Subarray steering direction, specified as either a 2-element column vector or a scalar.

If this argument is a 2-element column vector, it has the form [azimuth; elevation]. The azimuth angle must be between –180° and 180°, inclusive. The elevation angle must be between –90° and 90°, inclusive.

If STEERANG is a scalar, it specifies the direction’s azimuth angle. In this case, the elevation angle is assumed to be 0°.

Example: [20;-30]

Dependencies

To enable this argument, set the SubarraySteering to "Phase" or "Time".

Data Types: double

WS — Subarray element weights

complex-valued N_SE-by-N matrix

Subarray element weights.

Subarray element weights, specified as complex-valued N_SE-by-N matrix. Weights are applied to the individual elements within a subarray. All subarrays have the same dimensions and sizes. N_SE is the number of elements in each subarray and N is the number of subarrays. Each column of the matrix specifies the weights for the corresponding subarray.

Dependencies

To enable this argument, set the SubarraySteering to "Custom".

Data Types: double
Complex Number Support: Yes

Output Arguments

RESP — Voltage response

complex-valued N-by-M-by-L array | struct

Voltage responses of the subarrays of the phased array. The output depends on whether the array supports polarization or not.

• If the array is not capable of supporting polarization, the voltage response, RESP, has the dimensions N-by-M-by-L. The first dimension, N, represents the number of subarrays in the phased array, the second dimension, M, represents the number of angles specified in ANG, while L represents the number of frequencies specified in FREQ. Each column of RESP contains the responses of the subarrays for the corresponding direction specified in ANG. Each of the L pages of RESP contains the responses of the subarrays for the corresponding frequency specified in FREQ.

• If the array is capable of supporting polarization, the voltage response, RESP, is a MATLAB^® struct containing two fields, RESP.H and RESP.V, each having dimensions N-by-M-by-L. The field, RESP.H, represents the array’s horizontal polarization response, while RESP.V represents the array’s vertical polarization response. The first dimension, N, represents the number of subarrays in the phased array, the second dimension, M, represents the number of angles specified in ANG, while L represents the number of frequencies specified in FREQ. Each of the M columns contains the responses of the subarrays for the corresponding direction specified in ANG. Each of the L pages contains the responses of the subarrays for the corresponding frequency specified in FREQ.

Data Types: double
Complex Number Support: Yes

Object Functions

To use an object function, specify the System object as the first input argument. For example, to release system resources of a System object named obj, use this syntax:

release(obj)

Specific to phased.ReplicatedSubarray

beamwidth	Compute and display beamwidth of a subarray
collectPlaneWave	Simulate received plane waves
directivity	Directivity of replicated subarray
getElementPosition	Positions of array elements
getNumElements	Number of elements in array
getNumSubarrays	Number of subarrays in array
getSubarrayPosition	Positions of subarrays in array
isPolarizationCapable	Polarization capability
pattern	Plot replicated subarray directivity and patterns
patternAzimuth	Plot replicated subarray directivity or pattern versus azimuth
patternElevation	Plot replicated subarray directivity or pattern versus elevation
phased.ReplicatedSubarray.viewArray	View replicated subarray geometry

Common to All System Objects

step	Run System object algorithm
release	Release resources and allow changes to System object property values and input characteristics
reset	Reset internal states of System object

Examples

Azimuth Response of Array with Subarrays

Plot the azimuth response of a 4-element ULA composed of two 2-element ULAs. By default, the antenna elements are isotropic.

sArray = phased.ULA(NumElements=2,ElementSpacing=0.5);
sRSA = phased.ReplicatedSubarray(Subarray=sArray, ...
   Layout="Rectangular",GridSize=[1 2], ...
   GridSpacing="Auto");

Plot the azimuth response of the array. Assume the operating frequency is 1 GHz and the wave propagation speed is the speed of light.

fc = 1.0e9;
pattern(sRSA,fc,[-180:180],0, ...
    PropagationSpeed=physconst("LightSpeed"), ...
    Type="powerdb", ...
    Normalize=true, ...
    CoordinateSystem="polar")

Response of Subarrays with Polarized Antenna Elements

Create a 4-element ULA from two 2-element ULA subarrays consisting of short-dipole antenna elements. Then, calculate the response at boresight. Because the array elements support polarization, the response consists of horizontal and vertical components.

Create the arrays from subarrays.

sSD = phased.ShortDipoleAntennaElement;
sULA = phased.ULA(Element=sSD, ...
    NumElements=2,...
    ElementSpacing=0.5);
sRSA = phased.ReplicatedSubarray(Subarray=sULA, ...
    Layout="Rectangular", ...
    GridSize=[1 2], ...
    GridSpacing="Auto");

Show the vertical polarization response for the subarrays.

fc = 1.0e9;
ang = [0;0];
resp = sRSA(fc,ang,physconst("LightSpeed"));
disp(resp.V)

   -2.4495
   -2.4495

Independently Steered Replicated Subarrays

Create an array consisting of three copies of a 4-element ULA having elements spaced 1/2 wavelength apart. The array operates at 300 MHz.

c = physconst("LightSpeed"); 
fc = 300e6;
lambda = c/fc;
subarray = phased.ULA(4,0.5*lambda);

Steer all subarrays by a common phase shift to 10° azimuth.

array = phased.ReplicatedSubarray(Subarray=subarray,GridSize=[1 3], ... 
    SubarraySteering="Phase",PhaseShifterFrequency=fc); 
steer_ang = [10;0]; 
sv_array = phased.SteeringVector(SensorArray=array, ... 
    PropagationSpeed=c); 
wts_array = sv_array(fc,steer_ang);
pattern(array,fc,-90:90,0,CoordinateSystem="Rectangular", ... 
    Type="powerdb",PropagationSpeed=c,Weights=wts_array, ... 
    SteerAngle=steer_ang);
legend("phase-shifted subarrays")

Compute independent subarray weights from subarray steering vectors. The weights point to 5°, 15°, and 30° azimuth. Set the SubarraySteering property to "Custom".

steer_ang_subarrays = [5 15 30;0 0 0];
sv_subarray = phased.SteeringVector(SensorArray=subarray, ... 
    PropagationSpeed=c);
wc = sv_subarray(fc,steer_ang_subarrays); 
array.SubarraySteering = "Custom";
pattern(array,fc,-90:90,0,CoordinateSystem="Rectangular", ... 
    Type="powerdb",PropagationSpeed=c,Weights=wts_array, ... 
    ElementWeight=conj(wc)); 
legend("independent subarrays") 
hold off

Subarray Response

Calculate the response at boresight for two 2-element ULA arrays that form subarrays of a 4-element ULA array of short-dipole antenna elements.

Create a two-element ULA of short-dipole antenna elements. Then, arrange two copies to form a 4-element ULA.

antenna = phased.ShortDipoleAntennaElement;
array = phased.ULA(Element=antenna,NumElements=2,ElementSpacing=0.5);
replicatedarray = phased.ReplicatedSubarray(Subarray=array, ...
    Layout="Rectangular",GridSize=[1 2], ...
    GridSpacing="Auto");

Find the response of each subarray at boresight. Assume the operating frequency is 1 GHz and the wave propagation speed is the speed of light.

c = physconst("LightSpeed");
resp = replicatedarray(1.0e9,[0;0],c)

resp = struct with fields:
    H: [2×1 double]
    V: [2×1 double]

References

[1] Mailloux, Robert J. Electronically Scanned Arrays. San Rafael, CA: Morgan & Claypool Publishers, 2007.

[2] Mailloux, Robert J. Phased Array Antenna Handbook, 2nd Ed. Norwood, MA: Artech House, 2005.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• pattern, patternAzimuth, patternElevation, plotResponse, and viewArray methods are not supported.

• See System Objects in MATLAB Code Generation (MATLAB Coder).

Version History

Introduced in R2012a