Phased Array Antenna
The Phased Array Antenna model consists of many radiating elements. Each element is modeled as an isotropic pattern. By modifying the excitation (amplitude and phase) of each element differently, a phased array antenna can electronically steer its maximum gain toward a particular direction or main radiation axis. A phased array antenna not only can steer its maximum gain in a particular direction, but it can also steer nulls toward other directions to prevent radiation to and from other directions. The act of altering each element’s excitation is effectively accomplished through the assignment of weights to each element. This set of weights for a particular direction is called a steering vector and each weight is a complex number.
The phased array antenna configuration is broken down into five areas:
General Parameters represents a set of parameters that are general to the antenna. Element Configuration, Beam and Null Directions Providers, and Beam Former are phased array-specific parameters.
General Parameters
The following general antenna parameters are provided at the top of the Phased Array Antenna's Basic->Definition page.
| Parameter | Description |
|---|---|
| Design Frequency |
This is the frequency of the antenna. The antenna design frequency is independent of the operational frequency of a transmitter, receiver, or radar. Changing the frequency of a transmitter, receiver, or radar does not update an embedded antenna's design frequency, nor vice versa. The design frequency is solely used at antenna configuration time to compute the antenna size from its max gain or beamwidth settings. A mismatch between signal frequency and antenna design frequency typically causes performance degradation. |
| Backlobe Suppression | Amount of attenuation to apply to any angle in the back hemisphere. This enables you to model reduced gains due to a back plane or other type of physical construct that would hinder reception from the back side of the antenna. |
| Backlobe Suppression Type |
Constant. Applies the same Backlobe Suppression value to all angles. Cosine. Applies the Backlobe Suppression value as a function of the cosine of the angle with complete suppression when the angle is 0 degrees and the Backlobe Suppression value is at a 90 degree angle. |
| Element Factor |
Include Element Factor. Includes the individual element pattern. Disabling the element factor can be helpful when comparing with other tools that only consider the array factor. When this is disabled, be aware that the maximum gain will not vary with the steering angle. When enabled, this will use a general raised cosine function. Raised Cosine Exponent. Produces the cosine raised to the specified value. |
| Dimension |
Elements. Number of enabled elements. Width. Length, in meters, of the antenna. Height. Height, in meters, of the antenna. |
Element Configuration
The Element Configuration tab enables you to define the physical aspects of the antenna elements. It consists of two parts, a Viewport and a Designer section. The Viewport shows the layout of the currently configured elements. The Designer enables you to change the physical layout of the elements and the results are displayed in the Viewport, as shown below.
Element Configuration Viewport
The Element Configuration consists of element grid points, and each grid point has a unique ID number. ( Not all Element Configuration Types provide grid points other than the original element positions.) You can enable or disable grid points to represent failed elements, eliminated elements due to physical obstructions, or to model Minimum Redundant Arrays (MRA).
Enable the Show Grid check box to display extra elements that can be enabled or disabled.
Enable the Show Labels check box to display each unique element ID. This ID is important if you want to use an external file to assign complex weights to each element. See External Element Configuration File for more information.
To enable or disable an element, click the element's grid point.
Note: When an ASCII Data Element configuration file is used, the Viewpoint will show the element configuration but will not allow you to enable or disable the elements.
Element Configuration Designer
The Designer enables you change the physical layout of the elements. Element configuration choices include:
When changing the type of configuration, number of elements, or the lattice structure, all disabled elements will be lost.
For information on the Max Look Angle informational parameters, click here.
Lattice Structure
The elements are placed on a grid called a lattice structure. The lattice structure provides options for the general arrangement of the element placement. There are several options for the Lattice Structure of the element configuration. The type of lattice structure can be either triangular or rectangular. Setting the Equilateral option will enforce equal distance between the nearest neighbors.
| Parameter | Description |
|---|---|
| Triangular | Elements are staggered between rows and columns. |
| Rectangular | Elements are aligned between rows and columns. |
| Equilateral | For the triangular lattice structure, it will ensure the distance between all nearest neighbors are equal distance apart. For a rectangular lattice structure, it will ensure the distance in the x direction is equal to the distance in the y direction. |
Polygon
Represents a two-dimensional planar antenna array with N sides. The elements can be arranged on either a triangular or a rectangular Lattice Structure. Furthermore, the polygon shape does not necessarily have to be a regular-polygon, thus the number of elements in the X direction can be different than the number of elements in the Y direction.
| Parameter | Description |
|---|---|
| Number of Sides | The number of sides of the antenna shape. |
| Lattice Structure | Provides options that determine the general arrangement of the element placement. |
| Type |
Choices vary depending on the selected Element Configuration Type: Triangular. Elements are placed in a triangular structure. Rectangular. Elements are placed in a rectangular structure. |
| Equilateral | Each element is equal distance to its structural nearest neighbors. |
| Number of Elements |
X. Number of elements in the X direction of the center row. Y. Number of elements in the Y direction of the center column. |
| Spacing | Unit Type defines the X and Y element spacing in either Wavelength Ratio or Distance units. The Wavelength Ratio unit type spaces the elements relative to the wavelength (e.g., Design Frequency). The Distance unit type spaces the elements at an absolute distance. X. Distance, in the Unit Type, between the elements in the X direction. Y. Distance, in the Unit Type, between the elements in the Y direction. |
Hexagon
This is a specialization of the Polygon which has exactly six sides and is included primarily for your convenience. It represents a two-dimensional planar antenna array with an aperture shape consisting of six sides. Like the Polygon, the elements can be arranged on either a triangular or a rectangular Lattice Structure. Likewise, the hexagon shape does not necessarily have to be a regular hexagon, thus the number of elements in the X direction can be different than the number of elements in the Y direction. But, for a hexagon shape, the number of elements in X and Y must be odd.
| Parameter | Description |
|---|---|
| Lattice Structure | Provides options that determine the general arrangement of the element placement. |
| Type |
Choices vary depending on the selected Element Configuration Type: Triangular. Elements are placed in a triangular structure. Rectangular. Elements are placed in a rectangular structure. |
| Equilateral | Each element is equal distance to its structural nearest neighbors. |
| Number of Elements |
X. Number of elements in the X direction of the center row (must be odd). Y. Number of elements in the Y direction of the center column (must be odd). |
| Spacing | Unit Type defines the X and Y element spacing in either Wavelength Ratio or Distance units. The Wavelength Ratio unit type spaces the elements relative to the wavelength (e.g., Design Frequency). The Distance unit type spaces the elements at an absolute distance. X. Distance, in the Unit Type, between the elements in the X direction. Y. Distance, in the Unit Type, between the elements in the Y direction. |
Linear
Represents an antenna array in one dimension.
| Parameter | Description |
|---|---|
| Num Elements | Number of elements in the array. |
| Spacing |
Unit Type defines the element spacing as either Wavelength Ratio or Distance units. The Wavelength Ratio unit type spaces the elements relative to the wavelength (e.g., Design Frequency). The Distance unit type spaces the elements at an absolute distance. Spacing is the distance, in the Unit Type, between adjacent elements. |
Circular
Represents a planar antenna array with elements arranged in a circular pattern.
| Parameter | Description |
|---|---|
| Num Elements | Number of elements around the circle. |
| Spacing |
Unit Type defines the element spacing as either Wavelength Ratio or Distance units. The Wavelength Ratio unit type spaces the elements relative to the wavelength (e.g., Design Frequency). The Distance unit type spaces the elements at an absolute distance. Spacing is the distance, in the Unit Type, between adjacent elements. |
The Max Look Angle
The Max Look Angle fields contain informational parameters that identify the maximum steering angle that can be attained before grating lobes enter the antenna's view and cause ambiguities.
The maximum look angle does not restrict or constrain the simulation in any way and is not associated with any parameters associated with its parent.
When a transmitting antenna is steered beyond its maximum angle, then the antenna will produce maximum gain (and maximum radiation) in two different locations, one in the direction of the desired beam steering direction and the other in the direction of the grating lobe. Likewise, with a receiving antenna, it will have maximum reception gain in two different directions.
Beam and Null Direction Providers
The Beam Direction Provider and Null Direction Provider tabs enable you to select where the antenna points its beam and/or nulls. This information is delivered to the beam former, which handles forming and steering the beam toward the specified direction(s). The direction providers use a spherical azimuth and elevation coordinate system. See Phased Array Antenna Coordinate System for additional information.
Beam and Null direction providers can also be defined using:
Object
Selects the pointing directions (for beam or nulls) to be based on the STK Object(s) you selected. The Phased Array direction provider supports basic, temporal, vector, special, and STK plugin constraints on the selected object. But, all Comm and Radar constraints are still supported on their respective Comm and Radar objects. The following fields can be set on the Object Direction Provider:
| Parameter | Description |
|---|---|
| Enabled | When enabled, it will perform steering; otherwise, the antenna’s will not be steered. |
| Steering Object | The object which to steer the antenna’s beam or null toward. |
| Azimuth Steering Limit A | Relative to the mechanical boresight, electronically steering in the azimuth direction is bounded between this value and the value defined by AzimuthSteeringLimitB. The steering will be held at this value when attempting to steer beyond this value |
| Azimuth Steering Limit B | Relative to the mechanical boresight, electronically steering in the azimuth direction is bounded between this value and the value defined by AzimuthSteeringLimitA. The steering will be held at this value when attempting to steer beyond this value. |
| Elevation Steering Limit A | Relative to the mechanical boresight, electronically steering in the elevation direction is bounded between this value and the value defined by ElevationSteeringLimitB. The steering will be held at this value when attempting to steer beyond this value. |
| Elevation Steering Limit B | Relative to the mechanical boresight, electronically steering in the elevation direction is bounded between this value and the value defined by ElevationSteeringLimitA. The steering will be held at this value when attempting to steer beyond this value. |
| When steering limits exceeded |
Determines the behavior of the beam pattern when the direction of interest is outside the steering limits. Options include:
|
| Use mechanical boresight when zero Objects are in Field of Regard |
Determines the behavior of the beam pattern when there are zero directions of interest within the Field of Regard. When checked and there are zero directions (no access intervals for antenna and objects), the antenna will point along the mechanical boresight. When not checked and there are zero directions (no access intervals for antenna and objects), the antenna will have no gain pattern and thus a no gain value (i.e. antenna is turned off). This option is on the Beam Direction Provider tab only; it is irrelevant for the Null Direction Providers tab. |
Many objects can be added to the null steering list. A phased array only has M-1 degrees of freedom (where M is the number of elements). If a beam object is also selected, then the degrees of freedom is further reduced to account for the desired beam. Thus, STK considers only the first M-1 list items and the remaining are ignored.
Auto Pointing
The Auto Pointing Direction Provider is only available as a Beam Direction Provider. The Auto Pointing Direction Provider will steer the antenna’s beam toward the direction associated with the other Access object.
The Auto Pointing option will disable 2D Graphics Contours and 3D Volume Graphics.
The following fields can be set on the Auto Pointing Direction Provider:
| Parameter | Description |
|---|---|
| Azimuth Steering Limit A | Relative to the mechanical boresight, electronically steering in the azimuth direction is bounded between this value and the value defined by AzimuthSteeringLimitB. The steering will be held at this value when attempting to steer beyond this value. |
| Azimuth Steering Limit B | Relative to the mechanical boresight, electronically steering in the azimuth direction is bounded between this value and the value defined by AzimuthSteeringLimitA. The steering will be held at this value when attempting to steer beyond this value. |
| Elevation Steering Limit A | Relative to the mechanical boresight, electronically steering in the elevation direction is bounded between this value and the value defined by ElevationSteeringLimitB. The steering will be held at this value when attempting to steer beyond this value |
| Elevation Steering Limit B | Relative to the mechanical boresight, electronically steering in the elevation direction is bounded between this value and the value defined by ElevationSteeringLimitA. The steering will be held at this value when attempting to steer beyond this value. |
| When steering limits exceeded |
Determines the behavior of the beam pattern when the direction of interest is outside the steering limits. Options include:
|
Beamformer
The Beamformer tab enables you to select various beam and null steering algorithms, which compute the weights for each of the elements. These weights are then used to compute the antenna’s gain pattern.
There are two categories of beam formers, those that perform beam-steering and those that perform beam-steering and adaptive null-steering. The beam formers that do not perform adaptive nulling will implement an amplitude tapering to reduce the side-lobe levels. Currently, amplitude tapering is only implemented for Linear Element Configuration arrays, yet the Script and Ascii Data File beam formers provide the ability to specify a complex weight value.
Current beam former algorithms include:
MVDR
Minimum Variance Distortionless Response also referred to as a Capon beam former. Changes the phase and amplitude across the array elements to steer and shape the beam as well as the nulls. This performs adaptive beam forming to minimize the gain degradation in a desired direction while minimizing the gain in other directions. For more information see reference [“Optimum Array Processing Part IV of Detection, Estimation, and Modulation Theory” Harry L. Van Trees, Pg. 439]
| Parameter | Description |
|---|---|
| Constraint | Value to constrain the amount of main gain reduction, which can take place to null interference. |
Adaptive nulling beam formers can also be defined using:
Dolph-Chebyshev
Changes the phase and amplitude across the array elements to steer and shape the beam. Produces an amplitude distribution to achieve a minimum null-to-null beam width for a specified side lobe level. The Dolph-Chebyshev beam former will produce the optimal solution when spacing is >=wavelength/2. Setting the sidelobe level input to its most negative value (no sidelobes) will approach the binomial distribution. For more information see reference [“Antenna Theory Analysis and Design” Constatine A. Balanis, Pgs. 245 – 254]
| Parameter | Description |
|---|---|
| SidelobeLevel | Desired sidelobe level on max gain. |
Cosine
Changes the phase and amplitude across the array elements to steer and shape the beam. Provides a cosine amplitude distribution across the array to reduce the sidelobes at the cost of slightly increasing the width of the main lobe. The amplitude distribution is given by:
Cosine^x
Changes the phase and amplitude across the array elements to steer and shape the beam. Uses an exponential form of a cosine function to reduce sidelobe levels at the cost of slightly increasing the width of the main lobe. The amplitude distribution is given by:
| Parameter | Description |
|---|---|
| x | Value of the cosine’s exponential. |
Hann
Changes the phase and amplitude across the array elements to steer and shape the beam. Utilizes aspects of the uniform and the cosine-squared pattern to place a null near a sidelobe peak. The amplitude distribution is given by:
Hamming
Changes the phase and amplitude across the array elements to steer and shape the beam. Utilizes aspects of the uniform and the cosine-squared pattern to place a null near a sidelobe peak. The amplitude distribution is given by:
Raised Cosine
Changes the phase and amplitude across the array elements to steer and shape the beam. Combines aspects of the uniform and cosine weighting. The height of the first sidelobe will decrease by decreasing p. The amplitude distribution is given by:
| Parameter | Description |
|---|---|
| p | Input parameter characterizing the weighting family as shown in above equation. |
Raised Cosine-Squared
Changes the phase and amplitude across the array elements to steer and shape the beam. Like the Raised Cosine except for the cosine being squared. A parameter, p, value of 0.08 is equal to the Hamming beam former. The amplitude distribution is given by:
| Parameter | Description |
|---|---|
| p | Input parameter characterizing the weighting family as shown in above equation. |
Blackman-Harris
Changes the phase and amplitude across the array elements to steer and shape the beam. Implements the well-known Blackman-Harris distribution across the elements. The amplitude distribution is given by:
Minimum Redundant Arrays
The Phased Array Model can be made to model Minimum Redundant Arrays (MRA). By exploiting unique element spacing combinations, you can remove elements. In doing so, an MRA can provide the same main beam characteristics with fewer elements, thus reducing the cost of the antenna. Yet, the side lobe levels will increase. There can be many combinations of MRAs for a given number of elements. As an example, by starting with a 7-element array and disabling three elements such that the spacing between each enabled element is unique, we can get a 1-3-2 MRA, where 1-3-2 indicates the element separation between each of the enabled elements.
Phased Array Antenna Coordinate System
This antenna uses a spherical Az/El coordinate system referenced from the mechanical bore sight. The mechanical bore sight is aligned with the x axis when the Antenna’s Orientation Azimuth and Elevation values are both set to 0 degrees; yet, STK defaults the Antenna’s Orientation Elevation value to 90 degrees to align the boresight with the z axis. The elements of a linear array are aligned along the x axis when the tilt angle is 0. For rectangular arrays, the elements are located in the xy plane.