rcs

Calculate and plot monostatic and bistatic radar cross section (RCS) of platform, antenna, or array

Syntax

rcs(object,frequency)

rcs(object,frequency,azimuth,elevation)

rcs(___,Name=Value)

[rcsval,azimuth,elevation]
= rcs(object,frequency)

[rcsval,azimuth,elevation]
= rcs(___,Name=Value)

Description

rcs(object,frequency) plots the monostatic RCS of the platform, antenna, or array over a specified frequency. To learn more about monostatic and bistatic RCS, see What Is RCS?.

example

rcs(object,frequency,azimuth,elevation) plots the monostatic RCS of the platform, antenna, or array over a specified frequency for the specified azimuth and elevation angles.

rcs(___,Name=Value) plots the RCS with additional properties specified using one or more Name-Value Arguments. To plot a bistatic RCS, specify the TransmitAngle name-value argument as a 2-by-1 matrix with non-zero values.

[rcsval,azimuth,elevation] = rcs(object,frequency) returns the monostatic RCS value and corresponding azimuth and elevation angles of a platform, antenna, or array at the specified frequency.

[rcsval,azimuth,elevation] = rcs(___,Name=Value) returns the RCS value and corresponding azimuth and elevation angles using additional properties specified by one or more name-value arguments. To calculate a bistatic RCS, specify the TransmitAngle name-value argument as a 2-by-1 matrix. with non-zero values.

Examples

collapse all

RCS of Helix

Open Live Script

Create a default helix antenna and plot the RCS at 2 GHz.

ant = helix;
rcs(ant,2e9)

Figure contains an axes object and an object of type uicontainer. The hidden axes object contains 2 objects of type line, text. This object represents az=0° .

RCS of Linear Array

Open Live Script

Create a default linear array and plot the RCS at 75 MHz in the elevation pane.

array = linearArray;
rcs(array,75e6,0,0:1:360)

Figure contains an axes object and an object of type uicontainer. The hidden axes object contains 2 objects of type line, text. This object represents az=0° .

RCS of Reflector-Backed Dipole

Open Live Script

Create a reflector-backed dipole and plot the RCS at 1 GHz in the elevation plane at 90 degree azimuth.

ant = reflector;
rcs(ant,1e9,90,0:1:360)

Figure contains an axes object and an object of type uicontainer. The hidden axes object contains 2 objects of type line, text. This object represents az=90° .

RCS of Tetrahedron Platform

Open Live Script

Create a tetrahedron platform from an STL file.

p = platform;
p.FileName = "tetrahedra.stl"; 
p.Units = "m";
figure
show(p)

Figure contains an axes object. The axes object with title Platform object, xlabel x (m), ylabel y (m) contains 2 objects of type patch. This object represents PEC.

Mesh the platform with edge length of 0.1

figure
mesh(p,MaxEdgeLength=0.1)

Figure contains an axes object and an object of type uicontrol. The axes object with title Metal mesh, xlabel x (m), ylabel y (m) contains an object of type patch. This object represents PEC.

Sweep over the elevation with a vertically polarized E-field. Plot the RCS at 700 MHz in the azimuth plane.

az = 0:1:360;
el = 0;
figure 
rcs(p,700e6,az,el)

Figure contains an axes object and an object of type uicontainer. The hidden axes object contains 2 objects of type line, text. This object represents el=0° .

RCS of Corner Reflector

Open Live Script

Create a corner reflector-backed antenna.

f = 2e9;
c = design(reflectorCorner,750e6);

Plot the RCS in the elevation plane.

figure
rcs(c,f,0,0:2:360)

Figure contains an axes object and an object of type uicontainer. The hidden axes object contains 2 objects of type line, text. This object represents az=0° .

Plot the RCS in the azimuth plane.

figure
rcs(c,f,0:2:360,0)

Figure contains an axes object and an object of type uicontainer. The hidden axes object contains 2 objects of type line, text. This object represents el=0° .

Bistatic RCS of Offset Cassegrain Antenna

Open Live Script

Calculate bistatic RCS for a default offset cassegrain antenna at a frequency of 14 GHz.

S = rcs(cassegrainOffset,14e9,TransmitAngle=[30;60],ReceiveAngle=[30;45])

S = 
-2.9877

Input Arguments

collapse all

`object` — Platform, antenna, or array
platform object | antenna object | array object

Platform, antenna or array to calculate the RCS, specified as an object.

Example: platform(FileName="reflector.stl")

Example: reflectorParabolic

Example: linearArray(Element=dipole)

`frequency` — Analysis frequency
real-valued scalar

Analysis frequency to calculate the RCS, specified as a real-valued scalar in Hz.

Example: 70e6

Data Types: double

`azimuth` — Azimuth angles
`0` (default) | N-element real vector | real scalar

Azimuth angles to calculate the RCS, specified as an N-element real vector in degrees. When azimuth angle is specified as a vector, then the elevation angle must be a scalar.

Example: 90

Data Types: double

`elevation` — Elevation angles
`0:5:360` (default) | M-element real vector | real scalar

Elevation angles to calculate the RCS, specified as an M-element real vector in degrees. When elevation angle is specified as a vector, then the azimuth angle must be a scalar.

Example: 0:1:360

Data Types: double

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Example: CoordinateSystem="polar"

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: 'CoordinateSystem','polar'

`CoordinateSystem` — Coordinate system used to visualize RCS
`"polar"` (default) | `"rectangular"`

Coordinate system used to visualize the RCS, specified as a string.

Example: "rectangular"

Data Types: string

`Scale` — Scale used to visualize or compute RCS
`"log"` (default) | `"linear"`

Scale used to visualize or compute the RCS, specified as a string. Use "log" scale to calculate and plot the RCS in dBsm unit.

Example: "linear"

Data Types: string

`Polarization` — Transmit and receive wave polarization
`"VV"` (default) | `"HH"` | `"HV"` | `"VH"`

Transmit and receive wave polarization, specified as a string from one of these transmit-receive combinations:

HH – Horizontal polarized field is transmitted and received.
VV – Vertical polarized field is transmitted and received.
VH – Vertical polarized field is transmitted, and horizontal polarized field is received.
HV – Horizontal polarized field is transmitted, and vertical polarized field is received.

Example: "VV"

Data Types: string

`EnableGPU` — Use GPU to speedup RCS calculations
`0` (default) | `1`

Flag to enable or disable GPU to perform RCS calculations, specified as either 1 to enable the GPU or 0 to disable.

Example: 1

Data Types: logical

`TransmitAngle` — Transmit wave angle
`[0;0]` (default) | 2-by-1 real vector

Transmit wave angle, specified as a 2-by-1 real vector representing an azimuth and elevation pair in degrees.

Example: [30;60]

Data Types: double

`ReceiveAngle` — Receive wave angle
`[zeros(1,73);0:5:360]` (default) | 2-by-M real matrix

Receive wave angle, specified as a 2-by-M real matrix representing azimuth and elevation pairs in degrees.

Example: [30 60; 45 90]'

Data Types: double

`Solver` — Solver for RCS analysis
`"PO"` (default) | `"MoM"` | `"FMM"`

Solver for RCS analysis, specified as a string from these:

PO - Physical Optics
MoM - Method of Moments
FMM - Fast Multipole Method

Example: "MOM"

Data Types: string

`Type` — RCS value type
`"Magnitude"` (default) | `"Complex"`

Output type, specified as a string. Specify the type as "Magnitude" to calculate and plot the magnitude of RCS values. Specify the type as "Complex" to calculate the complex RCS values. Plotting complex RCS values is currently unsupported.

Example: "Complex"

Data Types: string

Output Arguments

collapse all

`rcsval` — RCS value of platform, antenna, or array object
1-by-M real-valued array (default) | N-by-1 real-valued array | 1-by-M complex-valued array | N-by-1 complex-valued array

RCS value of the platform, antenna, or array object, returned as an N-by-M real-valued array in dBsm or a complex-valued array depending on the Type specified in the input. The size of the array is equal to the number of azimuth values (N) multiplied by the number of elevation values (M). Since, both the azimuth and elevation angles cannot be specified as vectors simultaneously, the size of the RCS value vector is either 1-by-M for a scalar azimuth and vector elevation or N-by-1 for a vector azimuth and scalar elevation.

Data Types: double
Complex Number Support: Yes

`azimuth` — Azimuth angles of calculated RCS pattern
N-element real-valued vector

Azimuth angles of the calculated RCS pattern, returned as an N-element real-valued vector in degrees.

Data Types: double

`elevation` — Elevation angles of calculated RCS pattern
M-element real-valued vector

Elevation angles of the calculated RCS pattern, returned as an M-element real-valued vector in degrees.

Data Types: double

More About

collapse all

What Is RCS?

Radar Cross Section (RCS) is the measure of scattering cross section of an object interrogated by a plane wave. The assumption of a plane wave implies that the structure is in the far field of the radiator, which is typically a part of the radar system. RCS is a function of the object's shape, the frequency of the radar, the angle of interrogation of the wave, and the object's material parameters. RCS can also be measured in logarithmic units of dBsm, which is dB relative to a 1 m² reference area.

RCS is calculated using two typical configurations:

Monostatic
Bistatic

By default, the rcs function calculates a monostatic RCS. To calculate a bistatic RCS, restrict the "TransmitAngle" to 2-by-1.

Monostatic RCS

The monostatic RCS configuration is characterized by a radar system that transmits a signal and receives the backscattered signal from the object being interrogated at the same site. The source of the transmitted electromagnetic waves and the receiving system for the scattered wave are co-located.

Diagrammatic representation of a monostatic radar configuration to calculate the radar cross section of an aerial object.

Bistatic RCS

In the bistatic RCS configuration, the radar system consists of a fixed radar transmitting site and a fixed or mobile receiving site captures the backscattered waveform from the object.

Diagrammatic representation of a bi-static radar congiuration to calculate the radar cross section of an aerial object.

RCS Calculation

RCS is calculated in both a scalar form and a matrix form. Equations for both forms include electric (E) and magnetic (H) field quantities calculated or measured in the far field of the scattering object.

Scalar Form

In the scalar form of RCS, σ is defined as a ratio of the squared backscattered-field to the squared incident field, given by the equation:

$σ = \lim_{r \to \infty} 4 π r^{2} \frac{{| E^{s} |}^{2}}{{| E^{i} |}^{2}}$

where E^s and Eⁱ represent the scattered and incident electric fields at a specific point in 3-D space.

Matrix Form

The matrix form of the RCS decomposes the incident and the scattered fields into horizontal and vertical polarizations and then computes the ratios of the various combinations between the scattered and incident fields, given by the equation:

$(\begin{matrix} σ_{H H} & σ_{H V} \\ σ_{V H} & σ_{V V} \end{matrix}) = \lim_{r \to \infty} 4 π r^{2} (\begin{matrix} \frac{{| E_{H}^{s} |}^{2}}{{| E_{H}^{i} |}^{2}} & \frac{{| E_{H}^{s} |}^{2}}{{| E_{V}^{i} |}^{2}} \\ \frac{{| E_{V}^{s} |}^{2}}{{| E_{H}^{i} |}^{2}} & \frac{{| E_{V}^{s} |}^{2}}{{| E_{V}^{i} |}^{2}} \end{matrix})$

where E^s_H and Eⁱ_H represent the horizontal polarized components of the scattered and incident electric fields at a given point in 3-D space. E^s_V and Eⁱ_V represent the vertical polarized components of the scattered and incident electric fields at a given point in 3-D space.

Limitations of PO Solver

The classic physical optics (PO) formulation does not support multiple reflections from a physical structure illuminated by a plane wave. The PO current density is valid only in the illuminated region of the structure. This formulation does not handle any reflections from the illuminated region that result in secondary illumination of a different region of the structure.

Case 1: When the direction of the incident plane wave results in a reflection back in the direction of the incoming source.
Case 2: When the angle of the incident plane wave causes a second reflection from a different part of the structure, this reflection contributes significantly to the scattered field and is not be considered by the PO solver.

References

[1] Gurel, L., H. Bagrci, J. C. Castelli, A. Cheraly, F. Tardivel. "Validation Through Comparison: Measurement and Calculation of the Bistatic Radar Cross Section of a Stealth Target." Radio Science. Vol. 38, Number 3, 2003, pp.12-1 - 12-8.

[2] Rao, S.M., D. R. Wilton, A. W. Glisson. "Electromagnetic Scattering by Surfaces of Arbitrary Shape." IEEE Trans. Antennas and Propagation. Vol. AP-30, Number 3, 1982, pp.409-418.

[3] Jakobus, U., F. M. Landstorfer. "Improved PO-MM Formulation for Scattering from Three-Dimensional Perfectly Conducting Bodies of Arbitrary Shape.." IEEE Trans. Antennas and Propagation. Vol. AP-43, Number 2, 1995, pp.162-169.

Version History

Introduced in R2019b

rcs

Syntax

Description

Examples

RCS of Helix

RCS of Linear Array

RCS of Reflector-Backed Dipole

RCS of Tetrahedron Platform

RCS of Corner Reflector

Bistatic RCS of Offset Cassegrain Antenna

Input Arguments

`object` — Platform, antenna, or array
platform object | antenna object | array object

`frequency` — Analysis frequency
real-valued scalar

`azimuth` — Azimuth angles
`0` (default) | N-element real vector | real scalar

`elevation` — Elevation angles
`0:5:360` (default) | M-element real vector | real scalar

Name-Value Arguments

`CoordinateSystem` — Coordinate system used to visualize RCS
`"polar"` (default) | `"rectangular"`

`Scale` — Scale used to visualize or compute RCS
`"log"` (default) | `"linear"`

`Polarization` — Transmit and receive wave polarization
`"VV"` (default) | `"HH"` | `"HV"` | `"VH"`

`EnableGPU` — Use GPU to speedup RCS calculations
`0` (default) | `1`

`TransmitAngle` — Transmit wave angle
`[0;0]` (default) | 2-by-1 real vector

`ReceiveAngle` — Receive wave angle
`[zeros(1,73);0:5:360]` (default) | 2-by-M real matrix

`Solver` — Solver for RCS analysis
`"PO"` (default) | `"MoM"` | `"FMM"`

`Type` — RCS value type
`"Magnitude"` (default) | `"Complex"`

Output Arguments

`rcsval` — RCS value of platform, antenna, or array object
1-by-M real-valued array (default) | N-by-1 real-valued array | 1-by-M complex-valued array | N-by-1 complex-valued array

`azimuth` — Azimuth angles of calculated RCS pattern
N-element real-valued vector

`elevation` — Elevation angles of calculated RCS pattern
M-element real-valued vector

More About

What Is RCS?

RCS Calculation

Limitations of PO Solver

References

Version History

See Also

Topics

rcs

Syntax

Description

Examples

RCS of Helix

RCS of Linear Array

RCS of Reflector-Backed Dipole

RCS of Tetrahedron Platform

RCS of Corner Reflector

Bistatic RCS of Offset Cassegrain Antenna

Input Arguments

object — Platform, antenna, or array platform object | antenna object | array object

frequency — Analysis frequency real-valued scalar

azimuth — Azimuth angles 0 (default) | N-element real vector | real scalar

elevation — Elevation angles 0:5:360 (default) | M-element real vector | real scalar

Name-Value Arguments

CoordinateSystem — Coordinate system used to visualize RCS "polar" (default) | "rectangular"

Scale — Scale used to visualize or compute RCS "log" (default) | "linear"

Polarization — Transmit and receive wave polarization "VV" (default) | "HH" | "HV" | "VH"

EnableGPU — Use GPU to speedup RCS calculations 0 (default) | 1

TransmitAngle — Transmit wave angle [0;0] (default) | 2-by-1 real vector

ReceiveAngle — Receive wave angle [zeros(1,73);0:5:360] (default) | 2-by-M real matrix

Solver — Solver for RCS analysis "PO" (default) | "MoM" | "FMM"

Type — RCS value type "Magnitude" (default) | "Complex"

Output Arguments

rcsval — RCS value of platform, antenna, or array object 1-by-M real-valued array (default) | N-by-1 real-valued array | 1-by-M complex-valued array | N-by-1 complex-valued array

azimuth — Azimuth angles of calculated RCS pattern N-element real-valued vector

elevation — Elevation angles of calculated RCS pattern M-element real-valued vector

More About

What Is RCS?

RCS Calculation

Limitations of PO Solver

References

Version History

See Also

Topics

`object` — Platform, antenna, or array
platform object | antenna object | array object

`frequency` — Analysis frequency
real-valued scalar

`azimuth` — Azimuth angles
`0` (default) | N-element real vector | real scalar

`elevation` — Elevation angles
`0:5:360` (default) | M-element real vector | real scalar

`CoordinateSystem` — Coordinate system used to visualize RCS
`"polar"` (default) | `"rectangular"`

`Scale` — Scale used to visualize or compute RCS
`"log"` (default) | `"linear"`

`Polarization` — Transmit and receive wave polarization
`"VV"` (default) | `"HH"` | `"HV"` | `"VH"`

`EnableGPU` — Use GPU to speedup RCS calculations
`0` (default) | `1`

`TransmitAngle` — Transmit wave angle
`[0;0]` (default) | 2-by-1 real vector

`ReceiveAngle` — Receive wave angle
`[zeros(1,73);0:5:360]` (default) | 2-by-M real matrix

`Solver` — Solver for RCS analysis
`"PO"` (default) | `"MoM"` | `"FMM"`

`Type` — RCS value type
`"Magnitude"` (default) | `"Complex"`

`rcsval` — RCS value of platform, antenna, or array object
1-by-M real-valued array (default) | N-by-1 real-valued array | 1-by-M complex-valued array | N-by-1 complex-valued array

`azimuth` — Azimuth angles of calculated RCS pattern
N-element real-valued vector

`elevation` — Elevation angles of calculated RCS pattern
M-element real-valued vector