rcs

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

Syntax

rcs(object,frequency)

rcs(___,azimuth,elevation)

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

[___] = 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?.

rcs(___,azimuth,elevation) plots the monostatic RCS for the specified azimuth and elevation angles.

[rcsval,azimuth,elevation] = rcs(___) returns the monostatic RCS value and corresponding azimuth and elevation angles.

[___] = rcs(___,Name=Value) specifies additional options using one or more name-value arguments. For a bistatic RCS, specify the TransmitAngle name-value argument as a 2-by-1 matrix with non-zero values.

Examples

RCS of Helix

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

ant = helix;
rcs(ant,2e9)

RCS of Linear Array

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)

RCS of Reflector-Backed Dipole

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)

RCS of Tetrahedron Platform

Create a tetrahedron platform from an STL file.

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

Mesh the platform with edge length of 0.1

figure
mesh(p,MaxEdgeLength=0.1)

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)

RCS of Corner Reflector

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)

Plot the RCS in the azimuth plane.

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

Bistatic RCS of Offset Cassegrain Antenna

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

Calculate and Plot 3-D RCS Pattern

This example shows how to calculate and plot the 3-D RCS pattern of a platform.

Import the platform geometry stored in a STL file to workspace using the platform object. Define the azimuth and elevation angles to calculate the RCS. Use parallel pool to expedite the calculations.

p = platform;
p.FileName = "square_plate.stl";
p.Units = 'm'

p = 
  platform with properties:

         FileName: "square_plate.stl"
            Units: 'm'
    UseFileAsMesh: 0
             Tilt: 0
         TiltAxis: [1 0 0]

figure
show(p)

az = 0:1:360;
el = -90:1:90;
parfor k = 1:numel(el)
    rcsval(:,k) = rcs(p,9e9,az,el(k));
end

Define the phi and theta angles to plot the RCS pattern. Use the patternCustom function to plot the 3-D RCS pattern.

phi = az';
theta = (90-el);
MagE = rcsval;
P = PatternPlotOptions;
P.MagnitudeScale = [-40 0];
figure
patternCustom(MagE,theta,phi,PatternOptions=P);

Input Arguments

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"

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.

Note

You can use GPU for RCS calculations only when the Solver is set to "PO".

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

Range — Observation point distance

far-field distance (default) | positive scalar

Observation point distance from the target object, specified as a scalar in meters. The default far-field distance varies from 100λ to more based on the target object's dimensions.

Example: 20

Data Types: double

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

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

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.

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.

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:

$$\sigma =\underset{r\to \infty }{\lim }4\pi r^2\frac{{\left|E^{\text{s}}\right|}^2}{{\left|E^{\text{i}}\right|}^2}$$

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:

$$\left(\begin{array}{cc}{\sigma }_{HH}& {\sigma }_{HV}\\ {\sigma }_{VH}& {\sigma }_{VV}\end{array}\right)=\underset{r\to \infty }{\lim }4\pi r^2\left(\begin{array}{cc}\frac{{\left|E_H^{\text{s}}\right|}^2}{{\left|E_H^{\text{i}}\right|}^2}& \frac{{\left|E_H^{\text{s}}\right|}^2}{{\left|E_V^{\text{i}}\right|}^2}\\ \frac{{\left|E_V^{\text{s}}\right|}^2}{{\left|E_H^{\text{i}}\right|}^2}& \frac{{\left|E_V^{\text{s}}\right|}^2}{{\left|E_V^{\text{i}}\right|}^2}\end{array}\right)$$

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

R2025a: Calculate RCS of target from specified observation point

Use the new Range name-value argument in the rcs function to set the observation point distance. This allows you to calculate RCS of the target from a specified observation point.