rcs

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

Since R2019b

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 object over a specified frequency. To learn more about RCS, see What Is RCS?.

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

rcs(___,Name,Value) plots the RCS with additional properties specified using one or more Name, Value pair arguments. This parameter can be used with any of the input arguments from the previous syntaxes.

[rcsval,azimuth,elevation] = rcs(object,frequency) returns the RCS value of a platform, antenna, or array object at the specified frequency. azimuth and elevation are vectors over which the RCS value is calculated.

[rcsval,azimuth,elevation] = rcs(___,Name,Value) returns the RCS value with additional properties specified using one or more Name, Value pair arguments. This parameter can be used with any of the input arguments from the previous syntaxes.

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 = -1.5875

Input Arguments

object — Platform, antenna, or array element

object

Platform, antenna or array element, specified as an object.

frequency — Analysis frequency

real-valued scalar

Analysis frequency, specified as a real-valued scalar in Hz.

Example: 70e6

Data Types: double

azimuth — Azimuth angles

0 (default) | N-element real vector

Azimuth angles at which to visualize the RCS, specified as an N-element real vector in degrees.

Example: 90

Data Types: double

elevation — Elevation angles

0:5:360 (default) | M-element real vector

Elevation angles at which to visualize the RCS, specified as an M-element real vector in degrees.

Example: 0:1:360

Data Types: double

Name-Value Arguments

Example: 'CoordinateSystem','polar'

Specify optional comma-separated pairs of Name,Value pair arguments. Name is the argument name and Value is the corresponding value. Name must appear inside single quotes (''). You can specify several name and value pair arguments in any order as Name1, Value1, ..., NameN, ValueN.

CoordinateSystem — Coordinate system in which to visualize RCS

'polar' (default) | 'rectangular'

Coordinate system in which to visualize the RCS, specified as the comma-separated pair consisting of 'CoordinateSystem' and one of these values: 'polar' or 'rectangular'.

Example: 'CoordinateSystem','rectangular'

Data Types: char

Scale — Scale at which to visualize or compute RCS

'log' (default) | 'linear'

Scale at which to visualize or compute the RCS, specified as the comma-separated pair consisting of 'Scale' and 'log' or 'linear'. When you choose 'log', the RCS is calculated and plotted in dBsm.

Example: 'Scale','linear'

Data Types: char

Polarization — Transmit and receive wave polarization

'VV' (default) | 'HH' | 'HV' | 'VH'

Transmit and receive wave polarization, specified as the comma-separated pair consisting of 'Polarization' and one of these values:

• '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: 'Polarization','VV'

Data Types: char

EnableGPU — Use GPU to perform RCS calculations

0 (default) | 1

Use GPU to perform RCS calculations, specified as the comma-separated pair consisting of 'EnableGPU' and 0 to disable GPU or 1 to enable GPU.

Example: 'EnableGPU',1

Data Types: logical

TransmitAngle — Transmit wave angle

2-by-N real matrix

Transmit wave angle, specified as the comma-separated pair consisting of 'TransmitAngle' and a 2-by-N real matrix representing azimuth and elevation pairs, with each element unit in degrees.

Example: 'TransmitAngle',[30;60]

Data Types: double

ReceiveAngle — Receive wave angle

2-by-M real matrix

Receive wave angle, specified as the comma-separated pair consisting of 'ReceiveAngle' and a 2-by-M real matrix representing azimuth and elevation pairs, with each element unit in degrees.

Example: 'ReceiveAngle',[30;60]

Data Types: double

Solver — Solver for RCS analysis

'PO' (default) | 'MoM' | 'FMM'

Solver for RCS analysis, specified as the comma-separated pair consisting of 'Solver' and 'PO' (Physical Optics) or 'MoM' (Method of Moments) or 'FMM' (Fast Multipole Method).

Example: 'Solver', 'MOM'

Data Types: char

Type — Output type

'Magnitude' (default) | 'Complex'

Output type, specified as the comma-separated pair consisting of 'Type' and 'Magnitude' or 'Complex'.

Note

Plotting rcs will error if the 'Type' is 'Complex'

Example: 'Type', 'Complex'

Data Types: char

Output Arguments

rcsval — RCS value of platform, antenna, or array object

N-by-M real-valued array

RCS value of the platform, antenna, or array object, returned as an N-by-M real-valued array in dBsm. The size of the array is equal to the number of azimuth values (N) multiplied by the number of elevation values (M).

azimuth — Azimuth angles of calculated RCS pattern

N-element real-valued vector

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

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.

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.

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