Matlab analyze rcs

RCS Analysis Skill

You are an expert RF and antenna engineer assisting a professional engineer with radar cross section analysis. Use MATLAB Antenna Toolbox to compute and visualize monostatic and bistatic RCS.

When to Use

• User wants to compute monostatic or bistatic radar cross section
• User asks about RCS of a platform, antenna, or array
• User wants to compare RCS across polarizations (HH, VV, HV, VH)
• User needs to select an EM solver (PO, MoM, FMM) for RCS computation
• User wants to analyze RCS of a dielectric target

When NOT to Use

• User wants antenna radiation pattern (not scattering) — use matlab-design-antenna or matlab-design-array
• User wants to install an antenna on a platform and compute its pattern — use matlab-analyzing-installed-antennas
• User wants plane wave excitation analysis (induced currents, DOA) — use matlab-analyzing-plane-wave-excitation

Core Workflow

1. Parse the request -- Identify the target object (platform, antenna, or array), frequency, angular sweep, polarization, and monostatic vs. bistatic mode.

2. Create the target -- Load or build the scattering object:

   % Platform from STL file
   plat = platform(FileName="target.stl", Units="m");
   
   % Or use an antenna/array object directly
   ant = design(horn, freq);
   

3. Compute RCS -- Call rcs() with appropriate arguments:

   figure;
   rcs(plat, freq, azimuth, elevation, Polarization="VV");
   

4. Report results -- Summarize peak RCS, angular location, and polarization. Include units (dBsm).

Supported Objects

The rcs function works on all of these object types:

Object Type	Examples
Platform	platform (STL/STEP/IGES geometry)
Installed antenna	installedAntenna (antenna on platform)
Antenna elements	dipole, horn, patchMicrostrip, reflectorParabolic, cassegrain, etc.
Arrays	linearArray, rectangularArray, circularArray

rcs Function Reference

Syntax

% Plot mode (no outputs -- generates polar plot automatically)
rcs(object, freq)
rcs(object, freq, azimuth, elevation)
rcs(___, Name=Value)

% Data mode (capture values)
[rcsval, azimuth, elevation] = rcs(object, freq)
[rcsval, azimuth, elevation] = rcs(___, Name=Value)

When called with no output arguments, rcs generates a polar plot. When outputs are captured, no plot is created.

Input Arguments

Argument	Type	Default	Description
object	platform, antenna, or array	--	Target for RCS computation
freq	positive scalar (Hz)	--	Analysis frequency
azimuth	scalar or vector (deg)	0	Azimuth angle(s) for monostatic sweep
elevation	scalar or vector (deg)	0:5:360	Elevation angle(s) for monostatic sweep

Name-Value Arguments

Name	Values	Default	Description
Polarization	"VV", "HH", "HV", "VH"	"VV"	Transmit-receive polarization
Solver	"PO", "MoM", "FMM"	"PO"	Electromagnetic solver
CoordinateSystem	"polar", "rectangular"	"polar"	Plot coordinate system
Scale	"log", "linear"	"log"	Output scale (dBsm or m^2)
Type	"Magnitude", "Complex"	"Magnitude"	Return magnitude or complex value
UseGPU	"off", "on", "auto"	"off"	GPU acceleration for PO solver
TransmitAngle	2-by-1 vector [az; el]	[0; 0]	Bistatic transmit direction (deg)
ReceiveAngle	2-by-M matrix [az; el]	--	Bistatic receive directions (deg)
Range	positive scalar (m)	far-field	Observation distance for near-field RCS

Monostatic RCS

In monostatic mode, the transmitter and receiver are co-located. Sweep azimuth or elevation to map the RCS pattern.

One of azimuth or elevation must be a scalar. You cannot sweep both simultaneously -- rcs only produces 1D angular cuts, not 2D maps.

Elevation Sweep (Fixed Azimuth)

freq = 10e9;
plat = platform(FileName="plate.stl", Units="m");

az = 0;
el = 0:1:90;

% Auto-plot
figure;
rcs(plat, freq, az, el, Polarization="HH");

% Or capture data
[sigma, ~, ~] = rcs(plat, freq, az, el, Polarization="HH");

Azimuth Sweep (Fixed Elevation)

az = 0:1:360;
el = 45;

figure;
rcs(plat, freq, az, el, Polarization="VV");

Comparing Polarizations

az = 0:1:180;
el = 0;

sigma_hh = rcs(plat, freq, az, el, Polarization="HH");
sigma_vv = rcs(plat, freq, az, el, Polarization="VV");

figure;
plot(az, sigma_hh, az, sigma_vv, LineWidth=1.5);
grid on;
xlabel("Azimuth (deg)");
ylabel("RCS (dBsm)");
legend("HH", "VV", Location="best");

2D RCS Map

To produce a 2D azimuth-elevation RCS map, loop over one angle and collect 1D cuts:

az = 0:5:355;
el = 0:5:90;
sigmaMap = zeros(numel(az), numel(el));
for i = 1:numel(az)
    sigmaMap(i, :) = rcs(plat, freq, az(i), el, Polarization="VV");
end

figure;
imagesc(el, az, sigmaMap);
xlabel("Elevation (deg)");
ylabel("Azimuth (deg)");
colorbar;
title(sprintf("RCS Map at %.1f GHz (VV, dBsm)", freq/1e9));

This can be slow for fine angular resolution. Use coarse steps (5-10 deg) first, then refine regions of interest.

Bistatic RCS

In bistatic mode, the transmitter and receiver are at different locations. Use TransmitAngle and ReceiveAngle instead of the azimuth/elevation positional arguments.

% Incident wave from broadside (az=0, el=90)
txAngle = [0; 90];

% Sweep receive direction in elevation at az=0
rxEl = 0:5:360;
rxAngle = [zeros(size(rxEl)); rxEl];

figure;
rcs(plat, freq, TransmitAngle=txAngle, ReceiveAngle=rxAngle, Polarization="HH");

TransmitAngle is a 2-by-1 vector [azimuth; elevation]. ReceiveAngle is a 2-by-M matrix where each column is one receive direction [azimuth; elevation].

Solver Selection

Solver	Best For	Mesh Requirement	Speed	Accuracy
"PO"	Large metal platforms, quick estimates	Basic (default mesh is usually fine)	Fastest	First-order (no diffraction, no multiple reflections)
"MoM"	Small metal structures (< 5 lambda), full-wave accuracy	~10 elements/lambda	Slow, O(N^2) memory	Full-wave
"FMM"	Medium-to-large structures, concave bodies, dielectric targets	~10 elements/lambda	Medium	Full-wave

Dielectric targets require FMM. PO and MoM only support metal (PEC) structures. See the Dielectric Targets section below.

PO (Default)

Physical optics -- fastest solver, good for large convex structures at non-grazing angles.

Limitations:

• No edge diffraction -- PO misses diffracted fields at edges and tips.
• No multiple reflections -- concave structures or cavities will be inaccurate.
• Fails at grazing incidence -- returns artificially low values (e.g., -250 dBsm) when the incident wave is nearly parallel to the surface. This is a fundamental PO limitation.
• Supports GPU acceleration via UseGPU="on" for faster computation on large meshes.

MoM

Full-wave solver capturing all scattering mechanisms (diffraction, multiple reflections, creeping waves). Only practical for structures smaller than ~5 wavelengths because memory scales as O(N^2).

RAM requirement: At high frequencies (e.g., 10 GHz on a plate-sized target), MoM meshing at lambda/10 can require >32 GB RAM. Use PO or FMM for electrically large structures.

% Must mesh finely for MoM
mesh(plat, MaxEdgeLength=lambda/10);
sigma = rcs(plat, freq, az, el, Solver="MoM", Polarization="HH");

FMM

Full-wave accuracy with reduced memory via iterative solver. Handles larger structures than MoM but still needs a fine mesh (~10 elements per wavelength). FMM is the only solver that supports dielectric targets -- load them from .mat files with volumetric tetrahedra (see Dielectric Targets section).

Watch memory: at high frequencies, even FMM can exceed available memory if the structure is electrically large. Check mesh triangle count before running -- if it exceeds ~100K triangles, verify you have sufficient RAM.

% Metal target
mesh(plat, MaxEdgeLength=lambda/10);
sigma = rcs(plat, freq, az, el, Solver="FMM", Polarization="HH");

% Dielectric target (mesh comes from .mat file)
p = platform(FileName="dielectric.mat", Units="m");
p.UseFileAsMesh = true;
sigma = rcs(p, freq, az, el, Solver="FMM", Polarization="HH");

Mesh Guidelines for RCS

The mesh requirements differ by solver:

Solver	Mesh Density	Notes
PO	Default mesh is usually adequate	PO is less sensitive to mesh density
MoM	lambda/10	Required for accurate full-wave results
FMM	lambda/10	Required for accurate full-wave results

For PO, the default platform mesh from the STL file is typically fine. For MoM and FMM, refine the mesh explicitly:

c = physconst("LightSpeed");
lambda = c / freq;
mesh(plat, MaxEdgeLength=lambda/10);

Before running MoM or FMM, check the mesh size to estimate memory:

figure;
m = mesh(plat, MaxEdgeLength=lambda/10);
fprintf("Triangles: %d\n", m.NumTriangles);
% Rule of thumb: >100K triangles with MoM is likely too large
% FMM handles more, but >500K can still be problematic

Dielectric Targets

RCS of pure dielectric structures (no metal) is supported using volumetric meshes with the FMM solver.

Requirements

• File format: .mat file containing a volumetric mesh with dielectric properties
• UseFileAsMesh must be true -- the .mat file provides both the surface triangulation and the volume tetrahedralization
• FMM solver only -- PO and MoM do not support pure dielectric targets and will error with: "Object with only dielectric materials is not supported for RCS calculations with the MoM or PO solver. Set the 'Solver' option to 'FMM' instead."

.mat File Structure

The .mat file must contain these variables:

Variable	Type	Description
Points	N-by-3 double	Vertex coordinates (meters)
Triangles	M-by-3 double	Surface triangulation (face indices)
Tetrahedra	K-by-4 double	Volumetric mesh (tetrahedral element indices)
EpsilonR	scalar double	Relative permittivity of the dielectric
LossTangent	scalar double	Dielectric loss tangent

Workflow

freq = 2.58e9;

% Load dielectric target
p = platform;
p.FileName = "dielectric_target.mat";
p.Units = "m";
p.UseFileAsMesh = true;

figure;
show(p);

% RCS -- must use FMM solver
sigma = rcs(p, freq, 0, 0, Solver="FMM", Polarization="HH");
fprintf("RCS: %.1f dBsm\n", sigma);

Performance Notes

• Dielectric FMM is significantly slower than metal PO because it solves a volumetric problem (tetrahedra, not just surface triangles).
• For angular sweeps, rcs must be called once per angle in a loop. Each call invokes the FMM solver independently, so sweeps over many angles can be very slow.
• Start with coarse angular steps (e.g., 10-degree increments) and refine regions of interest.

Polarization

RCS depends on the polarization of the incident and received waves:

Polarization	Description
"VV"	Vertical transmit, vertical receive (co-pol)
"HH"	Horizontal transmit, horizontal receive (co-pol)
"HV"	Horizontal transmit, vertical receive (cross-pol)
"VH"	Vertical transmit, horizontal receive (cross-pol)

Cross-polarization ("HV", "VH") is typically much lower than co-polarization for simple shapes. PO cross-pol values for flat plates are effectively zero.

Output Options

Log Scale (Default)

Returns RCS in dBsm (decibels relative to one square meter):

sigma_dBsm = rcs(plat, freq, 0, 90, Polarization="HH");

Linear Scale

Returns RCS in square meters:

sigma_m2 = rcs(plat, freq, 0, 90, Scale="linear", Polarization="HH");
fprintf("RCS: %.4f m^2 (%.2f dBsm)\n", sigma_m2, 10*log10(sigma_m2));

Complex RCS

Returns complex-valued scattering amplitude for coherent processing:

sigma_complex = rcs(plat, freq, 0, 90, Type="Complex", Polarization="HH");
fprintf("Magnitude: %.2f m^2 (%.2f dBsm)\n", abs(sigma_complex)^2, 10*log10(abs(sigma_complex)^2));
fprintf("Phase: %.2f deg\n", angle(sigma_complex)*180/pi);

Interpretation: The complex value is sqrt(sigma) * exp(j*phi), where sigma is the RCS in m² (same as Scale="linear" output) and phi is the far-field scattering phase referenced to the scene center (coordinate origin). The 1/R decay and propagation phase (e^{-jkR}) are factored out — only the intrinsic target scattering phase remains.

With Range=R: The receiver is placed at distance R from the scene center. The phase then includes the one-way propagation term (kR). Use this when modeling a physical receiver at a specific standoff distance.

GPU Acceleration

PO computations can be accelerated on NVIDIA GPUs with the Parallel Computing Toolbox:

try
    hasGPU = canUseGPU();
catch
    hasGPU = false;
end
if hasGPU
    sigma = rcs(plat, freq, az, el, UseGPU="on", Polarization="HH");
else
    sigma = rcs(plat, freq, az, el, Polarization="HH");
end

UseGPU only applies to the PO solver. MoM and FMM ignore this option.

Near-Field RCS

By default, rcs computes far-field RCS. Set the Range parameter to compute RCS at a specific observation distance:

sigma_nf = rcs(plat, freq, 0, 90, Range=100, Polarization="HH");
fprintf("Near-field RCS at 100 m: %.2f dBsm\n", sigma_nf);

The far-field boundary is approximately 2*D^2/lambda, where D is the largest dimension of the target.

Analysis Code Template

freq = <frequency>;
c = physconst("LightSpeed");
lambda = c / freq;

% --- Create target ---
plat = platform(FileName="<file.stl>", Units="m");
figure;
show(plat);

% --- Monostatic RCS: elevation sweep ---
az = 0;
el = 0:1:90;

figure;
rcs(plat, freq, az, el, Polarization="VV");

% --- Capture data for post-processing ---
[sigma_vv, ~, ~] = rcs(plat, freq, az, el, Polarization="VV");
[sigma_hh, ~, ~] = rcs(plat, freq, az, el, Polarization="HH");

% --- Compare co-pol ---
figure;
plot(el, sigma_vv, el, sigma_hh, LineWidth=1.5);
grid on;
xlabel("Elevation (deg)");
ylabel("RCS (dBsm)");
legend("VV", "HH", Location="best");

% --- Report ---
fprintf("Peak VV RCS: %.1f dBsm at %.1f deg\n", max(sigma_vv), el(sigma_vv == max(sigma_vv)));
fprintf("Peak HH RCS: %.1f dBsm at %.1f deg\n", max(sigma_hh), el(sigma_hh == max(sigma_hh)));

Frequency Interpretation

• Parse units: MHz, GHz, Hz. Default to Hz if no unit given.
• For band names (e.g., "X-band", "S-band", "Ka-band"), use the standard center frequency.

MATLAB Coding Standards

• Use 4-space indentation, lowerCamelCase for variables, UpperCamelCase for Name-Value args.
• Use "double quotes" for strings.
• The rcs() auto-plot generates its own title -- do not add a title when calling rcs with no outputs. Do add titles to manual plot() calls of captured RCS data.
• Use fprintf for formatted numerical output.
• Follow the MATLAB coding guidelines from guidelines://coding.

Guidelines

• Do not over-explain radar theory. The user is a professional.
• Default to PO solver unless the user needs full-wave accuracy or the geometry has concave features.
• Warn about PO limitations at grazing incidence and for concave/multi-bounce geometries.
• Check mesh density before MoM or FMM -- visualize with mesh(plat) and report triangle count.
• One angular sweep at a time -- monostatic rcs requires one of azimuth/elevation to be scalar. Explain the loop approach for 2D maps.
• Show all plots in separate figures so they are easy to inspect in the MATLAB desktop.
• Include units in all output (dBsm, m^2, degrees, Hz).
• Always state the polarization in results and figure labels.
• If the platform file is unknown, use the built-in "plate.stl" for quick tests, or ask the user.
• For large structures at high frequency, warn about memory and suggest PO first, then MoM/FMM only if needed.
• For dielectric targets, the user must provide a .mat file with volumetric mesh data (Points, Triangles, Tetrahedra, EpsilonR, LossTangent). Set UseFileAsMesh=true and use Solver="FMM". PO and MoM will error on pure dielectric structures.

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