# rcsSignature

## Description

`rcsSignature`

creates a radar cross-section (RCS) signature object.
You can use this object to model an angle-dependent and frequency-dependent radar
cross-section pattern. The radar cross-section determines the intensity of reflected radar
signal power from a target. The object models both polarized and non-polarized signals. The
object support several Swerling fluctuation models.

## Creation

### Description

creates an
`rcssig`

= rcsSignature`rcsSignature`

object with default property values.

sets object properties using one or more `rcssig`

= rcsSignature(`Name,Value`

)`Name,Value`

pair arguments.
`Name`

is a property name and `Value`

is the
corresponding value. `Name`

must appear inside single quotes
(`''`

). You can specify several name-value pair arguments in any order
as `Name1,Value1,...,NameN,ValueN`

. Any unspecified properties take
default values.

**Note**

You can only set property values of `rcsSignature`

when constructing the
object. The property values are not changeable after construction.

## Properties

`EnablePolarization`

— Enable polarization

`false`

(default) | `true`

To enable polarization, set this property to `true`

. Set this
property to `false`

to ignore polarization.

**Data Types: **`logical`

`CrossPolarization`

— Cross-polarization specification method

`'Full'`

(default) | `'Symmetric'`

Polarization scattering matrix form, specified as `'Full'`

or
`'Symmetric'`

.

`'Full'`

makes no assumptions about the cross-polarization terms and the polarization matrix components must all be specified (`ShhPattern`

,`SvvPattern`

,`ShvPattern`

,`SvhPattern`

). When this input method is selected, the`ShvPattern`

and`SvhPattern`

properties are applicable.`'Symmetric'`

assumes reciprocity (monostatic geometry) and that the cross-polarization terms are equal (`ShvPattern`

=`SvhPattern`

). When this input method is selected, the`ShvPattern`

property is available. The`SvhPattern`

property is not available and is assumed to be equal to the`ShvPattern`

property.

#### Dependencies

To enable this property, set the `EnablePolarization`

property
to `true`

.

`Pattern`

— Sampled radar cross-section pattern

`[10 10; 10 10]`

(default) | *Q*-by-*P* real-valued matrix | *Q*-by-*P*-by-*K* real-valued
array

Sampled radar cross-section (RCS) pattern, specified as a scalar, a
*Q*-by-*P* real-valued matrix, or a
*Q*-by-*P*-by-*K* real-valued
array. The pattern is an array of RCS values defined on a grid of elevation angles,
azimuth angles, and frequencies. Azimuth and elevation are defined in the body frame of
the target.

*Q*is the number of RCS samples in elevation.*P*is the number of RCS samples in azimuth.*K*is the number of RCS samples in frequency.

. Units are in dBsm.

*Q*, *P*, and *K* usually match
the length of the vectors defined in the `Elevation`

,
`Azimuth`

, and `Frequency`

properties,
respectively, with these exceptions:

To model an RCS pattern for an elevation cut (constant azimuth), you can specify the RCS pattern as a

*Q*-by-1 vector or a 1-by-*Q*-by-*K*matrix. Then, the azimuth vector specified in the`Azimuth`

property must have length 2.To model an RCS pattern for an azimuth cut (constant elevation), you can specify the RCS pattern as a 1-by-

*P*vector or a 1-by-*P*-by-*K*matrix. Then, the elevation vector specified in the`Elevation`

property must have length 2.To model an RCS pattern for one frequency, you can specify the RCS pattern as a

*Q*-by-*P*matrix. Then, the frequency vector specified in the`Frequency`

property must have length 2.

**Example: **`[10,0;0,-5]`

#### Dependencies

To enable this property, set the `EnablePolarization`

property
to `false`

.

**Data Types: **`double`

`ShhPattern`

— Polarization scattering matrix *HH* component

`[1, 1; 1, 1]`

(default) | *Q*-by-*P* complex-valued matrix | *Q*-by-*P*-by-*K* complex-valued
array

Polarization scattering matrix co-polarized *HH* component, where
*HH* represents horizontal transmission and horizontal reception.
*Q* is the length of the vector in the `Elevation`

property. *P* is the length of the vector in the
`Azimuth`

property. If the pattern is three-dimensional, then
*K* is the length of the vector in the `Frequency`

property.

When defining patterns for azimuth or elevation only cuts, *P* or
*Q* can equal 1, but the corresponding `Azimuth`

or `Elevation`

property must still be a 2-element vector. In this
case, the `Azimuth`

or `Elevation`

property
defines the view angles over which the pattern is considered valid for the pattern's
dimension with length 1.

Units are in meters.

#### Dependencies

To enable this property, set the `EnablePolarization`

property
to `true`

.

**Data Types: **`double`

**Complex Number Support: **Yes

`SvvPattern`

— Polarization scattering matrix *VV* component

`[1, 1; 1, 1]`

(default) | *Q*-by-*P* complex-valued matrix | *Q*-by-*P*-by-*K* complex-valued
array

Polarization scattering matrix co-polarized *VV* component, where
*VV* represents vertical transmission and vertical reception.
*Q* is the length of the vector in the `Elevation`

property. *P* is the length of the vector in the
`Azimuth`

property. If the pattern is three-dimensional, then
*K* is the length of the vector in the `Frequency`

property.

When defining patterns for azimuth or elevation only cuts, *P* or
*Q* can equal 1, but the corresponding `Azimuth`

or `Elevation`

property must still be a 2-element vector. In this
case, the `Azimuth`

or `Elevation`

property
defines the view angles over which the pattern is considered valid for the pattern's
dimension with length 1.

Units are in meters.

#### Dependencies

To enable this property, set the `EnablePolarization`

property
to `true`

.

**Data Types: **`double`

**Complex Number Support: **Yes

`ShvPattern`

— Polarization scattering matrix *HV* component

`[0, 0; 0, 0]`

(default) | *Q*-by-*P* complex-valued matrix | *Q*-by-*P*-by-*K* complex-valued
array

Polarization scattering matrix co-polarized *HV* component, where
*HV* represents horizontal transmission and vertical reception.
*Q* is the length of the vector in the `Elevation`

property. *P* is the length of the vector in the
`Azimuth`

property. If the pattern is three-dimensional, then
*K* is the length of the vector in the `Frequency`

property.

When defining patterns for azimuth or elevation only cuts, *P* or
*Q* can equal 1, but the corresponding `Azimuth`

or `Elevation`

property must still be a 2-element vector. In this
case, the `Azimuth`

or `Elevation`

property
defines the view angles over which the pattern is considered valid for the pattern's
dimension with length 1.

Units are in meters.

#### Dependencies

To enable this property, set the `EnablePolarization`

property
to `true`

.

**Data Types: **`double`

**Complex Number Support: **Yes

`SvhPattern`

— Polarization scattering matrix *VH* component

`[0, 0; 0, 0]`

(default) | *Q*-by-*P* complex-valued matrix | *Q*-by-*P*-by-*K* complex-valued
array

Polarization scattering matrix co-polarized *HV* component, where
*VH* represents vertical transmission and horizontal reception.
*Q* is the length of the vector in the `Elevation`

property. *P* is the length of the vector in the
`Azimuth`

property. If the pattern is three-dimensional, then
*K* is the length of the vector in the `Frequency`

property.

*P* or
*Q* can equal 1, but the corresponding `Azimuth`

or `Elevation`

property must still be a 2-element vector. In this
case, the `Azimuth`

or `Elevation`

property
defines the view angles over which the pattern is considered valid for the pattern's
dimension with length 1.

Units are in meters.

#### Dependencies

To enable this property, set the `EnablePolarization`

property
to `true`

and set the `CrossPolarization`

property
to `'Full'`

.

**Data Types: **`double`

**Complex Number Support: **Yes

`Azimuth`

— Azimuth angles

`[-180 180]`

(default) | length-*P* real-valued vector

Azimuth angles used to define the angular coordinates of each column of the matrix
or array, specified by the `Pattern`

property. Specify the azimuth
angles as a length-*P* vector. *P* must be greater
than two. Angle units are in degrees.

When the `Pattern`

property defines an elevation cut,
`Azimuth`

must be a 2-element vector defining the minimum and
maximum azimuth view angles over which the elevation cut is considered valid.

**Example: **`[-45:0.5:45]`

**Data Types: **`double`

`Elevation`

— Elevation angles

`[-90 90]`

(default) | length-*Q* real-valued vector

Elevation angles used to define the coordinates of each row of the matrix or array,
specified by the `Pattern`

property. Specify the elevation angles as
a length-*Q* vector. *Q* must be greater than two.
Angle units are in degrees.

When the `Pattern`

property defines an azimuth cut,
`Elevation`

must be a 2-element vector defining the minimum and
maximum elevation view angles over which the azimuth cut is considered valid.

**Example: **`[-30:0.5:30]`

**Data Types: **`double`

`Frequency`

— Pattern frequencies

`[0 1e20]`

(default) | *K*-element vector of positive scalars

Frequencies used to define the applicable RCS for each page of the
`Pattern`

property, specified as a *K*-element
vector of positive scalars. *K* is the number of RCS samples in
frequency. *K* must be no less than two. Frequency units are in
hertz.

When the `Pattern`

property is a matrix,
`Frequency`

must be a 2-element vector defining the minimum and
maximum frequencies over which the pattern values are considered valid.

**Example: **`[0:0.1:30]`

**Data Types: **`double`

`FluctuationModel`

— Statistical signature fluctuation model

`'Swerling0'`

(default) | `'Swerling1'`

| `'Swerling3'`

Fluctuation models, specified as `'Swerling0'`

,
`'Swerling1'`

or `'Swerling3'`

. Swerling cases 2 and
4 are not modeled because they are determined from how the target is sampled and are not
an inherent target property.

Model | Description |
---|---|

`'Swerling0'` | The target RCS is assumed to be non-fluctuating. In this case the instantaneous RCS signature value retrieved by the value method is deterministic. This model represents ideal radar targets with an RCS that remains constant in time across the range of aspect angles of interest, e.g., a conducting sphere and various corner reflectors. |

`'Swerling1'` | The target is assumed to be made up of many independent scatterers of equal
size. This model is typically used to represent aircraft. The instantaneous RCS
signature value returned by the value method in this case is a random variable
distributed according to the exponential distribution with a mean determined by
the `Pattern` property. |

`'Swerling3'` | The target is assumed to have one large dominant scatterer and several
small scatterers. The RCS of the dominant scatterer equals
1+sqrt(2) times the sum of the RCS of other scatterers.
This model can be used to represent helicopters and propeller driven aircraft.
In this case the instantaneous RCS signature's value returned by the value
method is a random variable distributed according to the 4th degree chi-square
distribution with mean determined by the `Pattern`
property. |

**Data Types: **`char`

| `string`

## Object Functions

## Examples

### Radar Cross-Section of Ellipsoid

Specify the radar cross-section (RCS) of a triaxial ellipsoid and plot RCS values along an azimuth cut.

Specify the lengths of the axes of the ellipsoid. Units are in meters.

a = 0.15; b = 0.20; c = 0.95;

Create an RCS array. Specify the range of azimuth and elevation angles over which RCS is defined. Then, use an analytical model to compute the radar cross-section of the ellipsoid. Create an image of the RCS.

az = [-180:1:180]; el = [-90:1:90]; rcs = rcs_ellipsoid(a,b,c,az,el); rcsdb = 10*log10(rcs); imagesc(az,el,rcsdb) title('Radar Cross-Section') xlabel('Azimuth (deg)') ylabel('Elevation (deg)') colorbar

Create an `rcsSignature`

object and plot an elevation cut at $$3{0}^{\circ}$$ azimuth.

rcssig = rcsSignature('Pattern',rcsdb,'Azimuth',az,'Elevation',el,'Frequency',[300e6 300e6]); rcsdb1 = value(rcssig,30,el,300e6); plot(el,rcsdb1) grid title('Elevation Profile of Radar Cross-Section') xlabel('Elevation (deg)') ylabel('RCS (dBsm)')

function rcs = rcs_ellipsoid(a,b,c,az,el) sinaz = sind(az); cosaz = cosd(az); sintheta = sind(90 - el); costheta = cosd(90 - el); denom = (a^2*(sintheta'.^2)*cosaz.^2 + b^2*(sintheta'.^2)*sinaz.^2 + c^2*(costheta'.^2)*ones(size(cosaz))).^2; rcs = (pi*a^2*b^2*c^2)./denom; end

### RCS Distribution of Swerling 1 Target

Import the radar cross-section (RCS) measurements of a 1/5th scale Boeing 737. Load the RCS data into an `rcsSignature`

object. Assume the RCS follows a Swerling 1 distribution.

load('RCSSignatureExampleData.mat','boeing737'); rcs = rcsSignature('Pattern',boeing737.RCSdBsm, ... 'Azimuth', boeing737.Azimuth,'Elevation',boeing737.Elevation, ... 'Frequency',boeing737.Frequency,'FluctuationModel','Swerling1');

Set the seed of the random number generator for reproducibility of example.

rng(3231)

Plot sample RCS versus azimuth angle.

plot(rcs.Azimuth,rcs.Pattern) xlabel('Azimuth (deg)'); ylabel('RCS (dBsm)') title('Measured RCS from 1/5th scale Boeing 737 model')

Construct an RCS histogram and display the mean value.

N = 1000; val = zeros(1,N); for k = 1:N [val(k),expval] = value(rcs,-5,0,800.0e6); end

Convert to power units.

mean(db2pow(val))

ans = 406.9799

```
histogram(db2pow(val),50)
xlabel("RCS (dBsm)")
```

## References

[1] Richards, Mark A.
*Fundamentals of Radar Signal Processing*. New York, McGraw-Hill,
2005.

## Extended Capabilities

### C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

## Version History

**Introduced in R2021a**

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