surfaceReflectivityCustom

Normalized reflectivity of custom surface

Since R2022a

Description

This System object™ creates a normalized reflectivity object for custom surfaces. Use surfaceReflectivityCustom to generate normalized radar cross section (NRCS), and optionally speckle, as a function of frequency and grazing angle for custom surfaces. NRCS is the radar cross section (RCS) of a unit area of a surface. Multiplying by the total area of a surface or the illuminated area of a surface gives the total RCS.

NRCS is used to calculate RCS and surface clutter returns. Speckle is a multiplicative factor used to make surface clutter appear noisier and is especially applicable to imaging applications. Attach a surfaceReflectityLand object to a landSurface or seaSurface in radarScenario using SurfaceManager. See Radar Surface Clutter Simulation for more information.

To compute the normalized reflectivity:

1. Create the surfaceReflectivityCustom object and set its properties.

2. Call the object with arguments, as if it were a function.

To learn more about how System objects work, see What Are System Objects?

Creation

Syntax

refl = surfaceReflectivityCustom

refl = surfaceReflectivityCustom(PropertyName=Value)

Description

refl = surfaceReflectivityCustom creates a normalized reflectivity System object, refl, for a custom surface with default reflectivities. Use refl to generate normalized radar cross section as a function of frequency and grazing angle. The default custom surface has reflectivities set to 1 m²/m² for grazing angles from 0° – 90° and frequencies from 0 – 1e20 Hz.

refl = surfaceReflectivityCustom(PropertyName=Value) also creates a normalized reflectivity object for custom surfaces with each specified PropertyName set to the corresponding Value. For example, all normalized polarimetric reflectivity components can be specified when EnablePolarization is set to true and CrossPolarization is set to "Full". You can specify additional pairs of arguments in any order as (PropertyName1=Value1, … ,PropertyNameN=ValueN).

Properties

Unless otherwise indicated, properties are nontunable, which means you cannot change their values after calling the object. Objects lock when you call them, and the release function unlocks them.

If a property is tunable, you can change its value at any time.

For more information on changing property values, see System Design in MATLAB Using System Objects.

Reflectivity — Normalized radar cross section

ones(91,2) (default) | Q-by-R real-valued matrix | Q-by-R-by-P real-valued array

Normalized radar cross section (NRCS) or mean reflectivity values, specified as an Q-by-R real-valued matrix, where Q corresponds to the number of angles in GrazingAngle and R corresponds to the number of frequencies in the Frequency property.

For more than one surface, you can specify an Q-by-R-by-P real-valued array, where P is the number of surfaces.

Units are dimensionless but often expressed in m²/m².

Dependencies

To enable this property, set the EnablePolarization property to false.

Data Types: double

Frequency — Radar frequency (Hz)

[0 1e20] (default) | length-R row vector

Frequencies associated with Reflectivity or polarimetric reflectivity components, specified as a length-R row vector, where R is no less than two. When R is a 2-element vector, it defines the minimum and maximum frequencies over which the reflectivities are valid. Frequency units are in Hz.

Example: [1e6,10e6]

Data Types: double

GrazingAngle — Grazing angles (degrees)

[0:90] (default) | length-Q row vector

Grazing angles associated with Reflectivity or polarimetric reflectivity components, specified as a length-Q row vector, where Q is no less than two. When Q is a 2-element vector, it defines the minimum and maximum Grazing Angle over which the reflectivities are valid. Units are in degrees.

Example: [45:60]

Data Types: double

EnablePolarization — Enable polarization

false (default) | true

Enable polarization, specified as true or false. When EnablePolarization is set to true, the output argument nrcs includes polarimetric normalized radar cross section components. EnablePolarization enables additional properties when set to either true or false.

When set to true, EnablePolarization enables the CrossPolarization property. Specifying the CrossPolarization property enables additional polarization-related properties that are relevant for frequencies and grazing angles that you can specify using additional properties:

Enabled Property	Description
CrossPolarization, specified as "Full" or "Symmetric" – Enables cross polarization	CrossPolarization set to "Full" enables ReflectivityHV, and ReflectivityVH, ReflectivityHH, ReflectivityVV. CrossPolarization set to "Symmetric" enables ReflectivityHV, ReflectivityHH, and ReflectivityVV.

When set to false, EnablePolarization enables:

Enabled Property	Enabled Property
Reflectivity – Reflectivity values	Normalized radar cross section (NRCS), or reflectivity values.

Data Types: char | string

CrossPolarization — Cross polarization type

"Full" (default) | "Symmetric"

Cross-polarization type, specified as "Full" or "Symmetric".

When set to "Full", the CrossPolarization property enables additional polarization-related properties and impacts speckle:

Enabled Property	Description	Speckle
ReflectivityHV – HV cross-polarized reflectivity component	HV is the cross-polarized reflectivity component that represents horizontal transmission and vertical reception.	When the Speckle property is also set to any value other than "None", unique speckle values are generated for all polarimetric reflectivity components (HV, VH, HH, and VV).
ReflectivityVH – VH cross-polarized reflectivity component	VH is the cross-polarized reflectivity component that represents vertical transmission and horizontal reception.
ReflectivityHH – HH co-polarized reflectivity component	HH is the co-polarized reflectivity component that represents horizontal transmission and horizontal reception.
ReflectivityVV – VV co-polarized reflectivity component	VV is the co-polarized reflectivity component that represents vertical transmission and vertical reception.

When set to "Symmetric", the CrossPolarization property enables additional polarization-related properties and impacts speckle:

Enabled Property	Description	Speckle
ReflectivityHV – HV cross-polarized reflectivity component	HV is the cross-polarized reflectivity component that represents horizontal transmission and vertical reception. Reciprocity is assumed and the cross-polarization terms are set to be equal so that ReflectivityVH = ReflectivityHV.	When the Speckle property is also set to any value other than "None", speckle values corresponding to the HV and VH polarimetric reflectivity components are equivalent. Unique speckle values are generated for HH and VV polarimetric reflectivity components.
ReflectivityHH – HH co-polarized reflectivity component	HH is the co-polarized reflectivity component that represents horizontal transmission and horizontal reception.
ReflectivityVV – VV co-polarized reflectivity component	VV is the co-polarized reflectivity component that represents vertical transmission and horizontal vertical.

Data Types: char | string

ReflectivityHV — HV normalized reflectivity values

zeros(91,2) (default) | Q-by-R real-valued matrix | Q-by-R-by-P real-valued array

Specify normalized radar cross section (NRCS) or reflectivity values, for the cross-polarized HV reflectivity component. HV represents horizontal transmission and vertical reception. Q corresponds to the number of angles in GrazingAngle and R corresponds to the number of frequencies in the Frequency property.

For more than one surface, you can specify an Q-by-R-by-P array, where P is the number of surfaces.

The returned nrcs for cross-polarized components is calculated using nearest neighbor interpolation at a given grazing angle and frequency. Therefore, normalized reflectivity values should cover grazing angles from 0–90° and all expected frequencies to avoid interpolation errors. Units are dimensionless but commonly expressed as m²/m².

Dependencies

To enable this property, set the EnablePolarization property to true.

Data Types: double

ReflectivityVH — VH normalized reflectivity values

zeros(91,2) (default) | Q-by-R real-valued matrix | Q-by-R-by-P real-valued array

Specify normalized radar cross section (NRCS) or reflectivity values, for the cross-polarized VH reflectivity component. VH represents vertical transmission and horizontal reception. Q corresponds to the number of angles in GrazingAngle and R corresponds to the number of frequencies in the Frequency property.

For more than one surface, you can specify an Q-by-R-by-P array, where P is the number of surfaces.

The returned nrcs for cross-polarized components is calculated using nearest neighbor interpolation at a given grazing angle and frequency. Therefore, normalized reflectivity values should cover grazing angles from 0–90° and all expected frequencies to avoid interpolation errors. Units are dimensionless but commonly expressed as m²/m².

Dependencies

To enable this property, set the EnablePolarization property to true and set the CrossPolarization property to "Full".

Data Types: double

ReflectivityHH — HH normalized reflectivity values

zeros(91,2) (default) | Q-by-R real-valued matrix | Q-by-R-by-P real-valued array

Specify normalized radar cross section (NRCS) or reflectivity values, for the co-polarized HH reflectivity component. HH represents horizontal transmission and horizontal reception. Q corresponds to the number of angles in GrazingAngle and R corresponds to the number of frequencies in the Frequency property.

For more than one surface, you can specify an Q-by-R-by-P array, where P is the number of surfaces.

The returned nrcs for co-polarized components is calculated using nearest neighbor interpolation at a given grazing angle and frequency. Therefore, normalized reflectivity values should cover grazing angles from 0–90° and all expected frequencies to avoid interpolation errors. Units are dimensional but commonly expressed as m²/m².

Dependencies

To enable this property, set the EnablePolarization property to true.

Data Types: double

ReflectivityVV — VV normalized reflectivity values

zeros(91,2) (default) | Q-by-R real-valued matrix | Q-by-R-by-P real-valued array

Specify normalized radar cross section (NRCS) or reflectivity values, for the co-polarized VV reflectivity component. VV represents vertical transmission and vertical reception. Q corresponds to the number of angles in GrazingAngle and R corresponds to the number of frequencies in the Frequency property.

For more than one surface, you can specify an Q-by-R-by-P array, where P is the number of surfaces.

The returned nrcs for co-polarized components is calculated using nearest neighbor interpolation at a given grazing angle and frequency. Therefore, normalized reflectivity values should cover grazing angles from 0–90° and all expected frequencies to avoid interpolation errors. Units are dimensional but commonly expressed as m²/m².

Dependencies

To enable this property, set the EnablePolarization property to true.

Data Types: double

Speckle — Speckle distribution type

"None" (default) | "Lognormal" | "Rayleigh" | "Weibull"

Speckle distribution type, specified as one of "None", "Lognormal", "Rayleigh", or "Weibull". Speckle is a multiplicative factor used to make surface clutter appear noisier and is especially applicable to imaging applications. See Speckle Model for more information.

• "None" – No speckle is applied.

• "Lognormal" – Speckle has a lognormal distribution. Define the distribution using the SpeckleMean and SpeckleStandardDeviation properties. Default values of these properties create speckle with a normalized mean lognormal distribution.

• "Rayleigh" – Speckle has a Rayleigh distribution. Define the distribution using the SpeckleScale property. The default value of this property creates speckle with a unit mean Rayleigh distribution.

• "Weibull" – Speckle has a Weibull distribution. Define the distribution using the SpeckleScale and SpeckleShape properties. The default values of these properties create speckle with a unit mean Weibull distribution.

Data Types: char | string

SpeckleMean — Mean of value of lognormal-distributed speckle

-0.5*log(2) (default) | scalar

Mean value of lognormal-distributed speckle, specified as a scalar. When the Speckle property is set to "Lognormal", speckle has a lognormal distribution and you can define the distribution using the SpeckleMean and SpeckleStandardDeviation properties. Default values of these properties create speckle with a normalized mean lognormal distribution.

A lognormal distribution is parameterized with a mean, μ_log, and a standard deviation, σ_log. The expected value of the speckle distribution can be expressed as

$$speckle\_dist={{\displaystyle \text{e}}}^{({\mu }_{\log }+\frac{{\sigma }_{\log }^2}{2})}.$$

A μ_log of -0.5*log(2) and a σ_log of sqrt(log(2)) results in a speckle_dist equal to one.

Dependencies

To enable this property, set the Speckle property to "Lognormal".

Data Types: double

SpeckleStandardDeviation — Standard deviation of lognormal-distributed speckle

sqrt(log(2)) (default) | non-negative scalar

Standard deviation of lognormal-distributed speckle, specified as a non-negative scalar. When the Speckle property is set to "Lognormal", speckle has a lognormal distribution and you can define the distribution using the SpeckleMean and SpeckleStandardDeviation properties. Default values of these properties create speckle with a normalized mean lognormal distribution.

A lognormal distribution is parameterized with a mean, μ_log, and a standard deviation, σ_log. The expected value of the speckle distribution can be expressed as

$$speckle\_dist={{\displaystyle \text{e}}}^{({\mu }_{\log }+\frac{{\sigma }_{\log }^2}{2})}.$$

A μ_log of -0.5*log(2) and a σ_log of sqrt(log(2)) results in a speckle_dist equal to one.

Dependencies

To enable this property, set the Speckle property to "Lognormal".

Data Types: double

SpeckleScale — Scale parameter for Weibull and Rayleigh speckle distribution

sqrt(4/π) (default) | non-negative scalar

Scale parameter for speckle for the Rayleigh and Weibull distributions, specified as a positive scalar.

• When the Speckle property is set to "Rayleigh", speckle has a Rayleigh distribution. The default value of SpeckleScale creates speckle with a unit mean Rayleigh distribution. A Rayleigh distribution is parameterized only by the speckle scale, λ_scale. The expected value of the speckle distribution can be expressed as

  $$speckle\_dist\text{ = }{\lambda }_{scale}\sqrt{\frac{\pi }{2}}.$$

  A λ_scale of sqrt(4/π) results in a speckle_dist equal to one.

• When the Speckle property is set to "Weibull", speckle has a Weibull distribution and you can define the distribution using the SpeckleScale and SpeckleShape properties. The default values of these properties create speckle with a unit mean Weibull distribution. A Weibull distribution is parameterized by the speckle scale, λ_scale, and speckle shape, k_shape.

  $$speckle\_dist\text{ = }{\lambda }_{scale}\Gamma (1+\frac{1}{k_{shape}}),$$

  where is Γ is the gamma function. A λ_scale of sqrt(4/π) and a k_shape of 2 results in a speckle_dist equal to one.

Dependencies

To enable this property, set the Speckle property to "Rayleigh" or "Weibull".

Data Types: double

SpeckleShape — Shape value for Weibull distribution

2 (default) | positive scalar

Shape value for the Weibull speckle distribution, specified as a positive scalar. When the Speckle property is set to "Weibull", speckle has a Weibull distribution and you can define the distribution using the SpeckleScale and SpeckleShape properties. The default values of these properties create speckle with a unit mean Weibull distribution.

A Weibull distribution is parameterized by the speckle scale, λ_scale, and speckle shape, k_shape.

$$speckle\_dist\text{ = }{\lambda }_{scale}\Gamma (1+\frac{1}{k_{shape}}),$$

where Γ is the gamma function. A λ_scale of sqrt(4/π) and a k_shape of 2 results in a speckle_dist equal to one.

Dependencies

To enable this property, set the Speckle property to "Weibull".

Data Types: double

Usage

Syntax

nrcs = refl(graz,freq)

nrcs = refl(graz,freq,idx)

[nrcs,speck] = relf(___)

Description

nrcs = refl(graz,freq) returns the normalized radar cross section, nrcs, at grazing angle graz and frequency freq. When either graz or freq lies outside of the valid region defined by the GrazingAngle and Frequency properties, the nearest value of the normalized reflectivity is returned.

nrcs = refl(graz,freq,idx) also specifies the surface indices, idx, of the custom surfaces. To enable this syntax, specify the Reflectivity property or each polarimetric reflectivity component as an Q-by-R-by-P array, where P is the number of surfaces.

[nrcs,speck] = relf(___) also returns speckle values speck.

Input Arguments

graz — Grazing angle (degrees

nonnegative scalar | length-Q row vector of nonnegative values

Grazing Angle of surface relative to radar, specified as a scalar or a length-Q row vector of nonnegative values. Grazing angles must lie between 0° and 90°. Units are in degrees.

Data Types: double

freq — Transmitted frequencies (Hz)

R-length vector of positive values

Transmitted frequencies, specified as a positive scalar or R-length vector of positive values. Units are in Hz.

Example: freq = 70e9

Data Types: double

idx — Surface type index

scalar | length-N vector of positive values

Surface index, specified as a scalar or length-N vector of positive values. N must be less than or equal to P, the number of surfaces.

Dependencies

To enable this argument, specify the Reflectivity property or each polarimetric reflectivity component as an Q-by-R-by-P array, where P is the number of surfaces.

Data Types: double

Output Arguments

nrcs — Normalized radar cross section

real-valued Q-by-R matrix | real-valued N-by-Q-by-R matrix | real-valued 2-by-2-by-Q-by-R array | real-valued 2-by-2-by-N-Q-by-R array

Normalized radar cross section, also referred to as surface σ⁰. Units are dimensionless, but often expressed as m²/m². nrcs is returned as an array with dimensions that are determined by object properties and input arguments:

• For the non-polarimetric reflectivity case (EnablePolarization is false) and when idx is a scalar, nrcs is returned as a real-valued Q-by-R array, where Q is the length of graz and R is the length of freq.

• For the non-polarimetric reflectivity case (EnablePolarization is false) and when idx is a length-N vector, nrcs is returned as a real-valued N-by-Q-by-R array, where Q is the length of graz and R is the length of freq.

• For the polarimetric reflectivity case (EnablePolarization is true) and when idx is a scalar, nrcs is returned as a real-valued 2-b-2-by-Q-by-R array, where Q is the length of graz and R is the length of freq. For each value of Q and R, nrcs forms a polarimetric normalized radar cross section (NRCS) reflectivity matrix, σ⁰, of the form

  $${\sigma }^0=\left[\begin{array}{cc}{\sigma }_{HH}^0& {\sigma }_{HV}^0\\ {\sigma }_{VH}^0& {\sigma }_{VV}^0\end{array}\right]$$

  where σ⁰_HV and σ⁰_VH are the cross-polarization components specified by the ReflectivityHV and ReflectivityVH properties. The σ⁰_HH and σ⁰_VV are the co-polarized components specified by ReflectivityHH and ReflectivityVV.

• For the polarimetric reflectivity case (EnablePolarization is true) and when idx is a length-N vector, nrcs is returned as a real-valued 2-b-2-by-N-by-Q-by-R array, where Q is the length of graz and R is the length of freq. For each value of N, Q, and R, nrcs forms a polarimetric normalized radar cross section (NRCS) reflectivity matrix as described for the polarimetric reflectivity case when idx is a scalar.

The returned normalized reflectivity for polarization components σ⁰_HV, σ⁰_VH, σ⁰_HH, and σ⁰_VV is calculated using nearest neighbor interpolation at a given grazing angle and frequency. To avoid interpolation errors, the normalized reflectivity values in the ReflectivityHV, ReflectivityVH, ReflectivityHH, and ReflectivityVV properties should cover grazing angles from 0–90 degrees and all expected frequencies.

Dependencies

To enable the polarimetric reflectivity matrix, set the EnablePolarization to true.

speck — Multiplicative speckle

Q-by-R matrix | 2-by-2-by-Q-by-R matrix

Multiplicative speckle, returned as a Q-by-R matrix where Q is the length of ang and R is the length of freq. For the polarimetric reflectivity case, speckle is returned as a 2-by-2-by-Q-by-R array.

Object Functions

To use an object function, specify the System object as the first input argument. For example, to release system resources of a System object named obj, use this syntax:

release(obj)

Common to All System Objects

step	Run System object algorithm
release	Release resources and allow changes to System object property values and input characteristics
reset	Reset internal states of System object

Examples

Compute Custom Normalized Reflectivity as Standalone Function

Construct a table of normalized reflectivities of a land surface using the surfacegamma function. The table covers frequencies from 1 - 10 GHz and grazing angles from 0 - 7 degrees. Use the surfaceReflectivityCustom System object™ directly.

freqs = (1:10)*1e9;
angs = 0:.1:7;
gammaFarm   = db2pow(surfacegamma('farmland',freqs));
gammaHills  = db2pow(surfacegamma('wooded hill',freqs));

Create a constant gamma model by multiplying the reflectivity coefficients by the sine of the grazing angle. Add Rayleigh speckle.

nrcsTbl   = zeros(numel(angs),numel(freqs),2);
nrcsTbl(:,:,1) = gammaFarm.*sind(angs).';  % Farmland
nrcsTbl(:,:,2) = gammaHills.*sind(angs).'; % Wooded hills
refl = surfaceReflectivityCustom(Reflectivity = nrcsTbl, Frequency = freqs, ...
    GrazingAngle = angs, Speckle = 'Rayleigh');

Find the normalized reflectivity of farm land (in dB).

nrcs = pow2db(refl(6.3, 2.5e9, 1));
disp(nrcs)

  -27.2110

Find the normalized reflectivity of wooded hills (in dB).

nrcs = pow2db(refl(6.3, 2.5e9, 2));
disp(nrcs)

  -22.2110

Create Custom Surface in Radar Scenario

Create a land reflectivity model using the surfaceReflectivityCustom object and radarScenario.

First create a two hill scenario.

[x,y] = meshgrid(linspace(-100,100,201));
ht1 = 40*exp(-(x.^2 + y.^2)/30^2);
ht2 = 100*exp(-((x-60).^2 + y.^2)/25^2);
ht = ht1 + ht2;
p = surfc(x(1,:),y(:,1),ht);
shading interp

Construct a table of normalized reflectivities of a land surface using the surfacegamma function. The table covers frequencies from 1 - 10 GHz and grazing angles from 0 - 7 degrees.

freqs = (1:10)*1e9;
angs = 0:.1:7;
gammaFarm   = db2pow(surfacegamma('farmland',freqs));
gammaHills  = db2pow(surfacegamma('wooded hill',freqs));

Create a constant gamma model by multiplying the reflectivity coefficients by the sine of the grazing angle. Add Rayleigh speckle.

nrcsTbl   = zeros(numel(angs),numel(freqs),2);
nrcsTbl(:,:,1) = gammaFarm.*sind(angs).';  % Farmland
nrcsTbl(:,:,2) = gammaHills.*sind(angs).'; % Wooded hills
simTime = 3;
scene = radarScenario(UpdateRate = 1, ...
    IsEarthCentered = false,StopTime = simTime);
refl = surfaceReflectivityCustom(Reflectivity = nrcsTbl, Frequency = freqs, ...
    GrazingAngle = angs, Speckle = 'Rayleigh');
srf = landSurface(scene,RadarReflectivity = refl, ...
    Terrain = ht,Boundary = [-100,100;-100,100]);

Find the normalized reflectivity of farm land (in dB).

nrcs = pow2db(refl(6.3, 2.5e9, 1));
disp(nrcs)

  -27.2110

Find the normalized reflectivity of wooded hills (in dB).

nrcs = pow2db(refl(6.3, 2.5e9, 2));
disp(nrcs)

  -22.2110

Display Custom Reflectivity Matrix

Construct a table of normalized polarized reflectivities of a land surface using the surfacegamma function. The table covers frequencies from 1 - 10 GHz and grazing angles from 0 - 90 degrees. Create a constant gamma model by multiplying the reflectivity coefficients by the sine of the grazing angle. Add Rayleigh speckle. Define the reflectivities for the VV, HV, and VH components as proportional to the HH component.

freqs = (1:10)*1e9;
angs = 0:.1:90;
gamma = db2pow(surfacegamma('farmland',freqs));
xhh = sind(angs)'*gamma;
xvv = 0.5*sind(angs)'*gamma;
xhv = 0.1*sind(angs)'*gamma;
xvh = 0.12*sind(angs)'*gamma;

Create the surfaceReflectivityCustom System object™.

refl = surfaceReflectivityCustom(Frequency=freqs, ...
    GrazingAngle=angs,Speckle='Rayleigh',EnablePolarization=true, ...
    CrossPolarization='Full',ReflectivityHH=xhh,ReflectivityVV=xvv, ...
    ReflectivityHV=xhv,ReflectivityVH=xvh);

Plot the normalized reflectivity of farm land for all grazing angles..

nrcs = refl(angs,3e9);
plot(angs,pow2db(squeeze(nrcs(1,1,:))), ...
    angs,pow2db(squeeze(nrcs(1,2,:))), ...
    angs,pow2db(squeeze(nrcs(2,1,:))), ...
    angs,pow2db(squeeze(nrcs(2,2,:))))
grid on
xlabel('Grazing angle (deg)')
ylabel('NRCS (dB m^2/m^2)')
title('Polarized Surface Reflectivity')

More About

Speckle Model

Speckle is modeled as an uncorrelated, multiplicative factor I = σ*n, where σ is the clutter RCS and n represents random numbers drawn from an independent identically-distributed unity mean noise statistical distribution. Because speckle is correlated with underlying terrain RCS, it is usually applied to radar intensity. Speckle noise model distributions include lognormal, Rayleigh, and Weibull.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Version History

Introduced in R2022a