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reflectionCoefficient

Returns the reflection coefficient

Since R2024a

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    Syntax

    REFC = reflectionCoefficient(MDL,FREQ,GRAZ,POL)

    Description

    example

    REFC = reflectionCoefficient(MDL,FREQ,GRAZ,POL) returns the complex-valued reflection coefficient, REFC, for the SurfaceReflectionCoefficient model object, MDL. REFC is calculated for the radar's operating frequency, FREQ, for multipath reflections incident at grazing angles, GRAZ, with antenna polarization specified by POL.

    Examples

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    Open Live Script

    This example shows how to calclate the reflection coefficient from a SurfaceReflectionCoefficient model.

    % create a radar scenario
% set IsEarthCentered to false models a flat Earth
scene = radarScenario(UpdateRate=0,IsEarthCentered=false);  
 
% enable multipath modeling
scene.SurfaceManager.EnableMultipath = true; 
 
% create a land surface 
srf = landSurface(scene);

% calculate the reflection coefficient for 
% a frequency of 1000 MHz, a grazing angle of 1 degree,
% and horizontal antenna polarization
reflc=reflectionCoefficient(srf.ReflectionCoefficient,1000e6,1,"H")
    reflc = -0.7607 + 0.0002i

    Input Arguments

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    Surface reflection coefficient model object, specified as a SurfaceReflectionCoefficient object.

    Radar frequency, specified as a scalar in hertz (Hz)

    Example: 100e6

    Data Types: double

    Grazing angle of a surface relative to the radar that describes the geometry for multipath reflection, specified in units of degrees ranging from 0° to 90°. Grazing angles < 10° are most relevant to multipath calculations. The grazing angle is used to determine effective height standard deviation from the HeightStandardDeviation and Slope property of the input MDL SurfaceReflectionCoefficient object. The effective height standard deviation in meters is calculated as

    Effective HGTSD = HGTSD × (2 × GRAZ/β0)1/5,

    where β0 is the surface slope, given the condition that

    2 × GRAZ/β0 < 1,

    This calculation better accounts for shadowing. Otherwise, the effective height standard deviation is equal to HGTSD or the HeightStandardDeviation property.

    Transmitted wave polarization, specified as H for horizontal polarization or V for vertical polarization. Horizontal polarization is recommended for most applications.

    Example: "H"

    Data Types: char | string

    Output Arguments

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    REFC is equal to the Fresnel reflection coefficient times the percentage absorption from vegetation, VegetationFactor, times the specular scattering coefficient for a rough surface. The Fresnel reflection coefficient is calculated using the PermittivityModel and the specular scattering coefficient is determined from the HeightStandardDeviation and Slope specified in MDL.

    The Fresnel reflection coefficient is given by

    FRL=sin(GRAZ)−EPSC−cos(GRAZ)2sin(GRAZ)+EPSC−cos(GRAZ)2

    for horizontal polarization, where EPSC is the complex relative permittivity and GRAZ is the grazing angle.

    The Fresnel reflection coefficient is given by

    FRL=EPSC×sin(GRAZ)−EPSC−cos(GRAZ)2EPSC×sin(GRAZ)+EPSC−cos(GRAZ)2

    for vertical polarization, where EPSC is the complex relative permittivity and GRAZ is the grazing angle.

    The specular scattering coefficient for a rough surface is given by

    r=e−2(π×effHTSD×sin(GRAZ)λ)2,

    where effHTSD is the GRAZ-dependent effective height standard deviation and λ is the wavelength, or freq2wavelen(FREQ).

    References

    [1] Barton, David Knox. Radar Equations for Modern Radar. Artech House, 2013.

    [2] Blake, L.V. Machine Plotting of Radar Vertical-Plane Coverage Diagrams. Naval Research Laboratory, 1970 (NRL Report 7098).

    Version History

    Introduced in R2024a

    See Also