One-way radar propagation factor
calculates the one-way propagation factor assuming a surface target and a sea state of
F = radarpropfactor(
0. The calculation estimates the complex relative permittivity
(dielectric constant) of the reflecting surface using a sea water model described in  that is valid from
100 MHz to
10 GHz. The target height is assumed to
be the height of significant clutter sources above the average surface height. Specifically,
the target height is calculated as
3 times the standard deviation of the
surface height. Assuming the paths are the same, the two-way propagation factor is
F. Atmospheric refraction is taken into account through the use of
EffectiveEarthRadius that can be specified. Scattering and ducting
are assumed to be negligible.
radarpropfactor(___) plots the one-way propagation
factor in dB versus range in km. Default range units are km.
Plot the propagation factor for a
3 GHz S-band radar assuming an antenna height of 10 m and a target height of
1 km. Assume that the surface has a height standard deviation of
1 m, and the surface slope is
R = (30:0.5:180)*1e3; % Range (m) freq = 3e9; % Frequency (Hz) anht = 10; % Radar height (m) tgtht = 1e3; % Target height (m) hgtsd = 1; % Height standard deviation (m) beta0 = 0.05; % Surface slope (deg) radarpropfactor(R,freq,anht,tgtht,... 'SurfaceHeightStandardDeviation',hgtsd,... 'SurfaceSlope',beta0)
ans = 301×1 -0.3696 -0.3566 -0.3439 -0.3316 -0.3197 -0.3082 -0.2970 -0.2862 -0.2756 -0.2654 ⋮
R— Free space range
Free space range, specified as a scalar or an M-length vector. Units are in meters.
freq— Radar frequency
Radar frequency in hertz, specified as a positive real scalar or a vector.
ANHT— Antenna height
Antenna height as referenced from the surface, specified as a positive scalar. Units are in meters.
TGTHT— Target height
Target height as referenced from the surface, specified as a positive scalar. Units are in meters.
comma-separated pairs of
the argument name and
Value is the corresponding value.
Name must appear inside quotes. You can specify several name and value
pair arguments in any order as
Polarization— Polarization of transmitted wave
Polarization of the transmitted wave, specified as
'H' indicates horizontal polarization and
'V' indicates vertical polarization.
SurfaceRelativePermittivity— Complex relative permittivity
Complex relative permittivity (dielectric constant) of the reflecting surface,
specified as a complex scalar. The default value of dielectric constant depends on the
value of the
freq argument. The function uses a sea water model
in  that is valid up to
Complex Number Support: Yes
SurfaceHeightStandardDeviation— Standard deviation of surface height
0.01(default) | positive scalar
Standard deviation of the surface height in meters, specified as positive scalar.
The default value of
0.01 m indicates a sea state of
0. Units are in meters.
SurfaceSlope— Surface slope
Surface slope, specified as a nonnegative scalar. This value is expected to be 1.4 times the RMS surface slope. Given the condition that
2 × GRAZ/β0 < 1,
where GRAZ is the grazing angle of the geometry specified in degrees and β0 is the surface slope, the effective surface height standard deviation in meters is calculated as
Effective HGTSD = HGTSD × (2 × GRAZ/β0)1/5.
This calculation better accounts for shadowing. Otherwise, the
effective height standard deviation is equal to HGTSD. This argument defaults to the
surface slope value output by the
searoughness function for a sea state of
0. Units are
VegetationType— Vegetation type
Surface vegetation type, specified as
'Brush' are assumed to be dense vegetation.
'Grass' is assumed to be thin grass. Use this argument when using the function on surfaces different from the sea.
ElevationBeamwidth— Half-power elevation beamwidth
10(default) | scalar between 0° and 90°
Half-power elevation beamwidth in degrees, specified as a scalar between 0° and 90°. The
elevation beamwidth is used in the calculation of a
pattern. The default antenna pattern is symmetric with respect to the beam maximum and
is of the form sin(u)/u. The parameter u is given by u = k
sin(θ), where θ is the elevation angle in radians and
k is given by k = x0 /
sin(π × ELBW/360), where ELBW is the half-power elevation beamwidth and x0 ≈ 1.3915573 is a solution of sin(x) = x/√2.
AntennaPattern— Antenna elevation pattern
Antenna elevation pattern, specified as a real-valued column vector. Values for
'AntennaPattern' must be specified together with values for
'PatternAngles'. Both vectors must have the same size. If both an antenna pattern and an elevation beamwidth are specified,
radarpropfactor uses the antenna pattern and ignores the elevation beamwidth value. This argument defaults to a sinc antenna pattern.
PatternAngles— Antenna pattern elevation angles
Antenna pattern elevation angles specified as a real-valued column vector. The size of the vector specified by
PatternAngles must be the same as that specified by
AntennaPattern. Angle units are expressed in degrees and must lie between –90° and 90°. In general, the antenna pattern should fill the whole range from –90° to 90° for the coverage to be computed properly.
TiltAngle— Antenna tilt angle
0(default) | real-valued scalar
Antenna tilt angle, specified as a real-valued scalar. The tilt angle is the elevation angle of the antenna with respect to the surface. Angle units are expressed in degrees.
EffectiveEarthRadius— Effective Earth radius
Effective Earth radius in meters, specified as a positive scalar. The effective Earth radius is an approximation used for modeling refraction effects in the troposphere. The default value calculates the effective Earth radius using a refraction gradient of
-39e-9, which results in approximately
4/3 of the real Earth radius.
RefractiveIndex— Refractive index at surface
1.000318(default) | scalar greater than
Refractive index at the surface, specified as a nonnegative scalar. Defaults to
1.000318, which is the output of the
refractiveidx function at an altitude of
F— One-way propagation factor
The one-way propagation factor, returned as a scalar or M-length column vector. Units are in decibels.
 Blake, L.V. "Machine Plotting of Radar Vertical-Plane Coverage Diagrams." Naval Research Laboratory, 1970 (NRL Report 7098).
 Barton, David K. Radar Equations for Modern Radar. Norwood, MA: Artech House, 2013.