Vertical coverage diagram
calculates the vertical coverage pattern of a narrowband radar antenna. The
Vertical Coverage Pattern is the range of
vcpangles] = radarvcd(
vcp as a function of elevation angle
vcpangles. The vertical coverage pattern depends on
three parameters: maximum free-space detection range of the radar
rfs, the radar frequency
the antenna height
radarvcd(___) displays the vertical coverage
diagram for a radar system. The plot is the locus of points of maximum radar
range as a function of target elevation. This plot is also known as the
Blake chart. To create this chart,
radarvcd invokes the function
blakechart using default
parameters. To produce a Blake chart with different parameters, first call
radarvcd to obtain
vcpangles. Then, call
with user-specified parameters. This syntax can use any of the previous
Plot Vertical Coverage Pattern Using Default Parameters
Set the frequency to 100 MHz, the antenna height to 10 m, and the free-space range to 200 km. The antenna pattern, surface roughness, antenna tilt angle, and field polarization assume their default values as specified in the
Obtain an array of vertical coverage pattern values and angles.
freq = 100e6; ant_height = 10; rng_fs = 200; [vcp,vcpangles] = radarvcd(freq,rng_fs,ant_height);
To see the vertical coverage pattern, omit the output arguments.
Vertical Coverage Pattern with Specified Antenna Pattern
Set the frequency to 100 MHz, the antenna height to 10 m, and the free-space range to 200 km. The antenna pattern is a sinc function with 45° half-power width. The surface height standard deviation is set to m. The antenna tilt angle is set to 0°, and the field polarization is horizontal.
pat_angles = linspace(-90,90,361)'; freq = 100e6; ntn = phased.SincAntennaElement('Beamwidth',45); pat = ntn(freq,pat_angles'); ant_height = 10; rng_fs = 200; tilt_ang = 0; [vcp,vcpangles] = radarvcd(freq,rng_fs,ant_height,... 'RangeUnit','km','HeightUnit','m',... 'AntennaPattern',pat,... 'PatternAngles',pat_angles,... 'TiltAngle',tilt_ang,'SurfaceHeightStandardDeviation',1/(2*sqrt(2)));
radarvcd with no output arguments to display the vertical coverage pattern.
radarvcd(freq,rng_fs,ant_height,... 'RangeUnit','km','HeightUnit','m',... 'AntennaPattern',pat,... 'PatternAngles',pat_angles,... 'TiltAngle',tilt_ang,'SurfaceHeightStandardDeviation',1/(2*sqrt(2)));
Alternatively, use the
radarvcd output arguments and the
blakechart function to display the vertical coverage pattern to a maximum range of 400 km and a maximum height of 50 km. Customize the Blake chart by changing the color.
blakechart(vcp,vcpangles,400,50, ... 'FaceColor',[0.8500 0.3250 0.0980],'EdgeColor',[0.8500 0.3250 0.0980])
Plot Vertical Coverage Diagram For User-Specified Antenna
Plot the range-height-angle curve (Blake chart) for a radar with a user-specified antenna pattern.
Define a sinc-function antenna pattern with a half-power beamwidth of 90 degrees. The radar transmits at 100 MHz.
pat_angles = linspace(-90,90,361)'; freq = 100e6; ntn = phased.SincAntennaElement('Beamwidth',90); pat = ntn(freq,pat_angles');
Specify a free-space range of 200 km. The antenna height is 10 meters, the antenna tilt angle is zero degrees, and the surface roughness is one meter.
rng_fs = 200; ant_height = 10; tilt_ang = 0; surf_roughness = 1;
Create the radar range-height-angle plot.
radarvcd(freq,rng_fs,ant_height,... 'RangeUnit','km','HeightUnit','m',... 'AntennaPattern',pat,... 'PatternAngles',pat_angles,... 'TiltAngle',tilt_ang,... 'SurfaceHeightStandardDeviation',surf_roughness/(2*sqrt(2)));
freq — Radar frequency
real-valued scalar less than 10 GHz
Radar frequency, specified as a real-valued scalar less than 10 GHz (1010 Hz).
rfs — Free-space range
positive scalar | positive vector
Free-space range, specified as a positive scalar or vector.
rfs is the calculated or assumed free-space range
for a target or for a one-way RF system at which the field strength would
have a specified value. Range units are set by the
RangeUnit name-value argument.
anht — Radar antenna height
Radar antenna height, specified as a real-valued scalar. The height is
referenced to the surface. Height units are set by the
HeightUnit name-value argument.
Specify optional pairs of arguments as
the argument name and
Value is the corresponding value.
Name-value arguments must appear after other arguments, but the order of the
pairs does not matter.
Before R2021a, use commas to separate each name and value, and enclose
Name in quotes.
RangeUnit — Radar range units
'km' (default) |
HeightUnit — Antenna height units
'm' (default) |
Antenna height units denoting meters, nautical miles, miles,
kilometers, feet, or kilofeet. This argument specifies the units for the
anht and the
Polarization — Transmitted wave polarization
'H' (default) |
Transmitted wave polarization, specified as
horizontal polarization or
'V' for vertical
SurfaceRelativePermittivity — Complex permittivity of reflecting surface
frequency dependent model (default) | complex-valued scalar
Complex permittivity (dielectric constant) of the reflecting surface,
specified as a complex-valued scalar. The default value of this argument
depends on the value of
radarvcd uses a seawater model that is valid
for frequencies up to 10 GHz.
Complex Number Support: Yes
SurfaceHeightStandardDeviation — Standard deviation of surface height
0 (default) | real-valued scalar
Standard deviation of surface height, specified as a nonnegative
real-valued scalar. A value of
0 indicates a smooth
'HeightUnit' to specify the units of
The surface height standard deviation relates to the crest-to-trough "surface roughness" height through
Surface roughness = 2 × √2 × Surface height standard deviation.
SurfaceSlope — Surface slope
Surface slope in degrees, 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
0, indicating a smooth
VegetationType — Vegetation type
'None' (default) |
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
real-valued column vector
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,
radarvcd uses the antenna pattern and ignores the elevation beamwidth value. This argument defaults to a sinc antenna pattern.
PatternAngles — Antenna pattern elevation angles
real-valued column vector
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.
MaxElevation — Maximum elevation angle
60 (default) | real-valued scalar
Maximum elevation angle, specified as a real-valued scalar. The maximum elevation angle is the largest angle for which the vertical coverage pattern is calculated. Angle units are expressed in degrees.
MinElevation — Minimum elevation angle
0 (default) | real-valued scalar
Minimum elevation angle, specified as a real-valued scalar. The minimum elevation angle is the smallest angle for which the vertical coverage pattern is calculated. Angle units are expressed in degrees.
ElevationStepSize — Elevation angle increment
Elevation angle increment, specified as a positive scalar in degrees.
The elevation vector goes from the minimum value specified in
MinElevation and the maximum value specified in
MaxElevation in increments of
ElevationStepSize. The default value of this
argument is given by
Δ = 885.6/(π × fMHz × ha,ft),
where fMHz is the frequency in MHz and ha,ft is the antenna height in feet.
vcp — Vertical coverage pattern
real-valued vector | real-valued matrix
Vertical coverage pattern, returned as a real-valued column vector or
matrix. The vertical coverage pattern is the actual maximum range of the
radar. Each row of the vertical coverage pattern corresponds to one of the
angles returned in
vcpangles The columns of
vcp correspond to the ranges specified in
vcpangles — Vertical coverage pattern angles
Vertical coverage pattern angles, returned as a column vector. The angles
range from –90° to 90°. Each entry of
vcpangles specifies the elevation angle at which
the vertical coverage pattern is measured.
Vertical Coverage Pattern
The maximum detection range of a radar antenna can differ depending on placement. Suppose you place a radar antenna near a reflecting surface, such as the earth's land or sea surface and computed maximum detection range. If you then move the same radar antenna to free space far from any boundaries, it results in a different maximum detection range. This is an effect of multipath interference that occurs when waves, reflected from the surface, constructively add to or nullify the direct path signal from the radar to a target. Multipath interference gives rise to a series of lobes in the vertical plane. The vertical coverage pattern is the plot of the actual maximum detection range of the radar versus target elevation and depends upon the maximum free-space detection range and target elevation angle. See Blake .
The vertical coverage pattern is generally considered to be valid for antenna heights that are within a few hundred feet of the surface and with targets at altitudes that are not too close to the radar horizon.
 Blake, Lamont V. Machine Plotting of Radar Vertical-Plane Coverage Diagrams. Naval Research Laboratory Report 7098, 1970.
 Barton, David K. Radar Equations for Modern Radar. Norwood, MA: Artech House, 2013.
C/C++ Code Generation
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Usage notes and limitations:
Supported only when output arguments are specified.
Introduced in R2021a