models a reflected signal from a target with nonfluctuating or fluctuating
radar cross section (RCS). This object has the following modifiable
MeanRCSSource — Source
of the target's mean radar cross section
MeanRCS — Target's mean
Model — Statistical model
for the target's RCS
PropagationSpeed — Signal
OperatingFrequency — Operating
SeedSource — Source of
the seed for the random number generator to generate the target's
random RCS values
Seed — Seed for the random
Create a radar target with a nonfluctuating RCS of 1 square meter and an operating frequency of 300 MHz. Specify a wave propagation speed equal to the speed of light.
hr = phased.RadarTarget('Model','nonfluctuating','MeanRCS',1,... 'PropagationSpeed',physconst('LightSpeed'),... 'OperatingFrequency',3e8);
The waveform incident on the target is scaled by the factor:
Here, σ represents the target mean RCS, and λ is the wavelength of the operating frequency. Each element of the signal incident on the target is scaled by the preceding factor.
Create a target with a nonfluctuating RCS of 1 square meter. Set the operating frequency to 1 GHz. Set the signal incident on the target to be a vector of ones to demonstrate the gain factor.
hr = phased.RadarTarget('MeanRCS',1,'OperatingFrequency',1e9); x = ones(10,1); y = step(hr,x);
The output vector
y is equal to
The amplitude scaling factor equals:
lambda = hr.PropagationSpeed/hr.OperatingFrequency; G = sqrt(4*pi*1/lambda^2)
The previous examples used nonfluctuating values for the target's RCS. This model is not valid in many scenarios. There are several cases where the RCS exhibits relatively small or large magnitude fluctuations. These fluctuations can occur rapidly on pulse-to-pulse, or more slowly, on scan-to-scan time scales:
Several small randomly distributed reflectors with no dominant reflector — This target, at close range or when the radar uses pulse-to-pulse frequency agility, can exhibit large magnitude rapid (pulse-to-pulse) fluctuations in the RCS. That same complex reflector at long range with no frequency agility can exhibit large magnitude fluctuations in the RCS over a longer time scale (scan-to-scan).
Dominant reflector along with several small reflectors — The reflectors in this target can exhibit small magnitude fluctuations on pulse-to-pulse or scan-to-scan time scales, subject to:
How rapidly the aspect changes
Whether the radar uses frequency agility
To account for significant fluctuations in the RCS, you need to use statistical models. The four Swerling models, described in the following table, are widely used to cover these kinds of fluctuating-RCS cases.
|Swerling Case Number||Description|
|I||Scan-to-scan decorrelation. Rayleigh/exponential PDF — A number of randomly distributed scatterers with no dominant scatterer.|
|II||Pulse-to-pulse decorrelation. Rayleigh/exponential PDF — A number of randomly distributed scatterers with no dominant scatterer.|
|III||Scan-to-scan decorrelation — Chi-square PDF with 4 degrees of freedom. A number of scatterers with one scatterer dominant.|
|IV||Pulse-to-pulse decorrelation — Chi-square PDF with 4 degrees of freedom. A number of scatterers with one scatterer dominant.|
You can simulate a Swerling target model by setting the
step method and set the
the RCS value according to the specified probability model each time
step. If you set
the previous RCS value is used.
Model Pulse Reflection from a Nonfluctuating Target
This example creates and transmits a linear FM waveform with a 1 GHz carrier frequency. The waveform is transmitted and collected by an isotropic antenna with a back-baffled response. The waveform propagates to and from a target with a nonfluctuating RCS of 1 square meter. The target is located approximately 1414 meters from the antenna at an angle of 45 degrees azimuth and 0 degrees elevation.
% Create objects and assign property values % Isotropic antenna element hant = phased.IsotropicAntennaElement('BackBaffled',true); % Location of the antenna harraypos = phased.Platform('InitialPosition',[0;0;0]); % Location of the radar target hrfpos = phased.Platform('InitialPosition',[1000; 1000; 0]); % Linear FM waveform hwav = phased.LinearFMWaveform('PulseWidth',100e-6); % Transmitter htx = phased.Transmitter('PeakPower',1e3,'Gain',40); % Waveform radiator hrad = phased.Radiator('OperatingFrequency',1e9, ... 'Sensor',hant); % Propagation environment to and from the RadarTarget hspace = phased.FreeSpace('OperatingFrequency',1e9,... 'TwoWayPropagation',true); % Radar target hr = phased.RadarTarget('MeanRCS',1,'OperatingFrequency',1e9); % Collector hc = phased.Collector('OperatingFrequency',1e9,... 'Sensor',hant); % Implement system wf = step(hwav); % generate waveform txwf = step(htx,wf); % transmit waveform wfrad = step(hrad,txwf,[0 0]'); % radiate waveform % propagate waveform to and from the RadarTarget wfprop = step(hspace,wfrad,harraypos.InitialPosition,... hrfpos.InitialPosition,[0;0;0],[0;0;0]); wfreflect = step(hr,wfprop); % reflect waveform wfcol = step(hc,wfreflect,[45 0]'); % collect waveform