MATLAB: Notice of amplitude modulation in FMCW example

channelfmcwPhased Array System Toolboxphasedarrayradar

I was going through the example provided by phased array toolbox related to 'Model Pulse Reflection from a Nonfluctuating Target'
% 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
After the wave is collected I wanted to plot the absolute value of the collected waveform and I noticed a slight time dependent damping (or amplitude modulation) present in the collected signal. Can you provide the explanation for this effect observed.
plot(abs(wfcol));

Best Answer

This is due to the distortion of the propagation. In your setup, the distance between the radar and the target is approximately 1414 meters. If you compute the time delay needed for the signal to travel this distance and back, it is not at an exact sampling point. Thus you don't get the original signal back, but a fractional delayed version of the original signal. The damping there is the effect of the fractional delay filter. If you change your target location to
hrfpos = phased.Platform('InitialPosition',[1000; 1000*sqrt(8); 0]);
then the start of the return signal will be roughly on a sampled time instant and the damp disappears.
HTH
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