Objectives:
(a) Understanding the basic theory of
RADAR system.
(b) Implement the auto-correlation and
cross-correlation for Radar system in the noisy environment.
(c) Measuring the time delay by
computing cross-correlation.
Cross-correlation
is a measure of similarity of two waveforms as a function of time delay applied
to one of them. Auto-correlation is a cross-correlation between the signal and
itself. The correlation functions are of used in many applications in
communication systems. For example, in Radar and Sonar systems, it can be used
to detect the delay between the transmitted and received signals. Hence the
distance between the target and Sonar / Radar can be detected.
Let xa( t) be the transmitted signal and ya( t) be the received signal in a RADAR system, where
ya( t) = axa(t -td )+va( t)
and,
va( t) is additive random noise. The
signals xa( t) and ya( t)
are sampled in the receiver, according to the sampling theorem, and are
processed digitally to determine the time delay and hence the distance of the
object. The resulting discrete-time signals are
x [n ] = xa(nT)
y [n ] = ya(nT) = axa(nT -td )+va(nT)
= ax
[
n-D]+v [n ]
Understanding
Correlation
Cross-correlation is a
measure of similarity of two waveforms as a function of time delay applied to
one of them. Auto-correlation is a cross-correlation between the signal and
itself. The correlation functions are of used in many applications in
communication systems. For example, in Radar and Sonar systems, it can be used
to detect the delay between the transmitted and received signals. Hence the
distance between the target and Sonar / Radar can be detected.
Understanding Time
Delay
If we calculate the cross
correlation between both signals, the max(or min) of the cross correlation
function indicates the in time where the signals are best aligned ie. The time
delay between the signals is determined by the argument of the max or arg max
of cross-correlation
Barker Sequences
A barker sequence is a
finite sequence of N values from -1 to +1
In wireless communication
sequences are usually chosen for their spectral properties and for low cross
correlation with other sequences likely to interfere. The value of auto-correlation
function for barker sequence is either 0 or -1 at all offsets except 0 (where
it is +11).
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