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.

(d)  Calculating the distance of the target.

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). ##### Bhanu Namikaze

Bhanu Namikaze is an Ethical Hacker, Security Analyst, Blogger, Web Developer and a Mechanical Engineer. He Enjoys writing articles, Blogging, Debugging Errors and Capture the Flags. Enjoy Learning; There is Nothing Like Absolute Defeat - Try and try until you Succeed.