Application of compressed sensing to stretch processing in radar

Abstract

Stretch processing is a pulse compression technique used in Radio Detection and

ranging (RADAR) devices by which we can utilize the advantage of both short

pulse and long pulse. Short pulses help to achieve good range resolution and

long pulse with high transmitted power helps to recover targets at long

distances. Usually LFM signal is transmitted and it's reflected back again by the

scatterers. The reflected signal contains the information about the targets and we

need a de-chirping signal to remove the carrier and recover the information.

Thus the de-chirped signal is used to provide the information about the targets

which are present inside the range window. Stretch processing is mostly used in

high bandwidth systems where number of samples required to process the

information is quite huge.

After De-chirping the signal compressed sensing (CS) algorithm is applied to

approximate the sparse signal. Since the reflected signal is sparse, the essential

or nonzero coefficients can be recovered by means of reduced number of

measurements rather than sampling the signal in Nyquist rate. Thus the

complexity is reduced and time taken to reconstruct the target profile is also

reduced by which CS algorithm achieves an advantage over the conventional

sampling.

Compressive Sampling Matching Pursuit (CoSaMP) is a greedy iterative

algorithm for approximating the sparse signal by reduced number of

measurements and it's used for CS reconstruction. CoS aMP produces much

stable reconstruction by including much simpler sampling matrices and the

number of samples required is Jesser than other algorithms. CoSaMP algorithm

is even able to accurately reconstruct the closely spaced scatterers which are

contaminated by noise and CS can also be used to locate the off-grid targets.