Optimising Sidelobes and Grating Lobes in Frequency Modulated Pulse Compression

Abstract

Pulse compression is a signal processing technique used in radar systems to achieve long range
target detection capability, which is a characteristic of long duration pulse, without
compromising the high range resolution capability, which is characteristic of a short duration
pulse. For this, the received signal at the receiver is compressed by a matched filter to produce a
compressed version of the signal for better resolution. As the range resolution is inversely
proportional to the bandwidth, high range resolution is ensured by using a transmitted pulse of
greater bandwidth. LFM pulse is better used than a constant frequency pulse because of its larger
bandwidth. The bandwidth of a signal can further be increased by taking a train of pulses with
the center frequency of consecutive pulses stepped by some frequency step ∆f. A train of pulses
with each pulse of duration T, separated by time Tr gives rise to grating lobes in its
autocorrelation function (ACF), when T∆f>1. ACF of a single LFM pulse has also sidelobes of
its own. Grating lobes and sidelobes may act individually or together to mask smaller targets in
close vicinity of a larger target, hence are needed to be reduced.
In the first part of the work, two optimization algorithms called Clonal Particle Swarm
Optimization and Differential Evolution has been used to find out specific windows that shape an
LFM pulse to reduce the ACF sidelobes to their optimal minima. Temporal windows has been
found out using three coefficient window expressions and four coefficient window expressions.
Resulting windows have been found to reduce sidelobes to an extent which was not possible by
the classical windows. Grating lobes in a train of pulses can be lowered by the use of LFM
pulses instead of fixed frequency pulses. Nullification of the ACF grating lobes is possible when
T, ∆f, and B satisfy a special relationship that puts the ACF nulls due to a single LFM pulse
exactly at the positions of grating lobes. The scheme is valid if and only if Tr/T>2, which
restricts the extent of increase in bandwidth by limiting the number of frequency steps for a
signal of particular time duration. In the second part of the work presented in this thesis, a
scheme has been proposed that allows to accommodate more bandwidth by taking Tr/T=1. It
allows more number of pulses within the same signal time, and hence more number of frequency
stepping to result a larger total bandwidth.