Abstract:
Pseudo-Noise (PN) sequences with low out-of-phase autocorrelation and low cross-
correlation values have many applications as synchronization codes, masking or
scrambling codes, and for white noise signals in communication systems, signal sets in
Code Division Multiple Access (CDMA) communications, key stream generators in
stream cipher cryptosystems, random number generators, and as testing vectors in
hardware design. Besides, sequences with large linear span increase the linear
complexity of the sequence, thus makes difficult to generate a replica of the sequences
for eavesdropping and jamming purposes. This dissertation work focuses on study of
various nonlinear sequences and their correlation properties.
Bounds on correlation functions of signals play a major part in evaluating the
theoretical performance of the spreading sequences and in sequence set selection for
reliable, efficient and secure communication. Welch and Sidelnikov bounds have long
been used as a benchmark for testing the merit of signal sets in the design of good
CDMA sequence families. Besides, partial correlations are equally important in practice.
This dissertation work is focused on determination of the peak partial correlation bounds
of binary signals over fading channels.
Binary signals with 2-level autocorrelation values such as maximal length
sequences, GMW sequences, Cascaded GMW sequences, quadratic residue sequences,
Hall sextic sequences, have importance in synchronization, radar, cryptography etc. In
this dissertation, determination of upper bound on peak partial autocorrelation of
cascaded GMW sequences using underlying interleaving structure of m-sequence is
considered.
Synchronous CDMA systems require large set of families with low cross-
correlation values as signature sequences. Bent and Semi-bent signal sets have the best
nonlinearity possible which makes them more secure to use. This dissertation focuses on
obtaining lower bound on maximum correlation of binary signals over fading channels.
