CIF: Small: Algebraic Methods in the Study of Some Problems in Communication Engineering

Wright State University, Dayton OH

Investigators

Abstract

This research involves the study of some specific cases of the Correlation Problem, the instances of which are carefully chosen so that advances in any of these cases would constitute dramatic advances, and improve our understanding of the whole Correlation Problem. These cases are also chosen with an eye to practical applications. We would employ algebraic methods to generate block-Hankel weighing matrices, multi dimensional Hadamard matrices, almost difference sets and perfect sequences. Our motivation stems from their usefulness in several areas of communication engineering: quantum computing, MC-CDMA systems , quasi-synchronous CDMA , multiple antenna wireless communication systems , FHSS which are widely used in military radios, CDMA and GSM networks, radars and sonars, and Bluetooth communications - to name a few. Discrete mathematical structures that can be developed using modern algebra, number theory and finite geometry and other combinatorial structures are useful in constructing sequences and arrays with desirable correlation properties. They are systematically studied via their algebraic counterparts. The results obtained will lead to new mathematical theories that are of interest to combinatorial design theorists and communication engineers. We thus investigate sequence design problems, which have a variety of applications in communication engineering. Our methods will be very algebraic and would employ tools from algebra, finite fields, and algebraic number theory.