Group representation design of digital signals and sequences

TL;DR

This paper introduces the oscillator system, a new class of digital signals with favorable correlation properties, useful in radar and communication, along with an explicit construction algorithm.

Contribution

It presents the oscillator system, a novel set of signals with optimal properties and a method for their explicit construction, advancing digital signal design.

Findings

Oscillator system exhibits excellent auto- and cross-correlation properties.

System is closed under discrete Fourier transform.

Provides an explicit algorithm for construction.

Abstract

In this survey a novel system, called the oscillator system, consisting of order of p^3 functions (signals) on the finite field F_{p}, is described and studied. The new functions are proved to satisfy good auto-correlation, cross-correlation and low peak-to-average power ratio properties. Moreover, the oscillator system is closed under the operation of discrete Fourier transform. Applications of the oscillator system for discrete radar and digital communication theory are explained. Finally, an explicit algorithm to construct the oscillator system is presented.