Construction of zero autocorrelation stochastic waveforms

TL;DR

This paper presents a method to construct unimodular complex stochastic waveforms with arbitrarily small expected autocorrelation outside the origin, useful for radar and communication applications, including frame construction in complex spaces.

Contribution

It introduces a novel approach to generate low autocorrelation stochastic waveforms and analyzes their frame properties in complex spaces.

Findings

Waveforms with arbitrarily small expected autocorrelation are constructed.

Discrete and continuous low autocorrelation waveforms are developed.

Frames for complex spaces are constructed from these waveforms and their properties studied.

Abstract

Stochastic waveforms are constructed whose expected autocorrelation can be made arbitrarily small outside the origin. These waveforms are unimodular and complex-valued. Waveforms with such spike like autocorrelation are desirable in waveform design and are particularly useful in areas of radar and communications. Both discrete and continuous waveforms with low expected autocorrelation are constructed. Further, in the discrete case, frames for the d-dimensional complex space are constructed from these waveforms and the frame properties of such frames are studied.