Pulse Waveforms with a Correlation Criterion for Synthetic Aperture Imaging Systems

Abstract

We introduce a method for the synthesis of pulse waveforms that possess a given time-bandwidth product, have narrow auto-correlation functions, and simultaneously, small cross-correlation functions. Pulse sets with such characteristics are desirable in various contexts in communications and rang- ing applications: the narrow auto-correlation property provides noise-immunity and enhances temporal resolution, while small cross-correlations minimize mutual interference in multiple- access systems. We leverage the energy concentration property of the prolate spheroidal wave functions to ensure small pair- wise cross-correlations, and develop an iterative algorithm that enforces a desired shape on the auto-correlation functions of the resulting waveforms. The effectiveness of the method is illustrated with examples: the correlation functions of the pulses that we obtain show significant improvements over those of PN sequences, and of pulses obtained by a previously reported method. I. INTRODUCTION The correlation properties of the signal waveforms are important in several aspects of radar, sonar, and commu- nications engineering. In ranging applications, for example, an auto-correlation function (ACF) with a narrow main-lobe and rapidly decaying side-lobes is necessary for adequate temporal resolution. In the context of digital communications, a well-localized ACF is beneficial to timing acquisition and synchronization, and multipath resolution in mobile fading environments. In systems where multiple signals share the same channel, their cross-correlation properties are equally im- portant, as signal discrimination and interference suppression techniques primarily rely on the cross-correlation functions (CCFs) being nearly zero. Examples of such multiple-access systems include CDMA communications, multiple-transmitter synthetic aperture imaging (SAI), etc.. In the following we denote the correlation function of the complex-valued signals si(t) ,s j(t) at lag τ by ri,j(τ ) as defined by the formula