On Methodologies for GNSS Signal Design

Abstract

In this work we extend a previously established systematic approach to design optimum chip pulse shapes for DSCDMA systems. Instead of designing strictly band-limited signals we consider strictly time-limited chip pulse shapes, whose power is mainly concentrated within a specified bandwidth with controlled spill-over, and that minimize the Cramer-Rao lower bound for time-delay estimation. The proposed methodology enables to formulate the problem of designing optimum chip pulse shapes in terms of achieving a trade-off between synchronization accuracy and acquisition and tracking robustness as an optimization problem. Additionally, spectral separation to non-interoperable signals in the same band is considered. This methodology uses the prolate spheroidal wave functions (PSWF) as basis functions in order to transform the primal variational problem into a dual, tractable parametric optimization problem. This work shows the interesting capabilities of the presented signal design approach for DS-CDMA systems. The overall objective of this work is to prepare tools for GNSS signal design for the next generation of Galileo.