Systematic Approach to Optimum Chip Pulse Shape Design

Abstract

In this work we establish a systematic approach to design optimum chip pulse shapes for DS-CDMA systems which are absolutely bandlimited, whose energy is mainly concentrated in one chip duration, and thatminimize the Cramer-Rao lower bound for the time-delay. The proposed methodology makes it possible 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. This methodology is based on the prolate spheroidal wave functions (PSWF), which enable to transform the primal variational problem into the dual, tractable parametric optimization problem. This work shows the interesting capabilities of the presented signal design approach for DS-CDMA systems. Two design examples for signal design are shown for global navigation satellite systems (GNSS) considering different requirements and constraints.