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On chip pulse shape design for precise synchronization of DS‐CDMA systems

In this work, a methodology is established to design optimum chip pulse shapes which are absolutely bandlimited, their energy mainly concentrated in the chip duration, and which minimize the variance of the time‐delay estimation error of an unbiased estimator. The low‐complexity optimization method is based on the prolate spheroidal wave functions. Thus, the variational problem at hand can be transformed into a tractable parametric optimization problem. It is shown that the designed optimum chip pulse shapes significantly improve the synchronization performance of direct sequence code‐division multiple access systems by minimizing the Cramer–Rao lower bound (CRLB). The time‐delay estimation bias under the presence of multipath is compared with the conventionally used bandlimited rectangular chip pulse shape. Copyright © 2007 John Wiley & Sons, Ltd.