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