Design of User Codes for Deterministic Propagation Delay Estimation in Asynchronous CDMA Systems

Resorting to some facts from analytic number theory and the following simple but important property of complex exponentials, we propose a new propagation delay estimation scheme for asynchronous CDMA systems over Gaussian channels: a circular shift in a complex exponential vector looks like multiplying it by a unit-magnitude complex number with shift-appropriate phase angle. In spite of the most existing schemes, the proposed method is a deterministic approach and therefore its performance does not depend on the near-far ratio and sampled data used for statistics estimation. It will be shown that over noise-free Gaussian channels, the propagation delay can be deterministically estimated by transmitting only two training symbols. We will dramatically improve the performance in noisy environments by modifying the method through consuming several more symbols for training.