A Unified Approach for Time Delay Estimators in Spread Spectrum Communications

This paper addresses the problem of time-delay estimation and proposes an effective time-delay estimator for spread-spectrum communications. The main contribution of our work is twofold: first, we define a new objective function that analytically expresses the performance of different estimation criteria. Second, we introduce a new estimator that outperforms the conventional approaches. In particular, we develop a unified approach, deriving the performance trends of several time-delay estimators by one parametric closed form expression. Furthermore, we propose a new estimator that exploits a fast interpolation, running on few samples in the neighborhood of the coarse estimate, i.e. the (abscissa of the) estimated maximum of the ambiguity function. Mathematical expressions for bias and variance of the estimation error are derived and numerically evaluated by reduced Taylor's expansions up to the second order. The theoretical results, substantiated by computer simulations, have evidenced that the devised method is well suited for spread-spectrum satellite communications.