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.

I. Introduction

The accurate measurement of the delay between two (or more) signals is an important problem in different applications such as [1]: sonar, radar, biomedicine, ultrasonics and, above all, wireless communications. In particular, in the field of digital communication systems, the accuracy of the time-delay measurement is strictly connected with the system performances. In fact, Direct Sequence Spread Spectrum (DS/SS) Code-Division Multiple-Access (CDMA) has emerged as the incoming standard for a variety of wireless communication systems, including the third-generation (3G) radio-mobile transmission technology [2] and the satellite systems [3]. It offers significant advantages in terms of channel capacity, mobile power consumption, link quality and resilience to multi-path propagation [4]. However, in order to exploit the advantages of a SS signal in a CDMA system, receivers must synchronize the local pseudo-noise (PN) code with the incoming PN code [5] [6]. Thus, quickly achieving and then maintaining code-timing synchronization is a critical issue to be satisfied because even a small misalignment can cause dramatic signal-to-noise ratio (SNR) degradation. In satellite communications the accuracy of time-delay estimation (TDE) is directly related to user position accuracy [3]: in fact, in GPS or Galileo systems a DS/SS modulation in the physical layer for the communication is used.