An asymptotic blind time delay estimation

Abstract

This paper addresses a new approach to time-delay estimation based upon the autocorrelation estimator (AE) and asymptotic expansions especially in low SNR in a multipath channel. The following cases are considered for the estimation of time-delays: (1) different types of signals; (2) (non)-Gaussianity for signal and noise; and (3) (non)resolveability of the time-delays. The maximum likelihood estimator (MLE) and autocorrelation estimator (AE) are two computational tools that are used to determine the parameters of a multipath channel. MLE requires some a priori knowledge of the source signal and the channel; AE can be a blind estimator but it is more suitable for a simple propagation model (one extra path). The asymptotic expansion of the log-likelihood ratio is formed to provide a cost function to be extremized for the parameters of a multipath channel. The performance of this algorithm is examined for different signal-to-noise ratios and sample size.