Cramer-Rao bounds in the estimation of time of arrival in fading channels

Abstract

This paper computes the Cramer-Rao bounds for the time of arrival estimation in a multipath Rice and Rayleigh fading scenario, conditioned to the previous estimation of a set of propagation channels, since these channel estimates (correlation between received signal and the pilot sequence) are sufficient statistics in the estimation of delays. Furthermore, channel estimation is a constitutive block in receivers, so we can take advantage of this information to improve timing estimation by using time and space diversity. The received signal is modeled as coming from a scattering environment that disperses the signal both in space and time. Spatial scattering is modeled with a Gaussian distribution and temporal dispersion as an exponential random variable. The impact of the sampling rate, the roll-off factor, the spatial and temporal correlation among channel estimates, the number of channel estimates, and the use of multiple sensors in the antenna at the receiver is studied and related to the mobile subscriber positioning issue. To our knowledge, this model is the only one of its kind as a result of the relationship between the space-time diversity and the accuracy of the timing estimation.

Multistatic Sonar Localization With a Transmitter

“…The transmitter radiates a probing signal and all the receivers observe the signal through two paths: the direct propagation path from transmitter and the indirect reflection path from the object. Each receiver can obtain a differential delay time measurement of the two paths from autocorrelation technique [34] and a bearing angle measurement of the object from the array signal processing technique [35] if the conditions of these pre-processing steps (e.g. sufficient observation period and signal bandwidth) are satisfied.…”