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.
Highlights
Positioning of a mobile subscriber is a complex task that has the capability of adding value to services and applications such as navigational aids, and patient and personnel monitoring [1]
Where ρjj refers to the correlation between signatures at sensors j and j ; α refers to temporal correlation between channel estimates in two consecutive slots when temporal variation has been modeled as a first-order AR Markov process (AS 7); and ril refers to the correlation between delays in lags i and l, and k0 refers to the time of arrival (TOA) of the first path
When signal-to-noise ratio (SNR) was set to 0 dB, instead of 10 observations, 50 observations were required to have a similar performance along the whole range of the temporal correlation
Summary
Positioning of a mobile subscriber is a complex task that has the capability of adding value to services and applications such as navigational aids, and patient and personnel monitoring [1]. Since the final performance of a specific positioning technique depends on the way signal parameters are estimated, a general comparison of the different techniques is difficult For this reason, we study the problem of TOA estimation in both Rice and Rayleigh propagation conditions from a Cramer-Rao perspective since the lower bound of an unbiased estimator determines the best possible behavior in the estimation of a particular parameter of interest. It has been reported that in certain cases, results predicted by CRBs or BCRBs are too optimistic and some modifications to the classical CRBs have been proposed lately This requires the postponement of the application of an expectation operator required for Fisher information matrix (FIM) computation, in a way that matrix inversion is performed first and as a second step, an expectation operator is applied to compute the modified CRB (MCRB) [27].
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