Abstract-We address the problem of GPS signal delay estimation in a multipath environment with a low-complexity constraint. After recalling the usual early-late estimator and its bias in a multipath propagation context, we study the maximum-likelihood estimator (MLE) based on a signal model including the parametric contribution of reflected components. It results in an efficient algorithm using the existing architecture, which is also very simple and cheap to implement. Simulations show that the results of the proposed algorithm, in a multipath environment, are similar to these of the early-late in a single-path environment. The performance are further characterized, for both MLEs (based on the single-path and multipath propagation) in terms of bias and standard deviation. The expressions of the corresponding Cramér-Rao (CR) bounds are derived in both cases to show the good performance of the estimators when unbiased.Index Terms-Cramér-Rao bound, GPS, maximum-likelihood, multipath propagation, pseudo-random code, spread spectrum systems.
Of growing interest in the field of VDSL2 transmission is the evaluation of algorithms for improved performance using Far-end Crosstalk (FEXT) Cancellation Pre-coding. In order to perform fair evaluations of different algorithms, it is necessary to define a Multiple Input Multiple Output (MIMO) channel model that realistically represents the nature of the FEXT coupling dispersion that may be encountered in a multi-pair cable. This paper describes a general method for generating a MIMO channel model for a twisted wire pair cable that is extended from the currently defined 1% worst case FEXT coupling model. This extended model defines varying levels of FEXT cross-coupling values across the channel matrix and still preserves the 1% worst case crosstalk levels. Based on cable measurements, we determine a best fit probability density function to model the FEXT coupling dispersion; then for an example 25-pair 26-gauge (AWG) cable, we define four reference 25x25 channel matrices that contain varying degrees of channel dispersion: specifically, we define a 25x25 dispersion matrix for each of 'zero,' 'low,' 'medium,' and 'high' dispersion. Finally, we compute rate vs. reach performance of FEXT Cancellation Pre-coding with cancellation of 5 dominant disturbers for each channel matrix.
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