High Resolution Channel Estimation Using the Expectation Maximization Methods

Kurzfassung

One of the most important tasks of navigation systems consists of propagation delay estimation and timing tracking. Related problems appear when considering wideband code division multiple access (WCDMA) systems and the corresponding mobile radio channel, when transmitted spread spectrum signals propagate along reflected paths. These spreading sequences have an inherent resistance against interference errors. Contrary to mobile radio systems, even sub-chip synchronization accuracy is required for navigation systems to estimate the position and velocity accurately. The reason for this multipath sub-chip resolution is the connection between propagation delay errors and delay locked loop (DLL) tracking: The multipath propagation leads to a bias of the loop resulting in a positioning error even in the noiseless case. In order to mitigate this multipath effect, a maximum likelihood (ML) estimator is formulated taking into account the reflected signals. However, having several amplitudes and delays as parameters, the resulting system of equations does no longer suggest a straightforward exact solution without dramatic increase in complexity. The potential of the Expectation Maximization (EM) algorithm lies in the fact that it iteratively approximates the ML and significantly reduces the complexity by breaking down the multi-dimensional non-linear optimization problem of the ML into a number of one dimensional ones. This thesis investigates the performance of the EM algorithm, and its companion Space Alternating Generalized EM (SAGE) algorithm, for high resolution channel estimation of Global Navigation Satellite System (GNSS) signals, e.g., the Global Positioning System (GPS) and the Galileo navigation system. The study considers a two-tap statistical channel, with relatively strong multipath effect under low signal-to-noise ratios. In order to describe the performance of the algorithms, classical concepts like the bias, RMSE (root mean square error), and convergence rate are employed. Also, the efficiency of these algorithms are compared to the wide and narrow correlators, which are currently employed in GNSS receivers to mitigate the multipath effect. The results of the performed computer simulations and discussion indicate that the EM methods have the potential to be very powerful high resolution techniques to successfully estimate parameters of impinging waves for navigation systems, due to their good performance, fast convergence, and low complexity. Furthermore, the study presents novel extensions to the EM/SAGE algorithms, by combining their attractive features with the signal-matched and code-matched correlator techniques used in complexity reduction. The results are four high accurate, low complex estimation methods, that can reduce the GPS positioning error in the considered scenarios from 96 meters in conventional wide correlators, to about 0.3 meters.