Synchronization Issues for Continuous Phase Modulations

Continuous-phase modulations (CPMs) have been studied for many years. Mainly because of the attractive property of constant envelope, that make this family the most suitable modulations in the satellite field, they found their first relevant practical application in mobile communications, where they represent the standard signal format for GSM. In spite of the huge literature that is available on the subject, more elaborate CPM schemes have found no application until now because of the implementation complexity of the detector, and of synchronization problems. In the last few years several methods have been proposed to solve synchronization issues related to Continuous Phase Modulations (CPMs). Unfortunately most of these techniques are ad-hoc algorithms, developed to meet synchronization problems for a particular subclass of signals. In this thesis, we tackle the issue of both cyclostationary-based and soft-based synchronization for continuous phase modulations (CPMs), by extending to such signals (including the multi-h variant) the corresponding methods that were already proposed for linearly-modulated data signals. As first, we will examine the timing synchronization algorithm. The problem of blind timing recovery with linear modulations has several efficient solutions, irrespective of the complexity of the signal constellation. The workhorse in this respect is Gardner’s timing error detector, that is a closed loop estimator. Another approach is represented by the wellknown Oerder-Meyr’s (O&M) estimator, that is on the contrary an open loop method. Gini and Giannakis (G&G) showed that the O&M estimator is a particular sample of a larger class of estimators that exploit the cyclostationarity of a data signal. We will show in the following that the G&G approach can be extended to CPM signals, and we will perform an approximate analytical performance evaluation. The second part of this work is about another general synchronization method that can be applied to CPM signals, that exploit the trellis structure inherent in the modulator. In particular we will focus on phase estimation, being the phase the parameter that shows the lower implementation complexity. Our approach is the so-called code-aided synchronization, that take benefits from the a priori information available from the code structure applied to a linear modulation scheme. We try to extend this approach to CPMs, since this signals share with a coded system the trellis structure, due to the inherent memory of the CPM modulator. The algorithm starts with a first step, called Expectation- Maximisation. It is an iterative method which enables to solve ML optimisation problem. In the special case of the sole phase, being CPM a phase modulation, the computational complexity decreases and it is possible to find a closed form for the estimator, that is data aided and makes use of the state transition probabilities given by a symbol-based BCJR, developed in an ad-hoc way for an uncoded CPM signal.