• cpm
• cyclostationarity
• soft-based receiver
• synchronization

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.