On the Cramer-Rao bound for carrier frequency estimation in the presence of phase noise

We consider the carrier frequency offset estimation in a digital burst-mode satellite transmission affected by phase noise. The corresponding Cramer-Rao lower bound is analyzed for linear modulations under a Wiener phase noise model and in the hypothesis of knowledge of the transmitted data. Even if we resort to a Monte Carlo average, from a computational point of view the evaluation of the Cramer-Rao bound is very hard. We introduce a simple but very accurate approximation that allows to carry out this task in a very easy way. As it will be shown, the presence of the phase noise produces a remarkable performance degradation of the frequency estimation accuracy. In addition, we provide asymptotic expressions of the Cramer-Rao bound, from which the effect of the phase noise and the dependence on the system parameters of the frequency offset estimation accuracy clearly result. Finally, as a by-product of our derivations and approximations, we derive a couple of estimators specifically tailored for the phase noise channel that will be compared with the classical Rife and Boorstyn algorithm, gaining in this way some important hints on the estimators to be used in this scenario

Synchronization in digital communication systems: performance bounds and practical algorithms

Communication channels often transfer signals from different transmitters. To avoid interference the available frequency spectrum is divided into non-overlapping frequency bands (bandpass channels) and each transmitter is assigned to a different bandpass channel. The transmission of a signal over a bandpass channel requires a shift of its frequency-content to a frequency range that is compatible with the designated frequency band (modulation). At the receiver, the modulated signal is demodulated (frequency shifted back to the original frequency band) in order to recover the original signal. The modulation/demodulation process requires the presence of a locally generated sinusoidal signal at both the transmitter and the receiver. To enable a reliable information transfer, it is imperative that these two sinusoids are accurately synchronized. Recently, several powerful channel codes have been developed which enable reliable communication at a very low signal-to-noise ratio (SNR). A by-product of these developments is that synchronization must now be performed at a SNR that is lower than ever before. Of course, this imposes high requirements on the synchronizer design. This doctoral thesis investigates to what extent (performance bounds) and in what way (practical algorithms) the structure that the channel code enforces upon the transmitted signal can be exploited to improve the synchronization accuracy at low SNR