Performance Analysis and Algorithm Design for Synchronization in Alpha-Stable Impulsive Noise

Impulsive noise modeled as symmetric alpha-stable (S alpha S) distribution is commonly seen in many practical communication scenarios. In this paper, we focus on the synchronization of single-carrier signals in the mixture of S alpha S impulsive noise and Gaussian noise. We first derive the Cramer-Rao lower bound (CRLB) of the joint estimation of carrier phase and timing offsets for both liner modulation (LM) signals and continuous phase modulation (CPM) signals. In order to minimize the CRLB, the optimal training sequence (TS) is then designed for the synchronization of the LM signals and the CPM signals, respectively. We further propose a practical low-order cross-correlation based synchronization algorithm, which can be used for both LM and CPM signals. Numerical simulations show that our designed TS can outperform the pseudo-random (PN) sequence. By taking minimum shift keying (MSK) signals for instance, simulation results show that the performance of our proposed synchronization algorithm has negligible gap with the CRLB.