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Error Probability Expressions for Frame Synchronization Using Differential Correlation  

Kim, Sang-Tae (Department of Electronic Engineering, Sogang University)
Kim, Jae-Won (Department of Electronic Engineering, Sogang University)
Shin, Dong-Joon (Department of Electronic Engineering, Hanyang University)
Chang, Dae-Ig (Electronics and Telecommunications Research Institute)
Sung, Won-Jin (Department of Electronic Engineering, Sogang University)
Publication Information
Journal of Communications and Networks / v.12, no.6, 2010 , pp. 582-591 More about this Journal
Abstract
Probabilistic modeling and analysis of correlation metrics have been receiving considerable interest for a long period of time because they can be used to evaluate the performance of communication receivers, including satellite broadcasting receivers. Although differential correlators have a simple structure and practical importance over channels with severe frequency offsets, closedform expressions for the output distribution of differential correlators do not exist. In this paper, we present detection error probability expressions for frame synchronization using differential correlation, and demonstrate their accuracy over channel parameters of practical interest. The derived formulas are presented in terms of the Marcum Q-function, and do not involve numerical integration, unlike the formulas derived in some previous studies. We first determine the distributions and error probabilities for single-span differential correlation metric, and then extend the result to multispan differential correlation metric with certain approximations. The results can be used for the performance analysis of various detection strategies that utilize the differential correlation structure.
Keywords
Differential correlation; false alarm rate; frame synchronization; mis-detection probability; satellite transmission;
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