Abstract
Next generation satellite systems are required to perform robust frame synchronisation in the presence of large frequency offsets at low carrier-to-noise ratios. Differential correlation-based frame acquisition is an appealing choice for these systems as it provides adequate performance with reasonable complexity. However, the theoretical characterisation of the multi-span differential correlation metric is still an open problem due to the fact that the correlation outputs with multiple delays are correlated. In this study, the authors derived novel closed-form approximations for the distribution of the multi-span differential correlation metric as well as the probabilities of miss-detection and false alarm. The close agreement between the simulated and theoretical receiver operating curves validates the analysis. This analysis can be used to characterise the performance of multi-span differential correlation-based frame synchroniser in terms of the number of delays without running computationally extensive Monte Carlo simulations.
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