Performance analysis of noncoherent frame synchronization in satellite communications with frequency uncertainty

Emerging markets for satellite communications, such as maritime and aeronautical applications, require reliable communications in challenging conditions and low-cost, low-complexity user terminals. In this perspective, the synchronization chain is a fundamental part of the receiver and its design becomes critical. When a quadricorrelator is used as first stage of the synchronization chain so as to perform a coarse frequency estimation, then a noncoherent algorithm for frame synchronization can be employed as second stage. A popular algorithm for frame synchronization is the post-detection integration (PDI), whose noncoherent version (NCPDI) is quite robust to non-negligible residual frequency offsets. In this paper we will assess the performance of NCPDI in presence of a random uniformly-distributed residual frequency offset and will find a closed-form approximation for the probability of detection. Moreover, we will optimize the design parameters of NCPDI for a system operating at very low signal-to-noise ratio (VL-SNR) by minimizing the probability of missed detection for a given probability of false alarm.