[en] 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.