Preamble Design for Frame Synchronization in VLF Communication Based on Prolate Spheroidal Wave Function Sequences

We propose a novel preamble sequence generation approach for continuous phase modulation based on prolate spheroidal wave functions (CPM-PSWF) for very low-frequency (VLF) system that can be generated on the carrier without post-modulation. The original principle, inspired from the PSWF frequency shaping pulses, is presented. From the autocorrelation of the proposed preamble and correlation performance with the other received signals in VLF system, the excellent detection characteristic of the proposed preamble is verified, under both Gaussian and non-Gaussian noise. The correct detection probability of the proposed preamble is more than 84% under Gaussian noise when Eb/ $N_{{0}} \ge 0$ dB.