Analysis of Periodic Auto/Cross Correlation Function for Underwater Acoustic OFDM Signal

Abstract

Cyclic prefix orthogonal frequency division multiplexing (CP-OFDM) exhibits superior delay estimation capabilities in terrestrial integrated sensing and communication (ISAC) systems. However, existing analytical frameworks cannot be directly applied to the practical underwater acoustic (UWA) OFDM system with a comb pilot pattern, which utilizes a block-by-block receiver designed for rapidly varying UWA channels. In this paper, we derive the expectation of the squared periodic auto correlation function (P-ACF), and the periodic cross correlation function (P-CCF) with decoding error for UWA-OFDM systems, where the random data and deterministic comb pilot symbols are considered jointly. To facilitate the optimal design of pilot power, we define the expectation of main-lobe to integrated side-lobe ratio (E-MISR) as the performance metric for P-ACF/P-CCF. Based on E-MISR we prove that comb pilots with the uniform-power is the optimal design. Besides, OFDM signals with comb pilots consistently achieve a lower side-lobe indicator compared to the OFDM signal with all data subcarriers. Simulation results verify the proposed formula of P-ACF and P-CCF, and reveal the trade-off between determinism and randomness from the perspective of comb pilots. The sea trial conducted in the South China Sea further demonstrates the P-ACF/P-CCF performance through practical multipath UWA channels.