The filter bank multi-carrier with offset quadrature amplitude modulation (FBMC-OQAM) waveform demonstrates strong anti-interference capabilities due to its sub-carrier-level filtering. As a result, it is increasingly being adopted for underwater acoustic communication (UWAC) in challenging transmission environments. This paper presents a closed-form analytical expression for the bit error rate (BER) performance of FBMC-OQAM in shallow water, long-distance horizontal communication scenarios. The expression considers the residual Doppler frequency offset, multipath propagation, and ambient noise characteristic of underwater acoustic channels, accounting for the limitations of traditional non-uniform Doppler coarse compensation methods. Theoretical numerical results and Monte Carlo simulation results show that under any number of symbols, the derived closed-form expression consistently exhibits high computational accuracy, when facing the impact of Doppler spread or compression at any scale.
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