FRFT and Cyclic Prefix Refinement for Coarse-to-Fine Doppler Estimation in Coded OFDM Underwater Acoustic Communications

In underwater acoustic (UWA) orthogonal frequency division multiplexing (OFDM) systems, the orthogonality among subcarriers is highly susceptible to Doppler-induced scaling, leading to severe inter-carrier interference (ICI). This paper proposes a coarse-to-fine Doppler estimation approach for coded orthogonal frequency division multiplexing (OFDM) systems operating in underwater acoustic (UWA) channels. The proposed method first employs the fractional Fourier transform (FRFT) to obtain an initial Doppler factor estimate from a linear frequency modulation (LFM) probe, exploiting the energy concentration property of chirp signals in the fractional domain. This coarse estimate then guides a refinement stage that leverages the cyclic prefix (CP) inherent to each OFDM symbol, enabling symbol-by-symbol Doppler tracking without waiting for the entire packet. As a result, the required memory and processing latency are substantially lower than with full-packet resampling or iterative gradient-descent alternatives. Numerical simulations conducted under both time-invariant and time-variant Doppler conditions demonstrate that the proposed scheme achieves a mean squared error (MSE) below 0.5% at signal-to-noise ratios (SNR) of 5 dB and above. Moreover, the bit error rate (BER) remains within 0.2 dB of an ideal Doppler-free system at a BER of 10−3. The combination of low storage demand, symbol-level operation, and robust performance makes the proposed method well-suited for real-time underwater acoustic communication.