Time-Frequency Domain Turbo Equalization for Single-Carrier Underwater Acoustic Communications

Single-carrier frequency-domain equalization (SC-FDE) is a promising technique for coherent high-rate underwater acoustic (UWA) communications. In this paper, a time-frequency domain turbo equalization (TFD-TE) scheme is proposed for single-carrier modulation. The TFD-TE scheme is to couple a multi-channel frequency domain equalizer with phase rotation compensation and a low-order single-channel time-domain turbo equalizer. To mitigate the error propagation and further enhance receiver performance, a bidirectional equalizer that combined the soft outputs of a conventional equalizer and a backward equalizer is introduced into the proposed TFD-TE scheme (Bi-TFD-TF). The sparse channel is estimated by the improved proportionate normalized least mean squares (IPNLMS) algorithm block by block. Both the simulated and experimental results show the proposed TFD-TE can effectively improve system performance with acceptable complexity. The proposed TFD-TE scheme is evaluated using communication data collected from the DJK15 lake experiment. For the
$1\times 4$
single-input multiple-output (SIMO) communication system using quadrature phase shift keying (QPSK) and 8-phase shift keying (8PSK) modulations, the proposed scheme achieves error-free transmission after a few iterations. Our receiver achieves a maximum raw data rate of 12 kbit/s and a reliable net data rate of 4 kbit/s within 4-kHz bandwidth at a range of 10.8 km. Compared with conventional frequency domain turbo equalization (FD-TE), the proposed TFD-TE scheme can enhance 0.8–1.3 dB in terms of output signal-to-noise ratio (OSNR). The related bi-TFD-TE provides an additional 0.8–1.7-dB OSNR improvements.