Least Square and Trended Doppler Estimation in Fading Channel for High-Frequency Underwater Acoustic Communications

Hermes is an asymmetrical point-to-point underwater acoustic modem designed for short-range operations at very high bit rates in ports and shallow waters using broadband acoustic signaling (262-375 kHz). In exploring the possible conversion of Hermes into a multiple-input-multiple-output (MIMO) device, single-carrier phase-modulated spread-spectrum sequences were used for channel estimation and deconvolution purposes. It clearly appeared that the channel estimation and deconvolution routines were quite sensitive to rapid time changes in the acoustic channel impulse response (CIR), which usually reflects the presence of Doppler spread produced for the most part by moving boundaries and oscillating sensors. In this paper, the authors study the least square (LS) channel estimation routine ability to track the time-varying nature of the impulse response using broadband, single-carrier pseudonoise (PN) sequences transmitted by a single source and collected by a single receiver. In addition, the authors evaluate a trend estimation technique, based on the empirical modal decomposition (EMD) method applied to the LS estimate of the CIR. Simulated data produced with a Rayleigh channel model and experimental data collected in a marina are used. This paper shows that the channel estimation method can estimate the time-varying impulse response of the acoustic channel with a high resolution of both time and delay (down to 7 μs) at the expense of high computational requirements. In analyzing the time variation of the main and secondary echoes for a signal-to-noise ratio (SNR) of 32 dB, simulated results indicate that the root mean square error (RMSE) between theoretical and LS estimated response is 7.8% for the main path with an equivalent Doppler spread of 10 Hz and 15.7% for the second path with an equivalent Doppler spread of 15 Hz. Applying the trend estimation technique to the LS CIR greatly reduces this error, down to 2.9% for the main path and to 4.7% for the second path. The experimental data clearly show that the routine can closely track the time variations of the main echo and provide a meaningful estimate of the Doppler spread.