# A Time-Varying Filter for Doppler Compensation Applied to Underwater Acoustic OFDM
## 4 Validation Using Real Data
### Short-Range Ultra-Sonic Transmission  
In fall 2016, a sea trial was run in Shad Bay, Nova Scotia, to characterize the acoustic channel conditions in a shallow environment and to evaluate the performance of a short-range communication link, particularly for small telemetry nodes subject to mobility. The physical and geometrical parameters of the channel are summarized in Table 1. The transmitter consists of a digital signal processor interfaced to a wideband front-end operating at a center frequency near 125 kHz. The transmitter was deployed at a depth of approximately 26.5 m. The transmit output power was controlled to maintain a signal-to-noise ratio approximately equal to 5.5 dB at the receiver. Pre-recorded sound files were sent using a 16-bit data acquisition card. Waveforms were defined to allow channel characterization and the assessment of a physical layer relying on OFDM. At the receiver, the hydrophone projector was lowered to approximately 1.5 m from the sea surface. The receiver was attached to a boat, which was drifting at the surface with an average speed of approximately 0.3 m/s, as shown in Table 1. The received signal was saved to memory for post-processing. A standard cross-correlation channel sounder was implemented to extrapolate the channel impulse response as a function of time. Figure 8a shows the channel impulse response of the measured channel, while Figure 8b is the output of a shallow water channel simulator that was run for the defined deployment geometries. As can be observed, there is a strong first path arrival, and a second path can be faintly recognized at an additional delay of 5 ms. Since this deployment is in the ultra-sonic regime, it is expected that path delays that propagate over additional distance will suffer from much greater attenuation due to additional losses at high frequency, thus the main tap arrival is much stronger than for the later path arrivals. The channel amplitude remains relatively constant, and the main path delay increases from 26 to 30 ms within a 21 s time-span. The increasing path delay was corrected using the Doppler compensation algorithm described in Section 3. Note that, as can be seen, there is a good degree of resemblance between the measured and predicted model. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Total depth & 28 m \\ Depth of the transmitter & 26.5 m \\ Depth of the receiver & 1.5 m \\ Initial distance (\(d_{0}\)) & 68 m \\ Initial velocity (\(v_{0}\)) & \(-0.29\) m/s \\ Maximum velocity (\(v_{\max}\)) & \(-0.9\) m/s \\ Average acceleration (\(a\)) & \(-0.001\) m/s\({}^{2}\) \\ Signal to noise ratio & 5.5 dB \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Sea trial environmental characteristics. Next, to validate the Doppler compensation algorithm, each packet included a preamble for synchronization, followed by six OFDM symbols. There was a guard interval between the preamble and the OFDM symbols. A linear chirp signal was chosen as the preamble because of its robustness against Doppler. To compare the performance of the Doppler compensation and equalization, two OFDM packet configurations were tested, and their parameters are summarized in Table 2. Different number of sub-carriers, number of pilot sub-carriers, bandwidth, central frequency and maximum tolerable frequency shift were chosen for the two configurations. After frame synchronization, the received packets were decimated to the symbol rate. Then, the time-varying time-scaling factor estimator defined in Section 3 was applied to each packet. The estimated time-scaling factor for OFDM symbol was directly related to the relative velocity between the transmitter and receiver that was observed during this symbol. After Doppler compensation and block synchronization, the channel impulse response on each OFDM block was estimated using the least-square (LS) method and the received block was equalized. Finally, the equalized signal was applied to the demodulation and decoding blocks.