# A Time-Varying Filter for Doppler Compensation Applied to Underwater Acoustic OFDM
## 4 Validation Using Real Data
### Long-Range Reliable Link  
The Doppler shift compensation algorithm was applied to a low-frequency narrowband system deployed over a range of 10 km. This link was intended for the exchange of low bitrate command messages at high reliability. As demonstrated, when the transmitting and receiving platforms were immobile, Doppler compensation was unnecessary, but the algorithm provided an improvement when the transmitter was moving. In summer 2017, a three-day trial was run in the East Coast of Nova Scotia, near St-Margarets's Bay. A receiver with a five-element vertical line array was moored at 35 m from the surface, in a water depth of 80 m for the duration of the experiments. A 2-kHz transmitter with a bandwidth of 300 Hz was deployed from a vessel. The vessel was anchored at pre-defined coordinates to characterize the performance at five different ranges from 1 km to 10 km. Two additional communication tests were run: in the first, the vessel was allowed to drift, and, in the second, the captain piloted the boat in small concentric 30-m radius circles at an approximate speed of 1 knot and at 4 km from the receiver. Relatively low-speed was maintained to protect the transmit apparatus, and avoid entanglement with the vessel motor. The link channel impulse response is shown in Figure 11 measured using a set of concatenated pseudo-random sequences. As can be seen, over the 9-min period, there was significant Doppler scaling that induced a variable delay of arrival between the OFDM symbols. Figure 10: BER analysis of Config. #2. The red dotted lines in (**a**) show the value of BER at 5.5 dB for system with PA compensation (with and without coding). The horizontal lines in (**b**) are used to identify the average measured BER. The payload transmitted consisted of 12 consecutive frames. Each frame contained nine OFDM symbols with 512 subcarriers and a 400-chip long cyclic prefix. The first symbol was intended for synchronization and channel estimation. It contained 512 pilot sub-carriers. All other OFDM symbols had 256 null sub-carriers, 126 payload carriers, and 130 pilot sub-carriers. The total transmit window duration was 405 s.  
The receiver recorded the information for the entire duration of the trials. Post-processing was used to characterize the acoustic propagation conditions as well as receiver performance. In the communication band, the SNR was high, above 30 dB for all test ranges. For the tests in which the transmitter vessel was carefully anchored, the Doppler spread was measured to be approximately 0.2 Hz, and as such the coherence time was on the same order of magnitude as the 2.1-s OFDM symbol duration (without cyclic prefix). In these conditions, the Doppler compensation technique described in Section 3.2 did not improve the reliability of the link, or only marginally. For the mobile scenarios, the time-scaling factor \(\hat{\alpha}_{m}\) was estimated at the \(m\)th OFDM symbol and was compensated. For compensation, the time-scaling factors \(\hat{\alpha}_{m}\) for \(m=1,\cdots,8\) were interpolated such that an equivalent symbol arrival time \(\tau_{rx}(t)\) was obtained at a discrete time interval sampled at a rate of 10.240 kHz. To rescale the received signal, the TVFDL filter used a correction delay \(\tau_{corr}(t)\). The correction delay \(\tau_{corr}(t)\) was fixed at \(-\tau_{rx}(t)\), so that the corrected symbol arrival time became constant and equal to 0. The time-scaling estimation algorithm was assessed when the transmit vessel was drifting. Note that, when this test was run, the transmitter was at 2 km from the receiver. As shown in Figure 12, the transmitter velocity was estimated in the direction of propagation. The compensation delay is also shown to rescale the signal. As can be observed, the equivalent velocity was generally constant at a value of \(-0.1\) m/s. The negative sign indicates that the transmitter was moving towards the receiver. As can be seen, since the velocity was constant, the compensation delay increased, to a first-order approximation, linearly with time.