# A Time-Varying Filter for Doppler Compensation Applied to Underwater Acoustic OFDM
## 4 Validation Using Real Data
### Long-Range Reliable Link
At the end of the 400-s delay, the compensation was 24 ms.  
Next, the time-scaling was estimated when the boat was moving in a circular motion. When this test was run, the distance between the transmitter and receiver was 4 km. As shown in Figure 13, the maximum absolute speed of 0.5 m/s (1 knot) was estimated, consistent with the physical boat speed that the captain monitored. Note that the speed estimation curve follows a sinusoidal-like shape since for some duration the transmitter was driving towards the receiver, and otherwise it was going away. The correction delay \(\tau_{corr}(t)\) used to compensate for the boat mobility is also shown in Figure 13. As can be observed, when the boat was moving at a negative velocity, the compensation delay increased, otherwise it decreased. Figure 11: Channel impulse response as a function of time for the long range experiment. The communication link reliability was also simulated for the long range application. The frequency domain equalizer implemented in Section 4.1 was also used, and, to improve performance, the outputs of each OFDM symbol were combined to implement repetition coding. Since each frame contained eight OFDM symbols with payload, the performance was tested for repetition rates \(R_{c}\) of 1, 2, 4 and 8. The useful bit rate was calculated accordingly. Maximum ratio combining (MRC) was used to weight the output of the five receiver elements. The MRC filter coefficients were obtained from the interpolated channel estimated using each OFDM symbol's pilot tones. The bit error rate of the OFDM symbol without Doppler compensation is shown in Figure 14 as a function of bit rate for the different transmitter deployment stations. Note that the mobile deployment when the engines were turned on is omitted from this figure. The performance for the 2 km station was clearly much poorer than for the other station because the boat was drifting. Otherwise, for all other stations, the performance was relatively good and, for a bit rate of 16 bps, the probability of bit error was below \(10^{-3}\). Figure 12: Output of the velocity estimation algorithm, and resulting symbol delay correction while the transmit vessel was drifting. Figure 13: Output of the velocity estimation algorithm, and resulting symbol delay correction at the 4-km range. The transmit vessel was moving at approximately 1 knot in small concentric circles with a radius below 50 m such that the boat was moving towards the receiver for a period of time, and then away from the receiver. Next, the bit error rate of the OFDM symbol with Doppler compensation is shown in Figure 15 as a function of useful bit rate for the mobile conditions. As can be observed, the OFDM performance was very poor without compensation, particularly for the test in which the transmitter vessel engines were turned on. In this scenario, after one Doppler compensation iteration, the performance was only improved marginally. This is attributed to interpolation errors when the time-scaling factor varies significantly during an OFDM symbol. Consequently, two Doppler estimation and compensation iterations were run to improve the performance. After two iterations, improvements were no longer observed, and, for a bit rate of 8 bps, the BER was improved to 0.05 after two iterations for the scenario in which the vessel's engines were turned on. Although the performance was improved, this highlights the difficulty of establishing a reliable link using OFDM in mobile conditions. When the boat was drifting, the original Doppler shift was more benign, and the output BER was 0.003 for a bit rate of 8 bps. More efficient coding techniques can be applied to further improve the performance in mobile conditions. Figure 14: Measured bit error rate without Doppler compensation as a function of data rate for different ranges. Figure 15: Measured bit error rate with Doppler compensation as a function of data rate for mobile conditions.