Parallel Resampling of OFDM Signals for Fluctuating Doppler Shifts in Underwater Acoustic Communication

Reliable underwater acoustic communication is demanded for autonomous underwater vehicles (AUVs) and remotely operated underwater vehicles (ROVs). Orthogonal frequency-division multiplexing (OFDM) is robust with multipath interference; however, it is sensitive to Doppler. Doppler compensation is given by two-step processing of resampling and residual carrier frequency offset (CFO) compensation. -is paper describes the improvement of a resampling technique. -e conventional method assumes a constant Doppler shift during a communication frame. It cannot cope with Doppler fluctuation, where relative speeds between transmitter and receiver units are fluctuating.We propose a parallel resampling technique that a resampling range is extended by measured Doppler standard deviation. -e effectiveness of parallel resampling has been confirmed in the communication experiment. -e proposed method shows better performance in bit error rates (BERs) and frame error rates (FERs) compared with the conventional method.


Introduction
Autonomous underwater vehicles (AUVs) and remotely operated underwater vehicles (ROVs) are of wide interest for marine survey and offshore engineering.Reliable underwater communication is essential for command control and image/video data transmission.In recent underwater acoustic communication (UAC), orthogonal frequencydivision multiplexing (OFDM) is widely used in terms of high-frequency utilization [1].OFDM inserts a cyclic prefix (CP) or a guard interval (GI) into block data and makes use of frequency domain equalization (FDE) as multipath compensation.We have presented the countermeasure against strong multipath, where a multipath spread exceeds a CP length in [2].
Although OFDM is robust with multipath interference, it is sensitive to Doppler.Due to the low velocity of acoustic waves, the wideband modulation of OFDM is considerably affected by Doppler and results in intercarrier interference (ICI).Doppler compensation is mandatory for moving platforms such as AUVs and ROVs.Doppler compensation is given by two steps of resampling and residual carrier frequency offset (CFO) correction [3,4].
is paper describes the improvement of a resampling technique.
Doppler is expressed by frequency scaling in narrow band signals. is model is often used in electromagnetic wave communication.In UAC, the wideband model of time scaling (expansion or compression) is assumed when the signal bandwidth is close to carrier frequency.Resampling manipulates a received signal to compensate the time-scale change.e resampling ratio is determined according to the Doppler estimation result observed as the change of signal time length or frequency.
If a Doppler shift is simple and known, Doppler compensation would be perfectly performed by the incorporation of resampling and CFO correction.However, nonuniform Doppler shifts must be considered in actual communication.Nonuniform Doppler shifts are classified into Doppler spread and Doppler fluctuation as shown in Figure 1.Doppler spread is caused by the acoustic propagation that each path has an individual Doppler scale factor.In Figure 1(a), the transmitter unit has the same direction as the direct wave.
e reflected waves have the different directions, whose Doppler scales are slightly shifted from that of the direct wave.ese Doppler scales are measured as frequency spread in the receiver unit.e countermeasures of Doppler spread have been presented in recent papers such as multiple resampling [5], Bayesian resampling [6], frequency domain oversampling [7], and Doppler-resilient orthogonal signal-division multiplexing (D-OSDM) [8].
Doppler fluctuation is caused by the irregular motions of transmitter or receiver units.e case that the transmitter unit is moving in meandering trajectory is depicted in Figure 1 is paper presents a parallel resampling technique that a resampling range is extended by measured Doppler dispersion.If an OFDM block is affected by Doppler fluctuation, using Doppler shift average is insufficient for finding an appropriate resampling ratio.We apply statistical analysis that uses both mean and variance in Doppler estimation to cope with complicated Doppler shift variations.
e parallel resampling receiver takes multiple resampling blocks whose resampling ratios are settled according to Doppler mean and deviation.
e best decoded data are selected by checking data errors.e parallel resampling stricture is applicable to typical OFDM systems.e effectiveness of parallel resampling has been tested by our sea trial, where a transmitter unit moves with various speeds and directions.
A part of contents in this paper has been presented in the conference paper as our previous work [10].e following two points have been improved in this paper.One is the frequency allocation of a continuous wave (CW) whose signal is given by a sinusoidal function.e previous work requires frequency spacing between CW and OFDM bands to avoid their own interference, which results in lowfrequency utilization.is work has improved that CW is allocated as one of the OFDM subcarriers.e signal interference can be avoided by making use of frequency orthogonality of OFDM.e second is the dynamic control of branches in the parallel resampling receiver.
e parallel numbers of resampling units are controlled on frame-byframe basis according to the measured Doppler shift mean and deviation.It can reduce computational complexity of resampling compared with the fixed branches in our previous work.
is paper is organized as follows.Section 2 explains fundamentals of Doppler and resampling and reports examples of Doppler tolerance in OFDM.Section 3 investigates the influence of Doppler fluctuation.Section 4 proposes a parallel resampling technique.Section 5 reports the experimental results in the Doppler test.Section 6 summarizes our work.

Resampling
e velocity of acoustic waves (about 1500 m/s underwater) is much lower than that of electromagnetic waves.e effect of Doppler gives a great impact on acoustic communication.
e relative Doppler shift Δ is defined as a ratio of source relative velocity to propagation wave velocity.For a singlefrequency component f, the Doppler effect is expressed by a frequency scaling: In wideband signals, each frequency component is affected by a different amount.is Doppler effect is modeled by a time scaling (expansion or compression) of the signal waveform: where s(t) and r(t) are the source and received signals, repectively.When we use a discrete time-sampled source signal s[nT s ], where n is an integer number and T s is a sampling period, the received signal is expressed as e rate conversion of 1/(1 + Δ), i.e., resampling, eliminates the effect of Doppler by the following equation: Doppler estimation for resampling is accomplished by inserting a known sequence to a communication frame.A popular approach is to detect the times of arrival of preamble and postamble [11] shown in Figure 2. A Doppler shift can be measured as the change of signal length by (1 + Δ)LT s , where LT s is the interval between preamble and postamble.
e tolerance for Doppler estimation error can be investigated from a simple OFDM model in Figure 3. e relative Doppler shift is added to a transmit signal.e OFDM parameters of simulation are enumerated in Table 1.
ese parameters are just one of the examples because adequate OFDM parameters depend on acoustic propagation conditions.e similar parameters have been adopted for our experiment in Section 5.
e results of error vector magnitude (EVM) and bit error rate (BER) are plotted in Figure 4. e horizontal axis shows a Doppler shift corresponding to the residual error of Doppler estimation.A bit error occurs when EVM exceeds 40% when comparing the results in Figures 4(a) and 4(b).Since the center frequency is 45 kHz, a Doppler shift of 4.5 Hz is equivalent to 1/10000 in a relative Doppler shift.It indicates that a resolution of utmost 1/10000 is required within an allowable resampling ratio error.Frequency domain oversampling [7] can extend the error tolerance; however the tolerance is less than 5 Hz.We assume the Doppler deviation of 10 Hz in Doppler fluctuation, which is tested in Section 3.Only applying frequency domain oversampling cannot cope with this large Doppler fluctuation.Since the constant component Δ C can be eliminated by a typical Doppler compensation technique, we consider the Doppler shifts of 0, Δ, and −Δ by applying Δ C � 0. Figure 6 shows the OFDM block with Doppler shift patterns.One OFDM block with N samples is partitioned into three sections of A, B, and C. We make various Doppler shift patterns by shuffling the Doppler shifts in three sections so that all the shifts are allocated in a whole frame.Although further complex shifts should be considered in the actual environment, the proposed parallel resampling technique can cope with arbitrary unknown Doppler shifts (to be described later).We represent arbitrary shifts by shuffling the three Doppler shifts (expressing the swing of a transmitter unit as one of the examples) for simplification.Our model that a Doppler shift fluctuates with plus or minus in a whole frame can be observed in actual communication, which will be reported in Section 5.

Influence of Doppler Fluctuation
e resampling procedure is illustrated in Figure 7.We evaluate various resampling ratios of 1/(1 − Δ), 1/(1 − (Δ/2)), 1, 1/(1 + (Δ/2)), and 1/(1 + Δ) to observe which ratio is the best choice.e magnitude of Doppler shift is set by Δ • f C � 10 Hz, assuming the speed fluctuations of ± 1.2 km/h in moving platforms.f C (�45 kHz) denotes the center frequency of OFDM.e other simulation parameters are the same in Table 1.e OFDM block sample N becomes 7,740 including the guard interval.e frequency domain oversampling factor of 2 is applied to extend the Doppler tolerance.
e results of EVMs and BERs are shown in Tables 2  and 3. e OFDM block length is the same for all cases.e highlighted cell shows the best performance for each case.e average Doppler shift becomes zero for all Doppler shift patterns because the OFDM block length does not change.It indicates that resampling is not needed in the conventional approach.However, the appropriate resampling ratios having the lowest EVM and BER depend on Doppler shift patterns.If these Doppler shift patterns are known, the appropriate resampling ratios can be determined according to the results in Tables 2 and 3. Actual Doppler shift patterns are much complex and cannot be prospected.
e conventional approach takes the Doppler average in determining a resampling ratio.It induces the mismatch between determined and appropriate resampling ratios in the presence of large Doppler fluctuation.We take another approach to grasp the Doppler fluctuation, inserting a continuous wave (CW) into the OFDM frame to observe short-term Doppler shifts.e block diagram of CW-aided Doppler estimation is illustrated in Figure 8. e CW signal of sin(2πf CW t) and the OFDM transmitted signal are multiplexed in frequency.e CW signal is allocated as one of the OFDM subcarriers, and frequency spacing between CW and OFDM is not required.e Doppler-affected CW signal is extracted by the bandpass filter.
e short-term Doppler shifts can be measured by detecting phase offsets in IQ demodulation, where the observed Doppler shifts are plotted in Figure 8.
e statistical results based on short-term Doppler shifts are summarized in Table 4. e CW signal of 30 kHz is added into the OFDM block in Figure 6.When we look into the results of average, standard deviation, maximum, and minimum values, the standard deviation gives useful information.
ese standard deviation values are close to the Doppler fluctuation of 10 Hz.
e phenomena that the average values do not become zero would be caused by sudden changes in Doppler shifts.Doppler dispersion provides useful information to grasp large Doppler fluctuation.

Parallel Resampling
As reported in Section 3, it is difficult to find an optimal resampling ratio even for the simple Doppler shift patterns given by three sections if their Doppler shift patterns are unknown.Doppler shift patterns should be assumed as almost unknown for actual Doppler fluctuation caused by the irregular motions of transmitter or receiver units.We consider statistical information in short-term Doppler shifts and present a parallel resampling technique that a resampling range is extended by measured Doppler dispersion.
e conceptions of single and parallel resampling techniques are compared in Figure 9. e single resampling technique, regarded as a conventional method, determines a resampling ratio according to the Doppler mean.As long as the Doppler shift is time invariant, the single resampling can provide adequate performance for Doppler compensation.However, it cannot cope with Doppler fluctuation especially for the case that Doppler shift patterns are unknown.e parallel resampling technique uses both Doppler mean and standard deviation and extends the resampling range.e optimal resampling ratio is detected by checking all outputs in the extended resampling units (called as branches); i.e., the exhaustive search is adopted.e details of the exhaustive search are explained by the following receiver structure.
e block diagram of the parallel resampling receiver is illustrated in Figure 10.
e CW and OFDM signals are multiplexed across the communication frame in the transmitter side (Figure 10(a)).As shown in Figure 8, we have improved the frequency allocation of CW and OFDM that the CW is regarded as one of the OFDM subcarriers.
eir frequency bands are 30 kHz and 30 kHz to 60 kHz, respectively.Our previous work required frequency spacing, where CW and OFDM are allocated in 45 kHz and 50 kHz to 60 kHz [10].In the receiver side (Figure 10(b)), the CW signal is separated by the bandpass filter.
e Doppler e receiver takes multiple branches for resampling and OFDM demodulation blocks, where every branch has a di erent resampling ratio.As mentioned in Section 3, the appropriate resampling ratio depends on Doppler shift patterns.For unknown shift patterns, it is very di cult to nd the appropriate resampling ratio by only evaluating the received signals before OFDM demodulation.We apply the exhaustive search to cope with this problem.e parallel resampling receiver performs data checking for the outputted bit data after OFDM demodulation and selects the best branch having no data error.In the transmitter side, cyclic redundancy check (CRC) codes are inserted in bit data before forward error correcting (FEC) coding.In the receiver side, all branches are checked whether their outputted data have an error or not.e best branch having no error is selected, which corresponds to selecting the appropriate resampling ratio.If all branches have data errors, the nal data are generated by merging all decoded data of branches in the bit level.
e overhead of CRC codes might be counted.
e overhead would be very small as far using CRC-16 or CRC-8.e procedure of OFDM demodulation is shown in Figure 10(c), which is adopted in typical OFDM systems.

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Journal of Electrical and Computer Engineering e single resampling is highlighted by the dashed lines in Figure 10(b), where the resampling ratio is given by 1/(1 + Δ M ) according to the Doppler mean value Δ M .e performance comparison of single and parallel resampling techniques is reported in Section 5.
We mention examples of resampling range and number of branches in parallel resampling.Table 5 shows the examples of resampling ratios and number of branches (N P ).We express the resampling ratio by an integer format as where R relates the resolution of resampling as explained in Section 2. When we set R 10000, and Δ M 0, the resampling ratio becomes 10000 : 10000 + Δ D as an integer ratio.Note that the parameter of R depends on the Doppler tolerance.We set it according to the Doppler test results in Section 2. For the Doppler standard deviation value of 5 Hz (with zero mean), the parallel resampling receiver takes three branches whose ratios are 10000 : 9999, 10000 : 10000, and 10000 : 10001.It indicates that parallel resampling has a trade-o between improving communication performance and increasing computational complexity.
e number of branches has been xed as N P 11 based on the empirical data in our acoustic communication tests in our previous work [10]. is paper applied the dynamic control of branches (we call it variable branches) in order to reduce computational complexity.
e procedure for the variable branches is explained as follows: (a) Cut out a received signal for a certain frame (b) Calculate Δ M and Δ D from the extracted CW (c) Determine N P according to Δ D Since the resampling ratio is adjusted by the unit of 1/10000, the target signal for resampling should hold at least 10000 samples.For example, the numbers of samples per frame amount from 10,000 to 100,000 for 200 kHz sampling frequency and 1024 subcarriers.It is advantageous to perform both resampling and statistical analysis of Doppler mean and standard deviation for the entire frame.e calculation of standard deviation for every frame is required for the variable branches.Its computational cost is O(3N), which is much smaller than resampling processing itself given by O(20N 2 ) (N denotes the number of samples per frame).
When the magnitude of Doppler uctuation changes as time goes, the complexity reduction is available by changing the number of branches for each frame.

Experimental Results
We conducted the communication experiment on November 2017 in Mombetsu Port, Hokkaido, Japan.e  e measured delay profile at the RX unit is plotted in Figure 12.
e cluster of large delay waves is observed around 40 ms, inducing strong multipath interference.ese delay waves are caused by the reflection of sea surface, bottom, and two side walls near the RX unit.Table 6 enumerates the experimental parameters.Due to the severe conditions on Doppler and multipath, the transmit data rate was set to 3 kbps.We have compared communication performance in single and parallel resampling techniques.
e results of carrier-to-noise ratio (CNR) and relative Doppler speed are reported in Figures 13 and 14 for Test 1 and Test 2. e horizontal axis denotes the frame number.We can observe Doppler fluctuation that the relative speed changes with plus or minus because the transmitter unit moves in the meandering trajectory as well as Figure 1(b).
e CNR values are not uniform, which would be caused by the wave disturbance by a ship propeller and the ship direction.
e results of BER and number of branches (N P ) are plotted in Figures 15 and 16.We compared BER results in baseline (without resampling), single resampling, and parallel resampling (with fixed and variable branches).
e results of BER � 0 are plotted on the line of BER � 10    17.We can observe that the Doppler shift uctuates with plus or minus within an OFDM frame as mentioned in Section 3. e BERs for the frame numbers of 33, 49, and 102 are 0.17, 0.45, and 0.37 in single resampling and all zeros in parallel resampling.
eir results indicate that parallel resampling can improve communication performance under actual Doppler uctuation.
Table 7 shows the summary of experimental results.e overall results of frame error rate (FER) are 0.096 and 0.24 for the single resampling in Test 1 and Test 2. e parallel resampling achieves FERs of 0 and 0.10.e parallel resampling with the variable branches saves computational cost by 28% to 33% compared with the xed branches.
e parallel resampling has improved communication performance for large Doppler uctuation; however, it relies on the exhaustive search with low computation e ciency.
e further complexity reduction should be considered as a future issue.One of the key ideas is use of compressing sensing (CS).CS-based channel estimation in OFDM has been discussed in [13].In UAC, a doubly spread acoustic channel (dispersion in time and frequency) is estimated by orthogonal matching pursuit (OMP) algorithm in [14,15], which makes use of the sparse structure of channel impulse response.If Doppler uctuation could be accurately estimated by the similar approach, an optimal resampling ratio is detected without the exhaustive search.Since the computational cost of OMP algorithm is much higher than that of Doppler mean and standard deviation, we would have to compare the overall complexity including Doppler estimation, resampling, and demodulation.e e ectiveness of parallel resampling has been con rmed by evaluating communication performance comparing with single resampling.

Conclusion
e complexity reduction has been done by applying the variable branches in the parallel resampling receiver.It saves computational cost by 30 % compared with the xed branches.However, its computation cost remains rather high compared with the single resampling.
e further complexity reduction will be studied in our future work.
(b).A Doppler shift becomes positive in Point A and negative in Point B according to the relation between sound and transmitter velocity vectors.While the Doppler shift in Figure1(a) is regarded to be time invariant, the Doppler shift in Figure1(b) rapidly fluctuates with plus or minus as time goes on.ere are few papers to tackle Doppler fluctuation because of difficulty in acoustic propagation modeling.e authors in[9] have presented linear multiscale compensation by smoothing estimated Doppler scales.It assumes that a Doppler shift is linearly changing.is paper discusses more severe Doppler fluctuation where a Doppler shift changes with plus or minus.e conventional method assumes a time invariant (or linearly changing) Doppler shift during a communication frame.It cannot cope with severe Doppler fluctuation, where a relative speed between transmitter and receiver units is fluctuating within a communication frame.

e
influence of Doppler fluctuation is investigated by applying various Doppler shift patterns into an OFDM block.First, we explain our Doppler fluctuation model illustrated in Figure 5, comparing two types of Doppler shift models.e constant Doppler shift model gives the same direction in the sound and transmitter velocity vectors, where a constant Doppler shift of Δ C is observed.In the Doppler fluctuation model, the direction of a transmitter unit swings during sending one OFDM frame.e Doppler shift changes Δ C , Δ C + Δ, and Δ C − Δ due to the relation between sound and transmitter velocity vectors.

Figure 9 :
Figure 9: Conceptions of single and parallel resampling techniques.(a) Single resampling and (b) parallel resampling.

Table 5 :
Examples of resampling ratios and number of branches.Doppler std.(Δ D f C ) and Computer Engineering locations of transmitter (TX) and receiver (RX) units are plotted on aerial photograph in Figure 11.e sea depth was about 10 m. e receiver was fixed at 2 m below the sea surface.e TX unit was located at 1 m below the surface and moved by a ship with meandering trajectory.e average ship' speeds were about 3.7 km/h (2 knot) and 5.6 km/h (3 knot) in Test 1 and Test 2. e relative Doppler speeds between TX and RX units are not the same as the ship speeds because the directions of the ship do not agree with those of sound propagation.

− 4 .
e baseline degrades communication performance in the presence of Doppler, where most of frames have a larger BER close to 0.5.e single resampling can decrease BERs in TX RX Max.TX-RX distance 298 m Relative speed -4.3 to 5.3 km/
is paper improved a resampling technique for large Doppler uctuation in underwater acoustic communication.

Figure 13 :Figure 14 :Figure 15 :
Figure 13: Results of CNR and relative Doppler speed in Test 1.

Figure 16 :Figure 17 :
Figure 16: Results of BER and number of branches in Test 2.

Table 2 :
EVM results for various Doppler shift patterns and resampling ratios.

Table 3 :
BER results Doppler shift patterns and resampling ratios.

Table 4 :
Statistical results based on short-term Doppler shifts.

Table 7 :
Summary of experimental results.