Research Article  Open Access
Lei Wan, Zhaohui Wang, Shengli Zhou, T. C. Yang, Zhijie Shi, "Performance Comparison of Doppler Scale Estimation Methods for Underwater Acoustic OFDM", Journal of Electrical and Computer Engineering, vol. 2012, Article ID 703243, 11 pages, 2012. https://doi.org/10.1155/2012/703243
Performance Comparison of Doppler Scale Estimation Methods for Underwater Acoustic OFDM
Abstract
Doppler scale estimation is one critical step needed by the resampling operation in acoustic communication receivers. In this paper, we compare different Doppler scale estimation methods using either cyclicprefixed (CP) or zeropadded (ZP) orthogonalfrequency divisionmultiplexing (OFDM) waveforms. For a CPOFDM preamble, a selfcorrelation method allows for blind Doppler scale estimation based on an embedded repetition structure while a crosscorrelation method is available with the knowledge of the waveform. For each received ZPOFDM block, the existence of null subcarriers allows for blind Doppler scale estimation. In addition, a pilotaided method and a decisionaided method are applicable based on crosscorrelation with templates constructed from symbols on pilot subcarriers only and from symbols on all subcarriers after data decoding, respectively. This paper carries out extensive comparisons among these methods using both simulated and real experimental data. Further, the applicabilities of these methods to distributed multiuser systems are investigated.
1. Introduction
Underwater acoustic communications and networking have been under extensive investigation in recent years [1, 2]. Considerable progress on the physical layer communication techniques has been made for both singlecarrier and multicarrier communications; see, for example, [3–19]. Relative to the radio channel which has relative short delay spread and slow time variation, underwater acoustic channels typically exhibit long delay spread and fast time variation. The latter brings significant Doppler effects to underwater acoustic communication systems, hence estimation of the Doppler scaling factor is one key receiver module [4, 20, 21].
Typically, Doppler scale estimation is accomplished by inserting waveforms known to the receiver during the data transmission. Two popular approaches are described in the following.(i)One approach is to use a pulse train which is formed by the repetition of a Dopplerinsensitive waveform [22], such as linearfrequencymodulated (LFM) waveform [23] and hyperbolicfrequencymodulated (HFM) waveform [24]. A transmission format with one preamble and one postamble around the data burst is usually adopted [4, 20, 25], as shown in Figure 1. At the receiver side, by detecting the timesofarrival of the preamble and postamble, thus the interval change inbetween, an average Doppler scale estimate over the whole data burst can be obtained. Thanks to the Dopplerinsensitive property of the waveforms, a singlebranchmatched filtering operation is adequate even in the presence of Doppler distortion. However, this method is only suitable for offline processing due to the processing delay.(ii)The other approach is to use a Dopplersensitive waveform with a thumbtack ambiguity function. A Dopplersensitive waveform is usually transmitted as a preamble prior to the data burst, as shown in Figure 1. At the receiver side, a bank of correlators correlates the received signal with preambles prescaled by different Doppler scaling factors, and the branch with the largest correlation peak provides the estimated Doppler scale [25]. Typical Dopplersensitive waveforms include Costa waveforms [26], msequence [27], and polyphase sequence [28].
In this paper, we focus on an underwater acoustic communication system using zeropadded orthogonalfrequency divisionmultiplexing modulation (ZPOFDM), in which pilot subcarriers and null subcarriers are usually multiplexed with data subcarriers for channel estimation and residual Doppler shift mitigation, respectively [4]. A cyclic prefixed (CP) OFDM preamble is inserted prior to data transmission for detection, synchronization, and Doppler scale estimation [29]. This transmission format, as shown in Figure 2, has been implemented on DSPbased OFDM modem prototypes [30].
By exploiting the cyclic repetition structure of the CPOFDM preamble, a blind estimation with a bank of selfcorrelators was proposed in [29]. However, it does not leverage the knowledge of the waveform itself which is known to the receiver. Taking this method as the first approach, one can easily construct the following Doppler scale estimators for the OFDM transmission in Figure 2.(i)Crosscorrelation with the CPOFDM Preamble: Given the Doppler sensitivity of the OFDM waveform, a bank of crosscorrelators can use the prescaled versions of the CPOFDM waveform as local replicas.(ii)PilotAided Method for Each ZPOFDM Block: By taking the waveform constituted by the pilotsubcarrier components as a replica of the transmitted signal, the Doppler estimation method using a bank of crosscorrelators is directly applicable.(iii)NullSubcarrier Based Blind Estimation Method for Each ZPOFDM Block: As an extension of the blind carrier frequency offset (CFO) estimation method [31], the receiver rescales the received waveform with different tentative Doppler scaling factors and uses the energy on the null subcarriers to find the best fit.(iv)DecisionAided Method for Each ZPOFDM Block: Once a ZPOFDM block is successfully decoded, the transmitted waveform corresponding to this block can be reconstructed at the receiver. Taking the reconstructed waveform as a local replica, the Doppler estimation method using a bank of correlators can be deployed to refine the Doppler scale estimation for this block. The refined Doppler scale estimate can be passed to the next block.
The contributions of this paper are the following.(i)We carry out extensive performance comparisons among the aforementioned Doppler estimation methods. Specifically, we focus on the OFDM transmission format in Figure 2 in singleuser transmissions. Both simulations and experimental results reveal that the correlationbased methods have a decent performance in the low SNR region, and the blind estimation methods can catch up or even outperform the correlation methods in the high SNR region. As a performance benchmark, the CramerRao lower bound (CRLB) is also included for singlepath channels.(ii)We extend our investigation to a multiuser OFDM setting, where different users could have different Doppler scaling factors [32]. Simulation results show that the correlationbased methods are robust to the multiuser interference, while the blind method suffers severe performance degradation.
The rest of this paper is as follows. Different Doppler scale estimation methods for CPOFDM and ZPOFDM waveforms are presented in Sections 2 and 3, respectively. Simulation results of these methods are provided in Section 4, and experimental results are provided in Section 5. Extension to the multiuser scenario is described in Section 6. Conclusions are contained in Section 7.
2. Doppler Scale Estimation with a CPOFDM Preamble
Consider a CPOFDM preamble structure in Figure 2, which consists of two identical OFDM symbols of length and a cyclic prefix of length in front, with the embedded structure
Let denote the system bandwidth, and define as the number of subcarriers. The baseband CPOFDM signal is where is the transmitted symbol on the th subcarrier, and is a pulse shaping window, The passband signal can be obtained as , where is the center frequency.
Consider a multipath channel which consists of paths where and denote the amplitude and delay of the th path, respectively. Throughout this paper, we assume that the amplitude is constant within each OFDM block (about 200 ms for the system considered in this paper), that is, , which leads to
After transmitting the passband signal through the multipath channel, the received passband signal is converted to baseband as , where denotes the low pass filtering operation.
2.1. SelfCorrelation
If all the paths in the channel have the same Doppler scale factor it is shown in [29] that the embedded structure in the received waveform becomes which has a repetition period regardless of the channel amplitudes.
By exploiting the structure in (7), the timeofarrival and the Doppler scale of the CPOFDM symbol in the received signal can be jointly estimated via which does not require the knowledge of the channel and the data symbols. This method can be implemented with a bank of selfcorrelators [29].
2.2. CrossCorrelation
Rather than exploiting the structure of the CPOFDM preamble, the crosscorrelationbased method can be used, since the transmitted preamble is known at the receiver. Taking the basic unit of duration as the template, the joint timeofarrival and Doppler rate estimation can be achieved via This can be implemented via a bank of crosscorrelators, where the branch yielding the largest peak provides the needed Doppler scale estimate.
3. Doppler Scale Estimation with Each ZPOFDM Block
As described in [4], a ZPOFDM signal design multiplexing pilot and null subcarriers with data subcarriers can effectively deal with fast channel variations. Assume that the ZPOFDM system has subcarriers. Let denote the symbol duration and the guard interval. The total OFDM block duration is thus . Denote , , as the nonoverlapped sets formed by the data subcarriers, pilot subcarriers, and null subcarriers, respectively, which satisfy . The baseband transmitted ZPOFDM signal can be expressed by where describes the zeropadding operation, that is,
After transmitting the ZPOFDM symbol through a multipath channel defined in (5), we denote as the received passband signal, whose baseband version is . The availability of null subcarriers, pilot subcarriers, and data subcarriers can be used for Doppler scale estimation.
3.1. NullSubcarrierBased Blind Estimation
In [29], the null subcarriers in ZPOFDM system are exploited to perform carrier frequency offset (CFO) estimation. Here in this paper, the same principle is used to estimate Doppler scale factor.
Assume that coarse synchronization is available from the preamble. After truncating each ZPOFDM block from the received signal, we resample one block with different tentative scaling factors. The total energy of frequency measurements at null subcarriers are used as a metric for the Doppler scale estimation For each tentative , a resampling operation is carried out followed by fast Fourier transform. A onedimensional grid search leads to a Doppler scale estimate.
3.2. PilotAided Estimation
As introduced above, a set of subcarriers is dedicated to transmit pilot symbols. Hence, the transmitted waveform is partially known, containing
The joint timeofarrival and Doppler scale estimation is achieved via which can be implemented via a bank of crosscorrelators.
3.3. DecisionAided Estimation
For an OFDM transmission with multiple blocks, the Doppler estimated in one block can be used for the resampling operation of the next block assuming small Doppler variation across blocks. After the decoding operation the receiver can reconstruct the transmitted timedomain waveform, by replacing by its estimate , for all in. Denote the reconstructed waveform as .
Similar to the pilotaided method, the decisionaided method performs the joint timeofarrival and Doppler scale estimation via which again is implemented via a bank of crosscorrelators. The estimated can be used for the resampling operation of the next block.
Remark 1. Relative to the pilotaided method, the decisionaided method leverages the estimated information symbols, thus is expected to achieve a better estimation performance. Assuming that all the information symbols have been successfully decoded, the decisionaided method has knowledge about both the data and pilot symbols. Let and denote the numbers of pilot and data symbols, respectively. Using the template constructed from known symbols for cross correlation achieve a dB power gain in terms of noise reduction, relative to that using the template constructed from known symbols.
4. Simulation Results
The OFDM parameters are summarized in Table 1. For CPOFDM, the data symbols at all the 512 subcarriers are randomly drawn from a QPSK constellation. For ZPOFDM, out of 1024 subcarriers, there are null subcarriers with 24 on each edge of the signal band for band protection and 48 evenly distributed in the middle for the carrier frequency offset estimation; are pilot subcarriers uniformly distributed among the 1024 subcarriers, and the remaining are data subcarriers for delivering information symbols. The pilot symbols are drawn randomly from a QPSK constellation. The data symbols are encoded with a rate nonbinary LDPC code [33] and modulated by a QPSK constellation.

Three UWA channel settings are tested.(i)Channel Setting 1: A singlepath channel: (ii)Channel Setting 2: A multipath channel with paths, where all paths have one common Doppler scaling factor: (iii)Channel Setting 3: A multipath channel with paths, where each path has an individual Doppler scaling factor:
The interarrival time of paths follows an exponential distribution with a mean of 1 ms. The mean delay spread for the channels in and is thus 15 ms. The amplitudes of paths are Rayleigh distributed with the average power decreasing exponentially with the delay, where the difference between the beginning and the end of the guard time is dB. For each path, the Doppler scale is generated from a Doppler speed (with unit m/s): where m/s is the sound speed in water. In channel settings 1 and 2, the Doppler speed is uniformly distributed within m/s. In channel setting 3, the Doppler speeds are randomly drawn from the interval m/s.
In channel settings 1 and 2, the ground truths of and are known. We adopt the rootmeansquarederror (RMSE) of the estimated Doppler speed as the performance metric, which has the unit m/s. In channel setting 3, different paths have different Doppler scales, while the Doppler scale estimator only provides one estimate. RMSE is hence not well motivated. With the estimated Doppler scale to perform the resampling operation, we will use the blockerrorrate (BLER) of the ZPOFDM decoding as the performance metric.
4.1. RMSE Performance with CPOFDM
For the singlepath channel, Figure 3 shows the RMSE performance of two estimation methods at different SNR levels. One can see a considerable gap between the selfcorrelation method and the crosscorrelation method, while in the medium to high SNR region, both methods can provide a reasonable performance to facilitate receiver decoding.
For the multipath channel with a single Doppler speed, Figure 3 shows the RMSE performance of two estimation methods. One can see that the crosscorrelation method outperforms the selfcorrelation method considerably in the low SNR region. However, the former suffers an error floor in the high SNR region, while the later does not.
Relative to the RMSE performance in the singlepath channel, a considerable performance degradation can be observed for the crosscorrelation method in the multipath channel, whereas the performance of the selfcorrelation method is quite robust. The reason for the difference lies in the capability of the selfcorrelation method to collect the energy from all paths for Doppler scale estimation, while the crosscorrelation method aims to get the Doppler scale estimate from only one path, the strongest path.
4.2. RMSE Performance with ZPOFDM
Figure 4 shows the RMSE performance of three estimation methods for ZPOFDM in singlepath channels. In the low SNR region, one can see that the decisionaided method is the best, while the nullsubcarrierbased blind method is the worst. As discussed in Remark 1, the decisionaided method achieves dB power gain relative to the pilotaided method. In the medium and high SNR region, the pilotaided method suffers an error floor due to the interference from the data subcarriers, and the nullsubcarrierbased blind method gets a good estimation performance. The CramerRao lower bound (CRLB) with a known waveform is also included as the performance benchmark, whose derivation can be carried out similar to [34, 35].
Figure 5 shows the RMSE performance of three methods in multipath channels with a common Doppler speed. For each realization, the Doppler scale, the path amplitudes, and delays are randomly generated. The RMSE corresponding to each method is calculated by averaging the estimation error over multiple realizations. Again, one can see that in the low SNR region, the decisionaided method has the best performance, while the nullsubcarrierbased blind method is the worst. Different from the performance in the singlepath channel, the decisionaided method has an error floor in the high SNR region, since it only picks up the maximum correlation peak of one path. On the other hand, the nullsubcarrier method has robust performance in the presence of multiple paths.
4.3. Comparison of Blind Methods of CP and ZPOFDM
The selfcorrelation method for the CPOFDM preamble is closely related to the nullsubcarrierbased blind method for ZPOFDM. This can be easily verified by rewriting (2) as where when is odd and when is even. The cyclic repetition pattern in is generated by placing zeros on all odd subcarriers in a long OFDM symbol of duration . Hence, the selfcorrelation implementation could be replaced by the nullsubcarrierbased implementation for the CPOFDM preamble.
Figure 6 shows the performance comparison between the blind method for ZPOFDM and that for CPOFDM in the multipath channel with one Doppler scale factor, respectively. At low SNR, typically when it’s lower than 0 dB, the nullsubcarrierbased method in CPOFDM system has a better performance than that in the ZPOFDM system, which is due to the fact that CPOFDM system has 512 null subcarriers, more than 96 null subcarriers in the ZPOFDM block. At high SNR, the nullsubcarrierbased method in ZPOFDM has better performance. The possible reason is that null subcarriers in ZPOFDM are distributed with an irregular pattern, which could outperform the regular pattern in the CPOFDM preamble.
4.4. BLER Performance with ZPOFDM
With channels generated according to the channel setting 3, Figure 7 shows the simulated BLER performance, where the received OFDM blocks are resampled with the Doppler scale estimates from different estimators and processed using the receiver from [4] and the LDPC decoder from [33]. At each SNR point, at least 20 block errors are collected.
It is expected that the OFDM system can only work when the useful signal power is above that of the ambient noise. Regarding the simulation results in Figure 5, one can see that all the methods can reach a RMSE lower than 0.1 m/s. Hence, it is not surprising that these methods lead to quite similar BLER results as shown in Figure 7. This observation is consistent with the analysis in [29] that an estimation error of 0.1 m/s introduces a negligible error.
5. Experimental Results
This mobile acoustic communication experiment (MACE10) was carried out off the coast of Martha’s Vineyard, Massachusetts, June, 2010. The water depth was about 80 meters. The receiving array was stationary, while the source was towed slowly away from the receiver and then towed back, at a speed around 1 m/s. The relative distance of the transmitter and the receiver changed from 500 m to 4.5 km. Out of the two tows in this experiment, we only consider the data collected in the first tow. There are 31 transmissions in total, with a CPOFDM preamble and 20 ZPOFDM blocks in each transmission. We exclude one transmission file recorded during the turn of the source, where the SNR of the received signal is quite low.
The CPOFDM and ZPOFDM parameters and signal structures are identical to that in the simulation, as listed in Table 1.
Figure 8 shows the estimated Doppler speeds for ZPOFDM blocks from different methods. Clearly, the Doppler speed fluctuates from block to block. Figure 9 shows the estimated channel impulse responses for two ZPOFDM blocks from two data sets, where the time interval between these two data bursts is more than 1 hour. The channels have a delay spread about 20 ms but with different delay profiles.
(a) File ID: 1750155F1978_C0_S5
(b) File ID: 1750155F2070_C0_S5
Based on the recorded files, we carried out two tests.
(A) Test Case 1
In this test, we focus on one single file (file ID: ) and compare the RMSE performance of different approaches by adding artificial noise to the recorded signal. The ground truth of the Doppler scale factor is not available. When computing the RMSE using (20) for each method, we use the estimated Doppler scale of the original file without adding the noise as the ground truth. Figure 10 shows the estimation performance of several approaches. Similar observations as the simulation results in Figures 3 and 5 are found.
(B) Test Case 2
In this test, we compare the BLER performance of an OFDM receiver where the resampling operation is carried out with different Doppler scale estimates from different methods.
Due to the relatively high SNR of the recorded signal, we create a semiexperimental data set by adding white Gaussian noise to the received signal. Define as the estimated ambient noise power in the original recorded signal. Figure 11 shows the BLER performance with different Doppler estimation approaches by adding different amount of noises to the received files.
One can see that the methods for ZPOFDM outperform the methods for CPOFDM, as the Doppler scale itself is continuously changing from block to block, as illustrated in Figure 8. Another interesting observation is that the nullsubcarrierbased blind method has slight performance improvement relative to the pilot and decisionaided methods. This agrees with the simulation results in Figure 5 that in the high SNR region, the blind estimation method does not suffer an error floor in the multipath channel, hence enjoys a better estimation performance.
(a) Adding noise with power 𝜎 2
(b) Added noise with power 2 𝜎 2
6. Extension to Distributed MIMOOFDM
If the transmitters in a multiinput multioutput (MIMO) system are colocated, the Doppler scales corresponding to all transmitters are similar, and hence a singleuser blind Doppler scale estimation method would work well, as done in [10]. However, if the transmitters are distributed, for example in a system with multiple singletransmitter users, the Doppler scales for different users could be quite different, even with opposite signs [32]. We now investigate the performance of different Doppler scale estimation methods in the presence of multiuser interference. We will use the ZPOFDM waveform as the reference design; similar conclusions can be applied to the CPOFDM preamble. Only simulated data sets are used in the following tests.
6.1. Pilot and DecisionAided Estimation
We simulate a twouser system. Each user generates a multipath channel according to channel setting 2 independently. The positions of pilot, null, and data subcarriers are the same for different users. The pilot and data symbols of different users are randomly generated and hence are different.
Figure 12 depicts the RMSE performance of the pilot and decisionaided estimation methods. Compared with the performance in the singleuser setting in Figure 5, there is performance degradation and the error floors are higher. However, both methods can achieve RMSE lower than 0.1 m/s at low SNR values. Hence, both methods have robust performance in the presence of multiuser interference.
6.2. NullSubcarrierBased Blind Estimation
The nullsubcarrierbased blind estimation method exploits the transmitted OFDM signal structure. Since all the users share the same positions of null subcarriers, there is a userassociation problem even when multiple local minimums are found. We simulate a twouser system where the Doppler speeds of user 1 and user 2 are uniformly distributed within m/s and m/s, respectively. Without adding the ambient noise to the received signal, Figure 13 demonstrates both successful and failed cases using the objective function in (12). The objective functions in the singleuser settings are also included for comparison. One can see that the multiuser interference degrades the estimation performance significantly. Hence, although the blind method developed for the single user case can be used to colocated MIMOOFDM as in [10], it is not applicable to distributed MIMOOFDM where different users have different Doppler scales.
(a) Successful case
(b) Failed case
7. Conclusion
This paper compared different methods for Doppler scale estimation for a CPOFDM preamble followed by ZPOFDM data transmissions. Blind methods utilizing the underlying signalling structure work very well at medium to high SNR ranges, while crosscorrelationbased methods can work at low SNR ranges based on the full or partial knowledge of the transmitted waveform. All of these methods are viable choices for practical OFDM receivers. In a distributed multiuser scenario, crosscorrelation approaches are more robust against multiuser interference than blind methods.
Acknowledgments
This work is supported by the ONR Grant N000140910704 (PECASE) and the NSF Grant ECCS1128581. The authors thank Dr. Lee Freitag and his team for conducting the MACE10 experiment.
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Copyright
Copyright © 2012 Lei Wan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.