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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 cyclic-prefixed (CP) or zero-padded (ZP) orthogonal-frequency division-multiplexing (OFDM) waveforms. For a CP-OFDM preamble, a self-correlation method allows for blind Doppler scale estimation based on an embedded repetition structure while a cross-correlation method is available with the knowledge of the waveform. For each received ZP-OFDM block, the existence of null subcarriers allows for blind Doppler scale estimation. In addition, a pilot-aided method and a decision-aided method are applicable based on cross-correlation 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.

Underwater acoustic communications and networking have been under extensive investigation in recent years [

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.

One approach is to use a pulse train which is formed by the repetition of a

The other approach is to use a

Top: Doppler scale estimation with Doppler-insensitive waveforms. Bottom: Doppler scale estimation with Doppler-sensitive waveforms.

In this paper, we focus on an underwater acoustic communication system using zero-padded orthogonal-frequency division-multiplexing modulation (ZP-OFDM), in which pilot subcarriers and null subcarriers are usually multiplexed with data subcarriers for channel estimation and residual Doppler shift mitigation, respectively [

The data burst structure considered in this paper, which consists of a special CP-OFDM preamble and multiple ZP-OFDM blocks.

By exploiting the cyclic repetition structure of the CP-OFDM preamble, a blind estimation with a bank of self-correlators was proposed in [

The contributions of this paper are the following.

We carry out extensive performance comparisons among the aforementioned Doppler estimation methods. Specifically, we focus on the OFDM transmission format in Figure

We extend our investigation to a multiuser OFDM setting, where different users could have different Doppler scaling factors [

The rest of this paper is as follows. Different Doppler scale estimation methods for CP-OFDM and ZP-OFDM waveforms are presented in Sections

Consider a CP-OFDM preamble structure in Figure

Let

Consider a multipath channel which consists of

After transmitting the passband signal

If all the paths in the channel have the same Doppler scale factor

By exploiting the structure in (

Rather than exploiting the structure of the CP-OFDM preamble, the cross-correlation-based method can be used, since the transmitted preamble is known at the receiver. Taking the basic unit of duration

As described in [

After transmitting the ZP-OFDM symbol through a multipath channel defined in (

In [

Assume that coarse synchronization is available from the preamble. After truncating each ZP-OFDM 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

As introduced above, a set of subcarriers

The joint time-of-arrival and Doppler scale estimation is achieved via

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 time-domain waveform, by replacing

Similar to the pilot-aided method, the decision-aided method performs the joint time-of-arrival and Doppler scale estimation via

Relative to the pilot-aided method, the decision-aided 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 decision-aided method has knowledge about both the data and pilot symbols. Let

The OFDM parameters are summarized in Table

OFDM parameters in simulations.

System parameters | CP-OFDM | ZP-OFDM |
---|---|---|

Center frequency: | 13 kHz | 13 kHz |

Bandwidth: | 4.88 kHz | 4.88 kHz |

# of subcarriers: | ||

Time duration: | ||

Guard interval: |

Three UWA channel settings are tested.

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

In channel settings 1 and 2, the ground truths of

For the single-path channel, Figure

Performance of different estimators for the CP-OFDM preamble in single-path and multipath channels (channel settings 1 and 2).

For the multipath channel with a single Doppler speed, Figure

Relative to the RMSE performance in the single-path channel, a considerable performance degradation can be observed for the cross-correlation method in the multipath channel, whereas the performance of the self-correlation method is quite robust. The reason for the difference lies in the capability of the self-correlation method to collect the energy from all paths for Doppler scale estimation, while the cross-correlation method aims to get the Doppler scale estimate from only one path, the strongest path.

Figure

Performance of different estimators for ZP-OFDM in single-path channels (channel setting 1). The CRLB with all data known is included as a benchmark.

Figure

Performance of different estimators for ZP-OFDM in multipath channels with a common Doppler scale (channel setting 2).

The self-correlation method for the CP-OFDM preamble is closely related to the null-subcarrier-based blind method for ZP-OFDM. This can be easily verified by rewriting (

Figure

Null-subcarrier-based method in ZP-OFDM and CP-OFDM.

With channels generated according to the channel setting 3, Figure

The BLER performance in multipath multi-Doppler channels (channel setting 3).

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

This

The CP-OFDM and ZP-OFDM parameters and signal structures are identical to that in the simulation, as listed in Table

Figure

MACE10: Estimated Doppler speeds for 30 data bursts in MACE10, where each data burst has 20 OFDM blocks. The time interval between two consecutive date bursts is around 4 mins.

Estimated channel impulse responses for two different blocks at different bursts.

File ID: 1750155F1978_C0_S5

File ID: 1750155F2070_C0_S5

Based on the recorded files, we carried out two tests.

In this test, we focus on one single file (file ID:

MACE10: Performance comparison of Doppler estimation approaches, file ID: 1750155F1954_C0_S5.

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

One can see that the methods for ZP-OFDM outperform the methods for CP-OFDM, as the Doppler scale itself is continuously changing from block to block, as illustrated in Figure

MACE10: BLER Performance using different Doppler estimation methods by adding artificial noise to the received signal,

Adding noise with power

Added noise with power 2

If the transmitters in a multi-input multi-output (MIMO) system are co-located, the Doppler scales corresponding to all transmitters are similar, and hence a single-user blind Doppler scale estimation method would work well, as done in [

We simulate a two-user 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

Pilot- and decision-aided Doppler scale estimation in a distributed two-user ZP-OFDM system.

The null-subcarrier-based blind estimation method exploits the transmitted OFDM signal structure. Since all the users share the same positions of null subcarriers, there is a user-association problem even when multiple local minimums are found. We simulate a two-user system where the Doppler speeds of user 1 and user 2 are uniformly distributed within

Illustration of the objective functions of the null-subcarrier-based method in a two-user system

Successful case

Failed case

This paper compared different methods for Doppler scale estimation for a CP-OFDM preamble followed by ZP-OFDM data transmissions. Blind methods utilizing the underlying signalling structure work very well at medium to high SNR ranges, while cross-correlation-based 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, cross-correlation approaches are more robust against multiuser interference than blind methods.

This work is supported by the ONR Grant N00014-09-1-0704 (PECASE) and the NSF Grant ECCS-1128581. The authors thank Dr. Lee Freitag and his team for conducting the MACE10 experiment.