The Scientific World Journal

Volume 2016, Article ID 7528353, 11 pages

http://dx.doi.org/10.1155/2016/7528353

## An Acoustic OFDM System with Symbol-by-Symbol Doppler Compensation for Underwater Communication

^{1}Graduate School of Engineering and Science, University of the Ryukyus, No. 1 Senbaru, Nishihara, Okinawa, Japan^{2}Department of Information Engineering, University of the Ryukyus, No. 1 Senbaru, Nishihara, Okinawa 9030213, Japan

Received 5 October 2015; Revised 20 January 2016; Accepted 26 January 2016

Academic Editor: Kah Chan Teh

Copyright © 2016 Tran MinhHai 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.

#### Abstract

We propose an acoustic OFDM system for underwater communication, specifically for vertical link communications such as between a robot in the sea bottom and a mother ship in the surface. The main contributions are (1) estimation of time varying Doppler shift using continual pilots in conjunction with monitoring the drift of Power Delay Profile and (2) symbol-by-symbol Doppler compensation in frequency domain by an ICI matrix representing nonuniform Doppler. In addition, we compare our proposal against a resampling method. Simulation and experimental results confirm that our system outperforms the resampling method when the velocity changes roughly over OFDM symbols. Overall, experimental results taken in Shizuoka, Japan, show our system using 16QAM, and 64QAM achieved a data throughput of 7.5 Kbit/sec with a transmitter moving at maximum 2 m/s, in a complicated trajectory, over 30 m vertically.

#### 1. Introduction

Underwater acoustic communication has been receiving a lot of attention recently since it facilitates new industries and applications such as deep-sea mining, ocean monitoring, and submarine communication. We use acoustic OFDM and particularly aim to a vertical link communication between a robot at the sea bottom and a mother ship in the surface. One of the greatest challenges we encountered is the severe time varying Doppler shift. First, due to low propagation speed of sound in water 1500 m/s, the frequency offset caused by Doppler is significant compared to subcarrier space. For example, it might be up to 50% of subcarrier in our system. Second, while high frequency acoustic signal provides high data speed, it is attenuated quickly over short distance. Usually, to cover a range of few kilometers, frequency carrier around 24 kHz is used. Therefore, in many cases, acoustic OFDM systems can be considered as a wideband OFDM system since bandwidth and carrier frequency are comparable. For example, we utilize a carrier frequency of 24 kHz which is three times of system bandwidth of 8 kHz. To support further distance, lower carrier frequency is used, and so the system bandwidth is getting closer to the carrier frequency. Consequently, each subcarrier experiences a different amount of Doppler shift depending on the position of the subcarrier, that is the position-dependent Doppler shift or the so-called nonuniform Doppler. Methods for mitigating the time varying Doppler shift can be classified in to two main groups.

In radio wireless communication, state-of-the-art methods for mitigating the time varying channel were proposed in [1–5]. In short, those methods are capable of dealing with a Doppler spread up to 10% of subcarrier space and consider a general channel model with many delay paths, and each path has a different Doppler. However, in our case, the Doppler shift might be up to 50% of subcarrier space, and all paths have a similar Doppler shift. Therefore, applying the state-of-the-art methods in radio wireless communication is not reasonable.

In underwater wireless communication, a class of method called resampling based method has been proposed recently in [6–13]. The resampling based method considered the time expansion/compression caused by Doppler and used resampling in the time domain to compensate Doppler. A typical resampling based method was proposed in [11] and achieved impressive experimental results. However, since this method resamples a data frame of many OFDM symbols with a single factor, it does not work well when the velocity changes roughly over OFDM symbols. In addition, this method requires storing an entire data frame of many OFDM symbols to estimate the time expansion/compression. Most importantly, the Doppler effect does not always manifest itself significantly in time expansion/compression, so high accuracy estimation and time scale are not easy. For example, a moving speed of 1 m/s causes a Doppler shift of 16 Hz equivalent to 16% of subcarrier space (), but the expansion/compression is only 1 (sample/an OFDM symbol).

Our proposal overcomes the drawbacks of the resampling based method. Our ideas are using continual pilots (CP) to track Doppler shift over each OFDM symbol and compensating Doppler symbol-by-symbol in the frequency domain rather than resampling in time domain. Though velocity changed roughly during pulling/pushing transmitters in our experiments, our method tracked and compensated Doppler shift well. However, the maximum Doppler shift can be estimated by using CP as of subcarrier space in our case. To boost the estimation range, we propose a solution through monitoring the drift of Power Delay Profile (PDF) over OFDM symbols. The Doppler effect causes time expansion/compression; thus, when the FFT window is fixed at receivers PDF will be drifted over time. By measuring the drift amount of PDF, Doppler shift can be roughly estimated. Following the rough estimation is a fine Doppler shift estimation using continual pilots.

Then, the final estimation of Doppler shift is used in two stages to remove impacts of the Doppler shift. In the first stage, a simple phase derotation is performed before FFT. In the second stage, with an assumption that all delay paths has a similar Doppler rate, we separate impacts of Doppler shift from multipath channel and derive an ICI matrix which represents the position dependent Doppler shift. The ICI matrix is constructed using only the final estimation of Doppler shift and does not require estimation of channel transfer function yet. Thus, ICI is removed before channel estimation that is different from conventional ICI matrix in [1–5]. Overall, simulation and experiments results show that our method outperforms the typical resampling method [11].

The rest of this paper is organized as follows. Section 2 presents signal model. The proposed system is presented in Section 3. Section 4 presents simulation and experimental results. Finally, conclusion is given Section 5.

#### 2. Signal Model

The transmitted signal of OFDM symbol can be written asHere, and is the symbol length of an OFDM symbol excluded and included guard interval, respectively, and is the guard interval length. Totally, subcarriers are utilized to carry information data. and are carrier frequency and subcarrier space, respectively. denotes data at subcarrier of OFDM symbol . The relative moving between transmitters and receivers caused a Doppler rate as Here, is the relative moving speed between a transmitter and receivers, and is propagation speed of sound in the water. The time varying Doppler rate is assumed constant within two successive OFDM symbols but changes over OFDM symbols. In addition, we assumed that there are multipaths; each path has a gain of and a delay of , and all paths have a similar Doppler rate . Thus, the received pass-band signal is written as follows:In the time domain, the Doppler effect manifests itself in time expansion/compression that is over an OFDM symbol. Here, is number of discrete samples of an OFDM symbol, and is a sampling period. A straightforward idea is resampling the distorted signal to compensate the Doppler effect [6–13]. Different from those methods, we analyze and compensate impacts of the Doppler in frequency domain. After downconversion, the received signal at baseband can be written asAs in (4), all subcarriers experience a common frequency offset as . Each subcarrier experiences a different frequency offset of as depending on the position of the subcarrier. This is called position-dependent frequency offset, or the so-called nonuniform Doppler shift in [12]. The position-dependent frequency offset significantly degrades performance of high modulation such as 64QAM. In our case, a moving speed of 1 m/s causes the common Doppler shift of 16 Hz which is equal to 16% of subcarrier space. In addition, the edge subcarriers corresponding to suffers a frequency offset of ±2.5 Hz which is equivalent to of subcarrier space. The central subcarrier does not experience this kind of frequency offset. Therefore, we must take position-dependent frequency offset into account. Estimation of the Doppler rate and compensation of its impacts are presented in the next section.

#### 3. The Proposed System

Transducers attached to the bottom of the ship swing due to ocean wave and the robot at the sea bottom also move in a complicated trajectory. Therefore, time varying Doppler shift changes over OFDM symbols. To support such a case, the highlight of our system are time varying Doppler shift estimation, and symbol-by-symbol nonuniform Doppler compensation. In addition, impulsive noise cancellation [14–16] also is incorporated in our system. System parameters are shown in Table 1 and the overall system architecture is shown in Figure 1.