# Channel Equalization for Single Carrier MIMO Underwater Acoustic Communications

- Jun Tao
^{1}, - Yahong Rosa Zheng
^{2}, - Chengshan Xiao
^{2}Email author, - T. C. Yang
^{3}and - Wen-Bin Yang
^{4}

**2010**:281769

https://doi.org/10.1155/2010/281769

© Jun Tao et al. 2010

**Received: **28 October 2009

**Accepted: **18 May 2010

**Published: **15 June 2010

## Abstract

Multiple-input multiple-output (MIMO) underwater acoustic (UWA) channels introduce both space-time interference (STI) and time-varying phase distortion for transmitted signals. In such cases, the equalized symbols produced by conventional equalizer aiming for STI cancelation suffer phase rotation and thus cannot be reliably detected. In this paper, we propose a new equalization scheme for high data rate single carrier MIMO UWA channels. Different from existing methods employing joint equalization and symbolwise phase tracking technology, the proposed scheme decouples the interference cancelation (IC) operation and the phase compensation operation, leading to a generalized equalizer structure combining an IC equalizer with a phase compensator. The decoupling of the two functionalities leads to robust signal detection, which is most desirable in practical UWA applications. MIMO linear equalizer (LE) is adopted to remove space-time interference, and a groupwise phase estimation and correction method is used to compensate the phase rotation. In addition, the layered space-time processing technology is adopted to enhance the equalization performance. The proposed equalization scheme is tested to be very robust with extensive experimental data collected at Kauai, Hawaii, in September 2005, and Saint Margaret's Bay, Nova Scotia, Canada, in May 2006.

## 1. Introduction

Underwater acoustic (UWA) channel is recognized as one of the most challenging channels in practical use [1]. The obstacles imposed by the water media on acoustic propagation are reflected in four aspects. First, the available channel bandwidth is very limited due to the frequency-dependent attenuation. For example, in medium-range UWA communications, the bandwidth is on the order of a few tens of kilohertz. Second, the channel delay spread is very long due to the rich scattering environment. For instance, it could be over several tens of milliseconds (ms), leading to an equivalent discrete-time channel with several tens or even hundreds of channel taps in contrast to less than twenty taps in radio frequency (RF) communications. Third, the Doppler effect is very significant due to the low propagation speed of sound (about 1500 m/s in water). On one hand, the motion-induced Doppler shift causes a normalized carrier frequency offset (CFO) on the order of to , compared to to in RF channels. On the other hand, the motion-induced waveform compression or dilation incurs nonnegligible symbol offset requiring signal resampling. Finally, the temporal variation of the UWA channel is very fast due to the dynamics of the water mass, which imposes difficulty on both channel estimation and phase tracking.

In the past three decades, significant progress has been achieved in UWA communications [2–14]. Earlier UWA communications adopted noncoherent frequency-shift keying (FSK) technology which enabled simple energy-based signal detection combating the unpleasant effect of channel reverberation [2]. The drawback of FSK lies in its low transmission rate and also low bandwidth efficiency. The partial coherent modulation of differential phase shift keying (DPSK) was then chosen to achieve a bandwidth efficiency between noncoherent and fully coherent systems. It was until early 1990s, UWA transmission using the bandwidth-efficient coherent modulation appeared in [3]. Different from FSK, coherent transmission adopting modulations like phase shift keying (PSK) and quadrature amplitude modulation (QAM) requires proper cancelation of intersymbol interference (ISI) and compensation of phase distortion in signal detection; both tasks become very difficult under hash UWA channel conditions. Passive-phase conjugation (PPC) [4] and time reversal (TR) [5] technologies, both having different principles from equalization, have been proposed to mitigate ISI. The detection using PPC technology, however, has poor performance when only a small number of receiving hydrophones are available [6]. As a result, equalization technology is more commonly adopted for coherent detection. Generally, equalization can be performed in either time-domain (TD) [7–11] or frequency-domain (FD) [12–14]. In [7, 8], the classic joint design of decision feedback equalizer (DFE) and phase-locked loop (PLL) has been proposed, and its iterative implementation can be found in [9]. In [10], by coupling PPC technology with a single-channel DFE, the correlation-based DFE is proposed and tested to be robust to different acoustic environments. The phase rotation is tracked with PLL technology. In [11], linear equalization combined with proper phase compensation has been proposed to minimize error propagation due to incorrect decision feedback. In [12], single-carrier frequency-domain equalization (SC-FDE) followed by phase compensation is proposed for single-carrier systems, and the frequency-domain equalization for multiple-carrier orthogonal frequency division multiplexing (OFDM) systems has been proposed in [13, 14]. In [13], equalization is performed with adaptive channel estimation and phase tracking method. In [14], pilot-aided channel estimation is adopted for equalization, and a two-step Doppler compensation is adopted to remove phase rotation. While FD equalization enables low-complexity implementation even over highly dispersive channel, it usually requires extra guard intervals (GIs) among transmission blocks, which sacrifices the data transmission efficiency. Moreover, the inherent sensitivity of OFDM systems to carrier frequency offset makes robust signal detection very challenging especially with moving transceivers.

Despite the diverse equalization schemes, the demonstrated data rate of UWA communication is relatively low due to the natural limitation on the available channel bandwidth. In recent years, researchers have started to explore the spatial structure of the oceans to fundamentally improve the transmission rate. In the past years, MIMO UWA communications have been investigated in [15–19]. In [15], the number of the available degrees of freedom in the UWA channel is studied. In [16], coherent MIMO transmission has been presented, using a time reversal approach. In [17], the joint DFE and PLL scheme originally proposed in [7] for single input multiple output (SIMO) systems has been extended to MIMO cases. In [18], turbo linear equalization has been used for MIMO UWA communication. The FD equalization schemes proposed in [12, 14] have also been extended to MIMO systems in [19, 20], respectively.

In this paper, we propose a new time-domain MIMO equalization scheme for single carrier UWA communications. Different from conventional schemes performing joint equalization and phase tracking [3, 7–9, 17], where the requirement for careful tuning of DFE and PLL parameters makes the system less stable [1], the new scheme decouples the interference-cancelation functionality and phase-synchronization functionality leading to a generalized equalizer structure consisting of an interference-cancelation (IC) equalizer and a phase compensator. MIMO linear equalizer (LE) is adopted to achieve low-complexity equalization and also to avoid the error propagation in DFE especially under harsh channel conditions. A novel groupwise phase estimation and correction method proposed in [21], which is insensitive to noise disturbance, is used to compensate phase rotations in the equalized symbols. The proposed equalization scheme has been adopted in a layered receiver structure for UWA communications and has been tested by high-rate MIMO experimental data measured off the northwestern coast of Kauai, Hawaii, in September 2005, and by both moving-source and fixed-source SIMO experimental data measured at Saint Margaret's Bay, Nova Scotia, Canada, in May 2006. We have achieved successful equalization in both experiments.

The rest of the paper is organized as follows. In Section 2, a general MIMO UWA system model is given. Based on the system model, MIMO channel estimation is introduced in Section 3, as the basis for equalizer design. The new MIMO equalization scheme is then developed in Section 4, where the MIMO IC equalization, the groupwise phase estimation and compensation, and the layered space-time processing technology are discussed, respectively. Section 5 reports the results on experimental data processing, and conclusion is drawn in Section 6.

## 2. MIMO System Model

where is the effective transmission symbol of the th transducer observed at the receiver, and are the th complex fading coefficient and the phase drift of the time-varying subchannel between the th transducer and the th hydrophone, and is the channel length. The phase drift is a combining effect of the average Doppler shift, , the instantaneous Doppler, , and the coarse synchronization phase error, , and can be expressed as , where is the symbol interval. The term is the sample of a zero-mean additive white Gaussian noise (AWGN) with power , on the th hydrophone. For practical UWA channels, the fading coefficient usually changes slower than the instantaneous phase ; so it is appropriate to treat them separately [17].

where , , and are the received symbol, the fading coefficient, the phase drift, and the additive noise after Doppler preprocessing, respectively. The phase term, , may contain residual Doppler shift effect due to nonideal Doppler shift estimation and compensation. The noise is still zero-mean AWGN with variance power .

## 3. Channel Estimation for MIMO UWA Communications

where denotes matrix Hermitian transpose. The estimation in (7) is performed on all hydrophones to obtain MIMO channel estimation. It is noted that to guarantee the system equation (6) not to be underdetermined, a minimum of pilot symbols are required for each of the transducers. Last, the same channel estimation procedure discussed above will also be adopted in the decision-directed mode, where the previously detected symbols instead of the pilot symbols are used for channel estimation.

## 4. New Equalization Scheme for MIMO UWA Communication

A new equalization scheme is discussed in this section, where the conventional equalization is first adopted to cancel the space-time interference among transmitted symbols, and then a novel phase estimation and compensation method is applied to remove the phase rotations in the equalized symbols. The layered receiver structure adopting the proposed equalization scheme is then demonstrated.

### 4.1. MIMO Equalization for Space-Time Interference Cancelation

where
are nonnegative integers, and
denotes the
th linear equalizer coefficient corresponding to the received sample of the *m* th hydrophone for equalizing symbols of the
th stream. Without loss of generality, the same values of
are used for all
pairs, resulting in
equalizer taps in total.

where the derivation details are referred to the Appendix. In (13), the definitions of the channel matrix , the normalized transmission symbol correlation matrix , and the signal-to-noise ratio (SNR) are referred to (A.4), (A.6b), and (A.7), respectively. Since is constant, the MIMO LE matrix only depends on the knowledge of MIMO channel and SNR.

Remark 4.1.

In (13), two alternative solutions for the MIMO LE matrix are provided. In the first solution (first equality), matrix inversion of order is required. In the second solution, matrix inversion of order is involved. Since matrix inversion is the main source of the computational complexity, the solution with smaller-order matrix inversion is always favored in practical MIMO systems.

where is the diversity combining gain of hydrophones, is the overall residual interference, and is the effective noise consists of the residual interference and additive noise in the equalized symbol. Obviously, regardless of the effective noise, the equalized symbol in (16) is an amplitude-scaled and phase-rotated version of the original symbol . The phase rotation is a complicated term caused by phase drift . For systems employing coherent modulation schemes like phase shift keying (PSK), the phase rotation is hostile and must be compensated, which is the topic of the next subsection.

### 4.2. Groupwise Phase Estimation and Compensation

The groupwise phase estimation and correction method proposed in [21] is adopted to handle the phase rotations in the equalized symbol , as shown in (16). The motivation for the groupwise phase estimation and correction method comes from the fact that the instantaneous phase drift changes gradually while not arbitrarily from time to time due to the nature of ocean waters. In other words, the rotating phase tends to be a constant over a small group of consecutive equalized symbols. The procedure for performing the groupwise phase estimation and compensation algorithm is presented in the following.

Initialization

Step 1.

Step 2.

Step 3.

Step 4.

Increment by 1, repeat Steps 1–3 till .

The phase-compensated symbol is then ready for detection. It is pointed out that if the last group has less than symbols, then the calculation through (19)–(23) needs to be carried out based on the actual number of symbols. Finally, the groupwise phase estimation method takes the advantage of insensitivity to noise perturbations, due to the averaging operation in (21).

### 4.3. Layered Space-Time Processing

Layered space-time processing was first proposed in [24], for frequency-flat fading channels. It was extended to frequency-selective fading channels in [25]. The basic idea of the layered time-space processing is to detect multiple data streams one by one in a specific order [26], so that the overall detection performance of all streams can be improved compared to joint detection.

where denotes the received signal with the interference of the previous streams already subtracted out and is ready to be used for detecting the th stream. When detecting the th stream, we have . The procedure in (24)-(25) is repeated until all streams are detected.

## 5. Experimental Results

The layered receiver structure adopting the proposed equalization scheme as shown in Figure 1 has been tested by two undersea experiments: Makai05 and Unet06. We present the details on data processing for both experiments in this section.

### 5.1. Results of Makai05 Experiment

Single-band (SB) and multiband (MB) MIMO underwater experiments were conducted off the northwestern coast of Kauai, Hawaii, in September 2005. In MB experiment, six signal bands each having a symbol rate of 2 kilo symbols per second (ksps) were used. The adoption of MB transmission aims to reduce the equivalent symbol-spaced channel length (thus reduce the equalization complexity), while still achieve a high data rate. Its spectral efficiency, however, is lower than SB transmission due to the insertion of guard bands among multiple signal bands. Signal detection for MB transmission has been presented in [17], and no results for SB transmission have been previously reported yet.

In this paper, we focus on SB experiment, which further includes low band (LB) transmission and high band (HB) transmission. In LB transmission, the carrier frequency was kHz and the symbol interval was 0.1 ms. The occupied channel bandwidth was kHz due to the use of a pulse shaping filter with roll-off factor 0.4. In HB transmission, the carrier frequency was kHz and the symbol interval was 0.05 ms. The occupied channel bandwidth was kHz due to a pulse shaping filter with roll-off factor 0.25. The modulations included BPSK, QPSK, and 8PSK for both LB and HB transmissions. The transmitter was a ten-transducer array with 2 meters separation between adjacent transducer elements and was deployed over the side of the Kilo Moana research vessel. The receiver consisted of eight hydrophones with 2 meters separation between adjacent hydrophone elements and was allowed to drift freely. The transmission range was 2 kilometers (km).

*related channel energy*is defined as the summation of all related subchannel energies. Then a simple ordering criterion is to compare the

*related channel energies*among streams, and the stream having larger

*related channel energy*is detected earlier.

*related channel energy*in BPSK case as shown in Figure 5. In contrast, stream one has a larger

*related channel energy*than stream two in QPSK case, as shown in Figure 6. Third, the BER performance of all packets is improved with STTC decoding. The even-indexed packets have more significant improvement after STTC decoding than the odd-indexed packets, due to the use of symbol interleaving.

Packet index | Uncoded BER of Tx 1 | Uncoded BER of Tx 2 | Uncoded BER of Tx 1 and 2 | BER after STTC decoding |
---|---|---|---|---|

1 | 2.800e-3 | 4.178e-3 | 3.489e-3 | 2.000e-4 |

2 | 4.237e-4 | 1.695e-4 | 2.966e-4 | 0 |

3 | 1.556e-3 | 9.333e-4 | 1.244e-3 | 1.111e-4 |

4 | 1.316e-4 | 5.482e-4 | 3.399e-4 | 0 |

5 | 2.412e-4 | 1.096e-4 | 1.695e-4 | 6.579e-5 |

6 | 4.240e-5 | 1.271e-4 | 8.475e-5 | 0 |

7 | 8.114e-4 | 5.044e-4 | 6.579e-4 | 6.579e-5 |

8 | 1.059e-4 | 6.360e-5 | 8.475e-5 | 0 |

Mean | 7.645e-4 | 8.294e-4 | 7.954e-4 | 5.533e-5 |

Packet index | Uncoded BER of Tx 1 | Uncoded BER of Tx 2 | Uncoded BER of Tx 1 and 2 | BER after STTC decoding |
---|---|---|---|---|

1 | 1.656e-3 | 1.756e-1 | 8.863e-2 | 6.984e-2 |

2 | 1.126e-4 | 1.707e-2 | 8.592e-3 | 1.374e-3 |

3 | 1.351e-4 | 1.498e-3 | 8.164e-4 | 2.252e-5 |

Mean | 6.346e-4 | 6.472e-2 | 3.268e-2 | 2.375e-2 |

Packet index | Uncoded BER of Tx 1 | Uncoded BER of Tx 2 | Uncoded BER of Tx 1 and 2 | BER after STTC decoding |
---|---|---|---|---|

1 | 1.190e-4 | 1.212e-3 | 6.656e-4 | 1.082e-4 |

2 | 9.740e-5 | 7.359e-4 | 4.167e-4 | 0 |

3 | 1.840e-4 | 1.190e-3 | 6.872e-4 | 7.576e-5 |

4 | 7.325e-3 | 7.993e-3 | 7.659e-3 | 1.064e-3 |

5 | 6.494e-5 | 1.027e-2 | 5.168e-3 | 4.361e-3 |

6 | 1.447e-2 | 2.103e-2 | 1.775e-2 | 2.597e-4 |

Mean | 3.710e-3 | 7.072e-3 | 5.391e-3 | 9.781e-4 |

### 5.2. Results of Unet06 Experiment

SIMO UWA communication experiments with both moving-source transmission and fixed-source transmission were conducted at Saint Margaret's Bay, Nova Scotia, Canada, in May 2006. For moving-source transmission, the transmitter was deployed 21 meters deep in the water and towed at a speed up to 4 knots. The communication distance was ranging from 1 km to 3 km. For fixed-source transmission, the transmitter was suspended in water at 21 meters depth and 44 meters above the sea bottom, and the transmission range was fixed as 3.06 km. The receiver consisted of eight hydrophones arranged unequally on a 1.86-meter vertical array, which was suspended 30 meters deep in the water. QPSK modulation was used with a symbol rate of 4 ksps. The carrier frequency was kHz.

*m*-sequence of length 1023 is embedded in the packet, and the data payload carries 40397 symbols. The whole packet has a time duration of 15 seconds.

*m*-sequence attributing to its sensitivity to Doppler spread. In the left subfigure of Figure 12, the scattering function of the first moving-source packet in Table 5 is demonstrated. It is obvious that the Doppler spectrum centers around the average Doppler shift. For comparison, the scattering function for a fixed-source packet is also shown in the right subfigure. Since there is no relative transceiver motion, the Doppler spectrum centers around zero in this scenario. The average Doppler shift was compensated in the moving-source packet before detection started.

Doppler shift estimation in moving-source transmission (Hz).

Channel | Packet | ||||||
---|---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | 7 | |

1 | 15.98 | 15.71 | 12.44 | 10.80 | 10.79 | 11.25 | 8.29 |

2 | 15.98 | 15.71 | 12.44 | 10.80 | 10.79 | 11.25 | 8.38 |

3 | 15.98 | 15.71 | 12.44 | 10.80 | 10.79 | 11.25 | 8.02 |

4 | 15.98 | 15.71 | 12.44 | 10.80 | 10.79 | 11.25 | 8.02 |

5 | 15.98 | 15.71 | 12.44 | 10.80 | 10.79 | 11.25 | 8.46 |

6 | 16.16 | 15.71 | 12.44 | 10.89 | 10.79 | 11.25 | 8.36 |

7 | 15.98 | 15.71 | 12.44 | 10.80 | 10.79 | 11.25 | 8.26 |

8 | 15.98 | 15.71 | 12.44 | 10.80 | 10.79 | 11.25 | 8.29 |

Average uncoded BER for Unet06 Experiment.

Number of combining channels | Moving Source | Fixed Source |
---|---|---|

1 | 3.027e-1 | 3.135e-1 |

2 | 2.778e-1 | 2.139e-1 |

3 | 2.083e-2 | 1.064e-2 |

4 | 1.017e-2 | 1.740e-3 |

5 | 3.455e-3 | 1.490e-4 |

6 | 7.399e-4 | 1.366e-4 |

7 | 7.222e-4 | 6.621e-5 |

8 | 6.248e-4 | 3.104e-5 |

## 6. Conclusion

We have demonstrated a new time-domain MIMO equalization scheme for high data rate single-carrier underwater acoustic communications, where the separate interference cancelation and phase compensation operations have been performed during detection. MIMO linear equalization was operated in an ordered successive interference cancelation fashion to achieve enhanced performance. A novel groupwise phase estimation and compensation algorithm was used to remove the phase distortion in the equalized symbols. MIMO channel was estimated with pilot symbols in training mode and was tracked using previously detected symbols in decision-directed mode, incurring no more than training overhead, compared to in existing receiver designs. The proposed equalization scheme was tested by extensive experimental data measured off the northwestern coast of Kauai, Hawaii, in September 2005, and at Saint Margaret's Bay, Nova Scotia, Canada, in May 2006. Processing results have shown the effectiveness and robustness of the proposed new equalization scheme under different UWA transmission conditions.

## Appendix

### A. Calculation of MIMO LE Matrix

## Declarations

### Acknowledgments

This work was supported in part by the Office of Naval Research under Grants N00014-07-1-0219 and N00014-10-1-0174 and the National Science Foundation under Grants ECCS-0846486 and CCF-0915846. The work of T. C. Yang and W.-B. Yang was supported by the Office of Naval Research. The authors are grateful to Professor Tolga Duman and Dr. Subhadeep Roy for providing the transmitted data of MakaiEx05.

## Authors’ Affiliations

## References

- Kilfoyle DB, Baggeroer AB: State of the art in underwater acoustic telemetry.
*IEEE Journal of Oceanic Engineering*2000, 25(1):4-27. 10.1109/48.820733View ArticleGoogle Scholar - Garrood DJ: Application of the MFSK acoustical communication system.
*Proceedings of the MTS/IEEE Oceans Conference, 1981, Boston, Mass, USA*67-71.Google Scholar - Stojanovic M, Catipovic J, Proakis JG: Adaptive multichannel combining and equalization for underwater acoustic communications.
*Journal of the Acoustical Society of America*1993, 94(3, part 1):1621-1631. 10.1121/1.408135View ArticleGoogle Scholar - Rouseff D, Jackson DR, Fox WLJ, Jones CD, Ritcey JA, Dowling DR: Underwater acoustic communication by passive-phase conjugation: theory and experimental results.
*IEEE Journal of Oceanic Engineering*2001, 26(4):821-831. 10.1109/48.972122View ArticleGoogle Scholar - Edelmann GF, Akal T, Hodgkiss WS, Kim S, Kuperman WA, Song HC: An initial demonstration of underwater acoustic communication using time reversal.
*IEEE Journal of Oceanic Engineering*2002, 27(3):602-609. 10.1109/JOE.2002.1040942View ArticleGoogle Scholar - Yang TC: Differences between passive-phase conjugation and decision-feedback equalizer for underwater acoustic communications.
*IEEE Journal of Oceanic Engineering*2004, 29(2):472-487. 10.1109/JOE.2004.827122View ArticleGoogle Scholar - Stojanovic M, Catipovic JA, Proakis JG: Phase-coherent digital communications for underwater acoustic channels.
*IEEE Journal of Oceanic Engineering*1994, 19(1):100-111. 10.1109/48.289455View ArticleGoogle Scholar - Roy S, Duman T, Ghazikhanian L, McDonald V, Proakis J, Zeidler J: Enhanced underwater acoustic communication performance using space-time coding and processing.
*Proceedings of the MTS/IEEE Oceans Conference, November 2004*26-33.Google Scholar - Choi JW, Drost RJ, Singer AC, Preisig J: Iterative multi-channel equalization and decoding for high frequency underwater acoustic communications.
*Proceedings of the 5th IEEE Sensor Array and Multichannel Signal Processing Workshop, July 2008*127-130.Google Scholar - Yang TC: Correlation-based decision-feedback equalizer for underwater acoustic communications.
*IEEE Journal of Oceanic Engineering*2005, 30(4):865-880. 10.1109/JOE.2005.862126View ArticleGoogle Scholar - Tao J, Zheng YR, Xiao C, Yang TC, Yang W-B: Channel estimation, equalization and phase correction for single carrier underwater acoustic communications.
*Proceedings of the MTS/IEEE Oceans Conference, April 2008, Kobe, Japan*1-6.Google Scholar - Zheng YR, Xiao C, Yang TC, Yang W-B: Frequency-domain channel estimation and equalization for shallow-water acoustic communications.
*Physical Communication*2010, 3(1):48-63. 10.1016/j.phycom.2009.08.010View ArticleGoogle Scholar - Stojanovic M: Low complexity OFDM detector for underwater acoustic channels.
*Proceedings of the MTS/IEEE Oceans Conference, September 2006*1-6.Google Scholar - Li B, Zhou S, Stojanovic M, Freitag FL, Willett P: Multicarrier communication over underwater acoustic channels with nonuniform Doppler shifts.
*IEEE Journal of Oceanic Engineering*2008, 33(2):198-209.View ArticleGoogle Scholar - Kilfoyle DB, Preisig JC, Baggeroer AB: Spatial modulation experiments in the underwater acoustic channel.
*IEEE Journal of Oceanic Engineering*2005, 30(2):406-415. 10.1109/JOE.2004.834168View ArticleGoogle Scholar - Song HC, Roux P, Hodgkiss WS, Kuperman WA, Akal T, Stevenson M: Multiple-input-multiple-output coherent time reversal communications in a shallow-water acoustic channel.
*IEEE Journal of Oceanic Engineering*2006, 31(1):170-178. 10.1109/JOE.2005.850911View ArticleGoogle Scholar - Roy S, Duman TM, McDonald V, Proakis JG: High-rate communication for underwater acoustic channels using multiple transmitters and space-time coding: receiver structures and experimental results.
*IEEE Journal of Oceanic Engineering*2007, 32(3):663-688.View ArticleGoogle Scholar - Nordenvaad ML, Öberg T: Iterative reception for acoustic underwater MIMO Communications.
*Proceedings of the MTS/IEEE Oceans Conference, September 2006*1-6.Google Scholar - Zhang J, Zheng YR, Xiao C: Frequency-domain equalization for single carrier MIMO underwater acoustic communications.
*Proceedings of the MTS/IEEE Oceans Conference, September 2008*Google Scholar - Li B, Huang J, Zhou S, Ball K, Stojanovic M, Freitag L, Willett P: MIMO-OFDM for high-rate underwater acoustic communications.
*IEEE Journal of Oceanic Engineering*2009, 34(4):634-644.View ArticleGoogle Scholar - Xiao C, Zheng YR: Channel equalization and symbol detection for single carrier broadband MIMO systems with multiple carrier frequency offsets.
*Proceedings of the IEEE International Conference on Communications (ICC '08), May 2008, Beijing, China*4316-4320.Google Scholar - Sharif BS, Neasham J, Hinton OR, Adams AE: Computationally efficient Doppler compensation system for underwater acoustic communications.
*IEEE Journal of Oceanic Engineering*2000, 25(1):52-61. 10.1109/48.820736View ArticleGoogle Scholar - Eggen TH, Baggeroer AB, Preisig JC: Communication over Doppler spread channels—part I: channel and receiver presentation.
*IEEE Journal of Oceanic Engineering*2000, 25(1):62-71. 10.1109/48.820737View ArticleGoogle Scholar - Foschini GJ: Layered space-time architecture for wireless communication in a fading environment when using multi-element antennas.
*Bell Labs Technical Journal*1996, 1(2):41-59.View ArticleGoogle Scholar - Lozano A, Papadias C: Layered space-time receivers for frequency-selective wireless channels.
*IEEE Transactions on Communications*2002, 50(1):65-73. 10.1109/26.975751View ArticleGoogle Scholar - Wolnainsky PW, Foschini GJ, Golden GD, Valenzuela RA: V-BLAST: an architecture for achievingvery high data rates over the rich-scattering wireless channel.
*Proceedings of the International Symposium on Signals, Systems, and Electronics (ISSSE '98), September 1998, Pisa, Italy*Google Scholar - Tarokh V, Seshadri N, Calderbank AR: Space-time codes for high data rate wireless communication: performance criterion and code construction.
*IEEE Transactions on Information Theory*1998, 44(2):744-765. 10.1109/18.661517MathSciNetView ArticleMATHGoogle Scholar - Clark MV: Adaptive frequency-domain equalization and diversity combining for broadband wireless communications.
*IEEE Journal on Selected Areas in Communications*1998, 16(8):1385-1395. 10.1109/49.730448View ArticleGoogle Scholar

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