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Underwater communication channels are often complicated, and in particular multipath propagation may cause intersymbol interference (ISI). This paper addresses how to remove ISI, and evaluates the performance of three different receiver structures and their implementations. Using real data collected in a high-frequency (10–14 kHz) field experiment, the receiver structures are evaluated by off-line data processing. The three structures are multichannel decision feedback equalizer (DFE), passive time reversal receiver (passive-phase conjugation (PPC) with a single channel DFE), and the joint PPC with multichannel DFE. In sparse channels, dominant arrivals represent the channel information, and the matching pursuit (MP) algorithm which exploits the channel sparseness has been investigated for PPC processing. In the assessment, it is found that: (1) it is advantageous to obtain spatial gain using the adaptive multichannel combining scheme; and (2) the MP algorithm improves the performance of communications using PPC processing.

Coherent underwater acoustic communications are challenged by acoustic channels, which are often characterized as time-varying, dispersive, sparse,

One receiver cannot avoid deep fading in time-varying channels, and thus the equalizers fail to remove ISI. With multiple sensors exploiting spatial diversity, Stojanovic

Another novel method is the time reversal mirror (TRM), originally proposed by Fink [

An alternative technique for underwater communications is proposed by Rouseff

Stojanovic [

Zhang

PPC processing requires information of the channel characteristics, which can be estimated using training symbols. Underwater channels are often sparse, especially at the high-frequency regime, where there are a few dominant arrivals. The dominant arrivals can be estimated using the matching pursuit (MP) algorithm [

The above brief introduction shows that different approaches have been proposed and have been tested in field experiments. However, the experiments were conducted under different conditions, and it is therefore difficult to compare the performance of different receiver structures. This has motivated the work of this paper. A recent field experiment was conducted to collect data over a range of 7.4 km, when three modulation schemes were used. Four data rates with a maximal data rate of 4 kilo-bits/s have been achieved. Using the same real data, we compare the performance of three receiver structures: McDFE, PPC-DFE, and PPC-McDFE. These structures are frequently discussed in the literature, and in the future we may extend the discussion to other structures and modulation schemes.

As required, information of the channel characteristics for PPC processing can be obtained by a channel probe signal or estimated using training symbols. For example, using a linear frequency modulation pulse (LFM) chirp as a channel probe signal, when the chirp is also used as a shaping pulse at the transmitter, the received LFM is immediately used for PPC processing. Alternatively, the channel is estimated using training symbols, when a root-raised-cosine pulse (RRC) is used as a shaping pulse. In this paper, we have also tested the scenario using the two shaping pulses.

The contributions of this paper include: (1) experimental assessment of the difference between two shaping pulses—LFM and RRC; (2) performance comparison of the McDFE, PPC-DFE, and PPC-McDFE structures; (3) evaluation of the block-based approach for PPC-McDFE; and (4) assessment of the MP algorithm for both PPC-DFE and PPC-McDFE, in which PPC processing is implemented in two modes—one block and multi-block.

This paper is organized as follows: Section 2 introduces the field experiment conducted in Trondheim harbor on 7 September 2011. Section 3 shows the receiver structures: (1) McDFE; (2) PPC-DFE; and (3) PPC-McDFE. Section 4 briefly introduces channel estimations for PPC processing, the LS method and the MP algorithm. In Section 5, the results are presented and discussed, and performance of the three structures is shown. Finally, Section 6 summarizes the work.

The communication experiment was conducted on 7 September 2011, in Trondheim harbor (Norway), where the water depth varies from 10 m to 400 m. The transmitter was carried by the NTNU research vessel R/V Gunnerus, and it used a hemispherical acoustic transducer deployed at a depth of 20 m. The dynamic positioning system of R/V Gunnerus was activated during the trial to reduce drifting.

A cross receiving array of 12 hydrophones was deployed from a pier, where the water depth was about 10 m. The array consisted of a vertical array of eight hydrophones (hydrophones No. 1–8) with 1 m element spacing and a horizontal array with four hydrophones (hydrophones No. 9–12) with 1.5 m element spacing. Hydrophone No. 1 was located 0.5 m below the sea surface, and the depth of the horizontal array was 4.5 m. The range between the source and the receiving array was 7.4 km.

Digital modulations of phase shift keying (BPSK), quadrature phase shift keying (QPSK), and eight quadrature amplitude modulation (8QAM) were used. The carrier frequency of the transmitted signal was 12 kHz. A 0.1 s LFM chirp with a Hanning window was used for coarse time synchronization in each data packet, and its effective bandwidth was 2.2 kHz. When the LFM was used as the channel probe signal, it was also used as a shaping pulse. As a shaping pulse, the roll-off coefficient of RCC was 1.

Sound speed profile (SSP) measured by the R/V Gunnerus is shown by the left panel of

Generally, the receiver recovers distorted information by baseband signal processing, where multipath channels are often modeled as finite filters of multiple taps. In digitized form, the received signal at _{k}_{n}_{n}_{k}

_{k}

As suggested by Song [

The receiver structure PPC-McDFE is shown of

This section briefly introduces two channel estimation methods. Using training symbols, the channel estimations for PPC processing can be obtained using both the LS method [

By combining M observed symbols,

In the channel estimation problem, the information matrix _{k}

In practice, the LS method is sensitive to noise. When a channel is sparse, the CIR consists of a large number of zeros among several dominant taps, and the LS method will suffer from the noise between dominant taps. Besides, the LS method involves matrix inversion, and it sometimes suffers ill-conditioned problem of a matrix of large eigenvalue spread.

To exploit the sparse property of channels, the channel estimation problem can be reconsidered as an approximation problem. It is assumed that the received signal vector is approximated by:
_{pi} is the _{i}_{k}_{M}_{k}_{M}_{k}_{k}

The MP algorithm selects one column in matrix _{p−1}, where _{0} = _{k}_{p}

Correspondingly, the tap value
_{p}

This iteration is terminated until the preset

Recorded signals of 15 periods are processed with parameters given in ^{1}_{ff}^{1}_{fb}_{2} is chosen as 10 time smaller than the proportional tracking constant _{1}. In subsections of 5.2 and 5.3, the performance of McDFE is selected as a benchmark.

As mentioned in Section 2.1, both LFM and RRC were used as shaping pulses. In the scenario of using LFM as a shaping pulse, the peak-to-average power ratio (PAPR) is large [

In terms of output signal-to-noise ratio (SNR),

In this subsection, the channel is estimated only once for PPC processing in each data packet. The channel is estimated using training symbols, which are specified symbols in the beginning of communications. Following PPC processing, ISI is removed by the adaptive channel equalizers.

_{n}

The results of 15 periods are shown in

_{k}_{m}_{max} denotes the maximum absolute value of the correlation between _{k}_{m}_{k}

The strength of interchannel correlations correlates with the performance difference between PPC-McDFE and PPC-DFE, which is shown in

As shown in

Using both the MP and LS algorithms, performances of PPC-McDFE and PPC-DFE are compared.

It is well known that pulse compression degrades with time evolution, as the channel is time variant in practice. In the Section 5.2, the degradation is neglected, where the subsequent adaptive channel equalizers manage to track the channel variations. In the current subsection, the multi-block approach is used to counter for the variations within each data packet. It is understood that the channel can be assumed constant within a short time interval, correspondingly a data block.

The multi-block approach operates on the decision directed mode, and hence there is the issue of error-propagation. In the scenario of low input SNR, the LS method is sensitive to errors of detected symbols of the previous block, while the MP algorithm estimates only dominant arrivals with less impact from the errors. Temporal focusing is more enhanced by the MP algorithm, which leads to better performance. Therefore, the MP algorithm is suggested for the multi-block approach.

The multi-block approach may be better than the one block approach, but it depends on the rate of channel variation.

Three receiver structures have been assessed by processing data collected in a recent experiment conducted over a range of 7.4 km. In this high frequency (10–14 kHz) experiment, coherent underwater communications of different symbol rates were achieved, e.g., 1 to 2 kilo-symbol/s. In a large time scale, in terms of period of 202.044 s, the time-variant characteristics of underwater channel are observed by the communication results in terms of output SNR.

As shaping pulses, it is shown that the difference between LFM and RRC is minimal. The LFM shaping pulse provides a simple method for PPC processing, where the received channel probe signal of LFM is immediately used. Using a RRC shaping pulse, it is flexible to select a channel estimation method for PPC processing, e.g., the MP algorithm. In addition, the block-based approach can be implemented in time-varying channels.

As evident, PPC-DFE achieves the worst performance in the assessment, and the performance of PPC-McDFE approximates that of McDFE. Time-variant reverberations result in unpredictable spatial coherence, which may impact on the performance of PPC-DFE. Therefore, it is preferable that the adaptive multichannel combining obtains much spatial gain, especially in the scenarios of a small number of receivers. For instance, it is preferable to use PPC-McDFE instead of PPC-DFE in a channel of long time spread.

In the sparse channel, the MP algorithm has been assessed in two modes. One is the conventional single block approach, and the other is the multi-block approach. The multi-block approach assumes that the channel is constant within each block of a short time interval, and then PPC processing is extended to time-varying channels. Comparing with PPC-DFE, PPC-McDFE is less sensitive to the channel variations. It has been demonstrated that the MP algorithm improves the performance of communications using PPC processing, and thus the MP algorithm is suggested in sparse channels.

The authors would like to thank NTNU Ph.D. candidate Bo Peng for his comments, and Ph.D. candidates Yan Jiang and Qin Liu, all the participants, technical engineer Tim Cato Netland and crew of R/V Gunnerus at NTNU for their help during the sea trial on 7 September 2011.

Block diagrams of the transmitted signals using different shaping pulses shown in the parentheses. ^{a} The symbol rate was 1 kilo-symbol/s; ^{b} The symbols rate was 2 kilo-symbol/s.

Measured SSP (the left panel) and the ray traces (the right panel) from a source on the left. The source was at a depth of 20 m.

Modeled channel impulse response calculated by the PlaneRay program to the vertical array with five hydrophones spanning the depth of 0.5 m to 4.5 m.

Channel response at different depths. (

Block diagram of McDFE using the RLS algorithm. There are _{n}_{n}_{n}_{n}

Block diagram of passive time reversal receiver structure PPC-DFE.

Block diagram of PPC-McDFE.

Performance of PPC-DFE using different shaping pulses. (

Scatter plot of estimated 8-QAM symbols using different receiver structures. (

Performance in terms of output SNR for different modulations. (

Spatial coherence in different periods. (

CIR estimated by the LS method and the MP algorithm.

Performance in terms of output SNR at a symbol rate of 2 kilo-symbol/s.

Performance of PPC-DFE with different approaches. (

Performance of three receiver structures. There are 16 blocks for PPC processing.

Performance comparison between the one block approach and the multi-block approach.

Parameters used in the signal processing of the three receiver structures.

_{s} |
Sampling frequency at the receiver | 96 kHz |

_{c} |
Carrier frequency | 12 kHz |

Symbol rate | 1, 2 kilo-symbol/s | |

Number of taps in the MP processing | 4 | |

Over sampling factor | 2 | |

^{1}_{ff} |
Number of the feed-forward filter taps (McDFE) | 20 |

^{1}_{fb} |
Number of the feedback filter taps (McDFE) | 5 |

^{2}_{ff} |
Number of the feed-forward filter taps (PPC-DFE) | 8 |

^{2}_{fb} |
Number of the feedback filter taps (PPC-DFE) | 2 |

^{3}_{ff} |
Number of the feed-forward filter taps (PPC-McDFE) | 8 |

^{3}_{fb} |
Number of the feedback filter taps (PPC-McDFE) | 2 |

_{block} |
Time duration of each block | 1 s |

RLS forgetting factor | 0.999 | |

Number of receiving channels | 12 | |

_{1} |
Proportional tracking constant in DPLL | 0.01 |

_{2} |
Integral tracking constant in DPLL | 0.001 |