J. Sens. Actuator Netw. 2013, 2(4), 700-716; doi:10.3390/jsan2040700

Article
MIMO Underwater Acoustic Communications in Ports and Shallow Waters at very High Frequency
Gaultier Real 1,,, Pierre-Philippe Beaujean 1,* and Pierre-Jean Bouvet 2
1
Department of Ocean and Mechanical Engineering, Florida Atlantic University, 101 North Beach Road, Dania Beach, FL 33004, USA; E-Mail: real@lma.cnrs-mrs.fr
2
ISEN Brest, 20 Cuirassé Bretagne, CS 42807, Brest Cedex 2 29228, France; E-Mail: pierre-jean.bouvet@isen.fr
Current address: Laboratoire de Mécanique et d’Acoustique, CNRS UPR 7051, 31 Chemin Joseph Aiguier, Marseille 13402, France
Current address: Thales Underwater Systems SAS, 525 Route des Dolines, BP 157, Sophia-Antipolis Cedex 06903, France
*
Author to whom correspondence should be addressed; E-Mail: pbeaujea@fau.edu; Tel.: +1-561-297-0530; Fax: +1-561-297-3885.
Received: 14 August 2013; in revised form: 23 September 2013 / Accepted: 24 September 2013 /
Published: 11 October 2013

Abstract

: Hermes is a Single-Input Single-Output (SISO) underwater acoustic modem that achieves very high-bit rate digital communications in ports and shallow waters. Here, the authors study the capability of Hermes to support Multiple-Input-Multiple-Output (MIMO) technology. A least-square channel estimation algorithm is used to evaluate multiple MIMO channel impulse responses at the receiver end. A deconvolution routine is used to separate the messages coming from different sources. This paper covers the performance of both the channel estimation and the MIMO deconvolution processes using either simulated data or field data. The MIMO equalization performance is measured by comparing three relative root mean-squared errors (RMSE), obtained by calculations between the source signal (a pseudo-noise sequence) and the corresponding received MIMO signal at various stages of the deconvolution process; prior to any interference removal, at the output of the Linear Equalization (LE) process and at the output of an interference cancellation process with complete a priori knowledge of the transmitted signal. Using the simulated data, the RMSE using LE is −20.5 dB (where 0 dB corresponds to 100% of relative error) while the lower bound value is −33.4 dB. Using experimental data, the LE performance is −3.3 dB and the lower bound RMSE value is −27 dB.
Keywords:
MIMO; underwater; acoustic communications; channel estimation; equalization

1. Introduction

Hermes is a broadband, high-frequency (262 kHz–375 kHz) Under Water Acoustic (UWA) modem designed for very high-bit rate digital communications in ports and shallow waters. In its current form, this modem supports only a single source and a single receiver [1,2,3]. In this paper, the authors apply Multiple-Input-Multiple-Output (MIMO) technology to Hermes, so that multiple sources and receivers distributed over an area can be used simultaneously. While the channel estimation algorithm (previously presented in [4]) and the MIMO deconvolution technique presented here are well known in the literature [5,6,7], the important contribution of the paper is to present a performance analysis when applied to high-frequency MIMO data, either simulated or experimental.

MIMO UWA communication is achieved by modifying the signaling of the FAU Hermes uplink message. The limited bandwidth, reliability and flexibility observed with UWA communication systems can be partly resolved by the use of MIMO techniques [5,8,9,10,11,12,13]. Indeed, the capability to send different messages via each source can significantly increase the overall data rate of the UWA communication system. In addition, the coverage area of the UWA modem can be significantly increased. However, MIMO communication systems cannot guarantee perfect communications, as signal fading; Doppler spread and ambient noise impair the overall performance of any UWA modem [14,15,16].

The proper retrieval of MIMO messages requires both an accurate estimation of the acoustic channels and an effective channel equalization algorithm. The least-square (LS) channel estimation algorithm was presented in a previous paper [4]. Here, the authors focus on channel deconvolution (MIMO equalization), which is critical to properly separate the messages coming from multiple sources (this is also called co-antenna interference removal) and to remove inter-symbol interference due to acoustic multipath. The deconvolution is implemented as a Minimum Mean Square Error (MMSE) equalizer. The theoretical limit of the deconvolution process is computed with an Interference Cancellation Linear Equalizer (ICLE), which removes the co-antenna interference by using a priori information on the transmitted sequence. Finally, the system performance is studied using simulated data, experimental data and the upper performance bound.

2. System Model

2.1. Source Signals

The messages sent through the acoustic channels are obtained by modifying the signaling of Hermes [1,2,3]. In this paper, i represents the source index. The proposed message is composed of the source-dependent MIMO sequence si,h (t) followed after a predefined time delay τmsg with the traditional Hermes message si,msg(t), such that:

Jsan 02 00700 i001
si,h(t) consists of perfectly known pseudo noise (PN) sequences of length τ = 218.5 ms, up-sampled from the symbol frequency Fsym to the sampling frequency and pulse-shaped using a raised-cosine filter. Figure 1 shows an example of source signal. Given a carrier frequency F0 and a signal level SL, the transmitted signal is
Jsan 02 00700 i002
where
Jsan 02 00700 i003
here, β is the roll-off coefficient and Tsym is the symbol period.

Jsan 02 00700 g001 200
Figure 1. Real part of source message 1.

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Figure 1. Real part of source message 1.
Jsan 02 00700 g001 1024

In this paper, we assume that the message following the MIMO sequence does not change with the source. The MIMO sequences (one per source) have a very low cross-correlation to their auto-correlation peak ratio. We observed that the peak ratio is approximately 40 (which is equivalent to 16 dB).

2.2. Received Signals

In this section, we present the operations carried out at the receiver end. We first focus on the channel estimation algorithm, followed by the equalization. The derivations are provided in the discrete time domain, where k stands for the time index and l the delay index.

2.2.1. Channel Estimation

This process is performed over the duration of Nwin time windows, of time index twin and length Lwin. The received samples Jsan 02 00700 i004 at receiver j can be written in matrix form [4,17]:

Jsan 02 00700 i005
where Jsan 02 00700 i006 represents the augmented source signal array at the j th receiver. Jsan 02 00700 i007 represents the augmented channel impulse response array. Jsan 02 00700 i008 represents the noise array.

As depicted in Figure 2, k0(twin) denotes the beginning of the time window. Lij is the length of the channel impulse response between transmitter i and receiver j, and Jsan 02 00700 i009. Finally, Tj is the sum of the channel lengths over the total number of transmitters Nt, so that Jsan 02 00700 i010.

Jsan 02 00700 g002 200
Figure 2. Definition of the parameters of the time-window used to perform the channel estimation at receiver j.

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Figure 2. Definition of the parameters of the time-window used to perform the channel estimation at receiver j.
Jsan 02 00700 g002 1024

In the continuous time domain, the quantity Tj is noted TL (this term is also used in the results section). The index j must be dropped, as the tunable parameter TL is assumed identical across every receiver. We study the influence of this parameter on channel estimation and deconvolution in the results section. The channel estimation is performed through minimization of the following quantity [18],

Jsan 02 00700 i011

This leads to the LS estimation of Jsan 02 00700 i012 for every time window index twin,

Jsan 02 00700 i013
where ( )H represents the Hermitian operator. This operation requires a Tj × Tj matrix inversion.

2.2.2. MIMO Deconvolution

The MIMO deconvolution process presented in this paper compensates for co-channel and inter-symbol interferences using the LS channel estimation obtained in Equation (6). The critical parameters identified in this performance study are: (1) the length of the channel estimate TL; (2) the length Tk of the pre-cursor and post-cursor of the linear equalization filter. We consider two equalization structures: conventional Linear Equalization (LE) and Interference Cancellation Linear Equalization (ICLE). ICLE provides a theoretical lower bound of the equalization process.

2.2.2.1. Minimum Mean Squared Error Linear Equalization

The process presented in this section consists of a feed-forward multi-channel linear filter optimized under MMSE criterion. Let L represent the maximum value of the sub-channel length Lij,

Jsan 02 00700 i014

We define the matrices Jsan 02 00700 i015 and Jsan 02 00700 i016 as the received signal and noise over the total number of hydrophones:

Jsan 02 00700 i017
and
Jsan 02 00700 i018

Similarly, we define the transmitted signals Jsan 02 00700 i019 and channel impulse responses Jsan 02 00700 i020 as:

Jsan 02 00700 i021
Jsan 02 00700 i022

Therefore, the received signal becomes

Jsan 02 00700 i023

We now define κ1 and κ2 (Figure 3) as the pre-cursor and post-cursors of the linear equalization filter. In this case, Jsan 02 00700 i024, Jsan 02 00700 i025 and Jsan 02 00700 i026 are defined as

Jsan 02 00700 i027
Jsan 02 00700 i028
Jsan 02 00700 i029

Jsan 02 00700 g003 200
Figure 3. Multiple-Input-Multiple-Output (MIMO) deconvolution process: pre-cursor and post-cursor definition.

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Figure 3. Multiple-Input-Multiple-Output (MIMO) deconvolution process: pre-cursor and post-cursor definition.
Jsan 02 00700 g003 1024

In the results section, the influence of the pre-cursor and post-cursor is studied in the continuous time domain. In this paper, the length of these cursors is assumed to be the same and is represented by Tk. Next, we define the augmented matrix containing the matrices of channel impulse responses, denoted Jsan 02 00700 i030,

Jsan 02 00700 i031
so that
yk = Hxk + wk

The output of LE process can be expressed as:

Jsan 02 00700 i032

In the sense of the MMSE criterion without any a priori on transmitted symbols, the optimum equalization filter is [5,18],

Jsan 02 00700 i033
where I is the identity matrix of size (1 + κ1 + κ2) Nr, Jsan 02 00700 i034 is the variance of the noise and Jsan 02 00700 i035 is the variance of the original sequence SI,K. Jsan 02 00700 i036 denotes a column vector of size (L + κ1 + κ2) Nt with 1 at index i and 0 at other positions. Jsan 02 00700 i037 is the estimates of augmented channel matrix H or time window index twin Here, the estimated signal Jsan 02 00700 i038 depends on length of the time window, which in turns depends on the measured channel response. If Nwin = 1, the channel is stationary over a message duration and
Jsan 02 00700 i039

However, if Nwin ≥ 1, Jsan 02 00700 i040 becomes a function of twin. In this case, the equalized signal for each sliding window is cropped and forms a section of the equalized output Jsan 02 00700 i038,

Jsan 02 00700 i041

The variables twin, Lwin and OR represent the time window index, length and overlapping rate, respectively.

2.2.2.2. MMSE Interference Cancellation Linear Equalizer

The ICLE has been developed to evaluate the best possible performance of the deconvolution process by assuming that the source signal is perfectly known. The output of the ICLE may be expressed as follows [6,7,19],

Jsan 02 00700 i042
yk is defined in Equation (17). pi,k and qi,k respectively stand for the feed-forward and feed-back filters. vi,k is defined as
Jsan 02 00700 i043
where,
Jsan 02 00700 i044
KICLE is the discrete delay index induced by the equalizer, such that 0 ≤ KICLENICLE + L − 2, where NICLE represents the discrete ICLE length. Under MMSE optimization, the feed-forward and feed-back equalization vectors become equal to [7]:
Jsan 02 00700 i045
where
Jsan 02 00700 i046
and
Jsan 02 00700 i047
ek is a null column vector, with the exception of element Nt(k − 1) + i equal to 1. Jsan 02 00700 i034 represents the noise variance. The ICLE estimate Jsan 02 00700 i048 depend on the number of time windows used to perform the channel estimation, thus Equations (23)–(25) also apply to Jsan 02 00700 i048.

3. Simulated and Experimental Results

The results, in terms of MIMO deconvolution, are presented in this section. The simulation parameters and the metrics are first presented, followed with a description of the experimental setup. The simulated results are analyzed: in this case, the channel is stationary over the duration of the message. Finally, a set of field data is analyzed, where time variations of the channel are observed.

3.1. Experimental Setup

A series of experiments was carried out in the Florida Atlantic University Seatech marina (Figure 4). While the experimental setup presented here uses two sources and three receivers, this paper presents only the results obtained with two receivers. Table 1 provides a summary of the data collection. A first set of data was acquired on 27 September 2011. A second series of experiments took place on 31 August 2011. The two sources were alternatively placed at the two locations labeled “Pos1” and “Pos7” in Figure 4. Two splash proof boxes were built to prevent any damage to the modem sources and were installed on kayaks. Each box contained a set of Hermes source electronics, an ITC-1089 source transducer and a battery pack. The source level was 179 dB ref. 1 μPa at 1 m. The receivers used to carry out these missions were deployed off a small research vessel. The experimental ranges are given in Table 2. The signals presented in this paper were acquired at a maximum range of 27 m. This short range is mostly due to the high sound absorption loss (100 dB/km at 20 °C and at 300 kHz [20]).

Since the equipment did not have the ability to perform real-time MIMO communication, each source was used individually and the MIMO messages were constructed off-line. The signal-to-noise ratio SNRj was calculated at each receiver j. The value of SNRj, averaged across every messages within a mission, is shown in Table 3. The observed SNR value varied between 27.1 dB and 34.3 dB from mission to mission. These variations are mostly due to the time varying characteristics of the channel, which dramatically impacts the average power of the received signals.

Jsan 02 00700 g004 200
Figure 4. Experimental setup.

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Figure 4. Experimental setup.
Jsan 02 00700 g004 1024
Table 1. Summary of data collected.

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Table 1. Summary of data collected.
Mission Number and DateSource 1 PositionSource 2 PositionReceiver 1 PositionReceiver 2 PositionNumber of Messages Retained
1-07/27/2011Pos1Pos7Rx1Rx350
2-07/27/2011Pos7Pos1Rx1Rx350
3-08/29/2011Pos7Pos1Rx1Rx3100
4-08/29/2011Pos1Pos7Rx1Rx3100
Table 2. Experimental ranges.

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Table 2. Experimental ranges.
Distance on Figure 4Distance (m)
Rx1-Pos124
Rx1-Pos727
Rx3-Pos123.3
Rx3-Pos725.8
Pos1-Pos76.15
Rx1-Rx32.68
Table 3. Signal-to-noise ratio per mission and per receiver.

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Table 3. Signal-to-noise ratio per mission and per receiver.
Mission Number and DateSNR1(dB)SNR2(dB)
1-07/27/201127.127.3
2-07/27/201128.827.8
3-08/29/201130.934.3
4-08/29/201129.233.2

3.2. Simulation Parameters

The channel model, presented in detail in [4,17], combines a deterministic model (to determine the average echo intensities) [15,16] and a stochastic Rician model (to add some random fluctuation to every echo intensity) [4]. Sources and receivers’ separation and depth match the experimental setup presented in Section 3.1.

The simulation parameters (Table 4) are tuned to match the experimental data sets as closely as possible. Doppler shift and Doppler spread have been derived from the field data. The time window used to perform the channel estimation covers the duration of the MIMO sequence and the dead-time interval. Hence, the channel is assumed to be time-invariant over the transmission of a message. The coherence time of the channel therefore corresponds to the total length of the transmitted message: each new transmission would lead to a different channel to estimate.

For every transmitted message, we also adjust the time delay τ0 between the signals measured at every receiver. In this paper, we only consider full overlap between received messages. The results for partial overlap are presented in [17]. The channel model considered here includes both the specular reflection from the sea bottom and scattering from the sea surface and bottom.

Table 4. Simulation parameters. Some of the simulation parameters are not formally used in the equations listed in this paper. The parameter name is followed with references [4,17], where the equations using these parameters are provided.

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Table 4. Simulation parameters. Some of the simulation parameters are not formally used in the equations listed in this paper. The parameter name is followed with references [4,17], where the equations using these parameters are provided.
NameSymbolValue (units)NameSymbolValue (units)
Sources Depth [4,17]DSi1 mSource LevelSL179 dB re 1 µPa @ 1 m
Receivers Depth [4,17]DRj1.5 mNoise LevelNL83.7 dB re 1 µPa
Water Depth [4,17]DW3 mSampling FrequencyFS150 kHz in base band 750 kHz in pass band
Water Sound Speed [4,17]C1,500 m/sSymbol RateDsym75 kHz
Water Density [4,17]ρ1,023 kg/m3Carrier Frequencyf00 kHz in base band
300 kHz in pass band
Sandy Sediment Sound Speed [4,17]Cb1,800 m/sMIMO Sequence Durationτh218.5 ms
Sandy Sediment Density [4,17]ρb1,800 kg/m3Dead-Time Durationτmsg300 ms
Sea Bottom Loss [4,17]LSB5 dBCorrelation Threshold ParameterKthr20
Beginning of Time Window [4,17]k00Time Window Lengthτwin518.5 ms
Number of Transmitters [4,17]Nt2Number of ReceiversNr2
Distance Source 1 Receiver 1 [4,17]R1123.3 mDistance Source 1 Receiver 2 [4,17]R1224 m
Distance Source 2 Receiver 1 [4,17]R2125.8 mDistance Source 2 Receiver 2 [4,17]R2227 m

3.3. Performance Metrics

First, we present the performance of the channel estimation process. This performance is measured using the RMSE between the received MIMO header and the MIMO header convolved with the estimated channel, averaged across every message m and every receiver j [17]:

Jsan 02 00700 i049

The MIMO LE performance is measured using the relative RMSE between the deconvolved MIMO header and the original sequence. This metric indicates the accuracy of the co-antenna and inter-symbol interference removal process. In this case, the RMSE is given by [17]:

Jsan 02 00700 i050

In order to evaluate the impact of the linear equalization on the received signals, RMSEMIMO_LE is compared to another relative RMSE between emitted and raw received signals. This second metric is calculated by comparing the received MIMO header signal (prior to any interference removal) and the corresponding source signal [17]:

Jsan 02 00700 i051

The performance estimated with the ICLE represents the theoretical performance limit of the MIMO LE. The relative RMSE between emitted MIMO sequences and the output of the ICLE is [17]:

Jsan 02 00700 i052

3.4. MIMO Channel Estimation Results

Table 5 shows the values of RMSECE as a function of TL for both experimental and simulated data. The maximum value of TL is 5.33 ms, as higher values of TL lead to singularities and does not produce accurate results. As a reminder, RMSECE measures the error between the received signals and the emitted sequences convolved with the estimated channels. RMSECE is averaged across every receiver, so that the results presented in Table 5 translate the accuracy of the channel estimation across every sub-channel.

Table 5. Relative root mean-squared errors (RMSECE) as a function of TL.

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Table 5. Relative root mean-squared errors (RMSECE) as a function of TL.
TL(ms)Simulated RMSECE (dB)Experimental RMSECE (dB)
0.667−9.5−0.4
1.333−12.5−0.9
2.0−18.8−4.1
2.667−34.7−4.9
3.333−34.7−6.2
4.0−34.7−9.1
4.667−34.8−11.4
5.33−34.8−25.7

In both experimental and simulation cases, as TL increases, the accuracy of the channel estimation improves. However, while RMSE CE reaches a sweet-spot at TL = 2.667 ms using simulated data ( Jsan 02 00700 i053), the experimental results on RMSECE differ. Indeed, the minimum RMSECE is obtained for TL = 5.33 ms (RMSECE = −25.7 dB) as shown in Table 5 and Figure 5. If, as explained earlier on, values higher than TL = 5.33 ms cannot be considered, the minimum value of RMSECE using experimental data is of the same order of magnitude as RMSECE in the simulation framework. The channel estimation can therefore be considered as very accurate.

Figure 5 displays the influence of TL on the channel estimation accuracy in the specific case of mission 4. Figure 6 shows that RMSECE drops and the confidence interval [−σCE;σCE] gets narrower as TL increases.

Jsan 02 00700 g005 200
Figure 5. RMSECE and RMSECE ± σCE as a function of TL.

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Figure 5. RMSECE and RMSECE ± σCE as a function of TL.
Jsan 02 00700 g005 1024

The SNR is simply computed as the ratio of the received MIMO header power over the ambient noise power. It is also interesting to look at the impact of the SNR on the channel estimation performance for every receiver and every mission carried out. The best possible estimation of the channel impulse response is obtained when RMSECE at the output of the channel estimator (Equation (28)) is the inverse of the SNR. In this ideal case, the relationship can be rewritten in dB,

SNR(dB) = −RMSECE (dB)
where the SNR is simply computed as the ratio of the received MIMO header power over the ambient noise power.

In the more realistic case of imperfect channel estimation, Equation (4) should account for the residual error in estimating the channel impulse response at receiver j. This error can be modeled as an additive noise Jsan 02 00700 i054, such that:

Jsan 02 00700 i055

We can verify the validity of such an approximation by comparing the SNR as shown in Table 2 and the RMSECE(dB) (Equation (28)) obtained for each of the corresponding four missions and for each receiver. In theory, when the best possible estimation of the channel impulse response is calculated, Equation (32) applies, as shown using a solid line in Figure 6. The experimental results, labeled as individual points in Figure 6, remain very close to this theoretical limit, which indicates that the channel estimation algorithm works very well indeed. For example, the channel estimation in the data set recorded during in mission 2 at receiver 2 results in a value of RMSECE (dB) that is almost exactly the opposite of SNR(dB). Some discrepancies are also observed, as in mission 3 at receiver 2. In this case, the channel estimator produces significant amounts of additive noise.

Jsan 02 00700 g006 200
Figure 6. SNR(dB) vs. RMSECE(dB) at the output of the channel estimator.

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Figure 6. SNR(dB) vs. RMSECE(dB) at the output of the channel estimator.
Jsan 02 00700 g006 1024

3.5. MIMO Deconvolution Results

A comparison of the MIMO deconvolution capability between experimental data and simulation results has been completed, using the metrics defined in Equations (29)–(31). The results are shown in Table 6 and Table 7. The impact of the parameter TL on the performance metrics is clearly observed. The results are shown for Jsan 02 00700 i056, which lead to the lowest RMSE values [17]. Both simulations and experimental results (averaged over the total number of missions carried out) are presented in Table 6. Clearly, RMSEMIMO_LE and RMSEMIMO_ICLE decrease as TL increases using either simulated or field data. Note that the equalizer length is limited to TL = 5.33 ms, as higher values of TL led to singularities.

RMSEMIMO_LE, computed with both simulated and experimental data, is shown in Figure 7. Figure 7 shows the influence of the pre-cursor and post-cursor length: if TL is sufficiently large to provide accurate channel estimation, RMSEMIMO_LE drops as Tk increasing. Therefore, showing the influence of TL on RMSEMIMO_LE is not of great interest: this is why we chose to represent RMSEMIMO_LE as a function of Tk only (TL = 5.33 ms). For example, for an equalizer length TL = 5.33 ms, RMSEMIMO_LE = −6.2 dB with Tk = 0.7 ms and drops to RMSEMIMO_LE = −20.5 dB with Tk = 6.0 ms. As it has been shown in the channel estimation process results, the confidence interval also narrows as the process gets more and more reliable.

Table 6. RMSE between emitted and (Raw) received signals, RMSEMIMO_Raw as a function of TL.

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Table 6. RMSE between emitted and (Raw) received signals, RMSEMIMO_Raw as a function of TL.
TL (ms)RMSE MIMO_Raw (dB)
SimulationsExperiments
0.667 ms, 1.333 ms, 2 ms, 2.667 ms, 3.333 ms, 4 ms, 4.667 ms, 5.33 ms0.043
Table 7. RMSE between emitted and received Signals after LE processing, RMSEMIMO_LE and after ICLE processing, RMSEMIMO_ICLE as functions of TL.

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Table 7. RMSE between emitted and received Signals after LE processing, RMSEMIMO_LE and after ICLE processing, RMSEMIMO_ICLE as functions of TL.
RMSE MIMO_Raw (dB)RMSE MIMO_ICLE (dB)
SimulationsExperimentsSimulationsExperiments
TL (ms)0.6670.419.7−4.515.8
1.333−3.414.4−6.712.1
2.0−10.38.3−136.4
2.667−20.55.5−33.43.1
3.333−20.52.2−33.40.7
4.0−20.5−1.9−33.3−3
4.667−20.5−3.9−33.3−8.8
5.33−20.5−3.3−33.2−26.9
Jsan 02 00700 g007 200
Figure 7. RMSEMIMO_LE as a function of TL and Tk using simulated data.

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Figure 7. RMSEMIMO_LE as a function of TL and Tk using simulated data.
Jsan 02 00700 g007 1024

In the case of experimental data, severe distortions in the received signals impact the accuracy of the MIMO deconvolution process. Indeed, Tk = 6.0 ms varies dramatically when computed with simulation and experimental data. In the best case scenario, we use TL = 5.33 ms and Tk = 6 ms. Table 7 shows that RMSEMIMO_LE = −3.9 dB using real data vs. RMSEMIMO_LE = −20.5 dB using simulated data. Nevertheless, the LE process on experimental data dramatically improves the quality of the received signal: Table 6 shows that RMSEMIMO_Raw = 3 dB whereas Table 7 shows that RMSEMIMO_LE = −3.3 dB when TL = 5.33 ms.

The relatively significant differences between simulation and field data performances are related to the time-varying characteristics of the experimental channel but also to co-antenna interferences. Indeed, the experimental channel impulse responses presented a coherence time much shorter than in the simulation case, leading to a lack of accuracy in the co-antenna interference removal process. Figure 8 shows the variation of RMSEMIMO_ICLE as a function of TL: if the MIMO sequence is known, the accuracy of the process improves as TL increases. On average, RMSEMIMO_ICLE = −26.9 dB when TL = 5.33 ms using experimental data vs. −33.2 dB using simulated data.

Jsan 02 00700 g008 200
Figure 8. RMSEMIMO_ICLE and RMSEMIMO_ICLE ± σICLE as a function of TL.

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Figure 8. RMSEMIMO_ICLE and RMSEMIMO_ICLE ± σICLE as a function of TL.
Jsan 02 00700 g008 1024

As expected, the comparisons between RMSEMIMO_ICLE and RMSEMIMO_LE calculated using simulated and experimental data reveals that LE process does not reach the lower bound provided by ICLE structure. Using simulation data, we find that RMSEMIMO_ICLE = −33.2 dB while RMSEMIMO_LE = −20.5 dB. This phenomenon is especially pronounced in the case of experimental data, where RMSEMIMO_ICLE = −26.9 dB and RMSEMIMO_LE = −3.3 dB for TL = 5.33 ms. One can conclude that LE alone is not totally sufficient to remove the whole interference terms provided by the frequency selective channel and multi-antenna architecture. Non-linear approaches like iterative processing strategy or decision feedback equalization appear thus necessary.

4. Conclusions

The capability of Hermes to support MIMO technology was presented in this paper. The system performance was evaluated using both simulated and experimental data, using two sources and two receivers. The ability to retrieve emitted messages, using a Linear Equalizer (LE), in the presence of inter-symbol interferences, co-antenna interferences and noise was estimated.

The channel impulse response estimation performance was related to the value of the channel estimate length TL. Computer simulations showed that for TL ≥ 2.667 ms, the relative root mean-square error used to measure the accuracy of the estimation reached a plateau. In this configuration, the RMSE (labeled RMSECE (dB)) between the received MIMO header and the MIMO header convolved with the estimated channel (averaged across every message and every receiver) was equal to −34.8 dB. This performance was compared to experimental data: in this case the same metric was equal to −25.7 dB for TL = 5.33 ms, indicating that the proposed technique evaluated fairly accurately the acoustic channel between every source and receiver.

To measure the benefits of this linear equalizer, the RMSE between emitted and received messages was first computed for each individual source and receiver. An Interference Cancelation Linear Equalizer (ICLE) was also developed to measure the limit of the deconvolution process, using estimated channel impulse responses. Optimized under the MMSE criterion, the ICLE took advantage of the known source signal. Using simulated data, TL = 5.33 ms and Tk = 6 ms, the RMSE was estimated at 0.03 dB before equalization (labeled RMSEMIMO_Raw (dB)), −20.5 dB after LE (labeled RMSEMIMO_LE (dB)) and −33.3 dB after ICLE (labeled RMSEMIMO_ICLE (dB)). For experimental data (with the same values for TL and Tk), the RMSE was estimated at −3 dB before equalization, −3.3 dB after LE and to −26.9 dB after ICLE.

To conclude with the results presented in this paper, the channel estimator and ICLE processes produce fairly similar results in simulation and experimentations. The fact that the performance of the channel estimation process and the ICLE are very comparable indicates that the deconvolution process is very accurate; in this case, the residual errors are not due to the ICLE itself. The LE performs better with simulated data but still brings some benefits to the communication system in the case of field data. The encouraging results indicate that the FAU Hermes underwater acoustic modem could be successfully equipped with MIMO technology.

Acknowledgments

This work is sponsored by the Office of Naval Research, Code 321 OE.

Conflicts of Interest

The authors declare no conflict of interest.

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