MIMO Underwater Acoustic Communications in Ports and Shallow Waters at Very High Frequency

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 OPEN ACCESS J. Sens. Actuator Netw. 2013, 2 701 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.


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.

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 followed after a predefined time delay with the traditional Hermes message , such that: (1) consists of perfectly known pseudo noise (PN) sequences of length = 218.5 ms, up-sampled from the symbol frequency F sym to the sampling frequency and pulse-shaped using a raised-cosine filter.Figure 1 shows an example of source signal.Given a carrier frequency and a signal level SL, the transmitted signal is  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).

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.,, ( ) ( ) ( )

Channel Estimation
This process is performed over the duration of time windows, of time index and length .The received samples at receiver j can be written in matrix form [4,17]: where represents the augmented source signal array at the j th receiver.
represents the augmented channel impulse response array.represents the noise array.
As depicted in Figure 2, k 0 (t win ) denotes the beginning of the time window.L ij is the length of the channel impulse response between transmitter i and receiver j, and .Finally, T j is the sum of the channel lengths over the total number of transmitters N t , so that .In the continuous time domain, the quantity T j is noted T L (this term is also used in the results section).The index j must be dropped, as the tunable parameter T L 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], (5) This leads to the LS estimation of for every time window index t win , (6) where represents the Hermitian operator.This operation requires a T j × T j matrix inversion.

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 T L ; (2) the length T k 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.

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 L ij , (7) We define the matrices and as the received signal and noise over the total number of hydrophones: Similarly, we define the transmitted signals and channel impulse responses as: Therefore, the received signal becomes (12) We now define and (Figure 3) as the pre-cursor and post-cursors of the linear equalization filter.In this case, , and are defined as 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 T k .Next, we define the augmented matrix containing the matrices of channel impulse responses, denoted , The output of LE process can be expressed as: (18) In the sense of the MMSE criterion without any a priori on transmitted symbols, the optimum equalization filter is [5,18], (19) where is the identity matrix of size , is the variance of the noise and is the variance of the original sequence .denotes a column vector of size with 1 at index i and 0 at other positions.is the estimates of augmented channel matrix H or time window index t win Here, the estimated signal depends on length of the time window, which in turns depends on the measured channel response.If N win = 1, the channel is stationary over a message duration and However, if , becomes a function of t win .In this case, the equalized signal for each sliding window is cropped and forms a section of the equalized output , The variables t win , L win and O R represent the time window index, length and overlapping rate, respectively.

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], is defined in Equation (17) 23)-( 25) also apply to .

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.

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  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 SNR j was calculated at each receiver j.The value of SNR j , 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 to the time varying characteristics of the channel, which dramatically impacts the average power of the received signals.

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 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.

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]: 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]: (29) In order to evaluate the impact of the linear equalization on the received signals, RMSE MIMO_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] 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]: (31)

MIMO Channel Estimation Results
Table 5 shows the values of RMSE CE as a function of T L for both experimental and simulated data.The maximum value of T L is 5.33 ms, as higher values of T L lead to singularities and does not produce accurate results.As a reminder, RMSE CE measures the error between the received signals and the emitted sequences convolved with the estimated channels.RMSE CE is averaged across every receiver, so that the results presented in Table 5 translate the accuracy of the channel estimation across every sub-channel.In both experimental and simulation cases, as T L increases, the accuracy of the channel estimation improves.However, while reaches a sweet-spot at T L = 2.667 ms using simulated data ( ), the experimental results on RMSE CE differ.Indeed, the minimum RMSE CE is obtained for T L = 5.33 ms (RMSE CE = −25.7 dB) as shown in Table 5 and Figure 5. If, as explained earlier on, values higher than T L = 5.33 ms cannot be considered, the minimum value of RMSE CE using experimental data is of the same order of magnitude as RMSE CE in the simulation framework.The channel estimation can therefore be considered as very accurate.Figure 5 displays the influence of T L on the channel estimation accuracy in the specific case of mission 4. Figure 6 shows that RMSE CE drops and the confidence interval gets narrower as T L increases.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 RMSE CE 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, (32) 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 , such that: We can verify the validity of such an approximation by comparing the SNR as shown in Table 2 and the RMSE CE (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  

   r S h n ξ
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 RMSE CE (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.

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 Tables 6 and 7.The impact of the parameter T L on the performance metrics is clearly observed.The results are shown for , 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, RMSE MIMO _ LE and RMSE MIMO _ ICLE decrease as T L increases using either simulated or field data.Note that the equalizer length is limited to T L = 5.33 ms, as higher values of T L led to singularities.RMSE MIMO _ 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 T L is sufficiently large to provide accurate channel estimation, RMSE MIMO_LE drops as increasing.Therefore, showing the influence of T L on RMSE MIMO _ LE is not of great interest: this is why we chose to represent RMSE MIMO _ LE as a function of only (T L = 5.33 ms).For example, for an equalizer length T L = 5.33 ms, RMSE MIMO_LE = −6.2dB with and drops to RMSE MIMO_LE = −20.5 dB with .As it has been shown in the channel estimation process results, the confidence interval also narrows as the process gets more and more reliable.In the case of experimental data, severe distortions in the received signals impact the accuracy of the MIMO deconvolution process.Indeed, varies dramatically when computed with simulation and experimental data.In the best case scenario, we use T L = 5.33 ms and .Table 7 shows that RMSE MIMO _ LE = −3.9dB using real data vs.RMSE MIMO _ 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 RMSE MIMO _ Raw = 3 dB whereas Table 7 shows that RMSE MIMO _ LE = −3.3dB when T L = 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 RMSE MIMO _ ICLE as a function of T L : if the MIMO sequence is known, the accuracy of the process improves as T L increases.On average, RMSE MIMO _ ICLE = −26.9dB when T L = 5.33 ms using experimental data vs. −33.2dB using simulated data.As expected, the comparisons between RMSE MIMO _ ICLE and RMSE MIMO _ 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 RMSE MIMO _ ICLE = −33.2dB while RMSE MIMO _ LE = −20.5 dB.This phenomenon is especially pronounced in the case of experimental data, where RMSE MIMO _ ICLE = −26.9dB and RMSE MIMO _ LE = −3.3dB for T L = 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.

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 T L .Computer simulations showed that for T L ≥ 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 ) 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 T L = 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, T L = 5.33 ms and , the RMSE was estimated at 0.03 dB before equalization (labeled RMSE MIMO_Raw (dB)), −20.5 dB after LE (labeled RMSE MIMO_LE (dB)) and −33.3 dB after ICLE (labeled RMSE MIMO_ICLE (dB)).For experimental data (with the same values for T L and ), 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.
is the roll-off coefficient and T sym is the symbol period.

Figure 1 .
Figure 1.Real part of source message 1.

Figure 2 .
Figure 2. Definition of the parameters of the time-window used to perform the channel estimation at receiver j. j
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

Figure 5 .
Figure 5. RMSE CE and as a function of T L .

Figure 6 .
Figure 6.SNR(dB) vs. RMSE CE (dB) at the output of the channel estimator.

Figure 7 .
Figure 7. RMSE MIMO_LE as a function of T L and using simulated data.

Figure 8 .
Figure 8. and as a function of T L .

Table 1 .
Summary of data collected.

Table 3 .
Signal-to-noise ratio per mission and per receiver.

Table 5 .
Relative root mean-squared errors (RMSE CE ) as a function of T L .

Table 6 .
RMSE between emitted and (Raw) received signals, RMSE MIMO_Raw as a function of T L .

Table 7 .
RMSE between emitted and received Signals after LE processing, RMSE MIMO_LE and after ICLE processing, RMSE MIMO_ICLE as functions of T L .