MIMO Underwater Acoustic Communication in Shallow Water with Ice Cover

Although multiple-input multiple-output (MIMO) underwater acoustic (UWA) communication has been intensively investigated in the past years, existing works mainly focus on open-water environment. There is no work reporting MIMO acoustic communication in under-ice environment. This paper presents results from a recent MIMO acoustic communication experiment which was conducted in Bohai Gulf during winter. In this experiment, high frequency MIMO signals centered at 10 kHz were transmitted from a two-element source array to a four-element vertical receiving array at 1 km range. According to the received signal of different array elements, MIMO acoustic communication in under-ice environment suffers less effect from co-channel interference compared with that in open-water environment. In this paper, time reversal followed by a single channel decision feedback equalizer is used to process the experimental data. It is demonstrated that this simple receiver is capable of realizing robust performance using fewer hydrophones (i.e. 2) without the explicit use of complex co-channel interference cancelation algorithms, such as parallel interference cancelation or serial interference cancelation.


Introduction
Underwater acoustic (UWA) communication plays an important role in many scientific and industrial applications, such as ocean exploration and observation, navigation and positioning for autonomous underwater vehicles, etc. Moreover, urgent demand for high data rate UWA communication has been put forward in recent years in order to realize efficient and fast information transmissions. However, UWA channels are characterized by large multipath spreads resulting in severe inter symbol interference (ISI) which degrades the quality of the received signal and requires compensation (i.e., channel equalization) (Song, 2016;Qarabaqi and Stojanovic, 2013). Besides, the available bandwidth in UWA channels is limited due to severe frequency-dependent attenuation of the physical medium (Stojanovic, 2007). Therefore, it is challenging to realize high data rate communication in underwater environment.
Multichannel decision feedback equalizer (M-DFE) has been extensively studied over the last decades to suppress ISI which is introduced by UWA channels (Stojanovic et al., 1993(Stojanovic et al., , 1994Zhang and Dong, 2011). Its complexity increases quadratically with the total number of tap coefficients and the computation load becomes intolerable when multipath spread is very large (i.e. tens of milliseconds). Time reversal (TR) has attracted attention in UWA communications as an alternative to M-DFE on account of its robustness and lower computational complexity (Edelmann et al., 2002(Edelmann et al., , 2005Yang, 2003Yang, , 2004Rouseff et al., 2001). TR exploits spatial diversity to achieve spatial and temporal focusing. Its temporal focusing property can mitigate ISI and the performance will be further improved when it is subsequently cascaded with a single channel DFE to remove the residual ISI which is called TR-DFE or correlationbased DFE (Song et al., 2006;Song, 2013;Yang, 2005).
MIMO system was introduced into UWA communication in order to significantly improve the data transmission rate (Li et al., 2009;Yang, 2016;Kilfoyle et al., 2005;Zhang and Zheng, 2010). As data streams from different users are transmitted at the same time in MIMO communication, one user's signal interferes with that of the other users, which is referred to as co-channel interference (CoI). Removing CoI in UWA channel is a challenging task for channel equalizer. Recently, M-DFEs have been extended to MIMO system to jointly compensate for CoI and ISI (Stojanovic and Zvonar, 1996). Spatial focusing property of TR can also be employed in MIMO UWA communication. Providing multiple transmitters are well separated in depth from each other compared with the focal size, their channel to the vertical receiving array will be weakly correlated. The spatial diversity is used by TR to separate data streams from the superimposed multiple transmissions. Active TR and passive TR-DFE were successfully applied in MIMO UWA communication by Song et al. (2007Song et al. ( , 2010. It is demonstrated that up to 6 transmitters can be supported with 32 receivers at 3-4 kHz using active TR, as well as 3 transmitters can be supported with 16 receivers at 11-19 kHz using passive TR-DFE. In order to further suppress CoI, TR-DFE is also combined with some interference cancellation algorithms, such as serial interference cancellation (SIC) and parallel interference cancellation (PIC). Their performance was demonstrated by Song (Song et al., 2011;Song and Badiey, 2012) through the experiments conducted at Kauai, Hawaii.
Although UWA communication (SISO, SIMO, and MIMO) has been intensively investigated in the past years, existing works mainly focus on open-water acoustic communication. Only a few works have been reported about under-ice acoustic communication and navigation. It is demonstrated that acoustic communications and navigation can be performed on scales of 10-100 km using relatively inexpensive and compact hardware (Freitag et al., 2012). RE-MUS-100 AUV is also incorporated with a lower frequency transducer and associated hardware for navigation and communication in Arctic (Kukulya et al., 2010). In order to maintain robust connectivity between AUV and operators in Arctic, the AUV could adapt to the environment situation and the current source/receiver configuration by changing depth when connectivity is required based on onboard acoustic modeling and forecasting (Schmidt and Schneider, 2016). Initial experiments in the Fram Strait in 2010 have shown the utility of the single-tube source for transmitting long-range communication and navigation signals (Jones et al., 2013). Spread spectrum technique was also used in under-ice acoustic communication to realize multi-user communication (Tang et al., 2016;Yin et al., 2016). As far as we know, there is no work reporting under-ice MIMO acoustic communications. This paper presents results from a recent MIMO acoustic communication experiment which was conducted in Bohai Gulf during winter and the water column was covered with about 40-cm-thick ice. The paper is organized as follows. The MIMO system model and TR-DFE structure are briefly reviewed in Section 2. Channel estimation algorithms based on least square (LS) in MIMO communication are presented in Section 3. A detailed description of the acoustic communication is shown in Section 4. Section 5 gives the receiver performance using single-channel and multi-channel processing. Section 6 is a brief summary of this paper. Fig. 1 shows a typical MIMO system model with M transducers and N hydrophones. At the i-th transducer, an information sequence with K symbols is modulated to carrier frequency and transmitted. The transmitted signal can be expressed as:

TR-based MIMO acoustic communication
where, is the symbol duration, is the pulse shaping filter and where, is the roll-off factor. The M transmitted signals are independent of each other, but they use the same symbol rate R and carrier frequency . The transmitted signals propagate through the ocean channel, where it is distorted by multipath. Usually the transducers are separated by only several meters, therefore the transmitted signals from different transducers will arrive at each hydrophone almost at the same time. Let be the received passband signal at the jth hydrophone, then where, is the channel impulse response from the i-th transducer to the j-th hydrophone and "*" denotes the convolution operation. It will be convenient to assume that these signals observed at the receiver have already been brought to baseband, so the passband form of the received signal in Eq. (3) can be written in baseband form as: and L is the discrete channel impulse response length. Note that the received signal is sampled at a fractional symbol interval (i.e. ) in this paper when processing the experimental data. However, for notation convenience, symbol spaced signals are used throughout the paper. TR-DFE is used at the receiver to separate data streams from the superimposed signal, as illustrated in Fig. 2. A set of channel impulse responses are firstly estimated and TR is then used to extract data streams for each transducer by matched-filtering the received signals with the estimated channels. A single channel DFE is then followed to remove residual ISI and CoI. r k (n) The separated data stream for the k-th transducer after time reversal combining is In Eq. (5), " " denotes conjugate operation. The first term on the right side is the desired signal and can be regarded as the effective channel from the k-th transducer to the receiving array, which can be defined as: The second term on the right side is the interference from the other M-1 transducers and can be re- garded as the channel crosstalk between the k-th and i-th transducers ( ). It has been always expected that is very small or equal to zero under ideal condition. But in reality, the quantity could be relatively big, which depends on the spatial diversity between multiple transducers.
can be defined as: z k (n) The quantity is the noise component and The single-channel DFE with joint phase tracking is used to remove residual ISI and CoI. Recursive least square (RLS) algorithms adaptively update the equalizer weights according to the error between the equalized symbols and the decided symbols . The phase offset, caused by dynamic ocean environment or Doppler in , is corrected by a second-order phase lock loop (PLL) embedded in the DFE. The mean square error (MSE) at the DFE outputs and the bit error ratio (BER) will be used as performance metrics in this paper.

MIMO channel estimation
In this section, channel estimation algorithm based on LS will be introduced. The MIMO channels can be written as a matrix with elements and each element is a channel impulse response with L taps. MIMO channel estimation divides the channels into N MISO channels. Therefore, at each hydrophone we can estimate a set of channels from M transmitters and all these channels can be obtained when repeating the same procedure N times. The received data at the j-th hydrophone at the time index n can be expressed in a vector matrix notation as: where, . .
where, "T" denotes the transpose operation and is the number of symbols in an observing block. According to the LS criterion, the cost function can be written as: When the cost function reaches the minimum value, we can obtain where, "H" denotes the conjugate transpose operation.

MIMO acoustic communication with ice cover
The MIMO acoustic communication was conducted in Bohai Gulf during winter and the water column is covered with about 40-cm-thick sea ice. The experimental schematic is shown in Fig. 3. A source array with two transducers donated by Tx#1 and Tx#2 are used in this experiment. These two transducers are separated by 5 m in depth. A vertical receiving array with four hydrophones donated by P1, P2, P3, and P4 are used to collect signals. These four hydrophones are uniformly spaced 1.4 m. The source-receiver range is set to 1 km during this experiment.
The communication sequences of both transmitters are α = 1 f 0 modulated using QPSK and follow the frame structure in Fig. 4. The transmitted waveform is pulse shaped using a raised-cosine filter with a rolloff factor . The center frequency is 10 kHz, the symbol rate is 2 k symbols/s, and all signals are sampled at 96 kHz. Both transducers encode 32200 bits randomly generated information and the former 2000 bits are used as the training sequence (1000 symbols).
As the sync signals from two transducers were transmitted asynchronously, it gives us an opportunity to analyze the SNR of different data streams at each hydrophone.     shows the normalized received sync signals of two transducers at different hydrophones. It is interesting that a hydrophone whose depth is close to the depth of a transducer receives strong signal from this transducer. Conversely, a hydrophone whose depth is much different from the depth of a transducer receives weak signal from this transducer. For example, the depth of P1 is almost the same with the depth of Tx#1 (0.5 meter difference), P1 receives strong signal from Tx#1 as shown in Fig. 5a. The depth of P4 is far away from the depth of Tx#1 (4.7 meters difference), P4 receives weak signal from Tx#1 as shown in Fig. 5d. For Tx#2, the condition is just opposite to that for Tx#1. P1 receives weak signal from Tx#2 while P4 receives strong signal from Tx#2. As the sound speed profile in the experimental water column was almost constant and the communication range was relatively short, the phenomenon in Fig. 5 is reasonable. Table 1 shows the statistical SNR of the signal received at each hydrophone for two different transducers. It can be seen from Fig. 5a and Fig. 5b that the amplitude of the received signal for Tx#1 is almost the same, however, there is a 10.2 dB difference in SNR between these two elements. The main reason is that P1 suffers a strong noise interfer-ence which may come from the hardware. According to the analysis above, it will be plausible to obtain the conclusion that MIMO acoustic communication with ice cover has more advantages over that in open-water environment, especially in short range communications. One of the advantages is that the special under-ice propagation environment naturally "separates" data streams from different transducers which are deployed to different depths. It should be noted here that there is still CoI between different transmitters.

Communication results
In this section, single-channel and multiple-channel MIMO communication results using TR-DFE are presented. For multiple-channel receivers, different pairs of array elements from the vertical receiving array which includes P1 and P4 are chosen in the data processing. Fractionally spaced equalizers (two samples per symbol) are used for feed forward filters, and the numbers of feed forward and feedback taps are 40 and 30, respectively. The proportional and integral phase tracking constants for the PLL were and , respectively. The recursive least square (RLS) algorithm was employed to adaptively update the DFE equalizer coefficients with a forgetting factor . Fig. 6 and Fig. 7 show the channel estimation results for Tx#1 and Tx#2 at each array element respectively using LS method. Note that the color bars in Fig. 6 and Fig. 7 are with different maximum values.
According to the channel estimation results in Fig. 6 and Fig. 7, the following conclusions can be drawn: First, chan- HAN Xiao et al. China Ocean Eng., 2019, Vol. 33, No. 2, P. 237-244 nel impulse responses of Tx#1 and Tx#2 are very simple with small multipath spread. Moreover, the multipath structures are very stable throughout the whole communication period, which is mainly due to the ice cover which makes acoustic signals unaffected by surface waves during propagation. In this environment we do not have to frequently update the channel parameters which are required for demodulation. Second, acoustic energy of multipath from Tx#1 to vertical receiving array decreases when the array element goes deeper. Conversely, acoustic energy of multipath from Tx#2 to vertical receiving array increases when the array element goes deeper. This result is consistent with the statistical SNR of the received signal in Table  1. In order to analyze the experimental results, we introduce the signal to noise and interference ratio (SINR) in this paper. According to Eq. (4), the SINR for k-th transmitter at the j-th hydrophone can be expressed as: Suppose the transmitted data of each user and noise are all independent, then Eq. (12) can be further written as: According to the channel estimation results and the statistical SNR of the received signal, we can calculate the SINR for Tx#1 and Tx#2 at each hydrophone using Eq. (13), which is shown in Table 2. As the depth of array element increases, the SINR for Tx#1 becomes smaller while the SINR for Tx#2 becomes bigger. Table 3 gives the data processing results using the TR-DFE based on LS channel estimation algorithm. It can be seen that only a single hydrophone can obtain satisfying performance for a certain transducer. For example, both P1 and P2 can decode the data stream from Tx#1 with the equalized MSE -9.9 dB and -7.5 dB, respectively. -9.9 dB -7.5 dB X X Tx#2 X X -8.5 dB -10.5 dB Note: the symbol "X" in Table 3 means that the data cannot be correctly decoded  Table 4 shows the data processing results using different pairs of array elements. Note that all these pairs include P1 and P4 elements which have the highest SINR for Tx#1 and Tx#2 respectively. According to Table 4, the following conclusions can be made: First, only two array elements (P1&P4) can achieve great performance improvement compared with single-channel receiver and two hydrophones can realize acceptable performance with the overall BER at the level of 10 -2 in this MIMO communication experiment. Second, normally better decoding performance is expected when more channels are adopted because TR will have stronger ability to mitigate ISI and CoI by using spatial diversity. It is true from the perspective of the overall BER. But for a certain transmitter, more channels do not necessarily bring performance improvement. For example, the decoding performance using P1&P4 and P1&P2&P4 for Tx#2 is worse than that only using P4. This is because the received signal on some hydrophones from Tx#2 (i.e. P1 and P2) is so weak that multi-channel processing does not improve the SINR in spite of the spatial gain.

Conclusion
Recently, a high frequency (8-12 kHz) MIMO acoustic communication experiment was conducted which differed from the previous works in that the sea surface was covered with about 40-cm-thick ice. Experimental data were used to demonstrate the performance of TR-DFE between a twoelement source array and a four-element receiving array, which was separated by 1 km range. Owing to the almost constant sound speed profile in the experimental region, the acoustic ray does not bend during propagation. On the other hand, the range between the source and receiving array is very short. Therefore most of the acoustic energy radiating from the transducers distributes to the limited water layer corresponding to the depth of the transducer at the receiving end. It seems to naturally separate data streams from different transducers which show the advantages of MIMO communication in under-ice environment. Acceptable performance with the overall BER at the level of 10 -2 can be obtained using only two array elements. In the future, the differences of experimental results between under-ice environment and open-water environment will be studied.