Junyi Xi , Shefeng Yan ＊, Lijun Xu , Jing Tian

1 Institute of Acoustics, Chinese Academy of Sciences, Beijing, 100190, China

2 University of Chinese Academy of Sciences, Beijing, 100190, China

* The corresponding author, email： sfyan@ieee.org

I. INTRODUCTION

Multiple-Input Multiple-Output (MIMO)Underwater Acoustic (UWA) communication presents various technique challenges for robust high data-rate transmission, such as limited bandwidth, large Doppler spread,fast time-variation, severe Inter-Symbol Interference (ISI) and Co-Channel Interference(CCI) [1-3]. Those features make the UWA channel one of the most challenging channels.Therefore, efficient equalization schemes are naturally required to improve the detection performance. One of the widely used equalization schemes to combat severe ISI is the Decision Feedback Equalizer (DFE), which can be implemented in either time domain [4] or frequency domain [5, 6]. The DFE bene fits from the interference cancellation using feedback decision symbols, thereby effectively reducing error rate for UWA transmissions.

Motivated by the turbo decoding principle,turbo equalization is another powerful technology that could achieve satisfactory performance in the complicated UWA channels[7]. Different from the traditional DFEs with one-time iteration, turbo equalizers benefit from the soft-information exchange between the equalizer and the decoder, and implement detection iteratively. The initially proposed turbo equalizer is based on the MaximumA Posteriori(MAP) criterion [8], whose computational complexity is prohibitively high in the severe ISI channel. To achieve a performance-complexity tradeoff, more practical Minimum Mean Squared Error based Linear turbo Equalizer (MMSE-LE) [9] and Decision Feedback turbo Equalizer (MMSE-DFE) [10]are proposed. However, the hard-decision based MMSE-DFE suffers from catastrophic error propagation, thus resulting in even worse performance than the MMSE-LE. One of the effective means to deal with error propagation effect is replacing the feedback hard-decision symbols with more accurate soft-decision symbols, thus making the whole equalization system more robust, such as the Soft ISI Cancellation based turbo Equalizer (SICE) [11]and the Soft-Decision Feedback turbo Equalizer (SDFE) [12]. Bidirectional structure is another novel method to suppress error propagation. This ideal was first developed for the traditional hard-decision DFE by combining a conventional DFE with a time-reversed DFE[13]. Then, the bidirectional structure is incorporated with the Virtual Time Reversal Mirror(VTRM) technique for UWA communication systems [14]. In [15], a soft-in soft-out bidirectional turbo DFE with a low-complexity combining scheme is proposed and it is said to approach the performance of the MAP turbo equalizer after a large number of iterations.Recently, a bidirectional SDFE with an extrinsic information combining scheme is proposed for MIMO systems and its performance improvement over the single-direction one has been verified by a UWA communication experiment [16].

The aforementioned turbo equalizers either assume that the Channel Impulse Response(CIR) is perfectly known or require explicit channel coefficients estimation. Therefore,accurate CIR estimation plays a critical role in these Channel-Estimation based Turbo Equalizers (CE-TEQs). One main drawback of the CE-TEQ is the high computational complexity of the large-dimension matrix inversion in computing the equalizer coefficients, especially in a long delay-spread channel. Furthermore, to track the time-varying channel,channel re-estimation should be made by using the previous detected symbols, which will definitely lead to much more computational burden [17]. As an alternative to the CE-TEQ,the Direct-Adaptation based Turbo Equalizer(DA-TEQ) adapts equalizer coefficients directly without any channel estimation [18-20],thus saving large amounts of computational cost. However, most existing DA-TEQs suffer from a slow convergence rate due to the hard-decision error used to update equalizer coefficients. Recently, a Soft DA-TEQ utilizing theapriorisoft decision to direct the equalizer coefficients adaptation, namely, the Soft DA-TEQ, is proposed for MIMO UWA communication systems [21]. The derivation of the Soft DA-TEQ is based on the Expectation Maximization (EM) algorithm [22],which greatly speeds the convergence rate during turbo iterations.

In this paper, the authors propose a Soft Direct-Adaptation based Bidirectional Turbo Equalizer (Soft DA-BTEQ) for MIMO systems.

In this paper, we propose a Soft Direct-Adaptation based Bidirectional Turbo Equalizer(Soft DA-BTEQ) for MIMO systems. Compared with existing schemes, there are two enhanced features in the new equalization scheme.

First, the proposed scheme adopts the Soft DA-TEQ embedded with the Fast self-Optimized LMS (FOLMS) algorithm [23] to implement equalization. Due to relatively higher accuracy of soft decision error and self-adaptation of the step size, the combination of both the algorithms yields a faster convergence rate. Meanwhile, the second-order Phase-Locked Loop (PLL) [24] for MIMO systems is also employed during the equalization process, thus channel tracking in the time-varying UWA environment could be achieved.

Second, the Soft DA-TEQ is extended to the bidirectional structure, where a conventional Soft DA-TEQ is combined with a time-reversed Soft DA-TEQ. Based on the MMSE criterion, a weighted linear combining scheme is then derived for bidirectional combining. Attributed to low correlation between the outputs of the opposite-direction equalizers, the bidirectional diversity gain can be exploited, and the error propagation caused by the wrong decision symbols can be effectively eliminated. Both the simulation and experimental results show that the Soft DA-BTEQ achieves a lower Bit Error Rate (BER) than the single-direction Soft DA-TEQ, and the soft direct-adaptation type equalizers have a faster convergence rate than the hard ones.

The rest of this paper is organized as follows. Section 2 provides a short introduction of system model and preliminaries. Section 3 introduces the Soft DA-BTEQ, including the Soft DA-TEQ and the bidirectional combining scheme. Section 4 and Section 5 present the simulation and experimental results, respectively. Finally, Section 6 concludes this paper.

II. SYSTEM MODEL AND PRELIMINARIES

Consider a MIMO system withNtransducers andMhydrophones. The transmitting process is depicted in Figure 1. The information finite impulse response filter and the noise is assumed as Additive White Gaussian Noise(AWGN). Thus, the received baseband signal of them-th hydrophone at timekis expressed as

Next, several definitions of the traditional turbo equalizer are introduced. According to the Gaussian distributed assumption, the

Fig. 1 Structure of the transmission system

III. PROPOSED SOFT DIRECTADAPTATION BASED BIDIRECTIONAL TURBO EQUALIZER (SOFT DA-BTEQ)

The structure of the proposed Soft DA-BTEQ for MIMO systems is depicted in Figure 2,where two Soft DA-TEQs runs in parallel：one is the conventional Soft DA-TEQ and the other is the time-reversed Soft DA-TEQ. The time-reversed Soft DA-TEQ is implemented with the Time-Reversal (TR) operations mounted at both ends of the conventional one.

3.1 Soft direct-adaptation based turbo equalizer (Soft DA-TEQ)

Modified from the Hard DA-TEQ, the Soft DA-TEQ utilizes thea priorisoft decisions from last turbo iteration to adjust the equalizer’s coefficients [21]. Bene fiting from the EM algorithm [22], the Soft DA-TEQ provides the maximum likelihood estimation of the coefficients and achieves a faster convergence rate than the hard one. In this paper, the Soft DA-TEQ is incorporated with the FOLMS algorithm and the second-order PLL to track the time-varying channel, and then implemented with bidirectional structure to eliminate error propagation effect.

Fig. 2 Structure of the proposed Soft DA-BTEQ

The equalization process of the Soft DATEQ can be divided into two phases： the training phase and the decision-directed phase.In the training phase, the training sequence known to the receiver is used to adjust the equalizer coefficients first, thus making sure that the algorithm is convergent. After that,previous detected symbols are adopted to update the coefficients in the decision-directed phase. The output of the equalizer and the coefficients updated via the LMS algorithm are given by

It is worth noting that no signal is fed back to the equalizer in the first-time equalization and it is equivalent to implementing a linear equalization. Since the residual ISI and CCI cancellations are not perfectly addressed, the equalized results may not be satisfactory. In the next iterations, the estimated symbol vecspectively. With the interferences suppressed,the equalized result becomes more accurate than the previous iteration and the detection performance is improved. The iteration will continue until the equalizer converges.

3.2 Bidirectional combining scheme

The decision-feedback type equalizers suffer from error propagation which is caused by the feedback wrong decision symbols. To this end, a conventional Soft DA-TEQ is combined with a time-reversed Soft DA-TEQ to harvest bidirectional diversity and suppress error propagation. The diversity brought by the bidirectional structure can be explained by the following reason. If the channel impulse response is unsymmetrical, which is always the case in UWA systems, its equivalent time-reversed channel is different from the original one, which results in different error patterns and locations in the outputs of the opposite-directional equalizers. Besides, in this conventional equalizer, a primary error induces a burst of secondary errors that proceed in a forward direction. When the signal is processed using time-reversed equalizer, the error propagation runs in a backward direction. In other words, their error propagation directions are opposite. Both the factors result in a low correlation between the errors of two equalizers which provides bidirectional diversity to improve performance.

To facilitate the bidirectional combining, a weighted linear combining scheme is considered as

IV. SIMULATION RESULTS

Fig. 3 Frame structure

Fig. 4 Sound velocity pro file

Fig. 5 BER performance comparison

The BER performance under various Signal-to-Noise Ratios (SNRs) is demonstrated in Figure 5 by using Monte Carlo simulations with 1500 repetitions. Note that the BER curve of the Soft DA-TEQ in the first iteration is the same as that of the Hard DA-TEQ. This phenomenon can be explained by the reason that there is noa priorisoft decision symbol available in the first-time equalization, and linear equalization is adopted in the Soft DATEQ instead, which is the same case with the Hard DA-TEQ. Therefore, the Soft DATEQ equals to the Hard DA-TEQ in the firsttime equalization. After that, the Soft DATEQ usesthea priorisoft decision symbols to adjust equalizer coefficient while the Hard DA-TEQ use hard ones. After three iterations,the Soft DA-TEQ gains about 1 dB over the Hard DA-TEQ at the BER level of 10-2. With the help of the bidirectional structure, the Soft DA-BTEQ clearly outperforms the Soft DATEQ in the first iteration, and the performance gap becomes larger after three iterations. This performance enhancement is attributed to the weighted linear bidirectional combining scheme, which can effectively eliminate error propagation compared with the single-direction one. The simulation results of the Soft DA-BTEQ and the Hard DA-TEQ with the traditional LMS algorithm rather than the FOLMS algorithm are also included. As expected, not using FOLMS algorithm to adjust coefficients leads to 0.4 dB performance loss at the BER level of 10-3after three iterations for the Soft DA-BTEQ. For the Hard DATEQ, the performance improvement brought by the FOLMS is more obvious. At the BER level of 10-2, the Hard DA-TEQ with the FOLMS gains about 1.1 dB over the one with LMS after three iterations.

Fig. 6 Estimated CIR of the 500-m transmission

Fig. 7 Estimated CIR of the 1000-m transmission

V. EXPERIMENTAL RESULTS

The proposed method has been tested by a UWA communication experiment conducted in the Thousand Island Lake, Hangzhou, Zhejiang, China, in 2015. 2×4 MIMO system was considered in the experiment： two transducers and four hydrophones were placed with top ones 10 m below the lake surface. Both the transducer and hydrophone arrays were fixed vertically with 1-m spacing. The water depth was about 50 m. The experiments were conducted for two transmission ranges： 500 m and 1000 m. The processes of the encoding,interleaving, and modulation in the experiment are the same as those in the simulation,thus details are omitted here for brevity. We transmitted 138 frames and all of them were separated by some gaps to prevent inter-block interference.

The average BER performance of the 500-m and 1000-m transmissions with different iterations using various algorithms is summarized in Table 2. As we can see, the Hard DATEQ suffers from severe error propagation and has the worst performance. It cannot achieve convergence even after five iterations. Howev-er, with the Soft DA-TEQ, more satisfactory performance is obtained, and error-free detection is achieved after five iterations for the 1000-m transmission. Note that the Hard DATEQ and the Soft DA-TEQ exhibit identical BER performance after one-time equalization and decoding, which is consistent with the simulation results. Besides, the diversity gain brought by the bidirectional structure is also obvious. For the 500-m transmission, the Hard DA-BTEQ achieves BER=0.0009 after four iterations and it even outperforms the Soft DA-TEQ. With the Soft DA-BTEQ, error-free detection can be both achieved after only three iterations for the 500-m transmission and four iterations for the 1000-m transmission.In terms of convergence rate and BER, the Soft DA-BTEQ clearly outperforms the other equalization schemes. In addition, the BER performance comparison between the LMS and the FOLMS algorithms for the 500-m transmission is demonstrated in Table 3. It is apparent that the FOLMS can achieve a lower BER when the algorithms are convergent,compared with the LMS. Although both the algorithms can finally achieve error-free detection for the Soft DA-BTEQ, the FOLMS only requires two iterations while the LMS needs three iterations.

Table I O ptimal weighting factors for the Soft DA-BTEQ

Fig. 8 Phase estimate for the top transducer to the top (T1-H1) and deepest (T1-H4) hydrophones

T able II BER performance comparison among different equalization schemes

Table III BER performance comparison between the LMS and the FOLMS algorithms for the 500-m transmission

Fig. 9 EXIT charts of the 500-m transmission

Fig. 10 EXIT charts of the 1000-m transmission

VI. CONCLUSION

A Soft DA-BTEQ is proposed for MIMO UWA communication systems. The Soft DATEQ combined with the FOLMS and the second-order PLL is extended to the bidirectional structure. The conventional Soft DATEQ and the time-reversed Soft DA-TEQ are combined with a weighted linear combining scheme. Thus, the bidirectional diversity gain is exploited and the error propagation is suppressed. The efficiency of the proposed method has been veri fied by both the simulations and UWA communication experiments.The simulation and experimental results show that the Soft DA-BTEQ achieves performance improvement over the other equalization schemes, and error-free detection can be both achieved for the 500-m and 1000-m transmissions.

ACKNOWLEDGEMENTS

This work has been performed in the Key Project “Theory and technologies of data acquisition and reliable transmission for mobile underwater sensor node” supported by National Natural Science Foundation of China (No.61431020).

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