Iterative Equalization and Decoding Scheme for Underwater Acoustic Coherent Communications

Digital communications through underwater acoustic (UWA) channels differ from those in other media, such as radio channels, due to the high temporal and spatial variability of the acoustic channel which make the available bandwidth of the channel limited and dependent on both range and frequency. In order to overcome disadvantage factors and maximize performance to conduct real-time information understanding, underwater acoustic communications require the higher degree of information extraction and development from all kinds of onboard acoustic sensors and processing systems. A higher performance communication technology is needed in order to focus high-performance data processing on the problems and tasks faced by human operators and decision-makers. In order to establiseh reliable data commnication on the severely band-limited underwater acoustic channels, bandwidth-efficient modulation techniques (i.e. coherent communications) should be employed to overcome the inter-symbol interference (ISI) caused by channel multi-path propagation. The effective approach to eliminate the ISI caused by multipath propagation is that adaptive decision feedback equalizer (ADFE) integrates with spatial diversity. That is multi-channel adaptive decision feedback equalizer, which is applied in (Kilfoyle & Baggeroer, 2000; Stojanovic, 1996, 2005; Zhao et al., 2008) represents a more general approach to spatial and temporal signal processing.


Introduction
Digital communications through underwater acoustic (UWA) channels differ from those in other media, such as radio channels, due to the high temporal and spatial variability of the acoustic channel which make the available bandwidth of the channel limited and dependent on both range and frequency.In order to overcome disadvantage factors and maximize performance to conduct real-time information understanding, underwater acoustic communications require the higher degree of information extraction and development from all kinds of onboard acoustic sensors and processing systems.A higher performance communication technology is needed in order to focus high-performance data processing on the problems and tasks faced by human operators and decision-makers.In order to establiseh reliable data commnication on the severely band-limited underwater acoustic channels, bandwidth-efficient modulation techniques (i.e.coherent communications) should be employed to overcome the inter-symbol interference (ISI) caused by channel multi-path propagation.The effective approach to eliminate the ISI caused by multipath propagation is that adaptive decision feedback equalizer (ADFE) integrates with spatial diversity.That is multi-channel adaptive decision feedback equalizer, which is applied in (Kilfoyle & Baggeroer, 2000;Stojanovic, 1996Stojanovic, , 2005;;Zhao et al., 2008) represents a more general approach to spatial and temporal signal processing.However, Single technique, such as equalizer, is difficult to obtain satisfied data transmission because of the complexity of UWA channel, especially in shallow water channel.In recent years, more and more attention has been paid to Turbo codes, including parallel concatenated convolutional code (PCCC) (Berrou et al., 1993) and serially concatenated convolutional code (SCCC) (Benedetto & Montorsi, 1996), because of its near-capacity gains.The range of applications of Turbo codes has expanded to many areas of communications.Trellis-Coded Modulation (TCM) (Ungerboeck, 1982) is a kind of design option combining coding with modulation.It can provide over 3 dB coding gain without bandwidth expansion.Especially, it is interesting to combine PCCC or SCCC with TCM in order to improve the transmission spectral efficiency (i.e.parallel concatenated trellis codes modulation (PCTCM) (Benedetto et al., 1996;Chung & Lou, 2000;Legoff et al., 1994;Yang & Ge, 2005) and serial concatenated trellis codes modulation (SCTCM)) (Benedetto et,al., 1997;Divsalar & Pollara, 1997;Ho, 1997;Shohon et al., 2003) in order to improve the transmission spectral efficiency.
Therefore, iterative equalization and decoding (IED) based on equalizer and deocoding has been developed to obtain higher performance data transmission.Turbo equalizer (Berthet, 2000;Koetter et al., 2004) treats the channel encoder and channel itself as a serial concatenated system that can be decoded in an iterative scheme.A drawback of this iterative receiver is that the complexity of the turbo equalizer is orders of magnitude greater than the decision feedback equalizer (DFE).The turbo equalizer complexity grows exponentially with channel memory length.It isn't suit for the underwater acoustic channel with long delay spreads.In the structure of iterative euqalization and decoding, equalizer can use ADFE (Choi, 2008;Noorbakhsh et al., 2003) or equalizer based on channel estimation (Flanagan & Fagan, 2007;Otnes & Tuchler, 2004;Tuchler et al., 2002).For underwater acoustic channel with severely mutipath propagation and large time delay, adptive channel tracking can get better performance than channel estimation using trainning sequence or pilot symbols.
Comparing PCTCM, SCTCM has the following advantages: (1) It can further reduce the error floor of PCTCM to obtain lower BER (Soleymani & Gao, 2002).( 2) It has more flexible coding structure than PCTCM.In this chapter, SCTCM technique is adopted to increase bandwidth efficiency.Furthurmore, a rate R=1 recursive convolutional is adopted as inner encoder of SCTCM encode to get higher performance SCTCM scheme.Therefore, iterative equalization and decoding, based on multi-channel adaptive decision feedback equalizer with variant step tracking factor and decoder of SCTCM, is formed to aid weight update of equalizer utilizing decoding gain provided by decoder of SCTCM such that the performance of equalizer is enhanced.And then, the performance of communication system is improved greatly through iteration calculation between equalizer and decoder.
The structure of this chapter is as follows.Firstly an overview of the channel and system model is provided in Section 2.More specifically, the channel model based on sound speed profile (SSP) measured in the lake and Bellhop method and the system description are discussed in Sections 2.1 and 2.2, respectively.And then, the introduction of the proposed iterative equalization and decoding is presented in Section 3.More specifically, the structures of iterative equalization and decoding are discussed in Section 3.1.The proposed iterative equalization and decoding process is detailed in Section 3.2, commencing with a discussion of the multichannel adaptive equalizer structure in Section 3.2.1,followed by a description of the SCTCM decoding algorithm in Section 3.2.2, the method of the soft symbol estimation in Section 3.2.3.Our simulation results are provided in Section 4, while Section 5 concludes our findings.

Channel and system models
We begin with the channel model under consideration and then discuss the description for communication systems.

Underwater acoustic channel model
We adopt real measured data, sound speed profile (SSP), and a finite-element ray (FER) tracing method (Bellhop) (Porter & Liu, 1994) to model the underwater acoustic multipath propagation.Additionally we model the multipath components as fading due to acoustic propagation loss.
A given multipath arrival l is characterized by its magnitude gain l  and delay l  .These quantities are dependent on the ray length l l , which in turn is a function of the given propagation range R .The path magnitude gain is given by where, l  is the amount of loss due to reflection at the bottom and surface.The acoustic propagation loss, represented by   The path delay is given by , , 1 where, , li v is the sound speed of the ith water layer according to SSP.Thus, the overall channel impulse response is given by where, L is the multipath number, l A and l  are the amplitude and relative delay of the lth multipath arrival respectively.min ll tt   , min t is the minimus delay among the all path delays.
In the simulation section (Section 4), the SSP, measured on the lake (shown in Fig. 1), is adopted to model the multipath propagation.The SSP denotes the sound speed is changed with water depth.

Additionally, Doppler frequency
Where, c donotes underwater sound speed, r v is the relative speed between tranmiter and receiver, l  is the arrival angle for the lth arrival ray.

System description
The structure of transmitter is shown in Fig. 2. In comparison with high performance PCTCM scheme (Robertson & Woerz, 1998), the method in (Divsalar et al., 2000), with lower complexity, is adopted to design SCTCM, which can achieves with maximum free hamming distance as the outer code.An interleaver permutes the output of the outer code.The interleaved data enters a rate /1 i Rm m   recursive convolutional inner encoder.The m output bits are then mapped to one symbol belonging to a 2 m level modulation.In our system, the data symbol is QPSK modulated ( 2 m  ), i.e. x   with probability 1 4 .Before data symbol, the pilot symbol is transmitted to probe the channel impulse response (CIR).The LFM signal is used in our system.The frame structure is shown in Fig. 3.In receiver, Spatial diversity is achieved via multiple receiver arrays.The received signal at the kth array is given by where, cos is the Doppler frequency factor for lth multipah propagation,  nt is assumed to be a white Gaussian process with zero mean and variance 2 n  .
After demodulation by multiplying the local carrier frequency and Doppler frequency compensation, the received baseband signal at the kth array is given by where, k  is the remain phase distoration.
And then, the iterative equalization and decoding (IED) is performed on the received multichannel baseband signals.The concrete IED algorithm will be presented in the next section.

Iterative equalization and decoding (IED)
In this section, we first present the structures of iterative equalization and decoding and analyze the merits and drawbacks of different structures in Section 3.1.And then, the proposed iterative receiver is detailed in Section 3.2.

The structures of iterative equalization and decoding
Since the underwater acoustic ISI channel can be treated as a convolutional encoder with rate 1, it is possible to treat the channel encoder and channel itself as a serial concatenated system that can be decoded in an iterative scheme such as the turbo equalizer structure that is illustrated in Fig. 5.The motivation for the study of this receiver algorithm is to improve equalizer performance beyond that attainable by the optimum parameters decision feedback equalizer which also employs the all-training sequence.
The turbo equalizer consists of two soft input soft output (SISO) modules for the channel equalizer and the decoder that are arranged in a serial fashion.A drawback of this receiver algorithm is that the complexity of the turbo equalizer is orders of magnitude greater than the DFE.The turbo equalizer complexity grows exponentially with channel memory length, modulation level, and spatial diversity combining.It should be noted that traditionally the turbo equalizer has been used for known channels with reasonable ISI.It still needs to be demonstrated that this type of receiver can be used with modification to track the timevarying underwater channel and provide performance that exceeds the performance of the DFE using known training sequence throughout the entire data packet.
  The second structure is hard iterative (shown in Fig. 5.) The hard values of coded symbols

Fig. 5. Hard iteration
In this structure, the decoded symbols or hard decisions from the decoder after a first pass through the receiver system are then re-encoded to be used as the new training sequence to be used over the entire received data packet.Therefore, in the second pass or iteration, decision directed equalization after the short initial training sequence is not employed.Subsequent passes or iterations through the data in this fashion can be made.However diminishing improvements are obtained due to the hard decision nature of this algorithm.Feedback error propagation can still occur in this algorithm due to uncorrected errors at the output of the soft input hard output decoder.The desire for performance improvement by using SISO decoders as well as added information that the equalizer can provide to correct decoder errors provides the motivation for the soft iterative approach.
An improved receiver algorithm as compared to the hard iterative approach would be to employ all the information regarding the received symbols to generate the new training sequence by combining soft values of the coded symbols out of the decoder and the soft information about the detected symbols provided by the decision directed mode of the equalizer.This is intent of the soft iterative manner.
In the soft iteration, the decision feedback equalizer is modified so that it can use soft a priori information from the decoder from previous iterations.In order to obtain soft a priori information as opposed to hard decisions, the decoder structure must now take the form of a SISO device.One such device is the Maximum A posteriori (MAP) decoder.The method in which the information streams from the decoder and equalizer are combined is crucial because log likelihood ratio (LLR) values are produced from the decoder feedback path.In this chapter, the soft iteration structure is adopted.

Soft iterative equalization and decoding (IED)
The structure of the proposed IED with phase compensation is shown in Fig. 6.Fig. 6.The proposed IED As shown in Fig. 6, the received signal at each array elements is T/2 fractional sampled.The digital phase lock loop (DPLL) is adopted to correct phase distortion.Then, the feedforward and feedback filters are applied to obtain the estimation of transmitted symbol.In the IED scheme, the multichannel adaptive decision feedback qualizaer with phase compensation and decoder of SCTCM exchange soft information in an iterative manner.Specifically, at the output of the equalizer, the likelihood ratio (LLR) calculator computes soft information of coded bits based on the symbol estimation   dn.This soft information is delivered to the maximum a posteriori (MAP) decoder of SCTCM.In addition to providing the decoded output, the decoder also computes soft information on the coded bits, which is converted to soft estimates of the symbols.These soft symbol estimates are used to aid the operation of the equalizer and its adaptive weight update algorithm.

Mutichannel adaptive equalization
The received signal will carry out equalization proccessing (including carrier phase compensation) after demodulation.The main task of multichannel adaptive decision feedback qualizaer is eliminate inter-symbol interference (ISI) caused by multipath propagation.
According to minimum mean square error (MMSE) scheme, an error signal is used to update receiver parameters.The error signal   enof adaptive update algorithm as follows  As shown in Fig. 6., the baseband signals firstly perform carrier phase compensation.Using DPLL technology (Proakis, 2003), we can obtain carrier phase compensation as follows Where, A fast self-optimized LMS (FOLMS) algorithm (Bragard & Jourdain, 1990) is used to update the equalizer vector   w n .But in (Bragard & Jourdain, 1990), the formulations are conducted based on the single channel line equalizer (LE).In this chapter, we extent it to multi-channel decision feedback equalizer and consider the effect of carrier phase compensation.It can be deducted by the composite input data

 
u n and the error signal  en.So, we can rewrite the FOLMS algorithm as follows Where,  n  is the step-size factor for controlling the convergence ratio of the equalizer, which can adaptively update,   g n is temporary variant for updating   n  ,  is constant.
Re( )  denotes the real part of data.

Decoding of SCTCM
In order to simplify the decoding algorithm of SCTCM, the symbol decoding of SCTCM is transformed into bit decoding through calculating the LLR of coded bits.The position of LLR calculator is shown in Fig. 6.The calculation is detailed as follows.
For MPSK, the corresponding 2 log mM  coded bits are mapped to an M-ary signal.The probability   of ith coded bit of kth received symbol can be calculated as So, (19) can be simplified as The probability   of ith coded bit of kth received symbol can be calculated as The LLR value of ith coded bit of kth received symbol is We can simplify symbol decoding into bit decoding using Eq.( 25).The probability distributions of the output sequences In this chapter, log-map algorithm (Soleymani & Gao, 2002) is used to simplify calculation through transforming multiplication into addition.

Soft symbol estimation
As shown in Fig. 6, the LLR values of coded bits, output from decoder of SCTCM, are used to implement symbol estimation.And then, these symbols are fed back to feedback filter of MC-ADFE to perform joint iterative scheme.So, the symbol estimation is key module to perform soft IED.
There are two methods to estimate data symbol: hard estimation and soft estimation.
Compare with hard estimation, soft estimation can void error symbols spread during the course of iterations.What's more, soft estimation can more sufficiently utilize decoding gain to update system performance.In this chapter, soft method is adopted to estimate data symbols.
The soft symbol estimation can be obtained as follows:

Simulation results
In this section, we use simulation experiments to verify the performance of the proposed soft IED algorithm.The system parameters of computer simulation are shown in Table 1.
The outer decoders of SCTCM adopt convolutional codes encoder with 4-state 1/2 code rate for QPSK modulation.In this paper, we integrate the multi-path fading and additive white Gaussian noise to simulate underwater acoustic channel.
Based on the sound speed profile (SSP) measured in the lake and finite-element ray (FER) tracing method (Bellhop) (Porter & Liu, 1994), the channel impulse response is shown in Training symbols 200 sys Table 1.Simulation parameters

Soft iterative performance of iterative equalization and decoding
The system parameters of simulation are shown in Table 1.The channel impulse responses are shown in Fig. 7.As shown in Fig. 7, the multi-path propagation is very seriously.8 shows the BER curves of IED algorithm with soft iteration for QPSK modulation.As show in Fig. 8, the iteration algorithm can sufficient utilize the decoding gain provided by decoder of SCTCM to enhance the equalizer performance such that the system performance is increased and the data transmission with lower BER can be obtained.

Dual model of iterative equalization and decoding
The dual model IED is shown in Fig. 9.There are two parts: (1) iterative equalization and decoding; (2) iterative decoding.As mentioned in Section 3, the mutichannel ADFE and decoder of SCTCM exchange soft information in an iterative manner in the IED scheme.So, we can perform decoding iteration before IED.And thus, the accuracy of symbol estimation is further improved such that the equalizer performance is improved greatly.2, in dual model IED, the soft symbols estimation, based on the coded bits output from decoder of SCTCM, are more accurated.And thus, the propagation errors can be futherly reduced.

Conclusions
In this chapter, according to the characteristics of underwater acoustic channel, SCTCM technology with rate-1 inner code, is adopted to improve the bandwidth efficiency of underwater acoustic channel.Simultaneously, LLR calculation is introduced to simplify symbol decoder into bits decoder.The soft IED scheme with soft symbol estimation is proposed to overcome the multi-path fading of underwater acoustic channel and enhance the performance of equalizer through utilizing decoding gain provided by decoder and the information symbols with soft symbol estimation fed back to equalizer so that the performance of communication system is improved greatly.What's more, the dual model IED scheme is proposed to obtain lower BER in order to meet the demands of higher system performance.The simulation results verify the proposed algorithm can obtain satisfied data transmission with the small iterations, especially the dual model IED.

Fig. 1 .
Fig. 1.Sound speed profile (SSP) Fig. 2. The structure of transmitter Fig. 3. Data frame structure the received signal kkk y dn   ,and from the noise distribution it follows that the sets of all possible symbol values, in which the ith coded bit is 1 and 0 respectively.

Fig. 7 .
Fig.7.From the SSP (shown in Fig.1.),we know that the water with mixed gradient SSP is about 53m deep.The transmission distance is 2000m.
Fig. 7. Channel impulse response (2000m)Fig.8shows the BER curves of IED algorithm with soft iteration for QPSK modulation.As show in Fig.8, the iteration algorithm can sufficient utilize the decoding gain provided by decoder of SCTCM to enhance the equalizer performance such that the system performance is increased and the data transmission with lower BER can be obtained.

Fig. 9 .
Fig. 9. Dual model IED As shown in Table2, in dual model IED, the soft symbols estimation, based on the coded bits output from decoder of SCTCM, are more accurated.And thus, the propagation errors can be futherly reduced.
N and M denote the feedforward and feedback filter taps respectively, * denotes complex conjugate, H denotes transpose conjugate, T denotes transpose.

Table 2 .
Performance of dual model IED