Fang Fu，Dan-Feng Zhao

(College of Information and Communication Engineering，Harbin Engineering University，Harbin 150001，China)

1 Introduction

Underwater acoustic(UWA) channel is characterized byfrequency－timevarying， multipath propagation and bandwidth limited. Amplitude attenuations of received symbols are caused by both fast variation and ambient noise of UWA channel.Long range UWA communication system requires robust and spectrally efficient communication techniques for fading channels.To meet this requirement，significant research has been actively investigated［1－11］.

Although the bandwidth of UWA channel can be utilized efficiently by using phase shift keying(PSK)and pulse phase modulation (PPM)［1］， these approaches have phase ambiguity problems resulting from the estimation of carrier phase.Direct sequence spread spectrum(DS－SS)［2］，F(xiàn)lip Hop(FH)［3］and time reversal mirror(TRM)［4］are the good candidates for long－range UWA communication applications.

Toeliminate inter－symbolinterference(ISI)caused by multipath propagation，one effective approach is thatthe adaptive decision feedback equalizer(ADFE).Yin et al.［5］proposed that it is almost impossible to adopt liner minimum mean square error(MMSE)equalizer in the horizontal channel.The calculation complexity of MMSE algorithm increases exponentially with the increase of ISI length.Hence，linear mean square(LMS)equalizer is adopted in this system.Pelekankis et al.［6］analyzed beam forming technology to alleviate ISI due to the multipath effect.Beam forming can pick out line－of－sight path or shortcut from multipath.However，it has one common defect:it is sensitive to the locations of transmitter and receiver.Recently，low－density parity－check(LDPC)code has been aroused in UWA communication for its ability to achieve near Shannon limit performance［7－8］. To improve the reliability of long－range underwater communication systems，the possible error bursts due to momentary bad channel conditions or highly attenuated frequency bands must be minimized，and that is why the system must also include an LDPC encoder.

Iterative(“turbo”)processing can be done by exchanging soft information between information source decoder and channel decoder［9］，and also can be done by exchanging soft information between equalizer and channel decoder［10－11］.In contrast with their systems，iterative processing herein is implemented by exchanging information between demodulator and channel decoder.In the conventional methods，LDPC decoder and QPSK demodulator are independent.The output of QPSK demodulator directly goes into the LDPC decoder.LDPC decoder employs log－BP softdecision algorithm to compute extrinsic info rmation and outputbitvalue to information sink. However，conventionalmethodsare failed to eliminate ISI efficiently in long－range UWA communication.

The main contribution of this paper is as follows:LDPC－QPSK iterative SISO module is proposed to mitigate ISI problem，and Walsh－m composite sequence is also provided to increase transmission range.Three types of UWA channel models are simulated.

2 Underwater Acoustic Channel

UWA channel can be regarded as a low－frequency pass－band filter.Sound absorption loss increases with both range and frequency，and limits the available bandwidth.In addition，ambient noise in UWA channel consists of four kinds of noise:turbulence，shipping，waves and thermal noise.As a result of surface－bottom reflections，time－varying multipath effect impedes the acoustic signals.

Fig.1 represents the relationship between signalto－noise ratio(SNR)atthereceiverinput， the available range and bandwidth.For each transmission distance，there clearly exists an optimal frequency［12］.With the increase of the system range，the available bandwidth dramatically decreases.

Fig.1 SNR vs.carrier frequency

Most commonly，UWA communication system can be described as:

where s(n)denotes transmitted signal;r(n)denotes received signal;h(n)denotes channel impulse response，and w(n)denotes the additive white Gaussian noise(AWGN).

Channel transmission function H(z)，computed form the Z transform of h(n)，can represent channel characteristic.Considering UWA channel is space－time fast variant channel，it is difficult to estimate H(z).Within coherence time，the UWA channel can be treated as ascertainable linear time－invariant filter or ascertainable space－time filter.Thus，H(z)can be derived as:

where N denotes the multipath spread of the channel in symbol durations;Airepresents amplitude for each path;τirepresentstimedelay;T expressesthe sampling period，andillustratesmathematical expression of the rounding operation.

3 System Model

The system model of proposed LDPC－QPSK SISO iterative system is illustrated in Fig.2.

At the transmitter，Walsh－m composite sequence is used to keep orthogonality when synchronization and decrease cross correlation when asynchronism.Use primitive polynomial 1+x+x4to generate m sequence(1－1－1－1－1 1－1 1－1－1 1 1－1 1 1).Walsh sequence is(1 1 1 1－1－1－1－1 1 1 1 1－1－1－1－1).

Fig.2 System model

At the receiver，SISO module is employed.It consists of QPSK demodulator and LDPC decoder.SISO module uses the iterative algorithm to produce and exchange soft information.Soft－output of QPSK demodulator subtracts the soft－feedback from LDPC decoder toQPSK demodulatorand getonesoftinformation result.The result is taken as soft－input of LDPC decoder.Soft－output of LDPC decoder subtracts the input of decoder，and get another soft－information result.On the one hand，the result is taken as softinput of QPSK demodulator;on the other hand，the resultis taken as soft－feedback which willbe subtracted by the output of QPSK demodulator in the next iteration.

Li et al.［13］discussed the joint iterative method with hard－feedback， employing BICM scheme with 8PSK modulation. In thispaper， a soft－decision feedback is exploited. Namely， the extrinsic information of the coded bits in the form of loglikelihood ratio(LLR)is exchanged between decoder and demodulator. Compared with hard－decision feedback，soft feedback can not only improve the gain in coded modulation system but also mitigate error propagation.Meanwhile，bit－interleaver plays little role in increasing the distance between information bits in terms of LDPC codes.Because parity－check matrix H of LDPC codes is low density，LDPC codes can do well without bit－interleaver. In addition， bit－interleaver wastes much computation and goes against real time.Consequently，LDPC－QPSK joint iterative SISO module without bit－interleaver is proposed.

We stick to the following notations.Superscript q represents quantities during the q-th round of outer iteration.Subscript D→L denotes quantities passed from the demodulator to the LDPC decoder，and vice versa，D ← L.Let the variable L refer to all the extrinsic information，and define LLR as

The demodulator deals with both the received complex symbols y and the corresponding a priori(bi，j).The output extrinsic information(bi，j)of the soft demodulator is computed as follows:

At the initial iteration，it is assumed the equally likely prior p(xt)，and set(bi，j)to zero.In the last iterative，the soft decisions output from LDPC decoder are obtained based on the extrinsic bit information.

4 Simulation Results and Discussions

This section provides the simulation results to verify the effectsofunderwateracoustic channel model，signal mapping and spreading sequence on BER performance.The default parameters of proposed system are as follows:code－length of half rate LDPC is 1536;the step－size of equalizer is 0.02;the number of LDPC decoding iteration is 10，and the length of Walsh－m composite sequence is 240.In these figures，“no iteration”indicates the conventional method in which decoding and demodulation are independent.“n iteration(s)”represents the proposed method with n round(s)of joint iteration between LDPC decoder and QPSK demodulator.

4.1 Underwater Acoustic Channel Model

Generally，the offing near China is shallow sea，sound velocity section changes quickly with season.In winter，underwater acoustic channel appears to be isothermal，regarded as positive sound velocity gradients(PSVG).Nevertheless， in summer， it appears to be variant temperature obviously，treated as negative sound velocity gradients(NSVG)［14］.Anothertype ofunderwater acoustic channelis Invariable Sound Velocity Gradients(ISVG)where sound velocity is invariable［15］.

Type 1:ISVG

Channel transmission function in condition of ISVG channel is as follows:

For ISVG channel，the channel time domain impulse response h(n)is shown in Fig.3(a);the characteristicsofmagnitude－frequency and phasefrequency are shown in Fig.3(b);BER curves are plotted in Fig.3(c).

Fig.3(c)illustrates that during three iterations，the BER curves converge quickly.Compared with the case of“no iteration”，the proposed method can obtain 3 dB coding gain after three iterations when BER is 10－5.

Type 2:NSVG

Channel transmission function in condition of NSVG channel is as follows:

Fig.3 ISVG channel

For NSVG channel，depth ranges from 100 m to 300 m，and sound velocity decreases with the increase of depth.Given depth is 300 m，and then channel time domain impulse response h(n)is shown in Fig.4(a);the characteristics of magnitude－frequency and phase－frequency are shown in Fig.4(b);BER curves are plotted in Fig.4(c).

Fig.4(c)expresses that during two iterations;the BER curveshave a good convergence behavior.Compared with the case of“no iteration”，the proposed method can obtain 2.6 dB coding gain after two iterations when BER is 10－5.

Fig.4 NSVG channel

Type 3 PSVG

Channel transmission function in condition of PSVG channel is as follows:

For PSVG channel，depth is more than 1000 m，and sound velocity increases with the increment of depth.Given depth is 1100 m，and then channel time domain impulse response h(n)is shown in Fig.5(a);the characteristics of magnitude－frequency and phasefrequency are shown in Fig.5(b);BER curves are plotted in Fig.5(c).

Fig.5(c)illustrates that during three iterations;the BER curvesalso have a quick convergence behavior.When the SNR is －7.3 dB，for the case of“no iteration”，the BER is still as high as 10－3，but for the case of“three iterations”，the BER is as low as 10－6.It demonstrates that the proposed method can improve the BER performance from 10－3to 10－6.

Fig.6 gives the BER performance comparison of three types of underwater acoustic channel models aforementioned.It shows that as SNR increases，three BER curves dramatically decrease when iteration number is 2.In addition，ISVG channel performs best，and PSVG channel performs worst.

Theperformancecomparison in thesecond iteration is shown in Table 1.

Fig.5 PSVG channel

Fig.6 Performance comparison

Table 1 Performance comparison

4.2 Signal Mapping

In this paper，we discuss two kinds of signal mappings:Gray mapping and set－partitioning(SP)mapping.Graymappingismainly designed and optimized for the case with independent decoding，while SP mapping is better than Gray mapping for proposed system［16］. Fig.7 represents the BER performance using gray mapping.It illustrates that as SNR increases，BER does not decline drastically when iteration number is more than 2.Fig.8 gives the performance comparison ofgraymappingand SP mapping.It can be seen that when the iteration number is 2，SP mapping can obtain 0.8 dB coding gain over gray mapping at BER of 10－5.

Fig.7 Gray mapping performance

Fig.8 Performance comparison

4.3 Spreading Sequence

In this simulation experiments，the length of m sequence is denoted by M=15.The length of Walsh sequence is denoted by N=16.Repeat each bit of m sequence 16 times to get one new sequence，regarded as A.Repeat Walsh sequence 15 times to get another new sequence，regarded as B.Multiply A by B to generate Walsh－m composite sequence［17］.So，the length of Walsh－m composite sequence is K=MN=240.In the following，we analyzed the effect of Walshm sequence on bit rate and spreading gain.

Step 1:As it may be expected，the period of Walsh－m sequence can be obtained as follows:

where Tmrepresents the period of m sequence;Twrepresents the period of Walsh sequence.

Step 2:The bit rate of Walsh－m sequence is calculated according to the following equation:

where Rmrepresents the bit rate of m sequence;Rwrepresents the bit rate of Walsh sequence.

Step 3:Regarding Rc=Rw，Rb=Rwm，spreading gain denoted by G can be derived:

Step 4:The effect of Walsh－m sequence on spreading gain can be seen in Table 2.

Table 2 Effect of Walsh-m sequence on spreading gain

Fig.9 illuminates the advantage of Walsh－m complex spreading sequence，compared with m and Walsh sequences，when iteration numberis2.Obviously，Walsh－m sequence can achieve about 9 dB over the others.

Fig.9 Performance comparison of different spreading sequence

5 Conclusions

This paper provides an insight into long－range UWA communication.The proposed system based on LDPC－QPSK iterative SISO module spreads spectrum by Walsh－m composite sequence.By the use of SISO module，the system is capable of mitigating ISI.Walsh－m composite sequencecan notonly keep orthogonality when the system is in synchronous state，but also can decrease cross correlation when the system is in asynchronous state.

The performance of proposed system is demonstrated at three types of UWA channels，including positive，negative and invariable sound velocity gradients channel.The proposed method is suited for long－range UWA communication，even at low SNR such as －9 dB，the system can also perform well.Numerical results verify thatthe proposed method exceeds conventional methods.With the increase of demands of the transmission range and rate，the investigation of high performance signal mapping method and iterative soft feedback hasbecome an inevitable trend of underwater acoustic communication systems.

［1］Zhang G S，Hovem J M，Dong H F，et al.An efficient spread spectrum pulse position modulation scheme for point－to－point underwater acoustic communication.Applied Acoustic，2010，71(1):11 －16.

［2］Jamshidi A.Direct sequence spread spectrum point－to－point communication scheme in underwateracoustic sparse channels.IET Communications，2011，5(4):456－466.

［3］Edelmann G F，Akal T，Hddgkiss W S，et al.An initial demonstration of underwater acoustic communication using time reversal.IEEE Journal of Oceanic Engineering，2002，27(3):602－609.

［4］Huang J G，Chen Y，Zhang Q F，et al.Multi－frequency DPSK modulation forlong－range underwateracoustic communication.Proceedings of the Oceans 2005 Europe International Conference.2005.1074－1077.

［5］Yin J W，Hui J Y，Wang Y L，et al.M－ary chaotic spread spectrum Pattern time delay shift coding scheme for multichannel underwater acoustic communication. ACTA Physica Sinica，2007，56(10):5915－5921.

［6］Pelekanakis K，Baggeroer A B.Exploiting space－timefrequency diversitywith MIMO－OFDM forunderwater acoustic communications. IEEE Journal on Ocean Engineering，2011，36(4):502－513.

［7］Li Y X，Liang G L，Zhang G P，et al.Simulation of highorder modulation LDPC code in underwateracoustic channel.Journal of Harbin Institute of Technology，2010，42(9):1472－1475.

［8］Lu B，Yue G S，Wang X D.Performance analysis and design optimization of LDPC－Coded MIMO OFDM systems.IEEE Transactions on Signal Processing，2004，52(2):348－360.

［9］Zhang Y X，Sun J，Wang Y，et al.Joint source－channel decoding based on VLC and LDPC.Computer Engineering，2006，32(10):215－217.

［10］Zhao L.A novel receiver algorithm for underwater acoustic coherent communications.Technical Acoustics，2007，26(2):291－295.

［11］Zhao L，Ge J H.Joint iterative equalization and decoding for underwater acoustic coherent communication systems.Journal of Xidian University，2011，38(4):61－65.

［12］Stojanvic M.On the relationship between capacity and distance in an underwater acoustic communication channel.Proceedings of the First ACM International Workshop on Underwater Networks.2006.41－47.

［13］Li X，Chindapol A，Ritcey J A.Bit－interleaved coded modulation with iterative decoding and 8PSK signaling.IEEE Transactions on Communications，2002，50(8):1250－1257.

［14］Ai Y H，Hui J Y，Gao J.A simulation study on correlation equalization of underwater acoustic channels. Acta Acustica，1999，24(6):589－597.

［15］Xu X M，Chen Y G，Zhang L，et al.Comparison of the performance of LDPC codes over different underwater acoustic channels. Proceedings of the 12th IEEE International Conference on Communication Technology.Piscataway:IEEE Press，2010.155－158.

［16］Schreckenbach F，Gortz N，Hagenauer J，et al.Optimizations ofsymbolmappings forbit－interleaved coded modulation with iterative decoding.IEEE Communications Letters，2003，7(12):593－595.

［17］Guo L L，F(xiàn)u J Z，Cui Y S，et al.Using m－Walsh composite sequences to reduce narrow－band interference in direct sequence spread spectrum systems.Journal of Harbin Engineering University，2010，31(5):646－651.