Underwater communication link with iterativeequalization

Tommy Oberg, Bernt Nilsson, Niten Olofsson, Magnus Lundberg Nordenvaad, and Erland SangfeltSwedish Defence Research AgencySE-164 90 Stockholm, SWEDEN

Email: ,

Abstract-In this paper an acoustic underwater communi-cation link is presented. The channel has severe inter symbolinterference, which is dealt with by an iterative linear equalizerand a Turbo code. Experiments has been performed in the BalticSea using a 4QAM signal with bandwidth 4 kHz at a centerfrequency of 12 kHz. The raw data rate is 8 kbit/s but afterreduction for error correction coding the net bit rate is 2.88kbit/s. With a source level of 180 dB re. 1,uPa @ lm and a singlehydrophone receiver, a reliable communication is shown up to adistance of 60 km. Very important for a successful decoding isthe initial synchronization, which also is discussed.

I. INTRODUCTION

The excessive multipath encountered in acoustic underwater(UW) communication is creating inter symbol interference(ISI), which is a limiting factor to achieve a high data rate. Avariety of different methods to cope with this situation havebeen developed. In our application we assume that the channelis unknown by the transmitter and we will also keep the possi-bility of utilizing the diversity, offered by an environment withrich multipath. This restricts us to the subset of existingmethods where the ISI is handled at the receiver side. Forexample, the time reversal technique [1] is impossible.The optimal detector is a maximum likelihood detector,

which can be realized for example by a soft Viterbi algorithm.Due to the length of the impulse response in the UW-channelthe number of states in the decoder will be prohibitively many.Therefore this method is seldom used in practice but servesoften as a comparison for designed systems.One well proven method to counteract ISI is the decision

feedback equalizer (DFE), which has been used in many UW-communication links, [2,3]. However the DFE will havedifficulties when we have multipath with a number of arrivalsof equal strength or low SNR, with error propagation as aresult. This kind of multipath often occurs in UW-communications.Another way to cope with the multipath and still obtain a

reasonable high data rate is to use OFDM as transmissionmethod. Some of the drawbacks with OFDM [4] are therequirement that the channel needs to be fairly constant duringthe symbol length, and the Doppler shift needs to be preciselyestimated. This will cause problems when communicatingbetween moving platforms. Also, the high peak to average po-wer ratio creates a need to backoff, when peak power limited

amplifiers are being used. This will reduce the mean outputpower, which in turn will reduce the transmission range. Likeother methods, OFDM requires massive error correctingcoding and interleaving.To circumvent these problems a single carrier system, with

short transmission symbols, is used here. With short symbolswe are victims to severe ISI. To cope with this an iterativelinear equalizer is used, which constitutes an outer loop in thereceiver. An inner loop consists of the Turbo decoder. Theassembly utilizes the error correcting power of the Turbo codeto get an efficient equalizer. With short symbols time synch-ronization is crucial; this is also done recursively in conjunc-tion with the channel estimation. The interlaced loops arecomplex. However, we show that the problems are manage-able. This paper gives the basic theory, a description of oursystem and the results of some sea trials conducted in theBaltic Sea with an iterative linear equalizer.

II. THEORETICAL BACKGROUND

A. Channel modelThe received signal is subject to broadband Doppler. After

Doppler compensation, using interpolation and resampling,the signal is converted down to baseband, and the followingsignal model is assumed.The baseband signal is filtered, by a filter matched to the

transmitter pulse, and is sampled at symbol interval. Thesamples are collected in a vector Zn=[Zn-N, Zn+N ]T, where nis a time index and N1 and N2 is the length of the noncausaland causal part of the estimator filters, respectively. Thereceived samples consist of symbols, xn, transmitted over anISI channel, with hn,k representing the complex gain parameterfor path k at time n and wn representing the additive whitenoise. At the frequency band intended during our test the noiseis fairly white, even though we are using an acoustic UW-channel. The element n-m in vector Zn is:

M-1

n-m E n,kXn-k m+Wnk=O

(1)

The channel parameters are considered constant during asymbol interval and can be divided in two parts

1-4244-01 15-1/06/$20.00 ©2006 IEEE

hn,k = hn,k eXp(J(j tn +O nk)), where hn k is the amplitudeand 0,k is the phase angle of arrival k at time tn. A residual fre-quency error Aco is remaining after the Doppler compensation,due to for example a small difference in oscillator frequencies,at transmitter and receiver, and difference in Doppler for eacharrival. However the latter have been shown to be very smallso we absorb them in the time varying phase parameter anduse the same Aco for all arrivals.The channel coefficients hn,k are assumed known to the

detector and must therefore be estimated. In the followingdiscussion is hn,k therefore not a stochastic variable.

B. ReceiverOur intention is to use a soft equalizer, estimating a

continuous stochastic variable. Only at the last iteration, thereceiver makes a hypothesis about a limited number of out-comes. Therefore, the problem is discussed from an estimatingpoint of view. The optimal estimator in the Minimum MeanSquare Error (MMSE) sense is the conditional meanXn = E{xk lzn }, it attains the Cramer-Rao bound and is there-fore efficient. This will give an estimator, which is complica-ted to implement. If we restrict ourselves to a linear estimatorwe get an estimator that is easier to implement and isasymptotically efficient when the interference has a symmetri-cal probability density distribution, for example the Gaussiannoise, i.e. the estimator is efficient when the number of sam-ples goes to infinity. The basic idea in this paper is to use aniterative receiver consisting of a linear equalizer, [1]. Considerthe standard linear (affine) estimator x^ = a Hz + bn . If theestimator coefficients an are chosen according to the LMSsolution and bn is chosen to eliminate bias, the MMSEestimate of the signal xn given the observations Zn is, see forexample [5]:

Xn = an (Zn-EtZn})+ E{Xn} (2)

Note that E{zn} can be computed from E{xn} by using thesignal model (1).

Let us first look at a single symbol x, in the sequence oftransmitted symbols. The expectation value in (2) reflects oura priori knowledge of the transmitted symbol. Assume that thesymbol alphabet has zero mean and all symbols are equallylikely. At the first signal run through the estimator, i.e. thezero:th iteration, the expected value of the symbol x, is there-fore zero. The Turbo decoder computes the probabilities, forxn, to assume each one of the letters in the modulationalphabet. Out of that, an estimate of E{Xn} is computed. Thisis repeated for all n in the sequence. With these expectations, anew round in the linear estimator is made, followed by anadditional decoding in the turbo decoder, and thus obtainingnew E{Xn} :s. As the iteration proceeds, the expectations areapproaching the correct values, provided a correct decoding ispossible.

For 4QAM, which is a binary modulation on the I and Qaxis each, the probability of having a zero in the binarysymbol n is:

n(i) _ exp(L(4))1+-eXP(t(n (3)

where L(') is the likelihood ratio for symbol n and (i)indicates iteration i. This is obtained from the turbo decoder.A histogram of L(') for a typical sequence of iterations isshown in fig 1. For example, a likelihood value of 4.6 gives azero with a probability of 9900. The more symbols that get ahigh or low value of L(4), the more convinced is the turbodecoder of the decoded symbol and the probability is high thata small number of errors in the decoded message will occur.From fig. 1 it is obvious that the decoding starts from a veryinsecure situation and working its way to be very sure aboutthe decoded symbols.The computation of the likelihood ratio is for 4QAM, and a

Gaussian assumption on the noise, based on the distancebetween the estimator output and the possible signal points.For the symbol at the real axis we get:

exp Re{in }-(-1/a)anhna 2h a2J

L = )n 2

expC Retxn }-( 1/a) anh n /2(7(4)

where ± i/T is the possible symbols and ac2 is thevariance in the estimate. On the imaginary axis the computa-tion is done similarly but the Re operator is exchanged to anIm operator. Note that (4) can easily be simplified but is keptthe way as it stands to easily demonstrate the mathematicalbackground.

First iteration500

400In- 300

z 200

100

-4 -3 -2

600,

0Lprior

Fifth iteration

2 3 4

_ 400

z 200!

0'-800 -600 -400 -200 0 200 400 600 800

Lextrinsic

Figure 1. Histogram of the likelihood ratio L, computed after one and fiveiterations, n assumes all possible values. Notice the difference in scale at the

x-axes. At the last iteration the number of errors were zero.

The estimator (2) can be regarded as having two measure-ments of x,. The first is a sequence of samples of receivedsignal where the present estimation of the intersymbolinterference has been subtracted. This can be called a "trivial"measurement of x". It contributes to the estimate through thefilter a,. The second measurement is based on the expectationvalue of symbol n and is the a priori information about presentsymbol, based on previous iterations. When the reliability inthe decoding is increasing, the expectation value begins todominate the estimate, in. Finally a decision is made basedon the likelihood ratio.The description above is only intended as an orientation, for

details about the method we refer to [6].

C Channel estimatorIn a DFE, the channel is implicitly estimated by taking the

mean square error between the detector's input and outputsignals. By minimizing the error, the filter coefficients aredetermined. In the turbo decoder no firm decision is madeuntil the last iteration. Here the channel is instead computedby finding the least squares solution to the error function:

dk,n = Zk -hnE{xk}

where h,n is a column vector and element k is theestimate of hn,k at time n. The solution to (5) can be found byusing a standard method like RLS, LMS etc. We have used anLMS like approximated modified RLS algorithm, see [7]. Thisway of estimating the channel represents a complication sincethe expectation values are small at the first iterations. A risk ofoverestimating the channel values is apparent. Therefore, atthe first iterations, the channel estimation is only made duringthe training sequence and the values are kept stationary duringthe subsequent data sequence.The phase was corrected by using a correction factor, which

is computed by using the phase difference between successiveestimates of the impulse response. The phase of each responsek is weighted by the energy of that particular response:

v-, k2

,k

E h| n,k |2k

hY,n-l,k 2On-l,kk

E hn-l ,k 2

k

A correction phase AO, is generated by a lowpassfiltering (LPF) with zero lag and linear phase, i.e.

Aon= LPF{lA\¢j} . The received signal is then phasecompensated to the next iteration by the multiplication

z($f ) = 4 ) expK- j E mAOj In this way the phase of each

symbol can be individually corrected in an iteratively manner,based on the turbo decoding.

III. EXPERIMENT

D. Modulationformat and transmissonThe encoded sequence was modulated using 4QAM with

root-raised cosine shaped symbols at a rate of 4 kbaud, givinga bandwidth of 4 kHz, and with a carrier frequency of 12 kHz.The raw data rate was 8 kbit/s but since we used a rate 1/3Turbo code this corresponds to a net data rate of 2.66 kbit/s(symbols for synchronization included). Before the modula-tion mapper an S-random interleaver, H, was inserted. Thepurpose was to prevent correlation of the interference insuccessive bits, belonging to the same, 4:ary, modulationsymbol. The transmission was done in the Baltic Sea at adepth of 45 meters where a sound channel could be found.This location minimised reflections from sea floor and surface.An omni-directional acoustic source with a level of 180 dB re.1,uPa g Im was used. A single omni directional hydrophonewas used at the receiving side. The experiment was conductedboth with a stationary (i.e. drifting) and moving (4 knots)transmitter ship.

data Turbo 4QAMencoder modulation

Figure 2. Simplified diagram of the transmitter.

E. Acquisition and course synchronizationThe first frame of symbols was headed by a training

sequence consisting of either a 127 or 511 length PseudoRandom Binary Sequence (PRBS). This serves as an indicatorof the transmission start and a known sequence to obtain afirst channel estimate. The received sequence was correlatedby a number of replicas with different time compression orexpansion, respectively. The difference in compr./exp.between the neighbouring filters corresponded to 0.5 knot.After resampling for Doppler compensation still some frequ-ency shift, Aco, and a phase shift, on, remain. However in theacquisition phase we have no information about the individualsymbols. Therefore, only a mean phase 0, constant for thewhole interleaver length can be estimated. The residualDoppler is reduced by multiplication of the received signalwith exp[-j(Atn + 0 . The parameters A6 and 0 arefound by searching the values that minimise the mean squaredistance from the training sequence stored in the receiver.

L(l+1)n

Figure 3. Simplified diagram of the receiver.

F Receiver and equalizerThe receiver consisted of the linear MMSE estimator,

previously described, and a turbo decoder. The decoding ofthe received signal was done in a recursive fashion with acontinuously better estimate of the expectation values andcorrespondingly decreasing variance. The equalizer itselfconsists of two filters with the filter parameters an and hnrespectively. An interesting feature with this equalizertopology is that we get the channel impulse response as tapsin the filter feeding back the expectation of xn to createEl{zn, cf (1).

Since we have a linear system the summation can also bedone after the an filter, although with different filter coeffi-cients. We only point this out for the reader to see thesimilarity in topology with the DFE, where a hard decisionis fed back in place of the expectation values as is done inthe equalizer described here.

The filter taps in an are computed by an = C 1 Cwhere C is the covariance of the indexed variables. Theoutput of the equalizer xin consists of an estimate of themodulation symbols. However this estimate is not used forany other purpose than to compute binary likelihood ratios,see equ. (4). For higher order modulation the conversion isdone in the standard way, which for example is described in[6].

G. Turbo code and interleaverThe information to be transmitted was encoded by a rate

1/3 turbo code with identical recursive encoders having thegenerator polynomial 17/15 (octal). Two interleavers wheretested with depths of 127 and 5120 binary symbols, respec-tively. The interleavers are designed for good properties in a

turbo code and were taken from [8]. The correspondingdecoder was designed using a sliding window BCJR algo-rithm ref. [9], which gives an efficient implementation. Thechannel impulse response was estimated by a trainingsequence and thereafter updated using the estimatedsymbols.

Ship speed 4 knots0.05

0.045

0.04-

0.035-

0.03-

0.02-

0.015-

0.01

0.005-

0 \DO _AA L-0.02 -0.015 -0.01 -0.005 0 0.005 0.01 0.015 0.02

Time [s]

Figure 4. Snapshot of the impulse response at 20 km.

IV. RESULT AND CONCLUSIONS

H ChannelThe frequency dependent loss in the Baltic is around 0.5

dB/km at the carrier frequency, which is lower compared tothe great oceans. A time variant channel impulse responsewas found with a delay spread of about 10-20 ms., corre-sponding to 40-80 symbols. Among them, about five to ten

taps could be regarded as significant. A snapshot of thechannel impulse response is shown in fig. 4.The variation of the channel over a period of 30 seconds

is shown in figs 5 and 6. An approximate estimate is that thechannel coherence time was about one second. The ampli-tudes of the peaks in the impulse response remain fairlyconstant over a larger period of time, which indicates thatthe phase variations are quicker. The short training sequencegave channel estimates that were not reliable enough.Therefore sequences headed by the long sequence, 511,became our main choice. The impulse response develop-ment over time is somewhat surprising. The impulse respon-se from the channel is more stationary in the moving shipcase as compared to the drifting case, cf. figs. 5 and 6. Ourexplanation to that is: when the transmitter was towed, thedepth was held constant by the wings of the towing device.When the ship was drifting it was heaving with the seawaves so the sound transducer went up and down in thewater column. Since the correlation distance obviously isshorter vertically than horizontally the small heaving gave amore variant channel than the horizontally movement.

25

(D 15E

10

5

0.04 0.045 0.05 0.055 0.06Time-delay [s]

Figure 5. This is an example ofthe impulse response magnitude at 20kmand transmitter ship moving at 4 knots. Vertically, the development over

time is shown, and horizontally, the impulse response is shown.

25 igl| - |

ED 1 5-

E

0.01 0.015 0.02 0.025 0.03 0.035Time-delay [s]

Figure 6. Impulse response at 30 km with a drifting ship heaving on thewaves. All channel estimates are done by the method described in sect. C.

I. Communication resultAt distances up to 60 km. the reception of signals with

short interleaver was error free (limited to the length of themessage) within a few iterations. A long interleaver givesbetter properties in a Gaussian channel. The reason for thefailure with the long interleaver here was that the channelneeds to be fairly coherent over an interleaver length for thefirst decoding to be good enough to obtain convergence infollowing iterations.The use of the linear MMSE estimator supported by the

turbo decoder was found to be a very powerful decodingmethod for the underwater acoustic channel with its difficultinter-symbol interference.

TABLE IRESULT OF COMMUNICATION EXPERIMENT

dist- Number of iterations before zero errors occurredance, .Short interleaverkm. Short interleaver Long interleaver movingesip,4knkm. ~~moving ship, 4kn.

20 n <7 1

30 1 <7 n

60 <4 e n

80 e e n

e means that no convergence ofthe detector could beobtained n means that no test was performed.

J. ConclusionsThe iterative linear equalizer has shown to be a very effi-

cient tool in channels with severe ISI, such as the acousticUW channel. The use of a rate 1/3 code was shown to be alittle bit too much redundant to communicate at the shorterdistances. To increase the information rate a punctured codecould have been used with good result. Alternatively, it isour impression from the experiment, that the data rate couldhave been increased 500o by introducing 8PSK. Thelimiting part of the communication system was the coarsesynchronizer. If it gave a good enough first estimate of thechannel, i.e. an error probability of less than 300O in the firstiteration, the turbo decoding could bring the error rate downto zero. Future work will be directed towards synchroni-zation issues and a multi channel equalizer for hydrophonearrays.

ACKNOWLEDGMENT

The authors would like to thank Dr. Hugo Tullberg forproviding the code implementing the BCJR algorithm. It hasbeen working very well. The authors also would like tothank the crew of H1MS Fatrosund and their Captain SvenKarlsson, who were crucial for the success of theexperiment. Finally we also like to thank Dr. Roald Otnes at

the Norwegian FFI for valuable discussions during thiswork.

REFERENCES

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[2] Stojanovic, M.; Catipovic, J.A.; Proakis, J.G.; "Phase-coherentdigital communications for underwater acoustic channels". IEEEJournal of Oceanic Engineering, Jan. 1994 pp: 100 - 111.

[3] Stojanovic, M.; Catipovic, J.A.; Proakis, J.G.; "Adaptivemultichannel combining and equalization for underwater acousticcommunications" IEEE Journal of Oceanic Engineering, Jan. 1994pp:100 111.

[4] Lam, W.K.; Ormondroyd, R.F.; "A novel broadband COFDMmodu-lation schemefor robust communication over the underwater acousticchannel'. Proceedings of Military Com. Conf, 1998. MILCOM 98,pp: 128-133.

[5] McDonough R.N.; Whalen A.D.; "Detection of signals in noiseAcademic Press, 1995, ISBN 0-12-744852-7

[6] M. Tuichler, A. C. Singer, and R. "Koetter; Minimum Mean SquaredError Equalization Using A Priori Information". IEEE trans. onSignal Processing, Mar. 2002, pp. 673-683.

[7] Otnes, R.; Tuichler, M., "Iterative channel estimation for turbo equali-zation of time-varying frequency-selective channels", IEEE trans onWireless Communications, Nov. 2004 pp. 1918 - 1923.

[8] Hokfelt J.;. www.tde.lth.se/home/jht/interleaverdownload.html[9] S. Benedetto, D. Divsalar, G. Montorsi, and F. Pollara, "Soft-output

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