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Zhang, Youwen, Li, Junhuan, Zakharov, Yuriy orcid.org/0000-0002-2193-4334 et al. (4 more authors) (Accepted: 2019) Deep Learning based Single Carrier Communications over Time-Varying Underwater Acoustic Channel. IEEE Access. ISSN 2169-3536 (In Press)

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Deep Learning based Single CarrierCommunications over Time-Varying Underwater

Acoustic ChannelYouwen Zhang, Junxuan Li, Yuriy Zakharov,Senior Member, IEEE, Jianghui Li,Member, IEEE, Yingsong Li,

Member, IEEE, Chuan Lin, Xiang Li

Abstract—In recent years, deep learning (DL) techniques haveshown great potential in wireless communications. Unlike DL-based receivers for time-invariant or slow time-varying channels,we propose a new DL-based receiver for single carrier commu-nication in time-varying underwater acoustic (UWA) channels.Without the off-line training, the proposed receiver alternatelyworks with online training and test modes for accommodatingthe time variability of UWA channels. Simulation results show abetter detection performance achieved by the proposed DL-basedreceiver and with a considerable reduction in training overheadcompared to the traditional channel-estimate (CE) based decisionfeedback equalizer (DFE) in simulation scenarios with a mea-sured sound speed profile. The proposed receiver has also beentested by using the data recorded in an experiment in the SouthChina Sea at a communication range of 8 km. The performanceof the receiver is evaluated for various training overheadsandnoise levels. Experimental results demonstrate that the proposedDL-based receiver can achieve error free transmission for all288 burst packets with lower training overhead compared to thetraditional receiver with a CE-based DFE.

Index Terms—Channel equalization, deep learning, deep neu-ral network, DFE, machine learning, single carrier communica-tion, underwater acoustic network.

I. I NTRODUCTION

Underwater acoustic (UWA) channel features frequency-dependent limited bandwidth, long time-varying multipathspread and severe Doppler effect, which pose a great chal-lenge for reliable and effective UWA communications [1]–[7] and networks [8]–[10], leading to relatively low datarates in a range between a few bits/s (bps) to several tensof kbits/s (kbps) and often unsatisfied performance [11].

Youwen Zhang and Xiang Li are with the Acoustic Science and Tech-nology Laboratory and the College of Underwater Acoustic Engineering,Harbin Engineering University, Harbin, Heilongjiang, 150001, China. Email:zhangyouwen@hrbeu.edu.cn and lixianghrbeu1982@163.com.

Junxuan Li is with the College of Underwater Acoustic Engineering,Harbin Engineering University, Harbin, Heilongjiang, 150001, China. Email:lijunxuan@hrbeu.edu.cn.

Yuriy Zakharov is with the Department of Electronic Engineering, Univer-sity of York, York, YO10 5DD, UK. Email: yury.zakharov@york.ac.uk.

Jianghui Li is with the Institute of Sound and Vibration Research, Universityof Southampton, U.K., e-mail: J.Li@soton.ac.uk.

Yingsong Li is with the College of Information and CommunicationEngineering, Harbin Engineering University, Harbin 150001, China. Email:liyingsong@ieee.org.

Chuan Lin is with the Acoustics Science and Technology LaboratoryHarbinEngineering University, Heilongjiang, 150001, China. He is also with theKey Laboratory for Ubiquitous Network and Service Softwareof Liaoningprovince, School of Software, Dalian University of Technology, Dalian,116024, China. Email: chuanlin1988@gmail.com.

Generally, single-carrier (SC) modulation schemes with time-domain equalization techniques enjoy high spectral efficiencyand robust performance at the cost of a high receiver com-plexity [1], [4], [12]. Historically, in order to combat theinter-symbol interference (ISI) induced by the time-varyingmultipath spread, many channel equalization techniques havebeen thoroughly studied, g.e., linear equalizer (LE), decisionfeedback equalizer (DFE) etc. [13]–[16]. However, there isstilla great room for the improvement in UWA communicationsystems.

In recent years, machine learning techniques have attractedattention in different fields. In particular, deep learning(DL)techniques feature great potential for solving nonparametricproblems such as object detection and recognition, voicerecognition, and object tracking [17]–[19], [21]. Although DLhas been adopted for terrestrial radio wireless communicationonly recently [22]–[25], it has also been utilized in UWA com-munications [26]. In [22]–[24], DL techniques were proposedfor joint channel estimation and symbol detection in OFDMsystems. Simulation results demonstrate that deep neural net-work (DNN) has the ability to learn and analyze characteristicsof wireless channels with nonlinear distortion and interferencein addition to the frequency selectivity. In [25], learningassisted (LA) algorithms are proposed for estimation of time-varying channels. The DNN based channel estimators areutilized to track channel variations. Simulation results validatethe effectiveness of the algorithms in online tracking thechannel variations. In [26], inspired by the works in [23],[24], a DL-based UWA OFDM communication scheme isproposed and verified by simulation in a UWA channel witha measured sound speed profile (SSP). Despite the success ofDNN in time-invariant or slow time-varying channels, DNN-based wireless communication over fast time-varying channelsinduced by severe Doppler effects has not been studied yet.

In this paper, we propose a DL-based receiver for UWA SCcommunications over time-varying channels. As compared toexisting works, our main contributions are summarized below:

1) Different from the existing DL-based receivers with theoffline training and online test modes, we propose a DL-based receiver with online training and test modes foraccommodating time-varying UWA channels.

2) The performance of the proposed DL-based receiveris evaluated by a statistical channel simulator with ameasured SSP. Numerical results show that the proposedreceiver achieves a better detection performance than

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the traditional CE-based decision-feedback equalization(DFE) receiver and with lower training overhead.

3) The performance of the proposed receiver has beentested in the South China Sea experiment, at a commu-nication distance of8 km. We show that the proposedDL-based receiver can achieve a substantial performancegain over the traditional CE-based DFE receiver withthe second-order PLL. With less training overhead, theproposed receiver can achieve error-free transmission of288 data packets at the signal-to-noise ratio (SNR) aslow as SNR=5dB, while the traditional CE-based DFEreceiver cannot achieve that even at as high SNR asSNR = 15 dB and with a significantly longer trainingsequence. At the best of our knowledge, this is the firsttime that a DL based receiver is validated using datafrom a sea trial instead of simulated data.

The rest of this paper is organized as follows. In SectionII, the time-varying UWA SC communication system modelis presented and the CE-based DFE receiver with second-order PLL is reviewed. Section III presents the proposed DL-based receiver for UWA communication over time-varyingUWA channels. Simulation results are presented in SectionIV. Section V presents results from the sea trial. Conclusionsare drawn in Section VI.

Notation: Matrices and vectors are denoted by boldfaceuppercase and lowercase letters, respectively.(·)

†, (·)∗ and

(·)T denote the Hermitian transposition, complex conjugateand transposition, respectively.

II. SYSTEM MODEL FORUWA SC COMMUNICATIONS

OVER TIME-VARYING CHANNEL

A. Signaling Model

We consider a single-input single-output UWA SC com-munication system. Fig. 1 depicts the block diagram of thetransmitter. The binary information bit vectorb is split intogroups of P bits, whereP represents the number of bitsper symbol, and each group is mapped to one of the2P -arysymbols of the alphabetA = {αp}

P

p=1, whereαp is a complexnumber. The sequence of2P -ary symbols is multiplexed with atraining symbol sequence of lengthNt, producing the payloadsymbol vectorx

∆= {xn}

Ns

n=1. Symbols from the vectorx passthrough a square-root raised-cosine pulse-shaping filter withan impulse responseg (t) to produce the baseband signalb(t).The complex baseband signalb(t) is expressed as [27]

b (t) =

Ns∑

n=1

xng (t− nTs), (1)

where xn is the transmitted symbol,g (t) is a square-rootraised cosine pulse-shaping filter with roll-off factorγ, Ts isthe symbol interval. The signalb (t) is then modulated ontoa carrier of angular frequencyωc to produce the transmittedsignals(t) as [1], [27]

s (t) = Re{b (t) ejωct}. (2)

Preamble and postamble linear frequency modulation(LFM) waveforms are added before and afters(t) for the

purpose of the coarse frame synchronization and Dopplerestimation.

b t s t

Fig. 1. Block diagram of the transmitter for the UWA SC communicationsystem.

In this paper, we consider the narrowband signaling model,i.e., the Doppler effect can be represented as a carrier frequen-cy offset without time scaling. We assume that the maximumchannel delay (in symbol intervals) isL.

So the received baseband signal distorted by multipathspread and noise can be expressed as

yb(t) =L−1∑

l=0

βl(t)b(

t− τl)

ejωc(−τl) + η (t) , (3)

where βl(t) is time-varying amplitude fading factor corre-sponding to thel-th path,τl is the delay associated with thel-th path andη (t) is additive complex white Gaussian noise(AWGN) with zero mean and varianceσ2

η at hydrophone,which is independent fromb (t).

B. Traditional CE-based DFE Receiver with PLL

Fig. 2 depicts the receiver with the traditional CE-basedDFE and PLL. This type of DFE is widely used for combattingthe inter-symbol interference (ISI) and phase distortion inUWA communication channels [15], [27].

On the receiver side, the passband signalyp(n) is trans-formed into baseband signalyb(n) by a demodulator, and thebaseband signalyb(n) is downsampled intoy(k), wherek isthe time index in the symbol intervalTs. Assume that a DFEconsists of anLf -length feedforward filter (FFF) with the tapvector f(k) andLb-length feedback filter (FBF) with the tapvectorg(k), and the equalizer delay isl [27], [28].

At time instantk, the transmitted symbolx(k− l) estimatedby DFE as [28]

x(k − l) = yT (k)f(k) + xT (k)g(k), (4)

where y(k) = [y(k), y(k − 1), · · · , y(k − Lf + 1)]T ,

and the already estimated symbol vectorx(k) =[x(k − l − 1), x(k − l − 2), · · · , x(k − l− Lb)]

T . Fig. 3depicts the structure of this type DFE in details. Theequation (4) can be written in vector form as [27], [28]

x(k − l) = mT (k)n(k), (5)

where

m(k) =

[

y(k)

−x(k)

]

,n(k) =

[

f(k)

g(k)

]

. (6)

With an adaptive channel estimator, we can estimate theequivalent time-varying baseband channel matrixH(k) by

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p n b n y k x k l

k

k

k

j ke

Fig. 2. Block diagram of the receiver structure for the traditional CE-based DFE.

( )y k+

+

+( )1f k

å å

+

+

( )1g k

( )2g k

+ +

( )fLf k

( )1fLf k-

( )1bLg k-

( )x k l-

( )x k l-

Fig. 3. Structure of a symbol-spaced DFE.x(k−l) denotes the hard decisionof x(k − l)

using the training symbols or the hard decisions of estimateddata symbols [28]. Finally, the equalizer tapsf(k) andg(k) aregenerated and updated by solving the equivalent mean squareerror (MSE) equation as follows [27]

Γ(k)n(k) = Ψ(k), (7)

whereΓ(k) = E{

m(k)mH(k)}

, Ψ(k) = E {m(k)x∗(k−l)}.

In order to compensate the phase distortion induced by theDoppler effect, the second-order PLL is incorporated into theCE-based DFE for joint carrier phase synchronization andequalization [29]. For easy understanding, we set the decisiondelay l = 0, so at time instantk, output of the FFF is givenby

p(k) = f†(k)y(k)e−jθ(k), (8)

and the output of the FBF is written as

q(k) = g†(k)x(k), (9)

where the time-varying phase can be tracked by the second-order PLL as follows [29]

θ(k + 1) = θ(k) +Kf1Φ(k) +Kf2

k∑

i=0

Φ(i), (10)

whereKf1 andKf2 are proportional coefficient and integralcoefficient of loop filter, respectively.

III. PROPOSEDDL-BASED RECEIVER FORUWA SCCOMMUNICATION OVER TIME-VARYING CHANNELS

A. Review of DNN

DNN is an artificial neural network (ANN) with multiplehidden layers composed of many neurons [30]. Fig. 4 depictsthe general structure of a DNN model withQ > 3 layers,where the layer1 and layerQ are called as input layer andoutput layer, respectively, and the other layers are hiddenlayers. Data flow propagates from the input layer to the hiddenlayers, then the output layer.

( )11b

( )1

ˆ Qb

Input Layer Hidden Layers Output Layer

( )1j

( )11

( )1J

( )1jb

( )

( )1

1

Jb

( )

( )ˆQ

Q

Jb

( )2j

( )21

( )2J

( )qj

( )1q

( )qJ

( )1qj

-

( )11q-

( )1qJ

-

( )1Qj

-

( )11Q-

( )1QJ

-

( )1Q

( )QJ

Layer 1 Layer 2 qLayer QLayer

Fig. 4. General structure of a DNN model.

The input layer (i.e. layer 1) hasJ (1) variables in vector

b(1) =[

b(1)1 , · · · , b

(1)j , · · · , b

(1)

J(1)

]T

, then thej-th neuron’sinput of layer2 is

a(2)j =

J(1)∑

i=1

u(1)ij b

(1)i + v

(1)j , j = 1, 2, · · · , J (2), (11)

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where u(1)ij is a weight between thei-th neuron of layer1

and thej-th neuron of layer2, v(1)j is a bias of thej-th

neuron in layer2, J (2) is the number of neurons of layer2.In each hidden layer, there is a nonlinear activation functionf(·) which transforms the linear combinations of inputs tonon-linear outputs. Thej-th neuron’s output of layer2 is thusgiven by [30]

b(2)j = f (2)

(

a(2)j

)

. (12)

Then b(2) =[

b(2)1 , · · · , b

(2)j , · · · , b

(2)

J(2)

]T

will be the next

layer’s input. Similarly, thej-th neuron’s inputa(q)j and output

b(q)j of layer q are

a(q)j =

J(q−1)∑

i=1

u(q−1)ij b

(q−1)i + v

(q−1)j , j = 1, 2, · · · , J (q), (13)

b(q)j = f (q)

(

a(q)j

)

, (14)

whereJ (q−1) and J (q) are the number of neurons of layer(q − 1) andq, respectively.

The nonlinear activation functions may be the Sigmoid func-tion fS(n) =

11+e−n , or Rectified Linear Unit (ReLU) function

fR(n) =max(0, n) [30]. Hence, the final output of the DNN

b(Q) =[

b(Q)1 , · · · , b

(Q)j , · · · , b

(Q)

J(Q)

]T

is a cascade nonlinear

transformation of inputb(1) =[

b(1)1 , · · · , b

(1)j , · · · , b

(1)

J(1)

]T

,and can be expressed as

b(Q) = f(

b(1), · · · ,b(q), · · · ,b(Q−1);u(1), · · · ,u(q),

· · · ,u(Q−1); v(1), · · · ,v(q), · · · ,v(Q−1))

= f (Q−1)(

f (Q−2)(

· · · f (1)(

b(1))))

, (15)

where f (q)(·) is the activation function adopted by layerq.Vectorsu(q) andv(q) denote the weights and bias at layerq.Through the offline or online training process, the weights andbias can be optimized following a target function.

B. Proposed DL-based Receiver

In a time-invariant channel, a DL-based receiver usuallycomprises two stages: 1) offline training stage, and 2) onlinedeployment/test stage [23]. However, this type of traininganddeployment mode is not suitable for the DL-based receiverover time-varying channels.

In order to accommodate the time variability of UWAchannels, we propose a DL-based receiver with online trainingand test mode. As shown in Fig. 5(a), the proposed receiver isalternatively working at two modes: 1) online training mode,and 2) online test mode. As shown in Fig. 5(b), the wholepayload is divided intoD sub-blocks withNs symbols in each.For thei-th sub-block, the first{N i

p}Di=1 symbols are utilized

as the training symbols and the remainingN id = Ns − N i

p

symbols are the data symbols. So the number of total trainingsymbols isNp =

∑Di=1 N

ip. The resulting training overhead

is β = Np/Ns/D.

Yes

DNN

Model

b

Online test mode

( )p ny

Online training mode

( )ky

DNN

Model

No

vu

2L a£

Demodulator( )b ny

Downsampler

Training symbols

Received symbols

Received symbols

(a)

pilots ...data pilots data pilots data pilots data

training

mode

test

modeu v

training

mode

test

modeu v

training

mode

test

modeu v

...

1b

2b

ˆDb

1

pN1

dN2

pN2

dND

pND

dN1D

pN- 1D

dN-

1

ˆD-b

(b)

Fig. 5. Structure of the proposed DL-based receiver for time-varying UWAchannels: (a) DL-based receiver, and (b) alternatively working between thetraining mode and test mode.

When the receiver is receiving known training symbols, theDL-based receiver switches to the online training mode. Giventhe received symbolsy(k), the known training symbolsx(k)and estimated symbols of previous sub-block, the DNN utilizesthe Adam (Adaptive moment estimation) optimizer which isbased on the stochastic gradient descent algorithm [30] tominimize the mean-square error of the loss function given by

Li2 =

1

N ip

Nip−1∑

k=0

(

bi(k)− bi(k))2

, i = 1, 2, · · · , D. (16)

The online training mode is stopped ifLi2 becomes lower than

a predefined thresholda as shown in Fig. 5(a) or ifk = Np−1.When the training mode ends, the DNN produces the weightset u

∆={

u(q)}Q−1

q=1and bias setv

∆={

v(q)}Q−1

q=1, which are

utilized in the online test mode.The DL-based receiver switches into the online test mode

after obtaining the weights vectoru and bias vectorv. Inthe online test mode, we obtain the estimate{bi}Di=1 of thetransmitted symbols{bi}Di=1 by using the equation (15).

IV. SIMULATION RESULTS

In this section, we evaluate the performance of the proposedDL-based receiver and compare it to the traditional DFEreceiver with the recursive least squares (RLS) based channelestimator and embedded second-order PLL by using simulatedtime-varying channels.

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Fig. 6. Measured SSP and predicted TL with a source at 50 m depth. Thetransmission loss is shown in dB.

TABLE ISIMULATION PARAMETERSSETUP

sea depth (H) 250 mchannel distance (d) 800 mspreading factor (k) 1.7

speed of sound in bottom (cb) 1574 m/sdensity in bottom (ρb) 1.269 g/m3

attenuation coefficient in bottom (α) 0.01875 dB/wavelengthminimum frequency (fl) 8 kHz

carrier frequency (fc) 12 kHzbandwidth (B) 8 kHzmodulation type BPSK

sample frequency (fs) 48 kHzsymbol rate (Rs) 4 kHz

A. Simulation Environment

A statistical channel simulator [31] is used to generate thetime-varying UWA channels for evaluating the performance ofthe proposed DL-based receiver and the traditional CE-basedDFE receiver. The parameters for the time-varying channelsimulator are listed in Table I. We use a SSP measured ina sea experiment and shown in Fig. 6. We also compute thetransmission loss (TL) as shown in Fig. 6, the computation isdone using the Bellhop acoustic toolbox [31]. The maximumTL is approximately 60 dB. In order to investigate how thesurface and bottom affect the UWA channel characteristics,weconstruct three configurations of transducer-hydrophone pairlisted in Table II.

Following the parameters and configurations shown in Ta-ble I and Table II, we obtain the time-varying UWA CIRs andcorresponding channel scattering functions as shown in Fig. 7,Fig. 8, and Fig. 9. It can be seen that the simulated channelsare time varying.

B. Training Scheme

For short packet bursts, we adopt the same training schemefor both the proposed DL-based receiver and the traditionalCE-based DFE receiver as shown in Fig. 10. For each received

TABLE IIDEPTH OF THETRANSDUCER-HYDROPHONEPAIR

Configuration Transmitter Depth (m) Receiver Depth (m)C1 50 50C2 200 50C3 200 200

packet withNs = 500 symbols, the firstNp symbols are uti-lized as the training symbols and the remainingNd = Ns−Np

symbols are the data symbols. The resulting training overheadis β = Np/(Np + Nd), and the corresponding data rate is(1− β)×Rs kbps.

For the proposed DL-based receiver, the DNN hasQ = 4layers, in whichJ (1), J (2), J (3) and J (4) are set to128, 96,48, and32, respectively. All layers utilize the sigmoid functionas the active functions. The number of pilot symbolsNp is setto 64, then the resulting training overhead isβ = 12.8%.

p0ps pb

0 20 40 60 80Delay [ms]

0

20

40

60

Tim

e [s

]

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

(a)

0 20 40 60 80Delay [ms]

-30

-20

-10

0

10

20

30

Fre

quen

cy [H

z]

-50

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

(b)

Fig. 7. Simulated time-varying channel characteristics under the configurationC1: (a) time-varying CIRs, and (b) corresponding channel scattering function.

For the traditional CE-based DFE receiver as shown inFig. 2, we setNp to 200 for ensuring that the traditional CE-based DFE receiver can get good performance. The length ofthe feed forward filter and feedback filter are set according tothe CIRs shown in Fig. 7, Fig. 8, and Fig. 9, but the followingparameters are common for all the three configurations: for-getting factorλ of the RLS adaptive algorithm is set to 0.995,proportional coefficient and integral coefficient of PLL, i.e.Kf1 andKf2 , are set to 0.001 and 0.000001, respectively.

C. Test Results

Following the above three simulation configurations, wecompare the performance of the proposed DL-based receiverwith that of the traditional CE-based DFE receiver in termsof bit error rate (BER). As shown in Fig. 11(a), Fig. 11(b),and Fig. 11(c), with lower training overhead, the proposedDL-based receiver consistently outperforms the traditional CE-based DFE receiver.

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p0 pspb

0 20 40 60 80Delay [ms]

0

20

40

60

Tim

e [s

]

0.1

0.2

0.3

0.4

0.5

0.6

0.7

(a)

0 20 40 60 80Delay [ms]

-30

-20

-10

0

10

20

30

Fre

quen

cy [H

z]

-50

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

(b)

Fig. 8. Simulated time-varying channel characteristics under the configurationC2: (a) time-varying CIRs, and (b) corresponding channel scattering function.

p0 pspb

0 20 40 60 80Delay [ms]

0

20

40

60

Tim

e [s

]

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

(a)

0 20 40 60 80Delay [ms]

-30

-20

-10

0

10

20

30

Fre

quen

cy [H

z]

-50

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

(b)

Fig. 9. Simulated time-varying channel characteristics under the configurationC3: (a) time-varying CIRs, and (b) corresponding channel scattering function.

pN dN

Fig. 10. Training scheme for the proposed DNN-based receiver and thetraditional CE-based DFE receiver.

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V. EXPERIMENTAL RESULTS

A. Experimental Environment

The experiment was carried out in the South China Sea inNovember 2014. Fig. 12 depicts the layout of this experiment.The sea depth at the experimental site is about 99 m. Onetransducer was deployed to a depth of approximately 15 mfrom a ship. During the experiment, the ship was driftingon the sea surface. A receive vertical linear array of 48hydrophones was moored with the first hydrophone at about72 m below the surface, and other hydrophones evenly spacedby 0.25 m. The communication range was about 8 km atthe start of the experiment. The system timers of transmitterand received array are synchronized by the GPS time beforedeployment.

B. Data Structure

For transmission, the input bits were encoded by a rateRc = 1/2 convolutional coder with generator polynomial[171, 133] in octal format. The carrier frequency wasfc = 3

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Surface

M

Ship

8 km

15 m15 m

12 m

72 m

48-channel Vertical

Hydrophone Array

Transducer

Ship

Bottom

Fig. 12. Layout of the South China Sea experiment.

kHz and the symbol rate was1 k symbols per second (ksps).The pulse shaping filter was a square-root raised cosine filterwith a roll-off factor of 0.5 [27], leading to an occupiedchannel bandwidth of about 1.5 kHz. The sampling rate was 25kHz at the receiver end. The structure of the transmitted datastream and relevant parameters are shown in Fig. 13. Pream-ble up-chirp and postamble down-chirp, Doppler-insensitivewaveforms, were added before and after the data burst forcoarse frame synchronization and estimation of an averageDoppler shift over the whole data burst. Following the framesynchronization signal is one data packet (payload). Only datawith BPSK modulation was used for performance evaluationfor the proposed DL-based receiver. The payload is separatedfrom up-chirp or down-chirp signal by the gap of the duration150 ms for avoiding the inter-block interference. The lengthof each payload is 5500 symbols between two guard intervals.Each burst packet is transmitted every 6.1 s. The approximateSNR, which is estimated by using the signal part and silentpart of the received signal, is in the range of 15 dB to 16 dB.

LFMData

Sequence

Training

Sequence 1

Training

Sequence 2LFM

150ms 150ms 150ms150ms500ms 500ms4500ms

Guard

Time

Guard

Time

Fig. 13. Structure of the signal transmitted in the sea experiment.

In order to show characteristics of the UWA channel duringthe experiment, we estimate the CIRs by using the matchedfilter applied to the preamble and postamble chirp signals andthe RLS algorithm applied to the data signals. It can be seenthat the channel is fast time varying within a single burst. FromFig. 14, we can observe that the channel multipath spreadis about15 ∼ 30 ms, corresponding to a channel length of15 ∼ 30 taps in terms of the symbol rateRs = 1 ksps. Thearrival paths fluctuate very rapidly and CIRs are clustering.

C. Training Scheme

In order to evaluate the performance of the proposed DL-based receiver and traditional CE-based DFE receiver, we use6 transmitted bursts. For each burst, we have 48 received

packets, so in total we have 288 received packets. We choose5000 symbols including training sequence and data sequencein each packet depicted in Fig. 13 to test the performance ofabove receivers.

For the proposed DL-based receiver, the DNN hasQ = 5layers, in whichJ (1), J (2), J (3), J (4) and J (5) are set to96,48, 16, 8, and 1, respectively. All layers utilize the sigmoidfunction as the active functions. Training symbols are peri-odically inserted into the data to train the DNN. As shownin Fig. 15(a), the whole payload is divided intoD = 10 sub-blocks withNs = 500 symbols in each. For thei-th sub-block,the firstN i

p symbols are utilized as the training symbols andthe remainingNd = Ns −N i

p symbols are the data symbols.So the number of total training symbols isNp =

∑10i=1 N

ip.

The resulting training overhead isβ = Np/500/10.

For the traditional CE-based DFE receiver, as shown inFig. 15(b), we follow the training scheme usually used inthis receiver, then withNs = 5000, the firstNp symbols areutilized as the training symbols andNd = Ns −Np symbolsare the data symbols. The length of the feed forward filter andfeedback filter are set to 60 and 29 according to the channelcharacteristic analysis. Forgetting factor is0.995, proportionalcoefficient and integral coefficient of the PLL loop filter areset to0.001 and0.000001, respectively.

tN dN

(a)

pN dN

(b)

Fig. 15. Training schemes for (a) proposed DNN-based receiver; (b)traditional CE-based DFE receiver.

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0 5 10 15 20 25 30 35 40 45

Delay (Symbols)

50

100

150

200

250

CIR

Am

plit

ud

e

Channel Estimated using Preamble LFMThreshold amplitude with 1/10 of the main tap magnitude

(a)

0 5 10 15 20 25 30 35 40 45

Delay (Symbols)

20

40

60

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100

120

140

160

180

200

CIR

Am

plit

ud

e

Channel Estimated using Preamble LFMThreshold amplitude with 1/10 of the main tap magnitude

(b)

0 5 10 15 20 25 30 35 40 45

Delay (Symbols)

20

40

60

80

100

120

140

160

CIR

Am

plit

ud

e

Channel Estimated using Postamble LFMThreshold amplitude with 1/10 of the main tap magnitude

(c)

0 5 10 15 20 25 30 35 40 45

Delay (Symbols)

20

40

60

80

100

120

140

160

CIR

Am

plit

ud

e

Channel Estimated using Postamble LFMThreshold amplitude with 1/10 of the main tap magnitude

(d)

(e) (f)

Fig. 14. Examples of the CIR estimated over one burst transmission. The CIRs measured between transducer and first hydrophone are shown in (a), (c),(e). The CIRs measured between transducer and last hydrophone are shown in (b), (d), (f). CIR is measured using: (a) and (b) the preamble up-chirp withthe correlation method; (c) and (d) the postamble down-chirp with the correlation method; (e) and (f) data signals and the classical RLS algorithm withλ = 0.995.

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500 1000 1500 2000 2500 3000 3500 4000 4500 5000Symbols

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

Pha

se [r

ad]

Fig. 16. Phase estimated by PLL at SNR≈ 15 dB.

�� �� ��� ��� ��� ��� ���%���"� ��$ $���$"�������#'�� ��#'�� �#

��(�

��(�

��(�

���

��$��""

"�"�$����

���

�"���$� ���������#��� ���&�$����� ��!����"����

Fig. 17. BER versus the training overhead at SNR≈ 15 dB.

D. Test Results

Fig. 16 shows the time-varying phase estimated by using thePLL for one received signal packet. Fig. 17 shows how theperformance of receivers is effected by the training overhead.We observe that the total number of training symbolsNp

significantly affects the performance of the traditional CE-based DFE receiver. It can be seen that, whenNp is less than50, the traditional CE-based DFE receiver cannot converge.The performance of the proposed DL-based receiver can beimproved with a few training symbols per subblock. WhenN i

p = 5 for the i-th subblock, i.e. the total number of trainingsymbolsNp = 10 × 5 = 50, the BER can reach10−2. WithN i

p = 6, the proposed DL-based receiver can reach zero BERfor all 288 received packets. The traditional CE-based DFEreceiver needs at least 60 training symbols to converge to aBER below3.7× 10−4.

For the traditional CE-based DFE receiver, the improvementin BER performance is small with the increase of trainingsymbols. The error free transmission cannot be achieved evenwith a training overheadβ = 300/5000 = 6%, while theproposed DL-based receiver only needs 60 pilot symbols toachieve the error-free transmission for all 288 packets with atraining overhead as low asβ = 6× 10/5000 = 1.2%.

Since the data were originally acquired in a relativelyhigh SNR, we can evaluate the performance of the receiversover different noise levels by adding recorded noise into thereceived data. Fig. 18 and Fig. 19 show how the performance

�� �� ��� ��� ��� ��� ���%���"� ��$ $���$"�������#'�� ��#'�� �#

��(�

��(�

��(�

���

��$��""

"�"�$����

���

�"���$� ���������#��� ���&�$����� ��!����"����

Fig. 18. BER versus the training overhead at SNR≈ 10 dB.

�� �� ��� ��� ��� ��� ���%���"� ��$ $���$"�������#'�� ��#'�� �#

��(�

��(�

���

��$��""

"�"�$����

���

�"���$� ���������#��� ���&�$����� ��!����"����

Fig. 19. BER versus the training overhead at SNR≈ 5 dB.

of the receivers is effected by the lower SNR.Fig. 18 shows the performance at an SNR of10 dB. It can

be seen that, whenNp is less than 50, the traditional CE-basedDFE receiver cannot converge. WithNp = 60 BER can onlyreach BER=1.1×10−3. With the proposed DL-based receiver,when theN i

p = 5 for each subblock, i.e. the total trainingnumber is 50, all 288 packets can be received without errors.

Fig. 19 shows the receiver performance at SNR= 5 dB. Itcan be seen that, with the the lower SNR, the performance ofthe two receivers degrades. For the traditional CE-based DFEreceiver an error floor is BER=7.5× 10−3. The proposed DL-based receiver, withNp = 400, can reach zero BER with atraining overheadβ = 400/5000 = 8%.

VI. CONCLUSIONS

In this paper, we have proposed a DL-based receiver forUWA SC communications over time-varying UWA channels.Unlike the DL-based receivers over time-invariant channel,the proposed receiver works with the online training stageand online test stage for accommodating the time variabilityof UWA channels. Simulation results show that the proposedreceiver outperforms the traditional CE-based DFE receivereven if using a significantly shorter training sequence. Theproposed receiver has also been tested using sea trial datarecorder at a communication range of 8 km. The performanceof the receiver is evaluated for various training overheadsandSNRs. Experimental results demonstrate that the proposed DL-based receiver achieves error-free transmission at all SNRconditions with lower training overhead compared to thetraditional CE-based DFE receiver, which cannot provide theerror-free transmission.

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ACKNOWLEDGMENT

The work of Y. Zhang was supported in part by the NationalNatural Science Foundation of China under Grant 61471138,Grant 61531012, and Grant 50909029, in part by the ChinaScholarship Council Funding, in part by the Program of In-ternational Science and Technology Cooperation under Grant2013DFR20050, in part by the Defense Industrial TechnologyDevelopment Program under Grant B2420132004, and in partby the Acoustic Science and Technology Laboratory in 2014.The work of Y. Zakharov is partly supported by the U.K.Engineering and Physical Sciences Research Council underGrant EP/P017975/1 and Grant EP/R003297/1. The work ofC. Lin is partly Supported by the Fund of Acoustics Scienceand Technology Laboratory.

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