Underwater Acoustic Communication Receiver Using Deep Belief Network
11 Underwater Acoustic Communication Receiver Using DeepBelief Network
Abigail Lee-Leon ∗† , Chau Yuen ∗ , Dorien Herremans ∗ ∗ Singapore University ofTechnology and Design (SUTD), 8 Somapah Road, Singapore 487372 † Thales SolutionsAsia Pte Ltd, 21 Changi North Rise, Singapore 498788
Abstract —Underwater environments create a challeng-ing channel for communications. In this paper, we designa novel receiver system by exploring the machine learningtechnique–Deep Belief Network (DBN)– to combat the sig-nal distortion caused by the Doppler effect and multi-pathpropagation. We evaluate the performance of the proposedreceiver system in both simulation experiments and seatrials. Our proposed receiver system comprises of DBNbased de-noising and classification of the received signal.First, the received signal is segmented into frames beforethe each of these frames is individually pre-processed usinga novel pixelization algorithm. Then, using the DBN basedde-noising algorithm, features are extracted from theseframes and used to reconstruct the received signal. Finally,DBN based classification of the reconstructed signal occurs.Our proposed DBN based receiver system does showbetter performance in channels influenced by the Dopplereffect and multi-path propagation with a performanceimprovement of 13.2dB at − Bit Error Rate (BER).
Index Terms —Underwater Acoustic Communications,Receiver Systems, Machine Learning, Signal Processing,Doppler Effect
I. I
NTRODUCTION
Underwater Acoustic Communications (UWAC)is a knowledge rich field that has, in the recentyears, gained a tremendous amount of interest forits many applications in the field of ocean ex-ploration, defense, and marine commercial indus-tries. A few notable applications are underwaterexploration [1], underwater mine detection [2], andunderwater communications between submarines orunderwater nodes [3]. Due to a rapidly growing needfor data-heavy underwater systems, the expectationsand requirements of the underwater system designhas risen up to a point where a growing numberof researchers are starting to turn to unconventionalmethods like machine learning (ML) and deep learn-ing (DL) to combat the challenging underwater envi-ronment. In this paper, we propose a novel receiver system that utilizes the capabilities of Deep BeliefNetworks (DBNs) to redesign the de-noising anddemodulation blocks of the communication system.Generally, conventional signal processing algo-rithms in communications are based on strong math-ematical foundations and are designed specificallyfor a variety of specific channels and system models[4], [5]. For instance, the Binary Phase-Shift Key(BPSK) modulation was designed for the detectionof a constellation symbol in a channel of additivewhite Guassian noise (AWGN) [6]. These signalprocessing algorithms are constructed on expertknowledge of the tractable channel models, which inturn are established on a simplification of Maxwell’sequations [7].UWAC signals, however, are not electromagneticin nature [8], [9]. As such, the UWAC channel iswidely characterized as one of the most complexchannels to model and has yet to develop a palpableor definite model. Its high complexity is mostlyderived from its fast varying characteristics, such asthe Doppler effect and the propagation properties.Since communications are heavily reliant on thecharacteristics of sound, it shows a strong correla-tion with the properties of sound [8]. By understand-ing how sounds are influenced during sea trials, onecan optimize the efficiency of the communicationthrough adaptation. As sound propagates underwaterat a very low speed of approximately 1500 m/s [9],and propagation occurs over multiple paths, it isvery common to observe a delay spreading overtens or even hundreds of milliseconds which resultsin frequency-selective signal distortion. This motionalso results in an extreme Doppler effect.Multi-path propagation in the ocean is governedby three effects– (1) sound reflecting off underwatersurfaces like bubbles and the seabed, (2) soundrefraction in the water due to density change, and (3)energy loss [10]. These effects will cause an elon- a r X i v : . [ ee ss . A S ] F e b gation of the path traveled, and thus a time delay.The first also creates reverberation, which causes areflection phase change and a reflection amplitudechange. The second is a consequence of the spatialvariability of sound speed, which is dependent ontemperature, salinity, and pressure. These factorsvary with depth and location. The final effect isheavily dependent on the signal frequency, as wellas the pH level of the water. This dependence is aconsequence of absorption, where the signal energyis converted to heat. In addition to the absorptionloss, the signal typically experiences a spreadingloss, which increases with distance [8]. To correctfor the intersymbol interference (ISI) caused by thepropagation, the works done in [11], [12], [13] usedan adaptive equalizer to flexibly compensate for thechanges in the channel.Another distinguishing property of UWAC is thechannel’s time variability – (1) inherent changesin the propagation medium and (2) transmit-ter/receiver motion. Inherent changes include longterm changes like seasonal temperatures and in-stantaneous changes caused by shipping routes andmoving water surfaces. These factors result in botha scattering of the signal and a Doppler effectspreading due to the changing path length [10]. Acombination of these factors creates a complex chal-lenge of modeling a sufficiently accurate channelmodel. To combat Doppler shifts, many Dopplerscale estimation techniques have been proposed asseen in [14], [15].In recent years, ML and more specifically DLhave gained recognition for their performance infields known for their high modelling complex-ity [16], such as image recognition [17], naturallanguage processing [18], and handwriting analysis[19]. Currently researchers have begun to explorethe applications of ML and DL in the area of com-munications. For example, recent research by Wanget al. [20] exploited deep learning to detect signalmodulations in underwater channels. Other studieslike [21], [22] used deep neural network (NN)-basedauto encoders to demodulate received signals. Assuch, we can expect that applying ML techniquesto communication blocks in order to provide apromising solution to the complex channel problemwill yield significant improvements in decodingthe physical layer. Works in [23], [24] investigatethe use of DL based orthogonal frequency-divisionmultiplexing (OFDM) receiver to recover signals corrupted by the UWAC channel.In this paper, we explore a receiver system thatfundamentally rethinks the traditional communica-tions system design. The receiver system utilizesDBNs, more specifically a greedy layer-wise MLalgorithm that is able to automatically learn a newlatent representation of the data. The two main func-tions of the receiver system are – (1) de-noising thereceived signal and (2) classifying the signals intotheir binary representatives. The features extractedby the DBN are considered as the properties of inputdata and are formed by considering the output layerof the DBN. For the first aspect of the proposedreceiver, we train a DBN such that it learns toextract features of the received signal. The trainedDBN distinguishes the features of the segmentedpre-processed signal and groups them with the same“clean” framed training data. Furthermore, DBNis capable of reconstructing the input data basedon their reduced, learned representation. After theDBN, the classification part of our system uses thefeatures which can be tuned by back-propagationfor classification.The main contributions of this paper are as fol-lows:1) Developed a de-noising DBN model. Thetrained DBN model distinguishes the featuresextracted from a segmented pre-processed sig-nal. It then groups these features with thesame “clean” framed training data.2) Redesigned the demodulation block using aclassifying DBN model that utilizes featureextraction and back-propagation for classifi-cation of the received signals.3) The simulation results show that our proposedDBN based system is able to remain relativelyresolute against the different characteristics ofthe UWAC channel. Furthermore, a sea trialwas conducted to verify the performance ofthe proposed DBN-based receiver system in areal life environment.The remainder of this paper is organized asfollows. Section II describes the communicationsystem, underwater channel, and receiver systemmodels. Section III illustrates the proposed DBNbased de-noising technique used. Section IV pro-vided a description of the proposed DBN baseddemodulation technique used in the novel receiversystem. Section V discussed the results of theproposed receiver system and the sea trial used for validation. Finally, conclusions are drawn inSection VI.II. S YSTEM M ODEL O VERVIEW
In this section, we describe the proposed end-to-end communication system, represented in Fig. 1,comprising of a single transmitter and receiver.The following subsections will describe the over-all communication system model used to test ourproposed system, the derivation of the underwateracoustic channel model, and an overview of theproposed receiver system.
A. Communication System Model
First, let y ( n ) be the representation of the con-voluted transmitted bits, Y ( n ) , and the binaryrepresentation of the modulated target transmittedsignal z ( t ) during the n -th transmission. A seriesof transmission symbols y ( n ) are translated intodifferent transmission signal waveforms z ( t ) via aPhase Shift Key (PSK) modulator as described in[25].Second, let x ( t ) represent the overall transmittedsignal consisting of z ( t ) and a Hyperbolic Fre-quency Modulated (HFM) pilot [26]. x ( t ) is thenrelayed through a channel model to obtain thereceived signal s ( t ) : s ( t ) = H ( t ) · x ( t ) + no ( t ) (1)where H ( t ) is the channel equation, · representsthe dot product, and no ( t ) is the Additive WhiteGaussian Noise (AWGN).Finally, we generate a set of training data [ z t , y t ] , t = 1 , , ..., n , where z t is a training signal, y t is thecorresponding BPSK binary label vector consistingof 0s and 1s, and n is the number of the trainingsignals. Once detection and removal of the HFMpilot is completed, the desired section of the re-ceived signal s (cid:48) ( t ) acts as the input for the proposedreceiver system. The algorithm will build a modelfrom the training data L , such that for a given s (cid:48) ( t ) , the trained model will be able to predict areconstructed waveform ˜ z ( n ) and its correspondinglabel ˜ y ( n ) . Therefore, predicting the received bits, ˜ Y ( n ) . B. Underwater Channel
Underwater acoustic communication channels areregarded by researchers as one of the most com-plex communication channels to model. Multi-pathpropagation and Doppler effects are recognizedas one of the most challenging factors of theunderwater acoustic channel [27], [28], [29]. Themore common techniques to approximately simulatethe underwater acoustic channel vary from signal-to-noise ratio (SNR)-based channel models that relyon empirical equations as seen in [8] to modelsthat are based on the assumption of Rayleigh signalfading in [30], [31].In this subsection, the channel model used for thesimulation will be presented, taking into considera-tion multi-path propagation and Doppler effect.
1) Multi-path propagation:
Multi-path propaga-tion in the ocean is mostly governed by sound re-flecting off underwater surfaces like bubbles and theseabed [32]. These effects will cause an elongationof the path traveled, and thus a time delay. Thereceived signal in a mutli-path environment can begenerally represented as seen in [33], [34]: s ( t ) = N (cid:88) i =0 A ( t ) · x ( t − τ i ) (2)where A represents the reverberation created by thereflection and scattering. This phenomena results ina reflection phase change and a propagation loss[32]. As such, Eq. 2 can be further expressed as: s ( t ) = N (cid:88) i =0 a ai a bi ( θ ( t )) ◦ x ( t − τ i ) + no ( t ) (3)where a ai is the amplitude variation caused by thereverberation and fading of the channel, ◦ representsthe Hadamard product, and a bi ( θ ( t )) is the phasevariation and is modeled as seen in [35]: a b ( θ ( t )) = [1 e − jθ ( t ) ... e − jθ k − ( t ) ] where j represents the imaginary number, k isthe length of the signal and θ k is the phase shiftcorresponding to the change in angle.
2) Doppler Effect:
In underwater communica-tions, a combination of the low speed of underwatersound propagation and the relative movement ofthe transmitter and receiver introduces the Dopplereffect [8]. Let v denote the speed of the relativemovement of the transmitter and the receiver, and Fig. 1: End-to-end System Model f c denote the carrier frequency of the transmittedsignal. The carrier frequency at the receiver is givenby: f = (1 + ∆ rt ∆ s ) f c (4)where ∆ s denotes the sound propagation speedunderwater. Note that ∆ rt is positive in the eventthat the receiver is moving toward the transmitter,otherwise ∆ rt is negative.In the time domain, the Doppler effect can beconstrued as a lengthening or compression of thetransmitted waveform [36], [37]. The Doppler effectcan be depicted in the time-domain as: s ( t ) = x ((1 − α ) t ) + no ( t ) (5)where α is the Doppler co-efficient.Taking into consideration the above contributingcharacteristics, the channel model used in this paperis: s ( t ) = N (cid:88) i =0 a ai a bi ( θ ( t )) ◦ x ((1 − α i ) t − τ i ) + no ( t ) (6) C. Receiver System Model
The receiver model is comprised of two blocks –(1) de-noising and (2) demodulation.In the de-noising component, the input signal s (cid:48) ( t ) is first converted and normalized into a pix-elized matrix m ( t ) via the proposed pre-processingmethod. m ( t ) is then partitioned into i number of m i ( t ) to meet the requirement of the proposed al-gorithm for feature extraction. The learning featuresof the training data is used to find the closest matchto the features of m i ( t ) , which is then used as abasis for reconstruction via: ˜ z ( t ) = Ψ( W · m i ( t ) + b ) (7) where Ψ( · ) is a learning function, W and b repre-sents the weights and bias of the network.In the demodulation block, the reconstructedwaveform ˜ z is classified to a label ˜ y ( n ) via: ˜ y ( n ) = Φ(˜ z ( t )) (8)where Φ( · ) is a learning function.The focus of this paper is then to optimize thelearning functions, Ψ( · ) and Φ( · ) , and their corre-sponding weights and bias.III. P ROPOSED
DBN-
BASED D E - NOISING
In this section, the de-noising algorithm, con-sisting of both the pre-processing method and thede-noising DBN, is described. An overview of ourproposed algorithm is shown in Fig.2. The inputis the received signal s (cid:48) ( t ) and the output is thereconstructed signal ˜ z ( t ) .Fig. 2: Overview of De-noising Block A. Pre-processing
The pixelization method is defined as: m ( t ) = f ( normalized ( s (cid:48) ( t ))) The input signal s (cid:48) ( t ) is first normalized into therange of 0 to 1. We then proceed to pixelize the (a) Received Signal s (cid:48) ( t ) = 1 × n Matrix(b) Pre-processed Signal m i ( t ) Fig. 3: Visualization of the Pre-processing BlockDiagram presents the received signal (input) and thepixelized matrix m i ( t ) (output). The received signalis pre-processed into 4 matrices to provide the DBNbased de-noising algorithm with more features toextract.signal to form m ( t ) . Let P ix be the number ofpixels (length wise), which controls the resolutionof the pixelization. The implemented pixelizationalgorithm is shown in Algorithm 1. The input andoutput of the pixelization is shown in Fig.3a andFig.3b respectively.Lastly, m ( t ) is resized to various resolutions, asshown in Fig. 3. This allows for more features tobe extracted and used for the reconstruction. B. De-noising DBN (stacked RBMs)
DBNs are probabilistic generative algorithmswhich provide a joint probability distribution overobservable data and labels. Restricted BoltzmannMachines (RBMs) are the building blocks of aDBN. Hence, in this section first we briefly describe
Algorithm 1
Pixelization algorithm
Input: s (cid:48) and P ix
Output: m length s ← length of s (cid:48) m ← ones ( P ix, F l ); Res ← P ix ; range ← − Res : 0; for i ← to length s do D ← range (cid:48) − s (cid:48) ( i ) A ← min ( abs ( D )) loc ← D [ A ] m ( loc, i ) ← return m RBMs and then we will explore DBN. Fig.4 illus-trates the concept of stacking RBMs to form a DBN.Fig. 4: Overview of a DBN consisting of stackedRBMsA Boltzmann Machine (BM) is a particular formof a Markov Random Field (MRF), where its energyfunction is linear in its free parameters. Some of itsvariables (hidden units) allow the machine to repre-sent complicated distributions internally. However,they are unobserved.
1) RBMs:
The energy function of the joint con-figuration in Boltzmann machines is given as fol-lows: E ( v, h ) = − u v (cid:88) k =1 u h (cid:88) j =1 hW v − u v (cid:88) k =1 bv − u h (cid:88) j =1 ch = − h T Wv − b T v − c T h (9)where the visible nodes v ∈ R correspond to theinput and u v is the number of visible nodes, the hidden nodes h ∈ R represent the latent features and u h is the number of hidden nodes, W represents theconcurrent weights linking the nodes of the visibleto the hidden layer, b and c are the bias terms ofthe hidden and visible nodes respectively.The free energy can also be expressed in thefollowing form: F ( v ) = − log (cid:88) h e − E ( v,h ) = − log ( h T Wv + b T v + c T h )= − b T v − u h (cid:88) j =1 log (cid:88) h j e h j ( c j + W j v ) (10)Because visible and hidden units are conditionallyindependent of one-another, the following equationshold true. P ( v | h ) = (cid:89) j =1 p ( v j | h ) (11) P ( h | v ) = (cid:89) k =1 p ( h k | v ) (12)When binary units are used, so that v j and h k ∈ , , and a probabilistic version of the usual neuralactivation is obtained: P ( v j = 1 | h ) = sigm ( b j + W Tj h ) (13) P ( h k = 1 | v ) = sigm ( c k + W k v ) (14)The free energy of an RBM with binary unitsbecomes F ( v ) = − b T v − u h (cid:88) j =1 log(1 + e h j ( c j + W j v ) ) (15)Since RBMs are energy based algorithms, i.e.they associate a scalar energy to each configurationof the variables of interest, training them corre-sponds to modifying that energy function so that itsshape has desirable properties, such as low energyconfigurations.Energy-based probabilistic models define a prob-ability distribution through an energy function, asfollows: P ( v, h ) = 1 Z exp ( − E ( v, h )) (16)where Q is the partition function that is obtainedvia: Q = u v (cid:88) k =1 u h (cid:88) j =1 exp ( − E ( v, h )) (17) To optimize the parameters of the network at eachlayer k , the following optimization problem shownby Eqn. 18 is minimize via partial differentiationwith respects to W, b, c . g k ( v, h ) = − m m (cid:88) j =1 log( P ( v jk , h jk )) (18)
2) Stacking RBMs into a DBN:
A DBN is com-prised of stacked restricted Boltzmann machineswith a fast-learning algorithm that allows the struc-ture to achieve better results with less computationaleffort.It models the joint distribution between an ob-served vector x and l hidden layers h k as follows: P ( x , h , ..., h l ) = (cid:34) l − (cid:89) k =0 P ( h k | h k + ) (cid:35) P ( h l − | h l ) (19)where x = h , P ( h k | h k + )) is a conditionaldistribution for the visible units conditioned on thehidden units of the RBM at level k , and P ( h l − | h l ) is the visible-hidden joint distribution (output).TABLE I: The de-noising DBN structure consist of2 RBMs. Input Structure Output m i ( t ) No of layers 2 ˜ z ( t ) Nodes [875,625]Activation Function [Sig, Sig]Epoch 1000
3) Training:
To train a DBN such that it canperform matrix de-noising, the normalized pixelvalues of the pixelized signal are used as input. Byusing min-max normalization, m i ( t ) is transformedinto a floating-point number system with a range of0 and 1. Unlike the first and last layer of the DBN,hidden layers consist of binary nodes. The mainidea is to train a DBN to be able to associate noisy m i ( t ) to m i ( t ) with lower noise or no noise. Thisidea can be implemented by learning the featuresextracted from the noisy and clean m i ( t ) contents.These features are then presented in some nodes atthe last layer of the network.The network is trained with a variety of noisy m i ( t ) as input and clean m i ( t ) as the desired output.Using a standard basis called relative activity todetect noise nodes, each node is defined as the difference between two values of a particular nodewhich results from feeding the network a clean m i ( t ) and its corresponding noisy m i ( t ) . As a result,if a particular node is a noise node, it should havehigher relative activity. On the other hand, if it is aclean noiseless node, it should have a lower relativeactivity. This theory is justified by the fact that theactivation of m i ( t ) nodes should be same for bothclean noiseless and its corresponding noisy m i ( t ) .By performing the above action for all m i ( t ) and averaging the values of the last layer’s nodes,the average relative activity of the last layer iscomputed. The nodes with a higher average relativeactivity are still viewed as noise nodes. Once thenoise nodes are discovered, the next step is to lowertheir activity by selecting the average value of allthe noise nodes as their neutral values. As such, thenoise nodes are then considered inactive and a cleannoiseless m i ( t ) can be reconstructed. C. Results of DBN based De-noising
In this subsection, we evaluate the proposed DBNbased de-noising technique. As a baseline for com-parison, we used the conventional MLE methoddevised in [38] and the de-noising auto encoderin [39]. To analyze the only performance of the de-noising capability, the system used was uncoded.For the following simulation experiments, thesimulated BPSK dataset contains 100,000 trans-mitted signals periods, in which 50% is used fortraining, 20% on validation and the remaining 30%on testing. The dataset was generated using Eq.6 andTable.II. The f c , sampling frequency f s and bit rate Rb of the BPSK signals were set at kHz , kHz and kbits/s . The frequency of random change, f δ , was 2kHz. For consistency, the de-noising autoencoder used as a comparison in this section wastrained using the same dataset.TABLE II: Mean and Standard deviation of randomdistribution for simulated channel parameters Parameter µ σa a a b ( θ ) π π τ fs fs First, we conducted a simulation experiment toevaluate the proposed DBN based de-noising tech-nique’s ability to remove noise for channels with extremely high noise. Fig.5 shows the Bit ErrorRate (BER) of the proposed DBN based de-noisingtechnique under the AWGN channel. As a baselinefor comparison, we have provided the BER of theMLE and de-noising auto encoder to highlight thesubstantial gains for highly negative
EbNo . A reasonfor this could be the existence of noise invariableproperties in the features extracted by the DBNin the proposed DBN based de-noising technique.Evidence of this can be seen by the convergingperformance of the algorithm to the baseline asthe noise level decreases, resulting in a decreasein functionality of the noise invariant property. AtBER of − , the performance of the proposedDBN based de-noising technique has a significantlysmaller gain of 2.4dB for de-noising auto encoderand 2.6dB for the MLE.Fig. 5: De-noising BER Accuracy comparison withuncoded BPSK under AWGN channel. For consis-tency, MLE was used as the demodulation techniquefor all 3 methods.Fig.6 shows a visualization of the de-noisingoutcome. At EbNo = -30dB, the received signal ishighly distorted by the channel noise. However, theproposed technique is still able to partially predictthe waveform shape. At EbNo = -5dB, the waveformcan be almost perfectly reconstructed.The second simulation experiment we conductedtested the algorithm’s ability to remain resoluteagainst multi-path propagation. The simulated chan-nel distorted received signals, utilized as test casesin this experiment, were modelled by Eq. 2. Thenumber of multi-paths in the dataset was distributedas 40% 1-path, 30% 2-paths and 30% 3-paths. The Fig. 6: Visualization of proposed DBN based de-noising algorithm under AWGN channel presentsthe received signal (input) and the reconstructedsignal (output). The reconstructed signal, depictedby the magenta line, is shown in relation to thetransmitted signal (ideal output), depicted in green.results of the experiment are shown in Fig.7. Withthe increasing number of paths, the BER of theproposed DBN based de-noising algorithm achievesconsiderable gains while remaining relatively stablein comparison to the de-noising auto encoder andMLE.Fig. 7: De-noising BER Accuracy comparison withuncoded BPSK under Multi-path channel, modelledin Eq.3. For consistency, MLE was used as thedemodulation technique for all 3 methods.Finally, to test the influence of the Doppler effecton the proposed DBN based de-noising algorithm,a simulation experiment was conducted using Eq.5 for the channel. Fig.8 depicts the results underthree different scenarios, where the α = 0 . , , . resulting in a f c = 1 kHz, kHz, kHz . The BERof the proposed algorithm for all three scenarios areobserved to be similar. Thus implying that for acertain range of α , the algorithm is able to remainrelatively rigid to the influences of the Dopplereffect.Fig. 8: De-noising Demodulation BER Accuracycomparison with uncoded BPSK, modelled in Eq.5.For consistency, MLE was used as the demodulationtechnique for all 3 methods.IV. P ROPOSED
DBN-
BASED D EMODULATION
In this section, the demodulation algorithm, con-sisting of a classification DBN, is described.
A. Classification DBN
For the classification DBN, the same generalstacked energy based RBM algorithm is used asdescribed in Section III-B. The input is the recon-structed signal ˜ z ( t ) and the output consists of therespective binary labels ˜ y ( n ) of 0s and 1s. B. Determining the structure of Classification DBN
To determine the classification DBN structure,we investigated the influence of different networkstructures on the performance of the algorithm in theclassification task at
EbNo = The best classification BER results obtained wasusing the [1250 , structure. Although the struc-ture [1250 , seems to achieve approximatelythe same results, the time needed for training issignificantly larger.TABLE III: Effects of training epoch and numberof nodes on Classification DBN Number of units[Layer 1,Layer 2] ResultsEpoch Number BER Time (s) [650 ,
200 0.1712 65.79 [650 ,
500 0.1386 378.2 [650 , [1250 ,
200 0.0854 1261 [1250 ,
500 0.0825 5731 [1250 , [1250 ,
200 0.0883 5228 [1250 ,
500 0.0844 18674 [1250 , To minimize complexity and maximize the per-formance of the algorithm, we have chosen to usethe structure as illustrated in Table IV.TABLE IV: The final hyperparameters used in ourproposed classification DBN, which consists of 2layers of RDMs.
Input Structure Output ˜ z ( t ) No of layers 2 ˜ y ( t ) Nodes [1250,50]Activation Function [Sig, Sig]Epoch 1000
C. Results of Classification DBN
In this subsection, we evaluate the proposedclassification DBN. As a baseline for comparison,we used the conventional MLE method devisedin [38] to illustrate the similar performance of thedemodulation techniques.For the following simulation experiments, thesimulated dataset contains 100,000 transmitted sig-nals periods, in which 50% is used for training, 20%for validation, and the remaining 30% for testing.The dataset was generated using a AWGN channelmodel at a range of
EbNo = -10dB to 30dB. For a faircomparison with MLE, the f c of the BPSK signalsis set at 2kHz. Fig. 9: Demodulation BER Accuracy comparisonwith BPSK and QPSKUsing the MLE as a baseline, this experimentillustrates that the demodulation performance levelof the proposed classification DBN is similar toMLE. The results are shown in Fig. 9. This im-plies that the classification DBN has learned toextract significant features from the PSK modulationscheme. For a truly fair comparison, the proposedalgorithm is also compared to Quadrature PhaseShift Keying (QPSK), derived in [25], without muchextra training. As seen, at BER − , the algorithm’sperformance for QPSK has a BER of 0.67dB lessin comparison to MLE. A more inclusive trainingdataset for higher-order modulation schemes couldincrease the performance of the algorithm in thisarea. V. R ESULTS AND D ISCUSSION
This section will evaluate the proposed receiveras a whole as seen in Fig.1. First, the performanceof the receiver will analyzed using the simulatedunderwater model shown in Eq.6. Then, the condi-tions of the conducted sea trial will be described.Finally, the collected sea trial data was used tovalidate the real application of the proposed receiversystem.The data frame of the testing dataset used in boththe simulation experiments and sea trials is shownin Fig.10. The pilot consists of a single up-sweepand a down-sweep HFM signal, which is used fordetection of the incoming received data signal. TheHFM modulated signal has a bit rate of 50 bits/s and a frequency range of 1-4kHz. The data frameincludes 416 bits of coded BPSK modulated signals.The specifications of the data structure is recordedin Table.V.Fig. 10: Transmitted Data StructureTABLE V: Specifications on the simulated and seatrial data set Experiment Parameters ValueSampling Rate 40 kHzBit Rate of HFM 50 bits/s f c of HFM 1 – 4 kHzBit Rate of BPSK 1 kbits/s f c * of BPSK 1, 2, 3 & 4 kHz A. Simulation Overall Results
In this subsection, we evaluate the overall pro-posed receiver system. To assess performance undera underwater environment, we will be employing 5systems for evaluation – (1) MLE demodulation, (2)de-noising auto encoder with MLE demodulation,(3) the proposed DBN based receiver, (4) DL or-thogonal frequency-division multiplexing (OFDM)[23], and (5) SIC DL [24].For the following simulation experiments, thetraining data and channel model used to train theindividual parts of the proposed receiver systemwere the same as stated in Section IV and V. Forequitable contrast, the de-noising auto encoder didnot go through any extra training.The simulated BPSK testing dataset contains10,000 transmitted signals periods. The dataset wasgenerated using Eq.6 and the random distributionsseen in Table.VI. The number of multi-paths in thedataset was distributed as 40% 1-path, 30% 2-pathsand 30% 3-paths. The dataset contains dataset of60% kHz f δ and 40% kHz f δ in each multi-path cluster. The increase in f δ is used to furthersimulate the complex occurrence of the underwaterscattering. To fairly evaluate the performance of the proposed receiver with the two systems mentionedabove, the f c of the BPSK signals is set at 2kHz.TABLE VI: Mean and Standard deviation of randomdistribution for simulated overall channel parame-ters Parameter µ σa a a b ( θ ) π π α . τ fs fs In a previous investigation seen in [40], we dis-covered that the feature extraction ability of theDBN has created a characteristic that is invariantto the influences of the Doppler effect. Therefore,we assume that even though the classification DBNwas only trained on f c = 2 kHz , the performanceof the proposed classification DBN will not besignificantly degraded by the range of f c used inthe testing dataset used.Fig. 11: BER Accuracy comparison with codedBPSK and OFDM-BPSK under simulatedunderwater conditions, modelled by Eq.6Fig.11 depicts the performance of the five sys-tems with regards to the above described testingscenario. The proposed receiver (consisting of bothDBN De-noise and DBN Classification) is seen tooutperform the other algorithms over a large rangeof EbNo for both uncoded BPSK and OFDM-BPSK.This implies that the proposed receiver system isable to remain invariant to changes in instantaneousamplitude, phase and frequencies, such that theshown coding gain can be achieved. Table.VII compares the computational complex-ity of the five algorithms, where n represents inputsize n for each function. The results show that ourproposed system requires a large amount of trainingtime in comparison to the auto encoder and MLE.However, shown in Fig.11, our proposed algorithmoutperformed the auto encoder and MLE by 7.8dBand 12dB at EbN = 5 and EbN = 0 respectively forthe BPSK modulated system.TABLE VII: Algorithmic Computational Complex-ity Comparison Training TestingMLE - O( n )Auto-encoder O(1000 n ) O(100 n )DL OFDM [23] O(19200 n ) O(9600 n )DL SIC [24] O(9600 n ) O(4800 n )Proposed System O(16000 n ) O(100 n ) B. Sea Trial Set-up
The communication system used in theunderwater acoustic sea trial is depicted in Fig.12a.Before transmission, the desired transmitted signal x ( t ) is converted from digital values to analogsensor signals using a National Instruments-DataAcquisition (NI-DAQ) hardware unit. The signalis then amplified before being transmitted. At thereceiver end, the signal is first received by thehydrophone and amplified by ISO-TECH IPS-3303. The corresponding NI-DAQ will translatethe analog sensor signal to digital values for theproposed communication system.In March 2019, a sea trial was conducted in thewaters near Selat Pauh, Singapore, where the bottomis muddy with the deepest depth of approximately25m. The waters is considered to be relatively sta-tionary with occasional disturbance from the largevessels traveling to the port. In this trial, the distanceand depth of the transmitter and receiver was keptat about 300m and 9m respectively, with a variationof 50m and 1m due to the changing currents. Thecarrier frequency of the BPSK modulated signal wasvaried at 1kHz intervals for different trials. Thetrials were conducted at f c = 1 kHz, f c = 2 kHz, f c = 3 kHz and f c = 4 kHz. Due to the limitationsof the hardware used in the trial, the sampling ratewas set at 40 kHz. The specifications of the sea trialis recorded in Table.VIII. (a) Sea Trial End-to-End System Diagram(b) Transmitter Set-up(c) Receiver Set-up Fig. 12: Sea Trial On-site Set-upTABLE VIII: Specifications on the Sea Trial
Trial Parameters ValueDistance between Transducer & Hydrophone 300m ±
50 mDepth of Transducer 9m ± ± C. Sea Trial Results
In this subsection, the collected data from the seatrial described in Section V-B was used to validatethe real application of the proposed receiver system.The results of which are shown in Table.IX.The estimated average α was calculated usingthe up and down sweep of the HFM pilot signaland the SNR was estimated using MATLAB. Forthis evaluation, we collected data for 10 trials. TABLE IX: Sea Trial Data Results and AccuracyComparison between MLE with Doppler Synchro-nization and Proposed Receiver System
TrialNo. f c SNR α BER of MLE+ Doppler Sync. BER of ProposedReceiver System1 4kHz -6.081 1.02 0.485 0.01482 2kHz -1.845 1.00 0.435 0.03303 3kHz -4.818 1.12 0.490 0.00934 1kHz -4.638 1.00 0.465 0.01025 4kHz -21.409 1.09 0.535 0.07906 4kHz -22.019 0.90 0.495 0.08577 4kHz -28.468 0.87 0.492 0.09938 2kHz -23.466 1.01 0.486 0.08999 1kHz -28.781 1.14 0.502 0.124010 1kHz -24.951 0.99 0.512 0.0917
Trial 1-4 were conducted on Day 1 and the resultsobtained from the sea trial were significantly betterthan seen in Fig.11 with the most significant onExp.3 with an coded BER of 0.0093 in comparisonto BER of 0.045. This implies that during Day1, the complexity of the channel was significantlylower than that simulated in the above trial. Thedata collected from Trials 5 and 6 on Day 2 hada much lower performance significance with animprovement of 0.08. On Day 3, while carryingout Exp. 7-10, we experienced heavy rain, whichresulted in a more complex dataset. As such, theBER seen from the sea trials conducted on Day 3shows similar performance to the simulated results.Overall, our proposed receiver system is able tokeep a significant performance improvement fromthe − BER of the MLE with Doppler sync. to a − BER.VI. C
ONCLUSION AND O UTLOOK
In this paper, we have proposed a novel receiversystem that uses DBNs to redesign the de-noising and demodulation techniques for underwateracoustic communications. Our approach has alsoprovided an interesting and important pathway forthe application of machine learning techniques tounderwater communications systems.Firstly, although the performance of the receiversystem matches performance of traditional systems,without significant improvement, in the AWGNchannels, it does show better performance in themore realistically simulated underwater channelsinfluenced by Doppler and multi-path. A compar-ison with the traditional MLE and the promisingde-noising auto encoder was completed in variousunderwater scenarios. These simulated experiments revealed extremely competitive BER performanceswith a performance improvement of 13.2dB at − BER. Therefore, demonstrating the powerful po-tential for machine learning to be used in morecomplex underwater acoustic channels. As a fur-ther investigation, we will increase the complexityby accommodating different mixtures of noise likerayleigh noise and exponential noise.As an additional step, we collected real life data,through a sea trial, to analyze the performance of theproposed receiver in a real scenario. The results ofwhich were promising with a substantial improve-ment from a coded − BER using the traditionalMLE method with Doppler synchronization to acoded − BER with the proposed receiver. Thisimplies the real possibility of designing machinelearning based underwater acoustic communicationsystems.Finally, the strength of using DBNs to designour proposed receiver is denoted by its seeminglylearned ability to comprehend and classify differ-ing sets of received signals. Despite the varyingparameters– frequency, amplitude, phase and timeframes between each random shift– of the scenarioswe have chosen to examine the receivers under, ourproposed receiver has remained relatively invariantwith the largest variation of 5.2dB at an uncoded − BER between the presence of 1-path and 3-paths. This phenomena suggests that the DBNs havesuccessfully extracted meaningful features from thesignals that could potentially be unchanged to thefluctuations of the underwater channel.R
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