Performance Evaluation of SFBC-SOFDM forUnderwater Acoustic Channels

Prashant Kumar, Vijay Mukati, Preetam KumarDepartment of Electrical EngineeringIndian Institute of Technology Patna

Patna - 800013, IndiaEmail: {prashant,vijay.mtee13,pkumar}@iitp.ac.in

Abstract—This paper investigates the performance of spreadorthogonal frequency division multiplexing (SOFDM) with spacefrequency block coding (SFBC) technique for underwater acous-tic communication through simulation and semi realistic ex-perimentation. Performance of Walsh-Hadamard code spreadOFDM (WHSOFDM) and carrier interferometry code spread(CISOFDM) has been evaluated for underwater acoustic com-munication along with transmit diversity technique. The spread-ing technique helps overcome frequency-selectivity and providesreduced peak-to-average power ratio (PAPR) whereas the trans-mit diversity technique improves the data rate and reliability.CISOFDM with SFBC offers a SNR gain of 2.4 dB for a bit-error-rate (BER) of 1×10−6 over WHSOFDM with SFBC. The presentwork also demonstrates the design of a low cost experimentalsetup (testbed) to perform a large number of experiments relatedto underwater communication and prototype algorithm testing. Asimple two-transmit-one receive SFBC-CISOFDM scheme is usedto transmit images through the underwater channel to validatethe simulation.

I. INTRODUCTION

Underwater acoustic sensor networks (UWASN) are de-ployed for underwater infrastructure monitoring, harbor andport security, disaster detection and early warning generation,marine resource exploration, surveillance, etc. Radio wavessuffer from large attenuation, optical waves get scattered henceacoustic waves are the best carrier for underwater communi-cation. Acoustic propagation is characterized by three majorfactors: frequency dependent attenuation, multipath propaga-tion, and low speed of sound (1500 m/s) [1]. Underwateracoustic (UWA) channel is characterized as a large delayfrequency selective channel. Significant research efforts havebeen put in to apply different variants of orthogonal frequencydivision multiplexing (OFDM) for efficient and reliable highdata rate UWA communication. Several commercial acousticmodems like AquaSeNT and Aqua-fModem which use OFDMmodulation are available, but all of them have a relatively lowdata rate apart from being quite bulky and costly. Techniqueslike coded-OFDM, spread-OFDM (SOFDM) and multiple-input multiple-output (MIMO) OFDM have been demonstratedas better physical layer solution. Some hybrid schemes havealso been reported to improve performance. The underwaterexperiments/sea-trials are very difficult and expensive [2] toperform and require a lot of time, hence computer simulationis used to demonstrate the effectiveness of the new proposedschemes. Only preliminary results for UWA channels arereported in literature where both simulations and recorded data

are used to demonstrate the effectiveness of proposed schemes.Spread-OFDM enjoys the spreading gain of code divisionmultiple access (CDMA) along with the benifits of multicarriertransmission. This work targets at increasing the sturdinessof SOFDM for UWA communication schemes. This can bedone by using multiple projector and hydrophones where eachtransmitter-receiver pair counts as an additional communi-cation channel. The increased number of parallel channelsdrastically reduces the bit-error-rate (BER) of the link, i.e.the probability that all channels are experiencing simultaneousfading [3]. The number of transmit elements is limited by theamount of cross-talk that can be handled by a MIMO channelestimator hence a simple two-transmit one-receive system isevaluated. MIMO systems have been considered for UWAchannels both for increasing the system throughput via spatialmultiplexing and for improving the systems performance viaspatial diversity. In this work we use transmit diversity throughthe use of Alamouti coding [3] applied across the carriers ofan OFDM signal. Space frequency block coding (SFBC) isselected as it better suits acoustic communication. The reasonbeing that Alamouti coherence assumption may be challengedbetween two adjacent OFDM blocks on a time varying acousticchannel, but it will hold between two adjacent OFDM carriers.The frequency coherence assumption coincides with the basicOFDM design principle which calls for carriers to be spacedclosely enough such that the channel transfer function can beconsidered flat over each sub-band.The remaining part of the paper is organized as follows: sectionII presents the basics of SOFDM and diversity techniques.Section III discusses the proposed SFBC-SOFDM for UWAchannel, while IV describes the experimental setup. Section Vpresents the simulation and experimental results and sectionVI concludes the paper.

II. SPREAD OFDM WITH TRANSMIT DIVERSITY

Spectral nulls are always present in frequency selectiveUWA channel and can severely distort or annul out the OFDMcarriers that are in their neighborhood, resulting in a loss ofthe symbols carried by those subcarriers. This results in a highBER and bandwidth wastage because of the need for retrans-mission of the lost data. For long propagation delay UWAchannel retransmission is not appreciated. Another approach isto scatter the groups of data symbols over the entire bandwidth.This technique is known as spread-OFDM (SOFDM). Figure 1shows the block diagram of this scheme, spreading block maybe Walsh-Hadamard matrix (WH) or carrier interferrometry

978-1-4799-3646-5/14/$31.00 ©2014 IEEE

Fig. 1. System Model for Spread OFDM.

code (CI). The data symbols are scattered over the completebandwidth such that every individual subcarrier bears a linearcombination of all the data symbols. Even if some subcarriersare deeply faded, then also there is a possibility to maintaindesired quality-of-service at the receiver end. At the receiverspread symbols are simply separated by the use of linear matrixoperation. The performance of different SOFDM systems inthe UWA channel is evaluated using computer simulation in[4], [5].

A. WH Spread OFDM

The Walsh-Hadamard Transform (WHT) actually multi-plies a 2m-length vector by a 2m× 2m matrix given by

W2m =

[Wm Wm

Wm −Wm

](1)

where W1 = +1. Thus,

W2 =

[W1 W1

W1 −W1

]=

[+1 +1+1 −1

](2)

The WHT of a data symbol vector, ~s[n] is given by

~sW = ~s[n]× WN√N

(3)

where N is the length of the data symbol vector. The normal-ization constant is used to keep the average energy of the vectorunchanged. As the coefficients of WHT are always ±1, theIFFT of the vector sW [n] has a lower peak-to-average powerratio (PAPR) compared to standard OFDM. The inverse WHT(IWHT) is also obtained by multiplying the transformed vector,~sW [n], by the normalized WH matrix WN i.e.,

~s = ~sW ×WN√N

(4)

The WH-SOFDM system model is only a slightly modifiedOFDM model with a spreading block before the IFFT op-eration and a dispreading block after the FFT operation. InSOFDM, the frequency domain signal is multiplied by a WHspreading matrix before it is fed to the IFFT block [6]. TheWH transform is an orthogonal linear transform that can beimplemented by a butterfly structure as the IFFT and since theWH and IFFT transforms can be combined and calculated withless complexity than the IFFT alone, the system complexity isreduced by applying WH spreading. The transmitted OFDMsymbol is given by

~x = IFFT(~s WN√

N

)(5)

and the symbol the de-mapper receives is given by

~d =FFT(x ∗ ho + ~w)

Ho

× WN√N

= ~s +~w WN√NHo

(6)

where h0 is the channel impulse response, H0 is the channelfrequency response estimation, ~ω is an AWGN vector of sizeN and {∗} represents convolution operation.

B. CI Spread OFDM

A new multi-carrier modulation scheme for the UWAchannels known as Carrier Interferometry spread OFDM(CISOFDM) was introduced in [7]. Compared with OFDM,the CISOFDM has a low PAPR and inherent frequency se-lective combining, which makes it a very attractive signalingscheme for UWA channel [8]. In CISOFDM, each low-rateparallel symbol stream is simultaneously modulated onto allN carriers by application of a unique orthogonal complexspreading sequence (applied in the frequency domain). Thiscreates frequency diversity benefits for each symbol stream,leading to high performance. Additionally, the use of carefullyselected complex spreading sequences eliminates large peaksin power, thereby alleviating PAPR concerns. The complexityof the system increases from that of conventional OFDMto that of multi carrier-coded division multiple access (MC-CDMA), and MC-CDMA is a relatively low-cost systemfrom the implementation point of view. The CI spreadingis implemented using IFFT operation. In order to separatesymbols located on the same subcarrier, a phase offset knownas spreading code is used. The spreading code for the kth

information symbol is defined as (ej0, ej∆θk , ..., ej(N−1)∆θk),where ∆θk = (2π/N)k will ensure orthogonality amongthe N transmitted information symbols which occupy thesame subcarrier at the same time. The transmitted signal inCISOFDM can be expressed as [7]

s(t) =N−1∑k=0

sk(t) (7)

=1√N

N−1∑k=0

N−1∑i=0

akej 2πN kiej2πi∆ftej2πfct(0 ≤ t ≤ Ts)

s(n) =N−1∑k=0

sk

(nTs

N

)(8)

=1√N

N−1∑k=0

N−1∑i=0

akej 2πN kiej

2πN ni

=1√N

N−1∑i=0

N−1∑k=0

akej 2πN kiej

2πN ni(n = 0, 1, ..., N − 1)

CISOFDM corresponds to

s = K.IDFT [IDFT (α)] (9)

where s = (s(0), s(1), ..., s(N − 1)),α = (a0, a1, ..., aN−1)and K is a constant coefficient. Similarly at the receiving end

s = DFT [DFT (r)] (10)

where r = (r(0), r(1), ..., r(N − 1)). As IDFT could beperformed faster and simpler by an IFFT, the IDFT is replacedby the IFFT to achieve signal processing efficiency. ForN = 2m the transmitter and the receiver can be implementedby performing IFFT twice, respectively. This in turn reducesthe system complexity compared to the other PAPR reductiontechniques.

C. Transmission Diversity

Transmit diversity is a wireless communication techniqueusing signals coming from numerous independent sources thathave been modulated with identical message signals and thatmay vary in their transmission characteristics at any giveninstant. It can help in combatting fading, link-loss, and circuitfailures. In most scattering environments, antenna diversity isa practical, effective and hence, a widely applied techniquefor reducing the effect of multipath fading. The classical ap-proach is to use multiple antennas at the receiver and performcombining or selection and switching in order to improve thequality of the received signal. The major problem with usingthe receive diversity approach is the cost, size and power of theremote units. Transmit diversity schemes are more feasible forUWA communication. The transmit diversity scheme proposedby Alamouti in [3] along with spreading is depicted in figure2. In the present work transmit diversity is used to boost theperformance of SOFDM. In UWA system hydrophones areused instead of antenna as communication takes place viaacoustic waves and the basic idea of performance gain byspatial diversity is the same.

Fig. 2. System Model of SOFDM with transmission diversity

D. Space Frequency Block Coding OFDM

In space frequency block coding scheme the codeword istransmitted in two adjacent subcarriers of the same OFDMsymbol as shown in Table I. The SFBC-OFDM combines the

TABLE I. SFBC-OFDM TRANSMISSION MATRIX

Hydrophone-1 Hydrophone-2nth subcarrier, ith symbol s[n] −s[n+ 1]∗

n+ 1th subcarrier,(i)th symbol s[n+ 1] s[n]∗

two adjacent subcarriers of the same OFDM symbol to obtainthe transmission diversity. To achieve optimum performancethe channel frequency response at the frequency of the nth andthe (n+1)th subcarrier must be same. And the channel must betime invariant during one single OFDM symbol. SFBC-OFDMis more robust against Doppler effect when compared withspace time block coding (STBC)-OFDM, but SFBC-OFDM ismore vulnerable to the frequency selectivity than STC-OFDM.In this work a combination of SFBC and SOFDM has beenapplied for underwater communication. As spreading by WHand CI does not increase the complexity of OFDM by too muchhence incorporating SFBC scheme in the UWA communicationwill not result in a highly complicated system. The benefitsof SFBC are dependent upon frequency coherence whichincreases as more carriers are packed within a given bandwidthalso increasing the bandwidth efficiency. But there is a limitbeyond which inter carrier interference (ICI) predominatesmaking Alamouti detection complex. Virtually there is a trade-off between number of subcarriers and transmit diversity gain.Clipping causes inter carrier interference (ICI) which in caseof a SFC results in degradation of space frequency codeword,it is expected that the reduction of this non linearity results inbetter performance of SFC-SOFDM.

III. PROPOSED SFBC-SOFDM FOR UNDERWATERACOUSTIC CHANNELS

The block diagram of a simple OFDM system is shown infigure 1. The spreading blocks i.e. WH and CI blocks in theirrespective schemes spread information over several subcarrierswhich results in diversity gain in a frequency selective fadingchannel. The system model for the combination of SOFDMand SFBC diversity technique is shown in figure 2

A. Channel Model

Underwater signal fading can be Rayleigh, Rician, or Kdistributed, while other channels may just as well be charac-terized as being deterministic [9]. Noise comes from a widevariety of sources with different statistics, such as precipitation,marine mammals, sonar systems, and offshore civil works.Underwater tests have shown that the channel often exhibitpoor behaviour than a Rayleigh distributed channel modeling.Position and the time also has significant impact on the BERperformance of the ocean channels. Less deep acoustic channelhas been modeled as a four to five path Rayleigh channel.Temporal variant fading has to be included and additive noiseis taken from Rayleigh fading channel model [10], [11]. A timevariant and correlated fading factor in the signals amplitude orthe power accounts for the multiplicative fluctuation of eachindividual path. Additive white Gaussian noise (AWGN) forthe system is combined at the receiver. The channel impulseresponse can be expressed by

h(t, τ) =M∑i=1

ai(t)δ(t− τi(t)) (11)

TABLE II. SIMULATION PARAMETERS

Parameter SOFDMNo. of transmitted bits 1e8Mapping BPSKCarrier frequency 7kHzSignal frequency band: BW 10kHzNumber of subcarriers: N 64Coherent time: Tc = 1/τmax 210msMaximum Delay Spread: τmax 25msSubcarrier bandwidth: ∆f = BW/N 156.25HzValid symbol duration: ∆f 6.4msCyclic prefix period: TCP ≥ τmax 25msChannel real UW or 5−path UWA channel

where M represents the number of rays used in the multipathchannel model. ai(t) and τi(t) are the complex-valued timevarying channel magnitudes and the propagation delay of thekth path. A detailed study of parameters used can be found in[11].

B. Simulation Parameters

The system specifications are shown in Table II. OFDM,WH-SOFDM and CI-SOFDM have been simulated for oceanchannel with and without SFBC transmit diversity. The re-ceiver is implemented using matched filter and it is assumedthat the receiver has complete channel state information.

IV. EXPERIMENTAL TESTBED FOR SFBC-SOFDMUNDERWATER ACOUSTIC CHANNEL

Fig. 3. Experimental Setup.

The experimental testbed involves tank of the size of alarge aquarium (5m× 3m× 1.5m) serving as the water body.It is filled with water and impurities are added in a calculatedmanner to resemble the chemical composition of the seaenvironment [10] which is to be imitated. A slow speedpropeller is used to create waves. The bottom and surfaceof the water will cause reflection for multipath formation. Alow cost 27mm doubled brass piezo head coated passive ColdGold hydrophone and an electric-acoustic transducer basedDaravoc underwater speaker pair is used for transmission and

Fig. 4. Tranducer test.

Fig. 5. Wired communication.

Fig. 6. In-air acoustic communication.

Fig. 7. Underwater acoustic communication.

reception. Two laptops having Matlab software installed inthem are used as the transmitter and the receiver. A high gainamplifier is used to strengthen the signals before being sendthrough the water channel.The experiment has four phases as follows:

1) The hydrophone and the underwater speaker are testedusing standard function generator and digital oscilloscope fortheir sensitivity and characterization in the frequency rangeof operation as shown in figure 4.2) A wired link between two laptops is used to transmitand receive signals between the sound output of the firsttransmitting laptop and the microphone input of the secondreceiving laptop. Mono audio output and input setting is used.This step helps check the validity of the Matlab simulationover an AWGN channel as shown in figure 5.3) In-air transmission reception link is established between

the two laptops using underwater speaker and the hydrophoneas shown in figure 6. The distance between the laptops can beincreased by using suitable amplifier and calm environment.4) In-water transmission is established using two underwaterspeaker and a hydrophone in the experimental tank. Initiallythe hydrophone is placed very close to the speakers and oncerelatively error free communication is reached, the separationis increased using the amplifier as shown in figure 7.

All the software implementation is done in Matlab. Thissemi-realistic tank setup is a nice intermediate step betweenpure Matlab simulation and real sea trial. However there arepoints which account for large variation between simulationresults and real experimental outputs. For Matlab simulationof the channel generally a five path Rayleigh fading model isused and a maximum channel delay is fixed but in the tank ex-periment there exist a line-of-sight (LOS) component. Anotherimportant point is that as the distance between transmitter andreceiver is less hence the channel delay has to be accounted byincorporating a delay in the receiver end program. The delay isbased on the frequency used; as a 7kHz carrier is used whichis suitable for a range of about 50km, the delay is calculatedusing the speed of sound as 1490m/s.

V. RESULTS

The BER performance of the OFDM, WHSOFDM andCISOFDM has been evaluated over underwater acoustic chan-nel using Monte Carlo simulation in MATLAB. In the simula-tion, perfect frequency and phase synchronization are assumed.Figure 8 shows the plot of BER versus signal-to-noise ratio

Fig. 8. BER plot for OFDM, WHSOFDM and CISOFDM for UWA channel.

(SNR) for OFDM and different SOFDM schemes appliedto underwater acoustic channel. Simulation results illustratethat for WH-SOFDM, the error floor is observed at BER of4×10−4 whereas for CISOFDM the error floor is observed at1.2× 10−6. CISOFDM achieves a BER of 2× 10−6 at 20dBSNR.This gain in case of CISOFDM is also due to the polyphasenature of CI spreading code compared to the WH spreadingmatrices. The partial cross-correlations of CI codes (aftertransmission over a multipath fading channel) are independentof phase offsets between different paths. When WH codes areused the partial cross correlations are related to the squaredcosine of path phase offsets. This accounts for the betterperformance of CISOFDM.

OFDM, WHSOFDM and CISOFDM has been simulatedin Matlab with SFBC. With the application of SFBC and

Fig. 9. BER plot for SFBC OFDM, SFBC-WHSOFDM and SFBC-CISOFDM for UWA channel.

spreading techniques it is observed that the error floor fallto 1 × 10−6 and 6 × 10−7 for WHSOFDM and CISOFDMrespectively. The results of bit error rate performance areshown in figure 9. There is a SNR gain of 2.4dB at aBER of 1 × 10−6 when transmit diversity is used in case ofWHSOFDM and CISOFDM respectively. The results of biterror rate performance are shown in figure 9. The experimentalverification has been done by transmitting an image throughthe underwater channel in the tank. The picture obtained usingSFBC-CISOFDM is shown in figure 10(a), 10(b), 10(c) and10(d).

VI. CONCLUSION

To improve the bit error rate performance of underwatercommunication using OFDM two different techniques havebeen combined. Whereas spread OFDM offers diversitygain in frequency selective channel and reduced PAPR thetransmit diversity is used to boost the performance of spreadOFDM and help overcome the effects of fading, outages, andcircuit failures. The number of transmit elements is limitedby the amount of cross-talk that can be handled by a MIMOchannel estimator hence a two transmit one receive system isevaluated. Due to the hostile behavior of underwater channel,it is extremely difficult to achieve a SNR value of even 20dBat the receiver.

It is shown that CISOFDM with SFBC transmit diversitycan be used for as an effective scheme for data transmissionunderwater with a satisfactory QoS. As this scheme offers lowPAPR and low BER at less complexity it is quite suitable to beadopted in underwater acoustic sensor network as the physicallayer solution.

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(a) (b)

(c) (d)

Fig. 10. (a) Transmitted Image, Received image with (b) OFDM Transmission, (c) CISOFDM Transmission, (d) SFBC-CISOFDM Transmission.

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