Passive time reversal (pTR) is a low complexity receiver scheme that uses multichannel probing for time signal refocusing, thus reducing time spreading and improving inter-symbol interference. Recognizing that signals traveling through different paths are subject to arrival-angle-related Doppler displacements, this letter proposes a further improvement to pTR that applies correcting frequency shifts optimized for beams formed along each specific path arrival angle. The proposed channel equalizer is tested with real data, and the results show that the proposed approach outperforms both pTR and the modified pTR channel combiners providing an MSE gain of 4.9 and 4.2 dB, respectively. © 2015 Acoustical Society of America

Jesus, S. M.

Siddiqui, S.I.

Silva, A.

The Journal of the Acoustical Society of America

Universidade do Algarve

Path specific Doppler compensation in time-reversal communications

Sapientia (Univ. do Algarve)

Jesus, JASA-ELPath specific Doppler compensation in time-reversal communicationsSe´rgio M. Jesus, Salman Ijaz and Anto´nio SilvaLaboratory of Robotic Systems in Engineering and Science (LARsyS)Campus de Gambelas, University of Algarve8005-139, Faro, Portugal.sjesus@ualg.pt, sijaz.23@gmail.com, asilva@ualg.ptRunning title: Doppler in time-reversal communicationsAbstract: Passive Time Reversal (pTR) is a low complexity receiver scheme that usesmultichannel probing for time signal refocusing, thus reducing time spreading and improv-ing inter-symbol interference. Recognizing that signals travelling through different pathsare subject to arrival-angle-related Doppler displacements, this letter proposes a further im-provement to pTR that applies correcting frequency shifts optimized for beams formed alongeach specific path arrival angle. The proposed channel equalizer is tested with real data andthe results show that the proposed approach outperforms both pTR and the modified pTRchannel combiners providing an MSE gain of 4.9 dB and 4.2 dB, respectively.c©2014 Acoustical Society of AmericaPacs numbers: 4360.Dh, 4360.Fg, 4360.Gk1Jesus, JASA-ELI. INTRODUCTIONReliable underwater acoustic coherent communications is still a great challenge due to envi-ronmental effects distorting the signal between emitter and receiver. Among the most im-pairing effects are channel multipath causing signal time spread, and channel time-variabilityas well as source - receiver relative motion causing Doppler spread. The standard approach isto design adaptive channel equalizers that attempt to compensate for the channel multipathand track ocean variability constantly minimizing its effect on the underwater communicationsystem (see e.g. Stojanovic et al. 13 and references herein).In the last decade, passive Time Reversal (pTR) - also known as phase conjugation - hasemerged as an effective low-complexity channel multipath compensation technique Edelmannet al. 1 . In pTR communication the signals received in an array of sensors are correlated withthe time reversed versions of the estimated impulse responses (IR) of each channel, obtainedat a previous time. This effectively recreates an ocean-replica based matched-filter at eachsensor output that is then summed over all sensors to obtain spatial focusing and gain. Underoptimal conditions of channel reciprocity, channel stability and sufficient array physical span,the pTR output effectively deconvolves the channel from the transmitted signal, allowing foroptimal detection and decoding of the transmitted message with low intersymbol interference(ISI) and reduced mean square error (MSE) Rouseff 9 . In Preisig 8 , the author compares theperformance of the channel estimate-based Decision Feedback Equalizer (DFE) and pTR inpresence of imperfect channel estimates. The results suggest that the performance of pTRdegrades significantly in the presence of rapid channel variations, e.g. sea surface waves andsource-receiver motion. In addition to time spreading, the received signal also spreads in the2Jesus, JASA-ELfrequency domain due to environmental variations (e.g surface variations) and/or geometricvariations (e.g source - receiver relative motion) Eggen et al. 2 . These variations also affectthe temporal focusing of the pTR communication system resulting in loss of performance.In Song et al. 12 , it was shown that a continuous channel update and Doppler tracking arerequired before pTR operation in order to achieve acceptable performance in presence ofocean variability.In the multipath environment, the transmitted signal reaches the receiver through dif-ferent paths where each path is affected by environmental variations in a different manner,resulting in a different amount of Doppler in each path Ijaz et al. 6 . One way for dealing withthese Doppler-multipath dispersion is to beamform the data and steer nulls in the directionof any other paths but the main arrival LeBlanc 7 . In current Doppler compensation tech-niques, Doppler distortion is compensated with a single value which fails to give maximumcompensation Gomes et al. 3 ; Sharif et al. 10 . In Silva et al. 11 an improved version of pTR -frequency shift pTR (FSpTR) - was proposed that includes appropriate frequency shifts inthe pTR impulse response estimates so as to maximize the output power at each time instantduring the interval between successive probes. It was proved with both simulated and realdata that FSpTR could provide an MSE gain of several dB and in Vilaipornsawai et al. 14 aDFE was integrated with FSpTR to improve the performance of the communication system.However, since each path is affected differently by environmental variations, FSpTR - whichapplies a single frequency shift correction for all the paths - fails to compensate accuratelyfor channel variabilities resulting in residual ISI at the FSpTR system output. In this letter,a refinement of FSpTR is proposed where frequency shifts are adapted for each incoming3Jesus, JASA-ELwavefront separately, thus providing further compensation for path-specific environmentalvariations.This letter is organized as follows: Section II. will present the receiver structure usinga Delay-Doppler-based model. Section III. will present comparative performance resultsobtained on real data. Section IV. concludes this letter.II. RECEIVER STRUCTUREDelay-Doppler models are widely accepted for describing the transmission of narrow-bandsignals over time-varying channels Hlawatsch and Matz 4 . In such models the lth sensornoiseless received complex baseband signal over a deterministic P -path channel is written asrl(t) =P∑p=1hps(t− αlp − τp)ej2pi(t−αlp)νp , (1)where s(t) is the source transmitted signal, (hp, τp, νp) are the complex amplitude, time delayand Doppler shift characterizing path p, respectively, and αlp is the array geometry dependenttime delay for path p to reach sensor l. For a d-equispaced vertical line array (VLA) andassuming plane-wave propagation αlp = (l−1)d cos θp/c, where θp is the arrival angle of pathp and c is the sound speed. The simplification that consists in considering the parameters(hp, τp, νp) sensor independent is justified by the sensor averaging of phase aligned fieldsafter the conjugate multiplication (in the frequency domain) occurring in the time-reversalprocess (see section A.). After sensor averaging, the path amplitudes are simply the averageof signal magnitude squared over the array. Splitting the time delay of path p at sensorl as a delay τp and a plane-wave delay delay αlp has the advantage of putting in evidence4Jesus, JASA-ELthe beamform delay for applying the method proposed in section C.. The narrow-bandassumption generally implies that baseband - bandpass transformation maybe representedby a simple frequency shift, which generally assumes a signal band B  fc, where fc is thecarrier frequency. A frequency equivalent of Eq. (1) is given byRl(f) =P∑p=1hpal(θp)S(f − νp)e−j2pi(f−νp)τp , (2)where al(θp) = e−j2pifαlp , for the VLA case under the plane-wave assumption.One channel of the pTR receiver structure is shown in the block diagram of Fig. 1. Thesignal r′l(t) is the received probe at true time t = 0, stored in memory and then reused toprocess the actual signal rl(t) received at true time t > 0. Gray shaded blocks allow forimplementing the proposed variations of the basic pTR algorithm as described in the nextsections.A. The passive time reversal (pTR)The basic pTR receiver is obtained from the block diagram of Fig. 1 by following the pathwithout the gray-shaded blocks and allows to obtain the following array output (in thefrequency domain)Z(f) =P∑p=1hph′∗p S(f − νp)S∗(f − ν ′p)e−j2pif(τp−τ′p)ej2pi(νpτp−ν′pτ′p), (3)where it was assumed that the cross-sensor array summation was sufficient to eliminate thecross path terms. Without loss of generality, the same signal s(t) was used as probe andas message bearing signal. In actual communications the probe signal will be the signalingpulse shape, while s(t) will carry the information sequence a(n). In case of perfect channel5Jesus, JASA-ELmatch, which will most likely happen only in the first few instants after probe transmission,we will have hp = h′p, τp = τ′p and νp = ν′p, giving rise, from (3), to the inverse FT timeresponsezout(t) =P∑p=1|hp|2Cs(t)ej2piνpt, (4)where Cs(t) is the autocorrelation of signal s(t).B. The frequency-shift passive time reversal (FS-pTR)The objective of this algorithm is to compensate for the Doppler effect produced by themovement of the emitting source, either in range or in range and depth. Taking into accountblocks 1 and 2 of Fig. 1 the array output of FS-pTR becomesZ(f ; ∆f) =P∑p=1hph′∗p S(f − νp)S∗(f −∆f − ν ′p)e−j2pi[fτp−(f−∆f)τ′p]ej2pi(νpτp−ν′pτ′p)L∑l=1e−j2pi∆fαlp ,(5)where the ”optimal” frequency shift ∆f maximizes the power of the output over a range ofpossible frequency shifts. It can be seen from the previous expression that ∆f appears as acorrection term to align νp and ν′p as well as τp to τ′p. The last residual L-sensor summationterm in Eq. (5) taken over the P -path arrivals unfortunately shadows the output signal bothin the frequency and time domain.C. The beam frequency-shift passive time reversal (bFS-pTR)In the proposed method, channel compensation is taken one step further by individuallyfrequency shift compensating Doppler effects for each array arrival path p, incoming fromangle θp. In fact it is well known that source movement at relative speed vector vs will project6Jesus, JASA-ELinto each ray path p, a component vp depending on the ray launch angle θp. Therefore thesignal received along each path will be frequency shifted by an amount proportional to vp/c.The receiver structure is now modified including array steering delays for forming Kbeams into respective directions θk and summing over all the beams. This is performed byincluding blocks 3 and 4 of Fig. 1. Following the same approach as in the previous sections,the signal output can now be written asZ(f ; ∆f, θk) =P∑p=1hph′∗p S(f−νp)S∗(f−∆f−ν ′p)e−j2pi[fτp−(f−∆f)τ′p]ej2pi(νpτp−ν′pτ′p)L∑l=1e−j2pi∆f(αlp−αlk),(6)where αlk = (l − 1)d cos(θk)/c, is the delay applied to sensor l to steer beam k to directionθk. In the expression above, the last term is a beamformer response to incoming ray fromdirection θp when steered to θk. Its output will be maximum for θk = θp and greatly reducedfor all the other angles. Therefore the search of the maximum output power as a function offrequency shift will occur for each beam in blocks (1)-(2), and then summed up for all thebeams in block (4) (of Fig. 1). So, the difference introduced in bFS-pTR relative to FS-pTRis that Doppler compensation is now specific for each acoustic path. This compensationis achieved by matching the signal along each path with a time-reversed Doppler shiftedreplica of the acoustic field, so there is no need to explicitly know the number of pathsor their propagation delays. Its limitations are associated with the beam space resolutionachievable with a given array geometry.7Jesus, JASA-ELIII. EXPERIMENTAL RESULTSA. Experimental scenario and initial setupThe data set shown in this section was collected during the UAB’07 experiment in the Bayof Trondheim, Norway, in 2007. During this experiment the source was suspended by a cranefrom a fixed platform, 10 m from shore, at an initial depth of 4 m. Source depth was thenvaried between 4 and 10 m, by steps of 0.5 m at predetermined intervals. The receiver wasa surface suspended VLA with 16 hydrophones uniformly spaced at 4 m between 6 and 66m depth. The communication range was approximately 1 km with a water column depth of12 m at source location and about 120 m at array location. A more detailed description ofthe experiment can be found in Ijaz et al. 5 .Figure 2 (a) shows the channel IR estimates where it can be seen that a large number ofarrivals are reaching the receiver with different delays. Figure 2 (b) shows the angle of arrivalof different wavefronts. It can be seen that there are two strong arrivals at approximately3 degree and the third and fourth arrival at approximately 0 degree. Also there is anotherstrong arrival at approximately -30 degree. The angles shown in the y-axis of this plot areobtained by direct data beamforming assuming a vertical line array. In case the array hassome tilt within the source-receiver propagation plane, care should be taken in mappingthese angles with the true geometrical directions (+90 surface, -90 bottom).8Jesus, JASA-ELB. Channel compensation resultsThe transmitted signal, presented in this section, comprised a 50 chirp signal followed by adata set of 100 seconds. The chirp transmission was used for the channel IR estimation andto study the channel variability and Doppler spread. Each chirp has a bandwidth of 2.5 kHzranging from 5 to 7.5 kHz with 0.1 sec duration whereas data bandwidth ranges from 5.5 to 7kHz with BPSK modulation and baud rate of 1000 bits/sec. A carrier frequency of 6250 Hzwas used. Figure 3 (a) shows the performance of the bFS-pTR for an angular range of -10 to+10 degrees compared with that of the other two algorithms pTR and FS-pTR. During thistransmission a source depth change from 4m to 4.5m occurred at time 12 s. It can be seenthat bFS-pTR clearly outperforms both FS-pTR and pTR with a mean MSE gain of 1.8 dBand 2.8 dB respectively. Figure 3 (b) shows the performance in the same data set but theangular range of the bFS-pTR is increased to -50 to +50 degrees therefore including all thevisible arrivals of figure 2 and where the improvement in performance relative to the previouscase is clearly visible. The MSE performance of bFS-pTR results in a mean MSE gain of4.9 dB. On the other hand the performance of pTR and FSpTR degrades by 1 dB and 0.7dB respectively, which is due to the increase in the size of impulse response time window,increasing the number of uncompensated paths. The effect of increasing the angular rangecan be related to figure 2 (b) where the inclusion of all arrivals and their compensation bythe bFS-pTR improves the system performance and accounts for source depth movement.9Jesus, JASA-ELIV. CONCLUDING REMARKSThis letter presents a modified passive time-reversal technique for underwater communica-tions in presence of source depth variations during signal transmission. This technique takesadvantage of the existing sensor array for compensating source depth induced Doppler varia-tions along each path through beam separation. This is achieved by inserting the appropriateangle shifts in the pTR processor and applying frequency shifts that maximize the focusedsignal power output for each beam separately. This output is now focused in time and spacefor each arrival angle and then summed up over all beam angles for higher gain and inter-ference rejection. It is shown with experimental data where source depth was varied duringtransmission that the proposed method outperforms current pTR and its variant FSpTR byMSE gains of 4.9 and 4.2 dB, respectively. Thus the proposed algorithm effectively extendsthe ability of current pTR-based communication schemes to account for depth variations ofthe transmitting nodes which is likely to occur whenever autonomous vehicles and surfacesuspended receiving systems are involved in routine operations at sea.AcknowledgmentsThis work is supported by the Portuguese Foundation for Science Technology underCOGNAT (PTDC/MAR/112446/2009) project. This work was also supported by EU FP6through the Integrated Infrastructure Initiative HYDRALAB III within the TransnationalAccess Activities, Contract no. 022441. The authors are also deeply thankful to SINTEFand NTNU Biological Station personnel for their support during the UAB’07 experiment.References and links1. G.F. Edelmann, W.S. Hodgkiss, S. Kim, W.A. Kuperman, H.C. Song., and T. Akal.10Jesus, JASA-ELUnderwater acoustic communications using time-reversal. In Proc. of the MTS/IEEEOceans 2001, pages 2231–2235, Honolulu, Hawai, USA, 5-8 November 2001.2. T.H. Eggen, A.B. Baggeroer, and J.C. Preisig. Communication over doppler spreadchannels - part ii: receiver characterization and practical results. IEEE JournalOceanic Engineering, 26(4):612–621, October 2001. doi:http://dx.doi.org/10.1109/48.972101.3. J.P. Gomes, A. Silva, and S.M. Jesus. Adaptive spatial combining for passivetime-reversed communications. J. Acoust Soc. America, 124(2):1028–1053, August2008.4. F. Hlawatsch and G. Matz. Wireless Communications over Rapidly Time-VaryingChannels. Elsevier Lda., Burlington, USA, 2011.5. S. Ijaz, A. Silva, and S.M. Jesus. Compensating for source depth change andobserving surface waves using underwater communication signals. In Proc. Int. Conf.on Sensor Technologies and Applications, Venice, Italy, July 2010.6. S. Ijaz, A.J. Silva, O.C. Rodriguez, and S.M. Jesus. Doppler domain decompositionof the underwater acoustic channel response. In Proc. Oceans 2011 MTS/IEEEConference, Santander, Spain, June 2011. doi:http://dx.doi.org/10.1109/Oceans-Spain.2011.6003644.7. L.R. LeBlanc. Angular-spectral decomposition beamforming for acoustic arrays.IEEE Journal of Oceanic Engineering, OE-9(1):31–39, January 1984.11Jesus, JASA-EL8. J.C. Preisig. Performance analysis of adaptive equalization for coherent acousticcommunications in the time-varying ocean environment. J. Acoust. Soc. Am., 118:263–278, July 2005.9. D. Rouseff. Intersymbol interference in underwater acoustic communications usingtime-reversal signal processing. J. Acoust. Soc. America, 117(2):780–788, February2005. doi: http://dx.doi.org/10.1121/1.1841692.10. B.S. Sharif, J. Neasham, O.R. Hinton, and A.E. Adams. A computationally efficientdoppler compensation system for underwater acoustic communications. IEEEJournal of Oceanic Engineering, 25(1):52–61, January 2000. doi:http://dx.doi.org/10.1109/48.820736.11. A. Silva, S.M. Jesus, and J.P. Gomes. Environmental equalizer for underwatercommunications. In Proc. Oceans MTS/IEEE 2007, Vancouver BC, Canada,October 2007. doi: http://dx.doi.org/10.1109/OCEANS.2007.4449344.12. A. Song, M. Badiey, H.C. Song, W.S. Hodgkiss, M.B. Porter, and KauaiEx Group.Impact of ocean variability on coherent underwater acoustic communications duringthe kauai experiment (kauaiex). J. Acoust. Soc. America, 123(2):856–865, February2008.13. M. Stojanovic, L. Freitag, and M. Johnson. Channel-estimation-based adaptiveequalization of underwater acoustic signals. In Proc. of the MTS/IEEE Oceans 1999,pages 985–990, Seattle (USA), September 1999. doi:http://dx.doi.org/10.1109/OCEANS.1999.804768.12Jesus, JASA-EL14. U. Vilaipornsawai, A. Silva, and S.M. Jesus. Underwater communications for movingsource using geometry-adapted time reversal and dfe: Uan10 data. In Proc. of theMTS/IEEE Oceans 2011, Santander, Spain, June 2011. doi:http://dx.doi.org/10.1109/Oceans-Spain.2011.6003513.13Jesus, JASA-ELFigure CaptionsFigure 1: Block diagram of one channel of the receiver structure: passive time-reversal (non-shaded blocks), frequency-shift passive time-reversal (non-shaded blocks plus blocks (1) and(2)) and beamformer frequency-shift passive time-reversal receiver (all blocks).Figure 2: UAB’07 data set: depth-delay channel IR estimates (a) and angle-delay plot (b),color coded in relative magnitude squared.(Color online)Figure 3: UAB’07 data MSE performance comparison between pTR, FSpTR and bFSpTR,considering an angular range of -10 to +10 degrees (a) and considering an angular range of-50 to +50 degrees (b).14FTr′l(t) ej2pifαlk ∆fi (·)∗FTrl(t)ej2pifαlkL∑l=1(1)(3)Z(f ; ∆fi, θk)IFTK∑k=1∆f = arg max∆fi|z(t; ∆fi, θk)|2(2)(4)zout(t)(a)(b)(a)(b)

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Path specific Doppler compensation in time-reversal communications

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