Multiple-Input–Multiple-Output Coherent Time Reversal Communications in a Shallow-Water Acoustic Channel

170 IEEE JOURNAL OF OCEANIC ENGINEERING, VOL. 31, NO. 1, JANUARY 2006

Multiple-Input–Multiple-Output Coherent TimeReversal Communications in a Shallow-Water

Acoustic ChannelH. C. Song, Philippe Roux, W. S. Hodgkiss, Member, IEEE, W. A. Kuperman, T. Akal, and M. Stevenson

Abstract—A recent time reversal (TR) experiment demonstratedthat multiple foci can be projected from an array of sources to thesame range but at different depths. This multiple input/multipleoutput process can potentially increase the information data rate.This paper presents experimental results of coherent TR communi-cations (binary phase-shift keying, quaternary phase-shift keying,and 8-quadratic-amplitude modulation) at 3.5 kHz with a 1-kHzbandwidth where different messages were sent simultaneously toeither two or three different depths at an 8.6-km range in a 105-m-deep water.

Index Terms—Coherent communications, intersymbol interfer-ence (ISI), multiple-input–multiple-output (MIMO), multipath en-vironment, time reversal, time reversal mirror (TRM).

I. INTRODUCTION

MULTIPLE-INPUT–MULTIPLE-OUTPUT (MIMO)signal processing is an active area of research in wire-

less communications as a means to increase the aggregatesource–receiver data rate [1]. MIMO is a general term thatrefers to systems that use multiple sources and multiple re-ceivers. The natural bandwidth limitations of the underwateracoustic channel combined with a rich spatial propagationstructure suggest the ocean may be another fruitful applicationarea for MIMO techniques.

Underwater acoustic communications is a challengingproblem due to the intersymbol interference (ISI) caused bytime-varying dispersive multipath environments. Adaptivechannel equalizers involving multiple receivers have beenemployed successfully in coherent underwater acoustic com-munications since 1993 [2], [3].

Recently, a relatively simple time reversal (TR) approach hasbeen applied to underwater communications motivated by ad-vances in TR theory [4], [5] that involves multiple sources re-ferred to as a TR mirror (TRM) and a single receiver collocatedwith the probe source (PS) position. The spatial and temporal

Manuscript received May 21, 2004; revised December 20, 2004; acceptedJanuary 19, 2005. This work was supported by the Office of Naval Researchunder Contract N00014-01-0043-D06. Associate Editor: R. Spindel.

H. C. Song, P. Roux, W. S. Hodgkiss, and W. A. Kuperman are with theMarine Physical Laboratory, Scripps Institution of Oceanography, La Jolla, CA92093-0238 USA (e-mail: [email protected]; [email protected];[email protected]; [email protected]).

T. Akal was with NATO Undersea Research Centre, La Spezia, Italy. He isnow with TUBITAK-MAN, Marmara Research Center, Earth and Marine Sci-ence Research Institute, Kocaeli, Turkey (e-mail: [email protected]).

M. Stevenson is with NATO Undersea Research Centre, La Spezia, Italy(e-mail: [email protected]).

Digital Object Identifier 10.1109/JOE.2005.850911

focusing capability of the TRM suggests a potential applica-tion to the communications problem especially in an environ-ment with significant multipath. The preliminary system con-cept has been demonstrated using experimental data collectedin shallow-water [6]. The TR approach has attracted substantialattention due to simplicity in the processing [7]–[9]. In addition,the TR approach can be combined with adaptive channel equal-ization to further reduce any residual ISI [10].

A recent TR experiment demonstrated that TR can be imple-mented between an array of sources and an array of receiverswithout invoking reciprocity (see Fig. 1) [11]. This technique isa straightforward extension of Parvulescu and Clay’s approach[12] with a single transmitter and a single receiver to multipletransmitters and multiple receivers. The process allows mea-surement of the channel response matrix between the two arraysalmost instantly and then the channel responses at the receiverarray are transferred back to the source array (SRA) to facilitatea TR retransmission. This implementation thus requires radiotelemetry access to the receiver array data but does not requirea PS to be collocated with the receiver array as in a conven-tional TR system. Such a hardware configuration is primarilyconvenient for concept demonstration purposes. For actual ap-plications, there would be no radio telemetry link, but we stillneed to capture the channel responses from each of the intendedreceivers to the TR array elements that can be accomplishedthrough the use of multiple PSs. Here, we use the techniquesimply because it allowed us to obtain a large data set in a shorttime.

Since we are dealing with a linear system, multiple TR focalspots can be obtained simultaneously at different receiver depthsby combining the signals at the SRA corresponding to focusingat different receiver elements, thus resulting in a MIMO system.The direct application of the MIMO TR process to communi-cations suggests that different messages can be sent simultane-ously to multiple users (e.g., autonomous underwater vehicles)assuming that they are well separated in range or depth fromeach other compared to the focal size in the acoustic waveguide[13] in order to minimize interference. MIMO TR communi-cations can potentially increase the information rate betweensource and receiver arrays and also be applied in a network en-vironment.

This paper will present experimental results of coherentMIMO communications at 3.5 kHz with a 1-kHz bandwidth [bi-nary phase-shift keying (BPSK), quaternary phase-shift keying(QPSK), and 8-quadratic-amplitude modulation (8-QAM)]using a TR approach implemented during the focused acoustic

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Fig. 1. Implementation of MIMO TR. (a) A pulse s(t) is transmitted separately from each of the SRA sources with a time delay T . (b) The transmissionsobserved at the receiver array. The received signal at a specific element (filled circle) is sliced into pulses of duration T that are transferred back to the SRA byradio telemetry. (c) The channel responses are time reversed and transmitted simultaneously from the SRA. (d) TR focusing at the selected element.

fields 2003 experiment. The theory behind TR communicationis discussed briefly in Section II. Section III describes theMIMO TR communications approach implemented in theocean. Section IV presents the experimental results of coherentTR communications. Finally, concluding remarks are made inSection V.

II. THEORY OF TR

The theory behind the use of TR in an acoustic communica-tions context has been presented earlier [6]. Two-way TR can beseen as implementing actively a spatiotemporal matched filterof the impulse response (Green’s function) of the waveguide.When a known signal is transmitted from a PS in a wave-guide, the received signal on the th element of the TR array is

where is the channel impulse responseof the waveguide and denotes a convolution. The -elementTR array then retransmits the time-reversed version of the re-ceived signal . The signal received back at the originalPS position can be written as

(1)

where the term in the bracket has been called the -functionand is summed over the autocorrelation of each channel impulseresponse [7]. The performance of the TR focus depends on the

complexity of the propagating medium (i.e., the number of mul-tipaths), the number of TRM elements , and their spatial dis-tribution (diversity). Ideally, TR would yield a -function thatapproaches a delta function, thus recovering the time-reversedversion of the original signal at the PS position.

III. MIMO TR COMMUNICATIONS

A. Experimental Setup

A TR experiment was conducted with the NATO UnderseaResearch Center in April 2003, north of Elba Island off the westcoast of Italy [11]. The communications portion of the experi-ment reported in this paper was conducted on April 15 (JD105)in a relatively flat shallow-water region. The SRA had 29 trans-ducers spanning a 78-m aperture with 2.786-m spacing and waspositioned close to Elba (about 2 nmi north) in a 105-m-deepwater. The SRA covered the water column from 20 to 98 m. A32-element vertical receiver array (VRA) was also deployed at a8.6-km range north of the SRA spanning the water column from30 to 92 m with 2-m spacing. Both the SRA and the VRA arrayswere moored for stable operation during the experiment.

B. MIMO Implementation

TR can be implemented between an array of sources andan array of receivers without invoking reciprocity [11]. Thisprocess requires radio telemetry access to the receiver array data


Fig. 2. (a) Example of channel responses g (t) in (2). (b) Corresponding s (t) in (3).

Fig. 3. Multiple depth TR communication sequences: (a) BPSK on two channels and (b) QPSK on three channels.

but eliminates the requirement of actually having a PS collo-cated with the receiver array as in conventional TR [4].

The procedure is illustrated in Fig. 1. First, a pulse istransmitted separately from each SRA element in a round robinfashion and received on the VRA with a time delay of sec-onds between successive transmissions. During the communica-tions experiment, we used a 150-ms 2.5- to 4.5-kHz chirp witha Hanning window for , resulting in an effective 100-ms 3-to 4-kHz bandwidth chirp [see Fig. 1(a)]. The time delay waschosen to be 1/3 s. Typically, the signals received at the receiverarray are compressed (matched filtered) using the chirp signalas shown in Fig. 1(b). We observe that the pulses shown in thefirst column of Fig. 1(b) are generated by the first SRA elementin Fig. 1(a).

Second, a receiver element is chosen at a specific depth (filledcircle) equivalent to a PS in a conventional TR system. The re-ceived signal is then sliced into pulses of duration that cor-respond to the channel responses between the chosen receiverelement and each of the SRA elements denoted by

(2)Note that the term in the bracket is the autocorrelation of the 3-to 4-kHz chirp signal.

Third, these channel responses are transferred to the SRA byradio telemetry, time reversed [i.e., ], and transmittedsimultaneously by the SRA [see Fig. 1(c)]. Finally, Fig. 1(d)shows TR focusing at the selected element that can be writtenas

(3)

This is identical to (1) except for the additional linear processing(compression of the chirp signal) applied prior to retransmis-sion from the SRA. An example of measured channel responses

in (2) and the corresponding in (3) is shown inFig. 2(a) and (b), respectively. Fig. 2(b) indicates a mainlobewidth at the focus of about 2-ms that is equivalent to the com-pression of the original 3- to 4-kHz chirp signal, suggesting thata TR communication sequence can be treated as a signal withminimal ISI.

It should be pointed out that (3) assumes that the environ-ment is frozen during the process such that the initial impulseresponses from Fig. 1(a) and (b) are the same as the im-pulse responses from Fig. 1(c) and (d) during the retransmission.


Fig. 4. Digital modulator that will generate TR waveforms forM -ary PSK and QAM. The superscripts 1 (upper block) and 2 (lower block) denote two differentreceiver array elements on which transmissions will be focused. Note that different bit streams can be encoded for reception at different focal depths.

However, the ocean is a dynamic environment, and a change inthe environment would degrade the performance by introducingunwanted ISI at the intended receiver [10]. For the experimentaldata discussed in Section IV, it typically took about 10–25 minto complete the entire process (including the digital modulationstep shown in Fig. 4, but fortunately the environment was quitestable during this portion of the experiment, see Fig. 5).

Since the round robin procedure involves obtaining all of thechannel responses between the source and the receiver arrays(i.e., an matrix), the TR waveforms focusing at allreceiver depths are captured almost simultaneously. MultipleTR focusing can then be achieved simply by combining thechannel responses corresponding to different receiver depthsshown in Fig. 1(c), resulting in simultaneous focal spots (seeFig. 3). In [11], simultaneous focusing was demonstrated at upto six depths. Although the minimum distance between the focaldepths is dictated by the focal size in an acoustic waveguide[13], the multiple receiver depths are chosen here to be well sep-arated from each other to minimize cross talk in the results.

Fig. 5. Sound speed profiles measured during the communications portion ofthe experiment on April 15, 2003.


Fig. 6. Digital demodulation and detection ofM -ary PSK and QAM signals. In MIMO TR communications, each received signal r (t) is processed independentlyto recover the transmitted information. Similar to Fig. 4, the superscript j = 1; 2 refers to different receiver depths.

C. MIMO Communications

For TR communications, the time-reversed version ofthe vector of measured channel responses shown inFig. 2(a) is treated as one symbol. Using the principle of super-position, each symbol is copied and displaced by the symbolinterval that is the duration of the compressed chirpwaveform. Although there is substantial overlap of the trans-mitted symbols, the individual symbols are compressed backto their original duration at the intended receiver asshown in Fig. 2(b). In the case of BPSK modulation, there aretwo symbols that encode 1 b of information. Each element ofthe time-reversed vector of channel responses is multiplied byeither 1 or 1. These two vector waveforms are stored andused to generate a binary communications sequence.

In a more general context, Fig. 4 shows the block diagram ofa digital modulator that will generate TR transmit waveformsfor -ary PSK and QAM for reception at two different receiverarray elements. The first step is to complex baseband each time-reversed channel response to obtain the in-phaseand the quadrature components. Second, the quadraturecomponents are combined to map binary digital information se-quences into signal waveforms to be transmitted from the -el-ement SRA. For MIMO TR communications, we can combinethe outputs of the digital modulators corresponding to differentreceive array elements (i.e., depths) to construct signal wave-forms to be transmitted. Fig. 4 shows an example of simulta-neous two-channel communications. Note that we canencode different messages or bit streams so that they can be re-ceived at different depths on the receiving array.

IV. EXPERIMENTAL RESULTS: COHERENT COMMUNICATIONS

In this section, we present experimental results of MIMO TRcommunications between the two arrays (SRA and VRA) sep-arated by 8.6 km in a 105-m-deep water. We investigated threetypes of phase coherent modulation methods suitable for a band-width-limited ocean environment: BPSK, QPSK, and 8-QAM.BPSK encodes a symbol with 1 b of information on two

phase positions while QPSK encodes b of dataon four phase positions. 8-QAM encodes b of informationon eight phase positions combined with two levels of amplitude(circular constellation) as will be shown in Fig. 12. All com-munications sequences were 10 s long with the same symbolrate of such that the bit rates forBPSK, QPSK, and 8-QAM are and ,respectively. We explored simultaneous multiple depth coherentcommunications to either or depths as shown inFig. 3. The depths are well separated from each other to min-imize interference. The carrier and sampling frequencies were

and , respectively. The communica-tion sequences were transmitted 10–25 min after the initial cap-ture of the original channel responses [see Fig. 2(a)] from theround robin procedure described in Section III. The measuredsound speed profiles shown in Fig. 5 indicate a quite stable envi-ronment during the communications portion of the experiment.

The assignment of -bit symbols to the possible signalphases may be done in a number of ways [14]. Since no channelcoding was introduced, Gray encoding was used in the mappingsuch that the two adjacent -bit symbols differ by one binarydigit (or up to 2 b for circular 8-QAM).


Fig. 7. Phase offset estimate of the data shown in Fig. 3: (a) Costas loop for two-channel BPSK and (b) double squaring loop for three-channel QPSK. Theaverage slope of �0.04 Hz is due to a slight mismatch in the sampling rates between the SRA and the VRA.

A. Receiver Structure

Fig. 6 illustrates a simple receiver structure that consists ofa demodulator and a detector for TR -ary PSK or QAM sig-nals. This is identical to the optimum receiver for signals cor-rupted by additive white Gaussian noise in the absence of ISI.Channel equalization to accommodate the ISI is not essential inTR communications due to the temporal compression achievedat the receiver as discussed in Section III-B.

In coherent demodulation, however, carrier recovery is essen-tial. The phase-locked loop (PLL) shown in Fig. 6 is a nonlinearadaptive phase tracking device that estimates carrier frequencyoffset or phase distortion introduced in the transmission of thesignal through the channel. We used two nondecision-directedPLLs for the results reported in this paper: a squaring loop anda Costas loop [14], [15]. For most of the cases examined in thispaper, the Costas loop showed either a similar or a better per-formance over the squaring loop except the three-channel QPSKsignals shown in Fig. 11. It should be mentioned, however, thatthere are phase ambiguities of 360 and its multiples intro-duced by the nonlinear operation in the phase estimate for bothPLLs, which can be overcome by differential encoding or useof a training sequence [14]. In our experimental data, it is as-sumed that we have an absolute estimate of the carrier phase fordemodulation.

The other important issue in a digital communication systemis symbol synchronization (timing recovery) at the receiversince the output of the demodulator must be sampled periodi-cally at . The clock shown in Fig. 6 was synchronizedat the receiver when the envelope of the received signal attainsits maximum value for the first time. Recall from Fig. 2(b) thatthe received signal at the focal depth was the impulsive-likeautocorrelation function of the chirp pulse . In the presenceof noise, the identification of the peak value of the signal isgenerally difficult. However, the high signal-to-noise ratio(SNR) resulting from the spatial focusing property of TRenabled a reasonable timing estimate. We also found that aone- or two-sample offset (at the original data sampling rate of12 kHz) was negligible since the resulting carrier offset can becompensated by the corresponding phase estimate of the PLLemployed.

The carrier phase estimate of the received signal is thenused for the two correlators (or matched filters) to correlate thereceived signal with the two quadrature carrier signals

and where . Thedetector for -ary PSK is a phase detector that compares the re-ceived signal phase with the possible transmitted signal phases.In the case of QAM, the detector compares the Euclidean dis-tance between the received noise-corrupted signal point and the

possible transmitted points, and selects the signal closest tothe received point. Finally, note that the block diagram shown inFig. 6 is applied to each single receiver element at the intendedfocal depth. Thus, each receiver can recover different messages.

B. BPSK

In this subsection, we investigate coherent BPSK .Fig. 3(a) displays the BPSK signals received at two differentdepths [86 m for Ch1 (VRA El #4) and 54 m for Ch2 (VRAEl #20)]. The corresponding phase offset estimated by a CostasPLL is shown in Fig. 7(a). Note that the average negative slopeof is about in both channels, whichis equivalent to a frequency offset of 0.04 Hz. This was dueto a slight difference in the sampling rates between the SRAand the VRA. The sampling rates of SRA and VRA were

and , respectively. The effect ofthe mismatch of the sampling rates leads to a frequency offsetof , close to the value of 0.04 Hzabove. Since the two arrays were fixed during the experiment,significant Doppler shifts due to either source or receiver motionor both can be excluded. The deviation of the phase offset fromthe average slope is likely related to environmental fluctuationsduring the transmission.

Fig. 8 shows the results obtained with BPSK signals eachtransmitted at the rate of 500 b/s to two channels si-multaneously. There were no errors detected in either channeland the SNRs were 31 and 29.7 dB, respectively. Fig. 9 showsBPSK results transmitted to three channels simultane-ously. The depths were 86, 64, and 44 m, respectively. Again, wesee no errors detected in all of the channels. The performanceof the first channel appears the worst in terms of the spread ofthe signal points. The SNRs for the three channels were 23, 23,


Fig. 8. BPSK K = 2 channel performance.

Fig. 9. BPSK K = 3 channel performance.

Fig. 10. QPSK K = 2 channel performance.

and 26.5 dB, respectively. Note that the SNR for each channelin Fig. 9 has decreased from the 30 dB shown in Fig. 8 for thetwo-channel case. This is due to the normalization at the SRAsuch that the maximum value across all elements and time isequal to the maximum element source level of 178 dB in refer-ence to 1 . It is remarkable that TR communications is stillpossible even though the BPSK signals were transmitted 20 minafter the initial capture of the original channel responses.

C. QPSKFig. 10 shows the results obtained with four-phase

QPSK signals transmitted at the rate of 1000 b/s to two differentreceivers simultaneously (same VRA elements as inBPSK). The scatter plots show a completely open pattern, andthere were no errors in either channel as in the BPSK case. Thesymbol SNRs are around 30 dB for both channels as in the two-channel BPSK case shown in Fig. 8.


Fig. 11. QPSK K = 3 channel performance.

Fig. 12. 8-QAM K = 2 channel performance.

Fig. 11 illustrates the results of QPSK signals transmitted tothree receivers simultaneously (same VRA elementsas in BPSK), resulting in a total data rate of 3000 b/s. The QPSKsignals are shown in Fig. 3(b) where the SNRs for the threechannels were 25.5, 27.7, and 29.7 dB, respectively. The cor-responding phase offset estimated by a double squaring PLL isdisplayed in Fig. 7(b), which shows a similar behavior to theearlier BPSK results in Fig. 7(a). The bit error rates (BERs)obtained for each channel were 81/9800, 4/9800, and 4/9800,respectively, while the total BER is in the order of . Theworse performance of the first channel is due to the lower SNR.

D. 8-QAM

Fig. 12 illustrates the results obtained with 8-QAM signalstransmitted at the rate of 1500 b/s to two receivers

simultaneously (same VRA elements as in BPSK), resulting ina total data rate of 3000 b/s. This is the highest order constel-lation explored during the experiment, and we used the circularconstellation that is known to be the best for 8-QAM. In thiscase, the signals were transmitted 10 min after the initial captureof the channel responses. The SNR was 30 dB for both chan-nels as before and the corresponding BERs were 6/14 700 and16/14 700, respectively. The total BER then is in the order of

.

V. CONCLUSION

TR communications is a concept recently introduced to theunderwater acoustic community. The two-way TR processprovides a self-equalization that significantly reduces theISI inherent in multipath ocean environments. Consequently,the receiver for TR communications is simple to implement.During the April 2003 experiment, the TR approach has beenextended to enable focusing at multiple depths simultaneously.This MIMO process can potentially increase the informationrate when applied to acoustic communications.

We have investigated MIMO TR communications to two orthree depths simultaneously at an 8.6-km range in a 105-m-deepwater. The modulation schemes employed were coherent BPSK,QPSK, and 8-QAM. The symbol rate was 500 symbols/s at acarrier frequency of 3.5 kHz, and each communication sequencewas 10 s long. For two-channel communications, we had almosterror-free performance with all three modulation methods withabout 30 dB SNR. For three-channel communications, the per-formance degraded due to the lower SNR since the peak trans-mitted power remained the same. Nevertheless, there were noerrors in BPSK while the total BER for QPSK was in the orderof . In order to track the phase offset for coherent demod-ulation, we used both squaring loop and Costas PLLs. The ex-perimental results indicate that we can achieve at least 3 b/s/Hz


over the 8.6-km range in a shallow-water environment. It shouldbe mentioned that the data rate can be increased significantly bychannel coding combined with higher-order constellations.

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[13] S. Kim, G. F. Edelmann, W. A. Kuperman, W. S. Hodgkiss, H. C. Song,and T. Akal, “Spatial resolution of time-reversal arrays in shallow water,”J. Acoust. Soc. Am., vol. 110, no. 2, pp. 820–829, Aug. 2001.

[14] J. Proakis, Digital Communications. New York: McGraw-Hill, 2001.[15] W. Lindsey and M. Simon, Telecommunication Systems Engi-

neering. Englewood Cliffs, NJ: Prentice-Hall, 1972.

H. C. Song received the B.S. and M.S. degrees inmarine engineering and naval architecture in 1978and 1980, respectively, from the Seoul National Uni-versity, Korea, and the Ph.D. degree in ocean engi-neering in 1990 from the Massachusetts Institute ofTechnology, Cambridge.

From 1991 to 1995, he was with the Korea OceanResearch and Development Institute. Since 1996, hehas been a Scientist of the Marine Physical Labora-tory/Scripps Institution of Oceanography, Universityof California, San Diego. His research interests in-

clude time-reversed acoustics, robust matched field processing, and underwateracoustic communications.

Dr. Song is a Fellow of the Acoustical Society of America.

Philippe Roux received the Ph.D. degree from the University of Paris, France.He is an experimentalist who has an important background in ultrasonics.

He has intensively studied multiple scattering of ultrasonic waves combinedwith the concept of time reversal. He has also worked on the propagation ofelastic waves in a metallic cylinder in the ultrasound regime. After receiving thePh.D., he held a Postdoctoral position at the Marine Physical Laboratory, SanDiego, CA, where he learned the basics of theory and numerical computation inunderwater acoustics. He then received a full-time researcher position back inFrance and worked in Paris for three years on the coherence of the acoustic fieldin cavities in the multiple scattering regime. He is currently with the MarinePhysical Laboratory as a Research Associate and his research is focused on thestudy of the spatial–temporal coherence of ambient noise in the ocean.

W. S. Hodgkiss (S’68–M’75) was born in Bellefonte,PA, on August 20, 1950. He received the B.S. degreein electrical engineering from Bucknell University,Lewisburg, PA, in 1972, and the M.S. and Ph.D. de-grees in electrical engineering from Duke University,Durham, NC, in 1973 and 1975, respectively.

From 1975 to 1977, he worked with the NavalOcean Systems Center, San Diego, CA. From 1977to 1978, he was a Faculty Member in the ElectricalEngineering Department, Bucknell University. Since1978, he has been a Faculty Member of the Scripps

Institution of Oceanography, University of California, San Diego, and on thestaff of the Marine Physical Laboratory, San Diego, CA. His present researchinterests are in the areas of signal processing, propagation modeling, andenvironmental inversions with applications of these to underwater acousticsand electromagnetic wave propagation.

Dr. Hodgkiss is a Fellow of the Acoustical Society of America.

W. A. Kuperman had worked at the Naval ResearchLaboratory, the SACLANT Undersea ResearchCenter, La Spezia, Italy, and most recently at theScripps Institution of Oceanography, University ofCalifornia, San Diego, where he was a Professorand Director of its Marine Physical Laboratory. Hehas done theoretical and experimental researches inocean acoustics and signal processing.

T. Akal was a Principal Senior Scientist at theSACLANT Undersea Research Center, La Spezia,Italy, where, over the past 33 years, he has ledresearch projects related to underwater acousticand seismic propagation and marine sedimentacoustics. He is currently collaborating with theTUBITAK-Marmara Research Center, Earth andMarine Sciences Research Institute, Turkey, theMarine Physical Laboratory, Scripps Institutionof Oceanography, University of California, SanDiego, and the Lamont-Doherty Earth Observatory,

Columbia University Palisades, New York.

M. Stevenson graduated from the U.S. NavalAcademy, Annapolis, MA, and the Scripps Institu-tion of Oceanography, La Jolla, CA.

After graduating, he joined the Acoustic Branchof the Space and Naval Warfare Systems Center, SanDiego, CA. He is currently the Project Leader for fo-cused acoustic field studies at the NATO UnderseaResearch Centre, La Spezia, Italy. His past researchincludes design and deployment of acoustic measure-ment arrays under the Arctic icecap and in coastalshallow-water environments.

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Multiple-Input–Multiple-Output Coherent Time Reversal Communications in a Shallow-Water Acoustic Channel