Time Reversal Receivers for Underwater Acoustic Communication ...

Time Reversal Receivers for Underwater Acoustic Communication Using Vector Sensors Aijun Song and Mohsen Badiey

Paul Hursky

Ali Abdi

College of Marine and Earth Studies University of Delaware Newark, DE 19716 USA

Heat, Light, & Sound Research, Inc. 3366 North Torrey Pines Ct., La Jolla, CA 92037 USA

Electrical & Computer Engineering Dept. New Jersey Institute of Technology Newark, NJ, 07102 USA

Abstract—Acoustic communication often relies on a large size array with multiple spatially separated hydrophones to deal with the challenging underwater channel. This poses serious limitation to its application at compact size underwater platforms, for example, autonomous underwater vehicles. In this paper, we propose to use vector sensors to achieve reliable acoustic communication. Using experimental data, we show the usefulness of particle velocity channels for acoustic communication. Further, to deal with the dynamic ocean environment, a time reversal multichannel receiver is proposed to utilize particle velocity channels. Our results show that the receiver using vector sensors can offer significant size reduction, compared to the receiver based on the pressure sensors, while providing comparable communication performance.

scalar components of the acoustic field can be utilized for data reception, we consider a simple system in a underwater channel. As shown in Fig. 1, there is one transmit pressure sensor, shown by a black dot, whereas for reception we use a vector sensor, shown by a black square, which measures the pressure and the x, y, and z components of the particle velocity.

x

y Pressure Source

Vector sensors have long been considered for localization, tracking, and ranging of underwater objects [1], [2]. Acoustic vector sensors are capable of measuring orthogonal particle velocity components, in addition to the scalar pressure information. Such a feature gives vector sensors a significant advantage over hydrophones in these applications. In this paper, we investigate the feasibility of using vector sensors in acoustic communication. Acoustic communication is vital to a number of naval and civilian underwater applications. It often relies on a large size array with multiple spatially separated hydrophones to deal with the highly dynamic and dispersive underwater channel. However, it might be impossible to accommodate a large size array at compact underwater platforms, such as underwater autonomous vehicles, where space is very limited. Here we are seeking an alternative solution by utilizing the particle velocity channels measured by vector sensors. In [3] and [4], theoretical formulation is developed and Monte Carlo simulations are provided for communication via vector sensors. In this paper, we use the experimental data to confirm the usefulness of velocity channels in acoustic communication. A low complexity receiver has also been proposed to utilize the velocity channels for the dynamic underwater environment. II. S YSTEM E QUATIONS In this section, basic system equations for data detection via a vector sensor introduced in [3] and [4] are briefly presented. To demonstrate the basic concepts of how both the vector and

wx

p p

p

rx

wy r

y

wz rz

z

x

I. I NTRODUCTION

w r

Vector Sensor

y

pz

Fig. 1. A 1 × 4 vector sensor communication system, with a sound source and a vector sensor receiver, in the underwater environment. The vector sensor measures pressure and x, y, and z components of the acoustic particle velocity, all at a single point in space.

A. Pressure and Velocity Channels and Noise There are four channels in Fig. 1: the pressure channel p, represented by a straight dashed line, and three pressureequivalent velocity channels px , py , and pz , shown by curved dashed lines. To define px , py , and pz , we first define the particle velocities, v x , v y and v z . According to the linearized equation for time-harmonic waves, the x, y and z components of the velocity at the frequency f0 are given by [5] v x = −(jρ0 ω0 )−1 ∂p/∂x, v y = −(jρ0 ω0 )−1 ∂p/∂y, z

−1

v = −(jρ0 ω0 )

(1)

∂p/∂z,

√ where ρ0 is the density of the fluid, and j = −1. Eq.(1) states that the velocity in a certain direction is proportional to the spatial pressure gradient in that direction [5]. The associated pressure-equivalent velocity channels are defined as px = −ρ0 cv x , py = −ρ0 cv y and pz = −ρ0 cv z , which

gives

A. Channel Measurements during MakaiEx px = (jk)−1 ∂p/∂x, py = (jk)−1 ∂p/∂y, z

−1

p = (jk)

(2)

∂p/∂z,

where k = ω0 /c is the acoustic wavenumber and c is the sound speed. The additive ambient noise pressure at the receiver is shown by w in Fig. 1. Similar to Eq. (1), the x, y, and z components of ambient noise velocities are αx = −(jρ0 ω0 )−1 ∂w/∂x, αy = −(jρ0 ω0 )−1 ∂w/∂y, and αz = −(jρ0 ω0 )−1 ∂w/∂z, respectively. So we can obtain the pressure-equivalent ambient noise velocities as wx = (jk)−1 ∂w/∂x, wy = (jk)−1 ∂w/∂y, z

−1

w = (jk)

(3)

∂w/∂z.

B. Input-Output System Equations According to Fig. 1, the received pressure signal r in response to the signal s transmitted from the transmitter can be written as r = ps+w. Here stands for convolution in time and p is the pressure channel impulse response. We also define the pressure-equivalent received velocity signals as rx = (jk)−1 ∂r/∂x, ry = (jk)−1 ∂r/∂y, and rz = (jk)−1 ∂r/∂z. Based on (2) and by taking the spatial gradient with respect to x, y, and z axes, we obtain key system equations r = p s + w, r = px s + w x , x

r y = py s + w y , r z = pz s + w z .

(4)

Note that the four output signals are measured at a single point in space. With the assumption that the noise is spherically isotropic, the noise terms in Eq.(4) are uncorrelated [6]. As shown by the numerical acoustic simulations of [3] and [4], the pressure channel and the velocity channels can provide spatial diversity, similar to an array of spatially separated pressure sensors. Therefore, the pressure source and the vector sensor in Fig. 1 have the potential to form a single-input multiple-output (SIMO) system. In the following sections, we show the feasibility of using velocity channels in acoustic communication using experimental data. III. C HANNEL C HARACTERISTICS E STIMATED FROM E XPERIMENTAL DATA During the high frequency Makai acoustic communication experiment (MakaiEx) conducted west off the Kauai Island, Hawaii, in September and October of 2005 [7], a five element Wilcoxon TV-001 vector array was deployed multiple times. We present the measured characteristics of particle velocity channels and simulate the performance of particle velocity channels in data communication.

Each vector sensor of the Wilcoxon TV-001 array had three velocity-meters that were sensitive only along a specific direction, besides an embedded omni-directional pressure sensor [8]. Therefore, each vector sensor had four channels and generated four data streams: one pressure channel and three x, y, and z components of the particle velocity. The length of each vector sensor was 6.6 cm, and the element spacing (center-to-center distance) was 10 cm. In one deployment on September 23, 2005, a bottom mounted acoustic source continuously transmitted a series of communication signals at the carrier frequency of f0 = 12 kHz. During the acoustic measurements, the array was attached to A-frame steel cable of the drifting vessel, the R/V Kilo Moana. The array was considered vertical since a 200 pound weight was attached to the end of the array cable. The water depth at the site was about 100 m. The bottom element was about 40 m below the sea surface. The R/V Kilo Moana was set in drifting mode. As mentioned, a pressure source and a vector sensor can form a 1 × 4 SIMO communication system, as well as the four pressure channels of the four vector sensors. Note the four channels of a vector sensor are co-located at a single point in space, whereas the four pressure channels have an aperture of 30 cm. In what follows, channel characteristics and receiver performance of these two systems are compared. Fig. 2 shows an example of the impulse response functions obtained from the field data. A pseudo random BPSK signals at the carrier frequency of f0 = 12 kHz was used to probe the impulse response functions during the experiment. The symbol rate of the BPSK signal was 6 kilosymbols/s. The channel estimation was performed by a least squares QR (LSQR) algorithm. For this particular data, the source-receiver range was about 200 m. Fig. 2(a) shows an example of the measured impulse response amplitudes of a single vector sensor. As shown in Fig. 2(a), the x-y-z particle velocity channels have an arrival structure similar to the pressure channel. However, due to the weaker later arrivals, y and z particle velocity channels have smaller root mean square (RMS) delay spreads. The RMS delay spread of the pressure channel was 5.4 ms, whereas those of the x, y and z channels were 6.6 ms, 2.6 ms and 4.2 ms, respectively. Considering the 30 cm aperture of the pressure array, the four pressure channel impulse responses show similarity among themselves, as demonstrated in Fig. 2(b). The RMS delay spread of the four pressure channels are 5.4 ms, 5.6 ms, 5.9 ms, and 4.9 ms, respectively. Since a small delay spread corresponds to less ISI, the y- and z- velocity channels might offer better communication results than the pressure channels. Besides the RMS delay spread, channel/noise correlations are also relevant to the receiver performance. Table I shows the noise and channel correlation among the multiple channels of the vector sensor and the pressure sensor array. The correlation

15 20 25 30 Time (ms) (b) Velocity channel − x component: RMS delay spread: 6.6ms.

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15 20 25 30 Time (ms) (c) Velocity channel − y component: RMS delay spread: 2.6ms.

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15 20 25 30 Time (ms) (d) Velocity channel − z component: RMS delay spread: 4.2ms.

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(a) Pressure channel #1: RMS delay spread: 5.4ms.

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(a) Pressure channel: RMS delay spread: 5.4ms. 1

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15 20 25 30 Time (ms) (b) Pressure channel #2: RMS delay spread: 5.6ms.

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10 15 20 25 30 Time (ms) (c) Pressure channel #3: RMS delay spread: 5.9ms.

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10 15 20 25 30 Time (ms) (d) Pressure channel #4: RMS delay spread: 4.9ms.

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(a)

15 20 Time (ms)

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(b)

Fig. 2. (a) Normalized amplitudes of the measured impulse responses of pressure channel, x-velocity, y-velocity and z-velocity channels. (b) Normalized amplitudes of the measured impulse responses of the four pressure channels.

among some of the channels can be small. Further, note that most of the noise correlation numbers of the vector sensor are smaller than those of the pressure array. 0

10

single pressure element vector sensor: y component only four element pressure array single vector sensor element

−1

10

Bit error rate

numbers in Table I are the modulus of the complex correlation E[vm vn∗ ] − E[vm ]E[vn∗ ] γm,n = , (E[|vm |2 ] − |E[vm ]|2 |)(E[|vn |2 ] − |E[vn ]|2 |) (5) where vm , vn are two complex sequences and E[·] represents the expectation operation. The channel impulse responses shown in Fig. 2 are used for the correlation calculation. For the vector sensor, the pressure, x-velocity, y-velocity, and zvelocity channels are numbered as channel #1 to channel #4, respectively. The calculation of the noise correlation uses the 3.75 second ambient noise, which was recorded 20 seconds prior to the BPSK training sequence.

−2

10

−3

10

TABLE I C ORRELATION , CHANNEL POWERS , AND NOISE POWERS MEASURED FROM THE FIELD DATA

channel correlation

channel power (dB)

noise correlation

noise power (dB)

γ1,2 γ1,3 γ1,4 γ2,3 γ2,4 γ3,4 Ω1p Ω2p Ω3p Ω4p γ1,2 γ1,3 γ1,4 γ2,3 γ2,4 γ3,4 Ω1w Ω2w Ω3w Ω4w

Vector Sensor 0.3313 0.8053 0.8688 0.4128 0.3996 0.8785 0 11.3402 20.4270 10.7515 0.4395 0.5256 0.5293 0.4744 0.2066 0.3500 0 10.9290 8.0964 3.8581

−4

10

Pressure Array 0.4639 0.4096 0.5773 0.4079 0.5893 0.6717 0 -1.1439 4.7645 7.8532 0.6720 0.6770 0.5334 0.5633 0.6413 0.4598 0 -0.5771 -0.0075 0.0973

As shown in Table I, although the four channels of the vector sensor are co-located at a single point, correlation

−5

0

5 10 Average SNR per channel (dB)

15

20

Fig. 3. Performance of a vector sensor receiver, a four-element pressure array receiver, and a single pressure sensor. The impulse responses of Fig. 2 are used to generate the BER curves. The size of the four element array is 30 cm, whereas the vector sensor size is 6.6 cm (78% reduction in size).

B. Simulated Performance of a Vector Sensor Receiver In Fig.3, the bit-error-rates (BERs) of a vector sensor receiver, a pressure sensor receiver and a four-element pressure array receiver are shown. The experimental impulse responses shown in Fig. 2 were used, along with the multichannel zeroforcing equalizer in [3]. The BERs correspond to a 6 kilobits/s uncoded BPSK data stream at f0 = 12 kHz. As expected, the y-velocity channel receiver has a 4 dB gain over the single traditional pressure receiver. This can be attributed to the smaller delay spread of the y-velocity channel, and verifies the usefulness of a velocity channel. By using all the channels

of the vector sensor, a 10 dB gain can be obtained, compared to a single pressure receiver. The vector sensor receiver has also a 1 dB gain over the four-channel pressure array. The average signal-to-noise ratio (SNR) of each multichannel receiver is defined as ρ = (Ωp /Ωw + Ωxp /Ωxw + Ωyp /Ωyw + Ωzp /Ωzw )/4,

(6)

where Ωp , Ωxp , Ωyp , and Ωzp are the average powers of the pressure channel and of the particle velocity channels, and Ωw , Ωxw , Ωyw , and Ωzw are their respective noise powers. The channel/noise powers among the pressure channel and three velocity channels are obtained from the experimental measurement and are listed in Table I. Note that in Table I, the channel/noise powers are normalized by those of the first pressure channel. Moreover, the small size of the vector sensor, 6.6 cm, outperforms the long 30 cm pressure array, in terms of receiver size. In fact it provides a 78% size reduction. This is crucial in modem applications of small autonomous underwater vehicles where there are serious limitations on the receiver size. This benefit comes from the co-located velocity channels and can be measured by a compact vector sensor. This is a new alternative to spatially separated pressure sensors to achieve diversity. IV. A T IME R EVERSAL R ECEIVER WITH V ECTOR S ENSORS In addition to the severe ISI caused by multipath, the underwater channel usually experiences significant amplitude fading and fast phase fluctuations, introduced by the dynamic ocean environment and source/receiver motion. In this section, we present a practical receiver to utilize particle velocity channels in the underwater environment. To characterize the time varying, dispersive underwater channel, Eq. (4) can be re-written as ri (n) = ejθi (n) [hi (n, l) s(n)] + wi (n),

i = 1 to 4, (7)

where the pressure channel, x-velocity channel, y-velocity channel, and z-velocity channel corresponds to channel #1 to channel #4. In Eq. (7), θi (n) is the instantaneous carrier phase offset. hi (n, l), 0 ≤ l ≤ L − 1, is the discrete-time baseband channel impulse response function where L is the impulse function duration in symbols. Note that Eq. (7) can also be used as the input-output equation for a four element pressure array. Fig. 4 shows the proposed receiver structure. Similar to [9], the receiver consists of three parts: phase tracking and correction, channel estimation and time reversal multichannel combining, and finally a single channel decision feedback equalizer (DFE). The proposed receiver is a channel estimation based structure. Channel and phase estimation are performed frequently. For brevity, the most recent channel estimate on the ith ˆ i (n, l) and the most recent estimated channel is denoted by h linear trend (Doppler) in the carrier phase offset is denoted by fˆΔ,i (n).

A. Phase Tracking and Correction Here we model the fast phase fluctuation as θi (n) = 2πnfΔ,i (n)Ts , where fΔ,i (n) is the linear trend in the carrier phase offset (Doppler) and Ts is the symbol period. At the ith channel, the Doppler is obtained by N −1 Δ ri (n − p)(ˆ ri (n − p)ej2πpf Ts )∗ , fˆΔ,i (n) = arg max f p=0 (8) where rî (n) = sˆ(n)past ˆhi (n, l), sˆ(n)past represents the past decision results, and, NΔ is the Doppler observation block size in symbols. f search interval in Eq. (8) is given by fΔ0 ,i − 12 δf < f < fΔ0 ,i + 12 δf , where fΔ0 ,i is the coarse Doppler estimate and δf is the Doppler search range. Since Doppler is estimated frequently, fΔ0 ,i is set to the previous Doppler estimate. Phase correction is performed by offsetting the received signal ri (n) by the estimated Doppler, which ˆ yields rΔ,i (n) = ri (n)e−j2πnfΔ,i (n)Ts . B. Channel Estimation and Time Reversal Multichannel Combining ˆ i (n, l) can be obtained from the The channel estimate h phase corrected received signal rΔ,i (n) and the past decision results sˆ(n)past or the known symbols s(n) during the preamble. Various least squares algorithms can be used for channel estimation. In this paper, the fast LSQR algorithm is used [10]. The channel estimation block size is chosen to be twice the channel length, i.e., N0 = 2L. In a vector sensor, the noise power usually is not uniformly distributed among the pressure channel and the velocity channels [6]. It is advantageous to normalize each channel according to its noise power. The noise power in the channel estimator [10] can be used as an estimate for the ith channel noise power, N0 ˆ i (n, l) ∗ s(n)preamble |2 |rΔ,i (n) − h 2 , (9) σ î = n=1 N0 − L where s(n)preamble is the source symbol of the preamble. ˆ i (n, −l))∗ Then, time reversal multichannel combining uses (h to matched-filter the phase-corrected signals on each channel [11]. Therefore, the output after time reversal combining is c(n) =

M=4 i=1

1 ˆ (hi (n, −l))∗ rΔ,i (n) σ î2

(10)

= s(n) q(n, l) + w (n), where w (n) is the combined noise and q(n, l) is the effective CIR function. In order to accommodate fast channel variations, frequent channel estimation is needed. C. Single Channel DFE A single channel DFE with joint phase tracking [12] is used to equalize the residual inter-symbol interference in c(n). The exponentially weighted recursive least-squares (RLS) algorithm is used to update the equalizer tap weights. The residual carrier phase offset in c(n) is compensated for by a second

r1(n)

-j2πnfΔ, 1(n)Ts

e

-j2πnfΔ, Μ(n)Ts

e rM(n)

_1 σ1

phase tracking

Phase tracking and correction

( h1 (n,-l) )*

2

phase tracking

r1(n)

rM(n)

rΔ,1 (n)

x (n)past

rΔ,M (n)

_1 σM

Channel estimation

Σ

c(n)

FF filter

~ s (n)

FB filter

(hM (n,-l))*

2

x (n)past

s (n)

Channel estimation

Channel estimation and time reversal multichannel combing

Single channel DFE

Fig. 4. The proposed receiver is composed of three parts: (1) phase tracking and correction, (2) channel estimation and time reversal multichannel combining, and (3) single channel DFE.

order phase locked loop (PLL) embedded in the adaptive channel equalizer. Phase correction based on the PLL output is implemented at the input to the DFE feedforward filter. The SNR at the soft output of the DFE, s˜(n), and the BER of the hard decision, sˆ(n), are used as performance metrics in the next section. In the multichannel DFEs developed in [13], feedforward filters are applied to the individual channels and their outputs are combined prior to the feedback filter. Phase synchronization at the individual channels is optimized jointly with the equalizer tap weights. The number of adaptive feedforward taps increases with the number of channels. Compared with the multichannel DFEs developed in [13], the proposed receiver uses a single channel DFE after time reversal combining. An advantage of the proposed receiver structure is its low complexity [9], [13]. The complexity of a multichannel DFE increases at least with the square of the number of channels if RLS algorithms are used for fast tracking [14]. Since time reversal combining mixes multiple channels into a single channel, the complexity of the successive DFE remains unchanged if the number of channels is increased. Note although time reversal based, the proposed receiver has a different structure than the time reversal DFEs in [15], [16], and [17] where multichannel combining is performed based on channel probes or the known symbols at the beginning of the data packet. V. E XPERIMENTAL R ESULTS DURING M AKAI E X In this section, we present the demodulation results on the experimental data collected on September 23, 2005 during MakaiEx. A uniform set of receiver parameters are used to demodulate the experimental BPSK signals as listed in Table II. The only exception is L = 100 symbols for the 1000 m range, where the vector sensor array had significant motion. The received data are over-sampled and the over-sampling rate is K = 3. The number of the feedforward taps is KNf f = 45 for the fractionally spaced DFE [12], where Nf f = 5 is the

TABLE II R ECEIVER PARAMETERS

Parameters fs f0 R K M Npreamble L N0 N NΔ δf0 δf Nf f Nf b K f1 K f2 λ

Description sampling rate carrier frequency symbol rate over-sampling factor total number of the channels size of the preamble length of the CIR function channel estimation block size channel estimation update interval Doppler observation block size Initial Doppler search range Doppler search range after preamble Feedforward filter span in symbols Feedback filter tap number proportional tracking constant in PLL integral tracking constant in PLL RLS forgetting factor in the DFE

Value 48000 Hz 12000 Hz 6 kilosymbols/s 3 4 1600 symbols 200 symbols 1 2L symbols 200 symbols N0 symbols 10 Hz 1.6 Hz 15 symbols 5 symbols 0.0002 0.0002 0.999

feedforward filter span in symbols. At the beginning of the 3.75 s BPSK packet, Npreamble = 1600 symbols are used to carry out initial channel estimation, phase tracking, and DFE tap weight training. During the preamble, the initial Doppler search range is 10 Hz. The Doppler search range after the preamble is set to 1.6 Hz. The search step is 0.2 Hz. The RLS forgetting factor λ in the DFE is chosen to be 0.999. To eliminate the error propagation effects, the receiver runs in training mode even after the preamble. For the 5 BPSK transmissions at different ranges, the demodulation results are shown in Table III. The time reversal receiver presented in Section IV was applied to a single vector sensor and the four pressure channels of the four vector sensors (a pressure array). The average channel RMS delay spread and the average correlation coefficients are listed for each range in Table IV. The average is calculated over the 3.75 second 1 The

only exception is L = 100 symbols for the 1000 m range.

TABLE III D EMODULATION RESULTS DURING M AKAI E X Source-Receiver demodulation results for the vector sensor demodulation results for the pressure array

Range output SNR BER output SNR BER

200 m 15.4 dB BER=0 9.2 dB BER=5e-5

duration of the BPSK packet. As shown in Table III, the receiver with the vector sensor has better performance at close range. For example, at the 200 m range, the vector sensor receiver has about 6 dB gain over the pressure sensor receiver. The channel impulse responses of the vector sensor and the pressure array at this range are shown in Fig. 5 and Fig. 6, respectively. As shown, the y- and z- velocity channels have weaker later arrivals, which result in smaller RMS delay spreads. At the 250 m range, the vector sensor receiver has about 3 dB gain. The performance gain of the vector sensor at 200 m and 250 m can be attributed to the smaller RMS delay spread of the y- and z- velocity channels, as shown in Table IV. For the range of 400 m and 550 m, the pressure array has about 2 dB gain over the vector sensor. Note that 2 dB gain of the pressure array at these ranges comes with the price of a larger receiver, compared to a compact vector sensor. Fig. 7 and Fig. 8 show the channel impulse responses of the vector sensor and the pressure array at the 550 m range. At this range, the channels have more none-zero paths and later arrivals are highly fluctuating. These characteristics necessitate the use of a low complexity receiver that can track the channel and deal with the severe ISI, as the time reversal receiver proposed in Section IV. For the 1000 m range, the vector sensor performs 1.4 dB better than the pressure array. This may be due to the high correlation (over 0.9) among all the channels of the pressure array at the 1000 m range, as listed in Table IV. VI. C ONCLUSION In this paper, we utilize particle velocity channels provided by vector sensors for underwater acoustic communication. Using experimental data, we demonstrate the usefulness of velocity channels for underwater communication. A low complexity receiver is proposed and implemented to utilize particle velocity channels. Some channel parameters such as correlation and delay spread that affect data communication are reported as well. By comparing a vector sensor receiver with a pressure array receiver, we show that a vector sensor offer significant size reduction, as well as several dB gains at some communication ranges. Our results suggest that vector sensors can offer acoustic communication solutions that are particularly needed in the compact underwater platforms, such as unmanned undersea vehicles. ACKNOWLEDGMENT This research was supported by the Office of Naval Research (ONR) code 321OA, Contract No. N00014-01-1-0114.

250 m 7.4 dB BER=8e-4 4.2 dB BER=0.012

400 m 1.8 dB BER=0.047 4.0 dB BER=0.017

550 m 2.6 dB BER=0.031 4.6 dB BER=9e-3

1000 m 3.1 dB BER=0.025 1.7 dB BER=0.046

Authors wish to thank all the participants of MakaiEx. We also wish to give special thanks to Bruce Abraham (Applied Physical Sciences), who participated in the vector sensor experiment as part of MakaiEx. R EFERENCES [1] A. Nehorai and E. Paldi, “Acoustic vector-sensor array processing,” IEEE Trans. Signal Proc., vol. 42, no. 9, pp. 2481–2491, Sept. 1994. [2] M. Hawkes and A. Nehorai, “Acoustic vector-sensor beamforming and Capon direction estimation,” IEEE Trans. Signal Proc., vol. 46, no. 9, pp. 2291–2304, Sept. 1998. [3] A. Abdi, H. Guo, and P. Sutthiwan, “A new vector sensor receiver for underwater acoustic communication,” in Proc. Oceans, Vancouver, Canada, 2007. [4] A. Abdi and H. Guo, “A new compact multichannel receiver for underwater wireless communication networks,” IEEE Trans. Wireless Commun., accepted, 2008. [5] A. D. Pierce, Acoustics: An introduction to its physical principles and applications, Acoustical Society of America, Woodbury, New York, 2nd edition, 1989. [6] M. Hawkes and A. Nehorai, “Acoustic vector-sensor correlations in ambient noise,” IEEE J. Oceanic Eng., vol. 26, no. 3, pp. 337–347, Jul. 2001. [7] M. B. Porter, “The Makai experiment: High frequency acoustics,” in Proc. European Conf. Underwater Acoustics, Carvoeiro, Portugal, 2006. [8] J. Clay Shipps and B. M. Abraham, “The use of vector sensors for underwater port and waterway security,” in Proc. ISA/IEEE Sensors for Industry Conf., New Orleans, LA, 2004. [9] A. Song, M. Badiey, H.-C. Song, W. S. Hodgkiss, M. B. Porter, and the KauaiEx Group, “Impact of ocean variability on coherent underwater acoustic communications during the Kauai experiment (KauaiEx),” J. Acoust. Soc. Am., vol. 123, no. 2, pp. 856–865, Feb. 2008. [10] J. A. Flynn, J. A. Ritcey, D. Rouseff, and W. L. J. Fox, “Multichannel equalization by decision-directed passive phase conjugation: Experimental results,” IEEE J. Oceanic Eng., vol. 29, no. 3, pp. 824–836, Jul. 2004. [11] W. A. Kuperman, W. S. Hodgkiss, H. C. Song, P. Gerstoft, P. Roux, T. Akal, C. Ferla, and D. R. Jackson, “Ocean acoustic time reversal mirror,” in Proc. Fourth European Conf. Underwater Acoustics, 1998, pp. 493–498. [12] M. Stojanovic, J. A. Catipovic, and J. G. Proakis, “Phase-coherent digital communications for underwater acoustic channels,” IEEE J. Oceanic Eng., vol. 19, no. 1, pp. 100–111, Jan. 1994. [13] M. Stojanovic, J. Catipovic, and J. G. Proakis, “Adaptive multichannel combining and equalization for underwater acoustic communications,” J. Acoust. Soc. Am., vol. 94, no. 3, pp. 1621–1631, Sept. 1993. [14] J. G. Proakis, Digital Communications, McGraw-Hill, New York, 4th edition, 2000. [15] G. F. Edelmann, H. C. Song, S. Kim, W. S. Hodgkiss, W. A. Kuperman, and T. Akal, “Underwater acoustic communications using time reversal,” IEEE J. Oceanic Eng., vol. 30, no. 4, pp. 852–864, Oct. 2005. [16] T. C. Yang, “Correlation-based decision-feedback equalizer for underwater acoustic communications,” IEEE J. Oceanic Eng., vol. 30, no. 4, pp. 865–880, Oct. 2005. [17] H. C. Song, W. S. Hodgkiss, W. A. Kuperman, M. Stevenson, and T. Akal, “Improvement of time reversal communications using adaptive channel equalizers,” IEEE J. Oceanic Eng., vol. 31, no. 2, pp. 487–496, Apr. 2006.

TABLE IV M EASURED CHANNEL CHARACTERISTICS DURING M AKAI E X Range CH#1 CH#2 CH#3 CH#4 γ1,2 γ1,3 γ1,4 γ2,3 γ2,4 γ3,4 CH#1 CH#2 CH#3 CH#4 γ1,2 γ1,3 γ1,4 γ2,3 γ2,4 γ3,4

average RMS delay spread of the vector sensor

average channel correlation of the vector sensor

average RMS delay spread of the pressure array

average channel correlation of the pressure array

200 m 5.3 5.4 2.4 4.0 0.4804 0.7857 0.8509 0.4563 0.4831 0.8928 5.3 5.8 5.6 5.3 0.3592 0.4506 0.4854 0.5862 0.5989 0.6726

250 m 7.0 6.5 4.8 5.6 0.6433 0.5257 0.4462 0.8039 0.5595 0.8826 7.0 7.7 7.0 7.3 0.5509 0.6049 0.4296 0.4685 0.5201 0.8169

0

0

400 m 8.8 9.0 8.6 9.7 0.4802 0.6859 0.2744 0.6747 0.1736 0.6254 8.8 9.3 9.4 9.2 0.2451 0.4621 0.3055 0.3135 0.4333 0.2506

Average RMS delay spread: 5.3ms.

550 m 7.9 7.4 7.2 7.7 0.3653 0.1963 0.6009 0.7797 0.7535 0.7114 7.9 7.1 7.4 7.3 0.8190 0.5513 0.6870 0.7104 0.6801 0.6839

1000 m 3.2 3.4 3.3 3.3 0.7437 0.6762 0.7855 0.9521 0.6963 0.5678 3.2 3.2 3.3 3.3 0.9901 0.9603 0.9445 0.9794 0.9630 0.9772


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15 20 Arrival time (ms)

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3.5 0

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Geotime (s)

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3.5 0

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(d)

Fig. 5. The measured 3.75 second impulse responses of (a) pressure channel, (b) x-velocity, (c) y-velocity and (d) z-velocity channels at the source-receiver range of 200 m.



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Geotime (s)

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(c) Fig. 6.

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Geotime (s)

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0

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1.5 −15 2 −20

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3.5 0

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(d)

The measured 3.75 second impulse responses of the four pressure channels at the source-receiver range of 200 m.

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Geotime (s)

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(c)

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Geotime (s)

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1.5 −15 2 −20

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3.5 0

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(d)

Fig. 7. The measured 3.75 second impulse responses of (a) pressure channel, (b) x-velocity, (c) y-velocity and (d) z-velocity channels at the source-receiver range of 550 m.



0

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(a)


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(c) Fig. 8.

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Geotime (s)

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1.5 −15 2 −20

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3.5 0

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(d)

The measured 3.75 second impulse responses of the four pressure channels at the source-receiver range of 550 m.

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