Time Reversal Receivers for Underwater Acoustic Communication Using Vector Sensors

Transcription

1 Time Reversal Receivers for Underwater Acoustic Communication Using Vector Sensors Aijun Song and Mohsen Badiey College of Marine and Earth Studies University of Delaware Newark, DE 976 USA Paul Hursky Heat, Light, & Sound Research, Inc. 66 North Torrey Pines Ct., La Jolla, CA 97 USA Ali Abdi Electrical & Computer Engineering Dept. New Jersey Institute of Technology Newark, NJ, 7 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. I. INTRODUCTION Vector sensors have long been considered for localization, tracking, and ranging of underwater objects [], []. 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 [] 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. SYSTEM EQUATIONS In this section, basic system equations for data detection via a vector sensor introduced in [] and [4] are briefly presented. To demonstrate the basic concepts of how both the vector and 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., 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, andz components of the particle velocity. x y w Pressure Source Vector Sensor r p p x p y p z Fig.. A 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,andz 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. : the pressure channel p, represented by a straight dashed line, and three pressureequivalent velocity channels p x, p y,andp z, shown by curved dashed lines. To define p x, p y,andp z,wefirstdefinethe 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 f are given by [5] v x = (jρ ω ) p/ x, v y = (jρ ω ) p/ y, v z = (jρ ω ) p/ z, where ρ is the density of the fluid, and j =. Eq.() 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 p x = ρ cv x, p y = ρ cv y and p z = ρ cv z,which z w x r x w y r y w z r z ()

2 gives p x =(jk) p/ x, p y =(jk) p/ y, p z =(jk) p/ z, where k = ω /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.. Similar to Eq. (), the x, y, andz components of ambient noise velocities are α x = (jρ ω ) w/ x, α y = (jρ ω ) w/ y, and α z = (jρ ω ) w/ z, respectively. So we can obtain the pressure-equivalent ambient noise velocities as w x =(jk) w/ x, w y =(jk) w/ y, w z =(jk) w/ z. B. Input-Output System Equations According to Fig., the received pressure signal r in response to the signal s transmitted from the transmitter can be written as r = p s+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 r x = (jk) r/ x, r y =(jk) r/ y, andr z =(jk) r/ z. Based on () and by taking the spatial gradient with respect to x, y, andz axes, we obtain key system equations r = p s + w, r x = p x s + w x, r y = p y s + w y, r z = p z s + w z. 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 [] 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. 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. CHANNEL CHARACTERISTICS ESTIMATED FROM EXPERIMENTAL DATA During the high frequency Makai acoustic communication experiment (MakaiEx) conducted west off the Kauai Island, Hawaii, in September and October of 5 [7], a five element Wilcoxon TV- 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. () () (4) A. Channel Measurements during MakaiEx Each vector sensor of the Wilcoxon TV- 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, andz components of the particle velocity. The length of each vector sensor was 6.6 cm, and the element spacing (center-to-center distance) was cm. In one deployment on September, 5, a bottom mounted acoustic source continuously transmitted a series of communication signals at the carrier frequency of f = 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 pound weight was attached to the end of the array cable. The water depth at the site was about m. The bottom element was about 4 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 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 cm. In what follows, channel characteristics and receiver performance of these two systems are compared. Fig. shows an example of the impulse response functions obtained from the field data. A pseudo random BPSK signals at the carrier frequency of f =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 m. Fig. (a) shows an example of the measured impulse response amplitudes of a single vector sensor. As shown in Fig. (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,.6 ms and 4. ms, respectively. Considering the cm aperture of the pressure array, the four pressure channel impulse responses show similarity among themselves, as demonstrated in Fig. (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- andz- 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

3 .5 (a) Pressure channel: RMS delay spread: 5.4ms (b) Velocity channel x component: RMS delay spread: 6.6ms (c) Velocity channel y component: RMS delay spread:.6ms (d) Velocity channel z component: RMS delay spread: 4.ms (a).5 (a) Pressure channel #: RMS delay spread: 5.4ms (b) Pressure channel #: RMS delay spread: 5.6ms (c) Pressure channel #: RMS delay spread: 5.9ms (d) Pressure channel #4: RMS delay spread: 4.9ms Fig.. (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. (b) numbers in Table I are the modulus of the complex correlation E[v m vn γ m,n = ] E[v m]e[vn ] (E[ vm ] E[v m ] )(E[ v n ] E[v n ] ), (5) where v m, v n are two complex sequences and E[ ] represents the expectation operation. The channel impulse responses shown in Fig. are used for the correlation calculation. For the vector sensor, the pressure, x-velocity, y-velocity, and z- velocity channels are numbered as channel # to channel #4, respectively. The calculation of the noise correlation uses the.75 second ambient noise, which was recorded seconds prior to the BPSK training sequence. TABLE I CORRELATION, CHANNEL POWERS, AND NOISE POWERS MEASURED FROM THE FIELD DATA Vector Sensor Pressure Array γ,..469 γ, channel γ, correlation γ, γ, γ, Ω p channel Ω p power (db) Ω p Ω 4 p γ, γ, noise γ, correlation γ, γ, γ, Ω w noise Ω w power (db) Ω w Ω 4 w As shown in Table I, although the four channels of the vector sensor are co-located at a single point, correlation 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. Bit error rate 4 single pressure element vector sensor: y component only four element pressure array single vector sensor element 5 5 Average SNR per channel (db) Fig.. Performance of a vector sensor receiver, a four-element pressure array receiver, and a single pressure sensor. The impulse responses of Fig. are used to generate the BER curves. The size of the four element array is cm, whereas the vector sensor size is 6.6 cm (78% reduction in size). B. Simulated Performance of a Vector Sensor Receiver In Fig., 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. were used, along with the multichannel zeroforcing equalizer in []. The BERs correspond to a 6 kilobits/s uncoded BPSK data stream at f =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

4 of the vector sensor, a db gain can be obtained, compared to a single pressure receiver. The vector sensor receiver has also a db gain over the four-channel pressure array. The average signal-to-noise ratio (SNR) of each multichannel receiver is defined as ρ =(Ω p /Ω w +Ω x p /Ωx w +Ωy p /Ωy w +Ωz p /Ωz w )/4, (6) where Ω p, Ω x p, Ωy p,andωz p are the average powers of the pressure channel and of the particle velocity channels, and Ω w, Ω x w, Ωy w, and Ωz w 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 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 TIME REVERSAL RECEIVER WITH VECTOR SENSORS 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 r i (n) =e jθi(n) [h i (n, l) s(n)] + w i (n), i =to 4, (7) where the pressure channel, x-velocity channel, y-velocity channel, and z-velocity channel corresponds to channel # to channel #4. In Eq. (7), θ i (n) is the instantaneous carrier phase offset. h i (n, l), l L, 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 i th channel is denoted by ĥi(n, l) and the most recent estimated linear trend (Doppler) in the carrier phase offset is denoted by ˆf Δ,i (n). A. Phase Tracking and Correction Here we model the fast phase fluctuation as θ i (n) = πnf Δ,i (n)t s,wheref Δ,i (n) is the linear trend in the carrier phase offset (Doppler) and T s is the symbol period. At the i th channel, the Doppler is obtained by N Δ ˆf Δ,i (n) = arg max r i (n p)(ˆr i (n p)e jπpfts ), f p= (8) where ˆr i (n) = ŝ(n) past ĥi(n, l), ŝ(n) past represents the past decision results, and, N Δ is the Doppler observation block size in symbols. f search interval in Eq. (8) is given by f Δ,i δf < f < f Δ,i + δf, wheref Δ,i is the coarse Doppler estimate and δf is the Doppler search range. Since Doppler is estimated frequently, f Δ,i is set to the previous Doppler estimate. Phase correction is performed by offsetting the received signal r i (n) by the estimated Doppler, which yields r Δ,i (n) =r i (n)e jπn ˆf Δ,i(n)T s. B. Channel Estimation and Time Reversal Multichannel Combining The channel estimate ĥi(n, l) can be obtained from the phase corrected received signal r Δ,i (n) and the past decision results ŝ(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 []. The channel estimation block size is chosen to be twice the channel length, i.e., N =L. 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 [] can be used as an estimate for the i th channel noise power, N ˆσ i = n= r Δ,i(n) ĥi(n, l) s(n) preamble, (9) N L where s(n) preamble is the source symbol of the preamble. Then, time reversal multichannel combining uses (ĥi(n, l)) to matched-filter the phase-corrected signals on each channel []. Therefore, the output after time reversal combining is c(n) = M=4 i= (ĥi(n, l)) r Δ,i (n) ˆσ i = 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 [] 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

5 r (n) e -jπnf Δ, (n)t s r Δ, (n) _ σ ( h (n,-l) )* r (n) phase tracking x (n) past Channel estimation Σ c(n) FF filter ~ s (n) s (n) r M (n) -jπnf Δ, Μ (n)t e s r Δ,M (n) _ σ M ( )* h M (n,-l) FB filter r M (n) phase tracking x (n) past Channel estimation Phase tracking and correction Channel estimation and time reversal multichannel combing Single channel DFE Fig. 4. The proposed receiver is composed of three parts: () phase tracking and correction, () channel estimation and time reversal multichannel combining, and () 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, ŝ(n), are used as performance metrics in the next section. In the multichannel DFEs developed in [], 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 [], the proposed receiver uses a single channel DFE after time reversal combining. An advantage of the proposed receiver structure is its low complexity [9], []. 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 [4]. 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 [5], [6], and [7] where multichannel combining is performed based on channel probes or the known symbols at the beginning of the data packet. V. EXPERIMENTAL RESULTS DURING MAKAIEX In this section, we present the demodulation results on the experimental data collected on September, 5 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 = symbols for the m range, where the vector sensor array had significant motion. The received data are over-sampled and the over-sampling rate is K =. The number of the feedforward taps is KN ff = 45 for the fractionally spaced DFE [], where N ff = 5 is the TABLE II RECEIVER PARAMETERS Parameters Description Value f s sampling rate 48 Hz f carrier frequency Hz R symbol rate 6 kilosymbols/s K over-sampling factor M total number of the channels 4 N preamble size of the preamble 6 symbols L length of the CIR function symbols N channel estimation block size L symbols N channel estimation update interval symbols N Δ Doppler observation block size N symbols δf Initial Doppler search range Hz δf Doppler search range after preamble.6 Hz N ff Feedforward filter span in symbols 5 symbols N fb Feedback filter tap number 5 symbols K f proportional tracking constant in PLL. K f integral tracking constant in PLL. λ RLS forgetting factor in the DFE.999 feedforward filter span in symbols. At the beginning of the.75 s BPSK packet, N preamble = 6 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 Hz. The Doppler search range after the preamble is set to.6 Hz. The search step is. Hz. The RLS forgetting factor λ in the DFE is chosen to be.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.75 second The only exception is L = symbols for the m range.

6 TABLE III DEMODULATION RESULTS DURING MAKAIEX Source-Receiver Range m 5 m 4 m 55 m m demodulation results output SNR 5.4 db 7.4 db.8 db.6 db. db for the vector sensor BER BER= BER=8e-4 BER=.47 BER=. BER=.5 demodulation results output SNR 9. db 4. db 4. db 4.6 db.7 db for the pressure array BER BER=5e-5 BER=. BER=.7 BER=9e- BER=.46 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 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 5 m range, the vector sensor receiver has about db gain. The performance gain of the vector sensor at m and 5 m can be attributed to the smaller RMS delay spread of the y- andz- velocity channels, as shown in Table IV. For the range of 4 m and 55 m, the pressure array has about db gain over the vector sensor. Note that 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 55 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 m range, the vector sensor performs.4 db better than the pressure array. This may be due to the high correlation (over.9) among all the channels of the pressure array at the m range, as listed in Table IV. VI. CONCLUSION 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 OA, Contract No. N 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. REFERENCES [] A. Nehorai and E. Paldi, Acoustic vector-sensor array processing, IEEE Trans. Signal Proc., vol. 4, no. 9, pp , Sept [] M. Hawkes and A. Nehorai, Acoustic vector-sensor beamforming and Capon direction estimation, IEEE Trans. Signal Proc., vol. 46, no. 9, pp. 9 4, Sept [] A. Abdi, H. Guo, and P. Sutthiwan, A new vector sensor receiver for underwater acoustic communication, in Proc. Oceans, Vancouver, Canada, 7. [4] A. Abdi and H. Guo, A new compact multichannel receiver for underwater wireless communication networks, IEEE Trans. Wireless Commun., accepted, 8. [5] A. D. Pierce, Acoustics: An introduction to its physical principles and applications, Acoustical Society of America, Woodbury, New York, nd edition, 989. [6] M. Hawkes and A. Nehorai, Acoustic vector-sensor correlations in ambient noise, IEEE J. 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7 TABLE IV MEASURED CHANNEL CHARACTERISTICS DURING MAKAIEX Range m 5 m 4 m 55 m m CH# average RMS delay spread CH# of the vector sensor CH# CH# γ, γ, average channel correlation γ, of the vector sensor γ, γ, γ, CH# average RMS delay spread CH# of the pressure array CH# CH# γ, γ, average channel correlation γ, of the pressure array γ, γ, γ, Average RMS delay spread: 5.ms. Average RMS delay spread: 5.ms (a) (b) Average RMS delay spread:.4ms. Average RMS delay spread: 4.ms (c) (d) Fig. 5. The measured.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 m.

8 Average RMS delay spread: 5.ms. Average RMS delay spread: 5.ms (a) (b) Average RMS delay spread: 5.6ms. Average RMS delay spread: 5.ms (c) (d) Fig. 6. The measured.75 second impulse responses of the four pressure channels at the source-receiver range of m.

9 Average RMS delay spread: 7.9ms. Average RMS delay spread: 7.9ms (a) (b) Average RMS delay spread: 7.9ms. Average RMS delay spread: 7.7ms (c) (d) Fig. 7. The measured.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 55 m.

10 Average RMS delay spread: 7.9ms. Average RMS delay spread: 7.9ms (a) (b) Average RMS delay spread: 7.4ms. Average RMS delay spread: 7.ms (c) (d) Fig. 8. The measured.75 second impulse responses of the four pressure channels at the source-receiver range of 55 m.