Choo et al.: JASA Express Letters
[http://dx.doi.org/10.1121/1.4869822]
Published Online 28 March 2014
Range-dependence of acoustic channel with traveling sinusoidal surface wave Youngmin Choo and Woojae Seong Department of Naval Architecture and Ocean Engineering, Seoul National University, Seoul 151-744, Korea [email protected], [email protected]
Keunhwa Lee Research Institute of Marine Systems Engineering, Seoul 151-742, Korea [email protected]
Abstract: Range-dependence of time-varying acoustic channels caused by a traveling surface wave is investigated through water tank experiments and acoustic propagation analysis schemes. As the surface wave travels, surface reflected signals fluctuate and the fluctuation varies with source-receiver horizontal range. Amplitude fluctuations of surface reflected signals increase with increasing horizontal range whereas the opposite occurs in delay fluctuations. The scattered pressure field at a fixed time shows strong dependence on the receiver position because of caustics and shadow zones formed by the surface. The Doppler shifts of surface reflected signals also depend on the horizontal range. Comparison between measurement data and model results indicates the Doppler shift relies on the delay fluctuation under current experimental conditions. C 2014 Acoustical Society of America V
PACS numbers: 43.30.Cq, 43.30.Es [GD] Date Received: October 27, 2013 Date Accepted: March 18, 2014
1. Introduction Sea surface movement creates a time-varying acoustic channel and also induces Doppler shift that varies with the position of the receiver. In particular, delays and amplitudes of surface reflected signals change. These surface movement effects are detrimental to the operation of underwater acoustic systems, including acoustic communication. For investigation of the surface movement effects, two methods are generally used: simulation and experiment. Siderius and Porter1 simulated a time-varying acoustic channel using a ray-based numerical model and the Doppler shift of the acoustic channel was investigated with the simulation result. Preisig and Deane2 conducted a transmission experiment in the surf zone. Received signals show an abrupt change along the source transmitted ping time because of focusing and caustics formed by the surface wave. Tindle and Deane3 analyzed this phenomenon with numerically simulated acoustic channels. The model results indicate that multiple arrivals of surface bounce paths cause sudden changes in the acoustic channels. Subsequently, a small-scale water tank experiment was carried out and measurement data were acquired at a fixed sourcereceiver horizontal range for various surface wave heights.4 As the surface wave height increased, the acoustic channel changed more rapidly and became complicated. In this work, acoustic signal (20 kHz) transmission and reception experiments are conducted for varying source-receiver ranges. The measurement data are analyzed using a propagation analysis scheme to investigate the range-dependence of acoustic channels. In Sec. 2, water tank experiments are described and experimental results are shown. In Sec. 3, the measurement data are compared with numerical results and analyzed. Delay and amplitude fluctuations and Doppler shifts of surface reflected signals show range-dependence. Section 4 provides a summary of the present work.
EL206 J. Acoust. Soc. Am. 135 (4), April 2014
C 2014 Acoustical Society of America V
Choo et al.: JASA Express Letters
[http://dx.doi.org/10.1121/1.4869822]
Published Online 28 March 2014
2. Measurement data from water tank experiment For measurement of an acoustic channel with a traveling surface wave, water tank experiments were conducted at Seoul National University (SNU) and the Korea Institute of Ocean Science and Technology (KIOST). Source and receivers arrangement and surface wave properties (wave height and wavelength) are shown in Fig. 1(a). Omni-directional hydrophones B&K 8105 and 8103 were used as source and receiver, respectively. Depths of source and receiver are fixed at 1.5 and 1 m whereas their horizontal ranges vary from 3 to 7.5 m. The water tank in SNU had a constant sound speed of 1427 m/s. The sound speed in the water tank of KIOST had a little variation (1468–1475 m/s) but mostly maintained an isovelocity of 1469 m/s. The source signals in the water tank experiments were 20 kHz binary phase shift keying signals. The received signals were correlated with the source signals and channel impulse responses were derived along transmitted ping times of the source. Figures 1(b) and 1(c) show the time-varying acoustic channels from SNU and KIOST water tank experiments, respectively. Their source-receiver horizontal ranges are 3 and 5 m. The delays and amplitudes in this work are relative values. The delays are the difference from the mean arrival time of the direct path, and the amplitudes are also normalized by the mean amplitude of the direct path. The acoustic channels show regular patterns and do not show any diffracted signals. In this work, signals from three different paths were observed: direct, single surface reflected, and single bottom reflected paths. Direct and single bottom reflected signals in the acoustic channels are constant along the source transmitted ping times because these paths were unaffected by the traveling surface waves. On the other hand, the surface reflected signals periodically fluctuated and their periods were 1.5 s, which corresponds to the surface wave period. The surface wave effects on the acoustic channels show range-dependence. Maximum amplitude difference of surface reflected signals at 3 and 5 m are 3 and 7 dB, respectively. The delays of surface reflected paths vary from 0.6 to 0.67 ms at 3 m and from 0.36 to 0.41 ms at 5 m, respectively. Delay fluctuation was higher at 3 m than
Fig. 1. (Color online) Schematic of water tank experiment and measurement data: (a) side-plan showing experimental arrangement of source and receiver, surface wavelength, and surface wave height; (b), (c) channel impulse responses from the experiments at horizontal receiver ranges of 3 and 5 m, respectively.
J. Acoust. Soc. Am. 135 (4), April 2014
Choo et al.: Range-dependence of time-varying channel
EL207
Choo et al.: JASA Express Letters
[http://dx.doi.org/10.1121/1.4869822]
Published Online 28 March 2014
at 5 m, whereas the opposite occurred in the amplitudes. These signal fluctuations induced the Doppler shifts. 3. Surface movement effects on acoustic channel The measurement data from the water tank experiments were analyzed with two acoustic propagation analysis schemes: an integral equation with Kirchhoff approximation1 and a ray model.5 Amplitudes were computed using the integral equation and delays were calculated from the ray model. The numerical results were compared with the measurement data. Figure 2 shows the amplitudes, delays, and Doppler shifts of surface reflected signals at the horizontal ranges of 3 and 5 m, respectively, and the results are in good agreement with the measurement data. They have periodic time dependence in accordance with the surface wave and vary with the horizontal ranges. The curved surface effects are more pronounced in the amplitudes. The acoustic energies reflected from regions near the crest and trough of the surface wave, respectively, converge and diverge. The highest amplitudes of surface reflected signals depend on the horizontal ranges and they appear at different times as seen in Figs. 2(a) and 2(b). At 3 m
Fig. 2. Amplitudes, delays, and Doppler shifts of surface reflected signals from measurement data and numerical models: (a), (b) amplitudes at 3 and 5 m; (c), (d) delays at 3 and 5 m; (e), (f) Doppler shifts at 3 and 5 m, respectively.
EL208 J. Acoust. Soc. Am. 135 (4), April 2014
Choo et al.: Range-dependence of time-varying channel
Choo et al.: JASA Express Letters
[http://dx.doi.org/10.1121/1.4869822]
Published Online 28 March 2014
Fig. 3. (Color online) (a) Time-dependent amplitudes of surface reflected signals according to the horizontal ranges of receivers, (b) the amplitudes at the fixed time, 1.2 s.
horizontal range [Fig. 2(a)], the surface wave is seen to cause very weak focusing effect, whereas at 5 m horizontal range [Fig. 2(b)], the focusing becomes pronounced and the surface reflected signal amplitude reaches twice that of the direct signal. The ray diagrams (plots not seen in this paper) at the times when the amplitudes are highest reveal converging rays and they explain the maximum amplitude difference between 3 and 5 m. As described earlier, the amplitude fluctuations of surface reflected signals highly depend on the source-receiver horizontal ranges. For investigation of rangedependence of the amplitudes, additional water tank experiments were conducted along the horizontal range. Figure 3(a) shows amplitudes of surface reflected signals at horizontal ranges of 3, 6, 6.5, 7, and 7.5 m. The results from the measurement data and model are in fair agreement. The maximum amplitude or, equivalently, the focusing effect, becomes pronounced as the source-receiver separation increases. Figure 3(b) shows the amplitudes along horizontal ranges at a fixed time, 1.2 s. The result using the integral equation with Kirchhoff approximation shows good agreement with the measurement data as shown. The amplitudes gradually increase until the 6 m range, where weak focusing occurs. Then a strong focusing appears, resulting in rapid amplitude increase between ranges 6–7 m. This phenomenon can be explained with Fig. 4(a), which shows the contour of normalized surface reflected pressure at time 1.2 s. At 1 m depth, the focus is located near 6.5 m which is created by the surface wave crest acting like a convex lens. On the other hand, an area with a low level of surface reflected signal is observed just after 6.5 m. This phenomenon comes from destructive interference
Fig. 4. (Color online) (a) The contour of normalized surface reflected pressure field from the surface wave at time 1.2 s and (b) the contour of acoustic pressure field including direct and surface reflected signals at the same time. The circles indicate receiver positions in SNU water tank experiment.
J. Acoust. Soc. Am. 135 (4), April 2014
Choo et al.: Range-dependence of time-varying channel
EL209
Choo et al.: JASA Express Letters
[http://dx.doi.org/10.1121/1.4869822]
Published Online 28 March 2014
between surface reflected signals and this shadow zone is located near the boundaries of the energy convergence area (caustics) as seen in Figs. 3(b) and 4(a). The caustics and shadow zone due to the surface wave induce the abrupt change of the acoustic channel along the horizontal ranges. This feature is similar to that of the acoustic channel with caustics caused by sound refraction due to sound speed variation.6 Other focusing beams with decreasing grazing angles are produced from the forward crests of the surface wave. For reference, the acoustic pressure contour including direct and surface reflected signals is shown in Fig. 4(b), which is also computed from the integral equation with Kirchhoff approximation. The signals from the different paths interfere constructively or destructively. Unlike Lloyd mirror pattern with a flat surface,6 intensive acoustic energies are formed along the focusing beams in Fig. 4(a). As the surface wave travels, signals reflect off different parts of the surface and thus the delays fluctuate in accordance with the surface wave period of 1.5 s [Figs. 2(c) and 2(d)]. Since the longest and shortest paths of the signals are, respectively, reflected at the crest and trough of the surface wave, the delays of surface reflected signals are in phase with the surface wave. When the surface is smooth, the maximum of path difference is approximated as 2hssinh, where hs is the surface wave height and h is the specular reflection angle when the surface is flat.7 Thus, the delay differences at 3 and 5 m, respectively, should be 0.07 and 0.048 ms, which are almost the same as the results from measurement data and the ray model. The surface movements induce the time-varying acoustic channels, inevitably accompanied by the Doppler shifts, which vary along transmitted ping time. These instantaneous Doppler shifts were extracted from the measurement data using a modified orthogonal matching pursuit algorithm.8 The instantaneous Doppler shifts were also calculated from the ray model using the modified Doppler shift formula described below. Amplitude and delay of the surface reflected signal show time-dependence because of the traveling surface wave. The amplitude fluctuation alters the signal, which leads to frequency shift. However, the amplitude fluctuation is not considered in deriving the instantaneous Doppler shift because for all of our experiments, the amplitude difference of received signals at adjacent times was negligible. Under this condition, the phase difference of source signal between two adjacent transmitted ping times should be preserved for the received signal, and they can be written as follows: 2pf0 Dt ¼ 2pf 0 ðDt þ DsÞ;
(1)
where f0 and f 0 are frequencies of the signals at source and receiver, respectively, and Dt and Ds are time difference and delay difference between adjacent ping times, respectively. Then, the frequency shift (Df ¼ f 0 f0) is derived as Df ¼
ds=dt f0 : 1 þ ds=dt
(2)
Using Eq. (2) and the delays of surface reflected signals from the ray model, the instantaneous Doppler shifts are computed. The Doppler shifts from measurement data and model are shown in Figs. 2(e) and 2(f), and the model results show good agreement with the measurement data. The Doppler shifts at 3 and 5 m are between 3.1 and 3.0 Hz and 2.1 and 2.0 Hz, respectively. The Doppler shift is larger at 3 m than at 5 m since the delay difference is larger at 3 m as stated previously. 4. Summary For the purpose of observing range-dependence of surface movement effects on acoustic channel, water tank experiments were conducted at different source-receiver horizontal ranges and measurement data from the experiments were compared with analytic results. Amplitudes of surface reflected signals vary rapidly owing to the focusing effect of the curved surface wave. The pressure field at a fixed time shows caustics
EL210 J. Acoust. Soc. Am. 135 (4), April 2014
Choo et al.: Range-dependence of time-varying channel
Choo et al.: JASA Express Letters
[http://dx.doi.org/10.1121/1.4869822]
Published Online 28 March 2014
and shadow zones, which cause a dramatic change of acoustic signals along the horizontal ranges. Delays of surface reflected signals fluctuate periodically in phase with the surface wave and their fluctuation decreases with increasing horizontal range. The signal fluctuation causes the Doppler shift. Under the current water tank experiment conditions, the delay fluctuation dominantly determines the amount of instantaneous frequency shift. Thus, the Doppler shift is inversely proportional to the horizontal range between source and receiver. Acknowledgment This work was supported by Agency for Defense Development (ADD) funded by the Ministry of National Defense (No. 0457-2014001). References and links 1
M. Siderius and M. B. Porter, “Modeling broadband ocean acoustic transmissions with time-varying sea surfaces,” J. Acoust. Soc. Am. 124(1), 137–150 (2008). 2 J. C. Preisig and G. B. Deane, “Surface wave focusing and acoustic communications in the surf zone,” J. Acoust. Soc. Am. 116(4), 2067–2080 (2004). 3 C. T. Tindle and G. B. Deane, “Shallow water sound propagation with surface waves,” J. Acoust. Soc. Am. 117(5), 2783–2794 (2005). 4 C. T. Tindle, G. B. Deane, and J. C. Preisig, “Reflection of underwater sound from surface waves,” J. Acoust. Soc. Am. 125(1), 66–72 (2009). 5 Y. Choo and W. Seong, “Modeling and analysis of an acoustic channel with a moving surface,” J. Comput. Acoust. 21(4), 1350015 (2013). 6 F. B. Jensen, W. A. Kuperman, M. B. Porter, and H. Schmidt, Computational Ocean Acoustics (Springer, New York, 2011), Chaps. 2 and 3. 7 Y. Choo and W. Seong, “Analysis of a time-varying acoustic channel caused by a moving surface,” in Proceedings of IEEE UComms 2012, Sestri Levante, Italy (September 12–14, 2012). 8 S. H. Byun, W. Seong, and S. M. Kim, “Sparse underwater acoustic channel parameter estimation using a wideband receiver array,” IEEE J. Ocean. Eng. 38(4), 718–729 (2013).
J. Acoust. Soc. Am. 135 (4), April 2014
Choo et al.: Range-dependence of time-varying channel
EL211
Copyright of Journal of the Acoustical Society of America is the property of American Institute of Physics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use.
[http://dx.doi.org/10.1121/1.4869822]
Published Online 28 March 2014
Range-dependence of acoustic channel with traveling sinusoidal surface wave Youngmin Choo and Woojae Seong Department of Naval Architecture and Ocean Engineering, Seoul National University, Seoul 151-744, Korea [email protected], [email protected]
Keunhwa Lee Research Institute of Marine Systems Engineering, Seoul 151-742, Korea [email protected]
Abstract: Range-dependence of time-varying acoustic channels caused by a traveling surface wave is investigated through water tank experiments and acoustic propagation analysis schemes. As the surface wave travels, surface reflected signals fluctuate and the fluctuation varies with source-receiver horizontal range. Amplitude fluctuations of surface reflected signals increase with increasing horizontal range whereas the opposite occurs in delay fluctuations. The scattered pressure field at a fixed time shows strong dependence on the receiver position because of caustics and shadow zones formed by the surface. The Doppler shifts of surface reflected signals also depend on the horizontal range. Comparison between measurement data and model results indicates the Doppler shift relies on the delay fluctuation under current experimental conditions. C 2014 Acoustical Society of America V
PACS numbers: 43.30.Cq, 43.30.Es [GD] Date Received: October 27, 2013 Date Accepted: March 18, 2014
1. Introduction Sea surface movement creates a time-varying acoustic channel and also induces Doppler shift that varies with the position of the receiver. In particular, delays and amplitudes of surface reflected signals change. These surface movement effects are detrimental to the operation of underwater acoustic systems, including acoustic communication. For investigation of the surface movement effects, two methods are generally used: simulation and experiment. Siderius and Porter1 simulated a time-varying acoustic channel using a ray-based numerical model and the Doppler shift of the acoustic channel was investigated with the simulation result. Preisig and Deane2 conducted a transmission experiment in the surf zone. Received signals show an abrupt change along the source transmitted ping time because of focusing and caustics formed by the surface wave. Tindle and Deane3 analyzed this phenomenon with numerically simulated acoustic channels. The model results indicate that multiple arrivals of surface bounce paths cause sudden changes in the acoustic channels. Subsequently, a small-scale water tank experiment was carried out and measurement data were acquired at a fixed sourcereceiver horizontal range for various surface wave heights.4 As the surface wave height increased, the acoustic channel changed more rapidly and became complicated. In this work, acoustic signal (20 kHz) transmission and reception experiments are conducted for varying source-receiver ranges. The measurement data are analyzed using a propagation analysis scheme to investigate the range-dependence of acoustic channels. In Sec. 2, water tank experiments are described and experimental results are shown. In Sec. 3, the measurement data are compared with numerical results and analyzed. Delay and amplitude fluctuations and Doppler shifts of surface reflected signals show range-dependence. Section 4 provides a summary of the present work.
EL206 J. Acoust. Soc. Am. 135 (4), April 2014
C 2014 Acoustical Society of America V
Choo et al.: JASA Express Letters
[http://dx.doi.org/10.1121/1.4869822]
Published Online 28 March 2014
2. Measurement data from water tank experiment For measurement of an acoustic channel with a traveling surface wave, water tank experiments were conducted at Seoul National University (SNU) and the Korea Institute of Ocean Science and Technology (KIOST). Source and receivers arrangement and surface wave properties (wave height and wavelength) are shown in Fig. 1(a). Omni-directional hydrophones B&K 8105 and 8103 were used as source and receiver, respectively. Depths of source and receiver are fixed at 1.5 and 1 m whereas their horizontal ranges vary from 3 to 7.5 m. The water tank in SNU had a constant sound speed of 1427 m/s. The sound speed in the water tank of KIOST had a little variation (1468–1475 m/s) but mostly maintained an isovelocity of 1469 m/s. The source signals in the water tank experiments were 20 kHz binary phase shift keying signals. The received signals were correlated with the source signals and channel impulse responses were derived along transmitted ping times of the source. Figures 1(b) and 1(c) show the time-varying acoustic channels from SNU and KIOST water tank experiments, respectively. Their source-receiver horizontal ranges are 3 and 5 m. The delays and amplitudes in this work are relative values. The delays are the difference from the mean arrival time of the direct path, and the amplitudes are also normalized by the mean amplitude of the direct path. The acoustic channels show regular patterns and do not show any diffracted signals. In this work, signals from three different paths were observed: direct, single surface reflected, and single bottom reflected paths. Direct and single bottom reflected signals in the acoustic channels are constant along the source transmitted ping times because these paths were unaffected by the traveling surface waves. On the other hand, the surface reflected signals periodically fluctuated and their periods were 1.5 s, which corresponds to the surface wave period. The surface wave effects on the acoustic channels show range-dependence. Maximum amplitude difference of surface reflected signals at 3 and 5 m are 3 and 7 dB, respectively. The delays of surface reflected paths vary from 0.6 to 0.67 ms at 3 m and from 0.36 to 0.41 ms at 5 m, respectively. Delay fluctuation was higher at 3 m than
Fig. 1. (Color online) Schematic of water tank experiment and measurement data: (a) side-plan showing experimental arrangement of source and receiver, surface wavelength, and surface wave height; (b), (c) channel impulse responses from the experiments at horizontal receiver ranges of 3 and 5 m, respectively.
J. Acoust. Soc. Am. 135 (4), April 2014
Choo et al.: Range-dependence of time-varying channel
EL207
Choo et al.: JASA Express Letters
[http://dx.doi.org/10.1121/1.4869822]
Published Online 28 March 2014
at 5 m, whereas the opposite occurred in the amplitudes. These signal fluctuations induced the Doppler shifts. 3. Surface movement effects on acoustic channel The measurement data from the water tank experiments were analyzed with two acoustic propagation analysis schemes: an integral equation with Kirchhoff approximation1 and a ray model.5 Amplitudes were computed using the integral equation and delays were calculated from the ray model. The numerical results were compared with the measurement data. Figure 2 shows the amplitudes, delays, and Doppler shifts of surface reflected signals at the horizontal ranges of 3 and 5 m, respectively, and the results are in good agreement with the measurement data. They have periodic time dependence in accordance with the surface wave and vary with the horizontal ranges. The curved surface effects are more pronounced in the amplitudes. The acoustic energies reflected from regions near the crest and trough of the surface wave, respectively, converge and diverge. The highest amplitudes of surface reflected signals depend on the horizontal ranges and they appear at different times as seen in Figs. 2(a) and 2(b). At 3 m
Fig. 2. Amplitudes, delays, and Doppler shifts of surface reflected signals from measurement data and numerical models: (a), (b) amplitudes at 3 and 5 m; (c), (d) delays at 3 and 5 m; (e), (f) Doppler shifts at 3 and 5 m, respectively.
EL208 J. Acoust. Soc. Am. 135 (4), April 2014
Choo et al.: Range-dependence of time-varying channel
Choo et al.: JASA Express Letters
[http://dx.doi.org/10.1121/1.4869822]
Published Online 28 March 2014
Fig. 3. (Color online) (a) Time-dependent amplitudes of surface reflected signals according to the horizontal ranges of receivers, (b) the amplitudes at the fixed time, 1.2 s.
horizontal range [Fig. 2(a)], the surface wave is seen to cause very weak focusing effect, whereas at 5 m horizontal range [Fig. 2(b)], the focusing becomes pronounced and the surface reflected signal amplitude reaches twice that of the direct signal. The ray diagrams (plots not seen in this paper) at the times when the amplitudes are highest reveal converging rays and they explain the maximum amplitude difference between 3 and 5 m. As described earlier, the amplitude fluctuations of surface reflected signals highly depend on the source-receiver horizontal ranges. For investigation of rangedependence of the amplitudes, additional water tank experiments were conducted along the horizontal range. Figure 3(a) shows amplitudes of surface reflected signals at horizontal ranges of 3, 6, 6.5, 7, and 7.5 m. The results from the measurement data and model are in fair agreement. The maximum amplitude or, equivalently, the focusing effect, becomes pronounced as the source-receiver separation increases. Figure 3(b) shows the amplitudes along horizontal ranges at a fixed time, 1.2 s. The result using the integral equation with Kirchhoff approximation shows good agreement with the measurement data as shown. The amplitudes gradually increase until the 6 m range, where weak focusing occurs. Then a strong focusing appears, resulting in rapid amplitude increase between ranges 6–7 m. This phenomenon can be explained with Fig. 4(a), which shows the contour of normalized surface reflected pressure at time 1.2 s. At 1 m depth, the focus is located near 6.5 m which is created by the surface wave crest acting like a convex lens. On the other hand, an area with a low level of surface reflected signal is observed just after 6.5 m. This phenomenon comes from destructive interference
Fig. 4. (Color online) (a) The contour of normalized surface reflected pressure field from the surface wave at time 1.2 s and (b) the contour of acoustic pressure field including direct and surface reflected signals at the same time. The circles indicate receiver positions in SNU water tank experiment.
J. Acoust. Soc. Am. 135 (4), April 2014
Choo et al.: Range-dependence of time-varying channel
EL209
Choo et al.: JASA Express Letters
[http://dx.doi.org/10.1121/1.4869822]
Published Online 28 March 2014
between surface reflected signals and this shadow zone is located near the boundaries of the energy convergence area (caustics) as seen in Figs. 3(b) and 4(a). The caustics and shadow zone due to the surface wave induce the abrupt change of the acoustic channel along the horizontal ranges. This feature is similar to that of the acoustic channel with caustics caused by sound refraction due to sound speed variation.6 Other focusing beams with decreasing grazing angles are produced from the forward crests of the surface wave. For reference, the acoustic pressure contour including direct and surface reflected signals is shown in Fig. 4(b), which is also computed from the integral equation with Kirchhoff approximation. The signals from the different paths interfere constructively or destructively. Unlike Lloyd mirror pattern with a flat surface,6 intensive acoustic energies are formed along the focusing beams in Fig. 4(a). As the surface wave travels, signals reflect off different parts of the surface and thus the delays fluctuate in accordance with the surface wave period of 1.5 s [Figs. 2(c) and 2(d)]. Since the longest and shortest paths of the signals are, respectively, reflected at the crest and trough of the surface wave, the delays of surface reflected signals are in phase with the surface wave. When the surface is smooth, the maximum of path difference is approximated as 2hssinh, where hs is the surface wave height and h is the specular reflection angle when the surface is flat.7 Thus, the delay differences at 3 and 5 m, respectively, should be 0.07 and 0.048 ms, which are almost the same as the results from measurement data and the ray model. The surface movements induce the time-varying acoustic channels, inevitably accompanied by the Doppler shifts, which vary along transmitted ping time. These instantaneous Doppler shifts were extracted from the measurement data using a modified orthogonal matching pursuit algorithm.8 The instantaneous Doppler shifts were also calculated from the ray model using the modified Doppler shift formula described below. Amplitude and delay of the surface reflected signal show time-dependence because of the traveling surface wave. The amplitude fluctuation alters the signal, which leads to frequency shift. However, the amplitude fluctuation is not considered in deriving the instantaneous Doppler shift because for all of our experiments, the amplitude difference of received signals at adjacent times was negligible. Under this condition, the phase difference of source signal between two adjacent transmitted ping times should be preserved for the received signal, and they can be written as follows: 2pf0 Dt ¼ 2pf 0 ðDt þ DsÞ;
(1)
where f0 and f 0 are frequencies of the signals at source and receiver, respectively, and Dt and Ds are time difference and delay difference between adjacent ping times, respectively. Then, the frequency shift (Df ¼ f 0 f0) is derived as Df ¼
ds=dt f0 : 1 þ ds=dt
(2)
Using Eq. (2) and the delays of surface reflected signals from the ray model, the instantaneous Doppler shifts are computed. The Doppler shifts from measurement data and model are shown in Figs. 2(e) and 2(f), and the model results show good agreement with the measurement data. The Doppler shifts at 3 and 5 m are between 3.1 and 3.0 Hz and 2.1 and 2.0 Hz, respectively. The Doppler shift is larger at 3 m than at 5 m since the delay difference is larger at 3 m as stated previously. 4. Summary For the purpose of observing range-dependence of surface movement effects on acoustic channel, water tank experiments were conducted at different source-receiver horizontal ranges and measurement data from the experiments were compared with analytic results. Amplitudes of surface reflected signals vary rapidly owing to the focusing effect of the curved surface wave. The pressure field at a fixed time shows caustics
EL210 J. Acoust. Soc. Am. 135 (4), April 2014
Choo et al.: Range-dependence of time-varying channel
Choo et al.: JASA Express Letters
[http://dx.doi.org/10.1121/1.4869822]
Published Online 28 March 2014
and shadow zones, which cause a dramatic change of acoustic signals along the horizontal ranges. Delays of surface reflected signals fluctuate periodically in phase with the surface wave and their fluctuation decreases with increasing horizontal range. The signal fluctuation causes the Doppler shift. Under the current water tank experiment conditions, the delay fluctuation dominantly determines the amount of instantaneous frequency shift. Thus, the Doppler shift is inversely proportional to the horizontal range between source and receiver. Acknowledgment This work was supported by Agency for Defense Development (ADD) funded by the Ministry of National Defense (No. 0457-2014001). References and links 1
M. Siderius and M. B. Porter, “Modeling broadband ocean acoustic transmissions with time-varying sea surfaces,” J. Acoust. Soc. Am. 124(1), 137–150 (2008). 2 J. C. Preisig and G. B. Deane, “Surface wave focusing and acoustic communications in the surf zone,” J. Acoust. Soc. Am. 116(4), 2067–2080 (2004). 3 C. T. Tindle and G. B. Deane, “Shallow water sound propagation with surface waves,” J. Acoust. Soc. Am. 117(5), 2783–2794 (2005). 4 C. T. Tindle, G. B. Deane, and J. C. Preisig, “Reflection of underwater sound from surface waves,” J. Acoust. Soc. Am. 125(1), 66–72 (2009). 5 Y. Choo and W. Seong, “Modeling and analysis of an acoustic channel with a moving surface,” J. Comput. Acoust. 21(4), 1350015 (2013). 6 F. B. Jensen, W. A. Kuperman, M. B. Porter, and H. Schmidt, Computational Ocean Acoustics (Springer, New York, 2011), Chaps. 2 and 3. 7 Y. Choo and W. Seong, “Analysis of a time-varying acoustic channel caused by a moving surface,” in Proceedings of IEEE UComms 2012, Sestri Levante, Italy (September 12–14, 2012). 8 S. H. Byun, W. Seong, and S. M. Kim, “Sparse underwater acoustic channel parameter estimation using a wideband receiver array,” IEEE J. Ocean. Eng. 38(4), 718–729 (2013).
J. Acoust. Soc. Am. 135 (4), April 2014
Choo et al.: Range-dependence of time-varying channel
EL211
Copyright of Journal of the Acoustical Society of America is the property of American Institute of Physics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use.
