Acoustic impulse response fluctuations and coherent underwater acoustic communication in shallow waters under autumn conditions

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Abstract

The paper presents the results of a full-scale experiment aimed at assessing the temporal variability of the impulse response of a hydroacoustic channel and the efficiency of coherent underwater acoustic communications using bottom transmitters and receivers at frequencies of ~10 kHz on the Black Sea shelf in autumn. Three prominent maxima of variable amplitude were observed in the impulse response structure throughout the experiment (~36 h). The range of variability of the root-mean-square decoding error was ~11 dB, the bit error ratio varied from 0 to 0.10. We found a a strong relationship of the values of decoding errors with the amplitude of the maximum arrival in the structure of the reference impulse response corresponding to a group of rays with one reflection off the surface, as well as with the variation coefficient of high-frequency fluctuations of the amplitude of this arrival in the instantaneous estimate of the impulse response. Using numerical modeling, the hypothesis was confirmed that in autumn conditions, characterized by the absence of a pronounced seasonal thermocline, the main hydrophysical cause of the variability of the amplitude of the main arrival, and, as a consequence, the effectiveness of underwater acoustic communications, consisted in an insignificant (fractions of a degree) change of temperature in the upper layer of sea water.

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About the authors

A. V. Shatravin

Shirshov Institute оf Oceanology, Russian Academy of Sciences; Prokhorov General Physics Institute, Russian Academy of Sciences

Author for correspondence.
Email: ashatravin@ocean.ru
Russian Federation, Moscow, 117997; st. Vavilova 38, Moscow, 119991

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2. Fig. 1. Schematic diagram of the installation of autonomous hydroacoustic receiving and emitting stations at the testing ground in the area of ​​Rybatskaya (Golubaya) Bay near Gelendzhik. The positions of the stations are marked with stars, the red circle is the location of the Doppler current profiler (ADCP). The depth marks are shown by numbers. The distance between the stations is ~ 1 km.

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3. Fig. 2. (a) — Schematic diagram of the design of bottom receiving and emitting hydroacoustic stations, (b) — an example of a record of signals received by one of the stations: rectangle “1” marks the signal emitted by the same station, rectangle “2” — the signal emitted by the second station.

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4. Fig. 3. Typical examples of the channel impulse response. The blue curve is the estimate based on the signal emitted 5.5 hours after the start of the experiment, and the brown curve is the estimate after 30.51 hours. The horizontal axis shows the delay time in ms, and the vertical axis shows the modulus of the complex envelope of the impulse response estimate in relative units. Both estimates are normalized by the common coefficient that reduces the maximum response amplitude to unity at 30.51 hours (brown curve). The signals were received by station A (see Fig. 1).

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5. Fig. 4. Examples of soft decoding decisions (real and imaginary parts) for one signal using two algorithms. Blue and red dots denote symbols that have values ​​of −1 and 1 in the original sequence, respectively. (a) — Without equalization, the bit error rate BER = 0.04, rms. decoding error −3.3 dB, (b) — with MMSE-DFE equalization, the fraction of bit errors of decoding BER = 0.014, the rms decoding error is −6 dB.

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6. Fig. 5. (a) — Dependence of the amplitude of the channel impulse response function on time. The horizontal axis is the time in hours from the beginning of the experiment, the vertical axis is the propagation delay in ms. The numbers 0, 1, 2 and 3 on the right along the vertical axis mark the delays of the groups of rays reflected from the surface 0, 1, 2 and 3 times, respectively. The amplitude level is shown in color, the scale in dB relative to conventional units. (b) — Vertical profiles of temperature and sound speed near the acoustic path before the beginning of the experiment. (c) — Ray pattern of sound propagation for the profile in panel (b).

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7. Fig. 6. (a) — Empirical densities of arrival amplitudes of ray groups with one (designated as P1, blue columns), two (P2, brown columns) and three (P3, yellow columns) reflections from the surface. The amplitudes of all arrivals are normalized by a common coefficient that reduces the maximum recorded amplitude of arrival P1 to unity. (b) — Dependence of arrival amplitude P2 on arrival amplitude P1. (c) — Dependence of arrival amplitude P3 on arrival amplitude P1. All amplitudes refer to the reference estimate of the impulse response.

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8. Fig. 7. (a) — Variability of the bit error rate (BER) of decoding signals received by station A (see Fig. 1) during the experiment: red dots are the result of decoding without equalization, blue dots are with MMSE-DFE. The horizontal axis shows the time from the beginning of the experiment. Rectangles mark the periods of BER increase of 3.5–7 h, 15–17 h and 17.1–21 h from the beginning of the experiment. (b) — Corresponding empirical BER distribution functions. (c) — Empirical density functions of the distribution of the RMSE level of the decoding error (RMSE): red columns — without equalization, blue columns — with MMSE-DFE. (g), (e), (e) — Similar results for signals received by station B.

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9. Fig. 8. (a) — Amplitude of the main maximum in the estimate of the channel impulse response corresponding to a quadruple of rays with a single reflection from the surface, level in dB relative to conventional units, signals received by station A, (b) — RMSE level. soft decision error (RMSE) using the MMSE-DFE algorithm in dB, signals received by station A, (c) and (d) — similar results for signals received by station B. In all panels, blue dots are measurements for single signals, brown curves are the moving average for 1 hour.

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10. Fig. 9. (a) — Dependence of the rms decoding error using the MMSE-DFE equalizer on the amplitude of the main maximum of the reference estimate of the impulse response, corresponding to the quadruple of rays single reflected from the surface. The estimates of the amplitude of the maximum were obtained for the entire signal without taking into account high-frequency fluctuations. (b) — Dependence of the coefficient of variation of fluctuations of the main maximum in the instantaneous estimate of the impulse response on the amplitude of the main maximum of the reference estimate of the impulse response. (c) — Dependence of the rms coefficient decoding errors using the MMSE-DFE equalizer, on the coefficient of variation of the main maximum of the instantaneous estimate of the impulse response. The local relative density of points corresponding to individual transmissions of communication signals is shown in color.

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11. Fig. 10. (a) — Dependence of the decoding error rms using the MMSE-DFE equalizer on the arrival amplitude of the ray group with two reflections from the surface (P2). The amplitude estimates were obtained for the entire signal without taking into account high-frequency fluctuations. (b) — Dependence of the decoding error rms coefficient with MMSE-DFE on the variation coefficient of the P2 arrival amplitude in the instantaneous impulse response estimate. (c) — Dependence of the variation coefficient of the P2 arrival fluctuations in the instantaneous impulse response estimate on the P2 amplitude in the reference impulse response estimate. (g), (d), (e) — Similar dependencies for the arrival of a ray group with three reflections from the surface (P3). The local relative density of points corresponding to individual communication signal packets is shown in color.

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12. Fig. 11. (a) — Sound velocity profiles calculated based on STD probe measurements in the vicinity of the signal propagation path. (b) — Dependence of the amplitude of the main maximum in the estimate of the impulse response envelope on the porosity of the liquid bottom for the same sound velocity profiles in the water layer (in dB relative to conventional units). The dotted lines indicate the porosity values ​​for which the influence of the current velocity profile variability was modeled (Fig. 12).

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13. Fig. 12. (a) — Variability of the current velocity component in the direction from station B to station A based on ADCP measurements; the dots on the horizontal axis mark the time readings for which the effect of the current on the impulse response variability was modeled (see Fig. 12). (b) — Depth-averaged current velocity in the direction from station B to station A; the blue curve — measurements by the ADCP profiler; the brown curve — the result of reconstruction based on the difference in the delays of the main arrival in the envelope of the impulse response estimate corresponding to the group of rays with a single reflection from the surface. (c) — Example of extrapolation of the vertical profile of current velocity; the solid line — the measured profile in the 1.5–19.5 m layer; the dots mark the measurement horizons; the dotted line — the extrapolation segments to the surface and to the bottom. (d) — Sound velocity profile calculated based on STD measurements (solid line), and the same profile with corrections for the current corresponding to the profile shown in panel (c) for propagation in opposite directions (dashed lines). (d) — Dependence of the depth-averaged current velocity in the 1.5–19.5 m layer (measurement data) on the depth-averaged velocity in the extrapolated profiles.

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14. Fig. 13. The range of variability of the amplitude of the main maximum in the reference estimate of the impulse response, caused by adding a correction for the current velocity to the vertical profile of the sound velocity. (a) — When the signal propagates from station B to station A, (b) — when propagating in the opposite direction. The numbers of the sound velocity profiles correspond to Fig. 11. The time readings of the considered current velocity profiles are shown in Fig. 12a.

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