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With the advances of ship noise reduction technology, the working frequency of the passive sonar must be reduced in order to detect a target. For the conventional array, it requires a large array aperture, comparable to the wavelength, in order to achieve an acceptable angular resolution. Arrays of small physical size with high angular resolution are thus attractive for low-frequency direction-of-arrival estimation of underwater sound source. In this paper, we consider a 33 uniform rectangular array which consists of vector sensors with inter-sensor spacing much smaller than the wavelength. A broadband super-directive beamforming method is proposed for this vector sensor array, which extracts multi-pole modes of different orders from the spatial differentials of the sound field. By normalizing the amplitudes of the multi-pole modes, frequency invariant mode functions can be obtained, which are used to build the desired beam pattern, despite the Rayleigh limit on the achievable angular resolution. Vector sensors are used to replace the pressure difference operation, thus to achieve a desirable beam pattern, the order of spatial differential will be reduced. In other words, for the same array configuration, using the vector sensors provides higher directivity than using the pressure sensor. To concentrate on the sources, and to minimize all hindrances from around circumference, a suitable beam pattern is constructed as an example to analysis. To verify the algorithm, a prototype is built and tested in a water tank. Comparisons are carried out between the actually synthesized beam patterns and the theoretical ones. The experimental results show good agreement with the theoretical results, and that the directivity increases with the multi-pole mode order increasing, at the expense of lower robustness. The performances for different values of ka are also investigated, where k is the wave number and a denotes the inter-sensor spacing. Simulation results show that when the inter-sensor spacing is no more than one-sixth of the incident wave length, the error introduced by the approximations for muti-pole mode extraction can be neglected. It should be noted that this result of the inter-sensor spacing still applicable when considering array gain, showing that the array is insensitive to uncorrelated noise while preserving a relatively high array gain. Finally, the influence of the underwater acoustic waveguide on the array performance is analyzed. Simulations and experimental tests show that due to the small array aperture, the waveguide effects on the array performance are limited.
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Keywords:
- super-directive vector array /
- direction-of-arrival estimation for low-frequency underwater sound sources /
- multi-pole modes
[1] Yang S E 2012 Acoustics 2012 Hong Kong Conference and Exhibition Hong Kong SAR, China, May 13-18, 2012 p336
[2] Wang D Z, Shang E C 2013 Underwater Acoustics (Beijing: Science Press) pp545-549 (in Chinese) [汪徳昭, 尚尔昌 2013 水声学 (北京:科学出版社) 第 545-549 页]
[3] Wang Y, Yang Y X, Ma Y L, He Z Y 2014 J. Acoust. Soc. Am. 136 1712
[4] Parsons A T 1987 J. Acoust. Soc. Am. 82 179
[5] Olson H F 1946 J. Acoust. Soc. Am. 17 192
[6] Uzsoky M, Solymar L 1956 Acta Phys. 6 185
[7] Morris M L, Jensen M A, Wallance J W 2005 IEEE Trans. Antennas Propag. 53 2850
[8] Teutsch H, Kellermann W 2006 J. Acoust. Soc. Am. 120 2724
[9] Teutsch H 2007 Modal Array Signal Processing: Principles and Applications of Acoustic Wavefield Decomposition (Berlin: Springer-Verlag) pp33-113
[10] Elko G W 2004 Differential Microphone Arrays (Berlin: Springer-Verlag) pp33-94
[11] Thompson S C 2003 Hearing J. 56 14
[12] Chung K, Zeng F G, Acker K N 2006 J. Acoust. Soc. Am. 120 2216
[13] Benesty J, Souden M, Huang Yiteng 2012 IEEE Trans. Audio Speech Lang. Process. 20 699
[14] Benesty J, Chen J 2012 Study and Design of Differential Microphone Arrays (Berlin: Springer-Verlag) pp41-94
[15] Griffiths J W R, Griffiths H D, Cowan C F N, Eiges R, Rafik T 1994 Oceans 94/OSATES Conference on Oceans Engineering for Todays Technology and Tomorrows Preservation Brest, France, Sep. 13-16, 1994 p223
[16] Meyer J 2001 J. Acoust. Soc. Am. 109 185
[17] Ma Y L, Yang Y X, He Z Y, Yang K D, Sun C, Wang Y M 2013 IEEE Trans. Ind. Electron. 60 203
[18] Elko G W 1999 J. Acoust. Soc. Am. 105 1098
[19] Buck M 2002 Eur. T. Telecommun. 13 115
[20] Abhayapala T D, Gupta A 2010 J. Acoust. Soc. Am. 127 EL227
[21] Sena E D, Hacihabiboglu H, Cvetkovic Z 2012 IEEE Trans. Audio Speech Lang. Process. 20 162
[22] Zhang T W, Yang K D, Ma Y L 2010 Chin. Phys. B 19 124301
[23] Shi J, Yang D S, Shi S G 2012 Acta Phys. Sin. 61 124302 (in Chinese) [时洁, 杨德森, 时胜国 2012 物理学报 61 124302]
[24] Shi J, Yang D S, Shi S G, Zhu Z R 2016 Acta Phys. Sin. 65 124302 (in Chinese) [时洁, 杨德森, 时胜国, 朱中锐 2016 物理学报 65 024302]
[25] Sun G Q, Li Q H 2004 Acta Acust. 29 491 (in Chinese) [孙贵青, 李启虎 2004 声学学报 29 491]
[26] Guo J Y, Yang S E, Piao S C 2015 170th Metting Acoustical Society of America Jacksonville, Florida, United States, Nov. 2-6, 2015 p1737
[27] Zou N, Nehorai A 2009 IEEE Trans. Signal Process. 57 3041
[28] Gur B 2014 J. Acoust. Soc. Am. 135 3463
[29] Nehorai A, Paldi E 1994 IEEE Trans. Signal Process. 42 2481
[30] Smith K B, Vincent A, Leijen V 2007 J. Acoust. Soc. Am. 122 370
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[1] Yang S E 2012 Acoustics 2012 Hong Kong Conference and Exhibition Hong Kong SAR, China, May 13-18, 2012 p336
[2] Wang D Z, Shang E C 2013 Underwater Acoustics (Beijing: Science Press) pp545-549 (in Chinese) [汪徳昭, 尚尔昌 2013 水声学 (北京:科学出版社) 第 545-549 页]
[3] Wang Y, Yang Y X, Ma Y L, He Z Y 2014 J. Acoust. Soc. Am. 136 1712
[4] Parsons A T 1987 J. Acoust. Soc. Am. 82 179
[5] Olson H F 1946 J. Acoust. Soc. Am. 17 192
[6] Uzsoky M, Solymar L 1956 Acta Phys. 6 185
[7] Morris M L, Jensen M A, Wallance J W 2005 IEEE Trans. Antennas Propag. 53 2850
[8] Teutsch H, Kellermann W 2006 J. Acoust. Soc. Am. 120 2724
[9] Teutsch H 2007 Modal Array Signal Processing: Principles and Applications of Acoustic Wavefield Decomposition (Berlin: Springer-Verlag) pp33-113
[10] Elko G W 2004 Differential Microphone Arrays (Berlin: Springer-Verlag) pp33-94
[11] Thompson S C 2003 Hearing J. 56 14
[12] Chung K, Zeng F G, Acker K N 2006 J. Acoust. Soc. Am. 120 2216
[13] Benesty J, Souden M, Huang Yiteng 2012 IEEE Trans. Audio Speech Lang. Process. 20 699
[14] Benesty J, Chen J 2012 Study and Design of Differential Microphone Arrays (Berlin: Springer-Verlag) pp41-94
[15] Griffiths J W R, Griffiths H D, Cowan C F N, Eiges R, Rafik T 1994 Oceans 94/OSATES Conference on Oceans Engineering for Todays Technology and Tomorrows Preservation Brest, France, Sep. 13-16, 1994 p223
[16] Meyer J 2001 J. Acoust. Soc. Am. 109 185
[17] Ma Y L, Yang Y X, He Z Y, Yang K D, Sun C, Wang Y M 2013 IEEE Trans. Ind. Electron. 60 203
[18] Elko G W 1999 J. Acoust. Soc. Am. 105 1098
[19] Buck M 2002 Eur. T. Telecommun. 13 115
[20] Abhayapala T D, Gupta A 2010 J. Acoust. Soc. Am. 127 EL227
[21] Sena E D, Hacihabiboglu H, Cvetkovic Z 2012 IEEE Trans. Audio Speech Lang. Process. 20 162
[22] Zhang T W, Yang K D, Ma Y L 2010 Chin. Phys. B 19 124301
[23] Shi J, Yang D S, Shi S G 2012 Acta Phys. Sin. 61 124302 (in Chinese) [时洁, 杨德森, 时胜国 2012 物理学报 61 124302]
[24] Shi J, Yang D S, Shi S G, Zhu Z R 2016 Acta Phys. Sin. 65 124302 (in Chinese) [时洁, 杨德森, 时胜国, 朱中锐 2016 物理学报 65 024302]
[25] Sun G Q, Li Q H 2004 Acta Acust. 29 491 (in Chinese) [孙贵青, 李启虎 2004 声学学报 29 491]
[26] Guo J Y, Yang S E, Piao S C 2015 170th Metting Acoustical Society of America Jacksonville, Florida, United States, Nov. 2-6, 2015 p1737
[27] Zou N, Nehorai A 2009 IEEE Trans. Signal Process. 57 3041
[28] Gur B 2014 J. Acoust. Soc. Am. 135 3463
[29] Nehorai A, Paldi E 1994 IEEE Trans. Signal Process. 42 2481
[30] Smith K B, Vincent A, Leijen V 2007 J. Acoust. Soc. Am. 122 370
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