Abstract
High-performance sonar systems mostly combine a large sensor array and an efficient beamformer for enhancing the overall detection capabilities and estimation of Direction of Arrival (DoA) of the acoustic signal released from underwater targets in the ocean. The array geometry and the number of elements have direct influences on the beam width and the signal to noise ratio but increase the complexity in terms of hardware and computational requirement. Even when such hardware complexities are accommodated in complex systems, the performance of such systems is often par below its expected level because of the limitations of the beamformer. The efficacy of the beamforming lies in obtaining a narrow beamwidth for the main lobe with minimum sidelobe levels (SLL) while keeping the element utilization factor as maximum as possible. This in turn demands proper optimization over array parameters and beamforming methods. Several optimization techniques have been established over the years and practised in a variety of sonar systems. Statistical array processing with nested and sparse array concepts with virtual elements offer effective solutions to these challenges. This article proposes an approach comprising a novel product beamforming concept that uses the idea of destructive interference in tandem with the nested array concept to demonstrate that better sonar performance can be achieved. The former helps to minimize the SLL without affecting the veracity of the main lobe, while the latter helps to reduce the requirement of a large number of sensors and thereby reduce the system complexity.
Similar content being viewed by others
Availability of data and material
The authors confirm that the data supporting the findings of this study are available within the article. However, any datasets generated and/or analysed during the current study are available from the corresponding author on reasonable requests.
References
Abraham, D. A. (2019). Underwater Acoustic Signal Processing: Modeling, Detection, and Estimation, 1st ed. Switzerland: Springer
Agarwal, R. C., Chander, V., & Pillai, S. P. (1993). Issues in the design of towed array sonar systems. IETE Technical Review, 10(2), 93–99.
Ahrens, J., Rabenstein, R., & Spors, S. (2014). Sound field synthesis for audio presentation. Acoustics Today, 10(2), 15–25.
Ai, W., Xiong, J., & Zhang, X. (2016). Normal-mode based MUSIC for bearing estimation in shallow water using acoustic vector sensors. In International Conference on Mechatronics Engineering and Information Technology (ICMEIT 2016) (pp. 191–196). Atlantis Press.
Aksoy, E., & Afacan, E. (2010). Thinned non-uniform amplitude time-modulated linear arrays. IEEE Antennas Wireless Propagation Letters, 9, 514–517.
Ariananda, D. D., & Leus, G. (2013). Direction of arrival estimation for more correlated sources than active sensors. Signal Processing, 93(12), 3435–3448.
Butler, J. L., & Sherman, C. H. (2016). Transducers and Arrays for Underwater Sound, 2nd ed. Switzerland: Springer.
Chavali, V., Wage, K. E., & Buck, J. R. (2018). Multiplicative and min processing of experimental passive sonar data from thinned arrays. Journal of the Acoustical Society of America, 144(6), 3262–3274.
Cox, H., & Lai, H. (2004). Sub-aperture beam-based adaptive beamforming for large dynamic arrays. In Conference Record of the Thirty-Eighth Asilomar Conference on Signals, Systems and Computers-2004. Vol. 2, pp. 2355–2358. IEEE. https://doi.org/10.1109/ACSSC.2004.1399590
Eldar, Y., & Kutyniok, G. (2012). Compressed Sensing: Theory and Applications. Cambridge, UK: Cambridge University Press.
Elnashar, A. (2008). Efficient implementation of robust adaptive beamforming based on worst-case performance optimization. IEEE Transactions on Signal Processing, 2(4), 381–393.
Fazli, S., & Kleeman, L. (2005). Sensor design and signal processing for an advanced sonar ring. Robotica, 24, 433–446. https://doi.org/10.1017/S0263574705002432
Filipovic, V., Nedic, N., & Stojanovic, V. (2011). Robust identification of pneumatic servo actuators in the real situations. Forschung Im Ingenieurwesen, 75, 183–196.
Fischer, G., Davis, A. J., & Kasturi, P. (2007). A custom chip set for a frequency-agile high-resolution sonar array. IEEE Journal of Oceanic Engineering, 32(2), 416–427.
Freethy, S. J., Shevchenko, V. F., & Vann, R. G. L. (2012). Optimization of wide field interferometric arrays via simulated annealing of a beam efficiency function. IEEE Transactions on Antennas and Propagation, 60, 5442–5446.
Gaudette, J. E., & Simmons, J. A. (2014). Observing the invisible: using microphone arrays to study bat echolocation. Acoustics Today, 10(3), 16–25.
George, A. D., Markwell, J., & Fogarty, R. (2000). Real-time sonar beamforming on high-performance distributed computers. Parallel Computing, 26, 1231–1252.
Ghayoula, R., Fadlallah, N., Gharsallah, A., & Rammal, M. (2008). Design, modelling, and synthesis of radiation pattern of intelligent antenna by artificial neural networks. ACES Journal, 23, 336–344.
Glegg, S. A. L., Olivieri, M. P., Coulson, R. K., & Smith, S. M. (2001). A passive sonar system based on an autonomous underwater vehicle. IEEE Journal of Oceanic Engineering, 26(4), 700–710.
Goswami, B., & Mandal, D. (2013). A genetic algorithm for the level control of nulls and side lobes in linear antenna arrays. Journal of King Saud University-Computer and Information Sciences, 25, 117–126.
Gu, Y., Goodman, N. A., Hong, S., & Li, Y. (2014). Robust adaptive beamforming based on interference matrix sparse reconstruction. Signal Processing, 96, 375–381.
Hoctor, R. T., & Kassam, S. A. (1990). The unifying role of the coarray in aperture synthesis for coherent and incoherent imaging. Proceedings of the IEEE, 78(4), 735–752.
Huissoon, J. P., & Moziar, D. M. (1991). Optimization of the sound pressure level pattern for a curved array sonar transducer. Journal of Sound and Vibration, 149(1), 125–136.
Jackson, H. A., Needham, W. D., & Sigman, D. E. (1989). Bottom bounce array sonar submarine (BBASS). Naval Engineers Journal., 101, 59–72.
Karen Collins, (2013). Playing with sound: A theory of interacting with sound and music in video games. Cambridge, MA: MIT Press.
Khodier, M. M., & Christodoulou, C. G. (2005). Linear array geometry synthesis with minimum side lobe level and null controlling using particle swarm optimization. IEEE Transactions on Antennas and Propagation, 53(8), 2674–2679.
Kim, S., Chang, K., Park, D. C., Lee, S. M., & Lee, S. K. (2017). A systematic approach to engine sound design for enhancing sound character by active sound design. SAE International Journal of Passenger Cars-Mechanical Systems., 10(3), 691–702.
Kleeman, L., & Kuc, R. (1994). An optimal sonar array for target localization and classification. In Proceedings of the 1994 IEEE International Conference on Robotics and Automation, Vol. 4, pp. 3130–3135. IEEE. https://doi.org/10.1109/ROBOT.1994.351089
Liang, Lei, Sun, Jie, Li, Hailin, Liu, Jialing, Jiang, Yachao, & Zhou, Jianjiang. (2019). Research on side lobe suppression of time-modulated sparse linear array based on particle swarm optimization. International Journal of Antennas and Propagation, 7130106, 14.
Lorenz, R. G., & Boyd, S. P. (2005). Robust minimum variance beamforming. IEEE Transactions on Signal Processing, 53(5), 1684–1696.
Mandal, S. K., Mahanti, G. K., & Rowdra, G. (2013). Differential evolution algorithm for optimizing the conflicting parameters in time-modulated linear array antennas. Progress in Electromagnetics Research B, 51, 101–118.
Mucci, R. A. (1984). A comparison of efficient beamforming algorithms. IEEE Transactions on Acoustics, Speech, & Signal Processing, ASSP., 32(3), 548–558.
Ong, P. (2014). Adaptive cuckoo search algorithm for unconstrained optimization. The Science World Journal, 2014, 1–8.
Pal, P., & Vaidyanathan, P. P. (2010). Nested arrays: a novel approach to array processing with enhanced degrees of freedom. IEEE Transactions on Signal Processing, 58(8), 4167–4181.
Pekeris, C. L. (1948). Theory of propagation of explosive sound in shallow water. In Propagation of Sound in the Ocean, The Geological Society of America Memoir 27 (pp. 1–112). https://doi.org/10.1130/MEM27
Pyzdek, A. T., & Culver, R. L. (2014). Processing methods for coprime arrays in complex shallow water environments. Journal of the Acoustical Society of America, 135(4), 2392.
Robinson, J., & Rahmat-Samii, Y. (2004). Particle swarm optimization in electromagnetic. IEEE Transactions on Antennas and Propagation, 52, 397–407.
Somasundaram, S. D. (2013). Wideband robust capon beamforming for passive sonar. IEEE Journal of Oceanic Engineering, 38(2), 308–322.
Somasundaram, S. D., & Parsons, N. H. (2011). Evaluation of robust capon beamforming for passive sonar. IEEE Journal of Oceanic Engineering, 36(4), 686–695.
Tao, H., Li, X., Paszke, W., Stojanovic, V., & Yang, H. (2021). Robust PD-type iterative learning control for discrete systems with multiple time-delays subjected to polytopic uncertainty and restricted frequency-domain. Multidimensional Systems and Signal Processing, 32, 671–692.
Tomkiewicz, S. M., Fuller, M. R., Kie, J. G., & Bates, K. K. (2010). Global positioning system and associated technologies in animal behavior and ecological research. Philosophical Transactions of the Royal Society B, 365, 2163–2176.
Van Trees, H. L. (2002). Optimum Array Processing – Part IV of Detection, Estimation, and Modulation Theory. New York: John Wiley & Sons.
Urick, R. J. (2013). Principles of Underwater Sound, 3rd ed. Los Altos, California: Peninsula Publishing.
Vaccaro, R. J. (1998). The past, present, and future of underwater acoustic signal processing. IEEE Signal Processing Magazine, 15, 21–51.
Vaidyanathan, P. P., & Pal, P. (2011). Sparse sensing with co-prime samplers and arrays. IEEE Transactions on Signal Processing, 59(2), 573–586.
Vigness-Raposa, K. J., Scowcroft, G. A., Morin, H., & Knowlton, C. (2014). Underwater acoustics for everyone. Acoustics Today, 10(2), 50–59.
Vijayan Pillai, S., Santhanakrishnan, T., & Rajesh, R. (2021). An efficient destructive interference-based side lobe suppression method in SONAR beamforming. Advances in Military Technology, 16(1), 107–120.
Wachowski, N., & Azimi-Sadjadi, M. R. (2011). A new synthetic aperture sonar processing method using coherence analysis. IEEE Journal of Oceanic Engineering, 36(4), 665–678.
Wagner, D. H., Mylander, W. C., & Sanders, T. J. (2002). Naval Operations Analysis, 3rd ed. Annopolis, United States: Naval Institute Press.
Waite, A. D. (2002). Sonar for Practicing Engineers, 3rd ed. New York: John Wiley & Sons Inc.
Wallace, M.F., Mulvana, H., Marin, P., Mayne, K., Walsh, M. P., Wright, R., Marsh, R., Spence, B., Solomonidis, S., & Cochran, S. (2007). Parametric array design and characterization for underwater sonar and medical strain imaging applications. In 2007 IEEE Ultrasonics Symposium (pp. 305–308). IEEE. https://doi.org/10.1109/ULTSYM.2007.87
Wang, W., & Zhu, C. (2016). Nested array receiver with time-delayers for joint target range and angle estimation. IET Radar, Sonar & Navigation, 10(8), 1384–1393.
Wei, T., Li, X., & Stojanovic, V. (2021). Input-to-state stability of impulsive reaction–diffusion neural networks with infinite distributed delays. Nonlinear Dynamics, 103, 1733–1755.
Wojan, Z. (2001). Selected problems of the design of the multi-element sonar arrays. Hydroacoustics, 4, 253–256.
Xin, Xilin, Yidong, Tu., Stojanovic, Vladimir, Wang, Hai, Shi, Kaibo, He, Shuping, & Pan, Tianhong. (2021). Online reinforcement learning multiplayer non-zero sum games of continuous-time Markov jump linear systems. Applied Mathematics and Computation, 412(2022), 126537.
Yang, S., Gan, Y. B., & Qing, A. (2002). Sideband suppression in time-modulated linear arrays by the differential evolution algorithm. IEEE Antennas Wireless Propagation Letters, 1, 173–175.
Yang, T. C. (2020). Deconvolution of decomposed conventional beamforming. Journal of the Acoustical Society of America, 148(2), EL195–EL201.
Yang, X. S., & Deb, S. (2013). Multi-objective cuckoo search for design optimization. Computer & Operations Research, 40, 1616–1624.
Zaharis, Z. D., Gotsis, K. A., & Sahalos, J. N. (2012). Adaptive beamforming with low side lobe level using neural networks trained by mutated boolean PSO. Progress in Electromagnetics Research, 127, 139–154.
Zangene, A., Dalili Oskouei, H. R., & Nourhoseini, M. (2014). Reduction of side lobe level in non-uniform circular antenna arrays using the simulated annealing algorithm. Journal of Electrical Electronics Engineering Research, 6(2), 6–12.
Zhou, H., Hu, G., Shi, J., & Feng, Z. (2018). Multi-frequency based direction-of-arrival estimation for 2q-level nested radar & sonar arrays. Sensors, 3385(18), 1–16.
Zhu, C., Chen, H., & Shao, H. (2015). Joint phased-MIMO and nested-array beamforming for increased degrees-of-freedom. International Journal of Antennas and Propagation, 989517, 11. https://doi.org/10.1155/2015/989517
Zhu, Q., Yang, S., Zheng, L., & Nie, Z. (2012). Design of a low side lobe time modulated linear array with uniform amplitude and sub-sectional optimized time steps. IEEE Transactions on Antennas Propagation, 60, 4436–4439.
Ziomek, L.J. (2019). An Introduction to Sonar Systems Engineering. Boca Raton, Florida: CRC Press Inc.
Acknowledgements
The authors thank Dr. Samir V. Kamat, Director General of Naval Systems and Materials, DRDO, Ministry of Defence for the support and permission to publish the paper in the Multidimensional Systems and Signal Processing Journal.
Funding
The authors did not receive support from any organization for the submitted work.
Author information
Authors and Affiliations
Contributions
S. Vijayan Pillai and T. Santhanakrishnan conceived the research idea. S. Vijayan Pillai and T. Santhanakrishnan planned and designed the methodology. S. Vijayan Pillai and N. Suresh Kumar designed the required mathematics and wrote the simulation algorithms in MATLAB. T. Santhanakrishnan and R. Rajesh coordinated the research and conceived the ocean applications. T. Santhanakrishnan and N. Suresh Kumar carried out the data analysis. T. Santhanakrishnan wrote the manuscript with share contributions from S. Vijayan Pillai, N. Suresh Kumar and R. Rajesh. All the authors contributed to the manuscript, reviewed and have approved the submission of the final version of the manuscript.
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that there are no conflicts of interest that are relevant to the content of this article.
Code availability
Not applicable.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Pillai, S.V., Santhanakrishnan, T., Kumar, N.S. et al. Product beamforming and nested array in tandem for enhanced sonar performance. Multidim Syst Sign Process 33, 879–898 (2022). https://doi.org/10.1007/s11045-022-00825-z
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11045-022-00825-z