{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,23]],"date-time":"2026-01-23T11:52:34Z","timestamp":1769169154441,"version":"3.49.0"},"reference-count":56,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2017,10,11]],"date-time":"2017-10-11T00:00:00Z","timestamp":1507680000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000006","name":"Office of Naval Research","doi-asserted-by":"publisher","award":["N000141712476"],"award-info":[{"award-number":["N000141712476"]}],"id":[{"id":"10.13039\/100000006","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1550294"],"award-info":[{"award-number":["1550294"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Uniformly-spaced apertures or subapertures of large, densely-sampled, discrete linear receiver arrays are often used in remote sensing to increase the signal-to-noise ratio (SNR) by coherent beamforming that reduces noise coming from directions outside the signal beam. To avoid spatial aliasing or the presence of grating lobes in real spatial directions, the uniformly-spaced array inter-element spacing d sets a limit on the maximum frequency      f max  &lt; c \/ 2 d     of signals suitable for beamforming with the array, where c is the medium\u2019s wave propagation speed. Here, we show that a nonuniformly-spaced array, for instance, formed by combining multiple uniformly-spaced subapertures of a nested linear array, can significantly enhance the array angular resolution while simultaneously avoiding dominant grating lobes in real angular space, even for signals with frequencies beyond the maximum that the array is designed for. The array gain, beam width, and maximum grating lobe height are quantified for the Office of Naval Research Five Octave Research Array (ONR-FORA) for various combinations of its uniformly-spaced subapertures, leading to nonuniformly-spaced subarrays. Illustrative examples show angular resolution enhancement provided by the nonuniformly-spaced ONR-FORA subarrays over that of its uniformly-spaced individual subaperture counterparts in both active and passive ocean acoustic waveguide remote sensing, drawn from measurements in the Gulf of Maine 2006 Experiment.<\/jats:p>","DOI":"10.3390\/rs9101036","type":"journal-article","created":{"date-parts":[[2017,10,11]],"date-time":"2017-10-11T12:17:47Z","timestamp":1507724267000},"page":"1036","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":23,"title":["Angular Resolution Enhancement Provided by Nonuniformly-Spaced Linear Hydrophone Arrays in Ocean Acoustic Waveguide Remote Sensing"],"prefix":"10.3390","volume":"9","author":[{"given":"Delin","family":"Wang","sequence":"first","affiliation":[{"name":"Department of Electrical and Computer Engineering, Northeastern University, 360 Huntington Ave, Boston, MA 02115, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Purnima","family":"Ratilal","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, Northeastern University, 360 Huntington Ave, Boston, MA 02115, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,10,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"366","DOI":"10.1038\/nature16960","article-title":"Vast assembly of vocal marine mammals from diverse species on fish spawning ground","volume":"531","author":"Wang","year":"2016","journal-title":"Nature"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1734","DOI":"10.1126\/science.1169441","article-title":"Critical population density triggers rapid formation of vast oceanic fish shoals","volume":"323","author":"Makris","year":"2009","journal-title":"Science"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"660","DOI":"10.1126\/science.1121756","article-title":"Fish population and behavior revealed by instantaneous continental shelf-scale imaging","volume":"311","author":"Makris","year":"2006","journal-title":"Science"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Wang, D., Huang, W., Garcia, H., and Ratilal, P. (2016). Vocalization source level distributions and pulse compression gains of diverse baleen whale species in the Gulf of Maine. Remote Sens., 8.","DOI":"10.3390\/rs8110881"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Huang, W., Wang, D., and Ratilal, P. (2016). Diel and Spatial Dependence of Humpback Song and Non-Song Vocalizations in Fish Spawning Ground. Remote Sens., 8.","DOI":"10.3390\/rs8090712"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Huang, W., Wang, D., Garcia, H., God\u00f8, O.R., and Ratilal, P. (2017). Continental Shelf-Scale Passive Acoustic Detection and Characterization of Diesel-Electric Ships Using a Coherent Hydrophone Array. Remote Sens., 9.","DOI":"10.3390\/rs9080772"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"680","DOI":"10.1121\/1.4726073","article-title":"Scattering from extended targets in range-dependent fluctuating ocean-waveguides with clutter from theory and experiments","volume":"132","author":"Jagannathan","year":"2012","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"137","DOI":"10.3354\/meps08266","article-title":"Ocean acoustic waveguide remote sensing (OAWRS) of marine ecosystems","volume":"395","author":"Jagannathan","year":"2009","journal-title":"Mar. Ecol. Prog. Ser."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1865","DOI":"10.1121\/1.408702","article-title":"Long-range backscatter from the Mid-Atlantic Ridge","volume":"95","author":"Makris","year":"1994","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"3547","DOI":"10.1121\/1.412440","article-title":"Deterministic reverberation from ocean ridges","volume":"97","author":"Makris","year":"1995","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2649","DOI":"10.1121\/1.4932547","article-title":"Simultaneous localization of multiple broadband non-impulsive acoustic sources in an ocean waveguide using the array invariant","volume":"138","author":"Gong","year":"2015","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Gong, Z., Jain, A.D., Tran, D., Yi, D.H., Wu, F., Zorn, A., Ratilal, P., and Makris, N.C. (2014). Ecosystem scale acoustic sensing reveals humpback whale behavior synchronous with herring spawning processes and re-evaluation finds no effect of sonar on humpback song occurrence in the Gulf of Maine in Fall 2006. PLoS ONE, 9.","DOI":"10.1371\/journal.pone.0104733"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"104","DOI":"10.1121\/1.3268595","article-title":"Low-frequency target strength and abundance of shoaling Atlantic herring (Clupea harengus) in the Gulf of Maine during the Ocean Acoustic Waveguide Remote Sensing 2006 Experiment","volume":"127","author":"Gong","year":"2010","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1977","DOI":"10.1121\/1.1799252","article-title":"Long range acoustic imaging of the continental shelf environment: The Acoustic Clutter Reconnaissance Experiment 2001","volume":"117","author":"Ratilal","year":"2005","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"EL71","DOI":"10.1121\/1.3554707","article-title":"Long-range acoustic communication in deep water using a towed array","volume":"129","author":"Song","year":"2011","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"709","DOI":"10.1109\/JOE.2005.862130","article-title":"Geoacoustic parameter extraction using reverberation data from the 2000 Boundary Characterization Experiment on the Malta Plateau","volume":"30","author":"Preston","year":"2005","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_17","unstructured":"Kay, S.M. (1998). Fundamentals of Statistical Signal Processing Vol. II: Detection Theory, Prentice Hall PTR."},{"key":"ref_18","unstructured":"Johnson, D.H., and Dudgeon, D.E. (1993). Array Signal Processing: Concepts and Techniques, Prentice Hall PTR."},{"key":"ref_19","unstructured":"Urick, R. (1983). Principles of Underwater Sound, McGraw Hill."},{"key":"ref_20","unstructured":"Tolstoy, I., and Clay, C. (1987). Ocean Acoustics: Theory and Experiment in Underwater Sound, American Institute of Physics."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1802","DOI":"10.1121\/1.400201","article-title":"Optimal time-domain beamforming with simulated annealing including application of apriori information","volume":"88","author":"Kuperman","year":"1990","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1851","DOI":"10.1121\/1.406700","article-title":"Applications of optimal time-domain beamforming","volume":"93","author":"Collins","year":"1993","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1109\/TAC.1983.1103230","article-title":"Utilization of modified polar coordinates for bearings-only tracking","volume":"28","author":"Aidala","year":"1983","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"3705","DOI":"10.1121\/1.4821989","article-title":"Comparing passive source localization and tracking approaches with a towed horizontal receiver array in an ocean waveguide","volume":"134","author":"Gong","year":"2013","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"336","DOI":"10.1121\/1.2139074","article-title":"The array invariant","volume":"119","author":"Lee","year":"2006","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Becker, K., and Preston, J. (2003, January 22\u201326). The ONR five octave research array (FORA) at Penn State. Proceedings of the IEEE OCEANS 2003, San Diego, CA, USA.","DOI":"10.1109\/OCEANS.2003.178321"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Van Trees, H. (2002). Detection, Estimation, and Modulation Theory, Part IV Optimum Array Processing, Wiley-Interscience. Detection, Estimation, and Modulation Theory.","DOI":"10.1002\/0471221104"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1701","DOI":"10.1088\/0957-0233\/16\/9\/001","article-title":"High reynolds number experimentation in the US navy\u2019s William B Morgan Large Cavitation Channel","volume":"16","author":"Etter","year":"2005","journal-title":"Meas. Sci. Technol."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1121\/1.2932579","article-title":"SLITA: A new slim towed array for AUV applications","volume":"123","author":"Maguer","year":"2008","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"4167","DOI":"10.1109\/TSP.2010.2049264","article-title":"Nested arrays: A novel approach to array processing with enhanced degrees of freedom","volume":"58","author":"Pal","year":"2010","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"4694","DOI":"10.1109\/TSP.2012.2203814","article-title":"Nested arrays in two dimensions, part I: Geometrical considerations","volume":"60","author":"Pal","year":"2012","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"573","DOI":"10.1109\/TSP.2010.2089682","article-title":"Sparse sensing with co-prime samplers and arrays","volume":"59","author":"Vaidyanathan","year":"2011","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"964","DOI":"10.1049\/iet-rsn.2016.0517","article-title":"Passive beamforming with coprime arrays","volume":"11","author":"Martino","year":"2017","journal-title":"IET Radar Sonar Navig."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Adhikari, K., Buck, J.R., and Wage, K.E. (2013, January 26\u201331). Beamforming with extended co-prime sensor arrays. Proceedings of the 2013 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Vancouver, BC, Canada.","DOI":"10.1109\/ICASSP.2013.6638447"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Adhikari, K., Buck, J.R., and Wage, K.E. (2014). Extending coprime sensor arrays to achieve the peak side lobe height of a full uniform linear array. EURASIP J. Adv. Signal Process., 148.","DOI":"10.1186\/1687-6180-2014-148"},{"key":"ref_36","unstructured":"Cen, L., Ser, W., Yu, Z.L., and Rahardja, S. (April, January 31). An improved genetic algorithm for aperiodic array synthesis. Proceedings of the 2008 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2008), Las Vegas, NV, USA."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"406","DOI":"10.1109\/LAWP.2008.2005364","article-title":"Grating lobe reduction in aperiodic linear arrays of physically large antennas","volume":"8","author":"Barott","year":"2009","journal-title":"IEEE Antennas Wirel. Propag. Lett."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"76","DOI":"10.1109\/TAP.2007.913145","article-title":"Design of broadband planar arrays based on the optimization of aperiodic tilings","volume":"56","author":"Spence","year":"2008","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"929","DOI":"10.1109\/JOE.2014.2377454","article-title":"Low-cost acoustic cameras for underwater wideband passive imaging","volume":"40","author":"Trucco","year":"2015","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Trucco, A., Martelli, S., and Crocco, M. (2014, January 14\u201319). Passive underwater imaging through optimized planar arrays of hydrophones. Proceedings of the 2014 Oceans-St. John\u2019s, St. John\u2019s, NL, Canada.","DOI":"10.1109\/OCEANS.2014.7002999"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1109\/48.775291","article-title":"Stochastic optimization of linear sparse arrays","volume":"24","author":"Trucco","year":"1999","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"318","DOI":"10.1121\/1.408364","article-title":"Beamforming with dense random arrays: The development of a spatially shaded polyvinylidene fluoride acoustic transducer","volume":"95","author":"McGehee","year":"1994","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Yang, H., Chen, H., and Xu, L. (2015, January 18\u201321). Beamforming with nonsinusoidal signal for grating lobes suppression in underwater acoustic imaging. Proceedings of the OCEANS 2015-Genova, Genoa, Italy.","DOI":"10.1109\/OCEANS-Genova.2015.7271722"},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Camacho, J., Parrilla, M., and Fritsch, C. (2009). Phase coherence imaging. IEEE Trans. Ultrason. Ferroelectr. Freq. Control, 56.","DOI":"10.1109\/TUFFC.2009.1128"},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Camacho, J., Parrilla, M., and Fritsch, C. (2009, January 20\u201323). Grating-lobes reduction by application of phase coherence factors. Proceedings of the 2009 IEEE International Ultrasonics Symposium (IUS), Rome, Italy.","DOI":"10.1109\/ULTSYM.2009.5441770"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"79680R","DOI":"10.1117\/12.877777","article-title":"Transmit beamforming techniques for suppressing grating lobes in large pitch ultrasonic phased arrays","volume":"7968","author":"Torbatian","year":"2011","journal-title":"Proc. SPIE"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"2588","DOI":"10.1109\/TUFFC.2010.1725","article-title":"A split-aperture transmit beamforming technique with phase coherence grating lobe suppression","volume":"57","author":"Torbatian","year":"2010","journal-title":"IEEE Trans. Ultrason. Ferroelectr. Freq. Control"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"S359","DOI":"10.1016\/j.jmarsys.2009.01.034","article-title":"Extracting bottom information from towed-array reverberation data: Part I: Measurement methodology","volume":"78","author":"Preston","year":"2009","journal-title":"J. Mar. Syst."},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"McEachern, J.F., McConnell, J.A., Jamieson, J., and Trivett, D. (2006, January 18\u201321). ARAP\u2014Deep Ocean Vector Sensor Research Array. Proceedings of the OCEANS 2006, Boston, MA, USA.","DOI":"10.1109\/OCEANS.2006.307082"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"3659","DOI":"10.1121\/1.4763547","article-title":"Probability distribution for energy of saturated broadband ocean acoustic transmission: Results from Gulf of Maine 2006 experiment","volume":"132","author":"Tran","year":"2012","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_51","unstructured":"Center, N. (2012, January 5\u20139). Atlantic herring stock assessment for 2012. Proceedings of the 54th Northeast Regional Stock Assessment Workshop (54th SAW), Woods Hole, MA, USA."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1051\/alr\/2012003","article-title":"Aggregative patterns of pre-spawning Atlantic herring on Georges Bank from 1999\u20132010","volume":"25","author":"Jech","year":"2012","journal-title":"Aquat. Living Resour."},{"key":"ref_53","unstructured":"Overholtz, W.J., Jacobson, L.D., Melvin, G.D., Cieri, M., Power, M., Libby, D., and Clark, K. (2004). Stock Assessment of the Gulf of Maine\u2013Georges Bank Atlantic Herring Complex, 2003, Northeast Fisheries Science Center References Document 04-06."},{"key":"ref_54","first-page":"57","article-title":"Atlantic herring (Clupea harengus) demographics in the Gulf of Maine from 1998 to 2012","volume":"47","author":"Jech","year":"2015","journal-title":"J. Northwest Atl. Fish. Sci."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"1057","DOI":"10.1121\/1.3177271","article-title":"High resolution population density imaging of random scatterers with the matched filtered scattered field variance","volume":"126","author":"Andrews","year":"2009","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_56","doi-asserted-by":"crossref","unstructured":"Jain, A.D., and Makris, N.C. (2016). Maximum Likelihood Deconvolution of Beamformed Images with Signal-Dependent Speckle Fluctuations from Gaussian Random Fields: With Application to Ocean Acoustic Waveguide Remote Sensing (OAWRS). Remote Sens., 8.","DOI":"10.3390\/rs8090694"}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/9\/10\/1036\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:46:56Z","timestamp":1760208416000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/9\/10\/1036"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,10,11]]},"references-count":56,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2017,10]]}},"alternative-id":["rs9101036"],"URL":"https:\/\/doi.org\/10.3390\/rs9101036","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,10,11]]}}}