{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,2]],"date-time":"2026-01-02T07:38:53Z","timestamp":1767339533798,"version":"build-2065373602"},"reference-count":55,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2020,12,25]],"date-time":"2020-12-25T00:00:00Z","timestamp":1608854400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The superdirective beamformer, while attractive for processing broadband acoustic signals, often suffers from the problem of white noise amplification. So, its application requires well-designed acoustic arrays with sensors of extremely low self-noise level, which is difficult if not impossible to attain. In this paper, a new binaural superdirective beamformer is proposed, which is divided into two sub-beamformers. Based on studies and facts in psychoacoustics, these two filters are designed in such a way that they are orthogonal to each other to make the white noise components in the binaural beamforming outputs incoherent while maximizing the output interaural coherence of the diffuse noise, which is important for the brain to localize the sound source of interest. As a result, the signal of interest in the binaural superdirective beamformer\u2019s outputs is in phase but the white noise components in the outputs are random phase, so the human auditory system can better separate the acoustic signal of interest from white noise by listening to the outputs of the proposed approach. Experimental results show that the derived binaural superdirective beamformer is superior to its conventional monaural counterpart.<\/jats:p>","DOI":"10.3390\/s21010074","type":"journal-article","created":{"date-parts":[[2020,12,25]],"date-time":"2020-12-25T09:30:19Z","timestamp":1608888619000},"page":"74","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Binaural Heterophasic Superdirective Beamforming"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4437-3111","authenticated-orcid":false,"given":"Yuzhu","family":"Wang","sequence":"first","affiliation":[{"name":"Center of Intelligent Acoustics and Immersive Communications, Northwestern Polytechnical University, 127 Youyi West Road, Xi\u2019an 710072, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0083-9247","authenticated-orcid":false,"given":"Jingdong","family":"Chen","sequence":"additional","affiliation":[{"name":"Center of Intelligent Acoustics and Immersive Communications, Northwestern Polytechnical University, 127 Youyi West Road, Xi\u2019an 710072, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0036-5865","authenticated-orcid":false,"given":"Jacob","family":"Benesty","sequence":"additional","affiliation":[{"name":"INRS-EMT, University of Quebec, 800 de la Gauchetiere Ouest, Montreal, QC H5A 1K6, Canada"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2967-8379","authenticated-orcid":false,"given":"Jilu","family":"Jin","sequence":"additional","affiliation":[{"name":"Center of Intelligent Acoustics and Immersive Communications, Northwestern Polytechnical University, 127 Youyi West Road, Xi\u2019an 710072, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6825-7473","authenticated-orcid":false,"given":"Gongping","family":"Huang","sequence":"additional","affiliation":[{"name":"Andrew and Erna Viterby Faculty of Electrical Engineering, Technion-Israel Institute of Technology, Technion City, Haifa 32000, Israel"}]}],"member":"1968","published-online":{"date-parts":[[2020,12,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Benesty, J., Chen, J., and Pan, C. (2016). Fundamentals of Differential Beamforming, Springer.","DOI":"10.1007\/978-981-10-1046-0"},{"key":"ref_2","unstructured":"Benesty, J., Chen, J., and Huang, Y. (2008). Microphone Array Signal Processing, Springer."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Elko, G.W. (2000). Superdirectional microphone arrays. Acoustic Signal Processing for Telecommunication, Springer.","DOI":"10.1007\/978-1-4419-8644-3_10"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Brandstein, M., and Ward, D. (2001). Microphone Arrays: Signal Processing Techniques and Applications, Springer.","DOI":"10.1007\/978-3-662-04619-7"},{"key":"ref_5","unstructured":"Johnson, D.H., and Dudgeon, D.E. (1993). Array Signal Processing: Concepts and Techniques, PTR Prentice Hall."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1140","DOI":"10.1109\/TASLP.2017.2689681","article-title":"On the Design of Frequency-Invariant Beampatterns with Uniform Circular Microphone Arrays","volume":"25","author":"Huang","year":"2017","journal-title":"IEEE\/ACM Trans. Audio Speech Lang. Process."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2305","DOI":"10.1109\/TASLP.2018.2862826","article-title":"Insights into Frequency-Invariant Beamforming with Concentric Circular Microphone Arrays","volume":"26","author":"Huang","year":"2018","journal-title":"IEEE\/ACM Trans. Audio Speech Lang. Process."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Benesty, J., Chen, J., and Cohen, I. (2015). Design of Circular Differential Microphone Arrays, Springer.","DOI":"10.1007\/978-3-319-14842-7"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1109\/TASSP.1986.1164847","article-title":"Practical supergain","volume":"34","author":"Cox","year":"1986","journal-title":"IEEE Trans. Acoust. Speech Signal Process."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1079","DOI":"10.1109\/TASLP.2020.2980989","article-title":"A simple theory and new method of differential beamforming with uniform linear microphone arrays","volume":"28","author":"Huang","year":"2020","journal-title":"IEEE\/ACM Trans. Audio Speech Lang. Process."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Li, C., Benesty, J., Huang, G., and Chen, J. (2016, January 20\u201325). Subspace superdirective beamformers based on joint diagonalization. Proceedings of the IEEE ICASSP, Shanghai, China.","DOI":"10.1109\/ICASSP.2016.7471705"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1079","DOI":"10.1121\/1.4927690","article-title":"Design of robust differential microphone arrays with orthogonal polynomials","volume":"138","author":"Pan","year":"2015","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1109\/TASLP.2019.2949219","article-title":"Design of planar differential microphone arrays with fractional orders","volume":"28","author":"Huang","year":"2019","journal-title":"IEEE\/ACM Trans. Audio Speech Lang. Process."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"3024","DOI":"10.1121\/1.5038275","article-title":"A flexible high directivity beamformer with spherical microphone arrays","volume":"143","author":"Huang","year":"2018","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"13497","DOI":"10.1109\/TVT.2020.3029374","article-title":"Heterophasic Binaural Differential Beamforming for Speech Intelligibility Improvement","volume":"69","author":"Jin","year":"2020","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Elko, G.W., and Meyer, J. (2008). Microphone arrays. Springer Handbook of Speech Processing, Springer.","DOI":"10.1007\/978-3-540-49127-9_50"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"063297","DOI":"10.1155\/ASP\/2006\/63297","article-title":"Dual-channel speech enhancement by superdirective beamforming","volume":"1","author":"Lotter","year":"2006","journal-title":"EURASIP J. Appl. Signal Process."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"3236","DOI":"10.1121\/1.4983122","article-title":"Design of robust concentric circular differential microphone arrays","volume":"141","author":"Huang","year":"2017","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Benesty, J., and Chen, J. (2012). Study and Design of Differential Microphone Arrays, Springer.","DOI":"10.1007\/978-3-642-33753-6"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Mabande, E., Schad, A., and Kellermann, W. (2009, January 19\u201324). Design of robust superdirective beamformers as a convex optimization problem. Proceedings of the IEEE ICASSP, Taipei, Taiwan.","DOI":"10.1109\/ICASSP.2009.4959524"},{"key":"ref_21","first-page":"877","article-title":"Combined beamformers for robust broadband regularized superdirective beamforming","volume":"23","author":"Berkun","year":"2015","journal-title":"IEEE\/ACM Trans. Audio Speech Lang. Process."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2169","DOI":"10.1109\/TSP.2011.2106780","article-title":"Design of robust superdirective arrays with a tunable tradeoff between directivity and frequency-invariance","volume":"59","author":"Crocco","year":"2011","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2531","DOI":"10.1109\/TASLP.2016.2618003","article-title":"Superdirective Beamforming Based on the Krylov Matrix","volume":"24","author":"Huang","year":"2016","journal-title":"IEEE\/ACM Trans. Audio Speech Lang. Process."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1548","DOI":"10.1109\/TASLP.2016.2568044","article-title":"Reduced-order robust superdirective beamforming with uniform linear microphone arrays","volume":"24","author":"Pan","year":"2016","journal-title":"IEEE\/ACM Trans. Audio Speech Lang. Process."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2433","DOI":"10.1109\/TASL.2012.2203808","article-title":"Stochastic and analytic optimization of sparse aperiodic arrays and broadband beamformers with robust superdirective patterns","volume":"20","author":"Crocco","year":"2012","journal-title":"IEEE Trans. Audio, Speech, Lang. Process."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Berkun, R., Cohen, I., and Benesty, J. (2016, January 13\u201316). A tunable beamformer for robust superdirective beamforming. Proceedings of the IEEE IWAENC, Xi\u2019an, China.","DOI":"10.1109\/IWAENC.2016.7602952"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Blauert, J. (1997). Spatial Hearing: The Psychophysics of Human Sound Localization, MIT Press.","DOI":"10.7551\/mitpress\/6391.001.0001"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"806","DOI":"10.1121\/1.393471","article-title":"Spatial mapping of intracranial auditory events for various degrees of interaural coherence","volume":"79","author":"Blauert","year":"1986","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"536","DOI":"10.1121\/1.1906407","article-title":"The Influence of Interaural Phase on Interaural Summation and Inhibition","volume":"20","author":"Hirsh","year":"1948","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"196","DOI":"10.1121\/1.1906588","article-title":"The relation between localization and intelligibility","volume":"22","author":"Hirsh","year":"1950","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1122","DOI":"10.1121\/1.1918257","article-title":"Effect of interaural correlation on the precision of centering a noise","volume":"34","author":"Jeffress","year":"1962","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Kollmeier, B., Brand, T., and Meyer, B. (2008). Perception of speech and sound. Springer Handbook of Speech Processing, Springer.","DOI":"10.1007\/978-3-540-49127-9_4"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"893","DOI":"10.1016\/j.neuron.2005.07.019","article-title":"High binaural coherence determines successful sound localization and increased activity in posterior auditory areas","volume":"47","author":"Zimmer","year":"2005","journal-title":"Neuron"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1121\/1.1906584","article-title":"The intelligibility of interrupted speech","volume":"22","author":"Miller","year":"1950","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_35","first-page":"205","article-title":"Sound localization in the median plane","volume":"22","author":"Blauert","year":"1969","journal-title":"Acta Acust. United Acust."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1037\/h0061495","article-title":"A place theory of sound localization","volume":"41","author":"Jeffress","year":"1948","journal-title":"J. Comp. Physiol. Psychol."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"842","DOI":"10.1121\/1.1908052","article-title":"Localization of sound from single and paired sources","volume":"27","author":"Sandel","year":"1955","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"761","DOI":"10.1121\/1.1906434","article-title":"The role of interaural phase in loudness","volume":"20","author":"Hirsh","year":"1948","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"801","DOI":"10.1121\/1.1906692","article-title":"Binaural localization and masking","volume":"22","author":"Kock","year":"1950","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"416","DOI":"10.1121\/1.1908346","article-title":"Masking of tonal signals","volume":"28","author":"Jeffress","year":"1956","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1658","DOI":"10.1121\/1.1909077","article-title":"Formulas for the coefficient of interaural correlation for noise","volume":"34","author":"Jeffress","year":"1962","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_42","unstructured":"Stevens, S.S. (1951). The Perception of Speech. Handbook of Experimental Psychology, Wiley."},{"key":"ref_43","unstructured":"Beranek, L.L. (1986). Acoustics, Acoustic Society of America."},{"key":"ref_44","unstructured":"Gerald, K., and Colburn, H.S. (2017). Informational Masking in Speech Recognition, Springer."},{"key":"ref_45","first-page":"548","article-title":"Spatial release from informational masking declines with age: Evidence from a detection task in a virtual separation paradigm","volume":"146","author":"Zobel","year":"2019","journal-title":"IEEE\/ACM Trans. Audio Speech Lang. Process."},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Moore, B.C. (2020). Effects of hearing loss and age on the binaural processing of temporal envelope and temporal fine structure information. Hear. Res., 107991.","DOI":"10.1016\/j.heares.2020.107991"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"4041","DOI":"10.1121\/10.0001382","article-title":"The role of reliable interaural time difference cues in ambiguous binaural signals for the intelligibility of multitalker speech","volume":"147","author":"Esther","year":"2020","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Jutras, B., Lagac\u00e9, J., and Koravand, A. (2020). The development of auditory functions. Handbook of Clinical Neurology, Elsevier.","DOI":"10.1016\/B978-0-444-64150-2.00014-9"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1121\/1.1906358","article-title":"The Influence of interaural phase relations upon the masking of speech by white noise","volume":"20","author":"Licklider","year":"1948","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_50","unstructured":"Moore, B.C. (2012). An Introduction to the Psychology of Hearing, Brill."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"2162","DOI":"10.1109\/TASLP.2015.2471096","article-title":"Interaural coherence preservation in multi-channel Wiener filtering-based noise reduction for binaural hearing aids","volume":"23","author":"Marquardt","year":"2015","journal-title":"IEEE\/ACM Trans. Audio Speech Lang. Process."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"2449","DOI":"10.1109\/TASLP.2015.2486381","article-title":"Theoretical analysis of binaural transfer function MVDR beamformers with interference cue preservation constraints","volume":"23","author":"Hadad","year":"2015","journal-title":"IEEE\/ACM Trans. Audio Speech Lang. Process."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"1365","DOI":"10.1109\/TASSP.1987.1165054","article-title":"Robust adaptive beamforming","volume":"35","author":"Cox","year":"1987","journal-title":"IEEE Trans. Acoust. Speech Signal Process."},{"key":"ref_54","unstructured":"Golub, G.H., and Loan, C.F.V. (1996). Matrix Computations, The Johns Hopkins University Press. [3rd ed.]."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"422","DOI":"10.1016\/0047-259X(76)90050-6","article-title":"A maximization problem and its application to canonical correlation","volume":"6","author":"Eaton","year":"1976","journal-title":"J. Multivar. Anal."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/1\/74\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:46:00Z","timestamp":1760179560000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/1\/74"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,12,25]]},"references-count":55,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2021,1]]}},"alternative-id":["s21010074"],"URL":"https:\/\/doi.org\/10.3390\/s21010074","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2020,12,25]]}}}