{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:48:42Z","timestamp":1760240922287,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"21","license":[{"start":{"date-parts":[[2019,10,23]],"date-time":"2019-10-23T00:00:00Z","timestamp":1571788800000},"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>Underwater acoustic digital communications suffer from inter-symbol interference deriving from signal distortions caused by the channel propagation. Facing such kind of impairment becomes particularly challenging when dealing with shallow water scenarios characterized by short channel coherence time and large delay spread caused by time-varying multipath effects. Channel equalization operated on the received signal represents a crucial issue in order to mitigate the effect of inter-symbol interference and improve the link reliability. In this direction, this contribution presents a preliminary performance analysis of acoustic digital links adopting pulse position modulation in severe multipath scenarios. First, we show how the spectral redundancy offered by pulse position modulated signals can be fruitfully exploited when using fractional sampling at the receiver side, which is an interesting approach rarely addressed by the current literature. In this context, a novel blind equalization scheme is devised. Specifically, the equalizer is blindly designed according to a suitably modified Bussgang scheme in which the zero-memory nonlinearity is replaced by a M-memory nonlinearity, M being the pulse position modulation order. Numerical results not only confirm the feasibility of the technique described here, but also assess the quality of its performance. An extension to a very interesting complex case is also provided.<\/jats:p>","DOI":"10.3390\/s19214604","type":"journal-article","created":{"date-parts":[[2019,10,25]],"date-time":"2019-10-25T03:20:36Z","timestamp":1571973636000},"page":"4604","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Blind Fractionally Spaced Channel Equalization for Shallow Water PPM Digital Communications Links"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1120-707X","authenticated-orcid":false,"given":"Gaetano","family":"Scarano","sequence":"first","affiliation":[{"name":"DIET, Universit\u00e0 \u201cLa Sapienza\u201d di Roma, via Eudossiana 18, 00184 Roma, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5271-9373","authenticated-orcid":false,"given":"Andrea","family":"Petroni","sequence":"additional","affiliation":[{"name":"DIET, Universit\u00e0 \u201cLa Sapienza\u201d di Roma, via Eudossiana 18, 00184 Roma, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4830-2641","authenticated-orcid":false,"given":"Mauro","family":"Biagi","sequence":"additional","affiliation":[{"name":"DIET, Universit\u00e0 \u201cLa Sapienza\u201d di Roma, via Eudossiana 18, 00184 Roma, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5671-9087","authenticated-orcid":false,"given":"Roberto","family":"Cusani","sequence":"additional","affiliation":[{"name":"DIET, Universit\u00e0 \u201cLa Sapienza\u201d di Roma, via Eudossiana 18, 00184 Roma, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,10,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1109\/MCOM.2009.4752682","article-title":"Underwater acoustic communication channels: Propagation models and statistical characterization","volume":"47","author":"Stojanovic","year":"2009","journal-title":"IEEE Commun. Mag."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1109\/48.64882","article-title":"Adaptive equalization techniques for acoustic telemetry channels","volume":"16","author":"Proakis","year":"1991","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_3","unstructured":"Zhao, S., Zhang, X., and Zhang, X. (2016, January 19\u201323). Iterative frequency domain equalization combined with LDPC decoding for single-carrier underwater acoustic communications. Proceedings of the OCEANS 2016 MTS\/IEEE Monterey, Monterey, CA, USA."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Liu, L., Zhang, Y., Zhang, P., Zhou, L., and Niu, J. (2017, January 23). Channel coding for underwater acoustic single-carrier CDMA communication system. Proceedings of the 7th International Conference on Electronics and Information Engineering, Nanjing, China.","DOI":"10.1117\/12.2265470"},{"key":"ref_5","first-page":"259","article-title":"Underwater communication implementation with OFDM","volume":"44","author":"Chithra","year":"2015","journal-title":"Indian J. Geo-Mar. Sci."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/JPHOT.2018.2871958","article-title":"Experimental evaluation of OFDM-based underwater visible light communication cystem","volume":"10","author":"Hessien","year":"2018","journal-title":"IEEE Photonics J."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Ashri, R., Shaban, H., and El-Nasr, M. (2017). A novel fractional Fourier transform-based ASK-OFDM system for underwater acoustic communications. Appl. Sci., 7.","DOI":"10.3390\/app7121286"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1016\/j.apacoust.2017.01.018","article-title":"Biologically inspired covert underwater acoustic communication by mimicking dolphin whistles","volume":"120","author":"Liu","year":"2017","journal-title":"Appl. Acoust."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"634","DOI":"10.1109\/JOE.2009.2032005","article-title":"MIMO-OFDM for high-rate underwater acoustic communications","volume":"34","author":"Li","year":"2009","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Stojanovic, M. (April, January 31). OFDM for underwater acoustic communications: Adaptive synchronization and sparse channel estimation. Proceedings of the 2008 IEEE International Conference on Acoustics, Speech and Signal Processing, Las Vegas, NV, USA.","DOI":"10.1109\/ICASSP.2008.4518853"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Klein, A.G., and Johnson, C.R. (2004, January 20\u201324). MMSE decision feedback equalization of pulse position modulated signals. Proceedings of the EEE International Conference on Communications, Paris, France.","DOI":"10.1109\/ICC.2004.1313011"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"856","DOI":"10.1109\/TCOM.1976.1093381","article-title":"Fractional tap-spacing equalizer and consequences for clock recovery in data modems","volume":"24","author":"Ungerboeck","year":"1976","journal-title":"IEEE Trans. Commun."},{"key":"ref_13","first-page":"161","article-title":"Second-order statistics driven LMS blind fractionally spaced channel equalization","volume":"24","author":"Scarano","year":"2017","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"6077","DOI":"10.12733\/jics20102577","article-title":"Recursive least squares fractionally-spaced blind equalization algorithm for underwater acoustic communication","volume":"10","author":"Xiao","year":"2013","journal-title":"J. Inf. Comput. Sci."},{"key":"ref_15","unstructured":"Artman, D.J., Chari, S., and Gooch, R.P. (1992, January 26\u201328). Joint equalization and timing recovery in a fractionally-spaced equalizer. Proceedings of the 1992 Conference Record of the Twenty-Sixth Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, USA."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Nasir, A.A., Durrani, S., and Kennedy, R.A. (2010, January 21\u201324). Blind fractionally spaced equalization and timing synchronization in wireless fading channels. Proceedings of the 2010 2nd International Conference on Future Computer and Communication, Wuha, China.","DOI":"10.1109\/ICFCC.2010.5497663"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Scarano, G., Petroni, A., Cusani, R., and Biagi, M. (2018, January 3\u20137). Sampling phase estimation in underwater PPM fractionally sampled equalization. Proceedings of the 26th European Signal Processing Conference (EUSIPCO), Rome, Italy.","DOI":"10.23919\/EUSIPCO.2018.8553395"},{"key":"ref_18","unstructured":"Biglieri, E., and Benedetto, S. (1999). Principles of Digital Transmission, Kluwer Academic Publisher."},{"key":"ref_19","unstructured":"Scarano, G. (2017, September 22). Available online: https:\/\/www.amazon.it\/Elaborazione-Statistica-dei-Segnali-vol-II\/dp\/1549794752."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1111\/j.1365-2478.1981.tb00401.x","article-title":"Zero memory non-linear deconvolution","volume":"29","author":"Godfrey","year":"1981","journal-title":"Geophys. Pros."},{"key":"ref_21","unstructured":"Haykin, S.S. (1994). Bussgang Techniques for Blind Deconvolution and Equalization. Blind Deconvolution, Prentice Hall."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2798","DOI":"10.1109\/78.960427","article-title":"Bussgang-zero crossing equalization: An integrated HOS-SOS approach","volume":"48","author":"Jacovitti","year":"2001","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1860","DOI":"10.1109\/TSP.2005.845477","article-title":"Fractionally spaced Bussgang equalization for correlated input symbols: A Bussgang approach","volume":"52","author":"Panci","year":"2005","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1324","DOI":"10.1109\/TIP.2003.818022","article-title":"Multichannel blind image deconvolution using the Bussgang algorithm: Spatial and multiresolution approaches","volume":"12","author":"Panci","year":"2003","journal-title":"IEEE Trans. Image Process."},{"key":"ref_25","first-page":"2462","article-title":"Blind image deblurring driver by nonlinear processing in the edge domain","volume":"2004","author":"Colonnese","year":"2004","journal-title":"EURASIP J. Appl. Signal Process."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1109\/78.80937","article-title":"Cumulant series expansion of hybrid nonlinear moment of complex random variables","volume":"39","author":"Scarano","year":"1991","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"486","DOI":"10.1109\/TSP.1993.193184","article-title":"Cumulant series expansion of hybrid nonlinear moments of n variates","volume":"41","author":"Scarano","year":"1993","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1867","DOI":"10.1109\/TCOM.1980.1094608","article-title":"Self-recovering equalization and carrier tracking in two-dimensional data communications systems","volume":"28","author":"Godard","year":"1980","journal-title":"IEEE Trans. Commun."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Schreier, P.J., and Scharf, L.L. (2010). Statistical Signal Processing of Complex-Valued Data: The Theory of Improper and Noncircular Signals, Cambridge University Press.","DOI":"10.1017\/CBO9780511815911"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/21\/4604\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:28:32Z","timestamp":1760189312000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/21\/4604"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,10,23]]},"references-count":29,"journal-issue":{"issue":"21","published-online":{"date-parts":[[2019,11]]}},"alternative-id":["s19214604"],"URL":"https:\/\/doi.org\/10.3390\/s19214604","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2019,10,23]]}}}