{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,15]],"date-time":"2024-07-15T00:19:15Z","timestamp":1721002755134},"reference-count":54,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,6,18]],"date-time":"2021-06-18T00:00:00Z","timestamp":1623974400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Systems"],"abstract":"In this paper, we discuss the problem of channel identification by using eight algorithms. The first three algorithms are based on higher-order cumulants, the next three algorithms are based on binary output measurement, and the last two algorithms are based on reproducing kernels. The principal objective of this paper is to study the performance of the presented algorithms in different situations, such as with different sizes of the data input or different signal-to-noise ratios. The presented algorithms are applied to the estimation of the channel parameters of the broadband radio access network (BRAN). The simulation results confirm that the presented algorithms are able to estimate the channel parameters with different accuracies, and each algorithm has its advantages and disadvantages for a given situation, such as for a given SNR and data input. Finally, this study provides an idea of which algorithms can be selected in a given situation. The study presented in this paper demonstrates that the cumulant-based algorithms are more adequate if the data inputs are not available (blind identification), but the kernel- and binary-measurement-based methods are more adequate if the noise is not important (SNR\u226516 dB).<\/jats:p>","DOI":"10.3390\/systems9020046","type":"journal-article","created":{"date-parts":[[2021,6,18]],"date-time":"2021-06-18T08:10:47Z","timestamp":1624003847000},"page":"46","source":"Crossref","is-referenced-by-count":3,"title":["Channel Identification Based on Cumulants, Binary Measurements, and Kernels"],"prefix":"10.3390","volume":"9","author":[{"ORCID":"http:\/\/orcid.org\/0000-0002-2027-8507","authenticated-orcid":false,"given":"Hicham","family":"Oualla","sequence":"first","affiliation":[{"name":"Department of Mathematics and Informatics, Sultan Moulay Slimane University, Po. Box 592, 23000 Beni Mellal, Morocco"},{"name":"Laboratoire d\u2019Automatique de Caen, UNICAEN, ENSICAEN, Normandie University, 6, B. Marchal Juin, 14050 Caen, France"}]},{"ORCID":"http:\/\/orcid.org\/0000-0002-0574-2105","authenticated-orcid":false,"given":"Rachid","family":"Fateh","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Informatics, Sultan Moulay Slimane University, Po. Box 592, 23000 Beni Mellal, Morocco"}]},{"ORCID":"http:\/\/orcid.org\/0000-0001-8026-9189","authenticated-orcid":false,"given":"Anouar","family":"Darif","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Informatics, Sultan Moulay Slimane University, Po. Box 592, 23000 Beni Mellal, Morocco"}]},{"ORCID":"http:\/\/orcid.org\/0000-0003-3390-9037","authenticated-orcid":false,"given":"Said","family":"Safi","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Informatics, Sultan Moulay Slimane University, Po. Box 592, 23000 Beni Mellal, Morocco"}]},{"ORCID":"http:\/\/orcid.org\/0000-0002-2186-986X","authenticated-orcid":false,"given":"Mathieu","family":"Pouliquen","sequence":"additional","affiliation":[{"name":"Laboratoire d\u2019Automatique de Caen, UNICAEN, ENSICAEN, Normandie University, 6, B. Marchal Juin, 14050 Caen, France"}]},{"ORCID":"http:\/\/orcid.org\/0000-0003-2178-1814","authenticated-orcid":false,"given":"Miloud","family":"Frikel","sequence":"additional","affiliation":[{"name":"Laboratoire d\u2019Automatique de Caen, UNICAEN, ENSICAEN, Normandie University, 6, B. Marchal Juin, 14050 Caen, France"}]}],"member":"1968","published-online":{"date-parts":[[2021,6,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1080\/00949650213704","article-title":"MA system identification using higher order cumulants: Application to modelling solar radiation","volume":"72","author":"Safi","year":"2002","journal-title":"Int. J. Stat. Comput. Simul."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"855","DOI":"10.1080\/00207720412331297929","article-title":"Blind parametric identification of non-Gaussian FIR systems using higher order cumulants","volume":"35","author":"Safi","year":"2004","journal-title":"Int. J. Syst. Sci."},{"key":"ref_3","first-page":"158","article-title":"Blind non-minimum phase channel identification using 3rd and 4th order cumulants","volume":"4","author":"Safi","year":"2008","journal-title":"Int. J. Signal Process."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2729","DOI":"10.1109\/78.324738","article-title":"Estimation and detection in non-Gaussian noise using higher order statistics","volume":"42","author":"Sadler","year":"1994","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/002072196136896","article-title":"Criteria and algorithms for blind source separation based on cumulants","volume":"81","author":"Wang","year":"1996","journal-title":"Int. J. Electron."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"867","DOI":"10.1109\/TAC.2008.920222","article-title":"Identification input design for consistent parameter estimation of linear systems with binary-valued output observations","volume":"53","author":"Yin","year":"2008","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1892","DOI":"10.1109\/TAC.2003.819073","article-title":"System identification using binary sensors","volume":"48","author":"Zhang","year":"2003","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1905","DOI":"10.1016\/j.automatica.2011.06.008","article-title":"On identification of FIR systems having quantized output data","volume":"47","author":"Godoy","year":"2011","journal-title":"Automatica"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"671","DOI":"10.1080\/0232929021000015158","article-title":"Blind identification in noisy environment of nonminimum phase finite impulse response (FIR) system using higher order statistics","volume":"43","author":"Safi","year":"2003","journal-title":"Syst. Anal. Model. Simul."},{"key":"ref_10","unstructured":"Antari, J., Iqdour, R., Safi, S., Zeroual, A., and Lyhyaoui, A. (2006, January 14\u201319). Identification of quadratic non linear systems using higher order statistics and fuzzy models. Proceedings of the IEEE International Conference On Acoustic, Speech and Signal Process (ICASSP), Toulouse, France."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1007\/s11760-017-1138-z","article-title":"Extending HOC-based methods for identifying the diagonal parameters of quadratic systems","volume":"12","author":"Zidane","year":"2018","journal-title":"Signal Image Video Process."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Zidane, M., Safi, S., Sabri, M., and Boumezzough, A. (2014, January 27\u201328). Identification and equalization using higher order cumulants in MC-CDMA systems. Proceedings of the 2014 5th Workshop on Codes, Cryptography and Communication Systems, WCCCS 2014, El Jadida, Morocco.","DOI":"10.1109\/WCCCS.2014.7107925"},{"key":"ref_13","first-page":"13","article-title":"Broadband radio access network channel identification and downlink MC-CDMA equalization","volume":"5","author":"Zidane","year":"2014","journal-title":"Int. J. Energy Inform. Commun."},{"key":"ref_14","first-page":"230","article-title":"Adaptive equalization using controlled equal gain combining for uplink\/downlink MC-CDMA systems","volume":"4","author":"Frikel","year":"2008","journal-title":"Int. J. Signal Process."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1136","DOI":"10.1016\/j.dib.2018.02.005","article-title":"Measured and estimated data of non-linear BRAN channels using HOS in 4G wireless communications","volume":"17","author":"Zidane","year":"2018","journal-title":"Data Brief"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1109\/79.221324","article-title":"Signal processing with higher-order spectra","volume":"10","author":"Nikias","year":"1993","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Wang, A., and Li, R. (2019, January 12\u201313). Research on digital signal recognition based on higher order cumulants. Proceedings of the 2019 International Conference on Intelligent Transportation, Big Data & Smart City (ICITBS), Changsha, China.","DOI":"10.1109\/ICITBS.2019.00146"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"205","DOI":"10.13164\/re.2021.0204","article-title":"Automatic Modulation Classification of Real Signals in AWGN Channel Based on Sixth-Order Cumulants","volume":"30","author":"Simic","year":"2021","journal-title":"Radioengineering"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2436","DOI":"10.1049\/iet-com.2018.5497","article-title":"Higher order statistics for modulation and STBC recognition in MIMO systems","volume":"13","author":"Khosraviyani","year":"2019","journal-title":"IET Commun."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1021","DOI":"10.1109\/78.492561","article-title":"Noisy input\/output system identification using cumulants and the Steiglitz-McBride algorithm","volume":"44","author":"Anderson","year":"1996","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1016\/0165-1684(96)81013-9","article-title":"MA-model identification using modulated moment sequences","volume":"47","author":"Kaiser","year":"1995","journal-title":"Signal Process."},{"key":"ref_22","unstructured":"Proakis, J., and Salehi, M. (2007). Digital Communications, McGraw-Hill. [5th ed.]."},{"key":"ref_23","unstructured":"Ju, L., and Zhenya, H. (1998, January 13\u201315). Blind identification and equalization using higher-order cumulants and ICA algorithms. Proceedings of the International Conference Neural Networks and Brain (ICNN B\u201998), Beijing, China."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"2854","DOI":"10.1109\/78.324754","article-title":"FIR system identification using higher order statistics alone","volume":"42","author":"Zhang","year":"1994","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1016\/j.automatica.2015.06.030","article-title":"Recursive identification of FIR systems with binary-valued outputs and communication channels","volume":"60","author":"Guo","year":"2015","journal-title":"Automatica"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"280","DOI":"10.1016\/j.automatica.2016.12.034","article-title":"Identification of Wiener systems with quantized inputs and binary-valued output observations","volume":"78","author":"Guo","year":"2017","journal-title":"Automatica"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"535","DOI":"10.1016\/j.automatica.2005.12.004","article-title":"Joint identification of plant rational models and noise distribution functions using binary-valued observations","volume":"42","author":"Yin","year":"2006","journal-title":"Automatica"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Pouliquen, M., Menard, T., Pigeon, E., Gehan, O., and Goudjil, A. (July, January 29). Recursive system identification algorithm using binary measurements. Proceedings of the 2016 European Control Conference (ECC), Aalborg, Denmark.","DOI":"10.1109\/ECC.2016.7810477"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Goudjil, A., Pouliquen, M., Pigeon, E., Gehan, O., and M\u2019Saad, M. (2015, January 15\u201318). Identification of systems using binary sensors via support vector machines. Proceedings of the 2015 54th IEEE Conference on Decision and Control (CDC), Osaka, Japan.","DOI":"10.1109\/CDC.2015.7402729"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"2837","DOI":"10.1016\/j.automatica.2012.05.050","article-title":"Convergence analysis of an online approach to parameter estimation problems based on binary observations","volume":"48","author":"Jafari","year":"2012","journal-title":"Automatica"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"3396","DOI":"10.1016\/j.automatica.2013.08.011","article-title":"Recursive projection algorithm on FIR system identification with binary-valued observations","volume":"49","author":"Guo","year":"2013","journal-title":"Automatica"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Oualla, H., Pouliquen, M., Frikel, M., and Safi, S. (2021, January 23\u201325). Comparison of algorithms for identification of IIR systems from binary measurements on the output. Proceedings of the E3S Web of Conferences, EDP Sciences, Guizhou, China.","DOI":"10.1051\/e3sconf\/202122901049"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Liu, W., Principe, J.C., and Haykin, S. (2011). Kernel Adaptive Filtering: A Comprehensive Introduction, John Wiley & Sons.","DOI":"10.1002\/9780470608593"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1162\/neco.1995.7.2.219","article-title":"Regularization theory and neural networks architectures","volume":"7","author":"Girosi","year":"1995","journal-title":"Neural Comput."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1007\/BF00994018","article-title":"Support-vector networks","volume":"20","author":"Cortes","year":"1995","journal-title":"Mach. Learn."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"543","DOI":"10.1109\/TSP.2007.907881","article-title":"The kernel least-mean-square algorithm","volume":"56","author":"Liu","year":"2008","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2008\/784292","article-title":"Kernel affine projection algorithms","volume":"2008","author":"Liu","year":"2008","journal-title":"EURASIP J. Adv. Signal Process."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1299","DOI":"10.1162\/089976698300017467","article-title":"Nonlinear component analysis as a kernel eigenvalue problem","volume":"10","author":"Smola","year":"1998","journal-title":"Neural Comput."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"2275","DOI":"10.1109\/TSP.2004.830985","article-title":"The kernel recursive least-squares algorithm","volume":"52","author":"Engel","year":"2004","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1109\/TNNLS.2011.2178446","article-title":"Quantized kernel least mean square algorithm","volume":"23","author":"Chen","year":"2011","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"98","DOI":"10.1109\/LSP.2015.2503000","article-title":"Regularized kernel least mean square algorithm with multiple-delay feedback","volume":"23","author":"Wang","year":"2015","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1016\/j.neucom.2016.01.004","article-title":"Kernel least mean square with adaptive kernel size","volume":"191","author":"Chen","year":"2016","journal-title":"Neurocomputing"},{"key":"ref_43","unstructured":"Chellappa, R., and Theodoridis, S. (2014). Online learning in reproducing kernel Hilbert spaces. Signal Processing Theory and Machine Learning (Series Academic Press Library in Signal Processing), Academic."},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Fateh, R., and Darif, A. (2021). Mean Square Convergence of Reproducing Kernel for Channel Identification: Application to Bran D Channel Impulse Response. International Conference on Business Intelligence, Springer.","DOI":"10.1007\/978-3-030-76508-8_20"},{"key":"ref_45","unstructured":"Broadband Radio Acces Network (BRAN) (1999). Hyperlan type 2. Requirements and Archtiectures for Wireless Broadband Access, European Telecommunications Standards Institute (ETSI)."},{"key":"ref_46","unstructured":"Broadband Radio Acces Network (BRAN) (2001). Hyperlan type 2. Physical Layer, European Telecommunications Standards Institute (ETSI)."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1073\/pnas.42.1.43","article-title":"A central limit theorem and a strong mixing condition","volume":"42","author":"Rosenblatt","year":"1956","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1090\/S0002-9947-1950-0051437-7","article-title":"Theory of reproducing kernels","volume":"68","author":"Aronszajn","year":"1950","journal-title":"Trans. Am. Math. Soc."},{"key":"ref_49","unstructured":"Tobar, F. (2014). Kernel-Based Adaptive Estimation: Multidimensional and State-Space Approaches. [Ph.D. Thesis, Imperial College London]."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"1397","DOI":"10.1007\/s00034-020-01533-4","article-title":"A Novel Kalman Filter Formulation for Improving Tracking Performance of the Extended Kernel RLS","volume":"40","author":"Barreto","year":"2021","journal-title":"Circuits Syst. Signal Process."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"1391","DOI":"10.1002\/acs.2548","article-title":"Nonlinear adaptive filtering using kernel-based algorithms with dictionary adaptation","volume":"29","author":"Saide","year":"2015","journal-title":"Int. J. Adapt. Control. Signal Process."},{"key":"ref_52","doi-asserted-by":"crossref","unstructured":"Sch\u00f6lkopf, B., Herbrich, R., and Smola, A.J. (2001). A generalized representer theorem. International Conference on Computational Learning Theory, Springer.","DOI":"10.1007\/3-540-44581-1_27"},{"key":"ref_53","unstructured":"Li, K., and Principe, J.C. (2021, June 16). No-Trick (Treat) Kernel Adaptive Filtering Using Deterministic Features. Available online: https:\/\/arxiv.org\/abs\/1912.04530."},{"key":"ref_54","doi-asserted-by":"crossref","unstructured":"Martinek, R., Rzidky, J., Jaros, R., Bilik, P., and Ladrova, M. (2019). Least Mean Squares and Recursive Least Squares Algorithms for Total Harmonic Distortion Reduction Using Shunt Active Power Filter Control. Energies, 12.","DOI":"10.3390\/en12081545"}],"container-title":["Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-8954\/9\/2\/46\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,14]],"date-time":"2024-07-14T10:17:32Z","timestamp":1720952252000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-8954\/9\/2\/46"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6,18]]},"references-count":54,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2021,6]]}},"alternative-id":["systems9020046"],"URL":"https:\/\/doi.org\/10.3390\/systems9020046","relation":{},"ISSN":["2079-8954"],"issn-type":[{"value":"2079-8954","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,6,18]]}}}