{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,11]],"date-time":"2025-12-11T20:18:03Z","timestamp":1765484283106,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2022,3,15]],"date-time":"2022-03-15T00:00:00Z","timestamp":1647302400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Cognitive radios represent a real alternative to the scarcity of the radio spectrum. One of the primary tasks of these radios is the detection of possible gaps in a given bandwidth used by licensed users (called also primary users). This task, called spectrum sensing, requires high precision in determining these gaps, maximizing the probability of detection. The design of spectrum sensing algorithms also requires innovative hardware and software solutions for real-time implementations. In this work, a technique to determine possible primary users\u2019 transmissions in a wide frequency interval (multiband spectrum sensing) from the perspective of cognitive radios is presented. The proposal is implemented in a real wireless communications environment using low-cost hardware considering the sample entropy as a decision rule. To validate its feasibility for real-time implementation, a simulated scenario was first tested. Simulation and real-time implementations results were compared with the Higuchi fractal dimension as a decision rule. The encouraging results show that sample entropy correctly detects noise or a possible primary user transmission, with a probability of success around 0.99, and the number of samples with errors at the start and end of frequency edges of transmissions is, on average, only 12 samples.<\/jats:p>","DOI":"10.3390\/e24030411","type":"journal-article","created":{"date-parts":[[2022,3,16]],"date-time":"2022-03-16T03:34:13Z","timestamp":1647401653000},"page":"411","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Multiband Spectrum Sensing Based on the Sample Entropy"],"prefix":"10.3390","volume":"24","author":[{"given":"Yanqueleth","family":"Molina-Tenorio","sequence":"first","affiliation":[{"name":"Information Science and Technology, Metropolitan Autonomous University Iztapalapa, Mexico City 09360, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2661-2449","authenticated-orcid":false,"given":"Alfonso","family":"Prieto-Guerrero","sequence":"additional","affiliation":[{"name":"Electrical Engineering Department, Metropolitan Autonomous University Iztapalapa, Mexico City 09360, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3551-1500","authenticated-orcid":false,"given":"Rafael","family":"Aguilar-Gonzalez","sequence":"additional","affiliation":[{"name":"Faculty of Sciences, Autonomous University of San Luis Potosi, San Luis Potosi 78210, Mexico"}]}],"member":"1968","published-online":{"date-parts":[[2022,3,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1109\/98.788210","article-title":"Cognitive radio: Making software radios more personal","volume":"6","author":"Mitola","year":"1999","journal-title":"IEEE Pers. Commun."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2127","DOI":"10.1016\/j.comnet.2006.05.001","article-title":"NeXt generation\/dynamic spectrum access\/cognitive radio wireless networks: A survey","volume":"50","author":"Akyildiz","year":"2006","journal-title":"Comput. Netw."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1088","DOI":"10.1109\/SURV.2012.111412.00160","article-title":"Spectrum Decision in Cognitive Radio Networks: A Survey","volume":"15","author":"Masonta","year":"2013","journal-title":"IEEE Commun. Surv. Tutor."},{"key":"ref_4","unstructured":"Hattab, G., and Ibnkahla, M. (2014). Multiband Spectrum Sensing: Challenges and Limitations. arXiv."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Arjoune, Y., and Kaabouch, N. (2019). A Comprehensive Survey on Spectrum Sensing in Cognitive Radio Networks: Recent Advances, New Challenges, and Future Research Directions. Sensors, 19.","DOI":"10.3390\/s19010126"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Molina-Tenorio, Y., Prieto-Guerrero, A., Aguilar-Gonzalez, R., and Ruiz-Boqu\u00e9, S. (2019). Machine Learning Techniques Applied to Multiband Spectrum Sensing in Cognitive Radios. Sensors, 19.","DOI":"10.3390\/s19214715"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Molina-Tenorio, Y., Prieto-Guerrero, A., and Aguilar-Gonzalez, R. (2021). Real-Time Implementation of Multiband Spectrum Sensing Using SDR Technology. Sensors, 21.","DOI":"10.3390\/s21103506"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Welvaert, M., and Rosseel, Y. (2013). On the Definition of Signal-To-Noise Ratio and Contrast-To-Noise Ratio for fMRI Data. PLoS ONE, 8.","DOI":"10.1371\/journal.pone.0077089"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1719","DOI":"10.1007\/s11277-012-0659-6","article-title":"A Comparative Study of Different Entropies for Spectrum Sensing Techniques","volume":"69","author":"Zhu","year":"2013","journal-title":"Wirel. Pers. Commun."},{"key":"ref_10","unstructured":"Chen, X., and Nagaraj, S. (2008, January 24\u201326). Entropy based spectrum sensing in cognitive radio. Proceedings of the 2008 Wireless Telecomunications Symposium, Pomona, CA, USA."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"174","DOI":"10.1016\/j.sigpro.2008.07.022","article-title":"Entropy-based spectrum sensing in cognitive radio","volume":"89","author":"Nagaraj","year":"2009","journal-title":"Signal Process."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Li, H., Hu, Y., and Wang, S. (2021). A Novel Blind Signal Detector Based on the Entropy of the Power Spectrum Subband Energy Ratio. Entropy, 23.","DOI":"10.3390\/e23040448"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Cadena Mu\u00f1oz, E., Pedraza Mart\u00ednez, L.F., and Hernandez, C.A. (2020). R\u00e9nyi Entropy-Based Spectrum Sensing in Mobile Cognitive Radio Networks Using Software Defined Radio. Entropy, 22.","DOI":"10.3390\/e22060626"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"H2039","DOI":"10.1152\/ajpheart.2000.278.6.H2039","article-title":"Physiological time-series analysis using approximate entropy and sample entropy","volume":"278","author":"Richman","year":"2000","journal-title":"Am. J. Physiol.-Heart Circ. Physiol."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1109\/MEMB.2009.934629","article-title":"Approximate entropy for all signals","volume":"28","author":"Chon","year":"2009","journal-title":"IEEE Eng. Med. Biol. Mag."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"3403","DOI":"10.1103\/PhysRevA.45.3403","article-title":"Determining embedding dimension for phase-space reconstruction using a geometrical construction","volume":"45","author":"Kennel","year":"1992","journal-title":"Phys. Rev. A"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1109\/TAU.1967.1161901","article-title":"The use of fast Fourier transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms","volume":"15","author":"Welch","year":"1967","journal-title":"IEEE Trans. Audio Electroacoust."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"674","DOI":"10.1109\/34.192463","article-title":"A theory for multiresolution signal decomposition: The wavelet representation","volume":"11","author":"Mallat","year":"1989","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"651","DOI":"10.1016\/j.patrec.2009.09.011","article-title":"Data clustering: 50 years beyond K-means","volume":"31","author":"Jain","year":"2010","journal-title":"Pattern Recognit. Lett."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1016\/0167-2789(88)90081-4","article-title":"Approach to an irregular time series on the basis of the fractal theory","volume":"31","author":"Higuchi","year":"1988","journal-title":"Phys. Nonlinear Phenom."},{"key":"ref_21","first-page":"6","article-title":"Introduction to the Software-defined Radio Approach","volume":"10","author":"Selva","year":"2012","journal-title":"IEEE Lat. Am. Trans."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1023\/A:1022584911505","article-title":"Transceiver front-end technology for software radio implementation of wideband satellite communication systems","volume":"24","author":"Daneshgaran","year":"2003","journal-title":"Wirel. Pers. Commun."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1109\/SURV.2010.032910.00019","article-title":"Software Defined Radio: Challenges and Opportunities","volume":"12","author":"Ulversoy","year":"2010","journal-title":"IEEE Commun. Surv. Tutor."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Nastase, C.-V., Martian, A., Vladeanu, C., and Marghescu, I. (2018, January 14\u201316). Spectrum Sensing Based on Energy Detection Algorithms Using GNU Radio and USRP for Cognitive Radio. Proceedings of the 2018 International Conference on Communications (COMM), Bucharest, Romania.","DOI":"10.1109\/ICComm.2018.8484763"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Chamran, M.K., Yau, K.-L.A., Noor, R.M.D., and Wong, R. (2019). A Distributed Testbed for 5G Scenarios: An Experimental Study. Sensors, 20.","DOI":"10.3390\/s20010018"},{"key":"ref_26","unstructured":"(2022, March 12). LimeSDR Mini Is a $135 Open Source Hardware, Full Duplex USB SDR Board (Crowdfunding). Available online: https:\/\/www.cnx-software.com\/2017\/09\/18\/limesdr-mini-is-a-135-open-source-hardware-full-duplex-usb-sdr-board-crowdfunding\/."},{"key":"ref_27","unstructured":"(2022, March 12). HackRF One\u2014Great Scott Gadgets. Available online: https:\/\/greatscottgadgets.com\/hackrf\/one\/."},{"key":"ref_28","unstructured":"(2022, March 12). Nooelec\u2014Nooelec NESDR SMArt v4 SDR\u2014Premium RTL-SDR w\/Aluminum Enclosure, 0.5PPM TCXO, SMA Input. RTL2832U & R820T2-Based\u2014Software Defined Radio. Available online: https:\/\/www.nooelec.com\/store\/sdr\/nesdr-smart-sdr.html."},{"key":"ref_29","unstructured":"(2022, March 12). LimeSDR Mini. Available online: https:\/\/limemicro.com\/products\/boards\/limesdr-mini\/."},{"key":"ref_30","unstructured":"(2022, March 12). Cuadro Nacional de Atribuci\u00f3n de Frecuencias (CNAF)|Cuadro Nacional de Atribuci\u00f3n de Frecuencias (CNAF)\u2014IFT. Available online: http:\/\/cnaf.ift.org.mx\/."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1111\/j.2517-6161.1977.tb01600.x","article-title":"Maximum Likelihood from Incomplete Data Via the EM Algorithm","volume":"39","author":"Dempster","year":"1977","journal-title":"J. R. Stat. Soc. Ser. B Methodol."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"9221","DOI":"10.1109\/ACCESS.2020.2964210","article-title":"Wi-Fi\/LTE-U Coexistence: Real-Tome Issues and Solutions","volume":"8","author":"Sathya","year":"2020","journal-title":"IEEE Access"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/3\/411\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:36:47Z","timestamp":1760135807000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/3\/411"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,3,15]]},"references-count":32,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2022,3]]}},"alternative-id":["e24030411"],"URL":"https:\/\/doi.org\/10.3390\/e24030411","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2022,3,15]]}}}