{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,15]],"date-time":"2024-09-15T07:10:12Z","timestamp":1726384212235},"reference-count":53,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2022,2,23]],"date-time":"2022-02-23T00:00:00Z","timestamp":1645574400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100006769","name":"Russian Science Foundation","doi-asserted-by":"publisher","award":["22-29-01458"],"id":[{"id":"10.13039\/501100006769","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"This paper studies the performance of the energy-based sensing procedure in the presence of multipath fading and shadowing effects in terms of its average probability of detection (APD), average receiver operating characteristic (AROC) and the area under the AROC curve (AUC). A new generalization for the class of the fading channel moment generating functions (MGFs) (i.e., factorized power type (FPT) MGF) was proposed and applied for the construction of the unified framework for the analytical treatment of the formulated problem. The contiguity of the proposed model with the existing classical ones (Rayleigh, Nakagami-m, Hoyt, \u03b7\u2212\u03bc, \u03ba\u2212\u03bc shadowed and Mixture-Gamma) was demonstrated. Within the assumed MGF representation, the novel closed-form solutions and computationally efficient approximation for APD and AUC are derived. The obtained general expressions were then applied for derivation of the new results for the recent generalized fading channel models: Fluctuating Beckmann and Beaulieu-Xie shadowed. For each of the models, high-SNR asymptotic expressions were obtained. Lastly, numeric simulation was performed to verify the correctness of the derived results, to establish the dependencies of the sensing performance quality from the channel parameters and to identify the specific ranges of their asymptotic behavior.<\/jats:p>","DOI":"10.3390\/s22051742","type":"journal-article","created":{"date-parts":[[2022,2,24]],"date-time":"2022-02-24T05:53:26Z","timestamp":1645682006000},"page":"1742","source":"Crossref","is-referenced-by-count":6,"title":["A Novel Unified Framework for Energy-Based Spectrum Sensing Analysis in the Presence of Fading"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"http:\/\/orcid.org\/0000-0001-9308-4386","authenticated-orcid":false,"given":"Aleksey S.","family":"Gvozdarev","sequence":"first","affiliation":[{"name":"Intelligent Information Radiophysics Systems Department, P. G. Demidov Yaroslavl State University, 150003 Yaroslavl, Russia"}]}],"member":"1968","published-online":{"date-parts":[[2022,2,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Atapattu, S., Tellambura, C., and Jiang, H. (2014). Energy Detection for Spectrum Sensing in Cognitive Radio, Springer. Springer Briefs in Computer Science.","DOI":"10.1007\/978-1-4939-0494-5"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1109\/MSP.2012.2183771","article-title":"Spectrum Sensing for Cognitive Radio: State-of-the-Art and Recent Advances","volume":"29","author":"Axell","year":"2012","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"523","DOI":"10.1109\/PROC.1967.5573","article-title":"Energy detection of unknown deterministic signals","volume":"55","author":"Urkowitz","year":"1967","journal-title":"Proc. IEEE"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Simon, M.K., and Alouini, M.S. (2005). Digital Communication over Fading Channels, John Wiley & Sons, Inc.","DOI":"10.1002\/0471715220"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Peppas, K., Nistazakis, H., and Tombras, G. (2011). An Overview of the Physical Insight and the Various Performance Metrics of Fading Channels in Wireless Communication Systems. Advanced Trends in Wireless Communications, InTech.","DOI":"10.5772\/15028"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"258308","DOI":"10.1155\/2014\/258308","article-title":"Advances in the Statistical Characterization of Fading: From 2005 to Present","volume":"2014","author":"Paris","year":"2014","journal-title":"Int. J. Antennas Propag."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Shankar, P.M. (2017). Fading and Shadowing in Wireless Systems, Springer International Publishing.","DOI":"10.1007\/978-3-319-53198-4"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1109\/TCOMM.2006.887483","article-title":"On the Energy Detection of Unknown Signals Over Fading Channels","volume":"55","author":"Digham","year":"2007","journal-title":"IEEE Trans. Commun."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Atapattu, S., Tellambura, C., and Jiang, H. (2009, January 28\u201331). Energy detection of primary signals over \u03b7 \u2212 \u03bc fading channels. Proceedings of the 2009 International Conference on Industrial and Information Systems (ICIIS), Peradeniya, Sri Lanka.","DOI":"10.1109\/ICIINFS.2009.5429879"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Alam, S., Olabiyi, O., Odejide, O., and Annamalai, A. (2011, January 5\u20139). Energy detector\u2019s performance evaluation in a relay based cognitive radio network: Area under the ROC curve (AUC) approach. Proceedings of the 2011 IEEE GLOBECOM Workshops (GC Wkshps), Houston, TX, USA.","DOI":"10.1109\/GLOCOMW.2011.6162466"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"4193","DOI":"10.1109\/TWC.2011.111210.102115","article-title":"A Mixture Gamma Distribution to Model the SNR of Wireless Channels","volume":"10","author":"Atapattu","year":"2011","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1301","DOI":"10.1109\/LCOMM.2011.103111.111420","article-title":"MGF Based Analysis of Area under the ROC Curve in Energy Detection","volume":"15","author":"Atapattu","year":"2011","journal-title":"IEEE Commun. Lett."},{"key":"ref_13","unstructured":"Annamalai, A., and Olaluwe, A. (2014, January 3\u20136). Energy detection of unknown deterministic signals in \u03ba \u2212 \u03bc and \u03b7 \u2212 \u03bc generalized fading channels with diversity receivers. Proceedings of the 2014 International Conference on Computing, Networking and Communications (ICNC), Honolulu, HI, USA."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1944","DOI":"10.1049\/el.2014.2944","article-title":"Performance analysis of energy detection-based spectrum sensing in \u03ba \u2212 \u03bc shadowed fading","volume":"50","author":"Aloqlah","year":"2014","journal-title":"Electron. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"196","DOI":"10.1049\/iet-com.2014.0170","article-title":"Energy detection of unknown signals in Gamma-shadowed Rician fading environments with diversity reception","volume":"9","author":"Peppas","year":"2015","journal-title":"IET Commun."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"876","DOI":"10.1080\/10652469.2017.1381091","article-title":"Partial order generalized Marcum Q-function contour integral representation","volume":"28","author":"Gvozdarev","year":"2017","journal-title":"Integral Transform. Spec. Funct."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Bagheri, A., Sofotasios, P.C., Tsiftsis, T.A., Ho-Van, K., Loupis, M.I., Freear, S., and Valkama, M. (2016, January 3\u20136). Energy detection based spectrum sensing over enriched multipath fading channels. Proceedings of the 2016 IEEE Wireless Communications and Networking Conference, Doha, Qatar.","DOI":"10.1109\/WCNC.2016.7565141"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"553","DOI":"10.1109\/LWC.2015.2457895","article-title":"Performance Analysis of Cooperative Spectrum Sensing Over \u03ba \u2212 \u03bc Shadowed Fading","volume":"4","author":"Chandrasekaran","year":"2015","journal-title":"IEEE Wirel. Commun. Lett."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Aloqlah, M.S., and Alzubaidi, R.A. (2018, January 21\u201323). Energy-Detection performance for SIMO Cognitive Radio Systems with Selection Combining over \u03ba \u2212 \u03bc Shadowed Fading Channels. Proceedings of the 2018 28th International Telecommunication Networks and Applications Conference (ITNAC), Sydney, NSW, Australia.","DOI":"10.1109\/ATNAC.2018.8615219"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"7653","DOI":"10.1109\/TVT.2017.2678430","article-title":"The \u03ba \u2212 \u03bc Shadowed Fading Model With Integer Fading Parameters","volume":"66","author":"Paris","year":"2017","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Adebola, E., and Annamalai, A. (2013, January 2\u20136). Unified analysis of diversity average energy detectors over generalized fading channels. Proceedings of the 2013 International Conference on Connected Vehicles and Expo (ICCVE), Las Vegas, NV, USA.","DOI":"10.1109\/ICCVE.2013.6799780"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"3095","DOI":"10.1049\/iet-com.2014.0199","article-title":"Unified analysis of energy detectors with diversity reception in generalised fading channels","volume":"8","author":"Adebola","year":"2014","journal-title":"IET Commun."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"837","DOI":"10.1049\/el.2014.0010","article-title":"Unified approach to performance analysis of energy detection in generalised fading channels","volume":"50","author":"Wang","year":"2014","journal-title":"Electron. Lett."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1532","DOI":"10.1049\/iet-com.2016.0108","article-title":"Unified approach for probability of detection evaluation over generalised fading channels","volume":"10","author":"Ayadi","year":"2016","journal-title":"IET Commun."},{"key":"ref_25","unstructured":"Olver, F.W.J. (2010). NIST Handbook of Mathematical Functions, Cambridge University Press."},{"key":"ref_26","unstructured":"Paris, J.F. (2011). Unified Analysis of the Average Gaussian Error Probability for a Class of Fading Channels. arXiv."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"120513","DOI":"10.1109\/ACCESS.2020.3005527","article-title":"On Shadowing the \u03ba \u2212 \u03bc Fading Model","volume":"8","author":"Simmons","year":"2020","journal-title":"IEEE Access"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"518","DOI":"10.1109\/TVT.2013.2281213","article-title":"Statistical Characterization of \u03ba \u2212 \u03bc Shadowed Fading","volume":"63","author":"Paris","year":"2014","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"104","DOI":"10.1109\/LAWP.2016.2558455","article-title":"Unified Modeling of Composite \u03ba -\u03bc \/Gamma, \u03b7 -\u03bc\/Gamma, and \u03b1 -\u03bc\/Gamma Fading Channels Using a Mixture Gamma Distribution With Applications to Energy Detection","volume":"16","year":"2017","journal-title":"IEEE Antennas Wirel. Propag. Lett."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Al-Hmood, H. (2018, January 8\u20139). Performance of Cognitive Radio Systems over \u03ba \u2212 \u03bc Shadowed with Integer \u03bc and Fisher-Snedecor F Fading Channels. Proceedings of the 2018 International Conference on Engineering Technology and their Applications (IICETA), Al-Najaf, Iraq.","DOI":"10.1109\/IICETA.2018.8458088"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"2163","DOI":"10.1080\/09205071.2021.1934901","article-title":"Average quality description of energy detection for generalised multipath shadowed \u03ba \u2212 \u03bc fading channels","volume":"35","author":"Gvozdarev","year":"2021","journal-title":"J. Electromagn. Waves Appl."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"3826","DOI":"10.1109\/TVT.2017.2787204","article-title":"An Extension of the \u03ba \u2212 \u03bc Shadowed Fading Model: Statistical Characterization and Applications","volume":"67","author":"Paris","year":"2018","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Shi, Z., Zhang, H., Zhong, S., Yang, G., Ye, X., and Ma, S. (2018, January 18\u201320). On the Performance of Variable-Rate HARQ-IR over Beckmann Fading Channels. Proceedings of the 2018 10th International Conference on Wireless Communications and Signal Processing (WCSP), Hangzhou, China.","DOI":"10.1109\/WCSP.2018.8555645"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1489","DOI":"10.1109\/LWC.2019.2923786","article-title":"Coverage and Rate Analysis in Downlink L-Tier HetNets With Fluctuating Beckmann Fading","volume":"8","author":"Chen","year":"2019","journal-title":"IEEE Wirel. Commun. Lett."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"119541","DOI":"10.1109\/ACCESS.2019.2937631","article-title":"Performance Analysis of Physical-Layer Security Over Fluctuating Beckmann Fading Channels","volume":"7","year":"2019","journal-title":"IEEE Access"},{"key":"ref_36","unstructured":"Devarakonda, S.J.S., and Pamula, V.K. (2019, January 21\u201323). Error Rate Analysis of MPSK Signals over Fluctuating Beckmann Fading Channel. Proceedings of the 2019 International Conference on Wireless Communications Signal Processing and Networking (WiSPNET), Chennai, India."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"326","DOI":"10.1109\/LWC.2017.2685506","article-title":"Level Crossing Rate and Average Fade Duration for the Beaulieu-Xie Fading Model","volume":"6","author":"Olutayo","year":"2017","journal-title":"IEEE Wirel. Commun. Lett."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Kansal, V., and Singh, S. (2018, January 16\u201317). Analysis of Average Symbol Error Probability of MDPSK, MFSK and MPSK in the Beaulieu-Xie Fading. Proceedings of the 2018 6th Edition of International Conference on Wireless Networks & Embedded Systems (WECON), Rajpura, India.","DOI":"10.1109\/WECON.2018.8782053"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"916","DOI":"10.1109\/OJCOMS.2020.3008161","article-title":"A New Statistical Channel Model for Emerging Wireless Communication Systems","volume":"1","author":"Olutayo","year":"2020","journal-title":"IEEE Open J. Commun. Soc."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Kansal, V., and Singh, S. (2020, January 5\u20137). Average Bit Error Rate Analysis of Selection Combining over Beaulieu-Xie Fading Model. Proceedings of the 2020 6th International Conference on Signal Processing and Communication (ICSC), Noida, India.","DOI":"10.1109\/ICSC48311.2020.9182720"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1124","DOI":"10.1109\/LCOMM.2020.3044157","article-title":"The Generalized MGF Approach to Closed-Form Average Symbol Error Rate Calculation","volume":"25","author":"Gvozdarev","year":"2021","journal-title":"IEEE Commun. Lett."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"2678","DOI":"10.1109\/TVT.2014.2343453","article-title":"On the Sum of Correlated Squared \u03ba \u2212 \u03bc Shadowed Random Variables and Its Application to Performance Analysis of MRC","volume":"64","author":"Bhatnagar","year":"2015","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"1471","DOI":"10.1109\/25.966578","article-title":"Sum of gamma variates and performance of wireless communication systems over Nakagami-fading channels","volume":"50","author":"Alouini","year":"2001","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"935","DOI":"10.1109\/TCOMM.2016.2637926","article-title":"On High-Order Capacity Statistics of Spectrum Aggregation Systems Over \u03ba \u2212 \u03bc and \u03ba \u2212 \u03bc Shadowed Fading Channels","volume":"65","author":"Zhang","year":"2017","journal-title":"IEEE Trans. Commun."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1232","DOI":"10.1109\/TWC.2011.012411.100611","article-title":"Energy Detection Based Cooperative Spectrum Sensing in Cognitive Radio Networks","volume":"10","author":"Atapattu","year":"2011","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Alhussein, O., Hammadi, A.A., Sofotasios, P.C., Muhaidat, S., Liang, J., Al-Qutayri, M., and Karagiannidis, G.K. (2015, January 19\u201321). Performance analysis of energy detection over mixture gamma based fading channels with diversity reception. Proceedings of the 2015 IEEE 11th International Conference on Wireless and Mobile Computing, Networking and Communications (WiMob), Abu Dhabi, United Arab Emirates.","DOI":"10.1109\/WiMOB.2015.7347990"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1016\/0377-0427(88)90320-2","article-title":"On the computation of Lauricella functions of the fourth kind","volume":"21","author":"Kalker","year":"1988","journal-title":"J. Comput. Appl. Math."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1287\/ijoc.7.1.36","article-title":"Numerical Inversion of Laplace Transforms of Probability Distributions","volume":"7","author":"Abate","year":"1995","journal-title":"ORSA J. Comput."},{"key":"ref_49","unstructured":"Cohen, A.M. (2007). Numerical Methods for Laplace Transform Inversion, Springer. Numerical Methods and Algorithms."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"793","DOI":"10.1080\/10652469.2011.636651","article-title":"Some formulas for the Appell F1(a, b, b\u2019; c; w, z)","volume":"23","author":"Brychkov","year":"2011","journal-title":"Integral Transform. Spec. Funct."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"8289","DOI":"10.1109\/TWC.2017.2760822","article-title":"Outage Probability and Rate for \u03ba \u2212 \u03bc Shadowed Fading in Interference Limited Scenario","volume":"16","author":"Kumar","year":"2017","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"1021","DOI":"10.1109\/LSP.2019.2915000","article-title":"Kullback-Leibler Divergence Between Multivariate Generalized Gaussian Distributions","volume":"26","author":"Bouhlel","year":"2019","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_53","unstructured":"Srivastava, H., and Karlsson, P. (1985). Multiple Gaussian Hypergeometric Series, Halsted Press."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/5\/1742\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,26]],"date-time":"2024-07-26T14:42:04Z","timestamp":1722004924000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/5\/1742"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,2,23]]},"references-count":53,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2022,3]]}},"alternative-id":["s22051742"],"URL":"https:\/\/doi.org\/10.3390\/s22051742","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,2,23]]}}}