{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,16]],"date-time":"2026-02-16T17:06:07Z","timestamp":1771261567375,"version":"3.50.1"},"reference-count":49,"publisher":"MDPI AG","issue":"22","license":[{"start":{"date-parts":[[2021,11,18]],"date-time":"2021-11-18T00:00:00Z","timestamp":1637193600000},"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>Cognitive radio (CR) technology has the potential to detect and share the unutilized spectrum by enabling dynamic spectrum access. To detect the primary users\u2019 (PUs) activity, energy detection (ED) is widely exploited due to its applicability when it comes to sensing a large range of PU signals, low computation complexity, and implementation costs. As orthogonal frequency-division multiplexing (OFDM) transmission has been proven to have a high resistance to interference, the ED of OFDM signals has become an important local spectrum-sensing (SS) concept in cognitive radio networks (CRNs). In combination with multiple-input multiple-output (MIMO) transmissions, MIMO-OFDM-based transmissions have started to become a widely accepted air interface, which ensures a significant improvement in spectral efficiency. Taking into account the future massive implementation of MIMO-OFDM systems in the fifth and sixth generation of mobile networks, this work introduces a mathematical formulation of expressions that enable the analysis of ED performance based on the square-law combining (SLC) method in MIMO-OFDM systems. The analysis of the ED performance was done through simulations performed using the developed algorithms that enable the performance analysis of the ED process based on the SLC in the MIMO-OFDM systems having a different number of transmit (Tx) and receive (Rx) communication branches. The impact of the distinct factors including the PU Tx power, the false alarm probability, the number of Tx and Rx MIMO branches, the number of samples in the ED process, and the different modulation techniques on the ED performance in environments with different levels of signal-to-noise ratios are presented. A comprehensive analysis of the obtained results indicated how the appropriate selection of the analyzed factors can be used to enhance the ED performance of MIMO-OFDM-based CRNs.<\/jats:p>","DOI":"10.3390\/s21227678","type":"journal-article","created":{"date-parts":[[2021,11,19]],"date-time":"2021-11-19T02:43:09Z","timestamp":1637289789000},"page":"7678","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Performance Analyses of Energy Detection Based on Square-Law Combining in MIMO-OFDM Cognitive Radio Networks"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7691-582X","authenticated-orcid":false,"given":"Josip","family":"Lorincz","sequence":"first","affiliation":[{"name":"Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture (FESB), University of Split, 21000 Split, Croatia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ivana","family":"Ramljak","sequence":"additional","affiliation":[{"name":"Elektroprenos\u2013Elektroprijenos BiH\u201d a.d. Banja Luka, 88000 Mostar, Bosnia and Herzegovina"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dinko","family":"Begu\u0161i\u0107","sequence":"additional","affiliation":[{"name":"Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture (FESB), University of Split, 21000 Split, Croatia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,11,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1109\/MCOM.2008.4557045","article-title":"IEEE standards supporting cognitive radio and networks, dynamic spectrum access, and coexistence","volume":"46","author":"Sherman","year":"2008","journal-title":"IEEE Commun. Mag."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1354","DOI":"10.1016\/j.comnet.2009.01.002","article-title":"Trends in the development of communication networks: Cognitive networks","volume":"53","author":"Fortuna","year":"2009","journal-title":"Comput. Netw."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Pandit, S., and Singh, G. (2017). Spectrum sensing in cognitive radio networks: Potential challenges and future perspective in spectrum sharing in cognitive radio networks. Spectrum Sharing in Cognitive Radio Networks, Springer International Publishing AG. [1st ed.].","DOI":"10.1007\/978-3-319-53147-2"},{"key":"ref_4","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_5","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_6","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1109\/MWC.2013.6507397","article-title":"Wideband spectrum sensing for cognitive radio networks: A survey","volume":"20","author":"Sun","year":"2013","journal-title":"IEEE Wirel. Commun."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1109\/MCOM.2011.5723803","article-title":"Emerging cognitive radio applications: A survey","volume":"49","author":"Wang","year":"2011","journal-title":"IEEE Commun. Mag."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Xiao, Y., and Hu, F. (2008). Cognitive Radio Networks, Auerbach Publications. [1st ed.].","DOI":"10.1201\/9781420064216"},{"key":"ref_9","unstructured":"Al-Hmood, H. (2015). Performance Analysis of Energy Detector over Different Generalised Wireless Channels Based Spectrum Sensing in Cognitive Radio. [Ph.D. Dissertation, Depart. of Elect. and Comp. Eng., Brunel University London]."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Eduard, A.F., and Caballero, R.G.G. (2015, January 13\u201315). Experimental Evaluation of Performance for Spectrum Sensing: Matched Filter vs Energy Detector. Proceedings of the IEEE Colombian Conference on Communication and Computing (IEEE COLCOM 2015), Popayan, Colombia.","DOI":"10.1109\/ColComCon.2015.7152105"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Gorcin, A., Qaraqe, K.A., Celebi, H., and Arslan, H. (2010, January 4\u20137). An Adaptive Threshold Method for Spectrum Sensing in Multi-Channel Cognitive Radio Networks. Proceedings of the 17th International Conference on Telecommunications, Doha, Qatar.","DOI":"10.1109\/ICTEL.2010.5478783"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Kumar, A., Thakur, P., Pandit, S., and Singh, G. (2017, January 10\u201312). Fixed and Dynamic Threshold Selection Criteria in Energy Detection for Cognitive Radio Communication Systems. Proceedings of the 2017 Tenth International Conference on Contemporary Computing (IC3), Uttar Pradesh, India.","DOI":"10.1109\/IC3.2017.8284302"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Wang, N., Gao, Y., and Cuthbert, L. (2014, January 19\u201321). Spectrum Sensing Using Adaptive Threshold Based ED for OFDM Signals. Proceedings of the 2014 IEEE International Conference on Communication Systems, Macau, China.","DOI":"10.1109\/ICCS.2014.7024825"},{"key":"ref_14","unstructured":"Rwodzi, J. (2016). Energy-Detection Based Spectrum Sensing for Cognitive Radio on a Real-Time SDR Platform. [Master\u2019s Thesis, University of Cape Town]."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"4543","DOI":"10.1007\/s11277-017-4402-1","article-title":"A proposed scheme for dynamic threshold versus noise uncertainty in cognitive radio networks (DTNU)","volume":"96","author":"Arar","year":"2017","journal-title":"Wirel. Personal. Commun."},{"key":"ref_16","unstructured":"Thuo, N. (2015). An Adaptive Threshold Energy Detection Technique with Noise Variance Estimation for Cognitive Radio Sensor Networks. [Master\u2019s Thesis, University of Cape Town]."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1640","DOI":"10.1109\/TWC.2010.05.090102","article-title":"Subcarrier-pair based resource allocation for cooperative multi-relay OFDM systems","volume":"9","author":"Dang","year":"2010","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1","DOI":"10.17485\/ijst\/2016\/v9i16\/90230","article-title":"Analysis of OFDM system with energy detection spectrum sensing","volume":"9","author":"Nandhakumar","year":"2016","journal-title":"Indian J. Sci. Technol."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1049\/iet-com.2010.1038","article-title":"Sensing orthogonal frequency division multiplexing systems for cognitive radio with cyclic prefix and pilot tones","volume":"6","author":"Chen","year":"2012","journal-title":"IET Commun."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Chataut, R., and Akl, R. (2020). Massive MIMO Systems for 5G and beyond networks-overview, recent trends, challenges, and future research direction. Sensors, 20.","DOI":"10.3390\/s20102753"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1109\/JSAC.2003.809458","article-title":"From theory to practice: An overview of MIMO space-time coded wireless systems","volume":"21","author":"Gesbert","year":"2003","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_22","first-page":"304901","article-title":"Performance analysis of MIMO-STBC systems with higher coding rate using adaptive semiblind channel estimation scheme","volume":"2014","author":"Kumar","year":"2014","journal-title":"Res. Artic."},{"key":"ref_23","first-page":"1","article-title":"Sparse channel estimation of MIMO-OFDM systems with unconstrained smoothed l0\u2212norm-regularized least squares compressed sensing","volume":"282","author":"Ye","year":"2013","journal-title":"EURASIP J. Wirel. Commun. Netw."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Xu, J., and Choi, G. (2015, January 16\u201319). Compressive Sensing and Reception for MIMO-OFDM Based Cognitive Radio. Proceedings of the 2015 International Conference on Computing, Networking and Communications (ICNC), Garden Grove, CA, USA.","DOI":"10.1109\/ICCNC.2015.7069463"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"012001","DOI":"10.1088\/1742-6596\/1817\/1\/012001","article-title":"Performance of massive MIMO systems in cognitive spectrum sensing","volume":"1817","author":"Shamla","year":"2021","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_26","unstructured":"Hmida, A.B.H., Cherif, S., and Besbes, H. (April, January 29). Spectrum Sensing Based on STBC Higher Order Statistics for Cognitive Radio Systems. Proceedings of the Third International Conference on Communications and Networking, Hammamet, Tunisia."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"8874","DOI":"10.1109\/JIOT.2020.2997707","article-title":"MIMO spectrum sensing for cognitive radio-based Internet of things","volume":"7","author":"Zhang","year":"2020","journal-title":"IEEE Internet Things J."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Laikanok, R., Uthansakul, P., and Uthansakul, M. (2014, January 14\u201317). Spectrum Sensing with Integration of Energy Detector and Diversity Techniques for MIMO systems. Proceedings of the 2014 11th International Conference on Electrical Engineering\/Electronics, Computer, Telecommunications and Information Technology (ECTI-CON), Nakhon Ratchasima, Thailand.","DOI":"10.1109\/ECTICon.2014.6839790"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Cho, Y.S., Kim, J., Yang, W.Y., and Kang, C.G. (2010). MIMO-OFDM Wireless Communication with Matlab, John Wiley & Sons.","DOI":"10.1002\/9780470825631"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Arjoune, Y., and Kaabouch, N.A. (2019). 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_31","doi-asserted-by":"crossref","unstructured":"Gamit, J.S., and Trapasiya, S.D. (2013, January 3\u20135). Cognitive Radio Energy Based Spectrum Sensing using MIMO. Proceedings of the 2013 International Conference on Communication and Signal Processing, Melmaruvathur, India.","DOI":"10.1109\/iccsp.2013.6577147"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Atapattu, S., Tellambura, C., and Jiang, H. (2014). Energy Detection for Spectrum Sensing in Cognitive Radio, Springer International Publishing AG.","DOI":"10.1007\/978-1-4939-0494-5"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1109\/JPROC.2003.821912","article-title":"Broadband MIMO-OFDM wireless communications","volume":"92","author":"Stuber","year":"2004","journal-title":"Proc. IEEE"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1673","DOI":"10.1109\/TVT.2008.2004555","article-title":"OFDM and its wireless applications: A survey","volume":"58","author":"Yang","year":"2009","journal-title":"IEEE Trans. Veh. Tech."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1206","DOI":"10.1109\/ACCESS.2015.2461602","article-title":"A survey of 5G network: Architecture and emerging technologies","volume":"3","author":"Gupta","year":"2015","journal-title":"IEEE Access"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Kuppusamy, V., and Mahapatra, R. (2008, January 15\u201317). Primary User Detection in OFDM Based MIMO Cognitive Radio. Proceedings of the 2008 3rd International Conference on Cognitive Radio Oriented Wireless Networks and Communications (CrownCom 2008), Singapore.","DOI":"10.1109\/CROWNCOM.2008.4562561"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"\u00dcstok, R.F. (2009). Spectrum Sensing Techniques for Cognitive Radio Systems with Multiple Antennas. [Master\u2019s Thesis, Graduate School of Engineering and Sciences, Izmir Instititute of Technnology].","DOI":"10.1109\/SIU.2009.5136416"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Rodes, L., Kaushik, A., Sharma, S.K., Chatzinotas, S., and Jondral, F. (2016, January 18\u201321). Square-law Selector and Square-law Combiner for Cognitive Radio Systems: An Experimental Study. Proceedings of the 2016 IEEE 84th Vehicular Technology Conference (VTC-Fall), Montreal, QC, Canada.","DOI":"10.1109\/VTCFall.2016.7881236"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Ranjeeth, M. (2015, January 26\u201328). Cooperative Spectrum Sensing with Square Law Combining Diversity Reception. Proceedings of the 2015 3rd International Conference on Signal Processing, Communication and Networking (ICSCN), Chennai, India.","DOI":"10.1109\/ICSCN.2015.7219876"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"3575","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_41","doi-asserted-by":"crossref","unstructured":"Tellambura, C. (2018). Spectrum sensing methods and their performance. Handbook of Cognitive Radio, Springer Nature. [1st ed.].","DOI":"10.1007\/978-981-10-1394-2_6"},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Braga, A.J., De Souza, R.A.A., Da Costa, J.P.C.L., and Carre\u00f1o, J.D.P. (2014, January 5\u20137). Continuous Spectrum Sensing and Transmission in MIMO Cognitive Radio Network. Proceedings of the 2014 IEEE Latin-America Conference on Communications (LATINCOM), Cartagena, Colombia.","DOI":"10.1109\/LATINCOM.2014.7041891"},{"key":"ref_43","unstructured":"Ma, W., Wu, M.Q., Liu, D., and Wang, M.L. (2009, January 8\u201311). User sensing based on MIMO cognitive radio sensor networks. Proceedings of the 2009 2nd IEEE International Conference on Computer Science and Information Technology, Beijing, China."},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Marey, M., Dobre, O.A., and Inkol, R. (2013, January 9\u201313). Novel algorithm for STBC-OFDM identification in cognitive radios. Proceedings of the 2013 IEEE International Conference on Communications (ICC), Budapest, Hungary.","DOI":"10.1109\/ICC.2013.6654958"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1554","DOI":"10.1109\/TCOMM.2014.030214.130875","article-title":"Blind STBC identification for multiple-antenna OFDM systems","volume":"62","author":"Marey","year":"2014","journal-title":"IEEE Trans. Commun."},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Lorincz, J., Begu\u0161i\u0107, D., and Ramljak, I. (2018, January 13\u201315). Misdetection probability analyses of ofdm signals in energy detection cognitive radio systems. Proceedings of the 26th International Conference on Software, Telecommunications and Computer Networks (SoftCOM 2019), Split, Croatia.","DOI":"10.23919\/SOFTCOM.2018.8555811"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1016\/j.comcom.2019.09.013","article-title":"A review of the noise uncertainty impact on energy detection with different OFDM system designs","volume":"148","author":"Lorincz","year":"2019","journal-title":"Comput. Commun."},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Lorincz, J., Ramljak, I., and Begu\u0161i\u0107, D. (2021). A survey on the energy detection of OFDM signals with dynamic threshold adaptation: Open Issues and Future Challenges. Sensors, 21.","DOI":"10.3390\/s21093080"},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Lorincz, J., Ramljak, I., and Begusic, D. (2021). Algorithm for Evaluating Energy Detection Spectrum Sensing Performance of Cognitive Radio MIMO-OFDM Systems. Sensors, 21.","DOI":"10.3390\/s21206881"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/22\/7678\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:32:21Z","timestamp":1760167941000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/22\/7678"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,11,18]]},"references-count":49,"journal-issue":{"issue":"22","published-online":{"date-parts":[[2021,11]]}},"alternative-id":["s21227678"],"URL":"https:\/\/doi.org\/10.3390\/s21227678","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,11,18]]}}}