{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,10]],"date-time":"2026-01-10T02:28:45Z","timestamp":1768012125909,"version":"3.49.0"},"reference-count":31,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,1,7]],"date-time":"2021-01-07T00:00:00Z","timestamp":1609977600000},"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>With growing interest in Industry 4.0, machine-to-machine communication (M2M) will become the key enabler for low-power wide area networks (LPWANs) in connecting machines and sensor nodes distributed across a distance in the industrial environment. The choice of modulation and diversity techniques, and the selection of spectrum (licensed\/unlicensed) will impact and influence the requirements of wireless M2M systems. Link reliability is one of the most important requirements for LPWAN deployment in industrial scenarios. Rotating Polarization Wave (RPW) system has been recently proposed as an LPWAN solution for reliable M2M communication in high clutter environment and it deploys BPSK modulation with polarization diversity (PD). This paper proposes a new multi-level Rotating Polarization Phase-Shift Keying (RP-MPSK) modulation to provide high data rate and energy efficiency. A novel quaternion model for RPW system (Q-RPW) is also proposed to reduce the complexity in modeling, simulation, and implementation. Results using Q-RPW model show that RP-MPSK modulation offers a high diversity gain over BPSK with second-order diversity. Bit error rate (BER) performance of RP-MPSK modulation compared against other LPWAN modulation like MPSK, FSK and QAM has shown high reliability and substantial improvement in SNR. To overcome the degradation in error performance caused by the proposed higher-order modulation, sampling rates are recommended based on BER performance. BER performance of RP-MPSK under multipath and interference conditions is also investigated.<\/jats:p>","DOI":"10.3390\/s21020383","type":"journal-article","created":{"date-parts":[[2021,1,10]],"date-time":"2021-01-10T23:03:42Z","timestamp":1610319822000},"page":"383","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Quaternion Model of Higher-Order Rotating Polarization Wave Modulation for High Data Rate M2M LPWAN Communication"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6748-2727","authenticated-orcid":false,"given":"Zaid","family":"Ahmad","sequence":"first","affiliation":[{"name":"WiPNET Research Center, Department of Computer and Communication Systems Engineering, Universiti Putra Malaysia, Serdang, Selangor 43400, Malaysia"},{"name":"Department of Electrical and Computer Engineering, COMSATS University (CUI), Lahore 54600, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shaiful Jahari","family":"Hashim","sequence":"additional","affiliation":[{"name":"WiPNET Research Center, Department of Computer and Communication Systems Engineering, Universiti Putra Malaysia, Serdang, Selangor 43400, Malaysia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fakhrul Zaman","family":"Rokhani","sequence":"additional","affiliation":[{"name":"WiPNET Research Center, Department of Computer and Communication Systems Engineering, Universiti Putra Malaysia, Serdang, Selangor 43400, Malaysia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Syed Abul Rahman","family":"Al-Haddad","sequence":"additional","affiliation":[{"name":"WiPNET Research Center, Department of Computer and Communication Systems Engineering, Universiti Putra Malaysia, Serdang, Selangor 43400, Malaysia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Aduwati","family":"Sali","sequence":"additional","affiliation":[{"name":"WiPNET Research Center, Department of Computer and Communication Systems Engineering, Universiti Putra Malaysia, Serdang, Selangor 43400, Malaysia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ken","family":"Takei","sequence":"additional","affiliation":[{"name":"Research and Development Group, Hitachi Ltd., Tokyo 185-8601, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,1,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Alam, M., Nielsen, R.H., and Prasad, N.R. (2013, January 3\u20135). The evolution of M2M into IoT. Proceedings of the 1st International Black Sea Conference on Communications and Networking, Batumi, GA, USA.","DOI":"10.1109\/BlackSeaCom.2013.6623392"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"944","DOI":"10.1109\/JPROC.2019.2913443","article-title":"Industrial Communication Systems and Their Future Challenges: Next-Generation Ethernet, IIoT, and 5G","volume":"107","author":"Vitturi","year":"2019","journal-title":"Proc. IEEE"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1016\/j.comnet.2018.09.001","article-title":"Machine-to-Machine Communication: An Overview of Opportunities","volume":"145","author":"Amodu","year":"2018","journal-title":"Comput. Netw."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1016\/j.pmcj.2018.08.002","article-title":"Machine-to-machine wireless communication technologies for the Internet of Things: Taxonomy, comparison and open issues","volume":"50","author":"Montori","year":"2018","journal-title":"Pervasive Mob. Comput."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"17179","DOI":"10.1109\/ACCESS.2020.2968057","article-title":"Low-Power Wide-Area Networks: Design Goals, Architecture, Suitability to Use Cases and Research Challenges","volume":"8","author":"Buurman","year":"2020","journal-title":"IEEE Access"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"77454","DOI":"10.1109\/ACCESS.2018.2883151","article-title":"Low power wide area networks: A survey of enabling technologies, applications and interoperability needs","volume":"6","author":"Qadir","year":"2018","journal-title":"IEEE Access"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"214","DOI":"10.1109\/MNET.001.1900132","article-title":"Emerging Technologies for Machine-Type Communication Networks","volume":"34","author":"Xia","year":"2020","journal-title":"IEEE Netw."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Seferagi\u0107, A., Famaey, J., de Poorter, E., and Hoebeke, J. (2020). Survey on wireless technology trade-offs for the industrial internet of things. Sensors, 20.","DOI":"10.3390\/s20020488"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"6931083","DOI":"10.1155\/2018\/6931083","article-title":"LoRa Performance under Variable Interference and Heavy-Multipath Conditions","volume":"2018","author":"Staniec","year":"2018","journal-title":"Wirel. Commun. Mob. Comput."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Emmanuel, L., and Fernando, X. (2019, January 22\u201323). LoRa Wireless Link Performance in Multipath Underground Mines. Proceedings of the International Conference on Innovation and Intelligence for Informatics, Computing, and Technologies (3ICT 2019), Zallaq, Bahrain.","DOI":"10.1109\/3ICT.2019.8910316"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"144","DOI":"10.1109\/MWC.2014.7000982","article-title":"IEEE 802.11AH: The WiFi approach for M2M communications","volume":"21","author":"Adame","year":"2014","journal-title":"IEEE Wirel. Commun."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2553","DOI":"10.1109\/TSP.2002.803322","article-title":"Performance of multiantenna signaling techniques in the presence of polarization diversity","volume":"50","author":"Nabar","year":"2002","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_13","unstructured":"Stutzman, W. (2018). Polarization in Electromagnetic Systems, Artech House. [2nd ed.]."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1109\/LAWP.2019.2960311","article-title":"Massive MIMO Communication Strategy Using Polarization Diversity for Industrial Scenarios","volume":"19","author":"Challita","year":"2020","journal-title":"IEEE Antennas Wirel. Propag. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Challita, F., Laly, P., Lienard, M., Gaillot, D.P., Tanghe, E., Yusuf, M., and Joseph, W. (2019, January 17\u201321). Impact of Polarization Diversity in Massive MIMO for Industry 4.0. Proceedings of the European Conference on Networks and Communications, Valencia, Spain.","DOI":"10.1109\/EuCNC.2019.8801986"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1109\/COMST.2016.2606639","article-title":"Advances on Exploiting Polarization in Wireless Communications: Channels, Technologies, and Applications","volume":"19","author":"Guo","year":"2017","journal-title":"IEEE Commun. Surv. Tutor."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Wysocki, B.J., Wysocki, T.A., and Seberry, J. (2006, January 24\u201327). Modeling dual polarization wireless fading channels using quaternions. Proceedings of the Joint 1st Workshop on Sensor Networks and Symposium on Trends in Communications, Bratislava, Slovakia.","DOI":"10.1109\/TIC.2006.1708024"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1109\/LSP.2018.2799569","article-title":"Optimal polarization diversity gain in dual-polarized antennas using quaternions","volume":"25","author":"Qureshi","year":"2018","journal-title":"IEEE Signal. Process. Lett."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Yamada, H., and Takei, K. (2019, January 20\u201323). Highly-reliable rotating polarization wave transceiver with optimal polarization selection. Proceedings of the IEEE Radio and Wireless Symposium, Orlando, FL, USA.","DOI":"10.1109\/RWS.2019.8714345"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1002\/ecj.12146","article-title":"Highly reliable wireless communication system using polarization rotating wave for M2M application","volume":"102","author":"Takei","year":"2019","journal-title":"Electron. Commun. Jpn."},{"key":"ref_21","unstructured":"Eriksen, R. (2019). Energy Consumption of Low Power Wide Area Network Node Devices in the Industrial, Scientific and Medical Band. [Master\u2019s Thesis, School of Electrical Engineering and Computer Science (EECS), KTH]. Available online: http:\/\/urn.kb.se\/resolve?urn=urn:nbn:se:kth:diva-259508."},{"key":"ref_22","unstructured":"Anna, H. (2003). Wireless Sensor Network Designs, John Wiley & Sons."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Pejovic, V., and Belding, E.M. (2010, January 20). Energy-efficient communication in next generation rural-area wireless networks. Proceedings of the 2010 ACM Workshop on Cognitive Radio Networks (CoRoNet \u203210), Chicago, IL, USA.","DOI":"10.1145\/1859955.1859961"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Ahmad, Z., Hashim, S.J., Rokhani, F.Z., Al-Haddad, S.A.R., and Sali, A. (2020, January 1\u20133). Enhanced Rotating Polarization Wave for Robust Wireless Connectivity. Proceedings of the 9th IFIP\/IEEE International Conference on Performance Evaluation and Modeling in Wired and Wireless Networks (PEMWN), Berlin, Germany.","DOI":"10.23919\/PEMWN50727.2020.9293084"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2213","DOI":"10.1109\/LCOMM.2013.102913.131514","article-title":"Generalized BER expression of MPSK in the presence of phase error","volume":"17","author":"Jang","year":"2013","journal-title":"IEEE Commun. Lett."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Ferr\u00e9, G., and Giremus, A. (2018, January 9\u201312). LoRa Physical Layer Principle and Performance Analysis. Proceedings of the 25th IEEE International Conference on Electronics, Circuits and Systems (ICECS), Bordeaux, France.","DOI":"10.1109\/ICECS.2018.8617880"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Kulikov, G.V., van Dung, N., and Kulagin, V.P. (2020, January 11\u201313). Comparison of noise immunity of coherent and autocorrelation demodulators of M-PSK signals in a radio channel with a complex interference situation. Proceedings of the Moscow Workshop on Electronic and Networking Technologies (MWENT), Moscow, Russia.","DOI":"10.1109\/MWENT47943.2020.9067464"},{"key":"ref_28","unstructured":"Takabayashi, K., Tanaka, H., and Sakakibara, K. (September, January 29). A Study on SmartBAN Physical Layer Applying Multi-Level PSK Modulation. Proceedings of the XXXIIIrd General Assembly and Scientific Symposium of the International Union of Radio Science, Rome, Italy."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Darvishi, H., Ciuonzo, D., Eide, E.R., and Rossi, P.S. (2020). Sensor-Fault Detection, Isolation and Accommodation for Digital Twins via Modular Data-Driven Architecture. IEEE Sens. J.","DOI":"10.1109\/ICNSC52481.2021.9702175"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"4651","DOI":"10.1109\/TIE.2009.2028349","article-title":"Online and Remote Motor Energy Monitoring and Fault Diagnostics Using Wireless Sensor Networks","volume":"56","author":"Lu","year":"2009","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"948","DOI":"10.1017\/S1759078719000588","article-title":"Ultra-wideband elliptical patch antenna for microwave imaging of wood","volume":"11","author":"Saeidi","year":"2019","journal-title":"Int. J. Microw. Wirel. Technol."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/2\/383\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:08:19Z","timestamp":1760159299000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/2\/383"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1,7]]},"references-count":31,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2021,1]]}},"alternative-id":["s21020383"],"URL":"https:\/\/doi.org\/10.3390\/s21020383","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1,7]]}}}