{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,29]],"date-time":"2025-10-29T13:37:07Z","timestamp":1761745027067,"version":"build-2065373602"},"reference-count":44,"publisher":"MDPI AG","issue":"16","license":[{"start":{"date-parts":[[2019,8,15]],"date-time":"2019-08-15T00:00:00Z","timestamp":1565827200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Funda\u00e7\u00e3o para a Ci\u00eancia e Tecnologia","award":["SFRH\/BD\/129395\/2017"],"award-info":[{"award-number":["SFRH\/BD\/129395\/2017"]}]},{"name":"FCT\/MEC","award":["MASSIVE5G and UID\/EEA\/50008\/2019"],"award-info":[{"award-number":["MASSIVE5G and UID\/EEA\/50008\/2019"]}]},{"name":"European Regional Development Fund (FEDER)","award":["COMPETE 2020, CENTRO 2020, and LISBOA 14-20"],"award-info":[{"award-number":["COMPETE 2020, CENTRO 2020, and LISBOA 14-20"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Applied Sciences"],"abstract":"<jats:p>This paper considers a multiuser broadband uplink massive multiple input multiple output (MIMO) millimeter-wave (mmWave) system. The constant envelope orthogonal frequency division multiplexing (CE-OFDM) is adopted as a modulation technique to allow an efficient power amplification, fundamental for mmWave based systems. Furthermore, a hybrid architecture is considered at the user terminals (UTs) and base station (BS) to reduce the high cost and power consumption required by a full-digital architecture, which has a radio frequency (RF) chain per antenna. Both the design of the UT\u2019s precoder and base station equalizer are considered in this work. With the aim of maximizing the beamforming gain between each UT and the BS, the precoder analog coefficients are computed as a function of the average angles of departure (AoD), which are assumed to be known at the UTs. At the BS, the analog part is derived by assuming a system with no multi-user interference. Then, a per carrier basis nonlinear\/iterative multi-user equalizer, based on the iterative block decision feedback equalization (IB-DFE) principle is designed, to explicitly remove both the multi-user and residual inter carrier interferences, not tackled in the analog part. The equalizer design metric is the sum of the mean square error (MSE) of all subcarriers, whose minimization is shown to be equivalent to the minimization of a weighted error between the hybrid and the full digital equalizer matrices. The results show that the proposed hybrid multi-user equalizer has a performance close to the fully digital counterpart.<\/jats:p>","DOI":"10.3390\/app9163363","type":"journal-article","created":{"date-parts":[[2019,8,15]],"date-time":"2019-08-15T11:11:00Z","timestamp":1565867460000},"page":"3363","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Multiuser Equalizer for Hybrid Massive MIMO mmWave CE-OFDM Systems"],"prefix":"10.3390","volume":"9","author":[{"given":"Roberto","family":"Magueta","sequence":"first","affiliation":[{"name":"Instituto de Telecomunica\u00e7\u00f5es (IT) and Departamento de Eletr\u00f3nica, Telecomunica\u00e7\u00f5es e Inform\u00e1tica (DETI), University of Aveiro, 3810-193 Aveiro, Portugal"}]},{"given":"Sara","family":"Teodoro","sequence":"additional","affiliation":[{"name":"Instituto de Telecomunica\u00e7\u00f5es (IT) and Departamento de Eletr\u00f3nica, Telecomunica\u00e7\u00f5es e Inform\u00e1tica (DETI), University of Aveiro, 3810-193 Aveiro, Portugal"}]},{"given":"Daniel","family":"Castanheira","sequence":"additional","affiliation":[{"name":"Instituto de Telecomunica\u00e7\u00f5es (IT) and Departamento de Eletr\u00f3nica, Telecomunica\u00e7\u00f5es e Inform\u00e1tica (DETI), University of Aveiro, 3810-193 Aveiro, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7008-6773","authenticated-orcid":false,"given":"Ad\u00e3o","family":"Silva","sequence":"additional","affiliation":[{"name":"Instituto de Telecomunica\u00e7\u00f5es (IT) and Departamento de Eletr\u00f3nica, Telecomunica\u00e7\u00f5es e Inform\u00e1tica (DETI), University of Aveiro, 3810-193 Aveiro, Portugal"}]},{"given":"Rui","family":"Dinis","sequence":"additional","affiliation":[{"name":"Instituto de Telecomunica\u00e7\u00f5es (IT) and Faculdade de Ci\u00eancias e Tecnologia, University Nova de Lisboa, 1099-085 Lisboa, Portugal"}]},{"given":"At\u00edlio","family":"Gameiro","sequence":"additional","affiliation":[{"name":"Instituto de Telecomunica\u00e7\u00f5es (IT) and Departamento de Eletr\u00f3nica, Telecomunica\u00e7\u00f5es e Inform\u00e1tica (DETI), University of Aveiro, 3810-193 Aveiro, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2019,8,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1109\/MCOM.2011.5783993","article-title":"An introduction to millimeter-wave mobile broadband systems","volume":"49","author":"Pi","year":"2011","journal-title":"IEEE Commun. Mag."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1109\/MCOM.2014.6736746","article-title":"Five Disruptive Technology Directions for 5G","volume":"52","author":"Boccardi","year":"2014","journal-title":"IEEE Commun. Mag."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1109\/MCOM.2014.6736752","article-title":"Cellular architecture and key technologies for 5G wireless communication networks","volume":"52","author":"Wang","year":"2014","journal-title":"IEEE Commun. Mag."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Tan, W., Assimonis, S.D., Matthaiou, M., Han, Y., Li, X., and Jin, S. (2017, January 4\u20137). Analysis of different planar antenna arrays for mmWave massive MIMO systems. Proceedings of the IEEE 85th Vehicular Technology Conference, Sydney, NSW, Australia.","DOI":"10.1109\/VTCSpring.2017.8108586"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"132","DOI":"10.1109\/TAP.2017.2759842","article-title":"On the performance of spatially correlated large antenna arrays for millimeter-wave frequencies","volume":"66","author":"Neil","year":"2017","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"3648","DOI":"10.1109\/TMTT.2017.2743702","article-title":"Antenna deembedding for mmWave propagation modeling and field measurement validation at 73 GHz","volume":"65","author":"Zhang","year":"2017","journal-title":"IEEE Trans. Microw. Theory Tech."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Chafaa, I., and Djeddou, M. (2017, January 20\u201322). Improved channel estimation in mmWave communication system. Proceedings of the Seminar on Detection Systems Architectures and Technologies (DAT), Algiers, Algeria.","DOI":"10.1109\/DAT.2017.7889193"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1109\/MCOM.2018.1600731","article-title":"On low-resolution ADCs in practical 5G millimeter-wave massive MIMO systems","volume":"56","author":"Zhang","year":"2018","journal-title":"IEEE Commun. Mag."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"3205","DOI":"10.1109\/TVT.2017.2779407","article-title":"Millimeter wave analog beamforming with low resolution phase shifters for multiuser uplink","volume":"67","author":"Raviteja","year":"2017","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1499","DOI":"10.1109\/TWC.2014.011714.130846","article-title":"Spatially sparse precoding in millimeter wave MIMO systems","volume":"13","author":"Ayach","year":"2014","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"33577","DOI":"10.1109\/ACCESS.2019.2903166","article-title":"Hybrid Precoding for Massive mmWave MIMO Systems","volume":"7","author":"Liu","year":"2019","journal-title":"IEEE Access"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"608","DOI":"10.1109\/TCOMM.2016.2632732","article-title":"Hybrid iterative space-time equalization for multi-user mmW massive MIMO systems","volume":"65","author":"Magueta","year":"2017","journal-title":"IEEE Trans. Commun."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"12027","DOI":"10.1109\/ACCESS.2019.2892136","article-title":"Improved hybrid precoding scheme for mmWave large-scale MIMO Systems","volume":"7","author":"Lu","year":"2019","journal-title":"IEEE Access"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1801","DOI":"10.1109\/TCOMM.2016.2549517","article-title":"Frequency selective hybrid precoding for limited feedback millimeter wave systems","volume":"64","author":"Alkhateeb","year":"2016","journal-title":"IEEE Trans. Commun."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1432","DOI":"10.1109\/JSAC.2017.2698958","article-title":"Hybrid analog and digital beamforming for mmWave OFDM large-scale antenna arrays","volume":"35","author":"Sohrabi","year":"2017","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"4634","DOI":"10.1109\/TWC.2018.2828831","article-title":"Hybrid precoding with rate and coverage constraints for wideband massive MIMO systems","volume":"17","author":"Kong","year":"2018","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"5142","DOI":"10.1109\/TSP.2018.2864610","article-title":"Hybrid MIMO-OFDM beamforming for wideband mmWave channels without instantaneous feedback","volume":"66","author":"Lin","year":"2018","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"79017","DOI":"10.1109\/ACCESS.2019.2921530","article-title":"Hybrid multi-user equalizer for massive MIMO millimeter-wave dynamic subconnected architecture","volume":"7","author":"Magueta","year":"2019","journal-title":"IEEE Access"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2965","DOI":"10.1007\/s11277-017-4333-x","article-title":"CE-OFDM Schemes: Spectral Characterization and Optimum Performance","volume":"96","author":"Guerreiro","year":"2017","journal-title":"Wirel. Pers. Commun."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"284","DOI":"10.1109\/TWC.2003.808969","article-title":"Theoretical analysis and performance of OFDM signals in nonlinear fading channels","volume":"2","author":"Banelli","year":"2003","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1300","DOI":"10.1109\/TCOMM.2008.070043","article-title":"Constant envelope OFDM","volume":"56","author":"Thompson","year":"2008","journal-title":"IEEE Trans. Commun."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"4572","DOI":"10.1109\/TSP.2015.2441036","article-title":"Novel Low-Complexity Receivers for Constant Envelope OFDM","volume":"63","author":"Ahmed","year":"2015","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2165","DOI":"10.1109\/LCOMM.2016.2598334","article-title":"On the Detection of CE-OFDM Signals","volume":"20","author":"Guerreiro","year":"2016","journal-title":"IEEE Commun. Lett."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"555","DOI":"10.1109\/TCOMM.2010.02.080682","article-title":"Spectral precoding for constant-envelope OFDM","volume":"58","author":"Chung","year":"2010","journal-title":"IEEE Trans. Commun."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2001","DOI":"10.1109\/LCOMM.2017.2706260","article-title":"Iterative detection with amplitude-phase demodulator for dual-stream CE-OFDM","volume":"21","author":"Cui","year":"2017","journal-title":"IEEE Commun. Lett."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Cheng, W., Yushi, C., and Weidong, W. (2019). Data-Aided Frequency Offset Estimation for CE-OFDM Broadband Satellite Systems. Appl. Sci., 9.","DOI":"10.3390\/app9112310"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Magueta, R., Silva, A., Dinis, R., and Gameiro, A. (2016, January 27\u201330). Iterative Space-Frequency Equalizer for CE-OFDM mmW based Systems. Proceedings of the IEEE Symposium on Computers and Communication, Messina, Italy.","DOI":"10.1109\/ISCC.2016.7543826"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Sacchi, C., Rahman, T.F., Bartolomei, N., Morosi, S., Mazzinghi, A., and Ciabini, F. (2016, January 4\u20138). Design and assessment of a CE-OFDM based mm-wave 5G communication system. Proceedings of the IEEE Globecom Workshops (GC Wkshps) 2016, Washington, DC, USA.","DOI":"10.1109\/GLOCOMW.2016.7848876"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Rahman, T.F., and Sacchi, C. (2018, January 18\u201321). Space-Time Shift Keying and Constant-Envelope OFDM: A New Solution for Future Mm-Wave MIMO Multicarrier Systems. Proceedings of the European Conference on Networks and Communications (EuCNC) 2018, Ljubljiana, Slovenia.","DOI":"10.1109\/EuCNC.2018.8442674"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"9406","DOI":"10.1109\/TVT.2018.2854723","article-title":"Constant-envelope multicarrier waveforms for millimeter wave 5G applications","volume":"67","author":"Rahman","year":"2018","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"2500","DOI":"10.1109\/TCOMM.2015.2434383","article-title":"Efficient transmitter and receiver designs for SC-FDMA based heterogene-ous networks","volume":"63","author":"Castanheira","year":"2015","journal-title":"IEEE Trans. Commun."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1109\/JPROC.2009.2031562","article-title":"Single carrier modulation with non linear frequency domain equalization: An idea whose time has come\u2014Again","volume":"98","author":"Benvenuto","year":"2010","journal-title":"Proceed. IEEE"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1144","DOI":"10.1049\/el:20020767","article-title":"Block iterative DFE for single carrier modulation","volume":"39","author":"Benvenuto","year":"2002","journal-title":"Electron. Lett."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"2035","DOI":"10.1109\/TSP.2006.873485","article-title":"Block-iterative generalized decision feedback equalizers for large MIMO systems: Algorithm design and asymptotic performance analysis","volume":"54","author":"Liang","year":"2006","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1109\/TVT.2008.923655","article-title":"A comparison of frequency domain block MIMO transmission systems","volume":"58","author":"Kalbasi","year":"2009","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1851","DOI":"10.1109\/TCOMM.2012.051712.100072","article-title":"SC-FDE for offset modula-tions: An efficient transmission technique for broadband wireless systems","volume":"60","author":"Luzio","year":"2012","journal-title":"IEEE Trans. Commun."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"853","DOI":"10.1109\/TVT.2011.2177874","article-title":"Adaptive decision-feedback detection with constellation constraints for mimo systems","volume":"61","author":"Li","year":"2012","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1240","DOI":"10.1109\/TCOMM.2014.022514.130681","article-title":"Iterative frequency-domain detection for IA-precoded MC-CDMA systems","volume":"62","author":"Silva","year":"2014","journal-title":"IEEE Trans. Commun."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"662","DOI":"10.1109\/TCOMM.2017.2756882","article-title":"Hybridly connected structure for hybrid beamforming in mmWave massive MIMO systems","volume":"66","author":"Zhang","year":"2018","journal-title":"IEEE Trans. Commun."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"2381","DOI":"10.1109\/TSP.2003.815393","article-title":"Joint tx-rx beamforming design for multicarrier mimo channels: A unified framework for convex optimization","volume":"51","author":"Palomar","year":"2003","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1519","DOI":"10.1002\/j.1538-7305.1982.tb04356.x","article-title":"Memoryless nonlinearities with gaussian inputs: elementary results","volume":"61","author":"Rowe","year":"1982","journal-title":"Bell Syst. Tech. J."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1561\/0100000018","article-title":"MIMO Transceiver Design via Majorization Theory","volume":"3","author":"Palomar","year":"2007","journal-title":"Found. Trends Commun. Inf. Theory"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1186\/1687-1499-2013-292","article-title":"Performance evaluation of IB-DFE-based strategies for SC-FDMA systems","volume":"2013","author":"Silva","year":"2013","journal-title":"EURASIP J. Wirel. Commun. Netw."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"2065","DOI":"10.1049\/iet-com.2011.0674","article-title":"Single-carrier frequency domain equalisation with hierarchical constellations: an efficient transmission technique for broadcast and multicast systems","volume":"6","author":"Silva","year":"2012","journal-title":"IET Commun."}],"container-title":["Applied Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2076-3417\/9\/16\/3363\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:11:23Z","timestamp":1760188283000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2076-3417\/9\/16\/3363"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,8,15]]},"references-count":44,"journal-issue":{"issue":"16","published-online":{"date-parts":[[2019,8]]}},"alternative-id":["app9163363"],"URL":"https:\/\/doi.org\/10.3390\/app9163363","relation":{},"ISSN":["2076-3417"],"issn-type":[{"type":"electronic","value":"2076-3417"}],"subject":[],"published":{"date-parts":[[2019,8,15]]}}}