{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:43:11Z","timestamp":1760236991356,"version":"build-2065373602"},"reference-count":53,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2020,2,10]],"date-time":"2020-02-10T00:00:00Z","timestamp":1581292800000},"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>A method for channel estimation in wideband massive Multiple-Input Multiple-Output systems using hybrid digital analog architectures is developed. The proposed method is useful for Frequency-Division Duplex at either sub-6 GHz or millimeter wave frequency bands and takes into account the beam squint effect caused by the large bandwidth of the signals. To circumvent the estimation of large channel vectors, the posed algorithm relies on the slow time variation of the channel spatial covariance matrix, thus allowing for the utilization of very short training sequences. This is possibledue to the exploitation of the channel structure. After identifying the channel covariance matrix, the channel is estimated on the basis of the recovered information. To that end, we propose a novel method that relies on estimating the tap delays and the gains as sociated with each path. As a consequence, the proposed channel estimator achieves low computational complexity and significantly reduces the training overhead. Moreover, our numerical simulations show better performance results compared to the minimum mean-squared error solution.<\/jats:p>","DOI":"10.3390\/s20030930","type":"journal-article","created":{"date-parts":[[2020,2,11]],"date-time":"2020-02-11T09:25:21Z","timestamp":1581413121000},"page":"930","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["FDD Channel Estimation Via Covariance Estimation in Wideband Massive MIMO Systems"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7554-1758","authenticated-orcid":false,"given":"Jos\u00e9 P.","family":"Gonz\u00e1lez-Coma","sequence":"first","affiliation":[{"name":"Department of Computer Engineering &amp; CITIC Research Center, University of A Coru\u00f1a, 15001 Galicia, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6956-8428","authenticated-orcid":false,"given":"Pedro","family":"Su\u00e1rez-Casal","sequence":"additional","affiliation":[{"name":"Department of Computer Engineering &amp; CITIC Research Center, University of A Coru\u00f1a, 15001 Galicia, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0521-3465","authenticated-orcid":false,"given":"Paula M.","family":"Castro","sequence":"additional","affiliation":[{"name":"Department of Computer Engineering &amp; CITIC Research Center, University of A Coru\u00f1a, 15001 Galicia, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Luis","family":"Castedo","sequence":"additional","affiliation":[{"name":"Department of Computer Engineering &amp; CITIC Research Center, University of A Coru\u00f1a, 15001 Galicia, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,2,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1109\/MSP.2011.2178495","article-title":"Scaling Up MIMO: Opportunities and Challenges with Very Large Arrays","volume":"30","author":"Rusek","year":"2013","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1109\/MCOM.2014.6979963","article-title":"MIMO Precoding and Combining Solutions for Millimeter-Wave Systems","volume":"52","author":"Alkhateeb","year":"2014","journal-title":"IEEE Commun. Mag."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"574","DOI":"10.1109\/TWC.2017.2768423","article-title":"Massive MIMO Has Unlimited Capacity","volume":"17","author":"Hoydis","year":"2018","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"3917","DOI":"10.1109\/TCOMM.2015.2462350","article-title":"Massive MIMO in Real Propagation Environments: Do All Antennas Contribute Equally?","volume":"63","author":"Gao","year":"2015","journal-title":"IEEE Trans. Commun."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"951","DOI":"10.1109\/TIT.2003.809594","article-title":"How much training is needed in multiple-antenna wireless links?","volume":"49","author":"Hassibi","year":"2003","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"3590","DOI":"10.1109\/TWC.2010.092810.091092","article-title":"Noncooperative Cellular Wireless with Unlimited Numbers of Base Station Antennas","volume":"9","author":"Marzetta","year":"2010","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_7","unstructured":"Mailloux, R. (2018). Phased Array Antenna Handbook, Artech House."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"6169","DOI":"10.1109\/TSP.2015.2463260","article-title":"Spatially Common Sparsity Based Adaptive Channel Estimation and Feedback for FDD Massive MIMO","volume":"63","author":"Gao","year":"2015","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Luo, X., Zhang, X., Cai, P., Shen, C., Hu, D., and Qian, H. (2017, January 4\u20137). DL CSI acquisition and feedback in FDD massive MIMO via path aligning. Proceedings of the Ninth International Conference on Ubiquitous and Future Networks (ICUFN), Milan, Italy.","DOI":"10.1109\/ICUFN.2017.7993807"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Bj\u00f6rnson, E., Der Perre, L.V., Buzzi, S., and Larsson, E.G. (2018). Massive MIMO in Sub-6 GHz and mmWave: Physical, Practical, and Use-Case Differences. CoRR.","DOI":"10.1109\/MWC.2018.1800140"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Van Trees, H.L. (2002). Optimum Array Processing, Wiley.","DOI":"10.1002\/0471221104"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2905","DOI":"10.1109\/TSP.2018.2799164","article-title":"Learning the MMSE Channel Estimator","volume":"66","author":"Neumann","year":"2018","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1259","DOI":"10.1109\/LCOMM.2016.2555299","article-title":"Channel Estimation for Millimeter-Wave Massive MIMO with Hybrid Precoding Over Frequency-Selective Fading Channels","volume":"20","author":"Gao","year":"2016","journal-title":"IEEE Commun. Lett."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1109\/JSTSP.2018.2819130","article-title":"Channel Estimation and Hybrid Precoding for Frequency Selective Multiuser mmWave MIMO Systems","volume":"12","author":"Castedo","year":"2018","journal-title":"IEEE J. Sel. Top. Signal Process."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"8316","DOI":"10.1109\/TWC.2017.2760825","article-title":"Massive MIMO Pilot Decontamination and Channel Interpolation via Wideband Sparse Channel Estimation","volume":"16","author":"Haghighatshoar","year":"2017","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2563","DOI":"10.1109\/TSP.2002.803324","article-title":"Deconstructing multiantenna fading channels","volume":"50","author":"Sayeed","year":"2002","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Sun, G.R.M.J.S., and Rappaport, T.S. (2017, January 2\u20137). A novel millimeter-wave channel simulator and applications for 5G wireless communications. Proceedings of the International Conference on Communications (ICC), Washington, DC, USA.","DOI":"10.1109\/ICC.2017.7996792"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Gao, X., Tufvesson, F., Edfors, O., and Rusek, F. (2012, January 4\u20137). Measured propagation characteristics for very-large MIMO at 2.6 GHz. Proceedings of the Asilomar Conference on Signals, Systems and Computers (ASILOMAR), Pacific Grove, CA, USA.","DOI":"10.1109\/ACSSC.2012.6489010"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Sanguinetti, L., Bj\u00f6rnson, E., and Hoydis, J. (2019). Towards Massive MIMO 2.0: Understanding spatial correlation, interference suppression, and pilot contamination. arXiv.","DOI":"10.1109\/TCOMM.2019.2945792"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"3234","DOI":"10.1109\/TCOMM.2019.2893221","article-title":"Massive MIMO With Spatially Correlated Rician Fading Channels","volume":"67","author":"Larsson","year":"2019","journal-title":"IEEE Trans. Commun."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"6441","DOI":"10.1109\/TIT.2013.2269476","article-title":"Joint Spatial Division and Multiplexing: The Large-Scale Array Regime","volume":"59","author":"Adhikary","year":"2013","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Zhang, B., Cimini, L.J., and Greenstein, L.J. (2017, January 4\u201310). Efficient Eigenspace Training and Precoding for FDD Massive MIMO Systems. Proceedings of the IEEE Global Communications Conference (GLOBECOM), Singapore.","DOI":"10.1109\/GLOCOM.2017.8254883"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"863","DOI":"10.1109\/LSP.2018.2827323","article-title":"Covariance Matrix Estimation in Massive MIMO","volume":"25","author":"Neumann","year":"2018","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"546","DOI":"10.1109\/LSP.2018.2805725","article-title":"Covariance Matrix Estimation for Massive MIMO","volume":"25","author":"Upadhya","year":"2018","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"4206","DOI":"10.1109\/TWC.2018.2821667","article-title":"Channel Estimation for TDD\/FDD Massive MIMO Systems with Channel Covariance Computing","volume":"17","author":"Xie","year":"2018","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"5183","DOI":"10.1109\/TWC.2018.2838600","article-title":"Directional Training for FDD Massive MIMO","volume":"17","author":"Zhang","year":"2018","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_27","unstructured":"Khalilsarai, M.B., Haghighatshoar, S., Yi, X., and Caire, G. (2018). FDD Massive MIMO via UL\/DL Channel Covariance Extrapolation and Active Channel Sparsification. CoRR."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"3515","DOI":"10.1109\/TWC.2019.2915072","article-title":"Angle-Domain Aided UL\/DL Channel Estimation for Wideband mmWave Massive MIMO Systems With Beam Squint","volume":"18","author":"Jian","year":"2019","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"5893","DOI":"10.1109\/TSP.2019.2949502","article-title":"Beam Squint and Channel Estimation for Wideband mmWave Massive MIMO-OFDM Systems","volume":"67","author":"Wang","year":"2019","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Pal, P., and Vaidyanathan, P.P. (2011, January 4\u20137). Coprime sampling and the music algorithm. Proceedings of the Digital Signal Processing and Signal Processing Education Meeting (DSP\/SPE), Sedona, AZ, USA.","DOI":"10.1109\/DSP-SPE.2011.5739227"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1832","DOI":"10.1109\/TSP.2018.2795560","article-title":"Low-Complexity Massive MIMO Subspace Estimation and Tracking From Low-Dimensional Projections","volume":"66","author":"Haghighatshoar","year":"2018","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Romero, D., and Leus, G. (2013, January 2\u20137). Compressive covariance sampling. Proceedings of the Information Theory and Applications Workshop (ITA), San Diego, CA, USA.","DOI":"10.1109\/ITA.2013.6502949"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Shakeri, S., Ariananda, D.D., and Leus, G. (2012, January 17\u201320). Direction of arrival estimation using sparse ruler array design. Proceedings of the Workshop on Signal Processing Advances in Wireless Communications (SPAWC), Cesme, Turkey.","DOI":"10.1109\/SPAWC.2012.6292964"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"8047","DOI":"10.1109\/TWC.2018.2873592","article-title":"Spatial Channel Covariance Estimation for the Hybrid MIMO Architecture: A Compressive Sensing-Based Approach","volume":"17","author":"Park","year":"2018","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Haghighatshoar, S., Khalilsarai, M.B., and Caire, G. (2018). Multi-Band Covariance Interpolation with Applications in Massive MIMO. CoRR.","DOI":"10.1109\/ISIT.2018.8437890"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"465","DOI":"10.1112\/jlms\/s1-38.1.465","article-title":"A Note on Restricted Difference Bases","volume":"s1-38","author":"Wichmann","year":"2016","journal-title":"J. Lond. Math. Soc."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"11791","DOI":"10.1109\/ACCESS.2017.2715984","article-title":"Beam-Blocked Channel Estimation for FDD Massive MIMO With Compressed Feedback","volume":"5","author":"Huang","year":"2017","journal-title":"IEEE Access"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Schniter, P., and Sayeed, A. (2014, January 2\u20135). Channel estimation and precoder design for millimeter-wave communications: The sparse way. Proceedings of the 48th Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, USA.","DOI":"10.1109\/ACSSC.2014.7094443"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"160","DOI":"10.1112\/jlms\/s1-31.2.160","article-title":"On the Representation of 1, 2, \u2026, n by Differences","volume":"s1-31","author":"Leech","year":"1956","journal-title":"J. Lond. Math. Soc."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"276","DOI":"10.1109\/TAP.1986.1143830","article-title":"Multiple emitter location and signal parameter estimation","volume":"34","author":"Schmidt","year":"1986","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"3613","DOI":"10.1109\/TIT.2012.2189196","article-title":"Subspace Methods for Joint Sparse Recovery","volume":"58","author":"Lee","year":"2012","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"278","DOI":"10.1109\/TIT.2011.2171529","article-title":"Compressive MUSIC: Revisiting the Link Between Compressive Sensing and Array Signal Processing","volume":"58","author":"Kim","year":"2012","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"4167","DOI":"10.1109\/TSP.2010.2049264","article-title":"Nested Arrays: A Novel Approach to Array Processing With Enhanced Degrees of Freedom","volume":"58","author":"Pal","year":"2010","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"3435","DOI":"10.1016\/j.sigpro.2013.04.011","article-title":"Direction of arrival estimation for more correlated sources than active sensors","volume":"93","author":"Ariananda","year":"2013","journal-title":"Signal Process."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"996","DOI":"10.1109\/29.32277","article-title":"On unique localization of multiple sources by passive sensor arrays","volume":"37","author":"Wax","year":"1989","journal-title":"IEEE Trans. Acoust. Speech Signal Process."},{"key":"ref_46","unstructured":"Richards, M. (2005). Fundamentals of Radar Signal Processing, Mcgraw-Hill. Professional Engineering."},{"key":"ref_47","unstructured":"Kay, S. (1993). Fundamentals of Statistical Signal Processing, Prentice-Hall PTR."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1109\/TSP.2016.2616336","article-title":"Massive MIMO Channel Subspace Estimation From Low-Dimensional Projections","volume":"65","author":"Haghighatshoar","year":"2017","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"2414","DOI":"10.1109\/TSP.2018.2811742","article-title":"Efficient Compressive Channel Estimation for Millimeter-Wave Large-Scale Antenna Systems","volume":"66","author":"Tsai","year":"2018","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"4145","DOI":"10.1109\/TWC.2016.2535310","article-title":"Compressed CSI Acquisition in FDD Massive MIMO: How Much Training is Needed?","volume":"15","author":"Shen","year":"2016","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Zhao, P., Wang, Z., and Sun, C. (2017, January 2\u20137). Angular domain pilot design and channel estimation for FDD massive MIMO networks. Proceedings of the International Conference on Communications (ICC), Washington, DC, USA.","DOI":"10.1109\/ICC.2017.7996890"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"3261","DOI":"10.1109\/TSP.2014.2324991","article-title":"Distributed Compressive CSIT Estimation and Feedback for FDD Multi-User Massive MIMO Systems","volume":"62","author":"Rao","year":"2014","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"7590","DOI":"10.1109\/TWC.2017.2751046","article-title":"Channel Estimation for FDD Multi-User Massive MIMO: A Variational Bayesian Inference-Based Approach","volume":"16","author":"Cheng","year":"2017","journal-title":"IEEE Trans. Wirel. 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