{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,25]],"date-time":"2026-01-25T05:10:35Z","timestamp":1769317835305,"version":"3.49.0"},"reference-count":32,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2019,12,1]],"date-time":"2019-12-01T00:00:00Z","timestamp":1575158400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2019,12,12]],"date-time":"2019-12-12T00:00:00Z","timestamp":1576108800000},"content-version":"vor","delay-in-days":11,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Wireless Com Network"],"published-print":{"date-parts":[[2019,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>This paper considers the channel estimation problem for massive multiple-input multiple-output (MIMO) systems that use one-bit analog-to-digital converters (ADCs). Previous channel estimation techniques for massive MIMO using one-bit ADCs are all based on single-shot estimation without exploiting the inherent temporal correlation in wireless channels. In this paper, we propose an adaptive channel estimation technique taking the spatial and temporal correlations into account for massive MIMO with one-bit ADCs. We first use the Bussgang decomposition to linearize the one-bit quantized received signals. Then, we adopt the Kalman filter to estimate the spatially and temporally correlated channels. Since the quantization noise is not Gaussian, we assume the effective noise as a Gaussian noise with the same statistics to apply the Kalman filtering. We also implement the truncated polynomial expansion-based low-complexity channel estimator with negligible performance loss. Numerical results reveal that the proposed channel estimators can improve the estimation accuracy significantly by using the spatial and temporal correlations of channels.<\/jats:p>","DOI":"10.1186\/s13638-019-1587-x","type":"journal-article","created":{"date-parts":[[2019,12,12]],"date-time":"2019-12-12T17:05:02Z","timestamp":1576170302000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":23,"title":["Channel estimation for spatially\/temporally correlated massive MIMO systems with one-bit ADCs"],"prefix":"10.1186","volume":"2019","author":[{"given":"Hwanjin","family":"Kim","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9862-9020","authenticated-orcid":false,"given":"Junil","family":"Choi","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,12,12]]},"reference":[{"key":"1587_CR1","doi-asserted-by":"publisher","unstructured":"H. Kim, J. Choi, in 2018 IEEE Global Communications Conference (GLOBECOM). Channel estimation for one-bit massive MIMO systems exploiting spatio-temporal correlations, (2018), pp. 1\u20136. https:\/\/doi.org\/10.1109\/GLOCOM.2018.8647574.","DOI":"10.1109\/GLOCOM.2018.8647574"},{"issue":"11","key":"1587_CR2","doi-asserted-by":"publisher","first-page":"3590","DOI":"10.1109\/TWC.2010.092810.091092","volume":"9","author":"T. L. Marzetta","year":"2010","unstructured":"T. L. Marzetta, Noncooperative cellular wireless with unlimited numbers of base station antennas. IEEE Trans. Wirel. Commun.9(11), 3590\u20133600 (2010). https:\/\/doi.org\/10.1109\/TWC.2010.092810.091092.","journal-title":"IEEE Trans. Wirel. Commun."},{"issue":"1","key":"1587_CR3","doi-asserted-by":"publisher","first-page":"40","DOI":"10.1109\/MSP.2011.2178495","volume":"30","author":"F. Rusek","year":"2013","unstructured":"F. Rusek, D. Persson, B. K. Lau, E. G. Larsson, T. L. Marzetta, O. Edfors, F. Tufvesson, Scaling up MIMO: opportunities and challenges with very large arrays. IEEE Signal Proc. Mag.30(1), 40\u201360 (2013). https:\/\/doi.org\/10.1109\/MSP.2011.2178495.","journal-title":"IEEE Signal Proc. Mag."},{"issue":"2","key":"1587_CR4","doi-asserted-by":"publisher","first-page":"160","DOI":"10.1109\/JSAC.2013.130205","volume":"31","author":"J. Hoydis","year":"2013","unstructured":"J. Hoydis, S. ten Brink, M. Debbah, Massive MIMO in the UL\/DL of cellular networks: how many antennas do we need?IEEE J. Sel. Areas Commun.31(2), 160\u2013171 (2013). https:\/\/doi.org\/10.1109\/JSAC.2013.130205.","journal-title":"IEEE J. Sel. Areas Commun."},{"issue":"2","key":"1587_CR5","doi-asserted-by":"publisher","first-page":"186","DOI":"10.1109\/MCOM.2014.6736761","volume":"52","author":"E. G. Larsson","year":"2014","unstructured":"E. G. Larsson, O. Edfors, F. Tufvesson, T. L. Marzetta, Massive MIMO for next generation wireless systems. IEEE Commun. Mag.52(2), 186\u2013195 (2014). https:\/\/doi.org\/10.1109\/MCOM.2014.6736761.","journal-title":"IEEE Commun. Mag."},{"issue":"4","key":"1587_CR6","doi-asserted-by":"publisher","first-page":"539","DOI":"10.1109\/49.761034","volume":"17","author":"R. H. Walden","year":"1999","unstructured":"R. H. Walden, Analog-to-digital converter survey and analysis. IEEE J. Sel. Areas Commun.17(4), 539\u2013550 (1999). https:\/\/doi.org\/10.1109\/49.761034.","journal-title":"IEEE J. Sel. Areas Commun."},{"issue":"4","key":"1587_CR7","doi-asserted-by":"publisher","first-page":"2156","DOI":"10.1109\/TWC.2014.2382098","volume":"14","author":"S. Wang","year":"2015","unstructured":"S. Wang, Y. Li, J. Wang, Multiuser detection in massive spatial modulation MIMO with low-resolution ADCs. IEEE Trans. Wirel. Commun.14(4), 2156\u20132168 (2015). https:\/\/doi.org\/10.1109\/TWC.2014.2382098.","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"1587_CR8","doi-asserted-by":"publisher","unstructured":"S. Wang, Y. Li, J. Wang, in 2014 IEEE International Conference on Communications (ICC). Convex optimization based multiuser detection for uplink large-scale MIMO under low-resolution quantization, (2014), pp. 4789\u20134794. https:\/\/doi.org\/10.1109\/ICC.2014.6884078.","DOI":"10.1109\/ICC.2014.6884078"},{"issue":"11","key":"1587_CR9","doi-asserted-by":"publisher","first-page":"7738","DOI":"10.1109\/TWC.2016.2606592","volume":"15","author":"T. Zhang","year":"2016","unstructured":"T. Zhang, C. Wen, S. Jin, T. Jiang, Mixed-ADC massive MIMO detectors: performance analysis and design optimization. IEEE Trans. Wirel. Commun.15(11), 7738\u20137752 (2016). https:\/\/doi.org\/10.1109\/TWC.2016.2606592.","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"1587_CR10","doi-asserted-by":"publisher","unstructured":"Y. Jeon, S. Hong, N. Lee, in 2017 IEEE International Conference on Communications (ICC). Blind detection for MIMO systems with low-resolution ADCs using supervised learning, (2017), pp. 1\u20136. https:\/\/doi.org\/10.1109\/ICC.2017.7997434.","DOI":"10.1109\/ICC.2017.7997434"},{"issue":"3","key":"1587_CR11","doi-asserted-by":"publisher","first-page":"476","DOI":"10.1109\/LWC.2017.2787159","volume":"7","author":"Z. Shao","year":"2018","unstructured":"Z. Shao, R. C. de Lamare, L. T. N. Landau, Iterative detection and decoding for large-scale multiple-antenna systems with 1-bit ADCs. IEEE Wirel. Commun. Lett.7(3), 476\u2013479 (2018). https:\/\/doi.org\/10.1109\/LWC.2017.2787159.","journal-title":"IEEE Wirel. Commun. Lett."},{"key":"1587_CR12","doi-asserted-by":"publisher","unstructured":"Y. Jeon, N. Lee, S. Hong, R. W. Heath, in 2018 IEEE 87th Vehicular Technology Conference (VTC Spring). A low complexity ML detection for uplink massive MIMO systems with one-bit ADCs, (2018), pp. 1\u20135. https:\/\/doi.org\/10.1109\/VTCSpring.2018.8417580.","DOI":"10.1109\/VTCSpring.2018.8417580"},{"key":"1587_CR13","doi-asserted-by":"publisher","first-page":"27172","DOI":"10.1109\/ACCESS.2019.2901942","volume":"7","author":"Y. Cho","year":"2019","unstructured":"Y. Cho, S. Hong, One-bit successive-cancellation soft-output (OSS) detector for uplink MU-MIMO systems with one-bit ADCs. IEEE Access. 7:, 27172\u201327182 (2019). https:\/\/doi.org\/10.1109\/ACCESS.2019.2901942.","journal-title":"IEEE Access"},{"issue":"5","key":"1587_CR14","doi-asserted-by":"publisher","first-page":"2005","DOI":"10.1109\/TCOMM.2016.2545666","volume":"64","author":"J. Choi","year":"2016","unstructured":"J. Choi, J. Mo, R. W. Heath, Near maximum-likelihood detector and channel estimator for uplink multiuser massive MIMO systems with one-bit ADCs. IEEE Trans. Commun.64(5), 2005\u20132018 (2016). https:\/\/doi.org\/10.1109\/TCOMM.2016.2545666.","journal-title":"IEEE Trans. Commun."},{"issue":"10","key":"1587_CR15","doi-asserted-by":"publisher","first-page":"2541","DOI":"10.1109\/TSP.2015.2508786","volume":"64","author":"C. K. Wen","year":"2016","unstructured":"C. K. Wen, C. J. Wang, S. Jin, K. K. Wong, P. Ting, Bayes-optimal joint channel-and-data estimation for massive MIMO with low-precision ADCs. IEEE Trans. Signal Process.64(10), 2541\u20132556 (2016). https:\/\/doi.org\/10.1109\/TSP.2015.2508786.","journal-title":"IEEE Trans. Signal Process."},{"issue":"5","key":"1587_CR16","doi-asserted-by":"publisher","first-page":"1141","DOI":"10.1109\/TSP.2017.2781644","volume":"66","author":"J. Mo","year":"2018","unstructured":"J. Mo, P. Schniter, R. W. Heath, Channel estimation in broadband millimeter wave MIMO systems with few-bit ADCs. IEEE Trans. Signal Process.66(5), 1141\u20131154 (2018). https:\/\/doi.org\/10.1109\/TSP.2017.2781644.","journal-title":"IEEE Trans. Signal Process."},{"issue":"4","key":"1587_CR17","doi-asserted-by":"publisher","first-page":"2274","DOI":"10.1109\/TWC.2017.2661749","volume":"16","author":"J. Mo","year":"2017","unstructured":"J. Mo, A. Alkhateeb, S. Abu-Surra, R. W. Heath, Hybrid architectures with few-bit ADC receivers: achievable rates and energy-rate tradeoffs. IEEE Trans. Wirel. Commun.16(4), 2274\u20132287 (2017). https:\/\/doi.org\/10.1109\/TWC.2017.2661749.","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"1587_CR18","doi-asserted-by":"publisher","unstructured":"Z. Shao, L. T. N. Landau, R. C. de Lamare, in ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). Channel estimation using 1-bit quantization and oversampling for large-scale multiple-antenna systems, (2019), pp. 4669\u20134673. https:\/\/doi.org\/10.1109\/ICASSP.2019.8683750.","DOI":"10.1109\/ICASSP.2019.8683750"},{"key":"1587_CR19","first-page":"1","volume":"216","author":"J. J. Bussgang","year":"1952","unstructured":"J. J. Bussgang, Crosscorrelation functions of amplitude-distorted Gaussian signals. MIT Res. Lab. Elec. Tech. Rep.216:, 1\u201314 (1952).","journal-title":"MIT Res. Lab. Elec. Tech. Rep."},{"key":"1587_CR20","volume-title":"Fundamentals of Statistical Signal Processing: Estimation Theory, 1st edn","author":"S. M. Kay","year":"2000","unstructured":"S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory, 1st edn (Prentice Hall, New Jersey, 2000)."},{"issue":"15","key":"1587_CR21","doi-asserted-by":"publisher","first-page":"4075","DOI":"10.1109\/TSP.2017.2706179","volume":"65","author":"Y. Li","year":"2017","unstructured":"Y. Li, C. Tao, G. Seco-Granados, A. Mezghani, A. L. Swindlehurst, L. Liu, Channel estimation and performance analysis of one-bit massive MIMO systems. IEEE Trans. Signal Process.65(15), 4075\u20134089 (2017). https:\/\/doi.org\/10.1109\/TSP.2017.2706179.","journal-title":"IEEE Trans. Signal Process."},{"key":"1587_CR22","doi-asserted-by":"publisher","unstructured":"B. Clerckx, G. Kim, S. Kim, in 2008 IEEE Global Telecommunications Conference. Correlated fading in broadcast MIMO channels: curse or blessing? (2008), pp. 1\u20135. https:\/\/doi.org\/10.1109\/GLOCOM.2008.ECP.735.","DOI":"10.1109\/GLOCOM.2008.ECP.735"},{"key":"1587_CR23","doi-asserted-by":"publisher","unstructured":"J. Choi, D. J. Love, D. R. Brown, in 2014 48th Asilomar Conference on Signals, Systems and Computers. Channel estimation techniques for quantized distributed reception in MIMO systems, (2014), pp. 1066\u20131070. https:\/\/doi.org\/10.1109\/ACSSC.2014.7094619.","DOI":"10.1109\/ACSSC.2014.7094619"},{"issue":"1","key":"1587_CR24","doi-asserted-by":"publisher","first-page":"239","DOI":"10.1109\/18.272490","volume":"40","author":"G. Jacovitti","year":"1994","unstructured":"G. Jacovitti, A. Neri, Estimation of the autocorrelation function of complex Gaussian stationary processes by amplitude clipped signals. IEEE Trans. Inf. Theory. 40(1), 239\u2013245 (1994). https:\/\/doi.org\/10.1109\/18.272490.","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"5","key":"1587_CR25","doi-asserted-by":"publisher","first-page":"815","DOI":"10.1109\/JSTSP.2014.2316063","volume":"8","author":"N. Shariati","year":"2014","unstructured":"N. Shariati, E. Bj\u00f6rnson, M. Bengtsson, M. Debbah, Low-complexity polynomial channel estimation in large-scale MIMO with arbitrary statistics. IEEE J. Sel. Top. Signal Process.8(5), 815\u2013830 (2014). https:\/\/doi.org\/10.1109\/JSTSP.2014.2316063.","journal-title":"IEEE J. Sel. Top. Signal Process."},{"issue":"7","key":"1587_CR26","doi-asserted-by":"publisher","first-page":"3072","DOI":"10.1109\/18.959289","volume":"47","author":"S. N. Diggavi","year":"2001","unstructured":"S. N. Diggavi, T. M. Cover, The worst additive noise under a covariance constraint. IEEE Trans. Inf. Theory. 47(7), 3072\u20133081 (2001). https:\/\/doi.org\/10.1109\/18.959289.","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"2","key":"1587_CR27","doi-asserted-by":"publisher","first-page":"703","DOI":"10.1109\/TWC.2011.122211.110313","volume":"11","author":"J. Choi","year":"2012","unstructured":"J. Choi, B. Clerckx, N. Lee, G. Kim, A new design of polar-cap differential codebook for temporally\/spatially correlated MISO channels. IEEE Trans. Wirel. Commun.11(2), 703\u2013711 (2012). https:\/\/doi.org\/10.1109\/TWC.2011.122211.110313.","journal-title":"IEEE Trans. Wirel. Commun."},{"issue":"2","key":"1587_CR28","doi-asserted-by":"publisher","first-page":"546","DOI":"10.1109\/TSP.2003.821104","volume":"52","author":"J. H. Kotecha","year":"2004","unstructured":"J. H. Kotecha, A. M. Sayeed, Transmit signal design for optimal estimation of correlated MIMO channels. IEEE Trans. Signal Process.52(2), 546\u2013557 (2004). https:\/\/doi.org\/10.1109\/TSP.2003.821104.","journal-title":"IEEE Trans. Signal Process."},{"issue":"3","key":"1587_CR29","doi-asserted-by":"publisher","first-page":"1807","DOI":"10.1109\/TSP.2009.2037352","volume":"58","author":"E. Bjornson","year":"2010","unstructured":"E. Bjornson, B. Ottersten, A framework for training-based estimation in arbitrarily correlated Rician MIMO channels with Rician disturbance. IEEE Trans. Signal Process.58(3), 1807\u20131820 (2010). https:\/\/doi.org\/10.1109\/TSP.2009.2037352.","journal-title":"IEEE Trans. Signal Process."},{"issue":"5","key":"1587_CR30","doi-asserted-by":"publisher","first-page":"802","DOI":"10.1109\/JSTSP.2014.2313020","volume":"8","author":"J. Choi","year":"2014","unstructured":"J. Choi, D. J. Love, P. Bidigare, Downlink training techniques for FDD massive MIMO systems: open-loop and closed-loop training with memory. IEEE J. Sel. Top. Signal Process.8(5), 802\u2013814 (2014). https:\/\/doi.org\/10.1109\/JSTSP.2014.2313020.","journal-title":"IEEE J. Sel. Top. Signal Process."},{"key":"1587_CR31","doi-asserted-by":"publisher","unstructured":"U. Gustavsson, C. Sanch\u00e9z-Perez, T. Eriksson, F. Athley, G. Durisi, P. Landin, K. Hausmair, C. Fager, L. Svensson, in 2014 IEEE Globecom Workshops (GC Wkshps). On the impact of hardware impairments on massive MIMO, (2014), pp. 294\u2013300. https:\/\/doi.org\/10.1109\/GLOCOMW.2014.7063447.","DOI":"10.1109\/GLOCOMW.2014.7063447"},{"issue":"1","key":"1587_CR32","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1017\/S0017089500002135","volume":"15","author":"J. Bibby","year":"1974","unstructured":"J. Bibby, Axiomatisations of the average and a further generalisation of monotonic sequences. Glasg. Math. J.15(1), 63\u201365 (1974). https:\/\/doi.org\/10.1017\/S0017089500002135.","journal-title":"Glasg. Math. J."}],"container-title":["EURASIP Journal on Wireless Communications and Networking"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1186\/s13638-019-1587-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1186\/s13638-019-1587-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1186\/s13638-019-1587-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,12,11]],"date-time":"2020-12-11T00:18:44Z","timestamp":1607645924000},"score":1,"resource":{"primary":{"URL":"https:\/\/jwcn-eurasipjournals.springeropen.com\/articles\/10.1186\/s13638-019-1587-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,12]]},"references-count":32,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2019,12]]}},"alternative-id":["1587"],"URL":"https:\/\/doi.org\/10.1186\/s13638-019-1587-x","relation":{},"ISSN":["1687-1499"],"issn-type":[{"value":"1687-1499","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,12]]},"assertion":[{"value":"14 June 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 October 2019","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 December 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare that they have no competing interests.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"267"}}