{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T04:37:16Z","timestamp":1768711036351,"version":"3.49.0"},"reference-count":53,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T00:00:00Z","timestamp":1649030400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["KR 3517\/9-1"],"award-info":[{"award-number":["KR 3517\/9-1"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.mdpi.com"],"crossmark-restriction":true},"short-container-title":["Entropy"],"abstract":"<jats:p>Downlink precoding is considered for multi-path multi-input single-output channels where the base station uses orthogonal frequency-division multiplexing and low-resolution signaling. A quantized coordinate minimization (QCM) algorithm is proposed and its performance is compared to other precoding algorithms including squared infinity-norm relaxation (SQUID), multi-antenna greedy iterative quantization (MAGIQ), and maximum safety margin precoding. MAGIQ and QCM achieve the highest information rates and QCM has the lowest complexity measured in the number of multiplications. The information rates are computed for pilot-aided channel estimation and data-aided channel estimation. Bit error rates for a 5G low-density parity-check code confirm the information-theoretic calculations. Simulations with imperfect channel knowledge at the transmitter show that the performance of QCM and SQUID degrades in a similar fashion as zero-forcing precoding with high resolution quantizers.<\/jats:p>","DOI":"10.3390\/e24040504","type":"journal-article","created":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T05:50:43Z","timestamp":1649051443000},"page":"504","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Low-Resolution Precoding for Multi-Antenna Downlink Channels and OFDM"],"prefix":"10.3390","volume":"24","author":[{"given":"Andrei","family":"Nedelcu","sequence":"first","affiliation":[{"name":"Optical and Quantum Laboratory, Huawei Munich Research Center, 80992 Munich, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fabian","family":"Steiner","sequence":"additional","affiliation":[{"name":"Institute for Communications Engineering, Technical University of Munich (TUM), 80333 Munich, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3904-9181","authenticated-orcid":false,"given":"Gerhard","family":"Kramer","sequence":"additional","affiliation":[{"name":"Institute for Communications Engineering, Technical University of Munich (TUM), 80333 Munich, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,4,4]]},"reference":[{"key":"ref_1","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. 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