{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:35:21Z","timestamp":1760243721408,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2012,11,1]],"date-time":"2012-11-01T00:00:00Z","timestamp":1351728000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This paper provides a comprehensive introduction of large random matrix methods for input covariance matrix optimization of mutual information of MIMO systems. It is first recalled informally how large system approximations of mutual information can be derived. Then, the optimization of the approximations is discussed, and important methodological points that are not necessarily covered by the existing literature are addressed, including the strict concavity of the approximation, the structure of the argument of its maximum, the accuracy of the large system approach with regard to the number of antennas, or the justification of iterative water-filling optimization algorithms. While the existing papers have developed methods adapted to a specific model, this contribution tries to provide a unified view of the large system approximation approach.<\/jats:p>","DOI":"10.3390\/e14112122","type":"journal-article","created":{"date-parts":[[2012,11,1]],"date-time":"2012-11-01T12:53:20Z","timestamp":1351774400000},"page":"2122-2142","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Optimization of MIMO Systems Capacity Using Large Random Matrix Methods"],"prefix":"10.3390","volume":"14","author":[{"given":"Florian","family":"Dupuy","sequence":"first","affiliation":[{"name":"Thales Communications & Security, 4 av. des Louvresses, 92622 Gennevilliers, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Philippe","family":"Loubaton","sequence":"additional","affiliation":[{"name":"Universit\u00e9 Paris-Est\/Marne la Vall\u00e9e, LIGM, UMR CNRS 8049, 5 Bd. Descartes, Champs\/Marne, 77454 Marne la Vall\u00e9e Cedex 2, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2012,11,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"585","DOI":"10.1002\/ett.4460100604","article-title":"Capacity of multi-antenna gaussian channels","volume":"10","author":"Telatar","year":"1999","journal-title":"Eur. Trans. Telecommun."},{"key":"ref_2","unstructured":"Vu, M., and Paulraj, A. (, January November). Capacity Optimization for Rician Correlated MIMO Wireless Channels. Proceedings of the Thirty-Ninth Asilomar Conference on the Signals, Systems and Computers, Pacific Grove, CA, USA."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"684","DOI":"10.1109\/JSAC.2003.810294","article-title":"Capacity limits of MIMO channels","volume":"21","author":"Goldsmith","year":"2003","journal-title":"IEEE J. Select. Areas Commun."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1165","DOI":"10.1109\/TWC.2004.830822","article-title":"Transmitter optimization and optimality of beamforming for multiple antenna systems","volume":"3","author":"Jafar","year":"2004","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"4334","DOI":"10.1109\/TIT.2005.858968","article-title":"Monotonicity results for coherent MIMO Rician channels","volume":"51","author":"Hosli","year":"2005","journal-title":"IEEE Trans. Inform. Theory"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2545","DOI":"10.1109\/TIT.2003.817427","article-title":"MIMO capacity through correlated channels in the presence of correlated interferers and noise: A (not so) large N analysis","volume":"49","author":"Moustakas","year":"2003","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"3887","DOI":"10.1109\/TIT.2007.907468","article-title":"On the outage capacity of correlated multiple-path MIMO channels","volume":"53","author":"Moustakas","year":"2007","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"3490","DOI":"10.1109\/TIT.2008.926415","article-title":"Asymptotic mutual information statistics of separately correlated Rician fading MIMO channels","volume":"54","author":"Taricco","year":"2008","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_9","unstructured":"Wen, C., Jin, S., Wong, K., Chen, J., and Ting, P. (, January May). On the Ergodic Capacity of Jointly-Correlated Rician Fading MIMO Channels. Proceedings of IEEE International Conference on Acoustics, Speech and Signal, Prague, Czech Republic."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Tulino, A., and Verd\u00fa, S. (2004). Random Matrix Theory and Wireless Communications, Now Publishers Inc.","DOI":"10.1561\/9781933019505"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1048","DOI":"10.1109\/TIT.2009.2039063","article-title":"On the capacity achieving covariance matrix for Rician MIMO channels: An asymptotic approach","volume":"56","author":"Dumont","year":"2010","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"5737","DOI":"10.1109\/TIT.2011.2162190","article-title":"On the capacity achieving covariance matrix for frequency selective MIMO channels using the asymptotic approach","volume":"57","author":"Dupuy","year":"2011","journal-title":"Inf. Theory IEEE Trans."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"3493","DOI":"10.1109\/TIT.2011.2133151","article-title":"A deterministic equivalent for the analysis of correlated MIMO multiple access channels","volume":"57","author":"Couillet","year":"2011","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1109\/TCOMM.2005.863726","article-title":"Asymptotic analysis of MIMO wireless systems with spatial correlation at the receiver","volume":"54","author":"Wen","year":"2006","journal-title":"IEEE Trans. Commun."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"4123","DOI":"10.1109\/TIT.2011.2146610","article-title":"On the ergodic capacity of correlated Rician fading MIMO channels with interference","volume":"57","author":"Taricco","year":"2011","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2883","DOI":"10.1109\/TCOMM.2011.081111.100585","article-title":"On the sum-rate of multiuser MIMO uplink channels with jointly-correlated Rician fading","volume":"59","author":"Wen","year":"2011","journal-title":"IEEE Trans. Commun."},{"key":"ref_17","unstructured":"Luenberger, D. (1969). Optimization by Vector Space Methods, John Wiley and Sons."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1070\/SM1967v001n04ABEH001994","article-title":"Distribution of eigenvalues for some sets of random matrices","volume":"1","author":"Pastur","year":"1967","journal-title":"Math. USSR Sb."},{"key":"ref_19","unstructured":"Pastur, L., and Shcherbina, M. (2011). Mathematical Surveys and Monographs, American Mathematical Society."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Bai, Z., and Silverstein, J. (2009). Spectral Analysis of Large Dimensional Random Matrices (Springer Series in Statistics), Springer. [2nd ed.].","DOI":"10.1007\/978-1-4419-0661-8"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Girko, V. (2001). Theory of Stochastic Canonical Equations, Volume I, Kluwer Academic Publishers. Chapter 7.","DOI":"10.1007\/978-94-010-0989-8"},{"key":"ref_22","unstructured":"Taricco, G. (, January December). On the Capacity of Separately-Correlated MIMO Rician Channels. Proceedings of Global Telecommunications Conference, San Francisco, CA, USA."},{"key":"ref_23","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_24","doi-asserted-by":"crossref","first-page":"875","DOI":"10.1214\/105051606000000925","article-title":"Deterministic equivalents for certain functionals of large random matrices","volume":"17","author":"Hachem","year":"2007","journal-title":"Ann. Appl. Probab."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Borwein, J., and Lewis, A. (2000). Convex Analysis and Nonlinear Optimization : Theory and Examples, Springer.","DOI":"10.1007\/978-1-4757-9859-3"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Boyd, S., and Vandenberghe, L. (2004). Convex Optimization, Cambridge University Press.","DOI":"10.1017\/CBO9780511804441"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1109\/26.983319","article-title":"On the capacity of OFDM-based spatial multiplexing systems","volume":"50","author":"Bolcskei","year":"2002","journal-title":"IEEE Trans. Commun."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"4398","DOI":"10.1109\/TIT.2009.2027493","article-title":"Asymptotic performance of linear receivers in MIMO fading channels","volume":"55","author":"Kumar","year":"2009","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Moustakas, A., Kumar, K., and Caire, G. (,  2009). Performance of MMSE MIMO Receivers: A Large N analysis for Correlated Channels. Proceedings of IEEE Vehicular Technology Conference, Barcelona, Spain.","DOI":"10.1109\/VETECS.2009.5073796"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"4138","DOI":"10.1109\/TIT.2011.2145710","article-title":"On the precoder design of flat fading MIMO systems equipped with MMSE receivers: A large system approach","volume":"57","author":"Artigue","year":"2011","journal-title":"IEEE Trans. Inf. Theory"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/14\/11\/2122\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:53:14Z","timestamp":1760219594000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/14\/11\/2122"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,11,1]]},"references-count":30,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2012,11]]}},"alternative-id":["e14112122"],"URL":"https:\/\/doi.org\/10.3390\/e14112122","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2012,11,1]]}}}