{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,5]],"date-time":"2025-08-05T12:53:01Z","timestamp":1754398381843},"reference-count":45,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2012,4,12]],"date-time":"2012-04-12T00:00:00Z","timestamp":1334188800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/2.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["EURASIP J. Adv. Signal Process."],"published-print":{"date-parts":[[2012,12]]},"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>This article studies the transmission of a single cell-edge user's signal using statistical channel state information at cooperative base stations (BSs) with a general jointly correlated multiple-input multiple-output (MIMO) channel model. We first present an optimal scheme to maximize the ergodic sum capacity with per-BS power constraints, revealing that the transmitted signals of all BSs are mutually independent and the optimum transmit directions for each BS align with the eigenvectors of the BS's own transmit correlation matrix of the channel. Then, we employ matrix permanents to derive a closed-form tight upper bound for the ergodic sum capacity. Based on these results, we develop a low-complexity power allocation solution using convex optimization techniques and a simple iterative water-filling algorithm (IWFA) for power allocation. Finally, we derive a necessary and sufficient condition for which a beamforming approach achieves capacity for all BSs. Simulation results demonstrate that the upper bound of ergodic sum capacity is tight and the proposed cooperative transmission scheme increases the downlink system sum capacity considerably.<\/jats:p>","DOI":"10.1186\/1687-6180-2012-81","type":"journal-article","created":{"date-parts":[[2012,4,12]],"date-time":"2012-04-12T14:19:12Z","timestamp":1334240352000},"update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["On base station cooperation using statistical CSI in jointly correlated MIMO downlink channels"],"prefix":"10.1186","volume":"2012","author":[{"given":"Jun","family":"Zhang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bin","family":"Jiang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shi","family":"Jin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiqi","family":"Gao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kai-Kit","family":"Wong","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2012,4,12]]},"reference":[{"issue":"6","key":"219_CR1","doi-asserted-by":"publisher","first-page":"585","DOI":"10.1002\/ett.4460100604","volume":"10","author":"IE Telatar","year":"1999","unstructured":"Telatar IE: Capacity of multi-antenna Gaussian channels. Eur Trans Telecommun 1999, 10(6):585-595. 10.1002\/ett.4460100604","journal-title":"Eur Trans Telecommun"},{"key":"219_CR2","first-page":"1745","volume-title":"Proc IEEE Veh Tech Conf Spring","author":"S Shamai (Shitz)","year":"2001","unstructured":"Shamai (Shitz) S, Zaidel BM: Enhancing the cellular downlink capacity via co-processing at the transmission end. In Proc IEEE Veh Tech Conf Spring. Volume 3. Rhodes Island, Greece; 2001:1745-1749."},{"key":"219_CR3","first-page":"14","volume-title":"Proc Joint Workshop Commun and Coding","author":"S Shamai (Shitz)","year":"2004","unstructured":"Shamai (Shitz) S, Somekh O, Zaidel BM: Multi-cell communications: An information theoretic perspective. In Proc Joint Workshop Commun and Coding. Donnini, Florence, Italy; 2004:14-17."},{"issue":"12","key":"219_CR4","doi-asserted-by":"publisher","first-page":"4473","DOI":"10.1109\/TIT.2007.909170","volume":"53","author":"O Somekh","year":"2007","unstructured":"Somekh O, Zaidel BM, Shamai (Shitz) S: Sum rate characterization of joint multiple cell-site processing. IEEE Trans Inf Theory 2007, 53(12):4473-4497.","journal-title":"IEEE Trans Inf Theory"},{"issue":"7","key":"219_CR5","doi-asserted-by":"publisher","first-page":"3206","DOI":"10.1109\/TIT.2009.2021371","volume":"2009","author":"O Somekh","year":"2009","unstructured":"Somekh O, Simeone O, Bar-Ness Y, Haimovich AM, Shamai (Shitz) S: Cooperative multicell zero-forcing beamforming in cellular downlink channels. IEEE Trans Inf Theory 2009, 2009(7):3206-3219.","journal-title":"IEEE Trans Inf Theory"},{"key":"219_CR6","first-page":"222","volume":"2","author":"H Zhang","year":"2004","unstructured":"Zhang H, Dai H: Co-channel interference mitigation and cooperative processing in downlink multicell multiuser MIMO networks. EURASIP J Wirel Commun Netw 2004, 2: 222-235.","journal-title":"EURASIP J Wirel Commun Netw"},{"key":"219_CR7","first-page":"4333","volume-title":"Proc IEEE Int Conf Commun","author":"MK Karakayali","year":"2006","unstructured":"Karakayali MK, Foschini GJ, Valenzuela RA, Yates RD: On the maximum common rate achievable in a coordinated network. In Proc IEEE Int Conf Commun. Volume 9. Istanbul, Turkey; 2006:4333-4338."},{"key":"219_CR8","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1155\/2008\/586878","volume":"2008","author":"S Jing","year":"2008","unstructured":"Jing S, Tse DNC, Hou J, Soriaga JB, Smee JE, Padovani R: Multi-cell downlink capacity with coordinated processing. EURASIP J Wirel Commun Netw 2008, 2008: 1-19.","journal-title":"EURASIP J Wirel Commun Netw"},{"key":"219_CR9","first-page":"83","volume-title":"Proc Asilomar Conf Sig Sys and Comput","author":"S Venkatesan","year":"2007","unstructured":"Venkatesan S, Lozano A, Valenzuela R: Network MIMO: overcoming intercell interference in indoor wireless systems. In Proc Asilomar Conf Sig Sys and Comput. Pacific Grove, CA, USA; 2007:83-87."},{"issue":"6","key":"219_CR10","doi-asserted-by":"publisher","first-page":"2983","DOI":"10.1109\/TWC.2009.080179","volume":"8","author":"H Huang","year":"2009","unstructured":"Huang H, Trivellato M, Hottinen A, Shafi M, Smith P, Valenzuela R: Increasing downlink cellular throughput with limited network MIMO coordination. IEEE Trans Wirel Commun 2009, 8(6):2983-2989.","journal-title":"IEEE Trans Wirel Commun"},{"issue":"7","key":"219_CR11","doi-asserted-by":"publisher","first-page":"1691","DOI":"10.1109\/TIT.2003.813523","volume":"49","author":"G Caire","year":"2003","unstructured":"Caire G, Shamai S: On the achievable throughput of a multiantenna Gaussian broadcast channel. IEEE Trans Inf Theory 2003, 49(7):1691-706. 10.1109\/TIT.2003.813523","journal-title":"IEEE Trans Inf Theory"},{"issue":"8","key":"219_CR12","doi-asserted-by":"publisher","first-page":"1912","DOI":"10.1109\/TIT.2003.814483","volume":"49","author":"P Viswanath","year":"2003","unstructured":"Viswanath P, Tse D: Sum capacity of the vector Gaussian broadcast channel and uplink-downlink duality. IEEE Trans Inf Theory 2003, 49(8):1912-1921. 10.1109\/TIT.2003.814483","journal-title":"IEEE Trans Inf Theory"},{"issue":"9","key":"219_CR13","doi-asserted-by":"publisher","first-page":"1875","DOI":"10.1109\/TIT.2004.833336","volume":"50","author":"W Yu","year":"2004","unstructured":"Yu W, Cioffi J: Sum capacity of Gaussian vector broadcast channels. IEEE Trans Inf Theory 2004, 50(9):1875-1892. 10.1109\/TIT.2004.833336","journal-title":"IEEE Trans Inf Theory"},{"issue":"10","key":"219_CR14","doi-asserted-by":"publisher","first-page":"2658","DOI":"10.1109\/TIT.2003.817421","volume":"49","author":"S Vishwanath","year":"2003","unstructured":"Vishwanath S, Jindal N: A Goldsmith, Duality, achievable rates, and sum-rate capacity of Gaussian MIMO broadcast channels. IEEE Trans Inf Theory 2003, 49(10):2658-2668. 10.1109\/TIT.2003.817421","journal-title":"IEEE Trans Inf Theory"},{"issue":"6","key":"219_CR15","doi-asserted-by":"publisher","first-page":"2646","DOI":"10.1109\/TSP.2006.890905","volume":"55","author":"W Yu","year":"2007","unstructured":"Yu W, Lan T: Transmitter optimization for the multi-antenna downlink with per-antenna power constraints. IEEE Trans Signal Process 2007, 55(6):2646-2660.","journal-title":"IEEE Trans Signal Process"},{"issue":"4","key":"219_CR16","doi-asserted-by":"publisher","first-page":"2064","DOI":"10.1109\/TIT.2011.2177760","volume":"58","author":"L Zhang","year":"2012","unstructured":"Zhang L, Zhang R, Liang YC, Xin Y, Poor HV: On the Gaussian MIMO BC-MAC duality with multiple transmit covariance constraints. IEEE Trans Inf Theory 2012, 58(4):2064-2078.","journal-title":"IEEE Trans Inf Theory"},{"key":"219_CR17","first-page":"2664","volume-title":"Proc IEEE Int Sym Info Theory","author":"H Huh","year":"2009","unstructured":"Huh H, Papadopoulos H, Caire G: MIMO broadcast channel optimization under general linear constraints. In Proc IEEE Int Sym Info Theory. Seoul, Korea; 2009:2664-2668."},{"key":"219_CR18","first-page":"878","volume-title":"Proc IEEE Int Sym Personal, Indoor Mobile Radio Commun","author":"SA Ramprashad","year":"2009","unstructured":"Ramprashad SA, Caire G: Cellular vs. network MIMO: a comparison including channel state information overhead. In Proc IEEE Int Sym Personal, Indoor Mobile Radio Commun. Tokyo, Japan; 2009:878-884."},{"key":"219_CR19","first-page":"1811","volume-title":"Proc Asilomar Conf on Sig Sys and Comp","author":"SA Ramprashad","year":"2009","unstructured":"Ramprashad SA, Caire G, Papadopoulos HC: Cellular and network MIMO architectures: MU-MIMO spectral efficiency and costs of channel state information. In Proc Asilomar Conf on Sig Sys and Comp. Pacific Grove, CA, USA; 2009:1811-1818."},{"key":"219_CR20","first-page":"1","volume-title":"Proc Info Theory and App Workshop","author":"G Caire","year":"2010","unstructured":"Caire G, Ramprashad SA, Papadopoulos HC: Rethinking network MIMO: cost of CSIT, performance analysis, and architecture comparisons. In Proc Info Theory and App Workshop. San Diego, USA; 2010:1-10."},{"issue":"12","key":"219_CR21","doi-asserted-by":"publisher","first-page":"3111","DOI":"10.1109\/TIT.2004.838379","volume":"50","author":"G Barriac","year":"2004","unstructured":"Barriac G, Madhow U: Space-time communication for OFDM with implicit channel feedback. IEEE Trans Inf Theory 2004, 50(12):3111-3129. 10.1109\/TIT.2004.838379","journal-title":"IEEE Trans Inf Theory"},{"key":"219_CR22","doi-asserted-by":"publisher","first-page":"96","DOI":"10.1109\/TCOMM.2005.861665","volume":"54","author":"G Barriac","year":"2006","unstructured":"Barriac G, Madhow U: Space-time precoding for mean and convariance feedback: application to wideband OFDM. IEEE Trans Commun 2006, 54: 96-107.","journal-title":"IEEE Trans Commun"},{"issue":"3","key":"219_CR23","doi-asserted-by":"publisher","first-page":"502","DOI":"10.1109\/26.837052","volume":"48","author":"DS Shui","year":"2000","unstructured":"Shui DS, Foschini GJ, Gans MJ, Kahn JM: Fading correlation and its effect on the capacity of multielement antenna systems. IEEE Trans Commun 2000, 48(3):502-513. 10.1109\/26.837052","journal-title":"IEEE Trans Commun"},{"issue":"10","key":"219_CR24","doi-asserted-by":"publisher","first-page":"2636","DOI":"10.1109\/TIT.2003.817439","volume":"49","author":"H Shin","year":"2003","unstructured":"Shin H, Lee JH: Capacity of multiple-antenna fading channels: spatial fading correlation, double scattering, and keyhole. IEEE Trans Inf Theory 2003, 49(10):2636-2647. 10.1109\/TIT.2003.817439","journal-title":"IEEE Trans Inf Theory"},{"issue":"7","key":"219_CR25","doi-asserted-by":"publisher","first-page":"2491","DOI":"10.1109\/TIT.2005.850094","volume":"51","author":"AM Tulino","year":"2005","unstructured":"Tulino AM, Lozano A, Verd\u00fa S: Impact of antenna correlation on the capacity of multiantenna channels. IEEE Trans Inf Theory 2005, 51(7):2491-2509. 10.1109\/TIT.2005.850094","journal-title":"IEEE Trans Inf Theory"},{"key":"219_CR26","doi-asserted-by":"publisher","first-page":"90","DOI":"10.1109\/TWC.2006.1576533","volume":"5","author":"W Weichselberger","year":"2006","unstructured":"Weichselberger W, Herdin M, Ozcelik H, Bonek E: A stochastic MIMO channel model with joint correlation of both link ends. IEEE Trans Wirel Commun 2006, 5: 90-100.","journal-title":"IEEE Trans Wirel Commun"},{"key":"219_CR27","volume-title":"UW Tech Report","author":"Y Zhou","year":"2007","unstructured":"Zhou Y, Herdin M, Sayeed A, Bonek E: Experimental study of MIMO channel statistics and capacity via the virtual channel representation. UW Tech Report 2007. [http:\/\/dune.ece.wisc.edu\/pdfs\/zhou_meas.pdf]"},{"issue":"8","key":"219_CR28","doi-asserted-by":"publisher","first-page":"3735","DOI":"10.1109\/TIT.2009.2023737","volume":"55","author":"XQ Gao","year":"2009","unstructured":"Gao XQ, Jiang B, Li X, Gershman AB, McKay MR: Statisitical eigenmode transmission over jointly correlated MIMO channels. IEEE Trans Inf Theory 2009, 55(8):3735-3750.","journal-title":"IEEE Trans Inf Theory"},{"issue":"4","key":"219_CR29","doi-asserted-by":"publisher","first-page":"1165","DOI":"10.1109\/TWC.2004.830822","volume":"3","author":"SA Jafar","year":"2004","unstructured":"Jafar SA, Goldsmith A: Transmitter optimization and optimality of beamforming for multiple antenna systems. IEEE Trans Wirel Commun 2004, 3(4):1165-1175. 10.1109\/TWC.2004.830822","journal-title":"IEEE Trans Wirel Commun"},{"issue":"5","key":"219_CR30","doi-asserted-by":"publisher","first-page":"1543","DOI":"10.1109\/TWC.2004.833523","volume":"3","author":"E Jorswieck","year":"2004","unstructured":"Jorswieck E, Boche H: Channel capacity and capacity range of beamforming in MIMO wireless systems under correlated fading with covariance feedback. IEEE Trans Wirel Commun 2004, 3(5):1543-1553. 10.1109\/TWC.2004.833523","journal-title":"IEEE Trans Wirel Commun"},{"issue":"9","key":"219_CR31","doi-asserted-by":"publisher","first-page":"3647","DOI":"10.1109\/TWC.2008.070449","volume":"7","author":"X Li","year":"2008","unstructured":"Li X, Jin S, Gao XQ, Mckay MR, Wong KK: Transmitter optimization and beamforming op-timality conditions for doublescattering MIMO channels. IEEE Trans Wirel Commun 2008, 7(9):3647-3654.","journal-title":"IEEE Trans Wirel Commun"},{"issue":"10","key":"219_CR32","doi-asserted-by":"publisher","first-page":"5458","DOI":"10.1109\/TSP.2010.2055241","volume":"58","author":"H Wan","year":"2010","unstructured":"Wan H, Chen RR, Liang YB: Optimality of beamforming for MIMO multiple access channels via virtual representation. IEEE Trans Signal Process 2010, 58(10):5458-5463.","journal-title":"IEEE Trans Signal Process"},{"issue":"4","key":"219_CR33","doi-asserted-by":"publisher","first-page":"1171","DOI":"10.1109\/TCOMM.2009.04.070001","volume":"57","author":"A Soysal","year":"2009","unstructured":"Soysal A, Ulukus S: Optimality of beamforming in fading MIMO multiple access channels. IEEE Trans Commun 2009, 57(4):1171-1183.","journal-title":"IEEE Trans Commun"},{"issue":"5","key":"219_CR34","doi-asserted-by":"publisher","first-page":"2809","DOI":"10.1109\/TSP.2010.2041602","volume":"58","author":"X Li","year":"2010","unstructured":"Li X, Jin S, Gao XQ, Mckay MR: Capacity bounds and low complexity transceiver design for double-scattering MIMO multiple access channels. IEEE Trans Signal Process 2010, 58(5):2809-2822.","journal-title":"IEEE Trans Signal Process"},{"key":"219_CR35","doi-asserted-by":"publisher","first-page":"252","DOI":"10.1109\/TIT.2006.887069","volume":"53","author":"CK Wenm","year":"2007","unstructured":"Wenm CK, Wong KK: Asymptotic analysis of spatially correlated MIMO multiple-access channels with arbitrary signaling inputs for joint and separate decoding. IEEE Trans Inf Theory 2007, 53: 252-268.","journal-title":"IEEE Trans Inf Theory"},{"issue":"3","key":"219_CR36","doi-asserted-by":"publisher","first-page":"477","DOI":"10.1109\/TCOMM.2007.892449","volume":"55","author":"CK Wen","year":"2007","unstructured":"Wen CK, Wong KK, Chen JC: Spatially correlated MIMO multiple-access systems with macro-diversity: asymptotic analysis via statistical physics. IEEE Trans Commun 2007, 55(3):477-488.","journal-title":"IEEE Trans Commun"},{"issue":"3","key":"219_CR37","doi-asserted-by":"publisher","first-page":"662","DOI":"10.1109\/TWC.2006.1611096","volume":"5","author":"AM Tulino","year":"2006","unstructured":"Tulino AM, Lozano A, Verd\u00fa S: Capacity-achieving input convariance for single-user multi-antena channels. IEEE Trans Wirel Commun 2006, 5(3):662-671.","journal-title":"IEEE Trans Wirel Commun"},{"key":"219_CR38","doi-asserted-by":"publisher","first-page":"1963","DOI":"10.1109\/VETECF.2002.1040561","volume-title":"Proc IEEE Veh Tech Conf","author":"SK Jayaweera","year":"2002","unstructured":"Jayaweera SK, Poor HV: On the capacity of multi-antenna systems in the presence of Rician fading. In Proc IEEE Veh Tech Conf. Vancouver, BC, Canada; 2002:1963-1967."},{"issue":"3","key":"219_CR39","doi-asserted-by":"publisher","first-page":"1102","DOI":"10.1109\/TWC.2005.846970","volume":"4","author":"SK Jayaweera","year":"2005","unstructured":"Jayaweera SK, Poor HV: On the capacity of multiple antenna systems in Rician fading. IEEE Trans Wirel Commun 2005, 4(3):1102-1111.","journal-title":"IEEE Trans Wirel Commun"},{"issue":"6","key":"219_CR40","doi-asserted-by":"publisher","first-page":"2632","DOI":"10.1109\/18.945281","volume":"47","author":"E Visotsky","year":"2001","unstructured":"Visotsky E, Madhow U: Space-time transmit precoding with imperfect feedback. IEEE Trans Inf Theory 2001, 47(6):2632-2639. 10.1109\/18.945281","journal-title":"IEEE Trans Inf Theory"},{"issue":"6","key":"219_CR41","doi-asserted-by":"publisher","first-page":"2058","DOI":"10.1109\/TIT.2005.847724","volume":"51","author":"V Veeravalli","year":"2005","unstructured":"Veeravalli V, Liang Y, Sayeed AM: Correlated MIMO Rayleigh fading channels: capacity, optimal signaling and asymptotics. IEEE Trans Inf Theory 2005, 51(6):2058-2072. 10.1109\/TIT.2005.847724","journal-title":"IEEE Trans Inf Theory"},{"key":"219_CR42","volume-title":"Permanents","author":"H Minc","year":"1978","unstructured":"Minc H: Permanents. Addison-Wesley Publishing Company, Mass; 1978."},{"key":"219_CR43","unstructured":"Spatial channel model for multiple input multiple output (MIMO) simulations. 3GPP, TR 25.996, V7.0.0 2007."},{"key":"219_CR44","volume-title":"MATLAB implementation of the 3GPP spatial channel model (3GPP TR 25.996)","author":"J Salo","year":"2005","unstructured":"Salo J, Del Galdo G, Salmi J, Kyosti P, Milojevic M, Laselva D, Schneider C: MATLAB implementation of the 3GPP spatial channel model (3GPP TR 25.996).2005. [http:\/\/www.tkk.fi\/Units\/Radio\/scm\/]"},{"key":"219_CR45","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511810817","volume-title":"Matrix Analysis","author":"RA Horn","year":"1985","unstructured":"Horn RA, Johnson CR: Matrix Analysis. Cambridge University Press, Cambridge; 1985."}],"container-title":["EURASIP Journal on Advances in Signal Processing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1186\/1687-6180-2012-81.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1186\/1687-6180-2012-81\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/1687-6180-2012-81.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,9,1]],"date-time":"2021-09-01T19:08:25Z","timestamp":1630523305000},"score":1,"resource":{"primary":{"URL":"https:\/\/asp-eurasipjournals.springeropen.com\/articles\/10.1186\/1687-6180-2012-81"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,4,12]]},"references-count":45,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2012,12]]}},"alternative-id":["219"],"URL":"https:\/\/doi.org\/10.1186\/1687-6180-2012-81","relation":{},"ISSN":["1687-6180"],"issn-type":[{"value":"1687-6180","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,4,12]]},"assertion":[{"value":"25 October 2011","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 April 2012","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 April 2012","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"81"}}