{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:40:15Z","timestamp":1740123615533,"version":"3.37.3"},"reference-count":21,"publisher":"Springer Science and Business Media LLC","issue":"9","license":[{"start":{"date-parts":[[2023,1,13]],"date-time":"2023-01-13T00:00:00Z","timestamp":1673568000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2023,1,13]],"date-time":"2023-01-13T00:00:00Z","timestamp":1673568000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100004837","name":"Ministerio de Ciencia e Innovaci\u00f3n","doi-asserted-by":"publisher","award":["PID2020-113785RB-100","PID2019-106455GB-C21"],"award-info":[{"award-number":["PID2020-113785RB-100","PID2019-106455GB-C21"]}],"id":[{"id":"10.13039\/501100004837","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100012818","name":"Comunidad de Madrid","doi-asserted-by":"publisher","award":["MIMACUHSPACE-CM-UC3M"],"award-info":[{"award-number":["MIMACUHSPACE-CM-UC3M"]}],"id":[{"id":"10.13039\/100012818","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Ramon y Cajal Grant, Spain","award":["RYC-2017-22101"],"award-info":[{"award-number":["RYC-2017-22101"]}]},{"name":"Universidad Carlos III"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Supercomput"],"published-print":{"date-parts":[[2023,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Hybrid platforms combining multicore central processing units (CPU) with many-core hardware accelerators such as graphic processing units (GPU) can be smartly exploited to provide efficient parallel implementations of wireless communication algorithms for Fifth Generation (5G) and beyond systems. Massive multiple-input multiple-output (MIMO) systems are a key element of the 5G standard, involving several tens or hundreds of antenna elements for communication. Such a high number of antennas has a direct impact on the computational complexity of some MIMO signal processing algorithms. In this work, we focus on the channel estimation stage. In particular, we develop a parallel implementation of a recently proposed MIMO channel estimation algorithm. Its performance in terms of execution time is evaluated both in a multicore CPU and in a GPU. The results show that some computation blocks of the algorithm are more suitable for multicore implementation, whereas other parts are more efficiently implemented in the GPU, indicating that a hybrid CPU\u2013GPU implementation would achieve the best performance in practical applications based on the tested platform.<\/jats:p>","DOI":"10.1007\/s11227-022-05018-w","type":"journal-article","created":{"date-parts":[[2023,1,13]],"date-time":"2023-01-13T06:07:29Z","timestamp":1673590049000},"page":"9371-9382","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Hybrid CPU\u2013GPU implementation of the transformed spatial domain channel estimation algorithm for mmWave MIMO systems"],"prefix":"10.1007","volume":"79","author":[{"given":"Diego","family":"Lloria","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pablo M.","family":"Aviles","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jose A.","family":"Belloch","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sandra","family":"Roger","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Carmen","family":"Botella-Mascarell","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Almudena","family":"Lindoso","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,1,13]]},"reference":[{"key":"5018_CR1","doi-asserted-by":"crossref","unstructured":"Czarnul P, Proficz J, Drypczewski K (2020) Survey of methodologies, approaches, and challenges in parallel programming using high-performance computing systems. Sci Program 2020","DOI":"10.1155\/2020\/4176794"},{"issue":"1","key":"5018_CR2","doi-asserted-by":"publisher","first-page":"1686","DOI":"10.1007\/s11227-018-02739-9","volume":"75","author":"JA Belloch","year":"2019","unstructured":"Belloch JA, Amor-Martin A, Garcia-Donoro D, Mart\u00ednez-Zald\u00edvar FJ, Garcia-Castillo LE (2019) On the use of many-core machines for the acceleration of a mesh truncation technique for FEM. J Supercomput 75(1):1686\u20131696","journal-title":"J Supercomput"},{"issue":"8","key":"5018_CR3","doi-asserted-by":"publisher","first-page":"3796","DOI":"10.1109\/TVT.2012.2210576","volume":"61","author":"S Roger","year":"2012","unstructured":"Roger S, Ramiro C, Gonzalez A, Almenar V, Vidal AM (2012) Fully parallel GPU implementation of a fixed-complexity soft-output MIMO detector. IEEE Trans Veh Technol 61(8):3796\u20133800","journal-title":"IEEE Trans Veh Technol"},{"issue":"3","key":"5018_CR4","doi-asserted-by":"publisher","first-page":"1010","DOI":"10.1007\/s11227-012-0839-x","volume":"65","author":"C Ramiro","year":"2013","unstructured":"Ramiro C, Roger S, Gonzalez A, Almenar V, Vidal AM (2013) Multicore implementation of a fixed-complexity tree-search detector for MIMO communications. J Supercomput 65(3):1010\u20131019","journal-title":"J Supercomput"},{"issue":"2","key":"5018_CR5","doi-asserted-by":"publisher","first-page":"106","DOI":"10.1109\/MCOM.2014.6736750","volume":"52","author":"W Roh","year":"2014","unstructured":"Roh W, Seol J, Park J, Lee B, Lee J, Kim Y, Cho J, Cheun K, Aryanfar F (2014) Millimeter-wave beamforming as an enabling technology for 5G cellular communications: theoretical feasibility and prototype results. IEEE Commun Mag 52(2):106\u2013113","journal-title":"IEEE Commun Mag"},{"issue":"3","key":"5018_CR6","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1109\/MCOM.001.1900411","volume":"58","author":"M Giordani","year":"2020","unstructured":"Giordani M, Polese M, Mezzavilla M, Rangan S, Zorzi M (2020) Toward 6G networks: use cases and technologies. IEEE Commun Mag 58(3):55\u201361","journal-title":"IEEE Commun Mag"},{"issue":"9","key":"5018_CR7","doi-asserted-by":"publisher","first-page":"5926","DOI":"10.1109\/TWC.2021.3071315","volume":"20","author":"S Roger","year":"2021","unstructured":"Roger S, Cobos M, Botella-Mascarell C, Fodor G (2021) Fast channel estimation in the transformed spatial domain for analog millimeter wave systems. IEEE Trans Wirel Commun 20(9):5926\u20135941","journal-title":"IEEE Trans Wirel Commun"},{"key":"5018_CR8","doi-asserted-by":"crossref","unstructured":"Lee J, Gil G-T, Lee YH (2014) Exploiting spatial sparsity for estimating channels of hybrid MIMO systems in millimeter wave communications. in IEEE Global Communications Conference","DOI":"10.1109\/GLOCOM.2014.7037320"},{"key":"5018_CR9","doi-asserted-by":"crossref","unstructured":"Montagner S, Benvenuto N, Baracca P (2015) Channel estimation using a 2D DFT for millimeter-wave systems. in IEEE 81st Vehicular Technology Conference (VTC Spring)","DOI":"10.1109\/VTCSpring.2015.7145736"},{"key":"5018_CR10","doi-asserted-by":"publisher","first-page":"14756","DOI":"10.1007\/s11227-022-04479-3","volume":"78","author":"PM Aviles","year":"2022","unstructured":"Aviles PM, Lloria D, Belloch JA, Roger S, Lindoso A, Cobos M (2022) Performance analysis of a millimeter wave MIMO channel estimation method in an embedded multi-core processor. J Supercomput 78:14756\u201314767","journal-title":"J Supercomput"},{"key":"5018_CR11","unstructured":"Xilinx Inc, Zynq UltraScale+ MPSoC data sheet: overview. DS891 (v1.7) 2018"},{"key":"5018_CR12","doi-asserted-by":"crossref","unstructured":"Dongarra J, Croz JD, Hammarling S, Hanson RJ (1985) A proposal for an extended set of Fortran basic linear algebra subprograms. in ACM Signum Newsletter, pp 2\u201318","DOI":"10.1145\/1057935.1057936"},{"key":"5018_CR13","unstructured":"Tomov S, Dongarra J, Baboulin M (2008) Towards dense linear algebra for hybrid GPU accelerated manycore systems. LAPACK Working Note, Tech. Rep. 210, Oct. [Online]. Available: http:\/\/www.netlib.org\/lapack\/lawnspdf\/lawn210.pdf"},{"key":"5018_CR14","unstructured":"Olson T (2010) Mali-400 MP: a scalable GPU for mobile devices. in Hot3D Session. Proceedings International Conference on High Performance Graphics"},{"issue":"1","key":"5018_CR15","doi-asserted-by":"publisher","first-page":"2124","DOI":"10.1007\/s11227-020-03342-7","volume":"77","author":"JA Belloch","year":"2021","unstructured":"Belloch JA, Leon G, Badia JM, Lindoso A, San\u00a0Millan E (2021) Evaluating the computational performance of the Xilinx Ultrascale+ EG heterogeneous MPSoC. J Supercomput 77(1):2124\u20132137 (January)","journal-title":"J Supercomput"},{"key":"5018_CR16","unstructured":"Trompouki MM, Kosmidis L (2016) Towards general purpose computations on low-end mobile GPUs. in 2016 Design, Automation & Test in Europe Conference & Exhibition, DATE 2016, Dresden, Germany, March 14\u201318, 2016, pp 539\u2013542"},{"issue":"5","key":"5018_CR17","doi-asserted-by":"publisher","first-page":"831","DOI":"10.1109\/JSTSP.2014.2334278","volume":"8","author":"A Alkhateeb","year":"2014","unstructured":"Alkhateeb A, El Ayach O, Leus G, Heath RW (2014) Channel estimation and hybrid precoding for millimeter wave cellular systems. IEEE J Select Top Signal Process 8(5):831\u2013846","journal-title":"IEEE J Select Top Signal Process"},{"issue":"9","key":"5018_CR18","doi-asserted-by":"publisher","first-page":"7121","DOI":"10.1109\/TWC.2022.3155157","volume":"21","author":"X Ge","year":"2022","unstructured":"Ge X, Shen W, Xing C, Zhao L, An J (2022) Training beam design for channel estimation in hybrid mmWave MIMO systems. IEEE Trans Wirel Commun 21(9):7121\u20137134","journal-title":"IEEE Trans Wirel Commun"},{"issue":"6","key":"5018_CR19","doi-asserted-by":"publisher","first-page":"1164","DOI":"10.1109\/JSAC.2014.2328154","volume":"32","author":"MR Akdeniz","year":"2014","unstructured":"Akdeniz MR, Liu Y, Samimi MK, Sun S, Rangan S, Rappaport TS, Erkip E (2014) Millimeter wave channel modeling and cellular capacity evaluation. IEEE J Sel Areas Commun 32(6):1164\u20131179","journal-title":"IEEE J Sel Areas Commun"},{"key":"5018_CR20","doi-asserted-by":"crossref","unstructured":"Zhang C, Guo D, Fan P (2016) Tracking angles of departure and arrival in a mobile millimeter wave channel. in 2016 IEEE International Conference on Communications (ICC), May, pp 1\u20136","DOI":"10.1109\/ICC.2016.7510902"},{"issue":"2","key":"5018_CR21","doi-asserted-by":"publisher","first-page":"216","DOI":"10.1109\/JPROC.2004.840301","volume":"93","author":"M Frigo","year":"2005","unstructured":"Frigo M, Johnson SG (2005) The design and implementation of FFTW3. Proc IEEE 93(2):216\u2013231","journal-title":"Proc IEEE"}],"container-title":["The Journal of Supercomputing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11227-022-05018-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11227-022-05018-w\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11227-022-05018-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,24]],"date-time":"2023-04-24T11:15:06Z","timestamp":1682334906000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11227-022-05018-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,1,13]]},"references-count":21,"journal-issue":{"issue":"9","published-print":{"date-parts":[[2023,6]]}},"alternative-id":["5018"],"URL":"https:\/\/doi.org\/10.1007\/s11227-022-05018-w","relation":{},"ISSN":["0920-8542","1573-0484"],"issn-type":[{"type":"print","value":"0920-8542"},{"type":"electronic","value":"1573-0484"}],"subject":[],"published":{"date-parts":[[2023,1,13]]},"assertion":[{"value":"22 December 2022","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 January 2023","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no known competing financial interest or personal relationships that could have appeared to influence the work reported in this paper.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"Not applicable.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval"}}]}}