{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,27]],"date-time":"2026-06-27T15:31:40Z","timestamp":1782574300276,"version":"3.54.5"},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2026,1,22]],"date-time":"2026-01-22T00:00:00Z","timestamp":1769040000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,1,22]],"date-time":"2026-01-22T00:00:00Z","timestamp":1769040000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Wireless Pers Commun"],"published-print":{"date-parts":[[2026,2]]},"DOI":"10.1007\/s11277-026-11913-9","type":"journal-article","created":{"date-parts":[[2026,1,22]],"date-time":"2026-01-22T14:32:08Z","timestamp":1769092328000},"page":"935-965","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Practical IRS-Assisted 6G Wireless Communications: Tight Ergodic Capacity Approximations with Coupling and Amplitude-Phase Distortion"],"prefix":"10.1007","volume":"146","author":[{"given":"Md Sarfraz","family":"Alam","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ganesh","family":"Prasad","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Deepak","family":"Mishra","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Abhishek","family":"Mondal","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Prabina","family":"Pattanayak","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,1,22]]},"reference":[{"key":"11913_CR1","doi-asserted-by":"publisher","DOI":"10.1016\/j.phycom.2024.102543","volume":"68","author":"S Das","year":"2025","unstructured":"Das, S., Kumar, N., & Dixit, D. (2025). On the performance of dual-hop mixed THz-RF cooperative relay networks. Physical Communication, 68, Article 102543.","journal-title":"Physical Communication"},{"issue":"4","key":"11913_CR2","doi-asserted-by":"publisher","first-page":"2213","DOI":"10.1109\/COMST.2024.3387749","volume":"26","author":"H Lu","year":"2024","unstructured":"Lu, H., Zeng, Y., You, C., Han, Y., Zhang, J., Wang, Z., & Zhang, R. (2024). A tutorial on near-field XL-MIMO communications toward 6G. IEEE Communications Surveys & Tutorials,26(4), 2213\u20132257.","journal-title":"IEEE Communications Surveys & Tutorials"},{"issue":"5","key":"11913_CR3","doi-asserted-by":"publisher","DOI":"10.1002\/dac.6024","volume":"38","author":"S Sivasankar","year":"2025","unstructured":"Sivasankar, S., & Markkandan, S. (2025). A review on intelligent reflecting surfaces: Challenges and opportunities towards secured communications. International Journal of Communication Systems, 38(5), Article e6024.","journal-title":"International Journal of Communication Systems"},{"key":"11913_CR4","doi-asserted-by":"publisher","first-page":"29614","DOI":"10.1109\/ACCESS.2023.3261547","volume":"11","author":"B Rana","year":"2023","unstructured":"Rana, B., Cho, S. S., & Hong, I. P. (2023). Review paper on hardware of reconfigurable intelligent surfaces. IEEE Access, 11, 29614\u201329634.","journal-title":"IEEE Access"},{"issue":"5","key":"11913_CR5","doi-asserted-by":"publisher","first-page":"497","DOI":"10.1049\/cmu2.12571","volume":"17","author":"S Hassouna","year":"2023","unstructured":"Hassouna, S., Jamshed, M. A., Rains, J., Kazim, J. U. R., Rehman, M. U., Abualhayja, M., & Abbasi, Q. H. (2023). A survey on reconfigurable intelligent surfaces: Wireless communication perspective. IET Communications,17(5), 497\u2013537.","journal-title":"IET Communications"},{"issue":"2","key":"11913_CR6","doi-asserted-by":"publisher","first-page":"1442","DOI":"10.1109\/TCOMM.2022.3141097","volume":"70","author":"T Shafique","year":"2022","unstructured":"Shafique, T., Tabassum, H., & Hossain, E. (2022). Stochastic geometry analysis of IRS-assisted downlink cellular networks. IEEE Transactions on Communications,70(2), 1442\u20131456.","journal-title":"IEEE Transactions on Communications"},{"issue":"5","key":"11913_CR7","doi-asserted-by":"publisher","first-page":"4501","DOI":"10.1109\/TVT.2021.3069174","volume":"70","author":"Y Zhang","year":"2021","unstructured":"Zhang, Y., Zhang, J., Di Renzo, M., Xiao, H., & Ai, B. (2021). Performance analysis of RIS-aided systems with practical phase shift and amplitude response. IEEE Transactions on Vehicular Technology, 70(5), 4501\u20134511.","journal-title":"IEEE Transactions on Vehicular Technology"},{"issue":"8","key":"11913_CR8","doi-asserted-by":"publisher","first-page":"1646","DOI":"10.1109\/LCOMM.2020.2997027","volume":"24","author":"D Li","year":"2020","unstructured":"Li, D. (2020). Ergodic capacity of intelligent reflecting surface-assisted communication systems with phase errors. IEEE Communications Letters,24(8), 1646\u20131650.","journal-title":"IEEE Communications Letters"},{"key":"11913_CR9","doi-asserted-by":"publisher","first-page":"92263","DOI":"10.1109\/ACCESS.2021.3092335","volume":"9","author":"A-T Le","year":"2021","unstructured":"Le, A.-T., Ha, N.-D., Do, D.-T., Silva, A., & Yadav, S. (2021). Enabling user grouping and fixed power allocation scheme for reconfigurable intelligent surfaces-aided wireless systems. IEEE Access, 9, 92263\u201392275.","journal-title":"IEEE Access"},{"key":"11913_CR10","doi-asserted-by":"crossref","unstructured":"Kudathanthirige, D., Gunasinghe, D., & Amarasuriya, G. (2020). Performance analysis of intelligent reflective surfaces for wireless communication. In ICC 2020 IEEE International Conference on Communications (ICC), 1\u20136.","DOI":"10.1109\/ICC40277.2020.9148760"},{"issue":"12","key":"11913_CR11","doi-asserted-by":"publisher","first-page":"8068","DOI":"10.1109\/TWC.2020.3019088","volume":"19","author":"Y Jia","year":"2020","unstructured":"Jia, Y., Ye, C., & Cui, Y. (2020). Analysis and optimization of an intelligent reflecting surface-assisted system with interference. IEEE Transactions on Wireless Communications,19(12), 8068\u20138082.","journal-title":"IEEE Transactions on Wireless Communications"},{"issue":"1","key":"11913_CR12","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1109\/LCOMM.2020.3023759","volume":"25","author":"T Van Chien","year":"2021","unstructured":"Van Chien, T., Lam Thanh, T., Chatzinotas, S., & Ottersten, B. (2021). Coverage probability and ergodic capacity of intelligent reflecting surface-enhanced communication systems. IEEE Communications Letters, 25(1), 69\u201373.","journal-title":"IEEE Communications Letters"},{"key":"11913_CR13","doi-asserted-by":"crossref","unstructured":"Huang, X., Yu, X., Yu, K., & Dang, X. (2021). Ergodic capacity and outage probability analysis of intelligent reflecting surface aided communication systems. In 2021 IEEE 21st International Conference on Communication Technology (ICCT), 715\u2013719.","DOI":"10.1109\/ICCT52962.2021.9658116"},{"issue":"4","key":"11913_CR14","doi-asserted-by":"publisher","first-page":"2551","DOI":"10.1007\/s11277-024-11725-9","volume":"139","author":"T DhruvaKumar","year":"2024","unstructured":"DhruvaKumar, T., & Chaturvedi, A. (2024). Ergodic capacity and outage probability analysis for multiple intelligent reflecting surface assisted wireless networks. Wireless Personal Communications, 139(4), 2551\u20132576.","journal-title":"Wireless Personal Communications"},{"issue":"8","key":"11913_CR15","doi-asserted-by":"publisher","first-page":"11441","DOI":"10.1109\/TVT.2024.3376071","volume":"73","author":"MA Mosleh","year":"2024","unstructured":"Mosleh, M. A., H\u00e9liot, F., & Tafazolli, R. (2024). Ergodic capacity analysis of reconfigurable intelligent surface assisted MIMO systems with a practical phase shift and amplitude response. IEEE Transactions on Vehicular Technology, 73(8), 11441\u201311457.","journal-title":"IEEE Transactions on Vehicular Technology"},{"key":"11913_CR16","doi-asserted-by":"crossref","unstructured":"Ghosh, S., Bhowmick, A., Roy, S. D., & Kundu, S. (2023). Outage and Ergodic Capacity Analysis in UAV-RIS Assisted NOMA-D2D Network. In 2023 IEEE International Conference on Advanced Networks and Telecommunications Systems (ANTS), (762-767). IEEE.","DOI":"10.1109\/ANTS59832.2023.10469588"},{"key":"11913_CR17","doi-asserted-by":"publisher","first-page":"534","DOI":"10.1109\/OJCOMS.2021.3064873","volume":"2","author":"C Stefanovic","year":"2021","unstructured":"Stefanovic, C., Panic, S., Bhatia, V., & Kumar, N. (2021). On second-order statistics of the composite channel models for UAV-to-ground communications with UAV selection. IEEE Open Journal of the Communications Society,2, 534\u2013544.","journal-title":"IEEE Open Journal of the Communications Society"},{"issue":"2","key":"11913_CR18","doi-asserted-by":"publisher","first-page":"184","DOI":"10.1109\/LWC.2019.2947445","volume":"9","author":"M-A Badiu","year":"2020","unstructured":"Badiu, M.-A., & Coon, J. P. (2020). Communication through a large reflecting surface with phase errors. IEEE Wireless Communications Letters, 9(2), 184\u2013188.","journal-title":"IEEE Wireless Communications Letters"},{"issue":"7","key":"11913_CR19","first-page":"962","volume":"9","author":"W Zhao","year":"2020","unstructured":"Zhao, W., Wang, G., Atapattu, S., Tsiftsis, T. A., & Ma, X. (2020). Performance analysis of large intelligent surface aided backscatter communication systems. IEEE Wireless Communications Letters,9(7), 962\u2013966.","journal-title":"IEEE Wireless Communications Letters"},{"issue":"8","key":"11913_CR20","doi-asserted-by":"publisher","first-page":"1268","DOI":"10.1109\/LWC.2020.2987798","volume":"9","author":"L Yang","year":"2020","unstructured":"Yang, L., Yang, Y., Hasna, M. O., & Alouini, M.-S. (2020). Coverage, probability of SNR gain, and DoR analysis of RIS-aided communication systems. IEEE Wireless Communications Letters,9(8), 1268\u20131272.","journal-title":"IEEE Wireless Communications Letters"},{"key":"11913_CR21","doi-asserted-by":"publisher","first-page":"116753","DOI":"10.1109\/ACCESS.2019.2935192","volume":"7","author":"E Basar","year":"2019","unstructured":"Basar, E., Di Renzo, M., De Rosny, J., Debbah, M., Alouini, M.-S., & Zhang, R. (2019). Wireless communications through reconfigurable intelligent surfaces. IEEE Access,7, 116753\u2013116773.","journal-title":"IEEE Access"},{"key":"11913_CR22","doi-asserted-by":"crossref","unstructured":"Sahoo, S., & Kumar, N. (2024). On the performance of SWIPT-enabled two-way AF relay networks in $$\\kappa$$\u2013$$\\mu$$ fading. Physical Communication,64, Article 102308.","DOI":"10.1016\/j.phycom.2024.102308"},{"key":"11913_CR23","doi-asserted-by":"crossref","unstructured":"Singh, R. K., Das, S., Dixit, D., & Kumar, N. (2024). Performance analysis of energy harvesting-enabled relay networks in $$\\kappa$$\u2013$$\\mu$$ fading channels. Transactions on Emerging Telecommunications Technologies,35(4), Article e4976.","DOI":"10.1002\/ett.4976"},{"issue":"5","key":"11913_CR24","doi-asserted-by":"publisher","first-page":"938","DOI":"10.1109\/LWC.2021.3050826","volume":"10","author":"G Gradoni","year":"2021","unstructured":"Gradoni, G., & Di Renzo, M. (2021). End-to-end mutual coupling aware communication model for reconfigurable intelligent surfaces: An electromagnetic-compliant approach based on mutual impedances. IEEE Wireless Communications Letters,10(5), 938\u2013942.","journal-title":"IEEE Wireless Communications Letters"},{"issue":"5","key":"11913_CR25","doi-asserted-by":"publisher","first-page":"3313","DOI":"10.1109\/TCOMM.2021.3051897","volume":"69","author":"Q Wu","year":"2021","unstructured":"Wu, Q., Zhang, S., Zheng, B., You, C., & Zhang, R. (2021). Intelligent reflecting surface-aided wireless communications: A tutorial. IEEE transactions on communications,69(5), 3313\u20133351.","journal-title":"IEEE transactions on communications"},{"key":"11913_CR26","doi-asserted-by":"publisher","DOI":"10.1109\/twc.2024.3451548","author":"P Zheng","year":"2024","unstructured":"Zheng, P., Wang, R., Shamim, A., & Al-Naffouri, T. Y. (2024). Mutual coupling in RIS-aided communication: Model training and experimental validation. IEEE Transactions on Wireless Communications. https:\/\/doi.org\/10.1109\/twc.2024.3451548","journal-title":"IEEE Transactions on Wireless Communications"},{"issue":"14","key":"11913_CR27","doi-asserted-by":"publisher","first-page":"5297","DOI":"10.3390\/s22145297","volume":"22","author":"S Sun","year":"2022","unstructured":"Sun, S., & Tao, M. (2022). Characteristics of channel eigenvalues and mutual coupling effects for holographic reconfigurable intelligent surfaces. Sensors,22(14), 5297.","journal-title":"Sensors"},{"issue":"4","key":"11913_CR28","doi-asserted-by":"publisher","first-page":"937","DOI":"10.1109\/LCOMM.2024.3361648","volume":"28","author":"H Li","year":"2024","unstructured":"Li, H., Shen, S., Nerini, M., Di Renzo, M., & Clerckx, B. (2024). Beyond diagonal reconfigurable intelligent surfaces with mutual coupling: Modeling and optimization. IEEE Communications Letters,28(4), 937\u2013941.","journal-title":"IEEE Communications Letters"},{"issue":"6","key":"11913_CR29","doi-asserted-by":"publisher","DOI":"10.3390\/s22062390","volume":"22","author":"VDP Souto","year":"2022","unstructured":"Souto, V. D. P., Souza, R. D., Uch\u00f4a-Filho, B. F., & Li, Y. (2022). Intelligent reflecting surfaces beamforming optimization with statistical channel knowledge. Sensors, 22(6), Article 2390.","journal-title":"Sensors"},{"issue":"5","key":"11913_CR30","doi-asserted-by":"publisher","first-page":"3558","DOI":"10.1109\/TCOMM.2022.3162580","volume":"70","author":"K Zhi","year":"2022","unstructured":"Zhi, K., Pan, C., Ren, H., & Wang, K. (2022). Power scaling law analysis and phase shift optimization of RIS-aided massive MIMO systems with statistical CSI. IEEE Transactions on Communications,70(5), 3558\u20133574.","journal-title":"IEEE Transactions on Communications"},{"issue":"1","key":"11913_CR31","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1561\/0100000001","volume":"1","author":"AM Tulino","year":"2004","unstructured":"Tulino, A. M., & Verd\u00fa, S. (2004). Random matrix theory and wireless communications. Foundations and Trends in Communications and Information Theory,1(1), 1\u2013182.","journal-title":"Foundations and Trends in Communications and Information Theory"},{"issue":"2","key":"11913_CR32","doi-asserted-by":"publisher","first-page":"554","DOI":"10.1109\/TCOMM.2015.2506699","volume":"64","author":"D Mishra","year":"2016","unstructured":"Mishra, D., De, S., & Chiasserini, C.-F. (2016). Joint optimization schemes for cooperative wireless information and power transfer over Rician channels. IEEE Transactions on Communications, 64(2), 554\u2013571.","journal-title":"IEEE Transactions on Communications"},{"key":"11913_CR33","volume-title":"Table of integrals, series, and products","author":"IS Gradshteyn","year":"2014","unstructured":"Gradshteyn, I. S., & Ryzhik, I. M. (2014). Table of integrals, series, and products. Academic Press."},{"key":"11913_CR34","doi-asserted-by":"crossref","unstructured":"Van Chien, T., & Ngo, H.Q. (2020). Massive MIMO channels. In: Institution of Engineering and Technology, UK, 301\u2013333.","DOI":"10.1049\/PBTE093E_ch11"},{"key":"11913_CR35","doi-asserted-by":"crossref","unstructured":"Huang, Y., & Zou, Y. (2022). Upper-bound ergodic capacity analysis of RIS-aided energy-harvesting relay systems. In IEEE Global Communications Conference, (3235-3240).","DOI":"10.1109\/GLOBECOM48099.2022.10001587"},{"issue":"4","key":"11913_CR36","doi-asserted-by":"publisher","first-page":"268","DOI":"10.1007\/s12046-024-02605-w","volume":"49","author":"R Mahammad Rafi","year":"2024","unstructured":"Mahammad Rafi, R., Sudha, V., & Reshma, P. (2024). Ergodic capacity analysis of distributed RIS wireless communication system: How many RIS elements are required to beat direct LoS path? S\u0101dhan\u0101,49(4), 268.","journal-title":"S\u0101dhan\u0101"}],"container-title":["Wireless Personal Communications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11277-026-11913-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11277-026-11913-9","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11277-026-11913-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,9]],"date-time":"2026-02-09T14:39:02Z","timestamp":1770647942000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11277-026-11913-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1,22]]},"references-count":36,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2026,2]]}},"alternative-id":["11913"],"URL":"https:\/\/doi.org\/10.1007\/s11277-026-11913-9","relation":{},"ISSN":["0929-6212","1572-834X"],"issn-type":[{"value":"0929-6212","type":"print"},{"value":"1572-834X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,1,22]]},"assertion":[{"value":"6 September 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 January 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 January 2026","order":3,"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 no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}]}}