{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:39:45Z","timestamp":1760150385025,"version":"build-2065373602"},"reference-count":37,"publisher":"MDPI AG","issue":"21","license":[{"start":{"date-parts":[[2023,11,2]],"date-time":"2023-11-02T00:00:00Z","timestamp":1698883200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Konkuk University"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>As a strategy to coordinate inter-cell interference in cellular networks, a fractional frequency reuse (FFR) system is proposed, in which the frequency bandwidth is split into two orthogonal bands; users staying near the center of a FFR cell use the band with a frequency reuse (FR) factor of one (i.e., full FR), and users located close to the cell edge utilize the band with a FR factor greater than one (i.e., partial FR). Full FR coverage, which identifies full FR and partial FR regions (that is, near-center and near-edge regions) within a FFR cell, has a crucial effect on system performance. Some of the authors of this paper recently investigated the optimization of full FR coverage to maximize system throughput. They analytically showed that under the constraint of satisfying a specified target outage probability, the optimal full FR coverage is a non-increasing function of base station power when all base station powers in the cellular network are scaled at an equal rate. Interestingly, in this paper, it is proven that as the power of a single base station is scaled, the optimal full FR coverage in that cell is a non-decreasing function of base station power. Our results provide useful insight into the design of full FR coverage in relation to the transmit power of a base station. It gives a deeper understanding of the intricate relationship between important FFR system parameters of base station power and full FR coverage.<\/jats:p>","DOI":"10.3390\/s23218925","type":"journal-article","created":{"date-parts":[[2023,11,2]],"date-time":"2023-11-02T09:28:13Z","timestamp":1698917293000},"page":"8925","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Optimal Coverage of Full Frequency Reuse in FFR Networks in Relation to Power Scaling of a Base Station"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-2514-8438","authenticated-orcid":false,"given":"Minyoung","family":"Seo","sequence":"first","affiliation":[{"name":"Department of Smart ICT Convergence, Konkuk University, Seoul 05029, Republic of Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8982-6954","authenticated-orcid":false,"given":"Seok-Ho","family":"Chang","sequence":"additional","affiliation":[{"name":"Department of Smart ICT Convergence, Konkuk University, Seoul 05029, Republic of Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8467-6504","authenticated-orcid":false,"given":"Jong-Man","family":"Lee","sequence":"additional","affiliation":[{"name":"Hanwha Systems, Sungnam 13524, Republic of Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3519-0268","authenticated-orcid":false,"given":"Ki-Hun","family":"Kim","sequence":"additional","affiliation":[{"name":"Hanwha Systems, Sungnam 13524, Republic of Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2643-3130","authenticated-orcid":false,"given":"Hyun","family":"Park","sequence":"additional","affiliation":[{"name":"Hanwha Systems, Sungnam 13524, Republic of Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0660-5516","authenticated-orcid":false,"given":"Sang-Hyo","family":"Kim","sequence":"additional","affiliation":[{"name":"College of Information and Communication Engineering, Sungkyunkwan University, Suwon 16419, Republic of Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,11,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"102","DOI":"10.1109\/MCOM.2015.7010522","article-title":"Interference coordination for dense wireless networks","volume":"53","author":"Soret","year":"2015","journal-title":"IEEE Commun. Mag."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1007\/s12243-021-00869-5","article-title":"Iterative interference alignment with spatial hole sensing in MIMO cognitive radio networks","volume":"77","author":"Namdar","year":"2022","journal-title":"Ann. Telecommun."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"5156","DOI":"10.1109\/TWC.2016.2553660","article-title":"Impact of sub-band correlation on SFR and comparison of FFR and SFR","volume":"15","author":"Kumar","year":"2016","journal-title":"IEEE Trans. Wireless Commun."},{"key":"ref_4","first-page":"2776","article-title":"Throughput and optimal threshold for FFR schemes in OFDMA cellular networks","volume":"11","author":"Xu","year":"2012","journal-title":"IEEE Trans. Wireless Commun."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Assaad, M. (2008, January 21\u201324). Optimal Fractional Frequency Reuse (FFR) in Multicellular OFDMA System. Proceedings of the 2008 IEEE 68th Vehicular Technology Conference, Calgary, AB, Canada.","DOI":"10.1109\/VETECF.2008.381"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"4294","DOI":"10.1109\/TWC.2011.100611.110181","article-title":"Analytical evaluation of fractional frequency reuse for OFDMA cellular networks","volume":"10","author":"Novlan","year":"2011","journal-title":"IEEE Trans. Wireless Commun."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"3692","DOI":"10.1109\/TCOMM.2014.2358211","article-title":"A unified framework for the analysis of fractional frequency reuse techniques","volume":"62","author":"Mahmud","year":"2014","journal-title":"IEEE Trans. Commun."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Liu, L., Peng, T., Zhu, P., Qi, Z., and Wang, W. (2016, January 15\u201318). Analytical Evaluation of Throughput and Coverage for FFR in OFDMA Cellular Network. Proceedings of the 2016 IEEE 83rd Vehicular Technology Conference (VTC Spring), Nanjing, China.","DOI":"10.1109\/VTCSpring.2016.7504138"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2098","DOI":"10.1109\/TCOMM.2013.031213.120260","article-title":"Analytical evaluation of uplink fractional frequency reuse","volume":"61","author":"Novlan","year":"2013","journal-title":"IEEE Trans. Commun."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Lei, H., Zhang, L., Zhang, X., and Yang, D. (2007, January 3\u20137). A Novel Multi-Cell OFDMA System Structure Using Fractional Frequency Reuse. Proceedings of the 2007 IEEE 18th International Symposium on Personal, Indoor and Mobile Radio Communications, Athens, Greece.","DOI":"10.1109\/PIMRC.2007.4394228"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1491","DOI":"10.1109\/TVT.2013.2284337","article-title":"A generic interference model for uplink OFDMA networks with fractional frequency reuse","volume":"63","author":"Tabassum","year":"2014","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2074","DOI":"10.1109\/TCOMM.2013.022713.120340","article-title":"Fractional frequency reuse aided twin-layer femtocell networks: Analysis, design and optimization","volume":"61","author":"Jin","year":"2013","journal-title":"IEEE Trans. Commun."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"3869","DOI":"10.1109\/TCOMM.2015.2465907","article-title":"Coverage probability and achievable rate analysis of FFR-aided multi-user OFDM-based MIMO and SIMO systems","volume":"63","author":"Kumar","year":"2015","journal-title":"IEEE Trans. Commun."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1324","DOI":"10.1049\/iet-com.2014.0950","article-title":"Optimal design parameters for coverage probability in fractional frequency reuse and soft frequency reuse","volume":"9","author":"Kumar","year":"2015","journal-title":"IET Commun."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2029","DOI":"10.1109\/TCOMM.2012.061112.110477","article-title":"Analytical evaluation of fractional frequency reuse for heterogeneous cellular networks","volume":"60","author":"Novlan","year":"2012","journal-title":"IEEE Trans. Commun."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"3015","DOI":"10.1109\/TCOMM.2014.2336651","article-title":"On the outage capacity of opportunistic beamforming with random user locations","volume":"62","author":"Samarasinghe","year":"2014","journal-title":"IEEE Trans. Commun."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"550","DOI":"10.1109\/JSAC.2012.120405","article-title":"Modeling and analysis of K-tier downlink heterogeneous cellular networks","volume":"30","author":"Dhillon","year":"2012","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2658","DOI":"10.1109\/TWC.2013.050313.120160","article-title":"Optimal fractional frequency reuse and power control in the heterogeneous wireless networks","volume":"12","author":"Li","year":"2013","journal-title":"IEEE Trans. Wireless Commun."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"5314","DOI":"10.1109\/TWC.2009.090241","article-title":"Coverage in multi-antenna two-tier networks","volume":"8","author":"Chandrasekhar","year":"2009","journal-title":"IEEE Trans. Wireless Commun."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Al-Rimawi, A., and Dardari, D. (2015, January 8\u201312). Analytical Modeling of D2D Communications over Cellular Networks. Proceedings of the 2015 IEEE International Conference on Communications (ICC), London, UK.","DOI":"10.1109\/ICC.2015.7248638"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1109\/TAES.2019.2943048","article-title":"The optimal distance threshold for fractional frequency reuse in size-scalable networks","volume":"56","author":"Chang","year":"2020","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"5828","DOI":"10.1109\/TCOMM.2018.2859326","article-title":"Study on coverage of full frequency reuse in FFR systems based on outage probability","volume":"66","author":"Chang","year":"2018","journal-title":"IEEE Trans. Commun."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Chang, S.-H., Park, H.-G., Kim, S.-H., and Choi, J.P. (2017, January 12\u201317). Study on the Coverage of Fractional Frequency Reuse Cells. Proceedings of the Information Theory and Applications Workshop (ITA), San Diego, CA, USA.","DOI":"10.1109\/ITA.2017.8023444"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1109\/TIT.2010.2090222","article-title":"Open-loop spatial multiplexing and diversity communications in ad hoc networks","volume":"57","author":"Louie","year":"2011","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Stolyar, A.L., and Viswanathan, H. (2009, January 19\u201325). Self-Organizing Dynamic Fractional Frequency Reuse for Best-Effort Traffic through Distributed Inter-Cell Coordination. Proceedings of the IEEE INFOCOM 2009, Rio de Janeiro, Brazil.","DOI":"10.1109\/INFCOM.2009.5062043"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1109\/MCOM.2016.7470932","article-title":"Designing and implementing future aerial communication networks","volume":"54","author":"Chandrasekharan","year":"2016","journal-title":"IEEE Commun. Mag."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1109\/MCOM.2011.5783982","article-title":"Fundamental trade-offs on green wireless networks","volume":"49","author":"Chen","year":"2011","journal-title":"IEEE Commun. Mag."},{"key":"ref_28","unstructured":"Oestges, C., and Clerckx, B. (2007). MIMO Wireless Communications: From Real Word Propagation to Space-Time Code Design, Academic."},{"key":"ref_29","unstructured":"Larsson, E.G., and Stoica, P. (2008). Space-Time Block Coding for Wireless Communications, Cambridge University Press."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1109\/TWC.2010.01.081381","article-title":"Transmit diversity vs. spatial multiplexing in modern MIMO systems","volume":"9","author":"Lozano","year":"2010","journal-title":"IEEE Trans. Wireless Commun."},{"key":"ref_31","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_32","unstructured":"Paulraj, A., Nabar, R., and Gore, D. (2003). Introduction to Space-Time Wireless Communications, Cambridge University Press."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1109\/TVT.2013.2243851","article-title":"Optimal transmission of progressive sources based on the error probability analysis of SM and OSTBC","volume":"63","author":"Chang","year":"2014","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"5868","DOI":"10.1109\/TSP.2007.901134","article-title":"Outage and diversity of linear receivers in flat-fading MIMO channels","volume":"55","author":"Hedayat","year":"2007","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_35","unstructured":"Guess, T., Zhang, H., and Kotchiev, T.V. (2003, January 11\u201315). The Outage Capacity of BLAST for MIMO Channels. Proceedings of the IEEE International Conference on Communications, Anchorage, AK, USA."},{"key":"ref_36","unstructured":"Prasad, N., and Varanasi, M.K. (2003, January 1\u20135). Outage Analysis and Optimization for Multiaccess and V-BLAST Architecture over MIMO Rayleigh Fading Channels. Proceedings of the Annual Allerton Conference on Communication Control and Computing, Monticello, IL, USA."},{"key":"ref_37","first-page":"4188","article-title":"Scalable source transmission with unequal frequency reuse in MIMO cellular networks","volume":"65","author":"Chang","year":"2017","journal-title":"IEEE Trans. Commun."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/21\/8925\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:16:00Z","timestamp":1760130960000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/21\/8925"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,11,2]]},"references-count":37,"journal-issue":{"issue":"21","published-online":{"date-parts":[[2023,11]]}},"alternative-id":["s23218925"],"URL":"https:\/\/doi.org\/10.3390\/s23218925","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2023,11,2]]}}}