{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T03:38:16Z","timestamp":1778729896651,"version":"3.51.4"},"reference-count":34,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2017,9,11]],"date-time":"2017-09-11T00:00:00Z","timestamp":1505088000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61525101"],"award-info":[{"award-number":["61525101"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National High-Tech R&amp;D Program of China (863 Program)","award":["2015AA01A705"],"award-info":[{"award-number":["2015AA01A705"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Network densification is attracting increasing attention recently due to its ability to improve network capacity by spatial reuse and relieve congestion by offloading. However, excessive densification and aggressive offloading can also cause the degradation of network performance due to problems of interference and load. In this paper, with consideration of load issues, we study the optimal base station density that maximizes the throughput of the network. The expected link rate and the utilization ratio of the contention-based channel are derived as the functions of base station density using the Poisson Point Process (PPP) and Markov Chain. They reveal the rules of deployment. Based on these results, we obtain the throughput of the network and indicate the optimal deployment density under different network conditions. Extensive simulations are conducted to validate our analysis and show the substantial performance gain obtained by the proposed deployment scheme. These results can provide guidance for the network densification.<\/jats:p>","DOI":"10.3390\/s17092077","type":"journal-article","created":{"date-parts":[[2017,9,11]],"date-time":"2017-09-11T10:28:46Z","timestamp":1505125726000},"page":"2077","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Optimal Base Station Density of Dense Network: From the Viewpoint of Interference and Load"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3931-8783","authenticated-orcid":false,"given":"Jianyuan","family":"Feng","sequence":"first","affiliation":[{"name":"School of Information and Communication Engineering, Beijing University of Posts and Telecommunications (BUPT), Beijing 100876, China"}]},{"given":"Zhiyong","family":"Feng","sequence":"additional","affiliation":[{"name":"School of Information and Communication Engineering, Beijing University of Posts and Telecommunications (BUPT), Beijing 100876, China"}]}],"member":"1968","published-online":{"date-parts":[[2017,9,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Ericsson Inc. (2016). Cellular Networks for Massive IoT, Ericsson Inc.","DOI":"10.17016\/2573-2129.17"},{"key":"ref_2","unstructured":"Qualcomm Inc. (2013). 1000x: More Small Cells, Qualcomm Inc.. White Paper."},{"key":"ref_3","unstructured":"International Telecommunication Union (2015). IMT Vision-Framework and Overall Objectives of the Future Development of IMT for 2020 and Beyond, International Telecommunication Union. Technical Report; ITU-R Recommendation M.2083."},{"key":"ref_4","unstructured":"IMT-2020 Promotion Group (2015). White Paper on 5G Concept, IMT-2020 Promotion Group of China."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1109\/MVT.2015.2464831","article-title":"UltraDense Networks: The New Wireless Frontier for Enabling 5G Access","volume":"11","author":"Gotsis","year":"2016","journal-title":"IEEE Veh. Technol. Mag."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1267","DOI":"10.1109\/JSAC.2016.2545539","article-title":"Ultra Dense Small Cell Networks: Turning Density Into Energy Efficiency","volume":"34","author":"Samarakoon","year":"2016","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1109\/MCOM.2015.7010521","article-title":"Spectral and Energy Efficiency of Ultra-Dense Networks under Different Deployment Strategies","volume":"53","author":"Yunas","year":"2015","journal-title":"IEEE Commun. Mag."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"3194","DOI":"10.1109\/TWC.2015.2403321","article-title":"Backhauling in Heterogeneous Cellular Networks: Modeling and Tradeoffs","volume":"14","author":"Chen","year":"2015","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"7057","DOI":"10.1109\/TWC.2015.2464299","article-title":"Small Cell In-Band Wireless Backhaul in Massive MIMO Systems: A Cooperation of Next-Generation Techniques","volume":"14","author":"Li","year":"2015","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Obregon, E., Sung, K.W., and Zander, J. (2014, January 1\u20134). On the Sharing Opportunities for Ultra-Dense Networks in the Radar Bands. Proceedings of the IEEE International Symposium on Dynamic Spectrum Access Networks (DYSPAN), McLean, VA, USA.","DOI":"10.1109\/DySPAN.2014.6817798"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2450","DOI":"10.1109\/ACCESS.2016.2562498","article-title":"Coalitional Games for Joint Co-Tier and Cross-Tier Cooperative Spectrum Sharing in Dense Heterogeneous Networks","volume":"4","author":"Hajir","year":"2016","journal-title":"IEEE Access"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Shuai, P., En, T., Huilin, J., Zhiwen, P., Nan, L., and Xiaohu, Y. (2015, January 9\u201312). An Improved Graph Coloring Based Small Cell Discovery Scheme in LTE Hyper-dense Networks. Proceedings of the IEEE Wireless Communications and Networking Conference, New Orleans, LA, USA.","DOI":"10.1109\/WCNCW.2015.7122522"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"8657","DOI":"10.1109\/ACCESS.2016.2633434","article-title":"Hierarchical Resource Allocation Framework for Hyper-Dense Small Cell Networks","volume":"4","author":"Qiu","year":"2016","journal-title":"IEEE Access"},{"key":"ref_14","first-page":"1","article-title":"Traffic Characteristics Based Dynamic Radio Resource Management in Heterogeneous Wireless Networks","volume":"11","author":"Wen","year":"2014","journal-title":"China Commun."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Chen, M., Hao, Y., Qiu, M., Song, J., Wu, D., and Humar, I. (2016). Mobility-Aware Caching and Computation Offloading in 5G Ultra-Dense Cellular Networks. Sensors, 16.","DOI":"10.3390\/s16070974"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Hao, Y., Chen, M., Hu, L., Song, J., Volk, M., and Humar, I. (2017). Wireless Fractal Ultra-Dense Cellular Networks. Sensors, 17.","DOI":"10.3390\/s17040841"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Park, J., Kim, S.L., and Zander, J. (2014, January 8\u201312). Asymptotic Behavior of Ultra-Dense Cellular Networks and Its Economic Impact. Proceedings of the IEEE Global Communications Conference, Austin, TX, USA.","DOI":"10.1109\/GLOCOM.2014.7037588"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1109\/MWC.2016.7422407","article-title":"Cooperation for Spectral and Energy Efficiency in Ultra-Dense Small Cell Networks","volume":"23","author":"Yang","year":"2016","journal-title":"IEEE Wirel. Commun."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1522","DOI":"10.1109\/TVT.2015.2413394","article-title":"A Joint Cross-Layer and Colayer Interference Management Scheme in Hyperdense Heterogeneous Networks Using Mean-Field Game Theory","volume":"65","author":"Yu","year":"2016","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_20","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_21","first-page":"21","article-title":"Enhanced Power Allocation Scheme in Ultra-Dense Small Cell Network","volume":"13","author":"Gao","year":"2016","journal-title":"China Commun."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Cho, M.J., Ban, T.W., Jung, B.C., and Yang, H.J. (2015, January 8\u201312). A Distributed Scheduling with Interference-Aware Power Control for Ultra-Dense Networks. Proceedings of the IEEE International Conference on Communications, London, UK.","DOI":"10.1109\/ICC.2015.7248563"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"3122","DOI":"10.1109\/TCOMM.2011.100411.100541","article-title":"A Tractable Approach to Coverage and Rate in Cellular Networks","volume":"59","author":"Andrews","year":"2011","journal-title":"IEEE Trans. Commun."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"3484","DOI":"10.1109\/TWC.2012.081612.111361","article-title":"Heterogeneous Cellular Networks with Flexible Cell Association: A Comprehensive Downlink SINR Analysis","volume":"11","author":"Jo","year":"2012","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"575","DOI":"10.1109\/JSAC.2012.120407","article-title":"Distribution of Downlink SINR in Heterogeneous Cellular Networks","volume":"30","author":"Mukherjee","year":"2012","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_26","unstructured":"Jo, H.S., Sang, Y.J., Xia, P., and Andrews, J.G. (2011, January 5\u20139). Outage Probability for Heterogeneous Cellular Networks with Biased Cell Association. Proceedings of the IEEE Global Communications Conference, Houston, TX, USA."},{"key":"ref_27","unstructured":"Jeffrey, G., Andrews, A.K.G., and Dhillon, H.S. (arXiv, 2016). A Primer on Cellular Network Analysis Using Stochastic Geometry, arXiv."},{"key":"ref_28","unstructured":"Rappaport, T.S. (1996). Wireless Communications: Principles and Practice, IEEE Press."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2206","DOI":"10.1109\/TCOMM.2011.051811.100241","article-title":"Analysis of Non-Persistent CSMA Protocols with Exponential Backoff Scheduling","volume":"59","author":"Wong","year":"2011","journal-title":"IEEE Trans. Commun."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1109\/MWC.2011.5876496","article-title":"A survey on 3GPP heterogeneous networks","volume":"18","author":"Damnjanovic","year":"2011","journal-title":"IEEE Wirel. Commun."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1109\/MWC.2014.6812287","article-title":"An Overview of Load Balancing in HetNets: Old Myths and Open Problems","volume":"21","author":"Andrews","year":"2014","journal-title":"IEEE Wirel. Commun."},{"key":"ref_32","unstructured":"3GPP (2013). E-UTRA; Further Advancements for E-UTRA Physical Layer Aspects, 3GPP. Technical Report 36.814."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1561\/1300000015","article-title":"Interference in Large Wireless Networks","volume":"3","author":"Haenggi","year":"2009","journal-title":"Found. Trends Netw."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"76","DOI":"10.1109\/49.56383","article-title":"Optimum transmission ranges in a direct-sequence spread-spectrum multihop packet radio network","volume":"8","author":"Sousa","year":"1990","journal-title":"IEEE J. Sel. Areas Commun."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/9\/2077\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:44:38Z","timestamp":1760208278000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/9\/2077"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,9,11]]},"references-count":34,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2017,9]]}},"alternative-id":["s17092077"],"URL":"https:\/\/doi.org\/10.3390\/s17092077","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,9,11]]}}}