{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:40:14Z","timestamp":1760240414914,"version":"build-2065373602"},"reference-count":25,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2019,6,8]],"date-time":"2019-06-08T00:00:00Z","timestamp":1559952000000},"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":["61501140;61701136;61525103"],"award-info":[{"award-number":["61501140;61701136;61525103"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Due to the high splitting-gain of dense small cells, Ultra-Dense Network (UDN) is regarded as a promising networking technology to achieve high data rate and low latency in 5G mobile communications. In UDNs, each User Equipment (UE) may receive signals from multiple Base Stations (BSs), which impose severe interference in the networks and in turn motivates the possibility of using Coordinated Multi-Point (CoMP) transmissions to further enhance network capacity. In CoMP-based Ultra-Dense Networks, a great challenge is to tradeoff between the gain of network throughput and the worsening backhaul latency. Caching popular files on BSs has been identified as a promising method to reduce the backhaul traffic load. In this paper, we investigated content placement strategies and user association algorithms for the proactive caching ultra dense networks. The problem has been formulated to maximize network throughput of cell edge UEs under the consideration of backhaul load, which is a constrained non-convex combinatorial optimization problem. To decrease the complexity, the problem is decomposed into two suboptimal problems. We first solved the content placement algorithm based on the cross-entropy (CE) method to minimize the backhaul load of the network. Then, a user association algorithm based on the CE method was employed to pursue larger network throughput of cell edge UEs. Simulation were conducted to validate the performance of the proposed cross-entropy based schemes in terms of network throughput and backhaul load. The simulation results show that the proposed cross-entropy based content placement scheme significantly outperform the conventional random and Most Popular Content placement schemes, with with 50% and 20% backhaul load decrease respectively. Furthermore, the proposed cross-entropy based user association scheme can achieve 30% and 23% throughput gain, compared with the conventional N-best, No-CoMP, and Threshold based user association schemes.<\/jats:p>","DOI":"10.3390\/e21060576","type":"journal-article","created":{"date-parts":[[2019,6,10]],"date-time":"2019-06-10T03:16:51Z","timestamp":1560136611000},"page":"576","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Cross-Entropy Method for Content Placement and User Association in Cache-Enabled Coordinated Ultra-Dense Networks"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1849-6449","authenticated-orcid":false,"given":"Jia","family":"Yu","sequence":"first","affiliation":[{"name":"Communication Engineering Research Centre, Harbin Institute of Technology (Shenzhen), HIT Campus of University Town of Shenzhen, Shenzhen 518055, China"}]},{"given":"Ye","family":"Wang","sequence":"additional","affiliation":[{"name":"Communication Engineering Research Centre, Harbin Institute of Technology (Shenzhen), HIT Campus of University Town of Shenzhen, Shenzhen 518055, China"},{"name":"Peng Cheng Laboratory, Shenzhen 518055, China"}]},{"given":"Shushi","family":"Gu","sequence":"additional","affiliation":[{"name":"Communication Engineering Research Centre, Harbin Institute of Technology (Shenzhen), HIT Campus of University Town of Shenzhen, Shenzhen 518055, China"},{"name":"Peng Cheng Laboratory, Shenzhen 518055, China"}]},{"given":"Qinyu","family":"Zhang","sequence":"additional","affiliation":[{"name":"Communication Engineering Research Centre, Harbin Institute of Technology (Shenzhen), HIT Campus of University Town of Shenzhen, Shenzhen 518055, China"},{"name":"Peng Cheng Laboratory, Shenzhen 518055, China"}]},{"given":"Siyun","family":"Chen","sequence":"additional","affiliation":[{"name":"Communication Engineering Research Centre, Harbin Institute of Technology (Shenzhen), HIT Campus of University Town of Shenzhen, Shenzhen 518055, China"}]},{"given":"Yalin","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Electronic and Communication Engineering, Shenzhen Polytechnic, Shenzhen 518055, China"}]}],"member":"1968","published-online":{"date-parts":[[2019,6,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1109\/MCOM.2013.6495773","article-title":"Femtocaching and device-to-device collaboration: A new architecture for wireless video distribution","volume":"51","author":"Golrezaei","year":"2013","journal-title":"IEEE Commun. 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