{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:43:47Z","timestamp":1760237027195,"version":"build-2065373602"},"reference-count":40,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2020,2,17]],"date-time":"2020-02-17T00:00:00Z","timestamp":1581897600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Since the cloud radio access network (C-RAN) transmits information signals by jointly transmission, the multiple copies of information signals might be eavesdropped on. Therefore, this paper studies the resource allocation algorithm for secure energy optimization in a downlink C-RAN, via jointly designing base station (BS) mode, beamforming and artificial noise (AN) given imperfect channel state information (CSI) of information receivers (IRs) and eavesdrop receivers (ERs). The considered resource allocation design problem is formulated as a nonlinear programming problem of power minimization under the quality of service (QoS) for each IR, the power constraint for each BS, and the physical layer security (PLS) constraints for each ER. To solve this non-trivial problem, we first adopt smooth     \u2113 0    -norm approximation and propose a general iterative difference of convex (IDC) algorithm with provable convergence for a difference of convex programming problem. Then, a three-stage algorithm is proposed to solve the original problem, which firstly apply the iterative difference of convex programming with semi-definite relaxation (SDR) technique to provide a roughly (approximately) sparse solution, and then improve the sparsity of the solutions using a deflation based post processing method. The effectiveness of the proposed algorithm is validated with extensive simulations for power minimization in secure downlink C-RANs.<\/jats:p>","DOI":"10.3390\/e22020223","type":"journal-article","created":{"date-parts":[[2020,2,18]],"date-time":"2020-02-18T10:10:25Z","timestamp":1582020625000},"page":"223","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Robust Power Optimization for Downlink Cloud Radio Access Networks with Physical Layer Security"],"prefix":"10.3390","volume":"22","author":[{"given":"Yijia","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Information Science and Technology, Zhejiang Sci-Tech University, Hangzhou 310018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ruiying","family":"Liu","sequence":"additional","affiliation":[{"name":"College of Mechanical and Electrical Engineering, Jiaxing University, Jiaxing 314001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,2,17]]},"reference":[{"key":"ref_1","unstructured":"Chen, K., and Duan, R. 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