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This paper considers the downlink transmission of cloud-radio access networks (C-RANs) with limited fronthaul capacity. We formulate a joint design of remote radio head (RRH) selection, RRH-user association, and transmit beamforming for simultaneously optimizing the achievable sum rate and total power consumption, using the multi-objective optimization concept. Due to the non-convexity of per-fronthaul capacity constraints and introduced binary selection variables, the formulated problem lends itself to a mixed-integer non-convex program, which is generally NP-hard. Motivated by powerful computing capability of C-RAN and for benchmarking purposes, we propose a branch and reduce and bound based algorithm to attain a globally optimal solution. For more practically appealing approaches, we then propose three iterative low-complexity algorithms. In the first method, we iteratively approximate the continuous nonconvex constraints by convex conic ones using successive convex approximation (SCA) framework. More explicitly, the problem obtained at each iteration is a mixed-integer second order cone program (MI-SOCP) for which dedicated solvers are available. In the second method, we first relax the binary variables to be continuous to arrive at a sequence of SOCPs and then perform a post-processing procedure on the relaxed variables to search for a high-performance solution. In the third method, we solve the considered problem in view of sparsity-inducing regularization. Numerical results show that our proposed algorithms converge rapidly and achieve near-optimal performance as well as outperform the known algorithms. Index Terms-Base station selection, beamforming, cloud radio access networks, limited fronthaul, mixed integer second order cone programming, optimization.

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