Scalable sparse optimization in dense cloud-RAN

The cloud radio access network (Cloud-RAN) provides a revolutionary way to densify radio access networks, thereby addressing the challenges in the era of mobile data deluge. In this architecture, all the baseband signal processing is shifted to a single cloud data center, which enables centralized resource coordination and signal processing for efficient interference management and flexible network adaptation. Thus, it can resolve the main challenges for next-generation wireless networks, including higher energy and spectral efficiency, higher cost efficiency, lower latency, as well as massive connectivity. However, with multi-entity collaboration and enlarged network sizes in dense Cloud-RANs, unique issues arise in green networking and large-scale computing. Fundamental methodologies and algorithms need to be developed to address these challenges by exploiting the problem structures, e.g., group sparsity and low-rankness. In dense Cloud-RANs, due to the multi-entity network collaboration, network power consumption originated from the radio access network and the fronthaul network becomes huge. To design a green Cloud-RAN, a holistic approach is required for network power minimization. By exploiting the spatial and temporal mobile data traffic variation, we develop a group sparse beamforming framework to minimize the network power consumption by enabling network adaptation. This is achieved by adaptively selecting active remote radio heads (RRHs) and the corresponding fronthaul links via controlling the group sparsity structure of the aggregative beamforming vector at all the RRHs, thereby adapting to the spatial and temporal mobile data traffic fluctuations. In particular, the group sparsity structure is induced by minimizing the mixed `1/`2-norm of the aggregative beamforming vector. To further demonstrate the power of the group sparse beamforming framework, a more challenging scenario with multicast transmission and imperfect channel state information (CSI) is also investigated. In particular, we present the PhaseLift and semidefinite relaxation techniques to convexify the robust non-convex quadratic quality-of-service (QoS) constraints. A smoothed `p-minimization approach is further proposed to induce the group-sparsity structure in the aggregative multicast beamforming vector, which indicates those RRHs that can be switched off. To solve the resultant non-convex group-sparsity inducing optimization problem, an iterative reweighted-`2 algorithm is then proposed based on the principle of the majorization-minimization (MM) algorithm. As the design problem sizes scale up with the network size in dense Cloud-RANs, we xiii demonstrate that it is critical to take the inherent characteristics of wireless channels into consideration to reduce the CSI acquisition overhead, while new optimization methods will be needed. We first present a low rank matrix completion approach via Riemannian pursuit to maximize the achievable degrees of freedom (DoF) only based on the network topology information without the knowledge of CSI at transmitters. Furthermore, to deal with the uncertainty in the available CSI, a chance-constrained programming based stochastic coordinated beamforming framework is proposed. In particular, a novel stochastic difference-of-convex (DC) programming algorithm for the resultant highly intractable chance constrained programming problem is developed with optimality guarantee, while all the previous algorithms can only find feasible but sub-optimal solutions. The last part of the thesis is devoted to dealing with the computing issues in dense CloudRANs. This is motivated by the fact that the design problems in dense Cloud-RANs are entering a new era characterized by a high dimension and/or a large number of constraints as well as complicated structures. It is thus critical to exploit unique structures of the design problems, while convex optimization will serve as a powerful tool for such purposes. In particular, to enable scalable network densification and cooperation, we develop a two-stage framework to solve the general large-scale convex optimization problems. This is achieved by equivalently transforming the original convex problem into the standard conic optimization problem by the matrix stuffing technique. The operator splitting method, namely, the alternating direction method of multipliers (ADMM), is further adopted to solve the resultant large-scale self-dual embedding of the transformed cone programming problem. This enables the capability of parallel computing and infeasibility detection. In summary, the central theme of this thesis is developing scalable sparse optimization methodologies and algorithms to address the networking and computing issues for network densification in Cloud-RANs.