  The heterogeneous cloud radio access network (Cloud-RAN) provides a
revolutionary way to densify radio access networks. It enables centralized
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 efficiency and
spectral efficiency, higher cost efficiency, scalable connectivity, and low
latency. In this article, we shall provide an algorithmic thinking on the new
design challenges for the dense heterogeneous Cloud-RAN based on convex
optimization. As problem sizes scale up with the network size, we will
demonstrate that it is critical to take unique structures of design problems
and inherent characteristics of wireless channels into consideration, while
convex optimization will serve as a powerful tool for such purposes. Network
power minimization and channel state information acquisition will be used as
two typical examples to demonstrate the effectiveness of convex optimization
methods. We will then present a two-stage framework to solve general
large-scale convex optimization problems, which is amenable to parallel
implementation in the cloud data center.
