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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 will provide an algorithmic approach to 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 …