Wireless edge caching for mobile social networks (MSNs) has emerged as one of the prospective solutions to provide reliable and low-latency communication services for mobile users on social networking. In this chapter, we first give an overview of MSNs, including their development and challenges. We then discuss mobile edge caching (MEC) paradigms to address emerging issues for MSNs, e.g., service delay, users’ experience, and economic efficiency. In addition to the advantages, the development of MEC networks also places some key challenges’ such as hierarchical architecture of MEC networks, proactive caching, privacy, and security issues. The framework can authenticate MSN users based on public-key cryptography and predict their content demands utilizing a matrix factorization method. Based on the prediction, an optimal content caching policy for an MEC node is presented to minimize the average latency of all MSN users under the MEC nodes’ storage capacity constraints. Furthermore, this framework provides an optimal business model to maximize the revenue for MSN service providers based on the demands of the MSN users and the obtained optimal caching policy.

As mobile data traffic keeps growing and mobile applications pose increasingly stringent and diverse requirements, wireless networks are facing unprecedented pressures. Network infrastructure densification presents promises to further evolve wireless networks and maintain their competitiveness. Deploying more radio access points equipped with storage and computation capabilities can increase network capacity, improve network energy efficiency, provide low-latency services and access for massive devices. The benefits of network densification can be exploited using the emerging fog radio access network (Fog-RAN) architecture by pushing computation and storage resources to network edges. However, it comes with formidable technical challenges. Innovative methodologies are needed to operate such networks with various resources. This chapter develops a generalized low-rank optimization model for performance enhancements in ultra-dense Fog-RANs, supported by various motivating design objectives including mobile edge caching and topological interference alignment. A special attention is paid on algorithmic approaches for nonconvex low-rank optimization problems via Riemannian optimization.