  This work proposes a new resource allocation optimization framework for
cellular networks using "fog" or neighborhood-based optimization rather than
fully centralized or fully decentralized methods. In neighborhood-based
optimization resources are allocated within virtual cells encompassing several
base-stations and the users within their coverage area. As the number of
base-stations within a virtual cell increases, the framework reverts to
centralized optimization, and as this number decreases it reverts to
decentralized optimization. We address two tasks that must be carried out in
the fog optimization framework: forming the virtual cells and allocating the
communication resources in each virtual cell effectively. We propose
hierarchical clustering for the formation of the virtual cells given a
particular number of such cells. Once the virtual cells are formed, we consider
several optimization methods to solve the NP-hard joint channel access and
power allocation problem within each virtual cell in order to maximize the sum
rate of the entire system. We present numerical results for the system sum rate
of each scheme under hierarchical clustering. Our results indicate that proper
design of the fog optimization results in little degradation relative to
centralized optimization even for a relatively large number of virtual cells.
However, improper design leads to a significant decrease in sum rate relative
to centralized optimization.
