  Caching popular content at base stations is a powerful supplement to existing
limited backhaul links for accommodating the exponentially increasing mobile
data traffic. Given the limited cache budget, we investigate the cache size
allocation problem in cellular networks to maximize the user success
probability (USP), taking wireless channel statistics, backhaul capacities and
file popularity distributions into consideration. The USP is defined as the
probability that one user can successfully download its requested file either
from the local cache or via the backhaul link. We first consider a single-cell
scenario and derive a closed-form expression for the USP, which helps reveal
the impacts of various parameters, such as the file popularity distribution.
More specifically, for a highly concentrated file popularity distribution, the
required cache size is independent of the total number of files, while for a
less concentrated file popularity distribution, the required cache size is in
linear relation to the total number of files. Furthermore, we study the
multi-cell scenario, and provide a bisection search algorithm to find the
optimal cache size allocation. The optimal cache size allocation is verified by
simulations, and it is shown to play a more significant role when the file
popularity distribution is less concentrated.
