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.
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