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Most existing caching solutions for wireless networks rest on an unrealistic assumption that the file popularity distribution is perfectly known. In this paper, we consider optimal caching designs for perfect, imperfect and unknown file popularity distributions in large-scale multi-tier wireless networks. First, in the case of perfect file popularity distribution, we formulate the optimization problem to maximize the successful transmission probability (STP), which is a nonconvex problem. We develop an efficient parallel iterative algorithm to obtain a stationary point using parallel successive convex approximation (SCA). Then, in the case of imperfect file popularity distribution, we formulate the robust optimization problem to maximize the worst-case STP. To solve this challenging maximin problem, we transform it to an equivalent complementary geometric programming (CGP), and develop an efficient iterative algorithm which is shown to converge to a stationary point using SCA. To the best of our knowledge, this is the first work explicitly considering the estimation error of file popularity distribution in the optimization of caching design. Next, in the case of unknown file popularity distribution, we formulate the stochastic optimization problem to maximize the stochastic STP (i.e., the STP in the stochastic form), which is a challenging nonconvex stochastic optimization problem. Based on stochastic parallel SCA, we develop an efficient iterative algorithm to obtain a stationary point, by exploiting structural properties of the stochastic STP and making full use of instantaneous file requests. As far as we know, this is the first work considering stochastic optimization in a large-scale multi-tier wireless network. Finally, by numerical results, we show that the proposed solutions achieve significant gains over existing schemes in all three cases.

Optimal Caching Designs for Perfect, Imperfect, and Unknown File Popularity Distributions in Large-Scale Multi-Tier Wireless Networks