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

Most of the existing caching solutions for wireless networks rest on the ideal assumption that the file popularity distribution is perfectly known. In this paper, we consider optimal random caching designs for perfect, imperfect, and unknown file popularity distributions in a large-scale multi-tier wireless network. First, in the case of perfect file popularity distribution, we formulate the successful transmission probability (STP) optimization problem, which is nonconvex. We propose an efficient parallel iterative algorithm to obtain a stationary point based on parallel successive convex approximation (SCA). Then, in the case of imperfect file popularity distribution, we formulate the worst-case STP maximization problem. To solve this challenging robust optimization problem, we transform it into an equivalent complementary geometric programming (CGP) and propose an efficient iterative algorithm to obtain a stationary point based on the 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 STP (i.e., the STP in the stochastic form) maximization problem. This is a challenging nonconvex stochastic optimization problem, and we propose an efficient iterative algorithm to obtain a stationary point based on stochastic parallel SCA. As far as we know, this is the first work considering stochastic optimization in a large-scale wireless network. Finally, by numerical results, we show that the proposed solutions achieve notable gains over existing schemes in all three cases and reveal the values of the robust caching optimization and stochastic caching optimization in the cases of imperfect file popularity distribution and unknown file popularity distribution, respectively.