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A fundamental challenge in wireless heterogeneous networks (HetNets) is toeffectively utilize the limited transmission and storage resources in thepresence of increasing deployment density and backhaul capacity constraints. Toalleviate bottlenecks and reduce resource consumption, we design optimalcaching and power control algorithms for multi-hop wireless HetNets. Weformulate a joint optimization framework to minimize the average transmissiondelay as a function of the caching variables and thesignal-to-interference-plus-noise ratios (SINR) which are determined by thetransmission powers, while explicitly accounting for backhaul connection costsand the power constraints.  Using convex relaxation and rounding, we obtain a reduced-complexityformulation (RCF) of the joint optimization problem, which can provide aconstant factor approximation to the globally optimal solution. We then solveRCF in two ways: 1) alternating optimization of the power and caching variablesby leveraging biconvexity, and 2) joint optimization of power control andcaching. We characterize the necessary (KKT) conditions for an optimal solutionto RCF, and use strict quasi-convexity to show that the KKT points are Paretooptimal for RCF. We then devise a subgradient projection algorithm to jointlyupdate the caching and power variables, and show that under appropriateconditions, the algorithm converges at a linear rate to the local minima ofRCF, under general SINR conditions. We support our analytical findings withresults from extensive numerical experiments.

Transmission Delay Minimization via Joint Power Control and Caching in Wireless HetNets