Joint Optimization of Transmission-Order Selection and Channel Allocation for Bidirectional Wireless Links—Part I: Game Theoretic Analysis

In this two-part paper, we consider a system consisting of bidirectional wireless links that interfere with each other, which has been the of focus of intensive research recently in emerging wireless systems like Device-to-Device (D2D) communications underlaying cellular networks, heterogeneous networks, and small-cell networks. The problem is allocating the time resources (transmission orders) and frequency resources (channels) among the transmitters such that the overall network interference is minimized. Here, transmission order (TO) is a novel dimension for optimization. In Part I, we analyze the TO optimization problem in the presence of channel allocation (CA), i.e., joint CA and the TO optimization problem from a game theoretic perspective, and prove that the joint optimization problem can be formulated as an exact potential game, which has at least one “pure strategy Nash Equilibrium” for any subset of the complete CA-TO action set and for any initial CA and TO conditions. We also show that the proposed joint CA and TO game is equal to the max-cut of a novel TO-dependent holistic system interference graph. In Part II, we present novel joint CA-TO algorithms and their performance analysis in D2D communications underlays.