Discrete Power Control and Transmission Duration Allocation for Self-Backhauling Dense mmWave Cellular Networks

Wireless self-backhauling is a promising solution for dense millimeter wave (mmWave) small cell networks, the system efficiency of which, however, depends upon the balance of resources between the backhaul link and access links of each small cell. In this paper, we address the discrete power control and non-unified transmission duration allocation problem for self-backhauling mmWave cellular networks, in which each small cell is allowed to adopt individual transmission duration allocation ratio according to its own channel and load conditions. We first formulate the considered problem as a non-cooperative game <inline-formula> <tex-math notation="LaTeX">${\mathcal {G}}$ </tex-math></inline-formula> with a common utility function. We prove the feasibility and existence of the pure strategy Nash equilibrium (NE) of game <inline-formula> <tex-math notation="LaTeX">$ {\mathcal {G}}$ </tex-math></inline-formula> under some mild conditions. Then, we design a centralized resource allocation algorithm based on the best response dynamic and a decentralized resource allocation algorithm (DRA) based on control-plane/user-plane split architecture and log-linear learning to obtain a feasible pure strategy NE of game <inline-formula> <tex-math notation="LaTeX">${\mathcal {G}}$ </tex-math></inline-formula>. For speeding up convergence and reducing signaling overheads, we reformulate the considered problem as a non-cooperative game <inline-formula> <tex-math notation="LaTeX">${{\mathcal {G}}'}$ </tex-math></inline-formula> with local interaction, in which only local information exchange is required. Based on DRA, we design a concurrent DRA to obtain the best feasible pure strategy NE of game <inline-formula> <tex-math notation="LaTeX">${\mathcal {G}'}$ </tex-math></inline-formula>. Furthermore, we extend the proposed algorithms to the discrete power control and unified transmission duration allocation optimization problem. Extensive simulations are conducted with different system configurations to demonstrate the convergence and effectiveness of the proposed algorithms.