Price-based resource allocation for self-backhauled small cell networks

Heterogeneous cellular networks are promising solutions to address the need for the exponentially increasing data traffic demands by ensuring an acceptable level of quality of service. In such networks, base stations with different cell sizes serve the cellular areas (i.e., macro cells along with small cells). The access technologies of such base stations can be different as well. Small cell access points (SAP) are typically connected either directly to the core network through a wired link or to a macro-cell base station through a wireless backhaul link. In this paper, we consider the scenario where the SAP is connected to a macro-cell base station through a wireless backhaul link operating at the same frequency band as the access links from the SAP to its users. We consider amplify and forward (AF) protocol under both full/half duplex transmission modes for the SAP. Under such circumstances, we study the price-based resource allocation where the SAP charges each user equipment (UE) proportional to the amount of the power it allocates for transmission to that UE. A Stackelberg game is employed to model and investigate the joint utility maximization problem of the SAP and UEs. In our game model, the SAP is the leader and the UEs are the followers. We formulate the utility maximization problems for both the leader and the followers as optimization problems. We consider two pricing schemes, namely non-uniform and uniform. Moreover, we present a condition which gives a proper criterion for resignation of the UEs from the proposed Stackelberg game when transmitted power of the SAP is limited. We prove that both sub-games are convex optimization problems which ensures their tractability. We also propose a novel algorithm to obtain the optimal prices of Stackelberg equilibrium of the game. Numerical results validate the efficiency of our proposed priced based resource allocation scheme.