Distributed Optimal Power Allocation Using Game Theory in Underlay Cognitive Radios

Abstract

In underlay cognitive radio networks (CRNs), primary licensed user and secondary unlicensed users use the same spectrum simultaneously by adjusting transmit power of secondary user. Such CRN consists of many secondary base stations (sec-BSs), primary base stations (prim-BSs), secondary user terminals (sec-UTs), and primary user terminals (prim-UTs). In this case, the major concern is to limit the interference at each prim-UT. This concern becomes a constraint for the sec-BSs in assigning transmit powers. In this paper, we develop the complication of power allocation to the sec-BSs as a concave game where there is no cooperation and communication between sec-BSs. The sec-BSs are considered to be players and the interference constraints are imposed by the prim-UTs. Unlike using the traditional Nash Equilibrium for equilibrium selection, we use the Normalized Nash Equilibrium, which is found by solving the necessary KKT conditions and checking the existence of the Lagrangian multipliers. The problem is further improvised by considering the battery leakage. The simulation results demonstrate the optimal power allocation for the sec-BSs taking the battery leakage into account.