Game Theoretic Analysis for Spectrum Sharing with Multi-Hop Relaying

This paper studies spatial spectrum sharing (SSS) based multi-user cognitive radio (CR) networks that allow secondary users (SU) to access the licensed spectrum as long as the interference powers of primary users (PU) to be lower than a certain threshold. Although recent results have shown that multi-hop relaying has a great potential on improving the performance of CR networks, finding effective methods to control and manage SUs to achieve the optimal performance is still a challenging problem. In this paper, we model CR networks as a non-cooperative game in which each SU obtains benefits through both spectrum sharing by paying prices to PUs and multi-hop relaying by paying price to nearby SUs. Optimal power allocation methods for SUs are investigated under different assumptions and pricing functions. The conditions under which the optimal Nash Equilibrium (NE) is obtained when all SUs use multi-hop relaying are discussed. Our results are extended into large multi-user CR networks with K source-to-destination pairs. Two distributed algorithms are proposed. The first one is a sub-gradient based power allocation algorithm in which SUs can iteratively adjust their transmit powers to approach the payoff of a NE. The other one is a Q-learning based relay selection algorithm which enables each SU to iteratively search for a NE-achieving relaying scheme.