Spectrum Sharing for Device-to-Device Communications in Cellular Networks: A Game Theoretic Approach

This paper studies the spectrum sharing problem between device-to-device (D2D) and cellular communications in a cellular network. In this network, the D2D links can access the spectrum controlled by a mobile network operator. Each D2D link can either access the sub-bands occupied by cellular subscribers or obtain a sub-band for its exclusive use. The D2D links with exclusive use of sub-bands can also share spectrum with each other. We observe that the above spectrum sharing problem is complex and there may not exist a stable spectrum sharing structure. We establish a hierarchical matching market with incomplete information to model and analyze the above D2D spectrum sharing problem. In our model, each D2D link is selfish and autonomous. We seek a Bayesian equilibrium of our market that achieves a stable spectrum sharing structure among all the D2D links. We derive a sufficient condition for which the Bayesian equilibrium exists. We propose a distributed algorithm which can detect whether this sufficient condition is satisfied and, if satisfied, achieve the Bayesian equilibrium. Our algorithm does not require each D2D link to know the payoffs of others and has the worst case complexity of O(L-3 J) in each iteration where L is the number of D2D links, J is the number of cellular sub-bands.