Resource allocation for D2D communications under proportional fairness

This paper deals with the dynamic spectrum sharing between underlaying device-to-device (D2D) and cellular links in a multi-carrier cellular network to maximize the weighted network sum-rate while guaranteeing the minimum individual cellular link data rates and proportional fairness among D2D links. In particular, we formulate an NP-hard non-orthogonal resource allocation problem, and develop an iterative algorithm that alternates between the sub-carrier assignment and power allocation in each iteration until convergence. It is shown that the sub-carrier assignment problem corresponds to an integer linear program while the power allocation is reformulated into a difference-between-two-concave-functions (DC) problem. We establish the important properties of the developed algorithms and prove their convergence behavior. Illustrative results indicate that the proposed non-orthogonal resource allocation algorithm significantly outperforms the orthogonal spectrum sharing counterpart.