In this paper, we study the resource allocation in D2D underlaying cellular network with uncertain channel state information (CSI). For satisfying the diversity requirements of different users, i.e. the minimum rate requirement for cellular user and the reliability requirement for D2D user, we attempt to maximize the cellular users throughput whilst ensuring a chance constraint for D2D user. Then, a robust resource allocation framework is proposed for solving the highly intractable chance constraint about D2D reliability requirement, where the CSI uncertainties are represented as a deterministic set and the reliability requirement is enforced to hold for any uncertain CSI within it. Then, a symmetrical-geometry-based learning approach is developed to model the uncertain CSI into polytope, ellipsoidal and box. After that, we derive the robust counterpart of the chance constraint under these uncertainty sets as the computation convenient convex sets. To overcome the conservatism of the symmetrical-geometry-based uncertainty sets, we develop a support vector clustering (SVC)-based approach to model uncertain CSI as a compact convex uncertainty set. Based on that, the chance constraint of D2D is converted into a linear convex set. Then, we develop a bisection search-based power allocation algorithm for solving the resource allocation in D2D underlaying cellular network with different robust counterparts. Finally, we conduct the simulation to compare the proposed robust optimization approaches with the non-robust one.
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