Resource Sharing with Minimum QoS Requirements for D2D Links Underlaying Cellular Networks In the discussion of future wireless communication technologies, direct peer-to-peer traffic on spectrum licensed to cellular network services plays an important role. This paper studies device-to-device (D2D) communication as an underlay to cellular LTE networks that operate in the downlink. We address the problem of resource allocation in a scenario where local D2D links compete with each other to access and reuse spectrum resources being scheduled to cellular users. We consider reuse between one D2D connection and one cellular user per resource and include minimum resource requirements of the D2D links in the allocation problem. A novel algorithm enables QoS for the D2D communication while limiting the interference impact on cellular services. Our proposed multicriteria allocation scheme is based on a distributed college admissions game and can be implemented with exchange of coordination messages of small bit size. We provide numerical results for extensive system level simulations in an LTE-like network with a D2D underlay. Our resource sharing scheme is evaluated against a centralized allocation approach based on weighted sum-rate optimization which gives us a rate bound. We achieve both very good interference protection for the cellular services, expressed by high cellular user rates, and sufficient performance for the D2D communication partners.