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Device-to-device (D2D) communication has attracted substantial research attention recently, due to its potential to improve coverage, spectrum efficiency, and energy efficiency within the existing cellular infrastructure. One major challenge for spectrum resource sharing in D2D underlay lies in the mutual interference between cellular user equipments (CUEs) and D2D user equipments (DUEs). Considering this mutual interference constraint, this work investigates the problem of optimal matching of D2D links and CUEs to form spectrum-sharing partners to maximize ergodic sum rates under transmit power and outage constraints. Unlike previous works, full channel-state information (CSI) is not required. To solve the resulting high-complexity problem, candidate DUE sets are first narrowed down according to required outage probability constraints, which are used to construct a simplified bipartite graph. The weight of …