This paper studies imperfect underlay device-to-device (D2D) association in spectrumshared cellular networks. It addresses important system and design interference constraints, processing load limitations and transmit power constraints at D2D terminals. The paper proposes decentralized schemes for D2D communication between D2D terminals when downlink channel resources can be reused in the D2D network. The D2D transmitters are characterized considering their processing load limitation and allocated transmit power constraints. Moreover, the downlink channels that can be reused in the D2D network are quantified while meeting interference constraints imposed by the primary cellular network. Two schemes to identify reusable channels, which vary in terms of their efficiency, communication overhead requirement and implementation complexity, are described. Moreover, two D2D association schemes, namely the simultaneous and sequential D2D associations, are proposed and both aim to concurrently maximize the desired link quality and minimize the effect of interference effect at D2D receivers. Generalized analytical results that are applicable for various imperfect association scenarios are presented. The findings are applicable for any D2D channel models and performance metrics. They provide insights into various imperfect underlay D2D association scenarios under the practical system and design constraints.