Device-to-Device (D2D) communications underlaying cellular networks is a viable network technology that can potentially increase spectral utilization and improve power efficiency for proximitybased wireless applications and services. However, a major challenge in such deployment scenarios is the interference caused by D2D links when sharing the same resources with cellular users. In this work, we propose a channel allocation (CA) scheme together with a set of three power control (PC) schemes to mitigate interference in a D2D underlaid cellular system modeled as a random network using the mathematical tool of stochastic geometry. The novel aspect of the proposed CA scheme is that it enables D2D links to share resources with multiple cellular users as opposed to one as previously considered in the literature. Moreover, the accompanying distributed PC schemes further manage interference during link establishment and maintenance. The first two PC schemes compensate for large-scale path-loss effects and maximize the D2D sum rate by employing distance-dependent pathloss parameters of the D2D link and the base station, including an error estimation margin. The third scheme is an adaptive PC scheme based on a variable target signal-to-interference-plus-noise ratio, which limits the interference caused by D2D users and provides sufficient coverage probability for cellular users. Closed-form expressions for the coverage probability of cellular links, D2D links, and sum rate of D2D links are derived in terms of the allocated power, density of D2D links, and path-loss exponent. The impact of these key system parameters on network performance is analyzed and compared with previous work. Simulation results demonstrate an enhancement in cellular and D2D coverage probabilities, and an increase in spectral and power efficiency. The main motivation behind using Device-to-Device (D2D) communication underlaying cellular systems is to enable communication between devices in close vicinity with low latency and low energy consumption, and potentially to offload a telecommunication network from handling local traffic [1]-[5]. D2D is a promising approach to support proximity-based services such as social networking and file sharing [4]. When the devices are in close vicinity, D2D communication improves the spectral and energy efficiency of cellular networks [5]. Despite the benefits of D2D communications in underlay mode, interference management and energy efficiency have become fundamental requirements [6] in keeping the interference caused by the D2D users under control, while simultaneously extending the battery lifetime of the User Equipment (UE). For instance, cellular links experience cross-tier interference from D2D transmissions, whereas D2D links not only deal with the inter-D2D interference, but also with cross-tier interference from cellular transmissions. Therefore, power control (PC) and channel allocation (CA) have become necessary for managing interference levels, protecting the cellular UEs (CUEs), and providing energy-ef...