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D2D communication is a promising technology for enhancing spectral efficiency (SE) in cellular networks, and full-duplex (FD) has the potential to double SE. Due to D2D's short-distance communication and low transmittance power, it is natural to integrate FD into D2D, creating FD-D2D to underlay a cellular network to further improve SE. However, the residual self-interference (RSI) resulting from FD-D2D and interference arising from spectrum sharing between D2D users (DUs) and cellular users (CUs) can restrict D2D link performance. Therefore, we propose an FD-D2D underlying cellular system in which DUs jointly share uplink and downlink spectral resources with CUs. Moreover, we present two algorithms to enhance the performance experience of DUs while improving the system's SE. For the first algorithm, we tackle an optimization problem aimed at maximizing the sum rate of FD-DUs in the system while adhering to transmittance power constraints. This problem is formulated as a mixed-integer nonlinear programming problem (MINLP), known for its mathematical complexity and NP-hard nature. In order to address this MINLP, our first algorithm decomposes it into two subproblems: power control and spectral resource allocation. The power control aspect is treated as a nonlinear problem, which we solve through one-dimensional searching. Meanwhile, spectral resource allocation is achieved using the Kuhn–Munkres algorithm, determining the pairing of CUs and DUs sharing the same spectrum. As for the second algorithm, our objective is to enhance the individual performance of FD-DUs by maximizing the minimum rate among them, ensuring more uniform rate performance across all FD-DUs. In order to solve this optimization problem, we propose a novel spectral resource allocation algorithm based on bisection searching and the Kuhn–Munkres algorithm, whereas the power control aspect remains the same as in the first algorithm. The numerical results demonstrate that our proposed algorithm effectively enhances the performance of DUs in an FD-D2D underlying cellular network when compared to the sum rate maximization design. [ABSTRACT FROM AUTHOR]