In this paper, the interplay between non-orthogonal multiple access (NOMA), device-to-device (D2D) communication, full-duplex (FD) technology, and cooperation networks is proposed, and a resource allocation problem is investigated. Specifically, a downlink FD cooperative NOMA-based cellular system with underlaying D2D communications is proposed, where, in each NOMA group, the strong user assists the weak user as an FD relay with imperfect self interference (SI) cancellation. In terms of reaping spectral efficiency benefits, the system sum rate is to be maximized by optimizing channel allocation. This optimization is based on quality of service (QoS) constraints of D2D pairs and cellular users (CUs), power budget of base station and strong user (cooperative phase), and successive interference cancellation (SIC) constraints. Since the maximization formulated problem is computationally challenging to be addressed, a two-sided stable many-to-one matching algorithm, based on Pareto improvement, performs sub-channel assignment. Extensive simulations are implemented to demonstrate the system performance indicated by different metrics.