This paper focuses on the resource allocation within an asynchronous ad hoc network that utilizes two different modulation techniques: orthogonal frequency-division multiplexing (OFDM) and filter bank based multicarrier (FBMC). More specifically, we investigate the problem of downlink sum rate maximization. The NP-hard formulation is first decomposed into two subproblems in order to decrease the computational complexity of the sum rate optimization problem. We propose a heuristic subcarrier allocation scheme followed by a centralized power allocation algorithm that iteratively solves the convex formulation obtained from a conservative approximation. Simulation analyses are provided to further validate the efficiency of our proposed algorithm and highlight the advantages, in terms of both convergence speed and spectral efficiency, of using FBMC over OFDM.