This paper compares the sum rate achieved in an asynchronous ad hoc network with different multi-carrier modulations. The ad hoc network is obtained following a Poisson Point Process for both Access Points (AP) and mobile?s locations. Sub-bands are then allocated to the APs, either randomly or using clustering. Then, each AP independently maximizes its sum rate, taking into account the interference received by the other cells and from adjacent subcarriers. FBMC-PHYDYAS modulation allows to limit the number of subcarriers where interference is spread, compared to CP-OFDM and FBMC-IOTA. The advantages of FBMC-PHYDYAS are shown in terms of spectral efficiency, in several configurations.