Spectrum scarcity seems to be the most challenging issue to be solved in new wireless telecommunication services. It is shown that spectrum unavailability is mainly due to spectrum inefficient utilization and inappropriate physical layer execution rather than spectrum shortage. Daily increasing demand for new wireless services with higher data rate and QoS level makes the upgrade of the physical layer modulation techniques inevitable. Orthogonal Frequency Division Multiple Access (OFDMA) which utilizes multicarrier modulation to provide higher data rates with the capability of flexible resource allocation, although has widely been used in current wireless systems and standards, seems not to be the best candidate for cognitive radio systems. Filter Bank based Multi-Carrier (FBMC) is an evolutionary scheme with some advantages over the widely-used OFDM multicarrier technique. In this paper, we focus on the total throughput improvement of a cognitive radio network using FBMC modulation. Along with this modulation scheme, we propose a novel uplink radio resource allocation algorithm in which fairness issue is also considered. Moreover, the average throughput of the proposed FBMC based cognitive radio is compared to a conventional OFDM system in order to illustrate the efficiency of using FBMC in future cognitive radio systems. Simulation results show that in comparison with the state of the art two algorithms (namely, Shaat and Wang) our proposed algorithm achieves higher throughputs and a better fairness for cognitive radio applications.