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Orthogonal frequency-division multiplexing (OFDM), widely recommended for sharing the spectrum among different nodes in a dynamic spectrum access network, imposes tight timing and frequency synchronization requirements. We examine the use of filterbank multicarrier (FBMC), a some-what lesser known and understood alternative, for dynamic spectrum access in vehicular networks. FBMC promises very low out-of-band energy of each subcarrier signal when compared to OFDM. In order to fully understand and evaluate the promise of FBMC in mobile, outdoor settings, we first examine the use of special pulse shaping filters of the FBMC PHY layer in reliably transmitting data packets at a very high rate. Next, to gain an understanding of the cross-layer performance of FBMC, as well as to understand its impact beyond the PHY layer, we build a discrete event simulator using realistic models. Using extensive simulations, we show that FBMC consistently achieves an order of magnitude performance improvement over OFDM in terms of packet transmission delays and effective data transmission rate available to each node, over large distances in comparison to OFDM. Finally, our analysis in the case of multi-hop networks shows that FBMC can achieve about 20x smaller end-to-end data packet delivery delays, and relatively low packet drop probabilities in comparison to OFDM. In summary, our results can serve as guidelines for designing ad hoc, dynamic spectrum access communication standards for future vehicular networks.