DFT modulated filter banks for non-orthogonal multicarrier transmission are considered a strong tool to implement both dynamic spectrum access and spectrum sensing in cognitive radio systems where signaling schemes have to meet different objectives. A constrained optimization approach is presented to design a cognitive radio transceiver which can be tailored to system specifications with a reasonable trade-off between performance and implementation efficiency. In interweave cognitive radio, the secondary user receiver is synchronized in time and frequency by designing a synthesis filter bank preamble with periodic symbols in analogy to short training fields in IEEE 802.11a. A simple post-detection integration at the secondary user receiver is employed for differently coherent detection. In underlay cognitive radio, a novel transmission scheme for secondary user power adaptation is proposed aiming to minimize the secondary user average probability of error for bit-interleaved coded modulation. The powers of the subcarrier signals are adapted subject to total power and stochastic chance-based interference constraints in order to provide a confidence level for limiting the interference at the licensed primary user receiver.