Reconfigurable computing architectures are well suited for the dynamic data flow processing requirements of software-defined radio. The software radio concept has quickly evolved to include spectrum sensing, awareness, and cognitive algorithms for machine learning resulting in the cognitive radio model. This work explores the application of reconfigurable hardware to the physical layer of cognitive radios using non-contiguous multi-carrier radio techniques. The practical tasks of spectrum sensing, frame detection, synchronization, channel estimation, and mutual interference mitigation are challenges in the communications and the computing fields that are addressed to optimally utilize the capacity of opportunistically allocated spectrum bands. FPGA implementations of parameterizable OFDM and filter bank multi-carrier (FBMC) radio prototypes with spectrum awareness and non-contiguous sub-carrier allocation were completed and tested over-the-air. Sub-carrier sparseness assumptions were validated under practical implementation and performance considerations. A novel algorithm for frame detection and synchronization with mutual interference rejection applicable to the FBMC case was proposed and tested. / Ph. D.