  This paper investigates power control and relay selection in Full Duplex
Cognitive Relay Networks (FDCRNs), where the secondary-user (SU) relays can
simultaneously receive data from the SU source and forward them to the SU
destination. We study both non-coherent and coherent scenarios. In the
non-coherent case, the SU relay forwards the signal from the SU source without
regulating the phase; while in the coherent scenario, the SU relay regulates
the phase when forwarding the signal to minimize the interference at the
primary-user (PU) receiver. We consider the problem of maximizing the
transmission rate from the SU source to the SU destination subject to the
interference constraint at the PU receiver and power constraints at both the SU
source and SU relay. We then develop a mathematical model to analyze the data
rate performance of the FDCRN considering the self-interference effects at the
FD relay. We develop low-complexity and high-performance joint power control
and relay selection algorithms. Extensive numerical results are presented to
illustrate the impacts of power level parameters and the self-interference
cancellation quality on the rate performance. Moreover, we demonstrate the
significant gain of phase regulation at the SU relay.
