  This paper investigates power control and relay selection in Full Duplex
Cognitive Relay Networks (FDCRNs), where the secondary-user (SU) relays can
simultaneously receive and forward the signal from the SU source. 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 develop
low-complexity and high-performance joint power control and relay selection
algorithms. The superior performance of the proposed algorithms are confirmed
using extensive numerical evaluation. In particular, we demonstrate the
significant gain of phase regulation at the SU relay (i.e., the gain of the
coherent mechanism over the noncoherent mechanism).
