  This paper investigates a distant proactive eavesdropping system in
cooperative cognitive radio (CR) networks. Specifically, an amplify-and-forward
(AF) full-duplex (FD) secondary transmitter assists to relay the received
signal from suspicious users to legitimate monitor for wireless information
surveillance. In return, the secondary transmitter is granted to share the
spectrum belonging to the suspicious users for its own information
transmission. To improve the eavesdropping, the transmitted secondary user's
signal can also be used as a jamming signal to moderate the data rate of the
suspicious link. We consider two cases, i.e., non-negligible processing delay
(NNPD) and negligible processing delay (NPD) at secondary transmitter. Our
target is to maximize network energy efficiency (NEE) via jointly optimizing
the AF relay matrix and precoding vector at the secondary transmitter, as well
as the receiver combining vector at monitor, subject to the maximum power
constraint at the secondary transmitter and minimum data rate requirement of
the secondary user. We also guarantee that the achievable data rate of the
eavesdropping link should be no less than that of the suspicious link for
efficient surveillance. Due to the non-convexity of the formulated NEE
maximization problem, we develop an efficient path-following algorithm and a
robust alternating optimization (AO) method as solutions under perfect and
imperfect channel state information (CSI) conditions, respectively. We also
analyze the convergence and computational complexity of the proposed schemes.
Numerical results are provided to validate the effectiveness of our proposed
schemes.
