  In this paper, we investigate the power allocation of primary base station
(PBS) and cognitive base station (CBS) across different orthogonal frequency
division multiplexing (OFDM) subcarriers for energy-efficient secure downlink
communication in OFDM-based cognitive radio networks (CRNs) with the existence
of an eavesdropper having multiple antennas. We propose a secrecy energy
efficiency maximization (SEEM) scheme by exploiting the instantaneous channel
state information (ICSI) of the eavesdropper, called ICSI based SEEM
(ICSI-SEEM) scheme with a given total transmit power budget for different OFDM
subcarriers of both PBS and CBS. As for the case when the eavesdropper's ICSI
is unknown, we also propose an SEEM scheme through using the statistical CSI
(SCSI) of the eavesdropper, namely SCSI based SEEM (SCSI-SEEM) scheme. Since
the ICSI-SEEM and SCSI-SEEM problems are fractional and non-convex, we first
transform them into equivalent subtractive problems, and then achieve
approximate convex problems through employing the difference of two-convex
functions approximation method. Finally, new two-tier power allocation
algorithms are proposed to achieve $\varepsilon$-optimal solutions of our
formulated ICSI-SEEM and SCSI-SEEM problems. Simulation results illustrate that
the ICSI-SEEM has a better secrecy energy efficiency (SEE) performance than
SCSI-SEEM, and moreover, the proposed ICSI-SEEM and SCSI-SEEM schemes
outperform conventional SR maximization and EE maximization approaches in terms
of their SEE performance.
