  This paper investigates a secure energy efficiency (SEE) optimization problem
in a multiple-input single-output (MISO) underlay cognitive radio (CR) network.
In particular, a multi-antenna secondary transmitter (SU-Tx) simultaneously
sends secured information and energy to a secondary receiver (SU-Rx) and an
energy receiver (ER), respectively, in the presence of a primary receiver
(PU-Rx). It is assumed that the SU-Rx, ER and PU-Rx are each equipped with a
single antenna. In addition, the SU-Tx should satisfy constraints on maximum
interference leakage to the PU-Rx and minimum harvested energy at the ER. In
this CR network, we consider the transmit covariance matrix design with the
assumption of perfect channel state information (CSI) at the SU-Tx. In
addition, it is assumed that the ER is a potential passive eavesdropper due to
broadcast nature of wireless transmission. On the other hand, we consider the
worst-case scenario that ER's energy harvesting requirement is only satisfied
when it performs only energy harvesting without intercepting or eavesdropping
information intended for the SU-Rx. We formulate this transmit covariance
matrix design as a SEE maximization problem which is a non-convex problem due
the non-linear fractional objective function. To realize the solution for this
non-convex problem, we utilize the non-linear fractional programming and
difference of concave (DC) functions approaches to reformulate into a tractable
form. Based on these techniques and the Dinkelbach's method, we propose
iterative algorithms to determine the solution for the original SEE
maximization problem. Numerical simulation results are provided to demonstrate
the performance of the proposed transmit covariance matrix design and
convergence of the proposed algorithms.
