On MIMO Gaussian Wiretap Channels with Optimal Energy Harvesting

In this paper, we consider the problem of energy harvesting maximization in a wiretap channel model while keeping the secrecy rate higher than a given threshold and the transmit power lower than a given constant. In this model, the transmitted radio signal that conveys information is also considered as an energy carrier. The energy receiver (Eve) is a legitimate user who may benefit from the energy of the received signal that is sent to the information receiver (Bob) but she should not be able to decode the message itself. Energy harvesting maximization at Eve's side is a non-convex optimization problem and therefore intractable. To tackle this problem, we use rotation matrices to represent the covariance matrix of the transmitted signal and then apply the Karush-Kuhn-Tucker conditions. We derive an analytical solution for the case in which the number of transmit antennas is two whereas the numbers of receive antennas at Bob's and Eve's sides are arbitrary and finite. Finally, we verify the results by simulations.