Energy-efficient secure transmission in massive MIMO systems with pilot attack

In this paper, we focus on the problem of energy-efficient power allocation for secure transmission in massive multiple-input multiple-output (MIMO) systems, where an active multi-antennas eavesdropper sends pilot signals as that of destination receiver to transmitter simultaneously in the uplink training phase. Our aim is to maximize the energy efficiency (EE) of the system by considering the power allocation strategy, while guaranteeing the secrecy rate and the transmit power constraints. We first analyze the impact of pilot attack on the secrecy rate and then prove that the secrecy EE is a concave function with respect to transmit power. The optimization problem formulated can be efficiently solved by using Lagrange multiplier method. Finally, numerical results are provided to validate the proposed energy-efficient scheme outperforms the fixed transmit power scheme.