Optimal Power Allocation for Artificial Noise under Imperfect CSI Against Spatially Random Eavesdroppers

In this paper, we study the secure multiantenna transmission with artificial noise (AN) under imperfect channel state information (CSI) in the presence of spatially randomly distributed eavesdroppers. We derive the optimal solutions of the power allocation between the information signal and the AN for minimizing the secrecy outage probability (SOP) under a target secrecy rate and for maximizing the secrecy rate under an SOP constraint, respectively. Moreover, we provide an interesting insight that channel estimation error affects the optimal power allocation strategy in opposite ways for the two given objectives. When the estimation error increases, more power should be allocated to the information signal if we aim to decrease the rate-constrained SOP, whereas more power should be allocated to the AN if we aim to increase the SOP-constrained secrecy rate.