Secrecy Capacity Analysis of Artificial Noisy MIMO Channels—An Approach Based on Ordered Eigenvalues of Wishart Matrices

Abstract

Artificial noise (AN) can be used to confuse eavesdroppers in a physical layer security system. One of the main issues concerned in AN schemes is how to improve secrecy capacities. Most existing AN schemes were proposed based on an assumption that the number of transmit antennas $t$ is larger than that of receiver antennas $r$ , such that they can utilize all $r$ eigen-subchannels of a multiple-output multiple-input (MIMO) system to send messages, and use remaining $t-r$ null spaces for transmitting AN signals. These AN signals null out legitimate receivers and degrade eavesdropper channels. However, transmitting messages in all eigen-subchannels is not always a good strategy. In particular, when the number of transmit antennas is constrained or even smaller than those of receivers, the secrecy capacities of legitimate receivers will be impaired significantly if using all eigen-subchannels for message transmission. To improve secrecy capacity, we propose an AN scheme where messages are encoded in $s$ (which is a variable) strongest eigen-subchannels based on ordered eigenvalues of Wishart matrices, while AN signals are generated in remaining $t-s$ spaces. We derive the average secrecy capacity of a single-user MIMO wiretap channel in the presence of an eavesdropper with multiple antennas. We show that the numerical results are in a good agreement with simulation results. The secrecy capacity of the proposed AN scheme can be improved by approximately 20% ~ 40% if compared with existing AN schemes.