MIMOME Gaussian Channels with GMM Signals in High-SNR Regime: Fundamental Limits and Tradeoffs

Achievable secrecy rates over a multiple-input multiple-output multiple-eavesdropper (MIMOME) wiretap channel are considered, when the legitimate users have perfect knowledge only of the legitimate channel state and the eavesdropper channel is drawn from a (possibly unknown) continuous probability density. Legitimate users are assumed to deploy more antennas than the eavesdropper. A signaling transmission based on K-class Gaussian mixture model (GMM) distributions is proposed, which can be considered as an artificial-noise augmented signal, where the noise statistics are data-dependent. The proposed scheme is shown to achieve the secrecy capacity, log K, in the high signal-to-noise ratio (SNR) regime. Moreover, the tradeoff between secrecy and reliability at finite SNR is explored via the characterization of an upper bound to the error probability at the legitimate receiver, an upper bound to themutual information leakage to the eavesdropper and via numerical simulations.