Achieving Undetectable Communication

In this paper we consider the problem of achieving a positive error-free communications rate without being detected by an eavesdropper-we coin this the privacy rate. Specifically, we analyze the privacy rate over additive white Gaussian Noise (AWGN) channels with finite and infinite number of samples and Rayleigh single input-single (SISO) and multiple input-multiple output (MIMO) channels with infinite samples when an eavesdropper employs a radiometer detector and has uncertainty about his noise variance. Leveraging recent results on the phenomenon of a signal-to-noise ratio (SNR) wall when there is eavesdropper noise power measurement uncertainty, we show that a nonzero privacy rate is possible. We also show that in this scenario, the detector should not necessarily take as many samples as possible.