Achieving positive rate with undetectable communication over AWGN and Rayleigh channels

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 present the privacy rate over Additive White Gaussian Noise (AWGN) and Rayleigh channels when an eavesdropper employs a radiometer detector and has uncertainty about her noise variance. Leveraging recent results on the phenomenon of an Signal to Noise Ratio (SNR) wall when there is eavesdropper noise power measurement uncertainty, we show that a non-zero privacy rate is possible. We also find the SNR wall under Rayleigh fading. We conclude by presenting realizable privacy rates for several practical scenarios.