Here we address the closed-loop stabilization of a single-input single-output (SISO) unstable linear time invariant (LTI) plant model over an additive non-zero mean white noise (AWN) channel located either over the feedback path or the direct path. We study the stability of the resulting closed-loop in terms of the channel Signal-to-Noise Ratio (SNR) feedback constraint. We then consider a non-zero mean AWN channel with the added effect of a non-zero mean setpoint signal process entering the feedback loop.