Qualitative Analysis of Feedback Capacity of AGN Channels Driven by Unstable Versus Stable Autoregressive Moving Average Noise

In this paper we derive closed-form formulas of feedback capacity and nonfeedback achievable rates, for Additive Gaussian Noise (AGN) channels, driven by unstable i.e., nonstationary, autoregressive moving average (ARMA) noise (with one unstable pole and one unstable zero), based on channel inputs generated by optimal, two-parameter time-invariant feedback strategies or induced channel input distributions. From the analysis and simulations follows the surprising observations, (i) the use of time-invariant channel input distributions gives rise to multiple regimes of capacity that depend on the parameters of the ARMA noise, which may or may not use feedback, (ii) for an autoregressive noise, the higher the unstable pole the higher the capacity, (iii) for a moving average noise, the higher the unstable zero the higher the capacity, (iv) for the ARMA noise, as the pole and zero get closer together the capacity decreases.