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In this paper we derive closed-form formulas of feedback capacity andnonfeedback achievable rates, for Additive Gaussian Noise (AGN) channels drivenby nonstationary autoregressive moving average (ARMA) noise (with unstable onepoles and zeros), based on time-invariant feedback codes and channel inputdistributions. From the analysis and simulations follows the surprisingobservations, (i) the use of time-invariant channel input distributions givesrise to multiple regimes of capacity that depend on the parameters of the ARMAnoise, which may or may not use feedback, (ii) the more unstable the pole(resp. zero) of the ARMA noise the higher (resp. lower) the feedback capacity,(iii) certain conditions, known as detectability and stabilizability arenecessary and sufficient to ensure the feedback capacity formulas andnonfeedback achievable rates {\it are independent of the initial state of theARMA noise}. Another surprizing observation is that Kim's \cite{kim2010}characterization of feedback capacity which is developed for stable ARMA noise,if applied to the unstable ARMA noise, gives a lower value of feedback capacitycompared to our feedback capacity formula.

Feedback Capacity Formulas of AGN Channels Driven by Nonstationary Autoregressive Moving Average Noise