Upper bound on the capacity of Gaussian channels with noisy feedback

We consider an additive Gaussian channel with additive Gaussian noise feedback. We first derive an upper bound on the n-block capacity (defined by Cover [1]). It is shown that this upper bound can be obtained by solving a convex optimization problem. With stationarity assumptions on Gaussian noise processes, we characterize the limit of the n-block upper bound and prove that this limit is the upper bound of the noisy feedback (shannon) capacity.