In this paper, we address the analysis of the Costa setup under channel uncertainty. Since the Costa setup was entirely considered under the Gaussian assumptions about host and channel statistics, we assume that the channel is an additive white Gaussian noise (AWGN) with unknown variance defined on some interval. First, we solve the problem of average achievable rate optimization assuming that the distribution of noise variances is known. Then, we withdraw the previous assumption and consider that the variance distribution is unknown. The corresponding criteria are formulated and the performance of the Costa under these criteria is demonstrated