Optimal decoder for channels with estimation errors

Gaussian inputs and nearest neighbor decoder are optimal choices for the transceiver when perfect channel information is available. However, channel uncertainty is inevitable in practical systems due to additive noise and channel variation. Under such circumstances, Gaussian inputs are no longer optimal whereas the nearest neighbor decoder even loses part of the mutual information provided by Gaussian codebooks. In this letter, we tackle the issue of decoder optimization for channels with Gaussian inputs and channel estimation errors. The result is a normalized nearest neighbor decoder which is proved, by a semi-analytical method, capable of fully obtaining the mutual information with Gaussian inputs. We further show that the proposed decoder is capable of achieving the performance improvement provided by a better non-Gaussian codebook.