Nearest Neighbor Decoding and Pilot-Aided Channel Estimation for Fading Channels

We study the information rates of non-coherent, stationary, Gaussian, multiple-input multiple-output (MIMO) flat-fading channels that are achievable with nearest neighbor decoding and pilot-aided channel estimation. In particular, we investigate the behavior of these achievable rates in the limit as the signal- to-noise ratio (SNR) tends to infinity by analyzing the capacity pre-log, which is defined as the limiting ratio of the capacity to the logarithm of the SNR as the SNR tends to infinity. We demonstrate that a scheme estimating the channel using pilot symbols and detecting the message using nearest neighbor decoding (while assuming that the channel estimation is perfect) essentially achieves the capacity pre-log of non-coherent multiple-input single-output flat-fading channels, and it essentially achieves the best so far known lower bound on the capacity pre-log of non-coherent MIMO flat-fading channels. We then extend our analysis to the multiple-access channel.