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

The material in this paper was presented in part at the 2011 IEEE International Symposium on Information Theory (ISIT), Saint Petersburg, Russia, 31 July-5 August 2011 and the 49th Annual Allerton Conference on Communication, Control and Computing, Monticello, IL, USA, 28-30 September 2011.We study the information rates of noncoherent, stationary, Gaussian, and 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 noncoherent multiple-input single-output flat-fading channels, and it essentially achieves the best so far known lower bound on the capacity pre-log of noncoherent MIMO flat-fading channels. Extending the analysis to fading multiple-access channels reveals interesting relationships between the number of antennas and Doppler bandwidth in the comparative performance of joint transmission and time division multiple-access.The work of A.T.A was supported in part by the Yousef Jameel Scholarship at the University of Cambridge. T. K. received funding from the European's Seventh Framework Programme (FP7/2007-2013) under grant agreement No. 252663, from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement number 714161), and from the Spanish Ministerio de Economía y Competitividad under grant RYC-2014-16332. The work of A.G.i.F. has been funded by the European Research Council under ERC grant agreements 259663 and 725411