On the maximum Doppler diversity of high mobility systems with imperfect channel state information

This paper studies the maximum Doppler diversity order of high mobility systems operating in the presence of imperfect channel state information (CSI). High mobility of wireless terminals causes large Doppler spread, which provides Doppler diversity. However, channel estimation errors are usually inevitable in such systems due to fast time-varying fading caused by large Doppler spread, and they will negatively impact system performance. We study the fundamental tradeoff between Doppler diversity and channel estimation errors by identifying the exact analytical expression of the maximum Doppler diversity order achievable in the presence of imperfect CSI. The analytical study is enabled by a simple repetition code at the transmitter and a new optimum diversity receiver, which is developed by analyzing the statistical properties of channel estimation errors. The analytical results show that if the energy of pilot symbols scales linearly with that of data symbols, then systems with imperfect CSI can achieve the same Doppler diversity order as those with perfect CSI. A non-linear scaling between the energy of pilot and data symbols always results in a loss of Doppler diversity for systems with imperfect CSI.