High Mobility Wireless Communications With Doppler Diversity: Fundamental Performance Limits

The objective of this paper is to quantify the fundamental tradeoff between Doppler diversity and channel estimation errors in high mobility systems. Fast fading variation in high mobility systems introduces Doppler diversity that can benefit system performance. On the other hand, it is more difficult to estimate and track a fast changing channel, thus channel estimation errors are non-negligible and they may seriously degrade system performance. Such a tradeoff relationship is studied by identifying the exact analytical expressions of two performance metrics: the maximum Doppler diversity order achievable with imperfect channel state information (CSI), and the loss in signal-to-noise ratio (SNR) caused by channel estimation errors. The analytical study is enabled by a simple repetition code at the transmitter, and a new optimum diversity receiver developed by analyzing the statistical properties of channel estimation errors. With the analytical results, the optimum allocation of transmission energy between pilot symbols and data symbols are obtained to simultaneously maximize the Doppler diversity order and minimize the SNR loss, thus achieve the optimum tradeoff between the two. The results reveal the fundamental performance limits of Doppler diversity systems operating in the presence of imperfect CSI, and they can be used to guide the design of practical systems.