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This paper studies the fundamental performance limits of a single-input multiple-output (SIMO) high mobility wireless communication systems with imperfect channel state information (CSI). The fundamental limits are quantified in terms of the maximum diversity order (including both Doppler diversity and antenna diversity) that can be achieved by a high mobility system, and the loss in coding gain due to channel estimation errors. Due to severe Doppler effects caused by fast time-varying fading in high mobility systems, channel estimation errors are usually inevitable and might cause significant performance losses. On the other hand, Doppler effect provides potential Doppler diversity that can be harnessed to improve system performance. To quantify this fundamental tradeoff between Doppler diversity and channel estimation errors, we perform analytical studies of the asymptotic error performance of SIMO high mobility systems when the signal-to-noise ratio and the coding block length is large. The analytical results are obtained by analyzing and quantifying the impacts of channel estimation errors on the system performance. With the help of pilot-aided channel estimation and a simple repetition code, we identified the maximum diversity order achievable by a SIMO high mobility system with imperfect CSI and the loss in coding gains due to the inevitable channel estimation errors. The analytical results are then used to optimally allocate transmission energy to pilot symbols and data symbols to simultaneously maximize the Doppler diversity order and minimize the loss coding gain loss due to channel estimation errors. The results reveal the fundamental tradeoff between Doppler diversity and channel estimation errors and can be used to serve as a guide in the design of practical high mobility systems.

Fundamental Tradeoff Between Doppler Diversity and Channel Estimation Errors in SIMO High Mobility Communication Systems