Energy and spectral efficient Doppler diversity transmissions in high-mobility systems with imperfect channel estimation

This paper studies energy and spectral efficient Doppler diversity transmissions in the presence of imperfect channel state information (CSI). Fast time-varying fading in high-mobility communication systems introduces Doppler diversity that can benefit system performance. On the other hand, it is more difficult to estimate and track fast time-varying channel; thus, channel estimation errors might seriously degrade system performance in high-mobility systems. The trade-offs between channel estimation errors and Doppler diversity are studied by using two precoding schemes, a simple repetition code, and a rate 1 Doppler domain multiplexing (DDM) scheme. The repetition code can achieve the maximum Doppler diversity at the cost of a lower spectral efficiency, and the DDM scheme can achieve the energy and spectral efficient Doppler diversity transmissions. Unlike many other Doppler diversity systems that assume perfect CSI, we explicitly consider the impacts of imperfect CSI on the design and performance of both precoding schemes. Optimum and suboptimum receivers for both schemes are developed by studying the statistical properties of channel estimation errors. The analytical error probabilities of the receivers are expressed as functions of a number of system parameters, such as the maximum Doppler spread, the percentage of pilot symbols for channel estimation, the energy allocation between the pilot and data symbols, etc. The analytical and simulation results indicate that both precoding schemes can achieve the maximum Doppler diversity order through the optimization of the various parameters, even in the presence of imperfect CSI.