Maximum diversity order of SIMO high mobility systems with imperfect channel state information

This paper studies the maximum diversity order of single-input multiple-output (SIMO) high mobility communication systems. In high mobility systems, channel estimation errors are usually inevitable due to severe Doppler effects caused by fast time-varying fading, and this might have significant adverse impacts on system performance. On the other hand, Doppler effect provides potential Doppler diversity which can be exploited to improve system performance. Based on the statistical properties of minimum mean square error (MMSE) channel estimation, a new optimum diversity receiver for a SIMO system with imperfect channel state information (CSI) is proposed. The error probability of the new receiver is analytically identified. The result is expressed as an explicit function of the channel temporal correlation, pilot and data signal-to-noise ratios (SNRs). The maximum achievable diversity order of the SIMO system with imperfect CSI is obtained through asymptotic analysis. Analytical results show that, if the energy of pilot symbols scales linearly with that of data symbols, then a SIMO system with imperfect CSI can achieve the same diversity order as those with perfect CSI in a high mobility environment. However a non-linear scaling between the energies of pilot and data symbols always results in loss in Doppler diversity.