Design of the Periodic Training Sequence for Joint Channel and Frequency Estimation in MIMO Frequency-Selective Channels

This paper considers the design of a periodic training sequence (TS) for joint channel and frequency estimation in multiple-input, multiple-output (MIMO) frequency-selective channels. The design criterion for the periodic TS is to jointly minimize the mean-squared error (MSE) of the maximum likelihood channel estimation and the asymptotic Cramer-Rao bound (CRB) for the frequency estimation. This paper shows that all the TSs that minimize the MSE of the channel estimation have the same asymptotic CRB for the frequency estimation. Furthermore, they also minimize the asymptotic CRB as long as the channel is i.i.d. Rayleigh fading. The design of low-complexity frequency estimators based on the proposed periodic TS is also investigated. Finally, the performance of the proposed periodic TS is evaluated by simulation results.