Optimal training for MIMO fading channels with time- and frequency-selectivity

Demand for high data rate leads to frequency-selective propagation effects, whereas carrier frequency-offsets and Doppler effects induced by mobility introduce time-selectivity in wireless links. These fading channels, once acquired, offer joint multipath-Doppler diversity gains. In addition, space-time multiplexing and/or coding offer attractive means of combating fading, and boosting capacity of multi-antenna communications. As the number of antennas increases, channel estimation becomes challenging because the number of unknowns increases, and the power is split at the transmitter. Optimal training sequences have so far been designed for flat-fading and frequency-selective multi-antenna systems. In this paper, we design a low complexity optimal training scheme for block transmissions over time- and frequency (a.k.a. doubly)-selective channels with multiple antennas. The optimality in designing our training schemes consists of maximizing a lower bound on the ergodic (average) capacity that is shown to be equivalent to minimizing the mean-square error of the linear channel estimator. Simulation results confirm our theoretical analysis which applies to both single- and multi-carrier transmissions.