Optimal training for block transmissions over doubly-selective fading channels

High data rates give rise to frequency-selective propagation, while carrier frequency-offsets and mobility-induced Doppler shifts introduce time-selectivity in wireless links. To mitigate the resulting time- and frequency-selective (or doubly-selective) channels, an optimal training strategy is designed in this paper for block transmissions over doubly-selective channels, relying on a basis expansion channel model. The optimality in designing our PSAM parameters consists of maximizing a tight lower bound on the average channel capacity, that is also shown to be equivalent to the minimization of the minimum mean-square channel estimation error. Numerical results corroborate our theoretical designs.