Space-time coding for doubly-selective channels

Relying on a basis expansion model (BEM) to capture time- and frequency-selective propagation effects, we prove that the maximum achievable diversity of multi-antenna transmissions over doubly-selective channels is determined by the rank of the correlation matrix of the BEM coefficients from all channels. The diversity order is multiplicative in the effective degrees of freedom that the channels exhibit in space-, time-, and frequency-domains. Furthermore, we design a block precoded digital phase sweeping transmission that achieves full space-Doppler-multipath diversity for any number of transmit-receive antennas, and without bandwidth expansion. The theoretical diversity results are corroborated by simulations, and the BEM is validated.