Maximum-diversity transmissions over doubly selective wireless channels

High data rates and multipath propagation give rise to frequency-selectivity of wireless channels, while carrier frequency offsets and mobility-induced Doppler shifts introduce time-selectivity in wireless links. The resulting time- and frequency-selective (or doubly selective) channels offer joint multipath-Doppler diversity gains. Relying on a basis expansion model of the doubly selective channel, we prove that the maximum achievable multipath-Doppler diversity order is determined by the rank of the correlation matrix of the channel´s expansion coefficients, and is multiplicative in the effective degrees of freedom that the channel exhibits in the time and frequency dimensions. Interestingly, it turns out that time-frequency reception alone does not guarantee maximum diversity, unless the transmission is also designed judiciously. We design such block precoded transmissions. The corresponding designs for frequency-selective or time-selective channels follow as special cases, and thorough simulations are provided to corroborate our theoretical findings.