Diversity order of linear equalizers for doubly selective channels

Diversity order of linear equalization (LE) is investigated for the case of linearly precoded block transmission in doubly selective channels. A connection between the orthogonal deficiency od(.) of the effective channel matrix at the receiver and an earlier proof that LE achieves full diversity in frequency selective channels is highlighted. For doubly selective channels it is argued that od of the channel matrix at the receiver shares the same upper bound as that of a closely related matrix for which an od bound is derived. Finally, simulation results are provided to substantiate all arguments made in the paper.