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(.) [1] of the effective channel matrix at the receiver and an earlier proof that LE achieves full diversity in frequency selective channels [2] 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.