Maximum-diversity affine precoding for the noncoherent doubly dispersive channel

In this paper we characterize the maximally achievable diversity order for noncoherent block communication over the doubly dispersive channel, and propose affine precoders which facilitate such maximum-diversity reception. In fact, we show that, under mild channel conditions, almost any affine pre-coder is sufficient to facilitate maximum-diversity reception, regardless of precoding rate. By "noncoherent," we mean that the channel realization is unknown to both transmitter and receiver, and by "doubly dispersive," we mean that the channel exhibits both delay and Doppler spreading (i.e., the channel has a time-varying nontrivial impulse response).