Everything you always wanted to know about training: guidelines derived using the affine precoding framework and the CRB

In this paper, affine precoding is used to investigate the tradeoffs that exist while using the transmitter resources on training versus information symbols. The channel input is a training vector superimposed on a linearly precoded vector of symbols. A block-fading frequency-selective multi-input multi-output (MIMO) channel is considered. To highlight the tradeoffs between training and data symbols, the Fisher information matrix (FIM) is derived under two circumstances: the random parameter vector to be estimated contains 1) only fading channel coefficients and 2) unknown data symbols as well as the channel coefficients. While strategy 1 corresponds to the receiver structure in which the channel is estimated initially and the channel measurement is utilized to retrieve the data symbols, strategy 2 corresponds to the structure in which channel and symbol estimations are performed jointly. The interesting outcome of the study in this paper is that minimizing the channel Cramer-Rao bound (CRB) for strategies 1 and 2 under a total average transmit power constraint leads to different affine precoder design guidelines.