The best training depends on the receiver architecture

We consider a block fading frequency selective multi-input multi-output (MIMO) channel in additive white Gaussian noise (AWGN). The channel input is a training vector superimposed on a linearly precoded vector of Gaussian symbols. This form of precoding is referred to as affine precoding. We derive the Cramer-Rao bound (CRB) under two circumstances: the random parameter vector to be estimated contains (i) only fading channel coefficients, (ii) unknown data symbols as well as the channel coefficients. While case (i) corresponds to the decoding schemes in which the channel is estimated first and the channel measurement is utilized to recover the data symbols, case (ii) corresponds to methods in which channel and symbol estimation is performed jointly. The interesting outcome of our investigation is that minimizing trace of the channel CRB for cases (i) and (ii) under a total transmit power constraint leads to different affine precoder design guidelines.