Diversity order analysis of training codes for MIMO block fading channels

A general class of training-based space-time codes is considered for the noncoherent block correlated Rayleigh fading channel. Such codes can be efficiently decoded by first forming the MMSE estimate of the channel and then decoding the underlying coherent space-time code using the channel estimate as if it were perfect. The diversity order of this (in general, sub-optimal) estimator-decoder is obtained, and it is shown that under certain conditions on the channel correlation matrix, training codes inherit the diversity order of the underlying coherent code.