Capacity-optimal training for space-time modulation over a time-varying channel

Using a model based on the time-autocorrelation function for time-varying MIMO channels, we find a lower bound on capacity for trained modulation, and find the training signal, training power, and length of training signal which maximize this bound. An approximation for the training frequency that maximizes the bound at high SNR is given for Jakes' fading model. The capacity for differential unitary space-time modulation is discussed and compared with that for trained modulation. We present several numerical examples to illustrate our results.