  We consider the problem of determining the power ratio between the training
symbols and data symbols in order to maximize the channel capacity for
transmission over uncertain channels with a channel estimate available at both
the transmitter and receiver. The receiver makes an estimate of the channel by
using a known sequence of training symbols. This channel estimate is then
transmitted back to the transmitter. The capacity that the transceiver
maximizes is the worst case capacity, in the sense that given a noise
covariance, the transceiver maximizes the minimal capacity over all
distributions of the measurement noise under a fixed covariance matrix known at
both the transmitter and receiver. We give an exact expression of the channel
capacity as a function of the channel covariance matrix, and the number of
training symbols used during a coherence time interval. This expression
determines the number of training symbols that need to be used by finding the
optimal integer number of training symbols that maximize the channel capacity.
As a bi-product, we show that linear filters are optimal at both the
transmitter and receiver.
