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We consider the problem of determining the power ratio between the trainingsymbols and data symbols in order to maximize the channel capacity fortransmission over uncertain channels with a channel estimate available at boththe transmitter and receiver. The receiver makes an estimate of the channel byusing a known sequence of training symbols. This channel estimate is thentransmitted back to the transmitter. The capacity that the transceivermaximizes is the worst case capacity, in the sense that given a noisecovariance, the transceiver maximizes the minimal capacity over alldistributions of the measurement noise under a fixed covariance matrix known atboth the transmitter and receiver. We give an exact expression of the channelcapacity as a function of the channel covariance matrix, and the number oftraining symbols used during a coherence time interval. This expressiondetermines the number of training symbols that need to be used by finding theoptimal integer number of training symbols that maximize the channel capacity.As a bi-product, we show that linear filters are optimal at both thetransmitter and receiver.

Optimal Data and Training Symbol Ratio for Communication over Uncertain Channels