Optimal training for frequency-selective fading channels

Many communications systems employ training, ie, the transmission of known signals, so that the channel parameters may be learned at the receiver. This has a dual effect: too little training and the channel is improperly learned, too much training and there is no time left for data transmission before the channel changes. We use an information-theoretic approach to find the optimal amount of training for frequency selective channels described by a block-fading model. When the training and data powers are allowed to vary, we show that the optimal number of training symbols is equal to the length of the channel impulse response. When the training and data powers are instead required to be equal, the optimal number of symbols may be larger. We further show that at high SNR training-based schemes are capable of capturing most of the channel capacity, whereas at low SNR they are highly suboptimal