Optimal training in space-time systems

Multiple-antenna wireless communication links promise very high data rates with low error probabilities, especially when the wireless channel response is known at the receiver. In practice, knowledge of the channel is often obtained by sending known training symbols to the receiver. We show how training affects the capacity of a fading channel-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 compute the optimal amount of training as a function of the received signal-to-noise ratio, fading coherence time, and number of transmitter antennas. When the training and data powers are allowed to vary, we show that the optimal number of training symbols is equal to the number of transmit antennas-this number is also the smallest training interval length that guarantees meaningful estimates of the channel matrix. When the training and data powers are instead required to be equal, the optimal number of symbols may be larger than the number of antennas. We further conclude that at high SNR training-based schemes can capture most of the channel capacity, whereas at low SNR they can be highly suboptimal.