How much training is needed in multiple-antenna wireless links?

TLDR

Multiple‑antenna wireless links can deliver high data rates with low error rates when the channel is known, and this knowledge is typically obtained via training symbols. The authors compute a lower bound on the capacity of a channel learned by training and maximize it over SNR, fading coherence time, and number of transmitter antennas. The study finds that training length should match the number of transmit antennas when training and data powers vary, may exceed that when powers are equal, and that training‑based schemes are optimal at high SNR but suboptimal at low SNR.

Abstract

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 compute a lower bound on the capacity of a channel that is learned by training, and maximize the bound as a function of the received signal-to-noise ratio (SNR), 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 show that training-based schemes can be optimal at high SNR, but suboptimal at low SNR.