How Much Training is Needed in Multiple-Antenna Wireless Links?

How Much Training is Needed in Multiple-Antenna Wireless Links?

April 2003 | Babak Hassibi and Bertrand M. Hochwald
The paper investigates the optimal amount of training required in multiple-antenna wireless communication systems to maximize channel capacity. It shows that training affects the capacity of a fading channel, with too little training leading to poor channel estimation and too much training leaving insufficient time for data transmission. A lower bound on the capacity is computed and maximized as a function of the signal-to-noise ratio (SNR), fading coherence time, and number of transmitter antennas. The optimal number of training symbols is found to be equal to the number of transmit antennas when training and data powers can vary. However, when training and data powers are equal, the optimal number of symbols may be larger than the number of antennas. Training-based schemes can be optimal at high SNR but suboptimal at low SNR. The paper also shows that training-based schemes can achieve capacity close to the theoretical limit when the SNR is high and the coherence interval is much larger than the number of transmit antennas. The results are illustrated with plots showing the capacity lower bound as a function of the block length T for different values of SNR and number of antennas. The paper concludes that optimizing the training interval and power allocation is crucial for maximizing the capacity of multiple-antenna wireless communication systems.The paper investigates the optimal amount of training required in multiple-antenna wireless communication systems to maximize channel capacity. It shows that training affects the capacity of a fading channel, with too little training leading to poor channel estimation and too much training leaving insufficient time for data transmission. A lower bound on the capacity is computed and maximized as a function of the signal-to-noise ratio (SNR), fading coherence time, and number of transmitter antennas. The optimal number of training symbols is found to be equal to the number of transmit antennas when training and data powers can vary. However, when training and data powers are equal, the optimal number of symbols may be larger than the number of antennas. Training-based schemes can be optimal at high SNR but suboptimal at low SNR. The paper also shows that training-based schemes can achieve capacity close to the theoretical limit when the SNR is high and the coherence interval is much larger than the number of transmit antennas. The results are illustrated with plots showing the capacity lower bound as a function of the block length T for different values of SNR and number of antennas. The paper concludes that optimizing the training interval and power allocation is crucial for maximizing the capacity of multiple-antenna wireless communication systems.
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