An energy efficiency perspective on training for fading channels

In this paper, the bit energy requirements of training-based transmission over block Rayleigh fading channels are studied. Pilot signals are employed to obtain the minimum mean-square-error (MMSE) estimate of the channel fading coefficients. Energy efficiency is analyzed in the worst case scenario where the channel estimate is assumed to be perfect and the error in the estimate is considered as another source of additive Gaussian noise. It is shown that bit energy requirement grows without bound as the SNR goes to zero, and the minimum bit energy is achieved at a nonzero SNR value below which one should not operate. The effect of the block length on both the minimum bit energy and the SNR value at which the minimum is achieved is investigated. Flash training schemes are analyzed and shown to improve the energy efficiency in the low-SNR regime. Energy efficiency analysis is also carried out when peak power constraints are imposed on pilot signals.