The Impact of Statistical Delay Constraints on the Energy Efficiency in Fading Channels

This work analyzes the energy efficiency in fading channels under statistical delay constraints, imposed as limitations on the maximal delay violation probabilities. The maximum constant arrival rates are characterized with the aid of the notion of effective capacity, based on which the spectral efficiency-bit energy tradeoff is analyzed in the low-SNR regime. The analysis is performed under two assumptions: 1) perfect channel side information (CSI) at receiver only and 2) perfect CSI at both the transmitter and receiver. It is proven that the bit energy required at zero spectral efficiency is indeed the minimum bit energy. The expressions for the minimum bit energy and wideband slope are obtained. It is shown that the performances of the low-power and wideband regimes are the same, while the statistical queueing constraints have different behaviors. It is found that the minimum bit energy requirements increase as the statistical delay constraints become more stringent. Moreover, it is demonstrated that the minimum bit energy required is the same as that attained when only statistical queueing constraints are enforced in the wideband regime, while the bit energy increment is larger to achieve the same nonzero spectral efficiency. Overall, the impact upon the energy efficiency of statistical delay constraints is quantified.