Optimal Trade-off Between Energy Efficiency and Average Delay

In wireless networks consisting of sensors and mobile devices, battery power is a severe resource constraint. Energyefficient communication techniques are therefore crucial to the long-term survivability of the network. In communication theory, it is well known that for a bandlimited additive white Gaussian noise (AWGN) channel with bandwidth W and onesided noise spectral level N0, the minimum energy per information bit Eb,min achieves its minimum value N0 ln 2 as W →∞. Interpreting this trade-off between energy efficiency and bandwidth in the more general context of available degrees of freedom, it can be verified that, for a fixed bandwidth and noise level, the minimum energy per bit decreases as the transmission time per bit increases. Thus, greater energy efficiency is gained by using low power and long transmission delays. Using this observation, recent work in [1, 2] examines a scheduling problem in which energy efficiency is traded off with the need to transmit a finite number of packets by a fixed deadline. The findings in [1, 2] are important for communication scenarios where a group of time-sensitive data packets (such as observations from sensors) must be delivered to its destination (such as a sensor fusion site) by a given deterministic deadline. There are also many situations, however, where time-critical information must reach its destination promptly on an ongoing basis. In this paper, we focus on the latter scenario, and investigate the trade-off between energy efficiency and the average system delay of bits. We show that minimizing a weighted combination of energy per bit and average delay per bit is equivalent to a convex optimization problem which can be solved exactly using an iterative “off-line” algorithm, where packet arrival times and packet lengths are known beforehand. The structure of the solution turns out to be very different from that of the solution to the deadline problem of [1, 2].