Impact of processing energy on the capacity of wireless channels

Abstract

Power efficiency is a capital issue in the study of mobile wireless nodes owing to constraints on their battery size and weight. A careful examination of the power consumption in low-power nodes shows that, as the total power available to such nodes decreases, the ratio of power consumed for transmission purposes to the power consumed on other non-transmission processes also decreases. The latter power therefore constitutes a considerable fraction of the total power available to such devices. We perform our study in terms of power per unit of time, or energy. Traditional in- formation theoretic energy constraints consider only the energy used for transmission purposes. We study optimal transmission strategies by explicitly taking into account the energy expended by processes other than transmission, that run when the transmitter is in the 'on' state. We term this energy by 'processing energy'. We first derive the capacity of a single user Additive White Gaussian Noise (AWGN) channel in the presence of processing energy. We prove that, unlike the case where only transmission energy is taken into account, achieving capacity may require intermittent, or 'bursty', transmission. We show that in the low Signal to Noise Ratio (SNR) regime, burstiness becomes optimal when the processing energy is greater than half the square of the total energy available to the transmitter. This analysis is extended to the AWGN multiple access channel with M senders and a single receiver. We first show that, under a processing energy constraint, Time Division Multiple Access (TDMA) outperforms other known multiple access techniques in the maximization of the sum rate.

(cont.) We prove that, for that same purpose, burstiness is capacity achieving in the low SNR regime when the sum of the ratios of total energy to processing energy is less than unity. Moreover, we present numerical results that show the improvement in the shape of the general two-user achievable rate region obtained with a bursty transmission scheme. We compare the rates obtained by bursty signaling to the rates that can be achieved by TDMA and to the Cover-Wyner region under a processing energy constraint. Finally, we show that, in low SNR regime, a time-variable channel can be analyzed as a channel with no variability but with processing energy. In fact, the results we obtain for the bursty signaling in time-variable channels from the processing energy correspondence match those of other studies ([3], [4], [5]) that do not make use of the processing energy argument. This leads to posit a model in which energy can be regarded as a unifying cost or penalty for various communication impediments.