On the Effect of Processing Energy on Multiple Access Channels∗

Energy efficiency is an important issue in mobile wireless networks since the battery life of mobile terminals is limited. We are considering, besides the energy consumed for transmission, the energy consumed by being in the ‘on’ state, which we term ‘processing energy’. This energy constitutes a considerable fraction of the total energy available to battery-limited wireless devices, hence it is capital to take it into account in the capacity calculations. In [1], we have discussed the impact of processing energy on the capacity of a single user Additive White Gaussian Noise (AWGN) channel and proved that burstiness of signaling can be capacity achieving. We first show that in low SNR regime, there is an equivalence between the effect of channel variability and that of processing energy on capacity. Then, we extend the analysis of [1] to the AWGN multiple access channel with M senders and a single receiver. We, then, show that Time Division Multiple Access outperforms other multiple access techniques for the purpose of maximizing the sum rate. We prove that, for the 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; in this case, the 2-user capacity region is rectangular. Finally, we present numerical results that show the shape of the general 2-user achievable capacity region under a processing energy constraint and we compare it to the TDMA curve and the Cover-Wyner region obtained when no burstiness is allowed.