Communication by sleeping: Optimizing a relay channel under wake and transmit power costs

In many low-power networks, the power cost for a node to remain ON to listen to transmissions from other nodes or to transmit to other nodes can constitute a significant part of the total power consumption by the radio. Thus, unlike the traditional relay channel model, under a low power constraint, the relay node cannot stay ON and listen to the entire duration of the transmission. We study the slope of the capacity-power function at zero power for relay channels where the power cost of remaining ON is explicitly taken into account. We show that in this low-power limit, information is conveyed primarily through the ON-OFF activity of the source. The relay node should have significantly more power compared to the source node in order to improve the slope at zero power. The rough intuition is that, in order for a relay node to be useful, it needs to stay ON and listen during a significant portion of the time during which the source node may transmit. This fact limits the utility of the relay to those cases where the it has much higher power than the source node it is trying to help.