The long-term average capacity region per unit cost with application to protocols for sensor networks

We consider a wireless sensor network (WSN) where K sensors must deliver a message within a frame of N time slots by spending a given finite energy. If the message is not transmitted within the required delay then it becomes useless and the residual energy is wasted. The channel is block-fading, with independent fades for each sensor and each slot. Sensors know the fading levels up to the current slot but do not know the future fading levels. The receiver collects the signal on all the slots of the frame and performs joint decoding of all the messages. We characterize the region of long-term average achievable rates and we show that the optimal policy for N coincides with constant power allocation and, as N increases, it tends to waterfilling in time. In this setting, we also characterize the long-term average capacity region per unit energy by showing that the optimal policy is “one-shot”, totally decentralized and extremely simple, i.e., every user spends all its available energy on the first slot of the frame whose fading gain is larger than a pre-computed time varying threshold. Since capacity per unit energy is related to the minimumEb N required for reliable communication, the “one-shot” policy not only makes the most efficient use of the energy but also reduces to the minimum the interference to other users. These characteristics make the “one-shot” policy appealing for systems with severe energy limitation as WSN.