Ordered transmissions reduces the number of nodes that transmit in a wireless sensor network (WSN) and yet achieves the same performance as the conventional unordered transmissions scheme (UTS) in which all nodes transmit. However, it breaks down in energy harvesting (EH) WSNs because of missed transmissions by EH nodes that lack sufficient energy. For the Bayesian detection framework, we propose a novel scheme that addresses this challenge for the general case in which the log-likelihood ratio is bounded and has a continuous distribution function. Given the probability that a node misses its transmission, it reduces the average number of transmissions compared to UTS. For truncated Gaussian statistics, we then propose a novel refinement that requires even fewer transmissions and that simultaneously lowers the error probability. We also analyze its performance and show that it lends itself to a computationally-efficient Monte Carlo evaluation. When the time evolution of the battery energies of the nodes is tracked and the probability of a missed transmission becomes a function of the scheme itself, the proposed schemes achieve a markedly lower error probability than both UTS and sequential detection, except when the energy harvested is so less that very few nodes can transmit.

We propose a novel energy-efficient ordered transmissions scheme for Bayesian hypothesis testing in energy harvesting (EH) wireless sensor networks (WSNs), in which the EH nodes harvest energy from the environment and can replenish their batteries. The proposed scheme exploits the distributed timer scheme to ensure that the nodes transmit their readings to the fusion node in the decreasing order of their log likelihood ratios without any node knowing the readings of any other node. It addresses the new problem of missing transmissions that arises in EH WSNs because the energy harvested by the nodes is random. We show how the disruption caused in the sequence of ordered transmissions by these missing transmissions can be tackled. The proposed scheme not only reduces the number of transmissions, but also reduces the error probability compared to the conventional unordered scheme in which all the sensor nodes attempt to transmit in a pre-determined order. This is unlike several energy-efficient techniques that reduce the number of transmissions but increase the error probability.