The ordered transmissions scheme requires fewer sensor nodes to transmit their measurements than the conventional unordered transmissions scheme (UTS) in which all nodes transmit. Yet, it achieves the same error probability as UTS. For the practically relevant scenario in which the measurements of the sensor nodes are spatially correlated, we present a novel correlation-aware ordered transmissions scheme (CA-OTS) for the binary hypothesis testing problem with Gaussian statistics. It uses the timer scheme to make the nodes transmit their measurements in the decreasing order of the absolute values of the measurements without any node knowing the measurements of other nodes. CA-OTS applies to the general case where the hypotheses differ in the mean vector and covariance matrix, and markedly reduces the number of transmissions. It differs from the literature that assumes that the measurements of the nodes, when conditioned on the hypotheses, are statistically independent or the covariance matrix has a special structure. When the mean vector or covariance matrix is the same for the two hypotheses, we propose novel refinements that require even fewer transmissions. We also derive insightful upper bounds for them that apply to a general product-correlation model.

Ordered transmissions is an energy-efficient scheme that improves the lifetime of a wireless sensor network (WSN) and yet achieves the same performance as the conventional unordered transmissions scheme (UTS) in which all nodes transmit. We present a novel scheme for the binary hypothesis testing problem that exploits ordered transmissions to reduce the number of transmissions for the general and practically important scenario in which the measurements of the sensor nodes are correlated. It differs from the literature that assumes that, conditioned on the hypotheses, the measurements of different nodes are statistically independent or that the covariance matrix has a special structure. In our scheme, the nodes transmit their measurements in the decreasing order of the magnitudes of the measurements. We present two novel approaches to design the decision rules. These address the presence of crossterms between the measurements of different nodes that now arise in the decision statistic due to correlation and make a distributed implementation challenging. Both our approaches markedly reduce the average number of transmissions compared to UTS and ensure that the error probability remains the same.

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.

Opportunistic transmission schemes improve the lifetime of conventional wireless sensor networks (WSNs) by reducing the number of transmissions. However, this comes at the expense of performance since fewer measurements are available. We show that in energy harvesting (EH) WSNs, in which the sensor nodes harvest energy from the environment, this trade-off is fundamentally different. For a general model in which the nodes experience independent and non-identical fading and the EH process at a node is stationary and ergodic, we present lower bounds on the mean squared error (MSE) for two important classes of channel-based opportunistic transmission schemes, namely, censoring and ordered transmissions. For the latter, we present two novel variants that arise depending on whether the energy in the battery of an EH sensor node is accounted for before ordering or not. For censoring, the lower bound leads to an insightful and explicit characterization of the optimum censoring threshold for each node. For ordered transmissions, it helps determine the optimal number of nodes that should be selected to transmit. We find that the ordered transmission schemes can outperform the censoring scheme. We also propose a hybrid scheme that combines the best features of the above schemes for EH WSNs.

Censoring improves the lifetime of conventional wireless sensor networks (WSNs) by reducing the number of sensor node transmissions. However, this comes at the expense of performance since measurements from fewer nodes are available. We show that in energy harvesting (EH) WSNs, in which the sensor nodes harvest energy from the environment, this trade-off is fundamentally different. For a general model in which the nodes experience independent and non-identical fading and the EH process at a node is stationary and ergodic, we derive a lower bound on the mean squared error (MSE). It leads to an insightful and explicit characterization of the optimum censoring threshold for each node. We show that it is the point at which the probability that an EH node has sufficient energy to transmit becomes 1. We also analyze the MSE outage probability, which is an alternate and widely used performance measure, which characterizes the impact of channel fading.