OUTformation: Distributed Data-Gathering with Feedback under Unknown Environment and Communication Delay Constraints

Towards the informed design of large-scale distributed data-gathering architectures under real-world assumptions such as nonzero communication delays and unknown environment dynamics, this paper considers the effects of allowing feedback communication from the central processor to external sensors. Using simple but representative state-estimation examples, we investigate fundamental tradeoffs between the mean-squared error (MSE) of the central processor's estimate of the environment state, and the total power expenditure per sensor under more conventional architectures without feedback (INformation) versus those with broadcast feedback (OUTformation). The primary advantage of enabling feedback is that each sensor's understanding of the central processor's estimate improves, which enables each sensor to determine when and what parts of its current observations to transmit. We use theory to demonstrate conditions in which OUTformation maintains the same MSE as INformation with less power expended on average, and conditions in which OUTformation obtains less MSE than INformation at additional power cost. These performance tradeoffs are also considered under settings where environments undergo less variation, and sensors implement random backoff times to prevent transmission collisions. Our results are supported via numerical studies, which show that the properties derived in theory still hold even when some of the simplifying assumptions are removed.