  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.
