  The emergence of the Internet-of-Things and cyber-physical systems
necessitates the coordination of access to limited communication resources in
an autonomous and distributed fashion. Herein, the optimal design of a wireless
sensing system with n sensors communicating with a fusion center via a
collision channel of limited capacity k (k < n) is considered. In particular,
it is shown that the problem of minimizing the mean-squared error subject to a
threshold-based strategy at the transmitters is quasi-convex. As such, low
complexity, numerical optimization methods can be applied. When coordination
among sensors is not possible, the performance of the optimal threshold
strategy is close to that of a centralized lower bound. The loss due to
decentralization is thoroughly characterized. Local communication among sensors
(using a sparsely connected graph), enables the on-line learning of unknown
parameters of the statistical model. These learned parameters are employed to
compute the desired thresholds locally and autonomously. Consensus-based
strategies are investigated and analyzed for parameter estimation. One strategy
approaches the performance of the decentralized approach with fast convergence
and a second strategy approaches the performance of the centralized approach,
albeit with slower convergence. A hybrid scheme that combines the best of both
approaches is proposed offering a fast convergence and excellent convergent
performance.
