  This two-part paper presents a feedback-based cross-layer framework for
distributed sensing and estimation of a dynamic process by a wireless sensor
network (WSN). Sensor nodes wirelessly communicate measurements to the fusion
center (FC). Cross-layer factors such as packet collisions and the
sensing-transmission costs are considered. Each SN adapts its
sensing-transmission action based on its own local observation quality and the
estimation quality feedback from the FC under cost constraints for each SN. In
this first part, the optimization complexity is reduced by exploiting the
statistical symmetry and large network approximation of the WSN. Structural
properties of the optimal policy are derived for a coordinated and a
decentralized scheme. It is proved that a dense WSN provides sensing diversity,
so that only a few SNs with the best local observation quality need to be
activated, despite the fluctuations of the WSN. The optimal policy dictates
that, when the estimation quality is poor, only the best SNs activate,
otherwise all SNs remain idle to preserve energy. The costs of coordination and
feedback are evaluated, revealing the scalability of the decentralized scheme
to large WSNs, at the cost of performance degradation. Simulation results
demonstrate cost savings from 30% to 70% over a non-adaptive scheme, and
significant gains over a previously proposed estimator which does not consider
these cross-layer factors.
