  We consider the problem of communication allocation for remote state
estimation in a cognitive radio sensor network~(CRSN). A sensor collects
measurements of a physical plant, and transmits the data to a remote estimator
as a secondary user (SU) in the shared network. The existence of the primal
users (PUs) brings exogenous uncertainties into the transmission scheduling
process, and how to design an event-based scheduling scheme considering these
uncertainties has not been addressed in the literature. In this work, we start
from the formulation of a discrete-time remote estimation process in the CRSN,
and then analyze the hidden information contained in the absence of data
transmission. In order to achieve a better tradeoff between estimation
performance and communication consumption, we propose both open-loop and
closed-loop schedules using the hidden information under a Bayesian setting.
The open-loop schedule does not rely on any feedback signal but only works for
stable plants. For unstable plants, a closed-loop schedule is designed based on
feedback signals. The parameter design problems in both schedules are
efficiently solved by convex programming. Numerical simulations are included to
illustrate the theoretical results.
