In this paper, we consider a wireless sensor network that consists of a group of sensor nodes estimating multiple independent LTI systems. Each point-to-point link between the sensor nodes is a slow frequency-flat fading channel and the states of the channel are described by a finite-state Markov channel (FSMC) model. We propose a transmission schedule of the sensors such that the overall estimation error at the remote estimator is minimized. Furthermore, we present an event-based routing scheme with respect to channel state, i.e., online routing among the selected sensors to ensure the zero outage-probability at a constant transmission rate with the least transmission energy. Using channel inversion, we separate the sensor scheduling and routing as two independent steps. Simulation results for a simple wireless sensor network is presented to compare the energy cost with and without event-based routing.