To Sort or Not to Sort: Optimal Sensor Scheduling for Successive Compress-and-Estimate Encoding

In this paper, we address the problem of energy-efficient decentralized parameter estimation with wireless sensor networks (WSN). More precisely, we adopt the so-called compress & estimate successive encoding scheme and we analyze the impact of the ordering in which the sensor transmissions are scheduled on the resulting estimation accuracy. We consider two scenarios of interest: (i) sensors experiencing different channel gains to the FC (e.g. due to Rayleigh fading); and (ii) sensors with different observation qualities. For each scenario, we determine the optimal and worst-case scheduling orders for an arbitrary number of sensors. Besides, we propose a suboptimal yet efficient scheduling rule suitable for the case in which sensors experience both different channel gains and observation qualities. Performance assessment is carried out by means of computer simulations where we check how sensitive performance can be to the ordering for a varying number of sensors, transmit power and correlation among observations.