Optimal reconstruction of Gauss Markov field in large sensor networks

We consider the problem of reconstructing a one-dimensional Gauss Markov field measured by a large-scale sensor network. Two data retrieval strategies are considered: the scheduling that collects data from equally spaced sensors locations and random access. Assuming the sensors in the field form a Poisson field with density ρ, we examine the reconstruction performance of the signal field based on the data retrieved under the two strategies. Our comparison shows that, the performance under the optimal scheduling is sensitive to the outage probability P_out of sensors in a given region. If P_out is large than the threshold, the performance of scheduling suffers from missing data samples, and simple random access outperforms optimal scheduling.