Detection of Gauss-Markov Random Fields under Routing Energy Constraint

The problem of maximizing detection performance subject to an energy constraint is analyzed in an asymptotic setting. The correlation between the sensor measurements is incorporated through the Gauss-Markov random field with Euclidean nearest-neighbor dependency graph. An average energy constraint is imposed on a routing scheme with an approximation factor of two, and the resulting Neyman-Pearson error exponent is optimized with respect to the density of the deployed sensors. It is shown that the behavior of this optimal density crucially depends on the ratio between the measurement variances under the two hypotheses and displays a threshold behavior. Below the threshold value of the variance ratio, the optimal density tends towards infinity for any feasible energy constraint. On the other hand, when the variance ratio is above the threshold, the optimal density is characterized by the energy constraint. Index Terms — detection, Gauss-Markov random fields, Routing, error exponent.

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