The Effect of Correlated Observations on the Performance of Distributed Estimation

Abstract

Estimating unknown signal in Wireless Sensor Networks (WSNs) requires sensor nodes to transmit their observations of the signal over a multiple access channel to a Fusion Center (FC). The FC uses the received observations, which is corrupted by observation noise and both channel fading and noise, to find the minimum Mean Square Error (MSE) estimate of the signal. In this paper, we investigate the effect of the source-node correlation (the correlation between sensor node observations and the source signal) and the inter-node correlation (the correlation between sensor node observations) on the performance of the Linear Minimum Mean Square Error (LMMSE) estimator for three correlation models in the presence of channel fading. First, we investigate the asymptotic behavior of the achieved distortion (i.e., MSE) resulting from both the observation and channel noise in a non-fading channel. Then, the effect of channel fading is considered and the corresponding distortion outage probability, the probability that the distortion exceeds a certain value, is found. By representing the distortion as a ratio of indefinite quadratic forms, a closed-form expression is derived for the outage probability that shows its dependency on the correlation. Finally, the new representation of the outage probability allows us to propose an iterative solution for the power allocation problem to minimize the outage probability under total and individual power constraints. Numerical simulations are provided to verify our analytic results.

A Peak Synchronization Measure for Multiple Signals

“…Intuitively, synchronization should give us a measure of interdependence or similarity between two signals. This has been studied by different methods for different applications such as amplitude correlation [6], mutual information [7], phase synchronization [8], [9] etc. One common trend across all these methods is to determine mutual dependence based on one particular feature uniformly across a segment of signals.…”

“…Low value is desirable. 6 6.90% Number of seizures for which peak synchronization postseizure is more than during seizure.…”

Distributed Vector Estimation for Power- and Bandwidth-Constrained Wireless Sensor Networks

“…They are similar to (17) and (18), with the difference that D a is replaced by is a decreasing function of P k s and P tot (see Appendix X-B). Therefore, solving (SP3) for P k s, we find that…”

“…In contrast, when γ j < γ i < eλ * α , then P i > P j (water filling). • Solving (SP2) Given in (18): Finding a closed-form solution for this problem remains elusive due to the non-linearity of the cost function and the fact that the inequality constraint on L k s is not necessarily active. Let F = {L k : K k=1 L k ≤ B tot , L k ∈ R + , ∀k} be the feasible set of (SP2).…”

“…We note that [12]- [14] do not include a total bit constraint in their problem formulations. There is a collection of elegant results on energy efficient distributed parameter estimation with analog transmission, also known as Amplify-and-Forward (AF), examples are [15]- [19]. However, the problem formulations in these works naturally cannot have a bandwidth constraint.…”