Abstract
We consider the problem of optimal power allocation in a sensor network where the sensors observe a dynamic parameter in noise and coherently amplify and forward their observations to a fusion center (FC). The FC uses the observations in a Kalman filter to track the parameter, and we show how to find the optimal gain and phase of the sensor transmissions under both global and individual power constraints in order to minimize the mean squared error (MSE) of the parameter estimate. For the case of a global power constraint, a closed-form solution can be obtained. A numerical optimization is required for individual power constraints, but the problem can be relaxed to a semidefinite programming problem (SDP), and we show that the optimal result can be constructed from the SDP solution. We also study the dual problem of minimizing global and individual power consumption under a constraint on the MSE. As before, a closed-form solution can be found when minimizing total power, while the optimal solution is constructed from the output of an SDP when minimizing the maximum individual sensor power. For purposes of comparison, we derive an exact expression for the outage probability on the MSE for equal-power transmission, which can serve as an upper bound for the case of optimal power control. Finally, we present the results of several simulations to show that the use of optimal power control provides a significant reduction in either MSE or transmit power compared with a non-optimized approach (i.e., equal power transmission).
Highlights
3) We show how to find the optimal transmission gains that minimize the mean squared error (MSE) under individual sensor power constraints by relaxing the problem to a semidefinite programming (SDP) problem, and proving that the optimal solution can be constructed from the semidefinite programming problem (SDP) solution
We considered the problem of optimally allocating power in an analog sensor network attempting to track a dynamic parameter via a coherent multiple access channel
We analyzed problems with either constraints on power or constraints on achieved MSE, and we examined cases involving global sum and individual sensor power constraints
Summary
I N a distributed analog amplify-and-forward sensor network, the sensor nodes multiply their noisy observations by a complex factor and transmit the result to a fusion center (FC). We focus on tracking a dynamic parameter in a coherent MAC setting. Most prior work on estimation in distributed amplify-and-forward sensor networks has focused on the situation where the parameter(s) of interest are time-invariant, and either deterministic or i.i.d. Gaussian. The case of an orthogonal MAC, where the FC has access to the individual signals from each sensor, has been studied in [4]–[10]. In [15], both the orthogonal and coherent MAC were considered and two kinds of optimization problems were formulated: MSE minimization under a global sum transmit power constraint, and sum power minimization problem under an MSE constraint. The problem of minimizing the MSE outage probability for the orthogonal MAC with a sum power constraint was studied separately in [16]
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