Efficient Calculation of Sensor Utility and Sensor Removal in Wireless Sensor Networks for Adaptive Signal Estimation and Beamforming

Abstract

Wireless sensor networks are often deployed over a large area of interest and therefore the quality of the sensor signals may vary significantly across the different sensors. In this case, it is useful to have a measure for the importance or the so-called “utility” of each sensor, e.g., for sensor subset selection, resource allocation or topology selection. In this paper, we consider the efficient calculation of sensor utility measures for four different signal estimation or beamforming algorithms in an adaptive context. We use the definition of sensor utility as the increase in cost (e.g., mean-squared error) when the sensor is removed from the estimation procedure. Since each possible sensor removal corresponds to a new estimation problem (involving less sensors), calculating the sensor utilities would require a continuous updating of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> different signal estimators (where <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> is the number of sensors), increasing computational complexity and memory usage by a factor <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> . However, we derive formulas to efficiently calculate all sensor utilities with hardly any increase in memory usage and computational complexity compared to the signal estimation algorithm already in place. When applied in adaptive signal estimation algorithms, this allows for on-line tracking of all the sensor utilities at almost no additional cost. Furthermore, we derive efficient formulas for sensor removal, i.e., for updating the signal estimator coefficients when a sensor is removed, e.g., due to a failure in the wireless link or when its utility is too low. We provide a complexity evaluation of the derived formulas, and demonstrate the significant reduction in computational complexity compared to straightforward implementations.