Linear Estimation of Correlated Vector Sources for Wireless Sensor Networks with Fusion Center

Abstract

In this letter, we consider decentralized estimation of unknown random vectors by using wireless sensors and a fusion center (FC). We adopt a linear model for decentralized estimation of vector sources where both observation models and sensor operations are linear and the multiple access channel (MAC) is coherent. Each sensor observes a different vector source, where vector sources can be correlated. Sensors are designed to minimize the total mean square error (MSE) at the fusion center subject to transmit power constraints at the sensors. While a closed form solution cannot be found, an iterative algorithm is proposed. Simulations are provided to verify the analysis and present the performance of the proposed scheme.

High SNR Linear Estimation of Vector Sources

“…In this letter, we extend our prior work provided in [1] to specifically consider the high SNR regime. We adopt the linear model in [1] and [3] where observation models and sensor operations are both linear.…”

“…We adopt the linear model in [1] and [3] where observation models and sensor operations are both linear. The channel between the sensors and fusion center (FC) is a coherent multiple access channel (MAC).…”

“…The transmitted signals from all sensors will reach the FC coherently under the assumption of perfect synchronization between sensors and the FC. We consider a network with vector sources where each sensor can have several observations of a different vector source [1]. Furthermore, a general channel with intersymbol interference (ISI) is considered, i.e., there is ISI between the transmission of different sensors to the FC that is equipped with multiple antennas.…”

“…Furthermore, a general channel with intersymbol interference (ISI) is considered, i.e., there is ISI between the transmission of different sensors to the FC that is equipped with multiple antennas. The design targets to minimize the total [1]. Note that the solution provided in [1] is a general solution of the problem and provides optimum solution for all ranges of SNRs.…”

“…The design targets to minimize the total [1]. Note that the solution provided in [1] is a general solution of the problem and provides optimum solution for all ranges of SNRs. Notation: We use bold lower case for vectors, while bold capital letters are used for matrices.…”