On the Optimal Performance in Asymmetric Gaussian Wireless Sensor Networks With Fading

We study the estimation of a Gaussian source by a Gaussian wireless sensor network (WSN) where distributed sensors transmit noisy observations of the source through a fading Gaussian multiple access channel to a fusion center. In a recent work Gastpar, ["Uncoded transmission is exactly optimal for a Simple Gaussian Sensor Network," IEEE Trans. Inf. Theory, vol. 54, no. 11, pp. 5247-5251, Nov. 2008] showed that for a symmetric Gaussian WSN with no fading, uncoded (analog) transmission achieves the optimal performance theoretically attainable (OPTA). In this correspondence, we consider an asymmetric fading WSN in which the sensors have differing noise and transmission powers. We first present lower and upper bounds on the system's OPTA under random fading. We next focus on asymmetric networks with deterministic fading. By comparing the obtained lower and upper OPTA bounds under deterministic fading, we provide a sufficient condition for the optimality of the uncoded transmission scheme for a given power tuple P = (P-1, P-2, ... , P-L). Then, allowing the sensor powers to vary under a weighted sum constraint (this includes the sum-power constraint as a special case), we obtain a sufficient condition for the optimality of uncoded transmission and provide the system's corresponding OPTA.