Power Efficient Analog Forwarding for Correlated Data Fusion in Wireless Sensor Networks

In this paper we consider the problem of optimal power allocation for fusion of a deterministic signal in an inhomogeneous wireless sensor network (WSN) with correlated observations. We assume that each distributed node performs analog-relay amplifier local processing on its observation and transmits locally processed data to the fusion center over a wireless channel. We also assume that the channel between the fusion center and sensors undergoes fading and the fading coefficients are assumed to be known to the transmitter. We derive exact fusion error probability and an easy to optimize upper bound for the fusion error probability that is valid for sufficiently small correlations. The transmit power is allocated to sensor nodes to keep the fusion error probability bound under a required threshold while minimizing the total power spent by the network. It is shown that the optimal scheme inactivates the sensor nodes with poor observation quality and low fading coefficients. For the remaining active sensors the transmit power is determined by the individual channel gains, local observation quality, required fusion error probability bound and the correlation coefficient. From numerical results we see that this optimal scheme has a significant gain over the uniform power allocation scheme when either local observations are good or the number of sensors is large and the correlation coefficient is sufficiently small. It is also shown that the optimal power allocation scheme can be implemented distributively with a minimal feedback from the fusion center.