Optimal Power Allocation over a Fading MAC with Varying Observation SNRS in Resource Constrained Wireless Sensor Network

In a distributed multiple sensor multiple antenna setup, transmission over a fading multiple access channel results in incoherent fusion of sensor observation. With an overall sensor power constraint, uniform power allocation (PA) over the sensors is optimal when the channel between the sensors and the fusion center (FC) is Additive White Gaussian Noise (AWGN). However, with varying observation signal-to-noise ratios (SNR) at the sensors, uniform PA is not optimal even with AWGN channel. In this paper, we consider imperfect communication between the sensors and the FC and correlated noise at the sensors. We propose a joint power optimization scheme that maximizes the probability of detection (PD) at the FC, subject to an overall power constraint. Also, we derive a closed form expression for the optimization problem when the channel is AWGN. We verify the performance of our algorithm by conducting numerical experiments. We show that the maximum power is allocated to a sensor which is operating with the best SNR and channel condition. We further show that with optimal PA, we never unduly drain our on-board sensor energy and hence extend the battery life without compromising on the PD. Finally, we show that with optimal PA, the total system power requirement is brought down to nearly 10% of that with uniform PA, even when achieving the same PD.