Investigating the Robustness of Detection vis-à-vis the Detector Threshold in WSN with Fading MAC and Differing Sensor SNRs – Optimal Sensor Gains vs. Uniform Sensor Gains

摘要

In Wireless Sensor Networks, if the Multiple Access Channel between distributed sensors and multiple antennas is fading and the envelope of the channel gain distribution is unknown and time-varying, fusion at the antennas is usually incoherent. Often, the overall sensor power is upper bounded by a constraint on the onboard battery power. Then, the optimal sensor power allocation scheme which minimizes the probability of missed detection is known to outperform uniform sensor power allocation scheme. Further, if the observation signal-to-noise ratios at the sensors are non-identical, optimizing the probability of detection must take into account the combined effect of the differing sensor signal-to-noise ratios and the fading nature of the channel as seen by the sensors. Neyman-Pearson formulation of this problem sets out by setting an upper bound on the permissible probability of false alarm. Consequently, the detector threshold is governed by the power allocation scheme – uniform or optimal. We examine here the inter-dependencies between the probability of false alarm, the probability of detection and the detector threshold. We demonstrate that for robust detection vis-à-vis variations in detector threshold, there is an additional compelling case for optimal power allocation over uniform power allocation.