Asymptotically consistent one-bit detection in large sensor networks

Consider a wireless sensor network where n remote nodes deliver observed data to a common fusion center. A recent work by Blum and Sadler [1] proves that, by means of an ordered transmission policy, optimal detection performance is achieved when only a subset of the n samples has been received at the fusion center. Here we show that, when the network size n is made large enough, arbitrarily small detection errors can be achieved with a fusion center receiving just the first sample out of n: One-bit detection can be asymptotically consistent. In our scheme the “winner takes all”: the network global decision is the local decision of the first firing sensor, and key is the sample selection criterion — ordered transmissions — where more informative observations are delivered first.