Optimized Distributed Detection over a Two Sensor Binary Gaussian MAC Network

We consider a distributed detection system where two noisy sensors transmit a binary source over a Gaussian multiple access channel (MAC). We derive the constellation designs for the sensors which minimizes the system error probability under individual power constraints. Three distinct cases arise from this optimization, where in the most notable case (Case III), one of the sensors should not necessarily use all of its allocated power, hence enabling savings that can prolong the sensor’s battery life.