On the Optimal Precoding for MISO-WSN: One Time Slot Detection of Multiple Binary Data on the Same Frequency Band

A fast multi-target detection technique-using a devised precoding in a wireless sensor network (WSN)-is proposed. The targets are detected by binary wireless sensors which only have one or zero logical outputs, indicating a target's presence or absence. The goal is to simultaneously decode all sensors' data in one time slot at the receiver node, where all sensors transmit data simultaneously on the same frequency band. For this to happen, a specific geometric deployment of the sensors is presented in the paper. The concept in this work might have similarities to the bijective mappings in the superposition modulation. Different channel gains and the additive white Gaussian noise are included in the model. The system model is described in detail and the communication scheme to fulfill a simultaneous decoding is mathematically formulated. Then, the parametric solutions to this general digital modulation problem are studied step by step through several theorems, and the optimal solutions that minimize the detection error are found. The combined effects of the noise and the non-perfect channel state information on the signal constellations are both analytically and numerically investigated. In addition, two other detection scenarios with a priori information about the targets are studied.