Optimal One-Shot Detection of Preambles with Frequency Offset

Unidirectional low power wide area network (LP-WAN) transmissions originating from energy-constrained sensor nodes can only be detected once at the receiver or the transmitted information is lost forever. The usually low-budget transmitters are not synchronized with the receiver and have a significant frequency offset. Hence, we design an optimal detector that maximizes the probability of detection with a hypothesis testing approach using a likelihood ratio test (LRT). The theoretically optimal detector is simulated but not implementable. For practical applications, we present approximated detectors, which are very close to the ideal performance.