A comparison of methods for detecting preambles with frequency offset at low SNR

Low power wide area network (LPWAN) receivers must first decide about the presence of a transmission in order to retrieve the information that was being sent by wireless sensor nodes. This is exacerbated by the use of modern coding techniques that are able operate at very low signal to noise ratio (SNR), and inaccuracies originating from the transmitter hardware. Several, mostly low complexity methods of detecting preambles with frequency offset are investigated regarding their detection performance and computational intricacy. This is done in a likelihood ratio testing framework with a fixed probability of false alarm, maximizing the probability of detection. The receiver operating characteristic (ROC) of each detector is evaluated using analytical or numerical methods. Coherent and noncoherent addition of the received symbols is considered. Advice for various application scenarios is provided, stressing on low SNR and low complexity receivers.