On the LoRa Modulation for IoT: Optimal Preamble Detection and Its Performance Analysis

This article investigates the problem of preamble detection for the long-range (LoRa) modulation and analyzes its performance. For analysis, the inevitable multiuser interference is reasonably modeled as correlated noise. First, the optimal preamble detector is derived and the best preamble is designed to maximize the detection probability while achieving a target value of the false alarm rate. To reduce the required computational complexity and to gain more insights, the preamble detection problem is further investigated for two important special scenarios with: 1) a large spreading factor (SF) and 2) uncorrelated noise, respectively. The analysis is then extended to the case in the presence of phase offset. Our work reveals that the existing preamble detection methods are strictly suboptimal. In addition, various useful and interesting engineering insights into preamble detection with LoRa modulation are provided from the derived results, and the theoretical performance limit of the preamble detection with LoRa modulation is quantified. Extensive numerical results demonstrate the effectiveness and superiority of the proposed scheme. Particularly, the proposed scheme outperforms the existing schemes by more than 10 dB in terms of signal-to-noise ratio (SNR) at the detection probability of 80% and the target false alarm rate of 10%.