# Hybrid Chirp Signal Design for Improved Long-Range (LoRa) Communications
## 1 Introduction  
The Internet of Things (IoT) has become the key technology to connect the physical world with the cyber world. The IoT now connects billions of devices embedded into the physical world to the Internet and allows us to share the data generated by them. Low-power wide-area (LPWA) technologies are one of the key machine-type communications (MTC) technologies enabling IoT networks with low energy consumption and reasonable reliability. In recent years, a number of LPWA network (LPWAN) technologies have been proposed, including Sigfox, Narrow-Band IoT (NB-IoT), and LoRa, to name a few [1]. Of them, LoRa has attracted much attention because of its openness and flexibility, which has led to exceptional commercial growth of LoRa-based offerings among the evolving LPWANs [2]. Furthermore, LoRa offers several benefits over conventional communication schemes thanks to its chirp spread spectrum modulation technique, which includes a constant signal envelope, energy-efficient long-range communication, robustness against narrow-band interference, and Doppler effect [3]. Despite its advantages, interference poses a significant problem for LoRa modulation, as it uses ISM bands; a number of other wireless technologies share the same spectrum [4]. In this light, the co-existence of both LoRaWAN or other LPWA networks has been studied extensively in recent years. For example, coded [5] or independent [6] message replications through time diversity have been proposed for both LoRaWAN or other LPWA networks. The co-existence of LoRa with Sigfox and IEEE 802.15.4 g has also been studied in [7, 8], respectively. Since LoRa is popular technology, multiple independent LoRa networks are expected to be used in close vicinity. Therefore, LoRa signals are also vulnerable to the same spreading factor interference, particularly for large-scale LoRa IoT deployments. The demodulation of LoRa under such a condition (known as capture effect) has been analyzed with mathematical models in [9]. Spreading factor allocation strategies have been used to enhance LoRa capacity in [10]. The physical layer of LoRa has been modeled mathematically in [11], while a closed-form approximation of LoRa modulation BER performance is presented in [7]. Despite significant efforts towards mitigating noise/interference effects on LoRa-based systems, interference still poses a significant problem for LoRa modulation. The technical reason behind the noise/interference in the LoRa modulation scheme is it uses either up-or down-chirp as a basis to encode data in a cyclic manner, where a chirp is divided into two sub-chirps (Figure 1). As a result, when the symbol value (\(k\)) increases, the bandwidth of the first sub-chirp decreases (Figure 1). In this situation, when demodulation is performed, the strength of the demodulated signal becomes weaker [12]. Therefore, in the presence of the interference/noise, a false peak is detected. A detailed description of LoRa demodulation is given in Section 2. In this paper, we propose a modulation scheme for LoRa communication based on joint up- and down-chirps to solve this problem. The proposed system is inspired by the ultrasonic indoor positioning systems proposed in [12, 13], which demonstrated that a system that uses both up- and down-chirps at the same time is more resilient against noise/interference. The advantage of the proposed modulation scheme is that the bandwidth of the sub-chirps within a chirp does not reduce significantly with a higher symbol value (e.g., Figure 2d) compared to the conventional design (e.g., Figure 1d). To demodulate symbols in the proposed scheme, we propose a fast Fourier transform (FFT)-based demodulation scheme and develop a hybrid demodulation scheme for further enhancing the demodulation performance. We show that the proposed scheme significantly outperforms the conventional LoRa modulation scheme with and without interference scenarios.