# A New LoRa-like Transceiver Suited for LEO Satellite Communications +
###### Abstract
The presence of carrier frequency offset (CFO) causes a shift of all the Fourier transform peaks of a sequence of symbols to the right or the left of the desired frequency peak locations. 2. A sampling time offset (STO) causes the emergence of two main shifted peaks in the spectrum, which lead to inter-symbol interference (ISI). Based on these, accurate time and frequency synchronization are mandatory to achieve the theoretical sensitivity claims when using LoRa modulation [15]. Synchronization errors are some of the most important issues in IoT networks, especially when considering LEO satellite communication in unlicensed bands, due the random access to the radio channel, the low-cost local oscillators of connected devices, and the Doppler effects. Hence, to perform LoRa-like communications with LEO satellites, a sophisticated synchronization algorithm should be deployed. In the literature, LoRa has been extensively studied in many aspects. For instance, several works [16; 17; 18] provided detailed studies on the capacity of the latter technology to cope with the requirements of LPWAN ground-based communications, such as the long range, low energy consumption, and interference resilience. However, few papers have addressed the issue of synchronization, especially the Doppler effect, when considering LEO satellites communications. For instance, authors in [19; 14], propose to estimate the time and frequency offsets using a system of two equations produced by the estimation of the up-chirp symbols of the preamble and the down-chirp symbols of the SFD. However,this system could be solved only if the CFO is lower than \(\frac{B}{4}\)[20], where \(B\) is the bandwidth of the chirped signal. This maximum CFO estimable could be exceeded in the context of the LEO satellite, as we do with the practical values in Section 4. In addition, due to the sensitivity of chirp spread spectrum (CSS) signals to time and frequency synchronization errors, the CFO and the STO parameter estimations must be very precise and tracking algorithms have to be deployed as proposed by [14]. To overcome the latter constraint, we proposed in [21] a novel synchronization approach associated to the well-known technique referred to as differential CSS (DCSS), but we did not deal with Doppler time variation. Furthermore, in the case of a time varying CFO, authors in [22] propose an algorithm to estimate the Doppler variation using the LoRa preamble. However, this method has a high complexity and cannot maintain its robustness for long packets size. In fact, this estimation is not perfect and, thus, a remaining Doppler variation can shift the symbols along the frame, which would significantly impact the decoding process especially of the lowest data rates. Moreover, the CSS modulation has been modified in [23] as symmetric CSS (SCSS) to ensure higher robustness against destructive collision. This modification is performed to make CSS more suitable to LEO satellite communication since the probability of collision would increase given the huge surface covered by the latter satellites. However, in this study the influence of CFO is ignored. To that end, the same authors propose in [24] the asymmetry CSS (ACSS). This approach offers better performance compared to CSS and SCSS in the presence of interfering signals. Nevertheless, the latter two works did not deal with the Doppler shift variable in time, which is the case for LEO satellite communications. In the industrial field, Semtech recently developed the specification of her new physical layer long range frequency hopping spread spectrum (LR-FHSS) [25] to increase the capacity of LoRaWAN in dense and congested deployments. It has also been designed to support extremely long-range and large-scale communication scenarios, with a focus on reaching gateway devices installed on LEO satellites. In this paper, we propose a novel algorithm to deal with the time and frequency desynchronization that impact the decoding process of LoRa-like signals in the context of LEO satellite communication.