# A New LoRa-like Transceiver Suited for LEO Satellite Communications +
## 4 Results and Discussion
### Evaluating the Proposed Receiver with LEO Satellite Communication
#### 4.3.2 Decoding Performance of the Proposed Receiver  
After evaluating the performance of our receiver to estimate the parameters needed to perform an accurate synchronization, we present in Figure 10, a comparison of the decoding performance of our receiver and a classic LoRa one as function of the static CFO (i.e., without the DR) with a \(CR=1\). The FEC with \(CR=1\) only allows detecting the presence of errors and does not correct them. We used a \(CR>1\) in the upcoming simulations in order to reduce the impact of off-by-one demodulation errors caused by the residual fractional offsets, especially the DR. In this figure, we represent the PER with a number of transmitted packets equal to \(10^{4}\) and SNR equal to \(-5\) dB. This simulation confirms the constraint of a maximum allowed CFO of \(\frac{B}{4}\) for LoRa receivers, which is not the case when adopting our approach. In Figure 6, we compare the robustness of DCSS and CSS waveforms against the DR under the AWGN channel. In Figure 11, we propose the same comparison test between our DCSS receiver and CSS one, as described in [27], in the presence of the STO and CFO, but without compensating the DR. In this simulation, we used the configuration (\(SF=9\), \(B=\frac{B_{ref}}{2^{3}}\)), which has the same robustness to the DR as (\(SF=12\), \(B=B_{ref}\)). We notice in this figure that the CSS receiver is very sensitive to the Doppler variation since, for a DR = 10 Hz/s, an almost constant PER of 0.5 is obtained for SNRs greater than \(-13\) dB. On the other hand, the DCSS receiver maintains an acceptable decoding performance for DR values lower than 70 Hz/s. For instance, for a PER = \(10^{-3}\), our receiver has a loss of SNR of only 2.5 dB with a DR = 70 Hz/s compared to the perfect synchronization case. These results are consistent with those in Figure 6. However, we notice that the robustness of both receivers to DR in the presence of the CFO and the STO are lower than the perfect synchronization case as presented in Figure 6, since an uncompensated DR would affect the estimation of the latter desynchronization parameters. Figure 10: PER of CSS and DCSS receivers as functions of the CFO, with \(SF=7\), \(\text{SNR}=-5\) dB, \(B=B_{ref}\) and \(CR=1\). Figure 12 states the results of PER of our proposed receiver as a function of the SNR for all \(SF\)s. We consider the worst case of DR and the maximum of payload size with each \(SF\) as defined by the LoRaWAN standard in [33]. Thanks to the accuracy of our synchronization algorithm and the robustness of the DCSS technique to CFO and some STO values, we notice in Figure 12 that the decoding performance of our receiver is slightly degraded compared to the perfect synchronization case. It can be seen that PER is slightly increased for the lowest bin separation \(\Delta_{b}\) (i.e., slowest data rates, \(SF\in\{10,11,12\}\)). This result is explained by a higher sensitivity of the latter \(SF\)s to the time-varying Doppler shift and the fractional CFO. We also notice that the performance degradation, compared to the perfect synchronization case of the configuration \(SF=12\) and \(B=B_{ref}\), is almost the same than \(SF=7\) and \(B=\frac{B_{ref}}{2^{8}}\), since they have the same bin separations. It should also be noted that these two configurations have the same link budgets. Finally, in Figure 13 we present the SNR evolution of an uplink line of sight communication between the Eutelsat satellite and a terminal in its field of view (FoV) as a function of time. We also show the elevation angle from the terminal to the satellite during the visibility window [34]. Let \(d_{u}(t)\) be the distance between the satellite and the user device, which depends on the elevation angle of the satellite during its window of visibility. The SNR acquisitions, as shown in the latter figure and (34), are obtained by considering an omnidirectional transmitter antenna having a gain \(G_{Tx}=0\) dBi, a directional receiver antenna with a gain \(G_{Rx}=8\) dBi, and a polarization mismatch \(L_{P}=-3\) dB. \[