First Flight-Testing of LoRa Modulation in Satellite Radio Communications in Low-Earth Orbit

At present, the use of LoRa modulation in satellite radio communications and the construction of a CubeSat constellation for the satellite Internet of Things based on LoRa technology has already begun. However, the limits of applicability of LoRa modulation in low-Earth orbits have not yet been established. This paper presents the results of the first flight tests of LoRa modulation for robustness against the Doppler effect in the satellite-to-Earth radio channel, carried out using a NORBY CubeSat operating at 560 km. Flight tests confirmed the very high immunity of LoRa modulation to the Doppler effect for modes with spreading factor SF ≤ 11 and spread spectrum modulation bandwidth BW > 31.25 kHz. LoRa modulation in these modes can be used in satellite communication without any limitations caused by the Doppler effect. For BW = 31.25 kHz, the LoRa radio channel is affected by the static Doppler effect. Communication with the satellite is possible in this case only at high elevation angles. For SF = 12, the dynamic Doppler effect becomes significant, and communication is possible only at low satellite elevation angles, which leads to the formation of a “hole” in the center of the coverage area directly below the satellite. In both cases, the duration of the communication session is significantly reduced because of the Doppler effect. In the case of SF = 11 and 12 at BW = 31.25 kHz, both static and dynamic Doppler effect catastrophically affect the LoRa radio channel, so that communication with the satellite becomes impossible.

modulation directly in the satellite-to-Earth radio channel 97 have not yet been carried out. 98 In this paper, we present the results of the first flight tests 99 of LoRa modulation for robustness against the Doppler effect 100 in a satellite-to-Earth radio channel. Onboard experiments 101 were carried out using the NORBY CubeSat operating in 102 a low-Earth orbit [23]. The main purpose of the onboard 103 experiments was to verify the results of our laboratory studies 104 of LoRa modulation [13] and to determine the limits of appli-105 cability of LoRa modulation in satellite radio communica-106 tions in low Earth orbits. Particular attention in the conducted 107 experiments was given to LoRa modulation modes with 108 BW < 125 kHz, which have not been tested in the laboratory. 109 An important goal of the experiments was to detect, under 110 real conditions, the effect of radio communication disruption 111 predicted in [13] owing to the dynamic Doppler effect when 112 the satellite passes directly over the ground station. 113 The remainder of this paper is organized as follows. 114 Section 2 describes the methodology of on-orbit experiments. 115 The results of the experiments are presented in Section 3. 116 A summary of the results and conclusions are provided in 117 Section 4. 119 A. NORBY CubeSat 120 Nanosatellite NORBY is a 6U CubeSat designed for flight 121 tests of a new CubeSat-compatible platform developed by 122 Novosibirsk State University [23]. NORBY also carries a 123 payload for the registration of gamma rays and charged parti-124 cles as well as for testing SpaceFibre/SpaceWire technology. 125 The LoRa transmitter, which is part of the onboard radio 126 system, is essentially a payload for on-orbit studies of LoRa 127 modulation in satellite radio communication. 128 The NORBY CubeSat was successfully launched 129 on 28 September 2020 by a Soyuz-2.1b carrier rocket from 130 the Plesetsk cosmodrome into a near-polar orbit with an 131 inclination of 97.7 • , apogee of approximately 579 km, and 132 perigee of 545 km. 133 VOLUME 10, 2022 For more than a year, telemetry and data from NORBY 154 payloads have been successfully delivered to the ground 155 station via the LoRa radio channel, and control commands 156 have been transmitted from the ground station to NORBY. 157 The LoRa radio channel is also used to upload software to 158 NORBY for in-orbit software updates, which are required 159 when debugging on-board subsystems. 160 In accordance with the adopted concept of complete hard-161 ware redundancy of subsystems, NORBY has two identical 162 onboard radio systems. Only one of them can operate at any 163 given time. If the active BRC fails, it is switched off, and the 164 second BRC is switched on. Active BRC can also be selected 165 by commands from the ground station. 166 The NORBY on-board radio complex operates in the UHF 167 band at a frequency of 436.7 MHz. It should be noted that 168 NORBY CubeSat was not created to demonstrate any tech-169 nologies for satellite IoT, and its on-board radio complex 170 was originally intended to transmit telemetry and data from 171 payloads to the ground control complex. Therefore, the fre-172 quency range most frequently used on CubeSats was chosen 173 for BRC. Already in the process of implementing the project, 174 the idea arose to test LoRa modulation for resistance to the 175 Doppler effect, including with LoRa modulation parameters 176 that are interesting for IoT. And we used a tool that was 177 already ready for this -BRC, although it does not work in 178 the traditional IoT frequency range. We also note that the 179 NORBY-2 project currently being implemented is initially 180 focused on demonstrating and testing the capabilities of LoRa 181 modulation in satellite IoT in the 868 MHz and 2.4 GHz 182 frequency bands. 183 The output power of the BRC transmitter is adjustable in 184 the range of 0.1 to 4 W. At present, the default LoRa modu-185 lation parameters for NORBY radio sessions with the ground 186 station are SF = 10 and BW = 250 kHz, with an emitted BRC 187 transmitter power of 0.2 W. When NORBY is out of range 188 with the ground station, it transmits a beacon signal once per 189 minute containing basic telemetry data regarding the state of 190 NORBY. The beacon is transmitted alternately in the LoRa 191 and GFSK modes at a transmitter output power of 0.2 W. 192 Thus, the LoRa beacon is transmitted only once every two 193 minutes. 194 The antenna of each BRC is a pair of quarter-wave vibra-195 tors located at one of the ends of the satellite body (Fig. 1). 196 The antennas located at different ends of the satellite body are 197 completely identical. During the experiment, only one BRC 198 with its own antenna worked. The second was in reserve. The 199 radiation pattern of the NORBY antenna calculated using the 200 RF Module of COMSOL Multiphysics Simulation Software 201 is shown in Fig. 2. Here, the Z-axis is directed perpendicular 202 to the end face of the satellite body, while the X-and Y-axes 203 are directed perpendicular to the large and small sides of the 204 body, respectively. The radiation pattern was calculated for 205 the antenna with the satellite body including the deployed 206 solar panels. Figure 2 shows that the calculated nonuni-207 formity of the radiation pattern of the NORBY antenna is 208 approximately 7 dB.

209
At the time of LoRa modulation testing, the NORBY atti-210 tude determination and control system was in the debugging 211 stage. All orientation sensors were tested and operational. 212 The magnetic control system was able to slow down the 213 rotation of the satellite to approximately 0.   the satellite. The ground station's steerable antenna system 220 consists of two crossed Yagi-Uda antennas (Fig. 3). The

225
The antenna is driven by a BIG-RAS/HR azimuth and 226 elevation rotator [26]. The Gpredict program [27] is used to 227 point the antenna at the satellite, which allows the real-time 228 tracking of satellites and prediction of the orbit.  culates antenna pointing angles based on a two-line element 230 set (TLE) from the SATCAT catalogue [28]. The NORBY 231 satellite catalog number is 46494.

232
The rotator provides continuous pointing of the antenna 233 to the LEO satellite over the entire range of visibility of 234 the satellite from the ground station. However, when the 235 satellite passes a region close to the zenith, the antenna can-236 not accurately track the satellite due to the known keyhole 237 problem [29], which is inherent in antennas with an azimuth 238 and elevation type tracking mount. To clarify the problem, 239 consider the behavior of the antenna when tracking a satellite 240 flying near the zenith in a circular polar orbit (see Fig. 4). 241 In Figure 4, H is the orbit height, v is the satellite velocity, α 242 is the satellite azimuth, and θ is the satellite elevation angle. 243 If we do not take into account the sphericity of the Earth, then 244 by simple mathematical transformations it is easy to obtain 245 an expression for the azimuth angular velocity of the satellite 246 relative to the antenna ω a : where θ max is the maximum elevation angle of the satellite 249 at the point of the trajectory closest to the antenna at α = 250 90 • . It can be seen from (1) that as θ max approaches 90 • , ω a 251 increases without limit. That is, the antenna, when accurately 252 tracking the satellite near the zenith, must rotate very quickly 253 around the vertical axis. When the satellite approaches the 254 zenith along a trajectory with θ max = 90 • , the antenna in our 255 case is constantly oriented to the south in the horizontal plane, 256 and at the moment the satellite passes the zenith, it should 257 instantly reorient to the north. Naturally, no real antenna can 258 do this, since it takes some time.

259
The bottom panel of Fig. 4 shows ω a in the entire satellite 260 visibility zone calculated using a more accurate numerical 261 model that takes into account the sphericity of the Earth. The 262 calculations were performed for several NORBY trajectories 263 with different θ max . Here and below, it is assumed that the 264 satellite passes the trajectory point closest to the antenna at 265 time t = 0. The red dotted line in Fig. 4 shows the maxi-266 mum angular velocity of the antenna rotation provided by the 267 azimuth rotator. It can be seen from Fig. 4 that near the zenith, 268 when tracking a satellite on trajectories with θ max greater 269 than about 70 • , the azimuth angular velocity of the antenna 270 required for accurate tracking exceeds the angular velocity 271 provided by the antenna rotator. As a result, the antenna lags 272 behind the direction to the satellite. The lag of our antenna 273 can be up to about 37 • causing the satellite leaves the main 274 beam of the antenna. The result is attenuation of the received 275 radio signal, which becomes noticeable at satellite elevation 276 angles greater than 80 • and can reach about 20 dB at angles 277 greater than about 85 • .

278
The considered effect manifests itself at large satellite 279 elevation angles near the zenith. However, it is precisely when 280 the satellite moves in this area that the maximum values of the 281 Doppler rate are reached [13]. That is, possible failures of the 282 LoRa radio channel due to the dynamic Doppler effect are 283 expected primarily in this section of the satellite trajectory. 284 VOLUME 10, 2022

312
It should be noted that because NORBY transmits the 313 LoRa beacon at two-minute intervals, packet transmission 314 begins with an unpredictable delay of up to two minutes 315 after the satellite enters the radio coverage area of the ground 316 station. In cases in which the ground station operator did not 317 manage to send a command in time, this delay is even greater. 318 The main purpose of the experiments was to identify the 319 influence of the Doppler effect on the stability of the satel-320 lite LoRa radio channels. Therefore, during the experiments, 321 LoRa packets were transmitted at the maximum possible 322 power of the BRC transmitter of 4 W to avoid possible 323 radio communication disruptions owing to a weak signal or 324 external noise.

325
The SX1278 transceiver includes a received signal strength 326 indicator (RSSI), signal-to-noise ratio (SNR) meter, and an 327 indicator of the frequency difference between the carrier 328 frequency of the signal at the receiver input and the carrier 329 frequency of the receiver (frequency error, FER) [14]. All of 330 these parameters are recorded when a LoRa packet transmit-331 ted from NORBY is received at a ground station.

341
The data obtained allows us to determine the Doppler 342 frequency shift in the satellite radio channel for each data 343 packet. The Doppler shift can be directly calculated from 344 satellite trajectory data. During the experiment, trajectory 345 data were received from the GLONASS receiver onboard 346 NORBY. In addition, they can be determined from TLE data 347 from the SATCAT catalog [28]. If the transmitter emits a radio 348 signal with frequency F 0 , owing to the Doppler effect, the 349 receiver receives a signal with frequency [13] where v is the satellite velocity, n is the light speed, β is the 352 angle between the satellite velocity vector and the direction 353 to the ground station. Then, the Doppler frequency shift F D 354 can be expressed as shift for both the received and lost packets.

358
An additional contribution to the total frequency offset F 359 between the input signal and carrier frequency of the LoRa 360 receiver also comes from the frequency difference between 361 the reference oscillators of the receiver and transmitter F RT : (4) 363 We don't know of any other reasons that could contribute 364 to F.

375
According to (4), we assume that this difference is due to 376 F RT . This assumption is also confirmed by the observed 377 change in F − F D over time. This means that the observed 2.5 kHz change in the carrier 396 frequency of the transmitter is caused by heating by approx-397 imately 30 • C.

398
In all experiments performed, the absolute value of 399 F − F D did not exceed 2 kHz. This means that the change 400 in the carrier frequency of the received signal from NORBY 401 is mainly due to the Doppler effect. The frequency difference 402 between the reference oscillators of the receiver and transmit-403 ter only makes a small, albeit noticeable, contribution to the 404 total frequency offset.

406
The results of laboratory studies on LoRa modulation have 407 shown that LoRa radio communication with a satellite in 408 low Earth orbit can be disrupted in some cases owing to the 409 dynamic Doppler effect [13]. The maximum absolute value 410 of the Doppler rate is achieved when the satellite passes 411 at the zenith over the ground station (see Fig. 7c). Since 412 possible radio communication disruptions were expected at 413 high Doppler rates, NORBY orbits were chosen for our flight 414 experiments with a maximum satellite elevation above the 415 ground station of more than about 80 • .

416
As noted above, we could not completely stop the rotation 417 of the NORBY CubeSat during the experiments, and orient 418 it in the direction at the ground station. Therefore, during the 419 experiments, NORBY rotated unpredictably, and we ensured 420 that the rotation speed did not exceed a few degrees per 421 second.

422
As an example, Fig. 7 shows the results of experiment 423 No. 1 with LoRa modulation parameters SF = 7 and 424 BW = 500 kHz, at which, according to laboratory experi-425 ments [13], no influence of the Doppler effect was expected. 426 In total, during the radio communication session in this exper-427 iment, 773 packets of size L = 143 bytes were transmit-428 ted from NORBY, of which 748 packets were successfully 429 received by the ground station and 25 packets were lost.

430
The green curves in Figures 7a, 7b, and 7c show the 431 elevation angle, Doppler shift F D , and Doppler rate F D , 432 as NORBY passes over the ground station. The elevation 433 angle and Doppler shift were derived from the TLE data. The 434 Doppler rate is determined by differentiating F D . NORBY 435 was within the radio visibility of the ground station between 436 approximately −370 s and +370 s.

437
The bold blue dots in Figures 7a, 7b, and 7c indicate the 438 elevation angle, Doppler shift, and Doppler rate obtained 439 from the GLONASS receiver data contained in the received 440 packets. Once again, we note that the elevation angle, F D , 441 and F D obtained based on two different initial data prac-442 tically coincide. For lost packets, only the TLE data are 443 available. Therefore, in this case, the elevation angle, F D , 444 and F D were determined from the TLE data and the known 445 time of sending packets from NORBY. The lost packets are 446 marked in Fig. 7 and below with bold red dots.  noted that Fig. 6d shows that the actual non-uniformity of the 461 radiation pattern of the NORBY antenna noticeably exceeds 462 the calculated 7 dB. The weakening of the signal near the 25 th 463 second is due to the delay in pointing the ground antenna near 464 the direction to the zenith. It may also be superimposed by the 465 weakening associated with satellite rotation. 466 Packet loss at low elevation angles before the satellite 467 leaves the radio visibility zone (Fig. 7d) cannot be explained 468 by a weak signal, which remains above the LoRa receiver 469 sensitivity almost to the horizon. However, in Fig. 7e, in the 470 area of these losses, there are reduced SNR values in the form 471 of points that fall outside of the main data array. Such SNR 472 behavior was observed only in some daytime experiments, 473 during which powerful construction equipment was operating 474 in the immediate vicinity (∼30-50 m) of the ground receiving 475 antenna during the construction of a new university building. 476 We attribute these packet losses to electromagnetic interfer-477 ence generated by this technique.

478
For a single lost packet at −89 s (Fig. 7), no external 479 causes were found to explain its loss. More than five thousand 480 packets were transmitted from the NORBY CubeSat for all 481 communication sessions during which the described experi-482 ments were performed. However, only four such cases were 483 recorded, for which no explanation was found for the loss of 484 the transmitted packet.

485
As expected, the experiment showed no influence of the 486 Doppler effect on the satellite-to-ground LoRa radio channel 487 with modulation parameters SF = 7 and BW = 500 kHz.

488
It should be noted that the RSSI and SNR time variations 489 shown in Fig. 7 also contain variations due to propagation 490 loss. The distance between the satellite and the ground station 491 varies from approximately 560 to 2700 km as NORBY moves 492 in orbit from zenith to horizon. In this case, the signal is atten-493 uated by approximately 13.7 dB. The total variations of RSSI 494 in Fig. 7 are significantly larger than this value. In addition, 495 the transmitter power of 4 W during the experiments ensures 496 the signal value at the LoRa receiver input is significantly 497 higher than the receiver sensitivity, as well as the allowable 498 SNR value right up to the horizon. Therefore, the propagation 499 loss does not affect the results of experiments presented in this 500 section and below.

501
It should also be noted that we did not check during the 502 experiments for the presence of any other radio transmit-503 ters operating in the same frequency range near the ground 504 antenna. However, their presence should show up in the SNR 505 data. Neither in the described experiment No. 1, nor in all 506 the others, no signs of the impact of any third-party radio 507 transmitters were recorded.

508
Here, we specifically considered the results of the exper-509 iment with LoRa modulation parameters SF = 7 and BW = 510 500 kHz. The relatively low sensitivity of the LoRa receiver 511 and the relatively low noise immunity in this mode, which 512 was the lowest in the experiments conducted, were the worst 513 for conducting the experiment under non-ideal environmental 514 conditions. The results obtained under these conditions made 515 it possible to illustrate the operability of the equipment used 516 in the experiment and the possibility of an unambiguous 517 interpretation of the data obtained.

519
The main objective of this research is to verify under real 520 space conditions the robustness parameters of LoRa modu-521 lation to the Doppler effect in the satellite-to-ground radio 522 channel given in the SX1278 transceiver specification [14] 523 and obtained in laboratory experiments [13].   the ground station only if they are received without errors. 573 Otherwise, they were considered lost.

574
It should also be noted that the LowDataRateOpti-575 mize LoRa modulation parameter was activated during the 576 experiments.

582
Experiments for SF = 7 were performed for all selected 583 values of BW. This is a reference series of experiments 584 in which it is expected to register the influence of the 585 static Doppler effect in accordance with the LoRa SX1278 586 transceiver specification [14]. However, in these experiments, 587 it is not expected to detect any influence on the LoRa radio 588 channel of the dynamic Doppler effect [13]. The main objec-589 tives of these experiments are to verify the specifications 590 of the LoRa SX1278 transceiver [14] regarding immunity 591 to Doppler shift and to confirm the robustness of LoRa 592 modulation against the dynamic Doppler effect in NORBY 593 orbit in accordance with laboratory studies [13]. Special 594 experiments with BW = 250 kHz were not carried out, 595 since in numerous daily radio sessions of NORBY with the 596 ground station at SF = 10 and BW = 250 kHz, no influ-597 ence of Doppler effects on radio communication was ever 598 recorded. 599 VOLUME 10, 2022 The main objective of experiments with SF = 10, 11 and 600 12 is to detect the influence of the dynamic Doppler effect 601 on LoRa modulation. Laboratory experiments [13] found that 602 LoRa modulation becomes less resistant to Doppler rate as 603 SF increases and BW decreases. Theoretical analysis [18], 604 [19] also shows that as SF increases and BW decreases,   Table 2). The 619 immunity of LoRa modulation to the Doppler rate at SF = 620 7 and BW = 125 kHz, according to [13], is also sufficient 621 with a large margin for using LoRa modulation in satellite 622 radio communications. No. 1, which was performed last, only one packet loss due 655 to the unsuccessful orientation of the CubeSat antenna was 656 recorded (experiment No. 17). The relatively large number 657 of packet losses due to the unsuccessful orientation of the 658 CubeSat antenna in experiment No. 1 is also due to the low 659 sensitivity of the LoRa receiver at SF = 7 and BW = 500 kHz, 660 which is significantly less than in other experiments (see 661  Table 2).  In experiment No. 4 (Fig. 8), the command to switch to 669 continuous transmission of a sequence of packets was sent 670 to the CubeSat from the ground station only after the arrival 671 of the second NORBY beacon, that is, with an additional 672 two-minute delay. Therefore, the transmission of data packets 673 from NORBY in experiment No. 4 began only at −133 s, 674 approximately four minutes after the satellite entered the 675 radio visibility zone of the ground station. In this experiment, 676 all data packets transmitted from NORBY were successfully 677 received by the ground station. The satellite-to-ground radio 678 channel worked steadily while NORBY was in the radio 679 visibility zone of the ground station, that is, above the hori-680 zon. Communication was interrupted only when the satellite's 681 elevation angle became less than about 1.7 • .

682
In experiment No. 6 ( Fig. 9), the transmission of packets 683 from NORBY started at t = −351 s, but only packet No. 684 210 was received first at t = −79 s when the Doppler shift 685 F D decreased to 7.7 kHz. Communication with the satel-686 lite was again interrupted at +76 s, when the Doppler shift 687 again increased in absolute value to 7.6 kHz. Subsequently, 688 the ground station did not receive any data packet. Fig. 9d 689 and Fig. 9e show that in the time interval between −79 s 690 and +76 s, both the signal level and signal-to-noise ratio at 691 the receiver input were quite large, significantly exceeding 692 the LoRa receiver sensitivity and LoRa demodulator SNR, 693 respectively. We do not know the values of RSSI and SNR 694 at times when the data packets from the satellite were not 695 received by the ground station. However, the behavior of 696 RSSI and SNR in other experiments (Fig. 7 and Fig. 8) 697 indicates that their abrupt change, leading to the termina-698 tion of communication with the satellite for a long period, 699 is unlikely. Therefore, we attribute the packet loss observed 700 in experiment No. 6 to the Doppler effect.

701
As noted above, the total frequency offset F between 702 the carrier frequencies of the input signal and LoRa receiver 703 differs slightly from the Doppler shift because of the dif-704 ference in the frequencies of the reference generators of the 705 receiver and transmitter (4). Therefore, it is possible to more 706 accurately determine the maximum allowable value of F max 707 above which the LoRa radio communication is broken using 708 the FER data of the LoRa receiver of the ground station. In our 709 case, we get F max = 7.8 kHz and 7.7 kHz for t = −79 s 710  Table 2).  and stopped again at F D = −6.4 kHz. The conclusion is 725 similar to the previous one: the reason for the destruction of 726 the LoRa satellite-to-ground radio channel in experiment No. 727 7 is the Doppler shift. According to the FER data, the value 728 F max = 7.7 kHz was obtained both during a decrease and 729 increase in the absolute value of the Doppler shift. 730 We did not conduct experiments with BW = 250 kHz, 731 since the absence of the influence of the Doppler effect on 732 the LoRa radio channel in experiments with BW = 500, 733 125 and 62.5 kHz gives grounds to assume that it is absent for 734 BW = 250 kHz as well. It can also be noted that for almost 735 two years of NORBY operation, we did not find any influence 736 of the Doppler effect in regular radio sessions in the mode 737 BW = 250 kHz and SF = 10. Four experiments were performed with SF = 10 (Table 2).  As expected (see Table 2 Table 2). The results of experiments the ground station in experiment No. 12 for an unidentified 793 reason (see Fig. 12). In these experiments, no influence of the 794 Doppler effect on the satellite-to-ground LoRa radio channel 795 was observed. of the LoRa satellite-to-ground radio channel, caused by a 823 large absolute value of F D , that is, the dynamic Doppler 824 effect. Five experiments were performed with SF = 12 (Table 2). 827 In experiment No. 20, at BW = 31.25 kHz and L = 55 bytes, 828 the ground station did not receive a single packet out of about 829 70 transmitted from the satellite. This result is similar to that 830 obtained in the experiment described above with SF = 11 and 831 BW = 31.25 kHz. The lack of LoRa radio communication 832 with the satellite in this case appears to be due to both static 833 and dynamic Doppler effects. However, the complete absence 834 of any data in the experiment did not allow us to draw any 835 VOLUME 10, 2022 receiver input (see Fig. 14). No impact of the Doppler effect 850 on the LoRa satellite-to-ground radio channel was observed 851 in these experiments.

852
The results of experiments No. 18 and No. 19 with SF = 853 12 and BW = 62.5 kHz are shown in Fig. 15 and Fig. 16 for 854 L = 55 and 143 bytes, respectively. It can be seen that with 855 these LoRa modulation parameters, there was no radio com-856 munication with NORBY at high satellite elevation angles, 857 that is, in the region of maximum absolute values of the 858 Doppler rate. In experiment No. 18, data packets transmitted 859 from NORBY ceased to be received by the ground station 860 at t = −89 s, when the Doppler rate F D increased in 861 absolute value to 38 Hz/s (see Fig. 15c). The reception of 862 data packets resumed at t = 93 s when the absolute value 863  This is a rapid change in the Doppler frequency shift, that 878 is, the dynamic Doppler effect. Thus, in these experiments, 879 the effect of the disruption of LoRa radio communication 880 during the passage of a satellite directly over a ground station, 881 predicted in [13] based on laboratory studies, was observed 882 for the first time. 884 We have presented here the results of the first flight tests of 885 LoRa modulation in a satellite-to-ground radio channel. The 886 tests were carried out using the NORBY CubeSat, which is 887 located in a low-Earth orbit with an altitude of approximately 888 560 km. The main purpose of the flight tests was to verify in 889 real space conditions the robustness of the LoRa modulation 890 against the Doppler effect, determined in laboratory studies 891 [13]. It was also supposed to check the maximum allowable 892 frequency offset between the transmitter and receiver given in  Table 3.  to weak signal or low signal-to-noise ratio at the input of the 910 LoRa receiver, six packets were lost for an unknown reason, 911 and 1192 packets were not received by the ground station 912 owing to the Doppler effect. The destructive impact of the 913 Doppler effect on the satellite-to-ground LoRa radio channel 914 was recorded in nine communication sessions (shaded rows 915 in Table 3).

916
The static Doppler effect was clearly manifested in four 917 experiments with SF = 7 and SF = 10 at spread spec-918 trum modulation bandwidth BW = 31.25 kHz (Nos. 6, 7, 919 10, and 11 in Table 3). The maximum frequency offset 920 F max between the carrier frequencies of the LoRa receiver 921 and the received signal, above which the LoRa radio link 922 was disrupted, was determined in each experiment. In total, 923 in four experiments, we obtained eight values of F max , four 924 of which were obtained when the satellite approached the 925 ground station and the rest when moving away. The averages 926 of the two F max values obtained from each experiment are 927 listed in  was obtained also for SF = 12 but at BW = 125 kHz.  ies of LoRa modulation [13]. Table 4 shows that all  [14]. However, the datasheet [14] does 993 not contain any information regarding the criteria for LoRa 994 modulation stability when changing the frequency offset. The 995 results of laboratory experiments [13] concerning F max for 996 SF = 12 and BW = 125 kHz proved impossible to verify in 997 the NORBY orbit. There are no other experimental data on 998 the stability of the LoRa modulation to F ; therefore, there 999 is nothing to compare the obtained values of F max with. 1000 Table 5 shows in a visual form the Doppler effect restric-1001 tions on the use of LoRa modulation in radio communications 1002 with LEO satellites obtained in the NORBY experiments. For 1003 SF ≤ 11 and BW ≥ 62.5 kHz, there are no restrictions on the 1004 use of LoRa modulation in satellite radio communications. 1005 For BW = 31.25 kHz, the LoRa radio channel is affected 1006 by the static Doppler effect. Radio communication with the 1007 satellite is possible in this case only at high elevation angles 1008 of the satellite when flying directly over the ground station. 1009 For SF = 12, on the contrary, the dynamic Doppler effect 1010 becomes significant and radio communication is possible 1011 only at small satellite elevation angles at large distances from 1012 the ground station. In both latter cases, the duration of the 1013 communication session is significantly reduced due to the 1014 Doppler effect.

1015
In the case of SF = 11 and 12 at BW = 31.25 kHz, both 1016 static and dynamic Doppler effects catastrophically affected 1017 the LoRa radio channel. In this case, LoRa radio communi-1018 cation with a satellite in a low-Earth orbit is not possible.

1019
The restrictions imposed by the Doppler effect on the use 1020 of LoRa modulation relate primarily to LoRa modes that 1021 provide maximum receiver sensitivity and, consequently, the 1022 maximum radio communication range with minimum trans-1023 mitter power. Therefore, they are extremely important for the 1024 satellite Internet of Things. Our results show that the most 1025 super-sensitive LoRa modulation modes with SF = 11 and 1026 12 at BW ≤ 31.25 kHz are unsuitable for use in LEO satellite 1027 IoT networks due to the Doppler effect. This is the case unless 1028 some system is used to correct the carrier frequency of the 1029 LoRa receiver or transmitter on the base of the predicted 1030 Doppler shift and Doppler rate.

1031
The use of LoRa modulation modes with intermediate 1032 sensitivity, at which the influence of the Doppler effect 1033 begins, reduces the coverage area of the radio communi-1034 cation by one satellite. The static Doppler effect reduces 1035 the coverage area near the horizon. The dynamic Doppler 1036 effect results in a ''hole'' in the center of the coverage area 1037 directly below the satellite. The use of these LoRa modes 1038 in IoT satellite networks complicates the task of creating a 1039 globally contiguous coverage area using the LEO satellite 1040 constellation.

1041
LoRa modulation modes with SF ≤ 11 and BW > 1042 31.25 kHz can be used in satellite IoT without any limitations 1043 caused by the Doppler effect. The Doppler limits on the use of 1044 LoRa modulation in satellite radio communications obtained 1045 in the NORBY experiments are applicable to satellites in any 1046 orbit. However, it should be borne in mind that the orbital 1047 velocity of a satellite decreases with increasing orbit altitude. 1048 VOLUME 10, 2022 As a result, Doppler-induced restrictions become less critical when the IoT satellite constellation is placed in a higher orbit.
In general, the satellite experiments conducted made it 1051 possible to determine the limits of applicability of LoRa 1052 modulation in radio communications with LEO satellites. munication due to the dynamic Doppler effect was detected 1055 when the satellite passed directly over the ground station.
In conclusion, we would like to note that we are planning