## 2 System Model
### NB-IoT Signal Format for the Satellite Forward Link  
NB-IoT has been developed by 3 GPP to cope with the large demand on IoT connectivity that is foreseen by the designers of the future generations of mobile communication standards (i.e., 5G and beyond). NB-IoT has been conceived to be deployed in three different configurations or typologies, which are compatible with the spectrum allocation (channelization) that is used in contemporary mobile communication standards such as GSM (2G) and LTE (4G). An overview of these deployment typologies, which are known as stand-alone, in-band, and guard-band, can be appreciated in Figure 1.  
In the stand-alone deployment, the NB-IoT signal occupies the bandwidth that corresponds to one (or few) of the 200-kHz GSM radio channels of the 2G radio spectrum; note that this strategy is suitable for the re-farming process of the GSM bands. In the in-band deployment, the NB-IoT signal is placed on the radio spectrum that corresponds to one (or few) Physical Resource Blocks (PRB) of an LTE carrier, where each PRB spans over 180 kHz of bandwidth and is formed by 12 sub-carriers of a 15-kHz bandwidth each. Finally, in the third typology of deployment known as guard-band deployment, the NB-IoT signal is placed on the guard bands that are reserved to prevent adjacent-channel interference between LTE carriers. Note that these strategies of deployment do not imply any additional cost and time to enter in service, provided the operator owns a licence either in the 2G/4G radio bands. According to 3 GPP standardization, both NB-IoT uplink and downlink transmissions occupy a communication bandwidth of 180 kHz in the radio portion of the electromagnetic spectrum. Moreover, as the downlink of NB-IoT defines the technology to communicate from the base station (eNB) to the user terminal (IoT device), we focus on this direction of communication to design the radio frame that should be used in the forward link of the IoT satellite system. Specifically, the downlink of NB-IoT uses few 15 kHz sub-carriers, providing a sampling time unit of \(T_{\rm s}=1/(15000\times 2048)\) s., which is identical to the one used in the LTE standard. Similarly, the time slot duration in NB-IoT is \(T_{\rm slot}=15360\times T_{\rm s}~{}=~{}0.5\) ms [29]. Two consecutive NB-IoT time slots constitute a sub  
Figure 1: Typologies of NB-IoT deployment, namely stand-alone, in-band, and guard-band deployments. All these deployment configurations are compatible with the channelization that is used in contemporary mobile communication standards, such as GSM/2G (200 kHz channel) and LTE/4G (180 kHz Physical Resource Block). frame, which spans 1 ms. Similarly to LTE, a group of 10 subframes with total duration \(T_{\text{frame}}=10\times 2\times T_{\text{s}}=10\) ms constitutes a NB-IoT frame. The NB-IoT standard enables to repeat the transmission of the same information (block data) up to 2048 times, in order to extend the coverage range and increase the reliability of the data communication [29]. However, the higher the number of repetitions that are performed, the lower the spectral efficiency of the data communication that takes place. The NB-IoT link selects the Transport Block Size (TBS) on a MAC layer from a variety of sizes, which range from 2 bytes (16 bits) up to 317 bytes (2536 bits) [30]. The number of Modulation and Coding Schemes (MCS) that NB-IoT supports is equal to 14, and the combination of a number of subframes and MCS to be used for communication determines the code rate of the NB-IoT transmission. Regarding the error control coding, the downlink of NB-IoT uses a 1/3 tail-biting convolutional encoding mother code [31]. This encoding procedure is formed by three generator polynomials, which are known as the \(G_{0}=133\), \(G_{1}=177\), and \(G_{2}=165\) polynomials in the octal notation (see Figure 2 for more details). Then, after channel encoding, data rate matching is utilized to obtain the desired code rate.