## 1 Introduction
Regarding the potential techniques to increase the spectral efficiency of the optical feeder link, e.g., beamforming [15], NOMA [16], and frequency reuse [17], this paper resorts to the ones based on shrinking the transmitted pulses. The so-called Faster-Than-Nyquist or time-packed techniques. Initially proposed by [PERSON] in the 70s [18], has been proposed as a a potential technique for increasing the spectral efficiency of Beyond 5G systems [19]. From the satellite point of view, the possibility of reducing the transmission time without augmenting the transmission bandwidth fits very well for overcoming the drawbacks of the optical channel, which heavily depend on atmospheric conditions such as clouds [6]. By doing so, the link layer may adjust the transmission time of the frames without reducing the number of symbols to transmit according to weather forecasts [20]. This paper focuses on using optical feeder links for GEO satellite networks. Since initial studies about the introduction of satellites into the 3 GPP landscape have focused on low-latency applications, most of these satellite communication scenarios are dominated by the use of Low Earth Orbit (LEO) satellite constellations [21]. However, due to the longer space-to-ground link distances of GEO satellites, more spectral-efficient techniques should be introduced in their architectures. Furthermore, observing the evolution that 3 GPP standards have experienced in the past, first integrating vehicular and railway networks into 5G [8] and then airborne and satellites into 6G [7], it is highly probable that at some point in the future, extra-terrestrial communications will also be integrated into the 3 GPP ecosystem. In this latter scenario, GEO satellites are in a good position for relaying data from the Earth to the outer space, as discussed in the Moonlight initiative from ESA [22]. Therefore, this paper studies the approach that GEO satellites should use to forward the information that they receive from the satellite gateway [23]. In the \"ideal\" case of a GEO satellite that implements a fully regenerative payload, the optical feeder link would be terminated in the satellite, and a robust modulation and coding scheme should be selected to address the bit error bursts that the turbulent optical satellite wireless channel introduce [24]. In the transparent non-regenerative \"bent-pipe\" solutions, on the other hand, the instantaneous value of the radio signal is used to modulate the intensity of the optical carrier of the feeder link Laser Diode (LD) with the aid of an external Match-Zehnder Modulator (MZM) [25]. Moreover, if time-packing encoding is applied on the real-valued electrical signal that is used to modulate the intensity of the LD beam, the data throughput of the optical feeder link can be increased even further, without the necessity of using a wider communication bandwidth. This effect is obtained by shrinking the separation between adjacent transmitted pulses [26], mitigating part of the Inter-Symbol Interference (ISI) power that time-packing introduces with the aid of a linear equalizer that is placed on-board the GEO satellite before symbol detection [27]. It is important to highlight that the impact of the residual ISI, which remains in the forward link after the GEO satellite relaying, can be further mitigated with the proper selection of the Modulation and Coding Schemes (MCS) to communicate with the NB-IoT terminal [28]. The forward link of a satellite system can be divided into two parts, namely: (i) The optical feeder link (uplink), from the ground station to the GEO satellite, and (ii) the radio access link (downlink), from the GEO satellite to the NB-IoT user terminals.