# OTFS: A Potential Waveform for Space-Air-Ground Integrated Networks in 6G and Beyond
###### Abstract  
6G is expected to provide ubiquitous connectivity, particularly in remote and inaccessible environments, by integrating satellite and aerial networks with existing terrestrial networks, forming Space-Air-Ground Integrated Networks (SAGINs). These networks, comprising satellites, unmanned aerial vehicles (UAVs), and high-speed terrestrial networks, introduce severe Doppler effects due to high mobility. Traditional modulation techniques like Orthogonal Frequency Division Multiplexing (OFDM) struggle to maintain reliable communication under such conditions. This paper investigates Orthogonal Time Frequency Space (OTFS) modulation as a robust alternative for high-mobility scenarios in SAGINs. Using 6G exploration library in MATLAB, this study compares the bit error rate (BER) performance of OTFS and OFDM under static and multipath channels with varying mobility scenarios from 20 km/h to 2000 km/h, and varying modulation orders (BPSK, QPSK, and 8-PSK). The results indicate that OTFS significantly outperforms OFDM, while maintaining signal integrity under extreme mobility conditions. OTFS modulates information symbols in the delay-Doppler domain, demonstrating a strong robustness against Doppler shifts and delay spreads. This makes it particularly suitable for high-mobility applications such as satellites, UAVs, and high-speed terrestrial networks. Conversely, while OFDM remains effective in static and low-mobility environments, it struggles with severe Doppler effects, common in the proposed SAGINs. These findings reinforce OTFS as a promising modulation technique for SAGINs in 6G and beyond.  
orthogonal time frequency space (OTFS) modulation; orthogonal frequency division multiplexing (OFDM); delay-Doppler domain; space-air-ground integrated networks (SAGINs); high mobility channels; 6G +
Footnote †: journal: _Journal of the Optical Society of America_  
1025 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 111 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11(SAGINs) [1]. Figure 1 shows a simple SAGIN architecture. These networks leverage satellites, unmanned aerial vehicles (UAVs), and drones as relay nodes, providing flexibility and adaptability in communication networks which is unattainable using terrestrial networks only. SAGIN, which is a key enabling technology for 6G, is expected to enable seamless and global coverage, higher data rates, network resilience and reliability due to its multi-layered approach. These will enable applications like autonomous vehicles, high-speed trains, smart cities, drones, and robotics.  
The deployment of these new technologies and use cases will present significant challenges. The communication environment in SAGIN is characterized by high mobility of the transceivers or reflectors, multipath propagation due to reflectors in wireless environments, and severe attenuation due to the distance between the transmitter and receiver. These result in the channel varying in frequency and time, with multiple copies of the signal arriving at the receiver at different amplitude, phases, and times, causing the channel to change rapidly due to high mobility and Doppler shift, which is the frequency shift in the received signal due to relative motion between the transmitter and receiver. These introduce severe impairments such as inter-symbol interference (ISI) and inter-carrier interference (ICI), which affect the reliable transmission and reception of signals. Also, 6G is expected to provide Hyper-Reliable and Low-Latency Communication, even in these extreme environments with high mobility and multipath propagation, to enable seamless connectivity in these new applications [2].  
Hence, advanced modulation techniques must be employed to address these challenges posed by extreme multipath and high mobility in SAGINs. OTFS and OFDM are two prominent candidates, each with unique characteristics to be explored.