# OTFS: A Potential Waveform for Space-Air-Ground Integrated Networks in 6G and Beyond
## 4 Results and Discussion
### Channels with No Doppler Effects  
The simulated scenario in Figure 5 describes an ideal wireless channel with a single line of sight (LoS) path between a fixed transmitter and receiver. There is no mobility, hence there is no Doppler shift. The channel is constant over time, indicating a stationary environment. This is an ideal condition, suitable for experimental purposes and a benchmark for theoretical analysis. Figure 5 compares the BER performance of OTFS and OFDM for different modulation orders (BPSK, QPSK, and 8-PSK). It is observed that both OFDM and OTFS give a very good performance because the subcarriers experience a stable channel, and there is no ISI or ICI. However, OTFS slightly outperforms OFDM for all SNR ranges. This can be attributed to the fact that OTFS operates in the delay-Doppler domain and captures the full time-frequency diversity of the channel, even in simple LoS scenarios. On the other hand, OFDM modulates signals in the frequency domain and may suffer from small imperfections like frequency offset between transmitter and receiver.  
\begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Value** \\ \hline Number of Subcarriers (M) & 128 \\ Number of Sub-symbols per Frame (N) & 64 \\ Subcarrier Spacing & 480 kHz \\ Carrier Frequency & 100 GHz \\ Padding Length & 10 samples \\ Signal-to-Noise Ratio (SNR dB) & 30 dB \\  & 20–120 km/h (Cars, V2X, trains) \\ Mobility Scenarios and Application & 300–500 km/h (High Speed Trains and UAVs) \\  & 1000–2000 km/h (jets) \\ Modulation Order & BPSK, QPSK, 8-PSK \\ Channel Estimation Method & Linear MMSE \\ \hline \hline \end{tabular}
\end{table}
Table 1: Simulation Parameters.  
Figure 6 describes a static multipath channel with no mobility and, hence, no Doppler shift. The channel characteristics do not change over time, which indicates a stationary environment. This channel type is often encountered in indoor environments or fixed wireless links with multiple propagation paths, where the transmitter and receiver are relatively stationary. These multiple propagation paths can lead to the distortion of the signal in the frequency domain.  
In Figure 6, the BER performance of OTFS and OFDM is compared for different modulation orders (BPSK, QPSK, and 8-PSK) in a static multipath channel. OFDM performs well in a static multipath channel because it converts a frequency-selective wideband channel into multiple flat-fading narrowband subcarriers. This allows the system to deal with frequency selectivity more easily since each subcarrier experiences a flat-fading channel.  
OTFS is also designed to perform well in multipath channels by transforming the time-frequency selective fading into the delay-Doppler domain, where it can better capture  
Figure 5: BER performance comparison of OTFS and OFDM in a LoS channel with different modulation orders.  
Figure 6: BER performance comparison of OTFS and OFDM in a static multipath channel for different modulation orders.  
the channel's multipath structure and spread symbols over time and frequency resources. OTFS also spreads the symbols over time and frequency, which helps mitigate ISI and ensures that multipath components are combined constructively, leading to better detection. This provides better diversity gains compared to OFDM in a multipath environment. OTFS shows better BER performance than OFDM because of its ability to spread information across the entire time-frequency grid and exploit multipath diversity more effectively.