6G NTN Waveforms: A Comparison of OTFS, AFDM and OCDM in LEO Satellite Channels

Sixth generation (6G) physical layer (PHY) is evolving beyond the legacy orthogonal frequency division multiplexing (OFDM)-based waveforms. In this paper, we compare the bit error rate (BER) performance of three beyond-OFDM waveforms, namely, orthogonal time-frequency-space (OTFS) modulation, affine frequency division multiplexing (AFDM), and orthogonal chirp division multiplexing (OCDM), which are particularly suitable for the highly mobile non-terrestrial network (NTN) vertical of 6G. In order to characterize the effect of mobility and Doppler shift in low Earth orbit (LEO) satellites, we performed BER comparisons over four different NTN tapped-delay-line (TDL) models, TDL-A, TDL-B, TDL-C, and TDL-D, as specified in the 3rd generation partnership project (3GPP) technical report TR 38.811. After channel equalization, a minimum mean squared error with successive detection (MMSE-SD) algorithm was used to enhance the BER performance. It was found that AFDM and OTFS consistently outperformed OCDM across all TDL models, while AFDM performed better than OTFS in TDL-B and TDL-C, in the high signal-to-noise ratio (SNR) regime. The complete simulation framework is made available as an open-source code for quick validation and further development.

💡 Research Summary

The paper investigates the suitability of three beyond‑OFDM waveforms—Orthogonal Time‑Frequency‑Space (OTFS) modulation, Affine Frequency Division Multiplexing (AFDM), and Orthogonal Chirp Division Multiplexing (OCDM)—for the highly dynamic low‑Earth‑orbit (LEO) satellite links that will form a core component of 6G non‑terrestrial networks (NTN). Recognizing that the traditional OFDM waveform suffers severe inter‑carrier interference (ICI) under the large Doppler shifts (up to ±48 kHz in S‑band and ±480 kHz in Ka‑band) specified by 3GPP TR 38.811, the authors set out to quantify the error‑rate performance of the three candidate waveforms under identical system conditions.

The authors first construct a MATLAB‑based simulation framework that implements the transmitter and receiver chains for each waveform. OTFS maps symbols onto the delay‑Doppler plane, uses an inverse symplectic FFT (ISFFT) and Heisenberg transform for transmission, and a Wigner transform plus SFFT for reception. AFDM employs the discrete affine Fourier transform (DAFT) with two controllable digital chirp rates (c₁, c₂) that enable orthogonal placement of symbols in the integer‑normalized delay‑Doppler grid. OCDM is treated as a special case of AFDM with c₁ = c₂ = 1/(2N). All three waveforms share a common OFDM‑like backbone: an inverse transform at the transmitter and the corresponding direct transform at the receiver.

Channel modeling follows the 3GPP NTN specifications. Four tapped‑delay‑line (TDL) profiles—TDL‑A, TDL‑B (non‑line‑of‑sight) and TDL‑C, TDL‑D (line‑of‑sight)—are used, each providing normalized delay taps, power levels, and Rician K‑factors. The additional Doppler component caused by satellite motion is calculated using the expression α_addl = (v_sat/c)·(R/(R+h))·cos(φ_elev)·f_c, where v_sat, h, φ_elev, and f_c denote satellite speed, altitude, elevation angle, and carrier frequency, respectively. For each realization a Jakes Doppler spectrum is assumed, and the per‑path Doppler shift follows α_i = α_max·cos(θ_i) with uniformly distributed θ_i.

Detection is performed with a linear minimum mean‑square‑error (LMMSE) equalizer followed by a Minimum‑Mean‑Square‑Error with Successive Detection (MMSE‑SD) algorithm. Unlike plain LMMSE, MMSE‑SD computes a post‑detection SINR for each undetected symbol, orders symbols by descending SINR, detects the strongest one, applies hard decision, and cancels its contribution from the received vector before proceeding to the next symbol. This ordering yields an average SNR gain of 1–2 dB compared with conventional LMMSE.

Simulation parameters are kept identical across waveforms: carrier frequency 2.55 GHz, sub‑carrier spacing 15 kHz, 16‑QAM modulation, AFDM frame length N = 256, OTFS grid K = L = 16, and cyclic prefix omitted for pure BER comparison. The channel gains are modeled as zero‑mean complex Gaussian variables with variance equal to the inverse of the number of propagation paths.

Results show that OCDM suffers from an irreducible error floor in all four TDL scenarios, making it unsuitable for the considered LEO‑NTN environment. Both OTFS and AFDM achieve substantially lower BERs, with AFDM consistently matching OTFS at low SNR (≤ 15 dB) and surpassing it at higher SNRs. In the high‑SNR regime (SNR > 15 dB), AFDM outperforms OTFS by roughly 0.5–1 dB in TDL‑B and TDL‑C, while performance differences are marginal in TDL‑A and TDL‑D. The superiority of AFDM is attributed to its flexible chirp‑rate design, which better aligns the effective channel matrix with the integer‑normalized delay‑Doppler condition, thereby preserving orthogonality even under severe Doppler spreads.

The authors make the complete simulation code publicly available on GitHub, encouraging reproducibility and further exploration. They conclude that AFDM is the most robust waveform among the three for LEO‑NTN links, especially when high SNR operation is expected. OCDM is deemed impractical under the examined conditions. Future work is suggested in the form of hardware prototyping, multi‑user and massive‑MIMO extensions, real‑world over‑the‑air tests, and hybrid waveform strategies that could combine the strengths of OTFS and AFDM.