⚡ electrical engineering

Channel-Aware Waveform Selection Criteria Across Different Waveform Domains

This paper proposes a generalized channel model that captures dense urban and high-mobility complexities to reveal hidden interference structures, demonstrating that while AFDM and OTFS excel under sparse conditions, OFDM and DFT-s-OFDM offer superior reliability and stability in realistic, non-stationary 6G environments.

Original authors: Hamza Haif, Abdelali Arous, Huseyin Arslan

Published 2026-05-05

📖 4 min read☕ Coffee break read

CC BY 4.0

Original authors: Hamza Haif, Abdelali Arous, Huseyin Arslan

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Picture: Why We Need a New Map

Imagine you are trying to navigate a city. For a long time, engineers have used a very simple map to design the "roads" (waveforms) that carry our 6G internet signals. This old map assumed the city was quiet, the roads were straight, and the traffic was predictable. It worked well enough for simple trips.

However, the real world is a chaotic, bustling metropolis. In 6G, we are dealing with:

Dense cities where signals bounce off thousands of buildings.
High-speed travel (like cars or drones) where the environment changes instantly.
New applications like self-driving cars and digital twins that need to "see" the world, not just talk to it.

The old map is too simple. It misses the complexity of the real world. This paper argues that we need a new, more realistic map to decide which "road" (waveform) is best for the job.

The New Map: A Living, Breathing Channel

The authors created a new mathematical model to describe how radio waves travel. Instead of a static picture, they describe the channel as a living thing that changes over time. They identified four key "chaos factors" that the old models ignored:

Birth and Death of Clusters: Imagine a crowd of people (signal paths) appearing and disappearing as you walk through a market. Old models assumed the crowd was always the same. The new model accounts for groups of people suddenly forming and vanishing.
Doppler Spreading: When a siren passes you, the pitch changes. In the old model, this was a single, clean note. In the real world, because the signal bounces off many moving things, it sounds like a messy, smeared-out noise. The new model captures this "smear."
Time-Varying Delays: Signals don't just arrive late; they arrive at slightly different times that keep shifting, like a runner whose stride length keeps changing.
Local Stationarity: The chaos isn't the same everywhere. For a split second, things might be calm (stationary), but then they get chaotic again. The new model recognizes these short "calm zones" within the storm.

The Contest: Four Different Vehicles

The paper tests four different "vehicles" (waveforms) to see which one drives best on this new, chaotic road.

OFDM (The Standard Sedan): This is the current workhorse of 4G and 5G. It's reliable and sturdy.
DFT-s-OFDM (The Fuel-Efficient Hybrid): A variation of the sedan, great for saving power.
OTFS (The All-Terrain Off-Roader): Designed to handle extreme speed and chaos. It spreads the signal out in a grid to catch everything.
AFDM (The High-Speed Train): Another advanced design meant to handle complex movements very efficiently.

The Old Theory: Under the "simple map," the Off-Roader (OTFS) and the Train (AFDM) were supposed to be the clear winners. They were faster and more efficient because they could perfectly separate the messy signal paths.

The New Reality: When the authors drove these vehicles on their new, realistic map, the results flipped.

The Off-Roader and Train (OTFS/AFDM) started to struggle. Because the "birth and death" of signal paths and the "smearing" of noise were too complex, these vehicles got confused. They couldn't distinguish between a real signal and the noise, leading to errors.
The Standard Sedan and Hybrid (OFDM/DFT-s-OFDM) adapted better. By adjusting their settings (like widening the lanes), they could absorb the chaos and keep driving smoothly.

The Solution: A Smart GPS for Waveforms

The paper proposes a Channel-Aware Selection Framework. Think of this as a smart GPS that doesn't just pick one vehicle for the whole trip. Instead, it looks at the specific road conditions right now:

Is the road calm and predictable? (Sparse, stationary conditions).
- Decision: Use the Train or Off-Roader (AFDM/OTFS). They are faster and more efficient here.
Is the road chaotic, crowded, and changing fast? (Dense urban, high mobility).
- Decision: Switch to the Sedan or Hybrid (OFDM/DFT-s-OFDM). They are more robust and reliable here.

The Verdict

The main takeaway is that there is no "one-size-fits-all" waveform for 6G. The "best" technology depends entirely on the environment.

If the channel is simple: The fancy new waveforms (OTFS/AFDM) win.
If the channel is complex (like a real city): The proven, adaptable waveforms (OFDM) actually perform better and are more reliable.

The authors conclude that to build a successful 6G network, we must stop assuming the channel is simple and start using a system that dynamically chooses the right tool for the specific, messy reality of the moment.

Technical Summary: Channel-Aware Waveform Selection Criteria Across Different Waveform Domains

Problem Statement
Current evaluations of sixth-generation (6G) waveforms largely rely on sparse and quasi-stationary channel models. While these models offer mathematical tractability and facilitate the analysis of diversity gains and Doppler robustness, they obscure the propagation complexities inherent in dense urban environments, high-mobility scenarios, and heterogeneous network deployments. Specifically, conventional models fail to account for dynamic phenomena such as the birth and death of multipath clusters, Doppler spectral spreading (rather than discrete shifts), time-varying delays, and piecewise local stationarity. These limitations are particularly critical for applications like Integrated Sensing and Communication (ISAC) and digital twins, where the channel itself is an object of inference. Consequently, waveforms such as Orthogonal Time Frequency Space (OTFS) and Affine Frequency Division Multiplexing (AFDM), which theoretically outperform Orthogonal Frequency Division Multiplexing (OFDM) under sparse assumptions, have not gained standardization support, partly because their performance has not been rigorously verified under realistic, non-stationary channel models.

Methodology
The authors propose a generalized, scalable, and mathematically tractable channel model formulated in both continuous and matrix forms to bridge the gap between idealized sparse representations and realistic propagation.

Channel Modeling: The model incorporates intrinsic propagation properties, including:
- Cluster Birth-Death Dynamics: Multipath clusters appear and disappear over time, modeled via Poisson distributions for cluster and ray counts.
- Doppler Spectral Spreading: Instead of single discrete shifts, the model utilizes a Von Mises-Fisher distribution to generate continuous Doppler spectra based on ray angles.
- Time-Varying Delays: Delays evolve geometrically with mobility, introducing coupling between delay and Doppler parameters.
- Piecewise Stationarity: The model defines local stationarity regions (WSSUS) where parameters remain constant, separated by boundaries where "birth and death" events occur.
Derivation of Effective Channels: Using this model, the authors derive the input-output relationships and effective channel matrices for four prominent 6G waveforms: OFDM, DFT-s-OFDM, AFDM, and OTFS. This derivation highlights how each waveform maps the physical channel into a specific domain-specific interference structure.
Selection Framework: A channel-aware waveform prioritization framework is developed based on:
- Delay-Doppler resolvability conditions.
- Local stationarity constraints.
- Effective Signal-to-Interference-plus-Noise Ratio (SINR), accounting for leakage caused by fractional delays, fractional Doppler, and segmentation.
- User equipment (UE) cell distribution and aggregated SNR.

Key Contributions

Generalized Channel Model: A parametric model that captures real-world propagation effects (birth-death dynamics, Doppler spread, time-varying delays) while reducing to conventional sparse models under appropriate simplifying assumptions.
Waveform-Specific Effective Channels: Analytical derivations showing that the superiority of waveforms is regime-dependent. The paper demonstrates that AFDM and OTFS retain their spectral efficiency advantages only under sparse, resolvable, and stationary conditions. Conversely, OFDM and DFT-s-OFDM can be tuned (e.g., via subcarrier spacing) to achieve superior reliability under the proposed complex channel model.
Adaptive Selection Framework: A principled basis for waveform selection that jointly considers channel properties, interference leakage, and achievable rates, moving away from a "one waveform for all" approach.
Comprehensive Evaluation: Performance assessment using 3GPP Channel Delay Line (CDL) parameters, evaluating Bit Error Rate (BER), Spectral Efficiency (SE), Peak-to-Average Power Ratio (PAPR), and Channel Estimation (CE) Mean Square Error (MSE).

Results
Simulation results under the proposed channel model yield the following findings:

Channel Estimation (CE): Under the proposed model, AFDM and OTFS suffer significant NMSE degradation (approx. 3 orders of magnitude) compared to the sparse model due to ambiguity in distinguishing Doppler spectra from fractional spreads and the breaking of WSSUS regions. OFDM and DFT-s-OFDM show minimal degradation as they absorb interference by widening subcarrier spacing ( $\Delta f$ ).
BER Performance: AFDM and OTFS exhibit degraded BER even at high SNR under the proposed model due to unhandled leakage and correlation among multipath components. OFDM and DFT-s-OFDM maintain reliable BER levels with slight SNR adjustments.
Spectral Efficiency (SE): While AFDM and OTFS achieve higher SE under sparse models, OFDM and DFT-s-OFDM become superior under the proposed model. The extra overhead (pilot protection, guards) required by AFDM/OTFS to resolve channel parameters is no longer justified by reliable sparse reconstruction in non-stationary environments.
PAPR: DFT-s-OFDM exhibits the lowest PAPR. While OTFS shows lower PAPR than OFDM and AFDM in specific settings, the requirement for larger FFT sizes in AFDM/OTFS to achieve resolution increases their operational burden.
Cell-Level Performance: Rate maps indicate that AFDM and OTFS high-rate regions contract significantly under the proposed model, whereas OFDM and DFT-s-OFDM maintain stable spatial rate distributions.

Significance
The paper argues that waveform superiority is not universal but strictly dependent on the operating regime. The findings challenge the assumption that delay-Doppler domain waveforms (OTFS, AFDM) are inherently superior for 6G. Instead, the authors posit that OFDM and DFT-s-OFDM offer more robust performance in realistic, non-stationary environments characterized by cluster birth-death dynamics and Doppler spreading. The work provides a mathematical foundation for "channel-aware" waveform selection, suggesting that future 6G systems should adaptively select waveforms based on observed channel conditions (resolvability and stationarity) rather than adhering to a single fixed waveform standard. This approach aims to optimize reliability and spectral efficiency in complex deployment scenarios such as ISAC, V2X, and Non-Terrestrial Networks (NTN).

The Big Picture: Why We Need a New Map

The New Map: A Living, Breathing Channel

The Contest: Four Different Vehicles

The Solution: A Smart GPS for Waveforms

The Verdict

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