Channel-Aware Waveform Selection Criteria Across Different Waveform Domains

Abstract: Waveform evaluation for sixth generation (6G) networks has largely relied on sparse and quasi-stationary channel models that enabled mathematical tractability, diversity gains, and Doppler robustness. However, such models obscure the propagation complexity of dense urban environments, high mobility scenarios, and heterogeneous network deployments. This paper sheds light on a generalized and scalable channel model that incorporates cluster birth-death dynamics, Doppler spectral spreading, time-varying delays, and piecewise local stationarity. Based on this model, the effective input-output relationships of the main 6G waveforms are derived, exposing waveform dependent interference structures that remain hidden under conventional sparse assumptions. Building on these effective channels, a channel-aware waveform prioritization framework is developed based on delay-Doppler resolvability, stationarity conditions, effective signal-to-interference-plus-noise ratio (SINR), and user equipment (UE) cell distribution. Simulation results under the proposed channel model using 3GPP CDL parameters confirm that affine frequency division multiplexing (AFDM) and orthogonal time frequency space (OTFS) retain their spectral efficiency advantage and path combining gains only under sparse, resolvable, stationarity conditions, whereas orthogonal frequency division multiplexing (OFDM) and discrete Fourier transform spread (DFT-s)-OFDM can be both tuned to achieve superior reliability and more stable performance under the proposed channel model.

• The paper presents a generalized channel model embedding cluster birth-death processes to capture realistic 6G propagation dynamics.
• It derives input-output relationships for various waveforms, highlighting performance trade-offs between OFDM, DFT-s-OFDM, AFDM, and OTFS.
• The work proposes an adaptive waveform selection framework showing that conventional OFDM is more robust than sparse-domain alternatives under realistic scenarios.

Channel-Aware Waveform Selection under Realistic Propagation Models for 6G

Introduction

The proliferation of applications such as Integrated Sensing and Communication (ISAC), vehicular networks (V2X), digital twins, and non-terrestrial networks (NTN) is fundamentally altering the requirements and paradigms for 6G wireless physical layer design. Classical channel models—favoring sparsity, quasi-stationarity, and delay-Doppler separability—have historically enabled tractable performance analysis and algorithm development. However, these abstractions neglect critical real-world propagation phenomena including cluster birth-death, coupled time-varying delays and Doppler spreads, and the stochastic evolution of multipath density and dispersion. This paper, "Channel-Aware Waveform Selection Criteria Across Different Waveform Domains" (2605.01587), addresses these deficiencies by introducing a generalized parametric channel model designed to preserve computational tractability while incorporating the essential dynamics observed in advanced 6G environments.

Generalized Channel Model: Capturing Cluster Evolution and Non-Stationarity

The proposed channel model departs from conventional wide-sense stationary uncorrelated scattering (WSSUS) assumptions by embedding a birth-death process for multipath clusters, Doppler spectral spread, time-varying delays, and non-uniform angular incidence. It formalizes the continuous geometric evolution of propagation paths and provides a discrete-time matrix representation compatible with all major multicarrier and single-carrier waveform structures. Notably, the model encapsulates both intra-cluster and inter-cluster dynamics, with cluster and ray arrivals modeled via Poisson processes and angular/Doppler statistics governed by scenario-dependent distributions such as the Von Mises-Fisher model. This enables explicit modeling of mobility-driven non-stationary fading and the associated transition of clusters into and out of the channel support.

Figure 1: Dynamics of delay, Doppler, and channel coefficient evolution under sparse and proposed models, including single tap evolution contrasting WSSUS and non-WSSUS contexts.

The joint characterization of delay and Doppler—including their geometric coupling and segmentation over locally stationary regions—permits the analysis of signal distortion due to range migration, non-discrete Doppler, and WSSUS violations. The matrix form allows for modular implementation in simulation and direct integration within waveform-specific baseband processing.

Waveform-Domain Characterization: Input-Output Relationships and Effective Channel Structures

The paper systematically derives the input-output relationships and corresponding effective channel matrices for candidate 6G waveforms, including OFDM, DFT-spread-OFDM, Affine Frequency Division Multiplexing (AFDM), and Orthogonal Time Frequency Space (OTFS). For each waveform, the transform-domain structure induces a distinct interference and leakage profile based on how channel dynamics are projected and resolved.

Figure 2: Representative OFDM frequency-domain structure and processing chain.

The construction of these effective channel matrices exposes critical and previously unquantified regime dependencies:

• AFDM and OTFS: Exploit sparsity and combined delay-Doppler resolution, achieving maximal path-diversity and combining gains only under strict conditions of channel resolvability (large BW, long observation) and local stationarity.
• OFDM and DFT-s-OFDM: Primarily absorb and average channel effects through increased subcarrier spacing and shorter symbols, enabling greater robustness to non-stationarity and channel segmentation at the expense of resolving power.

  Figure 3: Pulse shape and Doppler spectrum interpretation in various waveform domains with non-uniform angular multipath impingement.

Effective leakage and transformation of the physical channel into domain-specific interference is analytically characterized. The model captures the non-orthogonality and increased interference arising under non-WSSUS, high-mobility, or dense-multipath conditions, accounting for leakage induced by fractional delays/Doppler, Doppler spectrum spread, and region transitions.

Figure 4: Block diagram of the proposed adaptive waveform prioritization framework.

Channel-Aware Adaptive Waveform Selection Framework

Drawing on effective channel properties, the work introduces a principled channel-aware waveform selection framework. The selection criteria encompass:

• Delay-Doppler resolvability: Quantified through normalized indicators for resolvability ($\chi_\tau$, $\chi_\nu$) based on system bandwidth, symbol duration, and channel spread.
• Local stationarity: Assessed via ratio of processing interval to local stationarity region duration.
• Effective SINR and leakage: Expressed via the decomposition of the effective channel into ideal (diagonal/sparse) and residual (leakage/interference) components, including explicit SINR floor analysis due to residual correlation and estimation mismatch.
• Resource efficiency: Consideration of spectral efficiency, bit error rate (BER), and practical limitations such as PAPR.

This framework breaks with "one-size-fits-all" assumptions and instead defines operational regimes where each waveform type is optimal, advocating for adaptive selection based on real-time channel statistics and spatial distribution within a cell.

Numerical Evaluation and Comparative Analysis

Extensive simulations under both classical sparse and proposed realistic channel models are presented. Strong claims, numerically validated, include:

• AFDM/OTFS domain approaches only outperform OFDM in scenarios with highly sparse, locally stationary channels—such as idealized or lab-grade measurements or ultra-high bandwidths.
• Under realistic urban cellular models (3GPP CDL), AFDM and OTFS suffer pronounced NMSE and BER degradation, especially under unresolvable Doppler and cluster birth-death, resulting in order-of-magnitude (up to $3\times$) error increases at moderate to high SNR.
• OFDM and DFT-s-OFDM, especially when subcarrier spacing is adaptively increased, maintain robust BER and channel estimation performance, exhibiting only minimal degradation under proposed channel regimes even at high mobility.

  Figure 5: CE NMSE versus SNR for sparse and proposed channel models; AFDM/OTFS show dramatic NMSE increase under non-ideal conditions.

  

  Figure 6: CE NMSE versus normalized Doppler—OTFS/AFDM degrade significantly in multi-Doppler per cluster settings.

  

  Figure 7: BER versus SNR with both perfect and estimated channel information, highlighting the emergence of BER floors for domain-based waveforms in realistic channels.

  

  Figure 8: BER versus SNR for varying modulation orders under the proposed model—OFDM requires 5 dB less SNR for similar BER compared to AFDM/OTFS at 64-QAM.

The resource-effective spectral efficiency and achievable-rate per cell are also presented, demonstrating that:

• Under realistic propagation, OFDM/DFT-s-OFDM deliver higher net rates and broader coverage, due to lower resource overhead and better ability to exploit stochastic channel evolution.
• AFDM/OTFS only regain superiority at cell centers under sparse-like, highly-resolvable channel scenarios.

  Figure 9: PAPR CCDF as a function of FFT size, showing DFT-s-OFDM’s best PAPR statistics, but noting the joint influence of required FFT scaling for real channels.

Theoretical and Practical Implications

The analysis has significant implications for 6G system design:

1. Practically, standardization decisions to retain OFDM for 6G are quantitatively validated by the inability of sparse-domain waveforms to maintain their theoretical diversity and resilience under realistic, dynamic propagation.
2. Waveform adaptivity—which selects the processing domain based on instantaneous channel resolvability and stationarity—is demonstrated to be superior to static waveform assignment.
3. The generalized channel model enables rigorous evaluation of physical-layer innovation under realistic, non-ideal conditions, facilitating more relevant algorithmic and architectural advances for high-mobility, sensing, and densified 6G networks.

Future Directions

The presented modelling and selection framework opens several research avenues:

• MIMO extension: Integrating spatial domain properties and correlation for massive MIMO and distributed antenna setups.
• ISAC and radar-communication coexistence: Tailoring waveform and channel estimation strategies for joint communication-sensing.
• Hardware impairments: Incorporating transmitter/receiver nonidealities and their cross-domain impact under non-stationary propagation.
• Online adaptation and learning: Deploying real-time estimation of channel resolvability and selection of optimal waveform on a per-link, per-user basis in 6G systems.

Conclusion

This work establishes a comprehensive, scalable channel modeling and waveform evaluation methodology for next-generation wireless. The findings demonstrate that advanced domain-structured waveforms such as AFDM and OTFS deliver their theoretical gains only under regimes of high sparsity and stationarity, which are rare in real environments. In contrast, OFDM and DFT-s-OFDM retain robust performance under the full range of channel conditions encountered in 6G settings. The proposed channel-aware prioritization presents a principled path to adaptive physical layer design, emphasizing the necessity of embedding physical channel complexity into both standardization and applied research (2605.01587).