Waveform-Domain NOMA Overview

• Waveform-domain NOMA is a multiplexing paradigm that distinguishes users by leveraging unique physical-layer waveform characteristics in domains like delay-Doppler and time-frequency.
• It overcomes power-domain limitations by enabling robust multi-user separation in power-balanced scenarios and high-mobility environments through optimized waveform design and low-complexity detection.
• Practical implementations integrate OFDM, OTFS, MC-CDMA, and AFDM waveforms to support ISAC applications in 6G networks, automotive radar systems, and massive MIMO deployments.

Waveform-domain Non-Orthogonal Multiple Access (NOMA) is a non-orthogonal multiplexing paradigm where users are distinguished using their physical-layer waveform characteristics, rather than solely by power, code, or resource partitioning. By assigning different waveforms (in time, frequency, delay-Doppler, or other transform domains) to multiplexing participants on the same resource elements, waveform-domain NOMA provides a distinct avenue for multi-user access. This architecture enables robust separation irrespective of channel gain disparities, enhances reliability in power-balanced scenarios, and underpins integration with sensing functionalities, as exemplified by recent 6G ISAC uplink designs and high-mobility automotive/radar systems.

1. Principles and Distinction from Other NOMA Schemes

Waveform-domain NOMA (WD-NOMA) allows multiple users to occupy the same time-frequency resource elements (REs), each transmitting a distinct waveform matched to its service requirements. Unlike power-domain NOMA (PD-NOMA), which superposes users by adjusting transmit powers (making separation contingent on power imbalances and effective successive interference cancellation), WD-NOMA utilizes inherent separability in a structural or transformation domain (e.g., delay-Doppler, affine, or code domains) (Şahin et al., 2020, Sari et al., 2017). This enables robust user separation even under near-equal received power, overcoming limitations of PD-NOMA when SIC becomes unreliable.

Classical OMA (orthogonal multiple access) achieves separation using time, frequency, or code orthogonality. MU-MIMO exploits spatial orthogonality. WD-NOMA orthogonalizes in the waveform domain and generalizes or extends many earlier overloading or hybrid multiple access techniques.

Key design options include:

• Assigning OFDM and OFDM-IM (index modulation) waveforms to different users (Şahin et al., 2020, Şahin et al., 2020),
• Superimposing OFDM with MC-CDMA or other spread-spectrum waveforms (Sari et al., 2017),
• Using DFT-s-OFDM-based waveforms such as AFDM and OTFS to project users into delay-Doppler or affine spaces (Zhu et al., 11 Nov 2025, Kulhandjian et al., 2024),
• Employing partial overlap in frequency support or pulse domain to control interference (Ali et al., 2021).

2. System Architectures and Signal Models

Canonical WD-NOMA systems may be constructed according to several models:

• OFDM/OFDM-IM: Users transmit OFDM and OFDM-IM signals simultaneously over the same REs. The index-modulated user exhibits sparsity in the frequency domain, providing a diversity mechanism for separation (Şahin et al., 2020, Şahin et al., 2020).
• OFDMA/MC-CDMA Layering: A base layer comprised of orthogonal subcarriers (OFDMA) is overloaded with a second set of spread-spectrum waveforms (e.g., Walsh-Hadamard MC-CDMA) (Sari et al., 2017).
• DFT-s-OFDM: AFDM/OTFS: Uplink adopts DFT-s-OFDM-derived waveforms (e.g. AFDM or OTFS), while downlink and/or ISAC echo occupies the standard OFDM domain. The transform (e.g. discrete affine Fourier or symplectic Fourier) maps symbols to an alternative domain, where interference from the OFDM echo appears as white Gaussian noise (Zhu et al., 11 Nov 2025).
• Pulse Orthogonality in Delay–Doppler: OTFS-NOMA systems allocate different orthogonal pulses in the delay-Doppler plane, such as Hermite functions, which ensure inter-user separability without code or power layering (Kulhandjian et al., 2024).
• Partial RE Overlap: Users have overlapping frequency bands with controlled overlap, exploiting matched filtering to suppress cross-user interference. Flexible-SIC (FSIC) decoding at the receiver dynamically chooses between full SIC and treating interference as noise (Ali et al., 2021).

The composite received signal generally takes the form: $r = \sum_{i=1}^K H_i s_i + w$ where $s_i$ is the i-th user's transmit waveform, $H_i$ is the channel, and user waveforms are designed for mutual (quasi-)orthogonality or statistical separability.

3. Receiver Design and Detection Techniques

WD-NOMA system receivers exploit waveform-specific structural properties:

• Iterative Hard/Symbol-Level Interference Cancellation: Many WD-NOMA schemes employ serial or parallel interference cancellation, enabled by the waveform-domain separation that reduces error propagation compared to PD-NOMA SIC. In AFDM/OTFS systems, the OFDM echo behaves as AWGN in the affine/delay-Doppler domain, allowing simple linear estimators such as MMSE (Zhu et al., 11 Nov 2025).
• Reliability-Zone (RZ) Detection: For OTFS-NOMA, iterative equalization with reliability-based symbol detection (using per-symbol post-equalization MSE and greedy threshold adjustment) suppresses multi-user interference with complexity scalable as O(MN log(MN)), where MN is the grid size (McWade et al., 2023, McWade et al., 2022).
• Matched Filtering and Pulse Projection: When user pulses are mutually orthogonal (as in OTFS-Hermite), matched filtering at the receiver eliminates inter-user interference, reducing complexity to O(KMN) for K users (Kulhandjian et al., 2024).
• Flexible SIC and Partial Overlap Decoding: Receivers in partial-overlap designs use cross-correlation integrals to reduce interference, combining matched filtering with adaptive SIC or direct decoding routes depending on instantaneous SINR conditions (Ali et al., 2021).
• Soft Interference Cancellation and LDPC Decoding: Soft-symbol reconstruction using extrinsic LLRs from LDPC decoders enhances cancellation robustness and eliminates error propagation common in hard-decoded SIC (Şahin et al., 2020).

4. Performance Analysis, Complexity, and Robustness

WD-NOMA provides the following documented performance advantages compared to conventional PD-NOMA and OMA:

• Power-Balanced Regimes: WD-NOMA yields strictly superior BLER and BER results in the critical "ambiguity" region of small user power differentials (|ΔP| ≤ 2 dB), where PD-NOMA's SIC is unreliable (Şahin et al., 2020, Şahin et al., 2020). For instance, an OFDM-IM+OFDM WD-NOMA can maintain BLER ≤ 10⁻³ at SNR ≈ 12 dB, while PD-NOMA exhibits deep error floors (Şahin et al., 2020).
• High Mobility and Doppler Robustness: DFT-s-OFDM-based WD-NOMA (AFDM/OTFS) maintains up to 2–3 dB BER advantage at BER=10⁻³, outperforming OFDM-uplink PD-NOMA, which suffers from ICI. LSQR+RZ detection schemes in OTFS-NOMA provide substantial SNR and SER gains (e.g., 3–6 dB at relevant error rates) as Doppler increases (McWade et al., 2023, McWade et al., 2022, Zhu et al., 11 Nov 2025).
• Spectral Efficiency and Scalability: Use of orthogonal Hermite pulses in OTFS-NOMA provides a full K-fold spectral-efficiency gain relative to code-domain NOMA with spreading length K (Kulhandjian et al., 2024).
• Implementation Complexity: WD-NOMA often replaces O((MN)³)-scaling MMSE solvers with O(MN log(MN)) iterative detection, enabling large grid and multiuser deployments without computational prohibitions (McWade et al., 2022, McWade et al., 2023).
• Energy and PAPR: Assignment of waveform types according to user-specific energy and latency requirements, as well as the use of low-PAPR waveforms (e.g., single-carrier) yields energy savings and hardware simplifications (Şahin et al., 2020, Ahmad et al., 2021).

Comparative BER/SER performance, achievable rate, PAPR, and spectral efficiency improvements are consistently reported across multiple papers, confirming the substantive practical benefits of waveform-domain multiplexing.

5. Waveform and Frame Design Strategies

Appropriate waveform selection and frame design underpins WD-NOMA's performance:

• Delay/Doppler and Affine Domain Transformations: DFT-s-OFDM variants (AFDM, OTFS) are selected to project user data into domains orthogonal to OFDM, leveraging the effective whiteness of the residual echo signal (Zhu et al., 11 Nov 2025). Frame regions are explicitly partitioned to allow for guard bands (channel, noise estimation) and reliable MMSE symbol detection.
• Pulse (Bi)orthogonality: For K-user OTFS-NOMA, Hermite pulses meet sufficient biorthogonality in the delay–Doppler grid, ensuring inter-user interference rejection with linear receiver complexity (Kulhandjian et al., 2024).
• Partial-Overlap Resource Allocation: Controlling the fraction of shared subcarriers (α) and private bands (β), and adjusting power and SINR thresholds, allows a continuum from pure OMA to NOMA. Optimized overlap and flexible SIC maximize cell sum-rate subject to throughput constraints (Ali et al., 2021).
• Joint Radar-Communication: Superimposing radar (FMCW chirps) and communication (OFDM) waveforms and exploiting joint frame design enables ISAC without the need for dedicated resources; the radar waveform facilitates channel estimation for the communication signal (Şahin et al., 2020).

Waveform- and context-specific resource allocation (e.g., per-user power optimization, guard interval sizing, code design) is critical to realized gains.

6. Applications, Extensions, and Open Directions

WD-NOMA techniques find applications in:

• Integrated Sensing and Communication (ISAC): WD-NOMA enables uplink data and downlink echo sensing to coexist, as in 6G ISAC monostatic radar scenarios, with AFDM/OTFS uplink providing robust separation and low-complexity MMSE detection (Zhu et al., 11 Nov 2025).
• Robust Power-Balanced Multiuser Access: WD-NOMA circumvents the SIC breakdown in power-balanced clusters prevalent in PD-NOMA, making it particularly suited for heterogeneous QoS and traffic patterns (Şahin et al., 2020).
• Machine-Type Communications (MTC): Waveform layering (OFDMA+MC-CDMA) elegantly accommodates low-rate machine-type devices alongside broadband services (Sari et al., 2017).
• High-Mobility Environments: OTFS- and AFDM-based systems, with adaptive low-complexity detection, achieve superior resilience to Doppler and channel dynamics (Kulhandjian et al., 2024, Zhu et al., 11 Nov 2025).
• Massive MIMO: When combined with robust waveform shaping (e.g., wavelet-OFDM), WD-NOMA can be extended to large-scale MIMO downlinks, reducing ICI, improving PAPR/out-of-band emissions, and enhancing spectral efficiency (Ahmad et al., 2021).

Research directions include:

• Waveform set and code design for optimal mutual separability,
• Multiuser generalizations (beyond two users) and dynamic scheduling,
• Sensing-communication co-design frameworks for radar/vehicular 6G systems,
• Blind/semi-blind or ML-based waveform discrimination and resource management,
• Cross-layer protocols for dense WD-NOMA deployment.

WD-NOMA thus represents a generalization of non-orthogonal access, providing a flexible and robust mechanism for future wireless networks, with proven gains in error performance, resource efficiency, and coexistence with sensing functionalities (Zhu et al., 11 Nov 2025, Şahin et al., 2020, Şahin et al., 2020, Sari et al., 2017, McWade et al., 2023, Kulhandjian et al., 2024, McWade et al., 2022, Ali et al., 2021, Ahmad et al., 2021).