Orthogonal Model Division Multiple Access

• OMDMA is a framework that assigns orthogonal resource components across physical, spatial, and semantic domains to eliminate inter-user interference and enhance capacity.
• It generalizes classical FDMA/TDMA principles by extending orthogonality to novel domains such as semantic feature shuffling and orbital angular momentum modes.
• Adaptive techniques like elastic multi-domain assignment and generative denoising optimize performance in high-mobility and resource-constrained scenarios.

Orthogonal Model Division Multiple Access (OMDMA) is a suite of frameworks and techniques for multi-user communication that generalizes the principle of orthogonality across diverse domains—including physical resources (time/frequency/space), semantic representations, and abstract channel models. OMDMA distinguishes users by assigning them orthogonal (or nearly orthogonal) resource components, thereby eliminating or minimizing inter-user interference and enhancing multi-user capacity. Modern variants of OMDMA also integrate domain-adaptive orthogonalization, interference randomization, and advanced generative denoising techniques, expanding its applicability far beyond classic physical-layer orthogonality.

1. Foundational Principles of OMDMA

OMDMA originates from the concept of leveraging orthogonality—traditionally in time, frequency, or code—to separate user signals in multi-access systems. In classical systems, schemes such as Frequency Division Multiple Access (FDMA) and Time Division Multiple Access (TDMA) assign disjoint resource blocks to users, ensuring that the allocation vectors or subspaces are non-overlapping. In this context, OMDMA is considered as the allocation of orthogonal resource “models” to users, which could be time/frequency slots, spatial modes, or, as later variants suggest, representations in higher-level domains such as semantics.

For example, FDMA assigns each user a non-overlapping frequency band ($W_1 = \alpha W$ and $W_2 = (1-\alpha)W$); similarly, TDMA splits the channel temporally. The theoretical underpinning is that such separation eliminates mutual interference, allowing each user to be decoded independently with single-user receiver complexity (1001.0357). However, orthogonality can be extended more abstractly to the design of JSCC model mappings or spatial mode decomposition via orbital angular momentum (OAM).

2. Mathematical Formulation and Capacity Characterization

In physical-layer OMDMA (FDMA/TDMA), the achievable capacity under finite input alphabets is governed by the mutual information between the transmitted and received symbols, constrained by the allocation of resources. The capacity region for two-user OMDMA over a Gaussian multiple access channel (GMAC) with finite alphabets is given by:

$$\begin{aligned} & R_1 \leq W \cdot I(\sqrt{\rho/W} x_1 : y \mid x_2) \ & R_2 \leq W \cdot I(\sqrt{\rho/W} x_2 : y \mid x_1) \ & R_1 + R_2 \leq W \cdot I(\sqrt{\rho/W} x_1 + \sqrt{\rho/W} x_2 : y) \end{aligned}$$

where $x_1, x_2$ are user symbols from finite alphabets, $W$ is the total bandwidth, and $\rho$ the average power (1001.0357).

In OMDMA systems that utilize OAM, user separation is achieved by assigning orthogonal OAM modes (each $\ell$ corresponds to a mode with a helical phase factor $e^{j\ell \varphi}$), and spatial resource allocation is determined by the geometry and alignment of transceiver arrays (Long et al., 2021).

Semantic-domain OMDMA, as advanced in recent frameworks (Zhang et al., 28 Jul 2025), employs an orthogonalization function (e.g., user-specific shuffling of JSCC feature vectors), yielding effective separation in latent vector space. The mapping for user $k$:

$$[C_k(f_k)]_i = f_{k,(p_k, i)} + j \cdot f_{k,(p_k, i+N)}$$

transforms the user’s features prior to transmission, where $p_k$ denotes a unique permutation. Provided no collision in shuffling patterns, the representations remain mutually orthogonal in expectation.

3. Orthogonality Mechanisms: From Physical to Semantic Domains

Classical OMDMA: Time, Frequency, and Spatial Orthogonality

Conventional OMDMA exploits resource partitioning schemes such as:

• Time division: Non-overlapping time intervals.
• Frequency division: Non-overlapping spectral bands.
• Spatial division: Disjoint antenna or mode subspaces (e.g., MIMO beams, OAM modes).

These schemes obviate the need for multi-user decoding but can result in inefficient resource utilization, particularly for finite-size constellations—even when sum capacity is theoretically achievable for Gaussian alphabets (1001.0357).

OMDMA in Semantic Domain

The latest OMDMA proposals (Zhang et al., 28 Jul 2025) target semantic communications, where raw channel orthogonality is infeasible due to interference in structured feature space. OMDMA achieves “semantic orthogonality” by using shuffled mappings of feature vectors. The interference induced by the superposition of differently shuffled vectors is shown to approximate white Gaussian noise (empirically validated via t-SNE and statistical tests), which is less detrimental than structured interference for downstream semantic decoders.

4. Advanced OMDMA Extensions: OAM and Multi-Domain Orthogonalization

Recent OMDMA frameworks introduce alternative orthogonality methods and multi-domain resource division:

• Orbital Angular Momentum-Based OMDMA: Utilizes mutually orthogonal OAM modes (distinct $\ell$) for user separation on the same frequency channel (Long et al., 2021). This form achieves high spectral efficiency (SE) and energy efficiency (EE) by layering spatial and modal orthogonality (termed joint spatial division and coaxial multiplexing, or JSDCM).
• Elastic Multi-Domain OMDMA: In the OTFS-MDMA architecture, the delay-Doppler domain is partitioned into resource slots, and orthogonality is dynamically assigned across time, frequency, spatial, and power domains. Adaptive selection among orthogonal (OMA), non-orthogonal (NOMA), or spatial-domain (SDMA) access methods in each slot yields substantial improvements, especially in high-mobility scenarios (Chen et al., 9 Sep 2024).

OMDMA Variant	Orthogonality Domain(s)	Key Mechanism
Classical FDMA/TDMA	Frequency/Time	Resource partitioning
OAM-based OMDMA	Spatial, modal (OAM $\ell$)	OAM multiplexing, JSDCM
Semantic OMDMA	Feature/semantic latent space	Shuffle-based mapping
OTFS-MDMA	Delay-Doppler, power, spatial	Elastic multi-domain assignment

5. Interference Suppression and Denoising Strategies

OMDMA methods universally target inter-user interference minimization. In classical forms, this occurs via resource exclusivity. In advanced semantic OMDMA, interference is initially randomized in latent space through shuffle-based orthogonalization, converting structured semantic overlap into Gaussian-like noise (Zhang et al., 28 Jul 2025). Decoding then uses a pre-trained diffusion denoiser, which iteratively removes aggregate interference-plus-noise, further enhancing semantic fidelity in challenging multi-user environments.

In OAM-based OMDMA, a two-stage preprocessing (multi-user null-space projection followed by inverse-mode-coupling compensation) achieves near-diagonalization of the composite channel, eliminating both co-mode and inter-mode interference. Analytical SINR expressions and simulation results confirm that such schemes achieve SE/EE levels close to idealized (perfect knowledge, single-user) regimes (Long et al., 2021).

6. Comparative Analysis: Orthogonality versus Non-Orthogonality

Comparative studies show that, under practical constraints (notably, finite alphabet signaling or high-mobility links), strictly orthogonal schemes may be strictly suboptimal in achievable rate regions relative to non-orthogonal or hybrid multi-access strategies. For instance, non-orthogonal schemes such as TCMA provide larger constellation-constrained capacity regions, especially at moderate-to-high SNR and low bandwidth (1001.0357).

Elastic frameworks like OTFS-MDMA further demonstrate that multi-domain orthogonality assignment—adaptively switching between OMA, NOMA, and SDMA—yields weighted-sum-rate enhancements unattainable with rigid OMDMA. Mathematical optimization of multi-domain assignment leverages advanced algorithms (dynamic programming, monotonic optimization, simulated annealing, and SCA) for near-optimal, scalable resource allocation (Chen et al., 9 Sep 2024).

7. Future Research Directions

Several key directions are identified for advancing OMDMA frameworks:

• Generalization to larger networks: Theoretical and algorithmic exploration of OMDMA in massive user environments and with arbitrary user heterogeneity (1001.0357, Al-Eryani et al., 2019, Zhang et al., 28 Jul 2025).
• Hybrid Orthogonality Models: Integration of orthogonality in physical, spatial, and semantic domains, and adaptive switching mechanisms for varied application scenarios (Chen et al., 9 Sep 2024, Long et al., 2021).
• Low-Complexity, Real-Time Algorithms: Development of practical clustering, power allocation, and interference cancellation strategies viable for ultra-dense, high-mobility or resource-constrained settings (Al-Eryani et al., 2019, Chen et al., 9 Sep 2024).
• Security and Privacy: Leveraging shuffling patterns (as implicit keys) and distributed encryption protocols, as in D-OMA and semantic OMDMA, to enhance confidentiality and robustness against eavesdropping (Al-Eryani et al., 2019, Zhang et al., 28 Jul 2025).
• Semantically-Aware Cooperative Schemes: Expansion of cooperative transmission methods that exploit task-level or data-level semantic correlations for further performance gains (Zhang et al., 28 Jul 2025).

Conclusion

OMDMA synthesizes a broad class of multi-user/multi-access strategies that share a central goal: exploiting orthogonality—be it physical, modal, or semantic—to disentangle simultaneous transmissions. New paradigms extend orthogonality’s definition through shuffling, modal decomposition, and multi-domain resource allocation, enabling higher spectral efficiencies and robustness in both classical and semantic communication scenarios. Comparative results consistently demonstrate that rigid orthogonality is often suboptimal in practical systems, motivating continued research into hybrid, adaptive, and semantically-aware OMDMA schemes for future wireless and semantic communication networks.