Non-Orthogonal Multiple Access (NOMA)

• NOMA systems are advanced multiple access schemes that allow simultaneous resource sharing using power, code, waveform, or noise domains to enhance spectral efficiency.
• They employ superposition coding and successive interference cancellation to multiplex users on the same channel, thereby improving throughput and connectivity in 5G/6G networks.
• Recent research extends NOMA to MIMO, mmWave/THz, and cooperative frameworks while addressing challenges such as SIC errors and hardware complexity for robust network performance.

Non-Orthogonal Multiple Access (NOMA) Systems are a foundational paradigm in modern wireless communication, enabling simultaneous resource sharing among multiple users via power, code, waveform, or noise-domain dimensions. Unlike traditional orthogonal multiple access (OMA) techniques that assign non-overlapping resource blocks (time, frequency, code) to avoid inter-user interference, NOMA leverages superposition coding and advanced receiver processing (notably successive interference cancellation, SIC) to multiplex users on the same resource, improving spectral efficiency, connectivity, and achieving theoretical capacity region boundaries in degraded broadcast channels. NOMA is central to both 5G and 6G architectures and has been demonstrated to provide significant throughput, fairness, and low-latency gains across single-antenna, MIMO, and hybrid mmWave/THz systems. Recent work explores new domains such as noise-domain NOMA and waveform-domain NOMA to overcome SIC and hardware complexity limitations.

1. Core Principles and Taxonomy

NOMA comprises several architectural categories and enabling mechanisms, primarily distinguished along the multiplexing dimension:

• Power-Domain NOMA (PD-NOMA): Users' streams are weighted by distinct power levels and superposed; receivers employ SIC to peel off stronger or weaker signals according to ordering by channel strength. Downlink PD-NOMA orders users with lower channel gains to receive higher power, while uplink PD-NOMA allows BS-side SIC in descending received-power order. Achievable rates for K users in downlink PD-NOMA are given by

$$R_i = \log_2\left(1 + \frac{p_i|h_i|^2}{\sum_{j>i} p_j|h_i|^2 + \sigma^2}\right)$$

for perfect SIC and user ordering $|h_1|^2 \leq |h_2|^2 \leq \ldots \leq |h_K|^2$ (Islam et al., 2019, Song et al., 2016).

• Code-Domain NOMA (CD-NOMA): Users are multiplexed via sparse low-correlation codebooks (e.g., SCMA, LDS-CDMA), allowing overloading (more users than orthogonal resources) and harnessing iterative multi-user detection (MPA) at receivers (Yue et al., 2019, Song et al., 2016). The diversity orders are proportional to both user order and codeword sparsity.
• Waveform-Domain NOMA: Users employ distinct waveform structures (e.g., OFDM, OFDM-IM) over the same RE; separation relies both on waveform diversity and multiuser detection, reducing reliance on strict power disparities (Şahin et al., 2020).
• Noise-Domain NOMA: User information is encoded in the artificial noise mean or variance, decoded via low-complexity statistical tests, and completely obviates the need for SIC (Yapici et al., 7 Oct 2024).

NOMA can also be realized in hybrid domains, including space (beam or cluster-based), frequency (multi-carrier), or via advanced relay/cooperative architectures (Wan et al., 2018).

2. Resource Allocation and Optimization

Resource management in NOMA is highly coupled and non-convex due to the superposition/interference structure. Both centralized and distributed optimization strategies are in widespread use:

• Joint Rate and Power Allocation: Downlink utility-maximization problems are formulated via Lyapunov drift-plus-penalty, balancing long-term queue stability, peak and average power, and concave network utility (e.g., proportional-fair log-sum-rate). An exact dynamic programming (DP) algorithm efficiently solves the non-convex per-slot power allocation by exploiting a “finite-point structure” and Bellman-optimality, achieving polynomial complexity and asymptotic optimality in (Bao et al., 2017).
• Many-to-Many Stable Matching: For uplink subchannel assignment, users and subchannels are paired via stable matching based on throughput improvement, followed by water-filling or geometric programming for per-user power reallocation (Ruby et al., 2017).
• Game-Theoretic Models: PD-NOMA uplink power control is modeled as a noncooperative game (utility = rate – power cost), with best-response updates converging to Nash equilibrium; user grouping and subcarrier assignment are formulated as coalition-formation or matching games for distributed, scalable management (Song et al., 2016).
• Robust/Outage/Secrecy Constraints: Resource allocation under channel uncertainty or secrecy outage (eavesdropper unknown CSI) leads to explicit closed-form power and rate vectors, order preservation in SIC, and proven gains over OMA in terms of max–min confidential throughput (He et al., 2016, Wei, 2019).
• Fairness and User Pairing: Power allocation regions guaranteeing every user at least its OMA rate (“Fair-NOMA”) have closed interval characterization and ensure both fairness and aggregate sum-rate gain, generalizable to arbitrary K (Oviedo et al., 2017).

3. SIC, Performance Limits, and Diversity Analysis

SIC fidelity critically determines system performance:

• Error and Diversity: Analytical and simulation results confirm that under perfect SIC, user i attains diversity order $d_i = i$ in PD-NOMA, generalizing to $d_i = iK$ for CD-NOMA with K subcarriers (Bariah et al., 2018, Yue et al., 2019). Imperfect SIC (residual interference, modelled via an interference variance parameter) collapses strong-user diversity to zero, yielding an error floor (Yue et al., 2019, Mouni et al., 2022).
• Finite-Blocklength Regime: For low-latency use cases (e.g., URLLC), finite-length coding rates are characterized using Polyanskiy's normal approximation; NOMA enables higher effective throughput or lower latency compared to OMA, especially when user targets are balanced (Sun et al., 2017).
• Secrecy Outage: Under practical eavesdropping models (unknown eavesdropper CSI), NOMA secrecy outage constraints leave the optimal user decoding order unchanged and often allocate more power to weak users to equalize confidential rate under increasing attack risk (He et al., 2016).

4. Extensions: MIMO, mmWave, THz, Cooperative and Random Access NOMA

NOMA exhibits unique behaviors and challenges in advanced physical-layer contexts:

• MIMO and Massive MIMO: Multi-antenna NOMA leverages spatial degrees: clustering, zero-forcing, and adaptive feedback bit assignments feed into a hierarchical resource allocation procedure maximizing sum-rate under both TDD/FDD modes. At low CSI/SNR, large clusters and SIC are optimal; at high SNR/CSI, orthogonal cluster-beamforming is near-optimal (Chen et al., 2017, Islam et al., 2019).
• Hybrid Beamforming and mmWave/THz: At mmWave/THz, tight beamwidth and high path loss motivate hybrid analog/digital beamforming, beamwidth control, and user clustering for scalable and robust multiuser support. Multi-beam and beam-squint techniques allow dynamic adjustment of analog beams to match spatially clustered users, maximizing energy and spectral efficiency (Magbool et al., 2021, Wei, 2019).
• Cooperative Relay NOMA: Multi-hop and composite NOMA exploiting decode-forward relays require aligned SIC order on both hops for optimality, with “hybrid” (partial CSI) power allocation strategies to control signaling overhead and maintain robustness (Wan et al., 2018).
• Random Access NOMA: In grant-free IoT networks, combining p-persistent ALOHA with layered NOMA (high/low power strata) and statistical guarantees for SIC enable 2–4$\times$ higher throughput versus classical slotted ALOHA (Chen et al., 2020).

5. Code, Waveform, and Noise-Domain Innovations

Emerging NOMA designs relax the dependence on SIC, power disparity, or codebook sparsity:

• Waveform-Domain NOMA: User data is mapped to distinct waveforms per RE (e.g., OFDM + OFDM-IM), enhancing robustness and enabling soft interference cancellation with low-density parity-check (LDPC) codes to mitigate error propagation under channel mismatch (Şahin et al., 2020).
• Noise-Domain NOMA: Information is embedded in controlled artificial noise mean or variance, with user data detected by minimum-distance and threshold tests; this design removes superposition decoding and SIC entirely. Monte-Carlo analyses confirm 3 dB BEP improvements over OMA-baseline at practical error rates, with ultra-low complexity and energy requirements, ideal for SWIPT-enabled or backscatter IoT nodes (Yapici et al., 7 Oct 2024).

6. System-Level Impact, Standardization, and Practical Considerations

NOMA has had measurable influence in industry and standardization:

• 3GPP Standardization: Multi-User Superposed Transmission (MUST) in LTE Rel-13/14, and multiple code/power-domain NOMA schemes in 5G NR, focus on grant-free UL access and collaborative DL transmission. Proposals include signature selection (SCMA, MUSA, PDMA), flexible grant assignment, and open-loop CoMP for dense or high-mobility scenarios (Chen et al., 2018).
• System Gains: Multiple experimental and simulation studies consistently report sum-rate, fairness, and connectivity gains—e.g., up to 30–50% sum-utility improvement over OMA with optimized PD-NOMA (Bao et al., 2017), nearly double the user satisfaction under URLLC constraints using SCMA (Chen et al., 2018), and up to 1 b/s/Hz ergodic sum-rate gap at high SNR in fair pairing (Oviedo et al., 2017).
• Limitations and Research Directions: SIC error floor, CSI uncertainty, and computational complexity persist as dominant bottlenecks. Current research focuses on robust clustering under imperfect SIC (Mouni et al., 2022), hybrid NOMA/OMA switching (Song et al., 2016), RIS-assisted NOMA (Islam et al., 2019), and noise/waveform domain innovations to handle 6G scenarios (ambient IoT, THz, etc.) (Yapici et al., 7 Oct 2024, Şahin et al., 2020).

7. Representative Performance Metrics and Results

System Aspect	PD-NOMA	CD-NOMA	New Domain Schemes
SIC Needed	Yes (multi-stage)	MPA/iterative, multiuser detection	Optional/none (waveform, noise)
Diversity Order	User order (i in K-users)	Order × spread sparsity (iK)	Scenario-dependent
Sum-Rate Gain over OMA	30–50% (heterogeneous)	Enhanced at high overloading	Up to 3 dB gain (noise-domain)
Robust to SIC Error	No (error floor for strong)	No (strong-user diversity=0)	Yes (e.g., ND-NOMA, waveform-NOMA)
Typical Use Case	DL/UL broadband, cell-edge	mMTC, grant-free, URLLC	Ambient IoT, energy harvesting

Analytical, asymptotic, and simulation-based results converge in confirming NOMA’s role as a critical multiple access scheme for both theoretical limits and deployable systems, especially as demand for massive connectivity, low-latency, and efficient resource utilization intensifies (Bao et al., 2017, Chen et al., 2017, Islam et al., 2019, Yapici et al., 7 Oct 2024).