Power-Domain NOMA in 5G/6G Wireless

• PD-NOMA is a multiple-access technique that employs signal superposition and successive interference cancellation to multiplex users at different power levels.
• It leverages optimized power allocation and order-based decoding to enhance spectral efficiency and fairness compared to traditional orthogonal schemes.
• Advanced implementations integrate MIMO, RIS, and network coding to support massive connectivity and improve outage performance in next-generation networks.

Power-Domain Non-Orthogonal Multiple Access (PD-NOMA) is a multiple-access technique leveraging superposition coding and successive interference cancellation (SIC) in the power domain to enable simultaneous transmission to multiple users over the same time-frequency resources. PD-NOMA fundamentally departs from orthogonal resource partitioning schemes by multiplexing users at distinct power levels, targeting spectral efficiency, massive connectivity, and flexible fairness in next-generation wireless systems (notably 5G/6G).

1. Fundamental Principles and System Model

PD-NOMA operates by superposing multiple user signals at the transmitter, assigning distinct power fractions according to users’ channel conditions. In the canonical two-user downlink model, a base station transmits

$$x = \sqrt{P_1}\,s_1 + \sqrt{P_2}\,s_2,\quad \text{with } P_1 + P_2 = P_\text{total}$$

where $s_1$ and $s_2$ are unit-power user symbols. The weaker user (poorer channel) is allocated higher power to guarantee its rate, while the stronger user receives less. At the receiver, decoding proceeds via SIC: the strong user successively decodes and strips off weaker users’ signals, then decodes its own symbol. A general K-user model extends these principles, sorting users by channel gain and recursively decoding from weakest to strongest (Islam et al., 2017, Liu et al., 2018).

Key advantages over OMA (TDMA, FDMA, OFDMA) include full resource reuse, substantial spectral efficiency increases, and configurable fairness via power assignment. PD-NOMA’s sum-rate region strictly encompasses that of OMA when user channels are heterogeneous (Islam et al., 2017).

2. Transmitter Power Allocation and Optimization

Power allocation is central to PD-NOMA’s rate, fairness, and outage behavior. Standard optimization objectives are:

• Sum-rate maximization: Maximize $\sum_i \log_2(1+\mathrm{SINR}_i)$ under total power, per-user minimum rate, and non-negativity constraints (Islam et al., 2016, Timotheou et al., 2015).
• Fairness-maximizing (max-min): Maximize the minimum user rate, solved via bisection or LP (Timotheou et al., 2015).
• Outage minimization (average CSI): Minimize worst-case user outage probability subject to power constraints.

Closed-form or polynomial complexity solutions exist in two-user and K-user scenarios. Under instantaneous CSI, optimal allocation ensures all users achieve equalized rates at the max-min optimum via recursive back-substitution (Timotheou et al., 2015). For average CSI, per-user outage thresholds are decoupled, enabling efficient bisection (Timotheou et al., 2015).

With minimum-rate constraints, the problem is convex for two-user cases but generally non-convex for larger clusters, though convex approximations and efficient greedy algorithms provide near-optimal solutions (Ali et al., 2018).

The diversity order in PD-NOMA is governed by user index: for the “far” user $m$ and “near” user $n$ (sorted so $|h_m|^2 < |h_n|^2$), under perfect SIC, $d_m = m$, $d_n = n$ (Yue et al., 2019, Yue et al., 2018).

3. Receiver Successive Interference Cancellation (SIC) and Practical Considerations

At the receiver, SIC enables separation of superposed signals. User $i$ (strongest) first decodes all weaker signals sequentially, subtracts each, and finally decodes its own, with SINR for $i$ as:

$$\mathrm{SINR}_i = \frac{p_i |h_i|^2}{\sum_{j=i+1}^K p_j |h_i|^2 + \sigma^2}$$

(Liu et al., 2018). SIC’s performance strongly depends on accurate ordering and channel estimation. Imperfect SIC yields residual interference that induces an irreducible error floor at high SNR, eliminating diversity gain for affected users (Yue et al., 2019, Yue et al., 2018). Receiver complexity grows with cluster size $K$, scaling as $O(K \log K)$ for sorting and $O(K)$ decoders (Islam et al., 2017).

In practice, cluster size is limited ($K\leq 2$ or $3$) to bound complexity and error propagation. Hardware limitations such as ADC dynamic range and quantization noise also constrain performance, particularly for weak signals in SIC chains (Islam et al., 2017, Islam et al., 2016).

4. Multiuser Extensions and Advanced Architectures

4.1. MIMO and Beamforming

PD-NOMA is compatible with multi-antenna base stations (MIMO), combining precoding and power-domain superposition. Cluster-based designs assign users to beams and then multiplex via PD-NOMA per beam. Zero-forcing (ZF) and MMSE beamformers suppress inter-beam interference; intra-beam users are separated by SIC (Jiang et al., 2018, Krishnamoorthy et al., 2020).

In pattern-division multiple access (PDMA), the transmitter jointly optimizes user-beam assignment and per-beam power allocation, achieving convexity in the power domain and combinatorial optimization in the beam domain. Beam assignment yields larger sum-rate improvements than fine-tuning power splits once the spatial pattern is fixed (Jiang et al., 2018).

4.2. Sparse-Dimensional Superposition

Power-Domain Sparse Dimensional Constellation Multiple Access (PD-SDCMA) extends PD-NOMA by sparsifying constellation allocation in high-dimensional signal spaces, assigning each user a subset of orthogonal dimensions (Li et al., 22 Feb 2025). This reduces mutual interference and supports more users at a fixed BER versus conventional PD-NOMA. Dimension selection strategies optimize minimum Euclidean distance among superposed constellations to enhance reliability. Typical simulation gains are 10–20 dB SNR and support for 5+ simultaneous users under QPSK/16QAM (Li et al., 22 Feb 2025).

4.3. Cooperative and Network-Coded Multiple Access

In cooperative scenarios, strong users relay weak user data, enhancing diversity and fairness. Network-Coded Multiple Access (NCMA) jointly applies physical-layer network coding and multiuser decoding, particularly useful in near power-balanced regimes where conventional SIC fails. Rate-diverse NCMA exploits symbol-splitting channel coding, yielding up to 80% throughput gain over homogeneous modulation in experiments (Pan et al., 2017).

4.4. Reconfigurable Intelligent Surfaces (RIS)

RIS-enabled PD-NOMA artificially increases channel gain disparities, allowing more effective power multiplexing and sum-rate improvements even when user direct-link channels are similar. Optimization of beamformers and RIS phase shifts is performed via DC-based alternating algorithms to minimize transmit power or maximize rate (Fu et al., 2019).

5. Performance Analysis and Comparative Metrics

5.1. Spectral Efficiency and Rate Region

PD-NOMA sum-rate gains over OMA (TDMA/OFDMA) are typically 10–40% in cell-edge scenarios and multiuser networks when channel heterogeneity is present (Islam et al., 2017, Liu et al., 2018). The achievable rate region strictly contains the OMA region, with maximum gain realized as the difference between strongest and weakest user channel increases (Liu et al., 2018).

Table: Comparative Sum-Rate Gains (illustrative, (Timotheou et al., 2015, Islam et al., 2017, Ali et al., 2018))

Scenario	OMA Sum-Rate	PD-NOMA Sum-Rate	Gain (%)
2-user, SISO	Baseline	+10–30%	Cell edge
MIMO, diverse	Baseline	+20%	Sufficient gain
Massive access	Baseline	Up to +40%	Sparse constell

Spectral efficiency gains are preserved under appropriate power allocation, cluster sizing, and SIC quality (Ali et al., 2018, Yue et al., 2018).

5.2. Fairness and Outage

Fairness-centric allocation (max-min rate or min-max outage) delivers worst-user rates nearly twice those of TDMA, with outage probabilities often reduced by an order of magnitude (Timotheou et al., 2015). Jain’s index is improved by allocating more power to weaker users, balancing throughput across heterogeneous channels (Islam et al., 2017).

5.3. Error Floors and Diversity

With imperfect SIC, residual interference yields a diversity order of zero (“error floor”) for affected users, confirmed by outage analyses (Yue et al., 2019, Yue et al., 2018). Under perfect SIC, diversity order equals user index, with overall performance dictated by the weakest link.

6. Implementation Issues and Security Aspects

Major practical challenges include:

• SIC Error Propagation: Degraded decoding affects all subsequent users; mitigated via symbol-level SIC and robust coding (Islam et al., 2016).
• Channel Estimation and CSI: Accurate instantaneous CSI is required for power ordering and allocation. Feedback quantization and estimation accuracy are critical (Islam et al., 2017).
• Resource Control: Mixed-integer optimization in subcarrier and power allocation is often solved via Lagrangian dual decomposition, matching theory, or greedy heuristics for scalable scheduling (Liu et al., 2018).
• Physical Layer Security: Joint subcarrier and power optimization can enhance sum secrecy rate, especially if eavesdroppers are prevented from performing SIC (Forouzesh et al., 2018). Robust formulations address imperfect CSI and provide significant secrecy gains (up to 82.5% in simulations) (Forouzesh et al., 2018).

7. Recent Innovations and Future Directions

Emerging enhancements include:

• Power Level Modulation: Encoding information not just in symbols but in the selected power levels can increase spectral efficiency by log₂(number of power levels) bits/s/Hz and reduce BER, particularly in finite-alphabet scenarios (Pei et al., 2021).
• Ultra-Massive Access: Schemes such as PD-SDCMA and hybrid sparse-domain multiplexing aim to support tens or hundreds of simultaneous users by careful dimension and power scheduling (Li et al., 22 Feb 2025).
• Integration with Millimeter-Wave, RIS, and Machine Learning: Ongoing research addresses NOMA in high-frequency bands, leveraging RIS for channel shaping, and using deep reinforcement learning for resource management (Fu et al., 2019, Liu et al., 2018).
• Standardization: 3GPP LTE-A Release 13–15 has adopted PD-NOMA under Multi-User Superposition Transmission (MUST), with continued industry and academic attention (Islam et al., 2017).

Limitations remain with respect to SIC complexity, error propagation, stringent channel gain disparity requirements, and multi-cell interference. Design guidelines recommend cluster-size optimization, prioritized beam-pattern assignment, simple power rules (geometric allocation), and robust SIC implementation for scalable deployment.

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In summary, Power-Domain NOMA is a rigorously validated multiple-access paradigm utilizing signal superposition and SIC, achieving multiplexing, high spectral efficiency, and fairness with manageable complexity and robust optimization frameworks. Ongoing enhancements in dimensional sparsity, RIS-assisted multiplexing, network coding, and power-level modulation indicate its adaptability and centrality in future wireless standards and architectures (Li et al., 22 Feb 2025, Jiang et al., 2018, Fu et al., 2019, Pan et al., 2017, Pei et al., 2021).