Power-Domain NOMA: Principles & Advances

Updated 7 April 2026

Power-Domain NOMA is a multiple-access scheme that overlaps user signals with different power levels based on channel conditions, ensuring efficient resource utilization.
It employs successive interference cancellation (SIC) to decode mixed signals, making it vital for enhancing spectral efficiency and user fairness in 5G and beyond.
Advanced power allocation and user pairing strategies optimize throughput and fairness while addressing the NP-hard resource allocation challenges inherent in complex wireless environments.

Power-Domain Non-Orthogonal Multiple Access (NOMA) is a multiple-access technique in which multiple users are overlapped in a shared time-frequency resource block by superimposing their signals at different power levels, such that each user’s share of power is commensurate with their channel conditions. At the receiver, user separation is accomplished through successive interference cancellation (SIC), enabling the system to approach the capacity region of the broadcast channel with higher spectral efficiency, user fairness, and massive connectivity than conventional orthogonal multiple access (OMA) schemes such as OFDMA or TDMA. Power-domain NOMA is a core technology for 5G and beyond wireless systems, with extensive research quantifying its performance limits, resource allocation trade-offs, and implementation challenges.

1. Signal Model and Core Principles

In the canonical downlink SISO (single-antenna) power-domain NOMA system, a base station transmits to $K$ users on the same time–frequency block. Let $x_i$ be the unit-power symbol for user $i$ , $h_i$ the complex base–user channel, and $P_i$ the allocated power ( $\sum_{i=1}^K P_i = P_\text{tot}$ ). The transmit signal is

$s = \sum_{i=1}^K \sqrt{P_i} x_i.$

The received signal at user $i$ is

$y_i = h_i s + n_i = h_i \sum_{j=1}^K \sqrt{P_j} x_j + n_i.$

Users are power-ordered so that users with weaker channels are allocated higher power. At the receiver, SIC is executed according to a decoding order matched to the power or effective SNR, removing higher-power (weaker-channel) users’ signals successively before decoding one’s own data (Islam et al., 2019, Islam et al., 2017, Islam et al., 2016).

The achievable rate for user $i$ (assuming perfect SIC for stronger users and treating weaker users as noise) is

$x_i$ 0

In uplink, the BS performs SIC, decoding the strongest user first (Islam et al., 2019).

2. Power Allocation and User Pairing

Efficient power allocation (PA) is central to exploiting NOMA’s potential. PA methods include:

Fixed allocation: Predefined power fractions regardless of instantaneous channel state. Typical for low-complexity deployment but suboptimal with respect to fairness or throughput.
Fractional Transmit Power Control (FTPC): $x_i$ 1 with $x_i$ 2, balancing fairness and throughput.
Optimization-based PA: Convex or quasi-convex programs maximizing weighted sum-rate, min–max rate, or $x_i$ 3-fair utilities under total power and QoS constraints (Islam et al., 2017, Islam et al., 2019, Islam et al., 2016). For $x_i$ 4 users, optimization is

$x_i$ 5

Fair-NOMA approaches: Impose per-user constraints ensuring that each user’s NOMA rate is at least as large as their OMA counterpart, constructing a closed-form feasible power region that is “safe” in the sense of monotonic improvement for all users, independent of scheduling (Oviedo et al., 2017, Oviedo et al., 2016, Timotheou et al., 2015).

User pairing or clustering (usually to $x_i$ 6 or $x_i$ 7 per group) is critical for scaling with $x_i$ 8. Pairing is typically based on maximizing channel gain disparity (pair strong/weak), aligning QoS, or exploiting spatial compatibility in MIMO regimes (Islam et al., 2017, Timotheou et al., 2015).

3. Successive Interference Cancellation: Principles and Limitations

SIC operates by having each user sequentially decode (and subtract) higher-power users’ signals before decoding its own. The decoding order is crucial and dictated by increasing channel gain (or decreasing allocated power).

Benefits include substantial suppression of inter-user interference for strong users; however, SIC’s practical performance is sensitive to:

Error propagation: Decoding errors at early SIC stages degrade subsequent users, setting practical limits on cluster size (commonly $x_i$ 9) (Liu et al., 2018, Islam et al., 2017).
SIC imperfections: Residual interference (e.g., due to channel estimation error or hardware limitations) introduces a performance floor for near users; under imperfect SIC, the diversity order for strong users collapses to zero, producing an error floor at high SNR (Yue et al., 2018, Yue et al., 2019).
Hardware complexity and energy cost: The computational and energy burdens of multiple decoding/subtraction stages grow with $i$ 0.

4. Resource Allocation, Complexity, and Solvability

The joint subcarrier and power allocation problem for multi-carrier power-domain NOMA is strongly NP-hard even for standard objectives including weighted sum-rate, proportional fairness, harmonic mean, and min–max fairness. Formally, for $i$ 1 users and $i$ 2 subcarriers, assigning at most $i$ 3 users per subcarrier and optimizing generalized-mean utilities subject to SIC order constraints cannot be solved in polynomial time unless $i$ 4 (Salaun et al., 2019).

Special cases where polynomial-time solutions exist include:

Fixed subcarrier–user assignments, reducing power optimization to convex programming.
The single-user or single-subcarrier regimes, where classical water-filling or sorting strategies suffice.
OFDMA settings ( $i$ 5), where assignments admit greedy or pseudoconvex algorithms.

Given computational intractability for large $i$ 6, practical systems rely on heuristics: sorted pairing, local search or greedy subcarrier assignment, fractional power control, and approximation algorithms with provable—but suboptimal—bounds.

Joint PA/SC allocation	Complexity	Applicability
Full joint optimization	NP-hard	General NOMA
Power only w/ fixed SC	Poly. time	Any SC fix
SC only (single user)	Poly. time	Water-filling
Heuristic/approximate	Poly. time	Large $i$ 7

5. Performance Metrics, Diversity, and Fairness

NOMA’s principal performance metrics include:

Spectral efficiency: NOMA achieves higher sum-rate than OMA especially when user channel disparities are wide. For two users, the sum-rate gain over OMA at high SNR is approximately $i$ 8.
Diversity order: For $i$ 9 users in perfect SIC, the $h_i$ 0-th ranked (weakest-channel) user experiences order $h_i$ 1 diversity; with imperfect SIC, strong users' diversity order drops to zero, producing an outage floor (Yue et al., 2018, Yue et al., 2019).
Fairness: Jain’s index and $h_i$ 2-fair utilities are typically used. Smart (fairness-enforcing) power allocation or pairing/pooling strategies can deliver per-user rate fairness or even guarantee each user never receives less than in OMA (Timotheou et al., 2015, Oviedo et al., 2017, Oviedo et al., 2016).

In multi-subcarrier (CD-NOMA) regimes, diversity orders scale with the code’s spreading factor $h_i$ 3, exceeding that of power-domain NOMA (e.g., $h_i$ 4 vs $h_i$ 5).

Throughput and delay-limited transmission regimes are also analyzed: sum throughput is the sum over scheduled user throughputs times their non-outage probability (Yue et al., 2018, Yue et al., 2019).

6. Advanced and Novel Power-Domain NOMA Variants

Several enhancements and generalizations of power-domain NOMA have been proposed:

Finite-constellation power-level modulation: Techniques such as PS-NOMA encode additional information in the power allocation coefficients themselves, providing throughput and BER improvements over conventional fixed-lever NOMA, especially at low–moderate SNR (Pei et al., 2021).
Sparse-dimension superposition (PD-SDCMA): Allocates each user’s constellation across a sparse subset of available high-dimensional signal space, reducing multi-user interference and enabling reliable access for more users compared to traditional NOMA (Li et al., 22 Feb 2025).
Power-balanced and network-coded NOMA: NOMA frameworks for near power-balanced cases (where SIC on its own degrades) exploit physical-layer network coding (PNC) and multiuser decoding to reliably separate users and improve system throughput without requiring large power disparities (Pan et al., 2017).

7. Extensions to MIMO, Distributed Antennas, RIS, and Integration with 5G/6G

Power-domain NOMA generalizes naturally to multi-antenna systems (MIMO-NOMA), leveraging joint spatial–power multiple access. Advanced precoder design—such as user-assisted simultaneous diagonalization—enables efficient implementation and ergodic rate region enlargement by matching spatial streams to users with self-interference cancellation at the strong user only (Krishnamoorthy et al., 2020). Further, distributed base station architectures can exploit the spatial diversity of multiple remote radio heads (RRHs) to support mutual SIC—yielding total transmit power reductions of 50–80% versus centralized deployments (Farah et al., 2017).

Emerging reconfigurable intelligent surfaces (RIS) can be incorporated to artificially induce favorable user channel gain differences, broadening NOMA’s applicability beyond inherently disparate channels. Joint beamforming and RIS phase control under NOMA are tractable via emerging convex–concave optimization frameworks, offering order-of-magnitude improvements in power efficiency (Fu et al., 2019).

NOMA is being tightly integrated into next-generation wireless standards (e.g., 3GPP LTE Release-13/14/15 for both eMBB and mMTC), and its research frontiers include robust resource management under imperfect CSI, cooperative NOMA with relaying or SWIPT, hybrid NOMA/OMA operation, and physical-layer security in the NOMA context (Islam et al., 2017, Islam et al., 2016, Liu et al., 2018, Islam et al., 2019).

References:

(Timotheou et al., 2015, Oviedo et al., 2016, Islam et al., 2016, Oviedo et al., 2017, Islam et al., 2017, Pan et al., 2017, Farah et al., 2017, Yue et al., 2018, Ali et al., 2018, Liu et al., 2018, Yue et al., 2019, Islam et al., 2019, Salaun et al., 2019, Fu et al., 2019, Krishnamoorthy et al., 2020, Pei et al., 2021, Li et al., 22 Feb 2025)