---
title: Power-Domain NOMA in 5G/6G Wireless
url: https://www.emergentmind.com/topics/power-domain-non-orthogonal-multiple-access
type: topic
---

# Power-Domain NOMA in 5G/6G Wireless

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 [1706.08215], [1808.00277].

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 [1706.08215].

## 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 [1609.06261], [1504.02300].
- **Fairness-maximizing (max-min):** Maximize the minimum user rate, solved via bisection or LP [1504.02300].
- **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 [1504.02300]. For average CSI, per-user outage thresholds are decoupled, enabling efficient bisection [1504.02300].

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 [1803.07866].

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, $d_m = m$, $d_n = n$ [1901.06755], [1801.08181].

## 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:
$$
\mathrm{SINR}_i = \frac{p_i |h_i|^2}{\sum_{j=i+1}^K p_j |h_i|^2 + \sigma^2}
$$
[1808.00277]. 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 [1901.06755], [1801.08181]. Receiver complexity grows with cluster size $K$, scaling as $O(K \log K)$ for sorting and $O(K)$ decoders [1706.08215].

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 [1706.08215], [1609.06261].

## 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 [1801.02308], [2005.02308].

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 [1801.02308].

### 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 [2502.16271]. 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 [2502.16271].

### 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 [1701.06825].

### 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 [1910.07361].

## 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 [1706.08215], [1808.00277]. The achievable rate region strictly contains the OMA region, with maximum gain realized as the difference between strongest and weakest user channel increases [1808.00277].

Table: Comparative Sum-Rate Gains (illustrative, [1504.02300], [1706.08215], [1803.07866])

| 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 [1803.07866], [1801.08181].

### 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 [1504.02300]. Jain’s index is improved by allocating more power to weaker users, balancing throughput across heterogeneous channels [1706.08215].

### 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 [1901.06755], [1801.08181]. 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 [1609.06261].
- **Channel Estimation and CSI:** Accurate instantaneous CSI is required for power ordering and allocation. Feedback quantization and estimation accuracy are critical [1706.08215].
- **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 [1808.00277].
- **Physical Layer Security:** Joint subcarrier and power optimization can enhance sum secrecy rate, especially if eavesdroppers are prevented from performing SIC [1806.02013]. Robust formulations address imperfect CSI and provide significant secrecy gains (up to 82.5% in simulations) [1806.02013].

## 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 [2107.12668].
- **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 [2502.16271].
- **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 [1910.07361], [1808.00277].
- **Standardization:** 3GPP LTE-A Release 13–15 has adopted PD-NOMA under Multi-User Superposition Transmission (MUST), with continued industry and academic attention [1706.08215].

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.

---

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 [2502.16271], [1801.02308], [1910.07361], [1701.06825], [2107.12668].

Source: https://www.emergentmind.com/topics/power-domain-non-orthogonal-multiple-access