Three-User ND-NOMA Scheme

• The paper demonstrates that encoding user data in noise parameters—mean, variance, and correlation—eliminates the need for successive interference cancellation.
• It details both uplink and downlink architectures where simple statistical estimators decode user bits, significantly reducing receiver complexity.
• Performance analysis under Rician fading confirms enhanced bit error rate performance and scalability, making the method ideal for energy-efficient IoT deployments.

A three-user noise-domain non-orthogonal multiple access (ND-NOMA) scheme is an advanced multiple access technique for wireless networks in which each user’s information is mapped onto independently modulated statistical properties of artificially generated or physical-layer Gaussian noise. Departing from the classic power-domain NOMA that relies on successive interference cancellation (SIC) and superposition coding, ND-NOMA multiplexes user data by embedding it in separate noise features—mean, variance, and correlation—allowing for low-complexity, energy-efficient, and highly scalable multi-user transmission. The three-user ND-NOMA concept has been demonstrated in both uplink and downlink scenarios, with empirical and theoretical evaluations confirming promising bit error rate (BER) performance under Rician fading channels, making it particularly suitable for Internet-of-things (IoT) deployments (&&&^^^^1^^^^&&&).

^^^^^^^^1 Statistical Domain Mapping and System Design

ND-NOMA for three users assigns distinct statistical attributes of the noise sequence to each user:

• User ^^^^^^^^1: Bit value encoded by shifting the mean of the Gaussian noise (e.g., +%%%%^^^^1^^^^%%%% for "^^^^^^^^1 or –%%%%^^^^^^^^1 for "^^^^1^^^^").
• User 2: Bit value encoded by selecting one of two prescribed variance levels ($\sigma_{2,l}^2$ or $\sigma_{2,h}^2$).
• User 3: Bit value encoded by modulating the correlation coefficient between pairs of consecutive samples, using bivariate Gaussian distributions with covariance matrices

$$\Sigma_k = \sigma_3^2 \begin{bmatrix} 1 & \rho_k \ \rho_k & 1 \end{bmatrix}$$

where $\rho_k$ is set to $\rho_l$ or $\rho_h$ depending on the transmitted bit.

This orthogonal mapping in the "noise domain" (mean, variance, correlation) ensures that each user’s data can be robustly detected without complex multi-user decoding or interference cancellation.

2. Uplink and Downlink Architectures

ND-NOMA supports both uplink and downlink operations:

• Uplink: Each user transmits a noise sequence modulated according to their assigned statistical domain. The base station receives the composite signal:

$$y^n = h_1 s_1^n + h_2 s_2^n + h_3 s_3^n + w^n, \quad n=1, \ldots, N$$

where $h_i$ is the channel coefficient for user %%%%^^^^^^^^1 %%%%^^^^^^^^1 is the %%%%^^^^^^^^1 noise sample from user %%%%^^^^^^^^1 and %%%%^^^^^^^^1 is additional noise. The BS performs joint detection by computing sample mean, sample variance, and sample correlation to decode each user’s bit.

• Downlink: The BS generates a composite signal with mean, variance, and correlation modulated for users ^^^^^^^^1 2, and 3, respectively. Each user receives this signal over its own channel and applies a domain-specific detector (mean, variance, or correlation estimator) to recover their bits, optionally subtracting known contributions from other domains if needed.

This architectural separation enables independent user decoding and facilitates scalable ND-MOMA schemes for practical network deployments (&&&^^^^1^^^^&&&).

3. Detection Algorithms for Each Statistical Domain

Detecting user bits in ND-NOMA schemes is performed using simple statistical estimators:

User	Statistic	Detector Rule
User ^^^^^^^^1	Mean	Minimum-distance: %%%%^^^^^^^^1 if %%%%^^^^^^^^1
User 2	Variance	Threshold: %%%%^^^^^^^^1 assigns "^^^^1^^^^"; %%%%^^^^^^^^1 assigns "^^^^^^^^1
User 3	Correlation	Minimum-distance on empirical correlation, %%%%^^^^^^^^1 if %%%%2^^^^1^^^^%%%%

Where

• %%%%2^^^^^^^^1
• $s_y^2 = \frac{1}{N-1}\sum_{n=1}^{N}|y^n-\bar{y}|^2$
• $$\hat{\rho}_y = \frac{2}{N}\sum_{n=1}^{N/2}\text{Re}\{(y^n-\bar{y}_1)(y^{n+N/2}-\bar{y}_2)^*\}$$

Thresholds $\gamma$ and expected means/correlations are precomputed based on the network parameters and noise-domain mapping. No SIC or iterative cancellation is required, which substantially reduces receiver complexity and processing latency.

4. Bit Error Rate Analysis and Performance Under Fading Channels

Theoretical and simulation results under Rician fading channels show that:

• Increasing the number of noise samples ($N$) per bit improves statistical estimation and decreases the BER for all users.
• The mean-modulated user generally achieves lower BER compared to variance and correlation users due to the robustness of mean detection.
• System BER expressions are derived using Q-functions:

$P_{b,i} = Q\left(\frac{m_{Di}}{\sigma_{Di}}\right)$

where $m_{Di}$ and $\sigma_{Di}$ are domain-specific means and variances, explicitly computed based on the model for each user.

Simulations confirm theoretical predictions: higher Rician factors (strong LOS component) further reduce BER. The error probability is mainly determined by SNR, the number of samples $N$, and the effective separation of the modulated parameters.

5. Advantages for Energy-Efficient, Low-Complexity, and Scalable IoT Networks

The three-user ND-NOMA scheme is characterized by:

• Low Power: User data is mapped onto statistical noise features rather than requiring actively modulated high-power signals. No transmitter waveform complexity is added beyond noise generation and simple parameter switching.
• Low Complexity: Both transmitters and receivers only compute basic statistics or perform threshold comparisons on observed noise samples.
• No SIC Required: The scheme eliminates the need for multi-stage interference cancellation prevalent in PD-NOMA, substantially reducing computational workload, latency, and error propagation potential.
• Scalability Potential: Additional noise dimensions (e.g., higher-order moments or spectral properties) could be exploited to multiplex more users. The correlation dimension serves as the third orthogonal feature in the present scheme, directly increasing multi-user capacity (&&&^^^^1^^^^&&&).
• IoT Suitability: Simplified hardware requirements and low transmit power consumption harmonize with the constrained nature of IoT devices, supporting deployment in dense networks and long-term, battery-powered scenarios.

A plausible implication is that further extension to higher-dimensional noise features could enable ND-NOMA for larger user groups without substantially increasing system complexity or power requirements.

6. Comparative Perspective and Theoretical Context

The ND-NOMA framework for three users stands in contrast to conventional PD-NOMA methods (e.g., (Yapici et al., 7 Oct 2024, Dai et al., 2017, Wei, 2019)) where the complexity and energy overhead of SIC and superposition coding grow with the number of simultaneous users. ND-NOMA’s domain-orthogonality enables truly simultaneous multi-user communication with straightforward detection and minimal interference effects. Analytical methodologies such as order statistics, joint detection, and Q-function-based BER analysis provide rigorous foundations for performance characterization in clustered or large-scale network settings (Tabassum et al., 2016).

In summary, three-user ND-NOMA achieves non-orthogonal multi-access by encoding user bits in orthogonal noise statistics—mean, variance, and correlation—accommodating scalable low-complexity and highly energy-efficient multi-user communication, particularly advantageous for next-generation IoT and sensor networks (&&&^^^^1^^^^&&&).