ADMM-based Detector for Large-scale MIMO Code-domain NOMA Systems (2306.02032v1)

Abstract: Large-scale multi-input multi-output (MIMO) code domain non-orthogonal multiple access (CD-NOMA) techniques are one of the potential candidates to address the next-generation wireless needs such as massive connectivity, and high reliability. This work focuses on two primary CD-NOMA techniques: sparse-code multiple access (SCMA) and dense-code multiple access (DCMA). One of the primary challenges in implementing MIMO-CD-NOMA systems is designing the optimal detector with affordable computation cost and complexity. This paper proposes an iterative linear detector based on the alternating direction method of multipliers (ADMM). First, the maximum likelihood (ML) detection problem is converted into a sharing optimization problem. The set constraint in the ML detection problem is relaxed into the box constraint sharing problem. An alternative variable is introduced via the penalty term, which compensates for the loss incurred by the constraint relaxation. The system models, i.e., the relation between the input signal and the received signal, are reformulated so that the proposed sharing optimization problem can be readily applied. The ADMM is a robust algorithm to solve the sharing problem in a distributed manner. The proposed detector leverages the distributive nature to reduce per-iteration cost and time. An ADMM-based linear detector is designed for three MIMO-CD-NOMA systems: single input multi output CD-NOMA (SIMO-CD-NOMA), spatial multiplexing CD-NOMA (SMX-CD-NOMA), and spatial modulated CD-NOMA (SM-CD-NOMA). The impact of various system parameters and ADMM parameters on computational complexity and symbol error rate (SER) has been thoroughly examined through extensive Monte Carlo simulations.

• The paper introduces an ADMM-based iterative detector that reformulates the maximum likelihood detection into a sharing optimization problem tailored for MIMO CD-NOMA systems.
• The method efficiently reduces computational complexity by enabling parallel processing across SIMO, SMX, and SM-CD-NOMA models while maintaining robust symbol error rates.
• Performance simulations confirm that the detector manages high modulation orders and overloading factors effectively, paving the way for real-time 6G system implementations.

Overview of ADMM-based Detector for Large-scale MIMO CD-NOMA Systems

This paper addresses a complex problem in next-generation wireless communications by proposing a computationally efficient detector for large-scale MIMO Code-Domain Non-Orthogonal Multiple Access (CD-NOMA) systems. The primary challenge tackled is designing detectors that maintain optimal performance with manageable computational complexity.

Key Contributions

1. ADMM-based Iterative Detector: The authors propose an iterative linear detector using the Alternating Direction Method of Multipliers (ADMM). This approach reformulates the maximum likelihood (ML) detection problem into a sharing optimization problem.
2. System Model Reformulation: The paper details new modeling techniques for three MIMO-CD-NOMA systems: SIMO-CD-NOMA, SMX-CD-NOMA, and SM-CD-NOMA. The reformulation allows the application of the ADMM detector, facilitating parallel processing in detection.
3. Complexity Reduction: By employing the distributive nature of ADMM, the paper significantly reduces computational complexity, making it feasible for real-time applications.
4. Performance Analysis: The authors conduct extensive Monte Carlo simulations to evaluate the impact of system and ADMM parameters on computational complexity and Symbol Error Rate (SER). The simulations show that ADMM outperforms traditional detectors like MPA and GSD under certain conditions, especially for large modulation orders.

Numerical Insights

• The proposed ADMM detector can handle large modulation orders and overloading factors efficiently, with computational costs remaining polynomial concerning other system parameters.
• For the SIMO-SCMA system with a $150\%$ overloading factor, the ADMM detector achieves comparable error rates to the MPA detector, while significantly reducing computational complexity.

Implications and Future Directions

This research presents significant implications for the design of detectors in advanced wireless networks where massive connectivity and high reliability are prerequisites. Practically, the reduced complexity of the ADMM-based detector opens avenues for real-time implementation in future wireless networks, such as 6G.

Theoretically, this work provides a foundation for exploring ADMM in other complex optimization problems beyond MIMO-CD-NOMA systems. Future research could explore the development of ADMM-based soft decision detectors for coded systems and investigate its integration with advanced coding techniques. Additionally, analysis of the detector's performance under dynamic channel conditions might offer further insights into its practical deployment.

In conclusion, this paper contributes to the ongoing research efforts in enhancing spectral efficiency and connectivity in modern communication systems. The application of ADMM provides a promising direction towards achieving these goals with computational efficiency.