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- Title
- Optimization of Large-Scale NOMA With Incidence Matrix Design and Physical Layer Security
- Creator
- Hwang, Eli W.
- Date
- 2024
- Description
-
The Non-Orthogonal Multiple Access (NOMA) system is recognized for its capability to achieve higher spectral efficiency and massive...
Show moreThe Non-Orthogonal Multiple Access (NOMA) system is recognized for its capability to achieve higher spectral efficiency and massive connectivity. NOMA is intended to transmit massive user communications. The incidence matrix governs the relationship between users and resources for the Code domain NOMA (CD-NOMA). However, NOMA studies focus less on the design and optimization of the incidence matrix.Therefore, this thesis aims to investigate the development of a secure and large-scale NOMA system based on incidence matrix design. The main contributions are outlined as follows: Firstly, this research introduces a novel NOMA system. Distinct from existing studies, the NOMA system is based on combinatorial design. This innovative approach, coupled with a unique constellation design, eliminates the surjective mapping from the linear adding data of multiusers, reducing the complexity of constellation design and Multiuser Detection (MUD). The characteristics of the incidence matrix designs, Simple Orthogonal Multi-Arrays (SOMA), are explored, which display a distinct Latin Square pattern. The SOMA design's unique structure allows for the creation of a highly flexible and fair resource allocation matrix. The NOMA system's theoretical performance analysis equations are established, supporting dynamic adaptability and optimization. The design is validated by Monte Carlo simulation. Compared to other NOMA schemes, it offers higher degrees of freedom and lower complexity while maintaining graceful error rates to transmit a larger number of users. Secondly, a novel NOMA system utilizing incidence matrix information in the uplink is investigated. The incidence matrix pattern is exploited for MUD to achieve large-scale user connectivity. The incidence matrix is designed based on two critical mathematical concepts: parallel classes in hypergraph theory and orthogonal arrays (OAs) in combinatorial designs. Unlike other NOMA schemes, which require modification of their receiver and transmitter to decode superimposed multiuser signals, the unique pattern of the OA structure enables the use of conventional modulators. Consequently, the system load increases and the complexity and latency are reduced. The order of magnitude of the decoding complexity can be significantly reduced from O(N^3) to O(N) compared to the conventional minimum mean-square estimation (MMSE) decoder. Monte Carlo simulation validates that this novel NOMA system outperforms other NOMA designs in terms of error rate, data rate, and system size. Finally, a reconfigurable convolutional encoder design that integrates security and error correction based on physical layer security (PLS) and randomness is developed. This design addresses concerns over privacy, security, and reliability of Internet of Things devices in edge computing networks. The lightweight Convolutional encoders are designed to ensure security by updating the transfer function dynamically with user data. The reconfigurability of the design is achieved by replacing the fixed adder that represents the generator polynomials with the switch adder, enabling the use of 87 billion distinct updating structures, thereby enhancing the versatility of the design. BER-based PLS paradigms are demonstrated in the simulation. In the simulation, the robustness and randomness of this design are further validated through tests suggested by the National Institute of Standards and Technology for cryptographically secure pseudorandom number generators, such as the monobits, longest one, and run tests.
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- Title
- A Kernel-Free Boundary Integral Method for Two-Dimensional Magnetostatics Analysis
- Creator
- Jin, Zichao
- Date
- 2023
- Description
-
Performing magnetostatic analysis accurately and efficiently is crucial for the multi-objective optimization of electromagnetic device designs...
Show morePerforming magnetostatic analysis accurately and efficiently is crucial for the multi-objective optimization of electromagnetic device designs. Therefore, an accurate and computationally efficient method is essential. Kernel Free Boundary Integral Method is a numerical method that can accurately and efficiently solve partial differential equations. Unlike traditional boundary integral or boundary element methods, KFBIM does not require an analytical form of Green’s function for evaluating integrals via numerical quadrature. Instead, KFBIM computes integrals by solving an equivalent interface problem on a Cartesian mesh. Compared with traditional finite difference methods for solving the governing PDEs directly, KFBIM produces a well-conditioned linear system. Therefore, the numerical solution of KFBIM is not sensitive to computer round-off errors, and the KFBIM requires only a fixed number of iterations when an iterative method (e.g., GMRES) is applied to solve the linear system.In this research, the KFBIM is introduced for solving magnetic computations in a toroidal core geometry in 2D. This study is very relevant in designing and optimizing toroidal inductors or transformers used in electrical systems, where lighter weight, higher inductance, higher efficiency, and lower leakage flux are required. The results are then compared with a commercial finite element solver (ANSYS), which shows excellent agreement. It should be noted that, compared with FEM, the KFBIM does not require a body-fitted mesh and can achieve high accuracy with a coarse mesh. In particular, the magnetic potential and tangential field intensity calculations on the boundaries are more stable and exhibit almost no oscillations.Furthermore, although KFBIM is accurate and computationally efficient, sharp corners can be a significant problem for KFBIM. Therefore, an inverse discrete Fourier transform (DFT) based geometry reconstruction is explored to overcome this challenge for smoothening sharp corners. A toroidal core with an airgap (C-core) is modeled to show the effectiveness of the proposed approach in addressing the sharp corner problem. A numerical example demonstrates that the method works for the variable coefficient PDE. In addition, magnetostatic analysis for homogeneous and nonhomogeneous material is presented for the reconstructed geometry, and results carried out from KFBIM are compared with the results of FEM analysis for the original geometry to show the differences and the potential of the proposed method.
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