Refinement of Extended Accelerated Over-Relaxation Method for Solution of Linear Systems

Given any linear stationary iterative methods in the form z^(i+1)=Jz^(i)+f, where J is the iteration matrix, a significant improvements of the iteration matrix will decrease the spectral radius and enhances the rate of convergence of the particular method while solving system of linear equations in the form Az=b. This motivates us to refine the Extended Accelerated Over-Relaxation (EAOR) method called Refinement of Extended Accelerated Over-Relaxation (REAOR) so as to accelerate the convergence rate of the method. In this paper, a refinement of Extended Accelerated Over-Relaxation method that would minimize the spectral radius, when compared to EAOR method, is proposed. The method is a 3-parameter generalization of the refinement of Accelerated Over-Relaxation (RAOR) method, refinement of Successive Over-Relaxation (RSOR) method, refinement of Gauss-Seidel (RGS) method and refinement of Jacobi (RJ) method. We investigated the convergence of the method for weak irreducible diagonally dominant matrix, matrix or matrix and presented some numerical examples to check the performance of the method. The results indicate the superiority of the method over some existing methods.

Research on Pseudo-2D Joint Inversion of TEM and CSAMT Based on Well Log Constraint

The transient electromagnetic method (TEM) and controlled-source audio-frequency magnetotellurics method (CSAMT) are commonly used in detecting water abundance of rock formation and faults in coal mines. However, these methods show low accuracy, given the multiplicity of their inversion results, especially for areas with minor differences in lithology and electrical property. To improve the accuracy of electromagnetic exploration, a pseudo-2D joint inversion is performed. The objective function of this pseudo-2D joint inversion is established, and the joint inversion process is constrained by resistivity logging data. Afterward, the symmetric successive over-relaxation (SSOR) is used to realize the pseudo-2D joint inversion calculation of TEM and CSAMT with well log constraint. The effectiveness of joint inversion is verified by combining synthetic and field data. Results show that the pseudo-2D joint inversion results of TEM and CSAMT with well log constraint correspond to the actual geological situation. Compared with either TEM or CSAMT, joint inversion has a significantly better capability of reflecting water abundance in rock formation and faults.

SSOR Preconditioned Gauss-Seidel Detection and Its Hardware Architecture for 5G and Beyond Massive MIMO Networks

With the limitedness of the sub-6 GHz bandwidth, the world is exploring a thrilling wireless technology known as massive MIMO. This wireless access technology is swiftly becoming key for 5G, B5G, and 6G network deployment. The massive MIMO system brings together antennas at both base stations and the user terminals to provide high spectral service. Despite the fact that massive MIMO offers astronomical benefits such as low latency, high data rate, improved array gain, and far better reliability, it faces several implementation challenges due to the hundreds of antennas at the base station. The signal detection at the base station during the uplink is one of the critical issues in this technology. Detection of user signal becomes computationally complex with a multitude of antennas present in the massive MIMO systems. This paper proposes a novel preconditioned and accelerated Gauss–Siedel algorithm referred to as Symmetric Successive Over-relaxation Preconditioned Gauss-Seidel (SSORGS). The proposed algorithm will address the signal detection challenges associated with massive MIMO technology. Furthermore, we enhance the convergence rate of the proposed algorithm by introducing a novel Symmetric Successive Over-relaxation preconditioner (SSOR) scheme and an initialization scheme based on the instantaneous channel condition between the base station and the user. The simulation results show that the proposed algorithm referred to as Symmetric Successive Over-relaxation Preconditioned Gauss-Seidel (SSORGS) provides optimal BER performance. At BER =10−3, over the range of SNR, the SSORGS algorithm performs better than the traditional algorithms. Additionally, the proposed algorithm is computationally more efficient than the traditional algorithms. Furthermore, we designed a comprehensive hardware architecture for the SSORGS algorithm to find the interrelated components necessary to build the actual physical system.

A Feasible Approach to Determine the Optimal Relaxation \\[6pt]Parameters in Each Iteration for the SOR Method

The paper presents a dynamic and feasible approach to the successive over-relaxation (SOR) method for solving large scale linear system through iteration. Based on the maximal orthogonal projection technique, the optimal relaxation parameter is obtained by minimizing a derived merit function in terms of right-hand side vector, the coefficient matrix and the previous step values of unknown variables. At each iterative step, we can quickly determine the optimal relaxation value in a preferred interval. When the theoretical optimal value is hard to be achieved, the new method provides an alternative choice of the relaxation parameter at each iteration. Numerical examples confirm that the dynamic optimal successive over-relaxation (DOSOR) method outperforms the classical SOR method.

Efficient Iterative Massive MIMO Detectors Based on Iterative Matrix Inversion Methods

Massive multiple-input multiple-output (MIMO) is a key technology in fifth generation (5G) communication systems. Although the maximum likelihood (ML) obtains an optimal performance, it is prohibited in realization because of its high computational complexity. Linear detectors are an alternative solution, but they contain a matrix inversion which is not hardware friendly. Several methods have been proposed to approximate or to avoid the computation of exact matrix inversion. This chapter garners those methods and study their applicability in massive MIMO system so that a generalist in communication systems can differentiate between different algorithms from a wide range of solutions. This chapter presents the performance-complexity profile of a detector based on the Neuamnn-series (NS), Newton iteration (NI), successive over relaxation (SOR), Gauss-Seidel (GS), Jacobi (JA), Richardson (RI), optimized coordinate descent (OCD), and conjugate-gradient (CG) methods in 8×64, 16×64, and 32×64 MIMO sizes, and modulation scheme is 64QAM.

Robot pathfinding with obstacle avoidance capabilities in a static indoor environment via TOR iterative method using harmonic potentials

Mobile robots are always in a state where they have to find a collision-free path in their environment from start to the target point. This study tries to solve the problem of mobile robot iteratively by using a numerical technique. It is based on potential field technique that was modelled using the Laplace’s equation to restrain the creation of a potential functions across regions in the mobile robot’s configuration space. The gradient formed by the potential field is then used to generate a path for the robot to advance through. The present paper proposes a Two-Parameter Over-Relaxation (TOR) iterative method that is used to solve Laplace’s equation for obtaining the potential field that is then utilized for finding path of the robot, thus solving the robot pathfinding problem. The experiment indicates that it is capable of producing a smooth path between the starting and target points through the use of a finite-difference technique. Furthermore, the simulation results show that this numerical approach executes quicker and provides a smoother trail than to the previous works, that includes Successive Over-Relaxation (SOR) and Accelerated Over-Relaxation (AOR) methods.