Matrix Algebraic Approach Research Articles

Block-wise Kaczmarz successive interference cancellation: a matrix algebraic approach

Block-wise Kaczmarz successive interference cancellation: a matrix algebraic approach

Distributed Stabilization of Interconnected Multiagent Systems using Structurally Nonsymmetric Control Layers

Recently, graph theoretic distributed protocols have been introduced for the stabilization of interconnected multiagent systems with separate agent and control layers. For the case of unstable local agent dynamics, the existing results focus on only the matched interconnections. Further, except for a multiagent system of first- and second-order agents, the existing results are limited to the structurally symmetric control layers based on the undirected communication among controllers. We aim to relax these restrictions for multiagent systems with partially known unmatched or matched interconnections. We propose two step-by-step procedures to design robust distributed stabilization gains for the candidate nonsymmetric control layers in the presence of agent- and multiagent system-level modeling uncertainties. Combined with an optimal control formulation, we develop a matrix algebraic approach for the unmatched scenario and a Lyapunov-based approach for the matched case. In each case, we prove that all state trajectories of the two-layer interconnected multiagent system exponentially converge to the origin. We examine the feasibility of the proposed ideas in simulation.

Slow invariant manifold assessments in multi-route reaction mechanism

A complex chemical scheme is need to reduce their complexity without losing their key features. A chemical reaction scheme has braked down in different available reaction routes. On matrix algebraic approach bases, we analyze key-components, key reactions and reaction routes. A model reduction technique Spectral Quasi Equilibrium Manifold (SQEM) has applied to reduce the dimension of reaction mechanism. However, for the case study the behaviour of different available routes of reaction mechanism presented graphically. The reaction routes and invariants for idealized H2/O six-step reversible system and comparison has not been reported so far. To overcome this difficulty a clue about reaction routes have addressed through analysis of stoichiometry, the route compression with respect to their slow invariant manifold (SIM), the physical behaviour of chemically reacting species near to equilibrium point and extension towards the high dimension are expressed graphically.

Kaczmarz successive interference cancellation: A matrix algebraic approach

In this work, we propose a new successive interference cancellation (SIC) structure that makes use of the rows of the system matrix instead of its columns. Up to our knowledge, no similar work within the field of multiuser detection and interference cancellation exists. We first analyze this structure using a matrix-algebraic approach and prove that it is equivalent to a matrix filtering of the received signal, which allows the derivation of an exact expression for the BER performance. We then discuss its convergence behavior and determine the conditions of convergence. Finally, we conduct extensive simulations to assess its performance in different scenarios. Simulation results indicate that our proposed row-action SIC scheme significantly outperforms the conventional column-action SIC scheme for highly loaded systems.

Daylighting simulation for external Venetian blinds based on HDR sky luminance monitoring with matrix algebraic approach

An accurate daylighting simulation can potentially improve the quality of pre-planing buildings and regulating daylighting to achieve the goal of green buildings. However, standard sky models can hardly reproduce real skies in real-time for a specific location within its micro-climate. This paper investigates an embedded photometric device based on high dynamic range (HDR) sky luminance monitoring with high resolution mapping in simulating real-time horizontal work-plane illuminance distribution. To increase time efficiency in the iterative process for the illuminance calculation, a matrix algebraic approach was employed and adapted for the device. The photometric device was validated experimentally in a daylighting test module with external Venetian blinds at different tilt angle of slats. The results indicate the embedded photometric device based on monitored sky can improve accuracy in simulating real-time daylighting provision by over 3 times, with 15%∼37% average error, compared with a common practice using the Perez all-weather model.

Regularized Reconstruction of a Surface from its Measured Gradient Field

This paper presents several new algorithms for the regularized reconstruction of a surface from its measured gradient field. By taking a matrix-algebraic approach, we establish general framework for the regularized reconstruction problem based on the Sylvester Matrix Equation. Specifically, Spectral Regularization via Generalized Fourier Series (e.g., Discrete Cosine Functions, Gram Polynomials, Haar Functions, etc.), Tikhonov regularization, Constrained Regularization by imposing boundary conditions, and regularization via Weighted least squares can all be solved expediently in the context of the Sylvester Equation framework. State-of-the-art solutions to this problem are based on sparse matrix methods, which are no better than $$\mathcal {O}\!\left( n^6\right) $$ algorithms for an $$m\times n$$ surface with $$m \sim n$$ . In contrast, the newly proposed methods are based on the global least squares cost function and are all $$\mathcal {O}\!\left( n^3\right) $$ algorithms. In fact, the new algorithms have the same computational complexity as an SVD of the same size. The new algorithms are several orders of magnitude faster than the state-of-the-art; we therefore present, for the first time, Monte-Carlo simulations demonstrating the statistical behaviour of the algorithms when subject to various forms of noise. We establish methods that yield the lower bound of their respective cost functions, and therefore represent the “Gold-Standard” benchmark solutions for the various forms of noise. The new methods are the first algorithms for regularized reconstruction on the order of megapixels, which is essential to methods such as Photometric Stereo.

Modeling Liquid Terminal Operation and Service System in a Port Using Linier Matrix Algebraic Approach

Modeling Liquid Terminal Operation and Service System in a Port Using Linier Matrix Algebraic Approach

A generic modeling framework for queueing-inventory systems with a single removable server

In this article, we use a quasi-birth-and-death (QBD) modeling approach to model queueing-inventory systems with a single removable server. We consider both finite and infinite queueing capacities. Breakdowns and start-up times are also taken into account. All stochastic times are allowed to be general distributions except for the breakdown intervals, which are assumed to be exponential. The general distributions are approximated by phase type representations, resulting in the matrix-algebraic approach to derive the probability vector of the queue length. Some performance measures of interest are obtained by using both hybrid and standard procedures to solve the proposed QBD models. An optimal control policy based on a two-critical number approach using some convexity properties is proposed and its validity is verified through extensive numeric studies.

Privacy Preserving Data Mining Using Matrix Algebraic Approach

Privacy Preserving Data Mining Using Matrix Algebraic Approach

A new chip‐level linear SOR‐SIC multiuser detector for long‐code systems

AbstractIn this work, we introduce a new chip‐level linear modified‐SIC multi‐user structure that is asymptotically equivalent to successive over‐relaxation (SOR) iteration, which is known to outperform the conventional Gauss–Seidel iteration by an order of magnitude in terms of convergence speed. The main advantage of this scheme is that it uses directly the spreading codes and not the cross‐correlation coefficients and thus reduces significantly the overall computational complexity. This is critical for the design of low‐complexity multiuser detectors for long‐code CDMA systems such as IS95 and UMTS. We use a matrix algebraic approach to show the equivalence of the proposed scheme to linear matrix filtering. This allows obtaining an analytical expression for both the bit‐error rate (BER) and the asymptotic multiuser efficiency (AME). Moreover, we study the convergence behavior of the proposed scheme and prove that it converges if the relaxation factor is within the interval ]0, 2[. Simulation results are in excellent agreement with theory. Copyright © 2008 John Wiley & Sons, Ltd.

A matrix-algebraic approach to linear parallel interference cancellation in CDMA

Linear parallel interference cancellation (PIC) schemes are described and analyzed using matrix algebra. It is shown that the linear PIC, whether conventional or weighted, can be seen as a linear matrix filter applied directly to the chip-matched filtered received signal vector. An expression for the exact bit-error rate (BER) is obtained, and conditions on the eigenvalues of the code correlation matrix and the weighting factors to ensure convergence are derived. The close relationship between the linear multistage PIC and the steepest descent method (SDM) for minimizing the mean squared error (MSE) is demonstrated. A modified weighted PIC structure that resembles the SDM is suggested which approaches the minimum MSE (MMSE) detector rather than the decorrelator. It is shown that for a K-user system, only K PIC stages are required for the equivalent matrix filter to be identical to the the MMSE filter. For fewer stages, techniques are devised for optimizing the choice of weights with respect to the MSE. One unique optimal choice of weights is found, which will lead to the minimum achievable MSE at the final stage. Simulation results show that a few stages are sufficient for near-MMSE performance.

A matrix-algebraic approach to successive interference cancellation in CDMA

In this paper, we describe linear successive interference cancellation (SIC) based on matrix-algebra. We show that linear SIC schemes (single stage and multistage) correspond to linear matrix filtering that can be performed directly on the received chip-matched filtered signal vector without explicitly performing the interference cancellation. This leads to an analytical expression for calculating the resulting bit-error rate which is of particular use for short code systems. Convergence issues are discussed, and the concept of /spl epsiv/-convergence is introduced to determine the number of stages required for practical convergence for both short and long codes.

Harmonic analysis and restoration of separation methods for periodic signal mixtures: Algebraic separation versus comb filtering

The problem of separating a mixture of periodic signals into its constituent components occurs in sound detection, biomedical signal processing, and in communications. Existing approaches to solving it are either based on harmonic selection in the frequency domain or on linear comb filtering in the time-domain. In this paper, the recently proposed matrix algebraic separation approach is analyzed in the frequency domain. The insight obtained via this analysis leads to the development of harmonic restoration techniques that fill in the information missing at the harmonics shared by the components and also to the development of constraints on the carrier frequencies and bandwidths for narrowband, bandpass, and periodic AM–FM components for minimum information loss. The restored methods are then applied to mixtures of sines and AM–FM signals. Differences between this improved approach and a similar improvement of the comb filtering approach are also emphasized.