scholarly journals Matrix Methods for Estimating the Coherence Functions from Estimates of the Cross-Spectral Density Matrix

1996 ◽  
Vol 3 (4) ◽  
pp. 237-246 ◽  
Author(s):  
D.O. Smallwood
Keyword(s):  
Density Matrix ◽  
Spectral Density ◽  
Multiple Input Multiple Output ◽  
Spectral Density Matrix ◽  
Multiple Input ◽  
Cross Spectral Density ◽  
Input Multiple Output ◽  
The Cross ◽  
Value Decomposition ◽  
Physical Order

It is shown that the usual method for estimating the coherence functions (ordinary, partial, and multiple) for a general multiple-input! multiple-output problem can be expressed as a modified form of Cholesky decomposition of the cross-spectral density matrix of the input and output records. The results can be equivalently obtained using singular value decomposition (SVD) of the cross-spectral density matrix. Using SVD suggests a new form of fractional coherence. The formulation as a SVD problem also suggests a way to order the inputs when a natural physical order of the inputs is absent.

Complex Coherence Constraint for the Definition of the Spectral Density Matrix

2018 ◽  
Vol 61 (1) ◽  
pp. 7-19
Author(s):  
Zhihua Liu ◽  
Chenguang Cai ◽  
Yan Xia ◽  
Ming Yang
Keyword(s):  
Density Matrix ◽  
Spectral Density ◽  
Random Vibration ◽  
Multiple Input Multiple Output ◽  
New Approach ◽  
Spectral Density Matrix ◽  
Multiple Input ◽  
Input Multiple Output ◽  
Recursive Formulas ◽  
Definition Of

Abstract The cross spectral density (CSD) for a multiple-input/multiple-output (MIMO) random vibration is typically defined by the complex coherence consisting of the modulus and the phase. The purpose of this paper is to present a constraint for the complex coherence to allow the CSD to be defined more easily. The study of the complex coherence constraint is based on Cholesky decomposition of the spectral density matrix (SDM). The complex coherence must be bounded in the interior or on the boundary of a constraint circle to ensure a physically realizable random vibration. This paper proposes a new approach to define the complex coherences of the SDM by using recursive formulas based on the constraint circle.

Minimum Input Trace for Multiple Input Multiple Output Linear Systems

2013 ◽  
Vol 56 (2) ◽  
pp. 57-67 ◽  
Author(s):  
David Smallwood
Keyword(s):  
Density Matrix ◽  
Minimum Energy ◽  
Multiple Input Multiple Output ◽  
Positive Definite ◽  
Vibration Test ◽  
Control Points ◽  
Spectral Density Matrix ◽  
Multiple Input ◽  
Input Multiple Output ◽  
Drive Signals

Specification of the cross spectra for a multiple-input/multiple-output (MIMO) vibration test is challenging. This paper presents a method for tests where the specifications of the output (the control points) autospectra are available. The autospectra of the outputs are specified and cross spectra between the outputs are derived that will minimize the trace of the autospectra of the inputs (the drive signals) with the constraint that the input spectral density matrix is positive definite. The hypothesis is that nature likes a minimum energy solution.

scholarly journals Generation of Stationary Non-Gaussian Time Histories with a Specified Cross-spectral Density

1997 ◽  
Vol 4 (5-6) ◽  
pp. 361-377 ◽  
Author(s):  
David O. Smallwood
Keyword(s):  
Density Matrix ◽  
Spectral Density ◽  
Probability Density ◽  
Complex Frequency ◽  
Spectral Density Matrix ◽  
Cross Spectral Density ◽  
Time Histories ◽  
The Cross ◽  
Non Gaussian ◽  
Skewness And Kurtosis

The paper reviews several methods for the generation of stationary realizations of sampled time histories with non-Gaussian distributions and introduces a new method which can be used to control the cross-spectral density matrix and the probability density functions (pdfs) of the multiple input problem. Discussed first are two methods for the specialized case of matching the auto (power) spectrum, the skewness, and kurtosis using generalized shot noise and using polynomial functions. It is then shown that the skewness and kurtosis can also be controlled by the phase of a complex frequency domain description of the random process. The general case of matching a target probability density function using a zero memory nonlinear (ZMNL) function is then covered. Next methods for generating vectors of random variables with a specified covariance matrix for a class of spherically invariant random vectors (SIRV) are discussed. Finally the general case of matching the cross-spectral density matrix of a vector of inputs with non-Gaussian marginal distributions is presented.

scholarly journals Broadband over Power Lines Systems Convergence: Multiple-Input Multiple-Output Communications Analysis of Overhead and Underground Low-Voltage and Medium-Voltage BPL Networks

2013 ◽  
Vol 2013 ◽  
pp. 1-30 ◽  
Author(s):  
Athanasios G. Lazaropoulos
Keyword(s):  
Modal Analysis ◽  
Review Paper ◽  
Low Voltage ◽  
Multiple Input Multiple Output ◽  
Power Lines ◽  
Mimo Channels ◽  
Medium Voltage ◽  
Multiple Input ◽  
Input Multiple Output ◽  
Value Decomposition

This review paper reveals the broadband potential of overhead and underground low-voltage (LV) and medium-voltage (MV) broadband over power lines (BPL) networks associated with multiple-input multiple-output (MIMO) technology. The contribution of this review paper is fourfold. First, the unified value decomposition (UVD) modal analysis is introduced. UVD modal analysis is a new technique that unifies eigenvalue decomposition (EVD) and singular value decomposition (SVD) modal analyses achieving the common handling of traditional SISO/BPL and upcoming MIMO/BPL systems. The validity of UVD modal analysis is examined by comparing its simulation results with those of other exact analytical models. Second, based on the proposed UVD modal analysis, the MIMO channels of overhead and underground LV and MV BPL networks (distribution BPL networks) are investigated with regard to their inherent characteristics. Towards that direction, an extended collection of well-validated metrics from the communications literature, such as channel attenuation, average channel gain (ACG), root-mean-square delay spread (RMS-DS), coherence bandwidth (CB), cumulative capacity, capacity complementary cumulative distribution function (CCDF), and capacity gain (GC), is first applied in overhead and underground MIMO/LV and MIMO/MV BPL channels and systems. It is found that the results of the aforementioned metrics portfolio depend drastically on the frequency, the power grid type (either overhead or underground, either LV or MV), the MIMO scheme configuration properties, the MTL configuration, the physical properties of the cables used, the end-to-end distance, and the number, the electrical length, and the terminations of the branches encountered along the end-to-end BPL signal propagation. Third, three interesting findings concerning the statistical properties of MIMO channels of distribution BPL networks are demonstrated, namely, (i) the ACG, RMS-DS, and cumulative capacity lognormal distributions; (ii) the correlation between RMS-DS and ACG; and (iii) the correlation between RMS-DS and CB. By fitting the numerical results, unified regression distributions appropriate for MIMO/BPL channels and systems are proposed. These three fundamental properties can play significant role in the evaluation of recently proposed statistical channel models for various BPL systems. Fourth, the potential of transformation of overhead and underground LV/BPL and MV/BPL distribution grids to an alternative solution to fiber-to-the-building (FTTB) technology is first revealed. By examining the capacity characteristics of various MIMO scheme configurations and by comparing these capacity results against SISO ones, a new promising urban backbone network seems to be born in a smart grid (SG) environment.

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