scholarly journals Cyclic spectral analysis of OFDM/QAM modulation using stochastic matrix-based method

2003 ◽  
Vol 16 (3) ◽  
pp. 343-353 ◽  
Author(s):  
Desimir Vucic
Keyword(s):  
Spectral Analysis ◽  
Continuous Time ◽  
Pulse Shaping ◽  
Stochastic Matrix ◽  
Cyclic Prefix ◽  
Spectral Correlation ◽  
Channel Identification ◽  
Exact Analytical Expression ◽  
Qam Modulation

The cyclostationarity of the OFDM/QAM signals induced by the use of cyclic prefix or pulse shaping is the key to blind synchronization, channel identification and equalization in these systems. Therefore, continuous-time and discrete-time spectral correlation characterization of the pulse shaping OFDM/QAM signals is performed by a matrix-based stochastic method based on Markov chain signal representation. Exact analytical expression for the cyclic spectrum of the continuous-time OFDM/QAM signal is derived applying the proposed method, the characteristic cyclic features according to the cyclic prefix and/or pulse shaping employing are analyzed and some graphed results are presented.

scholarly journals Income and Wealth Distribution in Macroeconomics: A Continuous-Time Approach

2021 ◽  
Author(s):  
Yves Achdou ◽  
Jiequn Han ◽  
Jean-Michel Lasry ◽  
Pierre-Louis Lions ◽  
Benjamin Moll
Keyword(s):  
Continuous Time ◽  
Wealth Distribution ◽  
Closed Form Solution ◽  
Form Solution ◽  
Heterogeneous Agent ◽  
Saving Behavior ◽  
Income And Wealth Distribution ◽  
Heterogeneous Agent Models ◽  
Special Case

Abstract We recast the Aiyagari-Bewley-Huggett model of income and wealth distribution in continuous time. This workhorse model – as well as heterogeneous agent models more generally – then boils down to a system of partial differential equations, a fact we take advantage of to make two types of contributions. First, a number of new theoretical results: (i) an analytic characterization of the consumption and saving behavior of the poor, particularly their marginal propensities to consume; (ii) a closed-form solution for the wealth distribution in a special case with two income types; (iii) a proof that there is a unique stationary equilibrium if the intertemporal elasticity of substitution is weakly greater than one. Second, we develop a simple, efficient and portable algorithm for numerically solving for equilibria in a wide class of heterogeneous agent models, including – but not limited to – the Aiyagari-Bewley-Huggett model.

Characterization of the conditional stationary distribution in Markov chains via systems of linear inequalities

2020 ◽  
Vol 52 (4) ◽  
pp. 1249-1283
Author(s):  
Masatoshi Kimura ◽  
Tetsuya Takine
Keyword(s):  
Markov Chains ◽  
Stationary Distribution ◽  
Continuous Time ◽  
State Transition ◽  
Convex Polytope ◽  
Linear Inequalities ◽  
Systems Of Linear Inequalities ◽  
Free Sets ◽  
Practical Implications

AbstractThis paper considers ergodic, continuous-time Markov chains $\{X(t)\}_{t \in (\!-\infty,\infty)}$ on $\mathbb{Z}^+=\{0,1,\ldots\}$ . For an arbitrarily fixed $N \in \mathbb{Z}^+$ , we study the conditional stationary distribution $\boldsymbol{\pi}(N)$ given the Markov chain being in $\{0,1,\ldots,N\}$ . We first characterize $\boldsymbol{\pi}(N)$ via systems of linear inequalities and identify simplices that contain $\boldsymbol{\pi}(N)$ , by examining the $(N+1) \times (N+1)$ northwest corner block of the infinitesimal generator $\textbf{\textit{Q}}$ and the subset of the first $N+1$ states whose members are directly reachable from at least one state in $\{N+1,N+2,\ldots\}$ . These results are closely related to the augmented truncation approximation (ATA), and we provide some practical implications for the ATA. Next we consider an extension of the above results, using the $(K+1) \times (K+1)$ ( $K > N$ ) northwest corner block of $\textbf{\textit{Q}}$ and the subset of the first $K+1$ states whose members are directly reachable from at least one state in $\{K+1,K+2,\ldots\}$ . Furthermore, we introduce new state transition structures called (K, N)-skip-free sets, using which we obtain the minimum convex polytope that contains $\boldsymbol{\pi}(N)$ .

Spectral synthesis and residually finite-dimensional algebras

2017 ◽  
Vol 16 (10) ◽  
pp. 1750200 ◽  
Author(s):  
László Székelyhidi ◽  
Bettina Wilkens
Keyword(s):  
Spectral Analysis ◽  
Abelian Group ◽  
Theoretical Approach ◽  
Abelian Groups ◽  
Spectral Synthesis ◽  
Residually Finite ◽  
Finite Dimensional ◽  
Analysis And Synthesis ◽  
Spectral Analysis And Synthesis

In 2004, a counterexample was given for a 1965 result of R. J. Elliott claiming that discrete spectral synthesis holds on every Abelian group. Since then the investigation of discrete spectral analysis and synthesis has gained traction. Characterizations of the Abelian groups that possess spectral analysis and spectral synthesis, respectively, were published in 2005. A characterization of the varieties on discrete Abelian groups enjoying spectral synthesis is still missing. We present a ring theoretical approach to the issue. In particular, we provide a generalization of the Principal Ideal Theorem on discrete Abelian groups.

Characterization of Tissue Microstructure Scatterer Distribution with Spectral Correlation

1993 ◽  
Vol 15 (3) ◽  
pp. 238-254 ◽  
Author(s):  
Tomy Varghese ◽  
Kevin D. Donohue
Keyword(s):  
Formation Process ◽  
Biological Tissue ◽  
Statistical Parameters ◽  
Spectral Correlation ◽  
Tissue Microstructure ◽  
Power Spectral ◽  
Spectral Peaks ◽  
Ultrasound Signal

Characterization of tissue microstructure from the backscattered ultrasound signal using the spectral autocorrelation (SAC) function provides information about the scatterer distribution in biological tissue. This paper demonstrates SAC capabilities in characterizing periodicities in A-scans due to regularity in the scatterer distribution. The A-scan is modelled as a cyclostationary signal, where the statistical parameters of the signal vary in time with single or multiple periodicities. This periodicity manifests itself as spectral peaks both in the power spectral density (PSD) and in the SAC. Periodicity in the PSD will produce a well defined dominant peak in the cepstrum, which has been used to determine the scatterer spacing. The relationship between the scatterer spacing and the spacing of the spectral peaks is established using a stochastic model of the echo-formation process from biological tissue. The distribution of the scatterers within the microstructure is modelled using a Gamma function, which offers a flexible method of simulating parametric regularity in the scatterer spacing. Simulations of the tissue microstructure for lower orders of regularity indicate that the SAC components reveal information about the scatterer spacing that are not seen in the PSD and the cepstrum. The echo-formation process is tested by simulating microstructure of varying regularity and analyzing their effect on the SAC, PSD and cepstrum. Experimental validation of the simulation results are provided using in vivo scans of the breast and liver tissue that show the presence of significant spectral correlation components in the SAC.

Strong ergodicity for continuous-time, non-homogeneous Markov chains

1982 ◽  
Vol 19 (3) ◽  
pp. 692-694 ◽  
Author(s):  
Mark Scott ◽  
Barry C. Arnold ◽  
Dean L. Isaacson
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Continuous Time ◽  
Homogeneous Markov Chain ◽  
Strong Ergodicity

Characterizations of strong ergodicity for Markov chains using mean visit times have been found by several authors (Huang and Isaacson (1977), Isaacson and Arnold (1978)). In this paper a characterization of uniform strong ergodicity for a continuous-time non-homogeneous Markov chain is given. This extends the characterization, using mean visit times, that was given by Isaacson and Arnold.

scholarly journals Analysis of cyclic prefix length effect on ISI limitation in OFDM system over a Rayleigh-fading multipath

2021 ◽  
Vol 11 (4) ◽  
pp. 3114
Author(s):  
Sarah Zanafi ◽  
Noura Aknin
Keyword(s):  
Rayleigh Fading ◽  
Cyclic Prefix ◽  
Modulation Scheme ◽  
Transmission Channel ◽  
Ofdm System ◽  
Length Effect ◽  
Qam Modulation

<span>In this work, the influence of the cyclic prefix on the performance of the OFDM system is studied. We worked out an OFDM transceiver using a 16 QAM modulation scheme, a comparison of the BER for various lengths of the cyclic prefix has been achieved, and the influence of the noise introduced in the channel has been highlighted, for both a Gaussian and Rayleigh noise. The simulation was carried out on MATLAB where the curves of the BER for various lengths of the cyclic prefix are given and compared. We also adopted as a metric the QAM constellation to show the dispersion of the carriers as a consequence of the transmission channel, the mitigation of this effect by the CP is noticeable.</span>

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