Journal Article•
Mathematical Analysis of Random Noise-Conclusion
About: This article is published in Bell System Technical Journal.The article was published on 1945-01-01 and is currently open access. It has received 807 citations till now.
Citations
More filters
TL;DR: A generalized version of the method of equal areas (MEA) that is well suited for the design of sum-of-cisoids (SOC) simulators for narrowband mobile Rayleigh fading channels characterized by any type of Doppler power spectral densities (DPSDs).
Abstract: We present in this paper a generalized version of the method of equal areas (MEA) that is well suited for the design of sum-of-cisoids (SOC) simulators for narrowband mobile Rayleigh fading channels characterized by any type of Doppler power spectral densities (DPSDs). Unlike the original MEA, the generalized MEA (GMEA) can be applied to the simulation of fading channels with asymmetrical DPSDs. This is an important feature because the simulation of such channels is of great interest for the laboratory analysis of mobile communication systems under non-isotropic scattering conditions. We show that irrespective of the underlying DPSD, the GMEA results in a very good approximation to the autocorrelation function, average Doppler shift, Doppler spread, and envelope distribution of the channel. We compare the performance of the GMEA with that of the Lp-norm method (LPNM), which is the method that has been most widely used for designing SOC simulators for fading channels with arbitrary DPSDs. The obtained results demonstrate that the performance of the GMEA measures up to that of the LPNM. In addition, the results show that the determination of the model parameters is easier and less time-consuming when applying the GMEA. Copyright © 2011 John Wiley & Sons, Ltd.
16 citations
TL;DR: In this paper, storm waves generated locally over deep water and travelling into shoaling water are assumed to be of the JONSWAP form, which is approximated by the Phillips spectrum with the same H mo.
16 citations
TL;DR: In this article, the joint distribution of consecutive wave heights in a real sea state was evaluated by a simulation methodology that is consistent with the Gaussian random wave model, and the resulting predictions of run and group length statistics differ from the Kimura theory.
16 citations
TL;DR: In this paper, the scaling-independent bias factors for the peak above a threshold for large separation angle and high threshold level are in agreement with the value expected for a pure Gaussian CMB.
Abstract: The clustering of local extrema will be exploited to examine Gaussianity, asymmetry, and the footprint of the cosmic-string network on the CMB observed by Planck. The number density of local extrema ($n_{\rm pk}$ for peak and $n_{\rm tr}$ for trough) and sharp clipping ($n_{\rm pix}$) statistics support the Gaussianity hypothesis for all component separations. However, the pixel at the threshold reveals a more consistent treatment with respect to end-to-end simulations. A very tiny deviation from associated simulations in the context of trough density, in the threshold range $\theta\in [-2-0]$ for NILC and CR component separations, are detected. The unweighted two-point correlation function, of the local extrema, illustrates good consistency between different component separations and corresponding Gaussian simulations for almost all available thresholds. However, for high thresholds, a small deficit in the clustering of peaks is observed with respect to the Planck fiducial $\Lambda$CDM model. To put a significant constraint on the amplitude of the mass function based on the value of $\Psi$ around the Doppler peak ($\theta\approx 70-75$ arcmin), we should consider $\vartheta\lesssim 0.0$. The scale-independent bias factors for the peak above a threshold for large separation angle and high threshold level are in agreement with the value expected for a pure Gaussian CMB. Applying the $n_{\rm pk}$, $n_{\rm tr}$, $\Psi_{\rm pk-pk}$ and $\Psi_{\rm tr-tr}$ measures on the tessellated CMB map with patches of $7.5^2$ deg$^2$ size prove statistical isotropy in the Planck maps. The peak clustering analysis puts the upper bound on the cosmic-string tension, $G\mu^{(\rm up)} \lesssim 5.59\times 10^{-7}$, in SMICA.
16 citations
TL;DR: In this paper, a nonlinear finite element model is established to simulate buried pipe networks that are subjected to earthquakes, and a connectivity index is defined to describe the connectivity between the source and the terminal.
16 citations