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.
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TL;DR: The obtained results are important to design efficient simulators for the performance analysis of systems and algorithms sensitive to the correlation properties of the channel's squared envelope, such as speed estimators and handover mechanisms.
Abstract: In this paper, we investigate the correlation and ergodic properties of the squared envelope of a class of autocorrelation-ergodic (AE) sum-of-cisoids (SOC) simulation models for mobile Rayleigh fading channels. Novel closed-form expressions are presented for both the ensemble and the time autocorrelation functions (ACFs) of the SOC simulation model's squared envelope. These expressions have been derived by assuming that the SOC model's inphase and quadrature (IQ) components have arbitrary autocorrelation and cross-correlation properties. This consideration makes the results herein presented more general than those given previously in other papers, where it is assumed that the IQ components of the simulation model are strictly uncorrelated. We show that under certain conditions, the squared envelope of the SOC model is an AE random process. In addition, we evaluate the performance of three fundamental methods for the computation of the model parameters--namely the generalized method of equal areas, the L p -norm method, and the Riemann sum method--regarding their accuracy for emulating the squared envelope ACF of a reference narrowband Rayleigh fading channel model. The obtained results are important to design efficient simulators for the performance analysis of systems and algorithms sensitive to the correlation properties of the channel's squared envelope, such as speed estimators and handover mechanisms.
7 citations
TL;DR: This work analyzes the fluctuation of the intensity and the phase of an NMR signal during repetition of experiments and investigates possibilities of using these information to judge suspicious peaks, whose true colors may be noises or genuine signals.
7 citations
TL;DR: In this article, the authors present a Procedia Technology Journal (Procedia Technology) article published in the journal: Procedia technology (http://dx.doi.org/10.1016/j.protcy.2012.03.004
7 citations
01 Jan 1975
TL;DR: In this article, a generalized Bessel prior distribution is used for the random sine wave problem and distributions for fluctuating radar targets with particular emphasis on amplitude, phase and component distributions.
Abstract: The objective of the paper is to show that a certain generalized Bessel distribution is a useful theoretical tool because, through mixing procedures, specialization of parameter values and integral representation considerations, it unifies the theory of a broad class of special distributions; and that it is a useful tool because it has applications in radio communication. The random sine wave problem and distributions for fluctuating radar targets are studied in terms of this distribution with particular emphasis on amplitude, phase and component distributions. The marginal pdf and characteristic function corresponding to Bennett’s (Rice’s) distribution of a random sine wave plus stationary Gaussian noise are obtained when the sine wave amplitude is assigned a generalized Bessel prior distribution. The Bennett problem is also reduced to a randomly phased sine wave without noise and the corresponding marginal pdf and characteristic function are obtained from the noise corrupted case. Non-uniform phase distributions are also treated in terms of generalized distributions and the corresponding amplitude and component pdfs are provided. The distribution of a useful quadrat if form in which the random variates are the squares of a generalized component corrupted by Gaussian noise is also provided. The quadratic form distribution is then used as a basic model for fluctuating radar cross section (RCS) and includes the Swerling RCS models and the Nakagami amplitude distributions as special cases. The authors also provide the corresponding pulse-train probability distributions for two pulse integration schemes using either scan-to-scan or pulse-to-pulse amplitude independence. Many of the pdfs and characteristic functions provided in the paper are expressed in terms of both closed form expressions and mixture representations.
7 citations