Search results for "probability density function"

A geometric street scattering channel model for car-to-car communication systems

2011

This paper presents a geometric street scattering channel model for car-to-car (C2C) communication systems under line-of-sight (LOS) and non-LOS (NLOS) propagation conditions. Starting from the geometric model, we develop a stochastic reference channel model, where the scatterers are uniformly distributed in rectangles in the form of stripes parallel to both sides of the street. We derive analytical expressions for the probability density functions (PDFs) of the angle-of-departure (AOD) and the angle-of-arrival (AOA). We also investigate the Doppler power spectral density (PSD) and the autocorrelation function (ACF) of the proposed model, assuming that the mobile transmitter (MT) and the mo…

Performance Analysis of M-DPSK Modulation over Fast-Hoyt Fading Channels under Non-Isotropic Scattering Conditions

2021

In this paper, we analyze the symbol error probability (SEP) performance of M-ary differential phase shift keying (M-DPSK) modulation schemes over frequency-flat fast-varying Hoyt multipath fading channels. Assuming general non-isotropic scattering conditions, we first derive a finite-range integral expression for the probability density function (PDF) of the phase difference between two non-isotropic Hoyt vectors perturbed by additive white Gaussian noise (AWGN). Based upon the theory of M-DPSK modulation and the obtained PDF formula, the SEP of M-DPSK and its corresponding asymptotic behavior in non-isotropic fast-Hoyt fading channels are derived. Specifically, a double semi-finite range …

Entropy, Benford’s first digit law, and the distribution of everything

2010

On the Statistical Properties of the Capacity of Spatially Correlated Nakagami-M MIMO Channels

2008

This paper studies the statistical properties of the channel capacity of spatially correlated Nakagami-m multiple- input multiple-output (MIMO) channels. We have derived closed- form expressions for the probability density function (PDF), the cumulative distribution function (CDF), the level-crossing rate (LCR), and the average duration of fades (ADF) of the lower bound on the channel capacity. In order to study the impact of the spatial correlation on the channel capacity, the analysis of the statistical properties of the channel capacity is carried out for different receiver antenna spacings. It is observed that the antenna spacing has a significant influence on the spread and maximum val…

On the statistical properties of the capacity of sparse multipath fading channels

2014

Most existing works in wireless communications assume rich scattering. However, there is growing experimental evidence that physical wireless channels can exhibit a sparse structure. By assuming an asymmetric Doppler power spectral density (PSD), we can model and simulate sparse channels by using a finite sum of weighted complex harmonic functions, also called sum of cisoids (SOC). In this paper, we focus on the analysis of the statistical properties of the instantaneous capacity of sparse SOC-based multipath fading channels under line-of-sight (LOS) conditions. The probability density function (PDF), the cumulative distribution function (CDF), the level-crossing rate (LCR), and the average…

Statistical Analysis of the Channel Capacity Outage Intervals in Massive MIMO Systems with OSTBC over Rayleigh Fading Channels

2015

This paper studies approximate solutions for the statistical properties of the outage intervals of the instantaneous capacity in massive multiple- input multiple- output (MIMO) sys- tems with orthogonal space-time block code (OSTBC) over Rayleigh fading channels. We take advantage from the fact that the probability density function (PDF) of the channel power gain can be approximated by a left-truncated Gaussian distribution if the number of transmit and receive antennas is large. Assuming a symmetrical Doppler power spectral density (PSD), a closed- form expression is presented for the Rice probability function of the outage durations. This function, in general, approximates the PDF of the …

On the statistical properties of the capacity of amplify-and-forward channels under LOS conditions

2008

Amplify-and-forward channels in cooperative networks provide a promising improvement in the network coverage and system throughput. Under line-of-sight (LOS) propagation conditions in such cooperative networks, the overall fading channel can be modeled by a double Rice process. In this article, we have studied the statistical properties of the capacity of double Rice fading channels. We have derived the analytical expressions for the probability density function (PDF), cumulative distribution function (CDF), level-crossing rate (LCR), and average duration of fades (ADF) of the channel capacity. The obtained results are studied for different values of the amplitudes of the LOS components in …

Stationary and non-stationary probability density function for non-linear oscillators

1997

A method for the evaluation of the stationary and non-stationary probability density function of non-linear oscillators subjected to random input is presented. The method requires the approximation of the probability density function of the response in terms of C-type Gram-Charlier series expansion. By applying the weighted residual method, the Fokker-Planck equation is reduced to a system of non-linear first order ordinary differential equations, where the unknowns are the coefficients of the series expansion. Furthermore, the relationships between the A-type and C-type Gram-Charlier series coefficient are derived.

Non-Gaussian probability density function of SDOF linear structures under wind actions

1998

Abstract Wind velocity is usually analytically described adding a static mean term to a zero mean fluctuation stationary process. The corresponding aerodynamic alongwind force acting on a single degree of freedom (SDOF) structure can be considered as a sum of three terms proportional to the mean wind velocity, to the product between mean and fluctuating part of the wind velocity and to the square power of the fluctuating wind velocity, respectively. The latter term, often neglected in the literature, is responsible for the non-Gaussian behaviour of the response. In this paper a method for the evaluation of the stationary probability density function of SDOF structures subjected to non-Gauss…

Power-law relaxation in a complex system: Omori law after a financial market crash

2003

We study the relaxation dynamics of a financial market just after the occurrence of a crash by investigating the number of times the absolute value of an index return is exceeding a given threshold value. We show that the empirical observation of a power law evolution of the number of events exceeding the selected threshold (a behavior known as the Omori law in geophysics) is consistent with the simultaneous occurrence of (i) a return probability density function characterized by a power law asymptotic behavior and (ii) a power law relaxation decay of its typical scale. Our empirical observation cannot be explained within the framework of simple and widespread stochastic volatility models.