On the Statistical Properties of Phase Crossings and Random FM Noise in Double Rayleigh Fading Channels | IEEE Journals & Magazine | IEEE Xplore

On the Statistical Properties of Phase Crossings and Random FM Noise in Double Rayleigh Fading Channels


Abstract:

In this paper, we study the statistics of phase processes and random frequency modulation (FM) noise encountered in double Rayleigh fading channels. The Rayleigh processe...Show More

Abstract:

In this paper, we study the statistics of phase processes and random frequency modulation (FM) noise encountered in double Rayleigh fading channels. The Rayleigh processes making up the double Rayleigh channel are assumed to be independent but not necessarily identically distributed. The Doppler power spectral densities of these processes are supposed to be symmetric about the carrier frequency. Under these fading conditions, we derive first an expression for the joint probability density function (jpdf) of the phase process and its rate of change. Capitalizing on this jpdf formula, we then investigate the probability density function (pdf) and cumulative distribution function (cdf) of random FM noise. Moreover, the average crossing rate of phase processes, as well as that of the Laplacian distributed in-phase and quadrature components of the complex channel gain, are obtained. Aside from the aforementioned statistics, we also provide exact expressions for the pdf, cdf, and second-order moment of the random FM noise at the output of a selection combiner, operating on independent and identically distributed (i.i.d.) branches. The validity of the analysis has been carried out by reducing the derived expressions to already-known results for single Rayleigh channels and by comparing our analytical results with the corresponding simulation results.
Published in: IEEE Transactions on Vehicular Technology ( Volume: 65, Issue: 4, April 2016)
Page(s): 1859 - 1867
Date of Publication: 25 March 2015

ISSN Information:


I. Introduction

The modeling of multiplicative fading channels, which are also called cascaded propagation channels, refers to the modeling of multipath fading as the product of classical fading processes, e.g., Rayleigh, Rice, and Nakagami- processes. In recent years, multiplicative fading models have gained recognition due to their potential of capturing the multipath effects encountered in new wireless applications such as mobile-to-mobile (M2M) communications like mobile ad hoc networks and wireless sensors networks, vehicle-to-vehicle (V2V) communications, and cooperative relaying systems. Existing investigations on multiplicative channels have mainly dealt with the double Rayleigh fading model. Based on measurement data in [1] and [2], Honcharenko et al. and Erceg et al., respectively, demonstrated that the double Rayleigh fading model well describes the multipath fading effects encountered in indoor and urban microcellular propagation environments where both the transmitter and the receiver are moving. Moreover, Kovacs et al. [3] showed that the cascaded Rayleigh model provides a perfect fit to measurement data collected in different suburban outdoor-to-indoor M2M propagation environments. The underlying fading model has also been used for the modeling of multiple-input multiple-output (MIMO) keyhole channels [4]– [6]. Recently, Matolak and Frolik showed in [7] that double Rayleigh processes are also suitable for modeling V2V propagation environments where the multipath fading effects are found to be more severe than those described by the classical Rayleigh [8]. More recently, measurement-based studies reported in [9] and [10], where measurement campaigns have been conducted under non-line-of-sight (NLOS) conditions, showed that radio-frequency identification channels can be statistically described by the double Rayleigh model.

References

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