Review Paper on Second Order Statistics ofVarious Fading Channels (original) (raw)
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Paper on Second Order Statistics of Various Fading Channels
2014
Radio-wave propagation through wireless channel is a complicated phenomenon characterized by fading which is the result of multipath propagation. In wireless communication system, random process associated with fading channels can usually characterized by their PDF (Probability Density Function) and CDF (Cumulative Distribution Function). Signal fading can drastically affect the performance of terrestrial communication systems. Several statistical models are available for describing the fading envelope of the received signal in which Rayleigh, Rician and Nakagami are the most frequently applied models. Higher-order statistics such as Level Crossing Rate (LCR) & Average Fade Duration render (AFD) insight into signals which is not always available at lower orders.
On the second order statistics of the multihop rayleigh fading channel
IEEE Transactions on Communications, 2000
Second order statistics provides a dynamic representation of a fading channel and plays an important role in the evaluation and design of the wireless communication systems. In this paper, we present a novel analytical framework for the evaluation of important second order statistical parameters, as the level crossing rate (LCR) and the average fade duration (AFD) of the amplify-and-forward multihop Rayleigh fading channel. More specifically, motivated by the fact that this channel is a cascaded one and can be modeled as the product of N fading amplitudes, we derive novel analytical expressions for the average LCR and the AFD of the product of N Rayleigh fading envelopes (or of the recently so-called N * Rayleigh channel). Furthermore, we derive simple and efficient closed-form approximations to the aforementioned parameters, using the multivariate Laplace approximation theorem. It is shown that our general results reduce to the corresponding ones of the specific dual-hop case, previously published. Numerical and computer simulation examples verify the accuracy of the presented mathematical analysis and show the tightness of the proposed approximations.
Vehicular Technology Conference Fall 2000. IEEE VTS Fall VTC2000. 52nd Vehicular Technology Conference (Cat. No.00CH37152)
Level crossing rate (LCR) and average fade duration (AFD) of the signal envelope are two important second-order channel statistics, which convey useful information about the dynamic temporal behavior of multipath fading channels. In this paper and for a general non-isotropic scattering scenario, in which the mobile receives signal only from particular directions with different probabilities, we derive expressions for the LCR and AFD of Rayleigh, Rice, and Nakagami fading models, including the effect of non-uniform signal angle-of-arrival distribution. The merits and limitations of all the above models in describing the first-and second-order statistics of multipath fading channels are explored through an extensive comparison of theoretical results with narrowband measurements taken in urban and suburban areas at 910.25 MHz.
Second-Order Statistics of η-μ Fading Channels: Theory and Applications
IEEE Transactions on Wireless Communications, 2000
In this work, a number of new closed-form expressions for the η-μ fading channels envolving the joint statistics of the envelope, phase, and their time derivatives are obtained. Level crossing rate (LCR), average fade duration (AFD), and phase crossing rate (PCR) are also derived. The expressions are thoroughly validated by reducing them to some particular known cases and, more generally, by means of Monte Carlo simulation. We then provide alternative (i) singlefold integral exact formulations and (ii) highly-accurate approximations to the level-crossing statistics of multibranch maximal-ratio combining (MRC) and equal-gain combining (EGC) systems, respectively, operating over independent Hoyt fading channels, for which the exact solutions appear in the literature in multifold integral forms.
New analytical models and probability density functions for fading in wireless communications
IEEE Transactions on Communications, 2002
This paper presents new envelope probability density functions (pdfs) that describe small-scale, local area fading experienced by narrow-band wireless receivers. The paper also develops novel pdfs that describe the local area fading of two specular multipath components in the presence of other diffusely propagating waves. These pdfs are studied in the context of classical fading pdfs such as the Rayleigh, Rician, and other distributions.
A generalisation of the Rayleigh distribution with applications in wireless fading channels
Wireless Communications and Mobile Computing, 2011
The signal received in a mobile radio environment exhibits rapid signal level fluctuations which are generally Rayleighdistributed. These result from interference by multiple scattered radio paths between the base station and the mobile receptor. Fading-shadowing effects in wireless channels are usually modelled by means of the Rayleigh-Lognormal distribution (RL), which has a complicated integral form. The K-distribution (K) is similar to RL but it has a simpler form and its probability density function admits a closed form; however, due to the Bessel function, parameter estimates are not direct. Another possible approach is that of the Rayleigh-inverse Gaussian distribution (RIG). In this paper, an alternative is presented, a generalisation of the Rayleigh distribution which is simpler than the RL, K and RIG distributions, and thus more suitable for the analysis and design of contemporary wireless communication systems. Closed-form expressions for the bit error rate (BER) for differential phase-shift keying (DPSK) and minimum shift keying (MSK) modulations with the proposed distribution are obtained. Theoretical results based on statistically well-founded distance measurements validate the new distribution for the cases analysed.
Conference on Decision and Control, 1999
This paper discusses the use of stochastic differential equations to model signal envelope variations over areas, which are subject to short-term fading effects. The short-term fading effects are modeled using Ornstein-Uhlenbeck processes and they are derived from first principles, using the scattering assumption of electromagnetic waves. This gives rise to signal envelope variations which follow a mean-reverting square-root process, which is elastically pulled towards a long-term mean which characterizes the propagation environment. The derived signal envelope distributions include generalizations of Rayleigh, Rician, Nakagami etc. distributions to their nonstationary analogs and thus generalizing channel models to include time variations. From these computations the second order statistics of the received signal are obtained
Higher Order Statistics for Composite Fading Models
IEEE Wireless Communications Letters, 2019
This Letter presents a novel, general second-order statistics framework for composite fading models. The aim is to obtain expressions for the Level Crossing Rate and Average Fade Duration statistics in any fading scenario. Two formulations are presented: (i) one that leads to exact expressions; and (ii) another that leads to approximate ones. By using the former, even for very simple fading scenarios, no closed-form formula can be found. By using the latter, as proposed here, closedform formulations may be found. Interestingly, it is shown that, in practical terms, the results in (i) and (ii) yield results that are almost indistinguishable from each other when applied to multipath-shadowing environments. As an application example, the α-µ scenario for both multipath and shadowing has been exercised.
Gateway to 21st Century Communications Village. VTC 1999-Fall. IEEE VTS 50th Vehicular Technology Conference (Cat. No.99CH36324), 1999
In this paper, a semi-deterministic propagation model for the prediction of short-term fading statistics in urban mobile cellular systems is presented. The model is based on digital map information and is also used to predict coverage areas. The short-term fading is modelled by the Nakagami distribution, where the two parameters defining the distribution for a local area around the mobile position can be obtained from the available digital map information of the urban area. Computer simulation results and measurement campaigns are compared, showing that the best approximation to the probability density function of the short-term fading in mobile urban channels is a Nakagami distribution.