Level Crossing Rate Research Articles

Fade Statistic Analysis of SC in Distributed Antenna System

Exact and closed form expressions for the average level crossing rate (LCR) and average fade duration (AFD) of the output signal envelope of selection diversity system are derived, assuming each branch is subject to independent but nonidentical composite fading in distributed antenna systems (DAS). Numerical results validate the derived expressions. It shows that DAS promise significant diversity gains over collocated multiple antenna system.

Human Body Influence on Terminal in Wireless Communication

This paper presents a statistical characterization of communication channel under influence of human body on mobile terminal using the concept of super antenna and geometry-based stochastic models. The disturbances are inserted into the channel trough modified radiation patterns. We have concluded in this work that the human body changes the communication channel from a Nakagami to a Weibull distribution for the studied scenarios. Furthermore, its presence in antenna near field results in worse level cross rate proportional to the distance between the terminal and disturbers.

Finite-State Markov Chain Models for the Intensity of Nakagami Fading

For the design, analysis, and simulation of communication systems with Nakagami-m fading channels, it is very convenient to model the fading by finite-state Markov chains in which the states represent fade levels or signal-to-noise ratios in decibels. Our approach to the development of such Markov chain models is to work with the intensity of the fading process, which is proportional to the logarithm of squared envelope of the faded signal. We demonstrate that all the parameters of the Markov chains can be determined from the bivariate distribution of the intensity of the Nakagami-m fading process. Several analytical results are derived from the bivariate distribution of the intensity, including expressions for the chain’s transition probabilities for both adjacent and nonadjacent states and the asymptotic distribution of the intensity for deep fades. For several values of m, we verify the accuracy of our Markov chain models as simulation tools by comparisons of the state probabilities and level-crossing rates obtained from simulations of the Markov chain with those obtained from our analytical expressions.

Average level crossing rate and fading duration of multiuser single relay cooperation wireless uplinks

We investigate the average Level Crossing Rate (LCR) and Average Fading Duration (AFD) of multiuser single relay cooperation wireless uplinks over independent and non-identically distributed (i.ni.d) Ray-leigh fading channels. We first present the statistical analyses of the first-hop equivalent envelope. Then, we investigate the LCR and AFD of an equivalent end-to-end envelope, and present the closed-form solutions to LCR and AFD, which are given with integral forms. Finally, we derive the Laplace approximations of LCR and AFD as well as the upper and lower bounds. The numerical results of LCR show that the upper bound is tight. For multiuser systems with different number of mobile users, the analyses indicate that the LCRs are approximately the same at the low level of the envelope. However, at the high level of the envelope there are reasonable differences among the curves of LCRs. Due to that fact that AFD is the inverse function of LCR, the results for AFD are the opposite.

Second-order statistics of dual-hop transmission with an amplify-and-forward relay over Rician and Weibull fading channels

The level-crossing rate (LCR) and average fade duration (AFD) are the second-order statistics that are useful for the design of adaptive transmission and coding systems over wireless fading channels. These second-order statistics are analyzed for dual-hop transmissions with a fixed-gain amplify-and-forward relay, where the Rician and Weibull fading channels are considered. To evaluate the LCR and AFD, we also derived the lower and upper bounds on the LCR and AFD which are useful when the exact closed-forms of the LCR and AFD are difficult to obtain. To illustrate the performance of the dual-hop relay channel, numerical results of the outage probability, the LCR and AFD are presented.

Dynamic Channel Modeling for Multi-Sensor Body Area Networks

A channel model for time-variant multi-link wireless body area networks (WBANs) is proposed in this paper, based on an extensive measurement campaign using a multi-port channel sounder. A total of 12 nodes were placed on the body to measure the multi-link channel within the created WBAN. The resulting empirical model takes into account the received power, the link fading statistics, and the link auto- and cross-correlations. The distance dependence of the received power is investigated, and the link fading is modeled by a log-normal distribution. The link autocorrelation function is divided into a decaying component and a sinusoidal component to account for the periodical movement of the limbs caused by walking. The cross-correlation between different links is also shown to be high for a number of specific on-body links. Finally, the model is validated by considering several extraction-independent validation metrics: multi-hop link capacity, level crossing rate (LCR) and average fade duration (AFD). The capacity aims at validating the path-loss and fading model, while the LCR and AFD aim at validating the temporal behavior. For all validation metrics, the model is shown to satisfactorily reproduce the measurements, whereas its limits are pointed out.

Short-Term Fading Behavior in High-Speed Railway Cutting Scenario: Measurements, Analysis, and Statistical Models

Cuttings are widely used in high-speed railway (HSR) transportation to ensure the flatness of rails. The special structure of cuttings results in rich reflection and scattering, and creates dense multipath components. This paper presents a series of measurements of the propagation channel at 930 MHz conducted along the “Zhengzhou-Xi'an” HSR of China, to characterize the small-scale fading behavior of rail-cutting scenarios as a function of the geometry of cuttings, including crown width and bottom width. Raw data are collected in six cuttings (five cuttings are used for developing the model, while the other one is used for validation) in rural and suburban environments. We propose a set of effective methods to statistically model the spatial/temporal variations - including fade depth (FD), level crossing rate (LCR), average fade duration (AFD), and Ricean <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> -factor - as a function of the structural parameters of cuttings. Akaike's Information Criterion (AIC)-based evaluation indicates that the Ricean distribution is the best to describe small-scale fading. In addition, the rich multipath and directionality of the transmitting antennas lead to a non-monotonous dependence of the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> -factor on the distance between transmitter and receiver. The autocovariance function of the deviation of the extracted <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> -factors from the proposed model is presented and the coherence length is investigated. Our results show that even though a cutting is a scenario with severe fading, a “wide” cutting (i.e., with both wide crown and bottom widths) is conducive to the reduction of the severity of fading.

Experimental characterisation of ultra‐wideband off‐body radio channels considering antenna effects

Experimental investigation to characterise the ultra-wideband (UWB) off-body radio propagation channel for body-centric wireless communication is presented. The measurements were performed in an indoor environment using active UWB wireless tags. Two different kinds of receiver antennas have been used; namely a small form factor (SFF) antenna and miniaturised co-planar waveguide-fed tapered slot antenna to investigate their effects on the radio channel behaviour. Statistical analysis is performed on the radio channel data and the results demonstrated that the lognormal distribution provides the best fit for off-body propagation channel path-loss models. Comparison of results shows that a reduction of 29% path-loss exponent is noticed for the SFF antenna. In addition to this, second-order channel parameters such as fade probability, level-crossing rate and average fade duration are also investigated and compared for the two antennas.

Second‐order statistics of multiuser relay cooperation systems over Nakagami‐m fading channels

SUMMARYTo attain overall recognition of the effect of Nakagami‐m channel parameters on the second‐order statistics and to present a guide to the design and configuration of systems, we investigate the average level crossing rate (LCR) and average fading duration (AFD) of multiuser single relay cooperation wireless communications, in which the multiple mobile users communicate with base station under the help of single relay. On the basis of the statistical channel state information (CSI) between mobile users and relay, a single user is selected to communicate with base station. For the multiuser relay cooperation communications, we first present the integral expressions to the LCR and AFD of equivalent end‐to‐end envelope by using strict mathematical proof. Then with appropriate approximation, we obtain the closed‐form solutions to the upper and lower bounds of average LCR and AFD as well as the ones of Laplace approximation. Finally, on the basis of the derivations, we validate the approximations to LCR and AFD, and investigate the effect of the system parameters on LCR and AFD. The comparison results show that the derivations match well the simulations, and the exact values can be bounded by the obtained upper and lower bounds. Copyright © 2013 John Wiley &amp; Sons, Ltd.

On the second order statistics of non-isotropic Nakagami Hoyt mobile to mobile fading channel

This paper presents second order statistical properties of the mobile to mobile Nakagami Hoyt channel model under non-isotropic condition. The spatial-time correlation function, the power spectral density (PSD), level crossing rate (LCR) and the average duration of fade (ADF) of the Nakagami Hoyt channel have been derived under the assumption that both the transmitter and receiver are non-stationary having non-omnidirectional antennas. Design of simulator using the Inverse Fast Fourier Transform (IFFT) based computation method has been applied for this model. The simulator and analytical results have been corroborated.

Millimetre‐wave path‐loss variability between two body‐mounted monopole antennas

Variation of on-body millimetre-wave propagation channels with body movements has been studied experimentally. A statistical description of the propagation channel is presented, including path-loss probability distributions, level-crossing rates and average fade durations. The median path losses for the considered practical links with omnidirectional monopole antennas lied within the range of 55–88 dB. The signal variation was found to consist of two superimposed variations, in general: the long-term and short-term fadings, but was dominated by the much stronger long-term fading. The use of a simple two-state Markov process model to describe on-body communication links is also proposed and its limitations are discussed.

Second order statistics of selection combining receiver over κ‐μfading channels subject to co‐channel interferences

Radio propagation performances in interference‐limited faded environment are studied in this paper. Selection combining (SC) based on signal‐to‐interference ratio (SIR) overκ‐μfading channels is performed. Probability density function (PDF) and cumulative distribution function (CDF) of the received SIR are determined. Based on the results obtained for PDF and CDF, infinite‐series expressions are derived for the output level crossing rate (LCR) and average fade duration (AFD). These second order statistical measures are regarded as necessary for supporting technical documentation in every radio communication link design. Influences of various system parameters such as fading severity and the number of co‐channel interferences affecting these measures are graphically presented and discussed.

Framework to calculate level-crossing rate and average fade duration in two-dimensional and three-dimensional scattering environments

This study proposes a framework for calculating level-crossing rate and average fade duration in wireless communication systems operating in Rayleigh fading channel environments. The complexity of the calculations involved is greatly reduced compared to the conventional way of calculating these two measures. To demonstrate the strength of the proposed framework, the authors applied it to two-dimensional and three-dimensional isotropic and non-isotropic scattering environments and the results are compared to available results in the literature.

Higher Order Statistics of Sampled Fading Channels With Applications

In this paper, we present a novel analytical framework for the calculation of the level crossing rate (LCR) and the average fade duration (AFD) of fading channels sampled at a certain sampling period TS. These expressions are valid for arbitrary fading distributions with arbitrary correlation and can be easily computed in terms of the cumulative distribution function (cdf) of the fading envelope and its bivariate cdf. This approach yields interesting insights into the effect of finite sampling in the higher order statistics of fading processes. We also demonstrate that the proposed expressions for sampled fading process converge with the existing expressions for continuous fading processes as the sampling period tends to zero. As a direct application, exact closed-form expressions are given for the LCR and AFD of sampled Rayleigh fading processes, which are suitable to characterize the higher order statistics of the equivalent frequency-domain fading process in multipath Rayleigh fading.

LCR and AFD of Decode-and-Forward Relay Networks with N^{th} Best Relay Selection Schemes in Rayleigh Fading Channels

The second-order statistics are of significance for the design of wireless relay networks. In this correspondence, we have theoretically derived the second-order statistics, level crossing rate (LCR) and average fade duration (AFD), of the Nth best proactive and reactive decode-and-forward (DaF) relaying schemes in Rayleigh fading channels. The above two schemes choose different relaying nodes to assist the signal transmission. It is shown that the theoretically derived LCR and AFD performances match the simulation results. It is also shown that for the Nth best DaF relaying, both proactive and reactive schemes have the same LCR and AFD performances.

On the Bivariate Nakagami-m Cumulative Distribution Function: Closed-Form Expression and Applications

In this paper, we derive exact closed-form expressions for the bivariate Nakagami-$m$ cumulative distribution function (CDF) with positive integer fading severity index $m$ in terms of a class of hypergeometric functions. Particularly, we show that the bivariate Nakagami-$m$ CDF can be expressed as a finite sum of elementary functions and bivariate confluent hypergeometric $\Phi_3$ functions. Direct applications which arise from the proposed closed-form expression are the outage probability (OP) analysis of a dual-branch selection combiner in correlated Nakagami-$m$ fading, or the calculation of the level crossing rate (LCR) and average fade duration (AFD) of a sampled Nakagami-$m$ fading envelope.

Level crossing rate of sea clutter: theory and measured data

Proposed and computed are the level crossing rate (LCR), average calm duration (ACD) and average surge duration (ASD) in the context of radar clutter and false alarm analysis. The derived formulas for the LCR, ACD and ASD are then compared to their measured values calculated from experimental radar sea clutter and are shown to be in good agreement.

Generalized Framework for the Level Crossing Analysis of Ordered Random Processes

This paper investigates the following general problem relating to ordered random processes: given n independent but not necessarily identical random processes, how frequently, on average, does any given process become one of the pth (p=1,2,..., n-1) largest processes? This is a fundamental problem arising in the design and analysis of contemporary multidimensional wireless communication systems (e.g., multiantenna, multiuser) employing opportunistic selection. We formulate this problem as one involving the level crossing rate (LCR) of a carefully defined ordered random process across the zero threshold, which we solve by developing a new mathematical framework based on the theory of permanents. For the case where the processes correspond to time-varying Rayleigh fading channels, we present exact closed-form formulas for the LCR, simplified tight upper bounds, as well as asymptotic results for n and p approaching infinity but with fixed ratio. These results reveal interesting fundamental limits for the LCR, and are shown to given meaningful insight even for small values of n and p . We further use our mathematical framework to characterize the required per-branch and overall switching rate of a generalized selection combining diversity receiver, allowing for different average powers for each branch. With the aid of majorization theory, we demonstrate that the overall switching rate is maximized when the power delay profile is uniform.

Performance Analysis of Multihop Wireless Links Over Generalized- $K$ Fading Channels

The performance of multihop links is studied in this contribution by both analysis and simulations when communicating over generalized- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">G</sub> ) fading channels. The performance metrics considered include symbol error rate (SER), outage probability, level crossing rate (LCR), and average outage duration (AOD). First, the expressions for both the SER and outage probability are derived by approximating the probability density function (pdf) of the end-to-end signal-to-noise ratio (SNR) using an equivalent end-to-end pdf. We show that this equivalent end-to-end pdf is accurate for analyzing the outage probability. Then, the second-order statistics of LCR and AOD of multihop links are analyzed. Finally, the performance of multihop links is investigated by either simulations or evaluation of the expressions derived. Our performance results show that the analytical expressions obtained can be well justified by the simulation results. The studies show that the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">G</sub> channel model and the expressions derived in this paper are highly efficient for the prediction of the performance metrics and statistics for the design of multihop communication links.

Average Level Crossing Rate of Dual Selection Diversity over Correlated Unbalanced Nakagami-m Fading Channels in the Presence of Cochannel Interference

A dual selection combining (SC) receiver which applies desired signal power algorithm and operates over correlated, but not necessary identically distributed Nakagami-m fading channels in the presence of cochannel interference (CCI) is considered in this letter. Actually, a novel infinite-series expression for the average level crossing rate (LCR) at the output of that SC receiver is obtained. Numerical results are presented to examine the effects of the fading severity, input signal-to-interference ratio (SIR) unbalance and the level of branch correlation on the average LCR, as well as the correctness of proposed analytical formulation.