Average Fade Research Articles

Second-order statistics for diversity-combining of non-identical correlated hoyt signals

In this paper, exact expressions for the level crossing rate (LCR) and average fade duration (AFD) for two-branch selection, equal-gain and maximal-ratio combining systems in a Hoyt fading environment are presented. The expressions apply to unbalanced, non-identical, correlated diversity channels and have been validated by specializing the general results to some particular cases whose solutions are known. In passing, the joint bidimensional envelope-phase Hoyt distribution with arbitrary fading parameters is obtained.

Non-coherent improved-gain diversity reception of binary orthogonal signals in Nakagami- q (Hoyt) mobile channels

A novel non-coherent receiver with diversity reception for binary orthogonal signals in non-identical Nakagami-q (Hoyt) fading channels (channels having arbitrary average fading powers and arbitrary fading parameters) is proposed. A closed-form expression for the average bit error probability of the proposed receiver is derived, which is given in terms of elementary functions, and can be readily evaluated numerically. In addition, the results clarify that the proposed receiver does not incur non-coherent combining loss, and at the same time, lower bounds the performance of the conventional non-coherent equal-gain combining (NC-EGC) receiver. Simulation results are provided to validate the mathematical analysis.

On the Fading-Paper Achievable Region of the Fading MIMO Broadcast Channel

We consider transmission over the ergodic multiple-antenna broadcast (MIMO-BC) channel with partial channel state information at the transmitter and full information at the receiver. Over the equivalent non-fading channel, capacity has recently been shown to be achievable using transmission schemes that were designed for the channel. We focus on a similar fading model. The evaluation of the paper capacity is difficult to obtain. We confine ourselves to the linear-assignment capacity, which we define, and use convex analysis methods to prove that its maximizing distribution is Gaussian. We compare our fading-paper transmission to an application of dirty paper coding that ignores the partial state information and assumes the channel is fixed at the average fade. We show that a gain is easily achieved by appropriately exploiting the information. We also consider a cooperative upper bound on the sum-rate capacity as suggested by Sato. We present a numeric example that indicates that our scheme is capable of realizing much of this upper bound.

Nonisotropic fading channel model for the highway environment

This article investigates the properties of several non-Jakes Doppler spectra proposed for the vehicle-to-vehicle nonisotropic scattering environment of the open highway. Expressions for the ideal model correlations, level-crossing rates, and average fade durations are derived. The classic Clarke channel model is modified to generate fading signals corresponding to the nonisotropic scattering profiles. The simulation results match well with the theoretical ideal channel.

Crossing rates and fade durations for diversity-combining schemes over α-μ fading channels

This paper derives exact expressions for the level crossing rate and average fade duration of multibranch pure-selection, equal-gain, and maximal-ratio combiners operating over independent non-identical α-μ (also called generalized Γ or Stacy) fading channels. The derived expressions are in closed form for pure-selection combining and in integral form for equal-gain and maximal-ratio combining. For the two latter schemes, accurate closed-form approximations are then provided. The analytical results are validated by reducing the general expressions to known particular cases and, more generally, by means of simulation. Numerical examples are also given to illustrate the high accuracy of the proposed closed-form approximations.

The Criterions with LCR and AFD of Dual-Branch SC Diversity over Specified Wireless Radio Fading Channels

In this paper we proposed the results of average LCR (level crossing rate) and AFD (average fading duration) criterions applied to evaluate the performance of dual-branch SC (selection combining) reception in the specified fading channels characterized as statistical distributions with correlated-Rayleigh and correlated-Rice models. Moreover, in order to unify and clarify the criterions of performance formulas with average LCR and AFD for SC diversity over different kinds of fading models, include such as Rayleigh, Rice, Nakagami-m, and Weibull distributions etc., almost all of the ever researched and published results from discussing about the LCR and AFD of SC diversity are comprehensively collected in this report. On the other hand, for the purpose of comparison, there are a large number of LCR and AFD performance formulas for SC diversity and the generalized fading statistic models are extracted and tabulated together, in which the cases of correlated and independent proprieties between diversity branches are taken into consideration too (some of the formulas are illustrated by the assumption of dual-branch SC diversity).

Level Crossing Rate and Average Fade Duration of EGC Systems With Cochannel Interference in Rayleigh Fading

Both the first-order signal statistics (e.g., the outage probability) and the second-order signal statistics [e.g., the average level crossing rate (LCR) and the average fade duration (AFD)] are important design criteria and performance measures for wireless communication systems, including the equal gain combining (EGC) systems in the presence of the cochannel interference (CCI). Although the analytical expressions for the outage probability of the coherent EGC systems are exposed to CCI and various fading channels are already known, the respective expressions for the average LCR and the AFD are not available in the literature. This paper presents such analytical expressions for the Rayleigh fading channel, which are obtained by utilizing a novel analytical approach that does not require the explicit expression for the joint probability density function (pdf) of the instantaneous output signal-to-interference ratio and its time derivative. Applying the characteristic function method and the Beaulieu series, we determined the average LCR and the AFD at the output of an interference-limited EGC system with an arbitrary diversity order and an arbitrary number of cochannel interferers in the form of an infinite integral and infinite series. For the dual diversity case, the respective expressions are derived in closed forms in terms of the gamma and beta functions.

General Exact Level Crossing Rate and Average Fade Duration for Dual-Diversity Combining of Nonidentical Correlated Weibull Signals

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> This paper derives general <emphasis emphasistype="boldital">exact</emphasis> expressions for the level crossing rate (LCR) and the average fade duration (AFD) of dual-branch selection, equal-gain, and maximal-ratio combiners operating over nonidentical correlated Weibull fading channels. Sample numerical results are discussed by specializing the general expressions to a space-diversity system using horizontally spaced antennas at a mobile station. It is verified that as the antenna spacing becomes larger, the LCR decreases, becoming oscillatory and convergent. In addition, when the direction of the mobile is perpendicular to the axis of the antenna, the AFD is loosely dependent on the antenna spacing. Some simulation results are presented to verify the correctness of the analytical formulation. </para>

Level Crossing Rate and Average Fade Duration of Dual Selection Combining With Cochannel Interference and Nakagami Fading

This letter provides closed-form expressions for the outage probability, the average level crossing rate (LCR) and the average fade duration (AFD) of a dual diversity selection combining (SC) system exposed to the combined influence of the cochannel interference (CCI) and the thermal noise (AWGN) in Nakagami fading channel. The branch selection is based on the desired signal power SC algorithm with all input signals assumed to be independent, while the powers of the desired signals in all diversity branches are mutually equal but distinct from the power of the interference signals. The analytical results reduce to known solutions in the cases of an interference-limited system in Rayleigh fading and an AWGN-limited system in Nakagami fading. The average LCR is determined by an original approach that does not require explicit knowledge of the joint PDF of the envelope and its time derivative, which also paves the way for similar analysis of other diversity systems.

Higher-order statistics for κ–μ distribution

Closed-form expressions for the level crossing rate and average fade duration of a κ–μ distributed fading signal envelope are presented. The proposed equations are validated by reduction to known Rice, Rayleigh and Nakagami-m special cases. They are also compared with measured data obtained from field trials analysing human body to body radio channels and shown to provide good agreement.

Dispersion effect and compensation in optical-carrier-suppressed modulation transport systems

We develop new expressions for power fading and average power fading that are induced by first-order polarization mode dispersion, polarization-dependent chromatic dispersion, chromatic dispersion, and chirp under both (i) carrier suppressed modulation and (ii) odd-order optical sideband and carrier suppression. Experimental results show the effectiveness of the theoretical analysis. Further, based on the expressions, we propose a technique for optically compensating the polarization mode dispersion-induced power fading in carrier suppressed modulation.

Level Crossing Rate and Average Fade Duration of EGC Systems With Cochannel Interference in Rayleigh Fading

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> Both the first-order signal statistics (e.g., the outage probability) and the second-order signal statistics [e.g., the average level crossing rate (LCR) and the average fade duration (AFD)] are important design criteria and performance measures for the wireless communication systems, including the equal gain combining (EGC) systems in presence of the cochannel interference (CCI). Although the analytical expressions for the outage probability of the coherent EGC systems exposed to CCI and various fading channels are already known, the respective ones for the average LCR and the AFD are not available in the literature. This paper presents such analytical expressions for the Rayleigh fading channel that are obtained by utilizing a novel analytical approach that does not require the explicit expression for the joint probability density function of the instantaneous output signal-to-interference ratio and its time derivative. Applying the characteristic function method and the Beaulieu series, we determined the average LCR and the AFD at the output of an interference-limited EGC system with an arbitrary diversity order and an arbitrary number of cochannel interferers in forms of an infinite integral and an infinite series. For the dual diversity case, the respective expressions are derived in closed forms in terms of the gamma and the beta functions. </para>

Time-Varying MIMO Channels: Parametric Statistical Modeling and Experimental Results

Accurate characterization of multiple-input multiple-output (MIMO) fading channels is an important prerequisite for the design of multiantenna wireless-communication systems. In this paper, a single-bounce two-ring statistical model for the time-varying MIMO flat fading channels is proposed. In the model, both the base and mobile stations are surrounded by their own ring of scatterers. For the proposed model, a closed-form expression for the spatio-temporal cross-correlational function between any two subchannels is derived, assuming single-bounce scattering. The new analytical expression includes several key physical parameters of interest such as the mean angle-of-departure, the mean angle-of-arrival, the associated angle spreads, and the Doppler spread in a compact form. The model includes many existing correlation models as special cases. Its utility is demonstrated by a comparison with collected MIMO data in terms of the spatio-temporal correlations, level crossing rate, average fade duration, and the instantaneous mutual information.

Statistical characteristics of the envelope in diversity combining of two correlated Rayleigh fading channels

Performance of diversity systems is often evaluated under the assumption of perfect interleaving and characterised in terms of long-term parameters such as the average bit-error rate, which does not capture the dynamics of fading channels. Statistical characteristics (static and dynamic) of the envelope of two correlated Rayleigh fading channels are explored using a physical model. For two popular diversity-combining schemes, maximal ratio combining and selection combining, both static and dynamic (level-crossing rate) properties of correlated fading channels are derived. These results are very useful for performance evaluation of diversity systems without bit-level simulations. The results can also provide very useful characteristics such as average duration of fades, fading rate and outage probability for two-channel diversity systems and can be extended to multiple fading channels.

Dispersion induced power fading for radio frequency signals and its application for fast online PMD and CD monitoring

We derive the expressions for the power fading including first-order polarization mode dispersion (PMD), chromatic dispersion, chirp parameter as well as polarization-dependent chromatic dispersion (PCD), which is dependent on the angle of precession of output state of polarization around the PMD vector. From the expression for radio frequency (RF) signals power fading, we get the average power fading for chromatic dispersion, chirp parameter, first-order PMD and PCD for both double sideband (DSB) modulation and single sideband (SSB) modulation. We also demonstrate a fast PMD and chromatic dispersion monitoring technology with reduced polarization-dependent gain. The measured results agree well with theoretical analysis.

Level Crossing Rates in Transmit Beamforming Systems

In this paper, the second-order statistics of the signal to noise ratio (SNR) at the output of a multiple-input-multiple-output (MIMO) system employing maximal ratio combining (MRC) are analyzed. Exact expressions for the level crossing rate (LCR) and the average fade duration (AFD) are derived for the Rayleigh propagation and arbitrary channel matrix dimensions. The analytical results are validated by simulation

New Error-Resilient Scheme Based on FMO and Dynamic Redundant Slices Allocation for Wireless Video Transmission

Video quality suffers significant degradation when transmitted over error-prone channel, due to packet loss, errors caused by fading in wireless channel and due to the video codec prediction mechanisms. The H.264/AVC standard suggests some new error-resilient features to enable reliable transmission of compressed video signal over lossy packet networks. Two of those new features are the Redundant Slices and the Flexible Macro-Block Ordering (FMO). In this paper we propose a new error-resilient scheme which merges the H.264/AVC FMO feature with a new technique for dynamic allocation of redundant slices depending on the wireless channel fading parameters. We suggest using a unique smart dynamic redundant slices allocation scheme which considers the dynamic wireless channel parameters rather than using the classical standard static allocation. The proposed redundant slice allocation algorithm is based on both Average Fade Duration (AFD), and Level Cross Rate (LCR) channel's characteristics. Moreover, we propose a new Explicit Spiral-Interleaved (ESI) flexible macroblocks ordering technique, which outperforms all other FMO types. The new ESI ordering results in effective error scattering which maximize the number of correctly received macroblocks located around corrupted macroblocks, leading to better error concealment. The proposed scheme greatly improves video transmission quality over lossy wireless transmission channels. Simulations results for wireless channel characterized by Rayleigh fading indicate that the proposed method improves the standard static allocation of redundant slices in terms of PSNR by about 2.5dB. Performance evaluations show that our approach is especially suited for applications such as video conferencing and mobile TV, where typically a specific main important Region of Interest should be more carefully protected

Optimal Pilot Spacing and Power in Rate-Adaptive MIMO Diversity Systems with Imperfect CSI

In this paper, performance of a rate-adaptive multiple-input multiple-output diversity system with imperfect channel state information is analyzed and optimized. Space-time block coding is utilized to exploit spatial diversity and to thereby combat some of the fading in wireless channel communications. The remaining fading is tacked by means of adaptive coded modulation. The pilot symbol period and the power allocated to pilot and data symbols are optimized in such a way that the average spectral efficiency is maximized. At the same time, the instantaneous (with respect to predicted channel-signal-to-noise ratio) bit error rate is maintained below a desired level. The average time duration that the channel stays within a certain interval, the average fade region duration, is also derived. A numerical example is given for uncorrelated flat Rayleigh fading subchannels with Jakes spectrum

A unified approach to average LCR and AFD performance of SC diversity in generalized fading environments

The average level crossing rate (LCR) and average fading duration (AFD) criterions are applied to analyze the selection combining (SC) diversity for wireless communication systems over correlated-Rayleigh and correlated-Rice fading in this paper. The scenarios of the fading channel models are characterized as 4 generalized and experimental distributions, e.g., Rayleigh, Rice, Nakagami- m, and Weibull distributed statistics. Moreover, both of independent and correlated proprieties between branches are also involved for consideration. For purpose of unifying and clarifying the average LCR and AFD performance formulas results from the evaluation for SC diversity, it is not only the results from our research presented, but some of the published results are also cited and illustrated by numerical evaluation again in this study.

Experimental results on the level crossing rate and average fade duration for urban fixed wireless channels

The temporal behavior of fixed wireless (FW) links is usually described in terms of fade depth distribution, level crossing rates and average fade duration. This knowledge is needed for the optimization of transceiver parameters such as modulation format, frame length, automatic gain control dynamics, etc. We present analytic and empirical results on the level crossing rate (LCR) and average fade duration (AFD) in FW links. We show that under certain conditions the LCR and AFD do not depend on the shape of the Doppler spectrum and that with a proper choice of parameters, expressions that have been justified for mobile wireless links are also applicable to FW. Results of extensive measurements validate the assumptions that sustain our model