Composite Fading Model Research Articles

MGF-based Analysis of Maximum Ratio Combining Receiver over Fisher-Snedecor Composite Fading Channel

Fisher Snedecor composite fading model is the combination of Nakagami-m and inverse Nakagami-m distribution. The Nakagami-m is used to characterize the small scale fading, whereas shadowing is modeled by inverse Nakagami-m distribution. In this paper, the closed-form expression for moment generating function (MGF) of instantaneous signal to noise ratio (SNR) over independent identically distributed (i.i.d) Fisher-Snedecor composite fading channel using maximum ratio combining (MRC) diversity technique is derived. By using newly derived MGF expression, we derive the closed-form expressions of average bit error rate (ABER) or average symbol error rate (ASER) for different binary and multilevel modulation schemes. The expressions for average channel capacity (ACC) under two adaptive transmission protocols like optimum rate adaption (ORA) and channel inversion with fixed rate (CIFR) are also derived using proposed MGF. Further, the numerical results of newly derived expression are presented and compared with the results of Rayleigh and Nakagami-m distribution which is the special case of Fisher Snedecor composite fading model.

MGF‐based analysis of κ‐μ/gamma composite fading model for indoor off body communication

AbstractThis paper presents the moment generating function (MGF)–based analysis of κ‐μ/gamma composite fading model, which is suitable for the indoor off‐body communication channel. In this paper, first of all, we derive an analytical expression for MGF of instantaneous signal‐to‐noise ratio. By using the derived MGF, the expressions of average symbol error rate (ASER)/average bit error rate (ABER) for binary and M‐ary modulation scheme are derived. Using the MGF approach, we also derive the expression of channel capacity for optimum rate adaption and channel inversion with fixed rate policy. The derived expressions for ABER/ASER and channel capacity are presented in the infinite series form. We further present the numerical results of error rate and channel capacity for different values of κ, μ, α, and β parameters. The result of ABER and channel capacity shows good agreement with the previously reported results as special cases that verify the derived expressions.

Unified Analysis and Optimization of D2D Communications in Cellular Networks Over Fading Channels

This paper develops an innovative approach to the modeling and analysis of downlink cellular networks with device-to-device (D2D) transmissions. The analytical embodiment of the signal-to-noise and-interference ratio analysis in general fading channels is unified due to the H-transform theory, a taxonomy never considered before in stochastic geometry-based cellular network modeling and analysis. The proposed framework has the potential, due to versatility of the Fox’s H functions, of significantly simplifying the cumbersome analysis procedure and representation of D2D and cellular coverage, while subsuming those previously derived for all the known simple and composite fading models. By harnessing its tractability, the developed statistical machinery is employed to launch an investigation into the optimal design of coexisting D2D and cellular communications. We propose novel coverage-aware power control combined with opportunistic access control to maximize the area spectral efficiency (ASE) of D2D communications. Simulation results substantiate performance gains achieved by the proposed optimization framework in terms of cellular communication coverage probability, average D2D transmit power, and the ASE of D2D communications under different fading models and link- and network-level dynamics.

A Comprehensive Analysis of the Achievable Channel Capacity in $\mathcal{F}$ Composite Fading Channels

The $\mathcal {F}$ composite fading model was recently proposed as an accurate and tractable statistical model for the characterization of the composite fading conditions encountered in realistic wireless communication scenarios. In the present contribution, we capitalize on the distinct properties of this composite model to derive an analytical framework and then to evaluate the achievable channel capacity over $\mathcal {F}$ composite fading channels under different channel state information (CSI) assumptions. To this end, we first consider that the CSI is known only at the receiver, for which we derive novel analytic expressions for the channel capacity under optimum rate adaptation as well as for the corresponding effective capacity. Then, by considering that the CSI is known both at the transmitter and at the receiver, we derive novel analytic expressions for the channel capacity under optimum power and rate adaptation, channel inversion with fixed rate and truncated channel inversion with fixed rate. The derived analytic expressions for the considered scenarios are provided in closed-form and benefit from being tractable both analytically and numerically. This enables the derivation of simple bounds as well as approximate and asymptotic expressions, which are shown to be useful as they provide meaningful insights on the effect of fading conditions and/or latency on the overall system performance.

SINR distribution approximation for maximal ratio communications

The SINR distribution is of key importance to wireless network performance analysis, planning and optimization. A realistic and usable SINR distribution has to consider both, the fast and the slow fading, i.e., to utilize a composite fading model. There have been only partial efforts in deriving a closed form and simple SINR distribution, using a realistic composite fading model and valid throughout the full SNR range. Recently, there is also a rising necessity for SINR distribution models that integrate the multi-antenna and multi-user aspects of the emerging 5G systems. This paper derives an analytical lognormal approximation to the SINR distribution in scenarios with maximal ratio communication using multiple transmit or receive antennas. The derivations incorporate a newly derived lognormal composite fading approximation and lognormal approximation to the distribution of the summary interference plus noise, in order to approximate the SINR distribution. The expressions are simple and closed form, which makes them applicable to a variety of communication network optimization and evaluation problems. The paper uses simulation analysis to prove the validity of the analytical SINR distribution approximation in homogeneous and heterogeneous cellular network deployments. The results show only few dBs of mismatch in these realistic cellular network scenarios.

CDF and MGF based analysis over Rayleigh TWDP shadowed fading channel for indoor communication

ABSTRACTRecently, the two-wave with diffuse power (TWDP) distribution has been extensively used to model the shadowing in multipath-faded/shadowed indoor environment. In this article, novel expressions for joint moments, mean, second moment, variance and cumulative distribution function for Rayleigh TWDP shadowed fading model are derived. By using the derived expression of mean and variance, the expression for amount of fading is obtained. Also, the outage probability, moment generating function and average bit error rate (ABER) for various modulation schemes namely binary phase shift keying (BPSK), binary frequency shift keying (BFSK), minimum shift keying (MSK), differentially coherent phase shift keying (DCPSK) and non-coherent frequency shift keying (NCFSK) are calculated. The derived expressions for cumulative distribution function, outage probability and ABER are presented in analytical format and have been numerically evaluated. Moreover, the numerical results of ABER using MSK and DPSK modulation schemes is compare with results of Rayleigh Gamma composite fading model. The study shows that better outage probability (0.01) is observed at 40dB average signal to noise ratio (SNR) with 5dB lowest threshold SNR, however, at higher threshold SNR (>5dB) with fixed average SNR (40dB), poor outage probability performance are obtained. Further, at higher shadowing (10dB), for fixed average SNR (15dB), minimum error probability (10−4) is observe, while at lower shadowing (less than 10dB), higher error probability (greater than 10−4) is observed that represents poor BER performance.

Dual-hop full duplex relay networks over composite fading channels: Power and location optimization

This paper investigates schemes for improving the outage performance of dual-hop full duplex (FD) and half duplex (HD) decode and forward (DF) based relay networks over composite Nakagami-m/log-normal fading channels. First of all, we derive new analytical expression for the outage probability of dual-hop FDR network considering the effects of interference caused by direct link from source-to-destination and the residual self-interference (RSI) at the full duplex relay (FDR). We also provide the asymptotic outage probability expression. We then investigate optimal power allocation (OPA); optimal relay location (ORL) and joint optimization of transmit power and relay location that minimizes the outage probability. We show that the first two problems are convex and devise modified Polak–Ribiere Conjugate Gradient Method to determine the OPA and ORL. Since the joint optimization problem is non convex, we devise an efficient, low complex and fast converging iterative algorithm based on alternating optimization technique. We repeat the investigations for dual-hop HDR networks as well assuming composite fading model. The results demonstrate that both OPA and ORL can improve the outage probability; however joint optimization leads to superior performance as compared to OPA, ORL and un-optimized cases.

Performance analysis of κ-μ/gamma shadowed fading model over indoor off body communication channel

The κ-µ/gamma distribution has an importance role to model the small scale fading and shadowing over human off body indoor communication channel. This composite fading model has various special cases like κ-µ, Rician, Nakagami-m, Rayleigh, Rayleigh/gamma, Nakagami/gamma and Rice/logormal. In this paper, the expression for bit error rate (BER) using various modulation schemes, average channel capacity (ACC) and outage probability (OP) over κ-µ/gamma shadowed fading channel are derived. All the derived expressions are novel and presented in analytical form. The expression for BER and channel capacity are in form of well-known Meijer G function, whereas the outage probability expression is obtained from cumulative distribution function (CDF) proposed in previous literature. The derived expressions of BER (BPSK), average channel capacity and outage probability reduces to special cases for validation purpose. The study shows that binary phase shift keying (BPSK) modulation technique has better BER performance as compare to other modulation techniques. Moreover, on increasing α and β while κ and µ kept constant and vice versa, the ACC get increases but below the Additive white Gaussian Noise (AWGN) channel capacity as expected. Also, better outage probability performance is obtained at lowest threshold signal to noise ratio (5 dB).

Performance of MRC receiver over Hoyt/lognormal composite fading channel

ABSTRACTIn this article, mixture gamma (MG) distribution is used for analysing the performance of L-Hoyt/lognormal composite fading channel. To overcome small-scale fading effect, micro-diversity using maximum ratio combining (MRC) is used at the receiver. Due to mathematical complexity, performance analysis of composite (L-Hoyt/lognormal) fading models is not present in closed form. The analytical expressions for the performance measure are derived in the form of received signal-to-noise ratio (SNR). The impact of system parameters on the energy detector (ED) performance is studied in terms of receiver operating characteristic (ROC) and area under the ROC curve (AUC). Further, the detection threshold parameter is optimised by minimising the total probability of error for L-Hoyt/lognormal channel. The accuracy of the proposed closed-form expressions is validated by comparing all the results with the Monte-Carlo/exact simulations.

On the Product of Two <inline-formula> <tex-math notation="LaTeX">$\kappa$ </tex-math> </inline-formula>–<inline-formula> <tex-math notation="LaTeX">$\mu$ </tex-math> </inline-formula> Random Variables and its Application to Double and Composite Fading Channels

In this paper, we perform a systematic investigation of the statistics associated with the product of two independent and non-identically distributed $\kappa$ – $\mu$ random variables. More specifically, we develop novel analytical formulations for many of the fundamental statistics of interest, namely, the probability density function, cumulative distribution function, and moment-generating function. Using these new results, closed-form expressions are obtained for the higher order moments, amount of fading and channel quality estimation index, while analytical formulations are obtained for the outage probability, average channel capacity, average symbol error probability, and average bit error probability. These general expressions can be reduced to a number of fading scenarios, such as the double Rayleigh, double Rice, double Nakagami- $m$ , $\kappa$ – $\mu$ /Nakagami- $m$ , and Rice/Nakagami- $m$ , which all occur as special cases. Additionally, as a byproduct of the work performed here, formulations for the $\kappa$ – $\mu /\kappa$ – $\mu$ composite fading model can also be deduced. To illustrate the efficacy of the novel expressions proposed here, we provide useful insights into the outage probability of a dual-hop system used in body area networks, and demonstrate the suitability of the $\kappa$ – $\mu /\kappa$ – $\mu$ composite fading for characterizing shadowed fading in device-to-device channels.

Performance of an energy detector over η-μ/lognormal composite channel with cooperative sensing

ABSTRACTThe η-μ/lognormal composite distribution corresponds to a physical realistic scenario where the multipath effect is characterised by well-known η-μ generalised model and shadowing effect is captured by the lognormal (LN) distribution. In this work, an approximate closed-form of η-μ/LN distribution is derived using Gauss-Hermite (GH) integration. Further, the derived probability density function is utilised to develop the closed-form expression as well as infinite series representation of the average probability of energy detection (PD) and average area under the receiver operating characteristics curve (AUC) along with their respective upper bound of the truncation error. Maximal ratio combining (MRC) microdiversity technique is applied over η-μ/LN composite fading model and then its average PD is derived. In order to reduce the total probability of error, the optimisation of the detection threshold parameter is done. The result clearly shows the significant improvement in the detection probability when the optimised threshold parameter is used. Further, an extensive analysis of the optimisation of the cooperative spectrum sensing (CSS) over η-μ/LN distribution with ‘v-out-of-U’ rule at fusion center assuming erroneous feedback channels is also carried out. The closed-form expressions are validated by comparing them with exact results and Monte Carlo simulation.

Relay Placement for Coverage Extension in Cellular Wireless Networks Under Composite Fading Model

In relay-assisted cellular networks, mobile stations are connected to base station through two or more single-hop communication links, where the intermediate nodes act as relay stations (RSs). The focus of this paper is on two-hop relay assisted cellular networks, where optimal relay placement is a crucial issue for achieving maximum extension of the cell coverage. However, the location of RS has significant impact on signal-to-interference plus noise ratio (i.e., SINR) and outage probability experienced on the access and backhaul links. Moreover, the frequency re-use factor also has significant influence on the SINR. In this paper, we develop analytical models for computing the SINR and outage probability performance of a two-hop relay assisted cellular network for both downlink (DL) as well as uplink (UL) transmission scenarios, considering the impact of path loss, shadowing, Nakagami fading and co-channel interference. We then investigate optimal placement of RS while satisfying the required criterion on probability of correct decoding, initially by considering the DL scenario alone and then by considering both DL and UL scenarios jointly. Through extensive evaluations, we report the impact of realistic propagation models on outage probability, optimal relay position and the cell coverage radius. Further, the model can be used to find the impact of co-channel re-use factor on optimal relay positioning in two-hop cellular networks.

The Fisher–Snedecor $\mathcal {F}$ Distribution: A Simple and Accurate Composite Fading Model

We consider the use of the Fisher-Snedecor ${\mathcal {F}}$ distribution, which is defined as the ratio of two chi-squared variates, to model composite fading channels. In this context, the root-mean-square power of a Nakagami- $m$ signal is assumed to be subject to variations induced by an inverse Nakagami- $m$ random variable. Comparisons with physical channel data demonstrate that the proposed composite fading model provides as good, and in most cases better, fit to the data compared to the generalized- $K$ composite fading model. Motivated by this result, simple novel expressions are derived for the key statistical metrics and performance measures of interest.

Shadowed Fading in Indoor Off-Body Communication Channels: A Statistical Characterization Using the $\kappa $ –$\mu $ /Gamma Composite Fading Model

This paper investigates the characteristics of the shadowed fading observed in off-body communications channels at 5.8 GHz. This is realized with the aid of the $\kappa $ – $\mu $ /gamma composite fading model, which assumes that the transmitted signal undergoes $\kappa $ – $\mu $ fading, which is subject to multiplicative shadowing. Based on this, the total power of the multipath components, including both the dominant and scattered components, is subject to non-negligible variations that follow the gamma distribution. For this model, we present an integral form of the probability density function (PDF) as well as important analytic expressions for the PDF, cumulative distribution function, moments, and moment generating function. In the case of indoor off-body communications, the corresponding measurements were carried out in the context of four explicit individual scenarios, namely: line of sight (LOS), non-LOS walking, rotational, and random movements. The measurements were repeated within three different indoor environments and considered three different hypothetical body worn node locations. With the aid of these results, the parameters for the $\kappa $ – $\mu $ /gamma composite fading model were estimated and analyzed extensively. Interestingly, for the majority of the indoor environments and movement scenarios, the parameter estimates suggested that dominant signal components existed even when the direct signal path was obscured by the test subject’s body. In addition, it is shown that the $\kappa $ – $\mu $ /gamma composite fading model provides an adequate fit to the fading effects involved in off-body communications channels. Using the Kullback-Leibler divergence, we have also compared our results with another recently proposed shadowed fading model, namely, the $\kappa $ – $\mu $ /lognormal LOS shadowed fading model. It was found that the $\kappa $ – $\mu $ /gamma composite fading model provided a better fit for the majority of the scenarios considered in this paper.

Closed-Form Exact and Asymptotic Expressions for the Symbol Error Rate and Capacity of the -Function Fading Channel

In this paper, we derive closed-form exact and asymptotic expressions for the symbol error rate (SER) and channel capacity when communicating over Fox's $H$ -function fading channel. The SER expressions are obtained for numerous practically employed modulation schemes in case of single-branch and three multiple-branch diversity receivers: maximal ratio combining (MRC), equal gain combining (EGC), and selection combining (SC). The derived exact expressions are given in terms of the univariate and multivariate Fox's $H$ -functions for which we provide a portable and efficient Python code. Since Fox's $H$ -function fading channel represents the most generalized fading model ever presented in the literature, the derived expressions subsume most of those previously presented for all the known simple and composite fading models. Moreover, easy-to-compute asymptotic expansions are provided to easily study the behavior of the SER and channel capacity at high values of the average signal-to-noise ratio (SNR). The asymptotic expansions are also useful in comparing different modulation schemes and receiver diversity combiners. Numerical and simulation results are also provided to support the mathematical analysis and prove the validity of the obtained expressions.

On the MIMO Capacity for Distributed System under Composite Rayleigh/Rician Fading and Shadowing

Wireless channels are commonly affected by short-term fading and long-term fading (shadowing). The shadowing effects must be taken into account also when mobility is present in the wireless scenario. Using a composite fading model, the total channel capacity can be studied for a scenario with short-term Rayleigh fading along with shadowing. This work provides quantitative results for these kinds of scenarios with Rayleigh fading and shadowing, considering also multiple-input and multiple-output systems, which have not been previously reported. In addition, the channel capacity has been studied in depth in its relation with the shadowing level, signal to noise ratio, and the number of elements in the multiple-input and multiple-output system. Moreover, the channel performance with shadowing has been compared to the one without it. Furthermore, Rician model with shadowing is studied and its results are reported. In addition, correlated and experimental results are provided. It is identified that the distributed MIMO systems can benefit from shadowing in Rician channels. This advantage has not been reported previously. This type of fading is proposed for massive MIMO by others and our results open the door to emulate massive MIMO on a reverberation chamber.

English

  In wireless communication the effect of multipath as well as shadowing takes place simultaneously over the channel and this phenomena leads to composite fading. G-distribution is frequently encountered distribution in wireless fading environment. Combination of multipath fading and shadowing model are used as composite fading model. This composite fading model is named as G-distribution. G-distribution is a combination of the Inverse-Gaussian distribution and the distribution. In this paper the Pade approximation approach is used to analyze the performance of composite multipath/shadowed fading channel. This distribution is used to approximate any system in form of closed form solution as well as for accurate approximation in several shadowing conditions. The Pade approximation is applied over the general expression that is given in terms of moment generating function and results are obtained by varying shadowing parameters as well as signal to noise power threshold ratio. Our study start by deriving the moment generating function of the G-distribution and approximate them by using the Pade approximation for the calculation of bit error rate and outage probability for different values of average Signal to noise ratio (SNR). All simulations are done using Maple-13 software tool and results are obtained for outage probability and bit error rate versus average SNR.   Key words: Pade’s approximation, G-distribution, moment generating function, inverse Gaussian distribution, Nakagami distribution and composite distributions, average signal to noise ratio, outage probability, bit error probability.

On the Performance of Transmit Antenna Selection Based on Shadowing Side Information

In this paper, a transmit antenna selection scheme, which is based on shadowing side information, is investigated. In this scheme, the selected single transmit antenna provides the highest shadowing coefficient between a transmitter and a receiver. By the proposed technique, the frequency of the usage of the feedback channel from the receiver to the transmitter and channel estimation complexity at the receiver can be reduced. We study the performance of our proposed technique, and in the analysis, we consider an independent but not identically distributed generalized- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> composite fading model. More specifically, exact and closed-form expressions for the outage probability, the moment-generating function, the moments of signal-to-noise ratio, and the average symbol error probability (SEP) are derived. In addition, asymptotic outage probability and SP expressions are also presented to investigate the diversity order and the array gain. Finally, our theoretical performance results are validated by Monte Carlo simulations.

Two Composite Fading Models for Diversity Reception in Mobile Wireless Networks

Composite Rayleigh-lognormal fading, also known as Suzuki fading, is a cascaded product of a multipath fast fading channel and a shadowing slow fading channel. In spatial diversity reception using maximum ratio combining, the Suzuki fading model only provides diversity in the local multipath fast fading Rayleigh component, here called the micro-diversity fading model. In this paper, we propose the macro-diversity composite fading model by which diversity is obtained over the whole transmission link from the transmitter to the mobile receiver, ie. in both the slow lognormal fading and the fast Rayleigh fading. Methods for solving the “sum of Suzuki random variables” problem involved in the macro-diversity model is presented in the paper. The Gauss-Hermite quadrature polynomial is extensively used to avoid sensitive integrations and to derive elegant and computationally fast closed-form expressions for bit error rate of micro-diversity and macro-diversity reception in mobile networks.

Two composite fading models for diversity reception in mobile wireless networks

Two composite fading models for diversity reception in mobile wireless networks