Arbitrary Fading Parameters Research Articles

Closed-Form Hyper-Rayleigh Mode Analysis of the Fluctuating Double-Rayleigh with Line-of-Sight Fading Channel

The research studies hyper-Rayleigh behavior of a wireless communication system functioning in the presence of the generalized multipath fading. Although the initial metric (hyper-Rayleigh mode (HRM)) is quite informative, it is defined only asymptotically (i.e., for the infinitely increasing SNR). In spite of mathematical simplifications brought by such a definition (i.e., in this case most of the performance characteristics defining the HRM can be easily evaluated), it sufficiently limits its applications since, evidently, the real-life systems function in the presence of a finite (and usually not very high) SNR. The study presents a novel approach to the fading channel analysis (i.e., finite signal-to-noise ratio hyper-Rayleigh mode (fHRM)). The proposed metric (fHRM) is studied on the newly presented channel model-fluctuating double-Rayleigh with Line-of-Sight (fdRLoS) fading model. To accomplish this, the novel expressions for two channel-dependent system characteristics (i.e., the Amount of Fading (AoF) and the Outage Probability (OP)) were derived in exact form valid for arbitrary fading parameters. Based on the derived expressions, the finite SNR hyper-Rayleigh map is obtained, which helps to identify the parameters’ values corresponding to the specific propagation scenarios, which were further deployed to analyze the problem of the communication link physical layer security quantified in terms of the probability of strictly positive secrecy capacity (SPSC). Numerical verification of the derived closed-form expressions was performed. Several peculiarities of the system performance are observed and discussed.

Secrecy Outage Probability of MIMO Diversity Schemes Over Integer and Real-Valued Nakagami Fading Channels

This letter studies the secrecy outage probability of diversity schemes (i.e., antenna-user selection with maximal ratio combining (AUS-MRC) scheme and the user selection with space-time block coding (US-STBC)) over arbitrary (i.e., integer and real valued) Nakagami fading channels. The exact secrecy expressions of the diversity schemes is derived for integer-valued fading index expressed as a finite sum and for real-valued fading index expressed as an infinite sum. Also, the secrecy diversity order and the secrecy SNR gain of the secrecy performance for the diversity schemes are quantified for arbitrary Nakagami fading channels. The first new insight provided by this letter is that the secrecy diversity order of the diversity schemes is proportional to the fading index for arbitrary fading parameters. Also, this letter shows that the secrecy diversity order of the diversity schemes is only affected by the parameters of the diversity scheme, not by eavesdropper’s parameters for arbitrary Nakagami fading channels.

Performance Analysis of Hybrid Radio Frequency and Free Space Optical Communication Networks with Cooperative Spectrum Sharing

This paper investigates the impact of cooperative spectrum sharing policy on the performance of hybrid radio frequency and free space optical wireless communication networks, where primary users and secondary users develop a band of the same spectrum resource. The radio frequency links obey Nakagami-m distribution with arbitrary fading parameter m, while the free space optical link follows gamma-gamma distributed atmospheric turbulence with nonzero pointing error. Because the secondary users access the spectrum band without payment, their behavior needs to be restricted. Specifically, the power of the secondary users is dominated by the tolerable threshold of the primary users. Considering both heterodyne and intensity modulation/direct detection strategies in optical receiver, the performance of optical relaying networks is completely different from that of traditional networks. With the help of bivariable Fox’s H function, new expressions for cumulative distribution function of equivalent signal to noise ratio at destination, probability density function, outage probability, ergodic capacity and symbol error probability are built in closed forms.

Comments and Corrections to “New Results on the Fluctuating Two-Ray Model With Arbitrary Fading Parameters and Its Applications”

In “New Results on the Fluctuating Two-Ray Model With Arbitrary Fading Parameters and Its Applications,” by Zhang et al. , closed-form expressions were proposed for the distribution of the received signal-to-noise ratio in the fluctuating two-ray fading model with arbitrary fading parameters for millimetre wave bands. This correspondence provides some comments and corrections to the published closed-form expressions along with several novel analytical results.

Pre-detection dual EGC receiver over correlated η-μ channels with arbitrary fading parameters

ABSTRACT In this letter, we derive a novel expression of the correlated joint PDF of the η–µ distribution to evaluate the performance of correlated equal gain combining (EGC) receiver over η–µ fading channels. The joint PDF is derived from the correlated chi-square distribution using the method of random variable transformations and some algebraic calculations. The derived expressions which consider arbitrary channel parameters along with the correlation and non-identical fading will be closer to the practical scenario as these effects are frequently encountered in practical situations. In the analytical section, we have analyzed the effect of non-identical fading condition along with the impact of correlation and fading severity on the bit error rate (BER) and outage. The results were verified with the help of Monte Carlo simulations and found to be in close.

Physical Layer Security Over <inline-formula> <tex-math notation="LaTeX">$\alpha$</tex-math> </inline-formula>-<inline-formula> <tex-math notation="LaTeX">$\kappa$</tex-math> </inline-formula>-<inline-formula> <tex-math notation="LaTeX">$\mu$</tex-math> </inline-formula> and <inline-formula> <tex-math notation="LaTeX">$\alpha$</tex-math> </inline-formula>-<inline-formula> <tex-math notation="LaTeX">$\eta$</tex-math> </inline-formula>-<inline-formula> <tex-math notation="LaTeX">$\mu$</tex-math> </inline-formula> Fading Channels

In this correspondence, the physical layer security of wireless systems under generalized $\boldsymbol {\alpha }$ - $\boldsymbol {\kappa }$ - $\boldsymbol {\mu }$ and $\boldsymbol {\alpha }$ - $\boldsymbol {\eta }$ - $\boldsymbol {\mu }$ fading with arbitrary fading parameters is analyzed in terms of the secrecy outage probability (SOP). To this end, novel analytical expressions for the lower bound of the SOP are derived. Moreover, an asymptotic secrecy analysis is investigated for each corresponding SOP to get the secrecy diversity gain. Monte Carlo simulations are provided to assess the accuracy of the proposed analytical framework.

New Results on the Fluctuating Two-Ray Model With Arbitrary Fading Parameters and Its Applications

The fluctuating two-ray (FTR) fading model provides a much better fit than other fading models for small-scale fading measurements in millimeter wave communications. In this paper, using a mixture of gamma distributions, new exact analytical expressions for the probability density and cumulative distribution functions of the FTR distribution with arbitrary fading parameters are presented. Moreover, the performance of digital communication systems over the FTR fading channel is evaluated in terms of the channel capacity and the bit error rate. The interaction between channel fading parameters and system performance is further investigated. Our newly derived results extend and complement previous knowledge of the FTR fading model.

Error rate performance analysis of multiantenna MC DS-CDMA system over η–μ frequency selective fading channels with arbitrary parameters

Wireless communication channels have harmful impact on the performance of the wireless communication systems due to the severe influences of multipath fading, path loss, shadowing, intentional and unintentional interference, and noise, respectively. In this paper, we investigate the performance of the orthogonal multicarrier direct sequence code division multiple access (MC DS-CDMA) system coupled with multiple input multiple output (MIMO) system operating over independent nonidentically distributed (i.ni.d) η–μ multipath fading channels in terms of average error probability. Based on moment generating function (MGF) and probability density function (PDF) approaches, closed form expressions for average error probability of binary phase shift keying (BPSK), multilevel phase shift keying (MPSK), and square M-ary quadrature amplitude modulation (MQAM) schemes are derived and expressed in terms of Appell's hypergeometric functions and Lauricella's multivariate hypergeometric functions. The numerical results show that the effects of arbitrary fading parameters, decaying power factor (d), and signal constellation size on the system performance can be reduced using spatial and temporal path diversities. We validate the correctness of the analytical approaches using Monte Carlo simulation techniques.

Exact Closed-Form Expression for End-to-End Average SNR of Dual-Hop Amplify-and-Forward in Wireless Relaying Systems

In this paper, we investigate the end-to-end average signal-to-noise ratio (SNR) of dual-hop amplify-and-forward wireless communication systems operating over independent but not necessarily identically distributed (i.n.i.d.) $$\eta {-}\mu $$?-μ fading channels. Specifically, we derive a novel exact closed-form expression for the generalized end-to-end average SNR for arbitrary fading parameters $$\eta $$? and $$\mu $$μ. Using the obtained closed-form expression for the generalized end-to-end average SNR, some important performance metrics such as the average end-to-end SNR, the amount of fading and the channel capacity can be easily obtained. The effect of the fading parameters and the power imbalance on the overall system performance is investigated. The analytical results are validated by means of Monte-Carlo simulations.

On the Efficient Generation ofα-κ-μandα-η-μWhite Samples with Applications

This paper is concerned with a simple and highly efficient random sequence generator for uncorrelatedα-κ-μandα-η-μvariates. The algorithm may yield an efficiency of almost 100%, and this high efficiency can be reached for all special cases such asα-μ, κ-μ, η-μ, Nakagami-m, Nakagami-q, Weibull, Hoyt, Rayleigh, Rice, Exponential, and the One-Sided Gaussian. This generator is implemented via the rejection technique and allows for arbitrary fading parameters. The goodness-of-fit is measured using the Kolmogorov-Smirnov and Anderson-Darling tests. The maximum likelihood parameter estimation for theκ-μdistribution is proposed and verified against true values of the parameters chosen in the generator. We also provide two important applications for the random sequence generator, the first one dealing with the performance assessment of a digital communication system over theα-κ-μandα-η-μfading channels and the second one dealing with the performance assessment of the spectrum sensing with energy detection over special cases of these channels. Theoretical and simulation results are compared, validating again the accuracy of the generators.

Performance analysis of modulation diversity with OSTBC transmission over Nakagami-m fading channels

In this paper performance of modulation diversity with multiple-input multiple-output transmission is studied over flat Nakagami-m fading channels with arbitrary fading parameter m. In the system, orthogonal space-time block coding and maximal ratio combining like combiner are used for transmission and reception, respectively. Exact pairwise error probability expression is derived to observe performance of the system. Moreover, in order to obtain the diversity order of the system, asymptotic pairwise error probability expression is also derived. Optimum rotation angles are analytically obtained for binary and quadrature phase shift keying modulations. Theoretical results are validated by Monte Carlo simulations.

A Simple Performance Approximation of General-Order Rectangular QAM With MRC in Nakagami- $m$ Fading Channels

The sampling property of the delta impulse function is applied to various Q-function approximations to obtain the probability of error in Nakagami- m fading channels. It is shown that the sampling bit error probability (BEP) exhibits reliable behavior, regardless of the Q-function approximation form. The result is extended to general-order rectangular quadrature amplitude modulation (QAM) with maximal-ratio combining (MRC) to quantify the average symbol error probability (SEP). The proposed approximation presents the SEP in a simple closed form and eliminates the hypergeometric function in the solution. The proposed sampling SEP is accurate and applicable for an arbitrary real-valued fading parameter.

Asymptotic analysis of multi-branch two-way amplify-and-forward relaying in Nakagami-m fading with arbitrary fading parameter

Two-way relay networks have received lots of attention, thanks to its ability to overcome the loss in the spectral efficiency due to half-duplex transmission. Asymptotic performance analysis can provide valuable insights into practical system designs. However, this is a gap in two-way relay network. In this paper, the asymptotic performance is studied for multi-branch dual-hop two-way amplify-and-forward (AF) relaying networks in independently but not necessarily identically distributed (i.n.i.d.) Nakagami-m fading channels, with arbitrary m ≥ 5. The approximate probability density function (PDF) of the instantaneous dual-hop link power at high SNR region is derived. Then we present the asymptotic outage probability expression, and analyze the diversity order and coding gain. Simulations are performed to verify the tightness of the presented analysis at medium and high SNR regions.

Practical, Highly Efficient Algorithm for Generating κ-μ and η-μ Variates and a Near-100% Efficient Algorithm for Generating α-μ Variates

In this letter, we propose a simple and highly efficient random sequence generator for κ -μ and η -μ variates and a near-100% efficient algorithm for generating α -μ variates. The proposed algorithm may yield an efficiency higher than 80% for η -μ , 87.5% for κ -μ and almost 100% for α -μ . These generators are implemented via the rejection technique and allow for arbitrary fading parameters. The goodness-of-fit is objectively measured using the the p-value of the Kolmogorov-Smirnov test.

Symbol Error Rate of Decode-and-Forward Relaying in Two-Wave with Diffuse Power Fading Channels

We analyze the symbol error rate (SER) of selective decode-and-forward (DF) relaying for the practical case of independent but not necessarily identically distributed two-wave with diffuse power (TWDP) fading. We first derive new exact SER expressions with M-ary phase-shift keying and M-ary quadrature amplitude modulation. We then derive tight upper bounds on the exact SER in closed form to avoid the numerical integration involved in the exact results. Furthermore, we derive concise yet valuable expressions for the asymptotic SER, which characterizes the system behavior in the high signal-to-noise ratio (SNR) regime in terms of the diversity order and the coding gain. Based on the asymptotic SER, we confirm that TWDP fading parameters have no impact on the diversity order, but affect the coding gain. We also demonstrate that the contribution of the source-destination link to the SER is higher than that of the source-relay link or the relay-destination link. Our analytical results are valid for general operating scenarios with arbitrary average SNRs and distinct TWDP fading parameters in each hop.

Asymptotic Performance Analysis of Multihop Relaying with Co-Channel Interference in Nakagami-m Fading Channels

In this letter, the asymptotic performance of channel state information-assisted amplify-and-forward multihop relaying with co-channel interference (CCI) at both relays and destination over Nakagami-m fading channels is investigated. Assuming integer fading parameter m for source → relay → destination links and arbitrary fading parameter m for CCI links, we derive closed-form expressions for bit error rate of the system at high signal-to-interference-plus-noise regime and characterize the diversity order and coding gain achieved by the system. Simulation results are provided to validate the analysis.

Bivariate Weibull-gamma composite distribution with arbitrary fading parameters

Infinite series representations are derived for the bivariate (correlated) Weibull-gamma composite distribution with arbitrary fading parameters. The joint probability density function, the joint moments, and the joint cumulative distribution function are obtained. Based on these theoretical expressions, the outage probability of dual-branch selection diversity is evaluated. Furthermore, the joint characteristic function is also derived.

Sum of Nonidentical Squared $\kappa {-} \mu$ Variates and Applications in the Performance Analysis of Diversity Receivers

In this paper, a generalized Laguerre polynomial expansion for the probability density function and the cumulative distribution function of the sum of independent nonidentically distributed squared κ-μ random variables is proposed. Based on these statistical results, we investigate the performance of maximal-ratio-combining diversity techniques operating over κ-μ fading channels with arbitrary fading parameters. Our newly derived formulas are mathematically tractable and include as special cases several results available in the technical literature, namely, those of Rice and Nakagami-m fading channels. The proposed analysis is substantiated by numerically evaluated results compared with Monte Carlo simulations.

A New Generation Method for Spatial-Temporal Correlated MIMO Nakagami Fading Channel

A new generation method for spatial and temporal correlated multiple-input multiple-output (MIMO) Nakagami fading channel is proposed, which has low complexity and is applicable for arbitrary fading parameters and prespecified correlation coefficients of different subchannel. The new scheme can be divided into two steps: (1) generate independent Nakagami fading sequences for each subchannel based on a novel rejection method; (2) introduce the temporal and spatial correlation based on the relationships between Rayleigh, Gamma, and Nakagami random processes. The analysis and simulation results show that the proposed simulator has a good agreement with the theoretical model on fading envelope distribution, spatial-temporal correlation characteristic.

On the Multivariate $\alpha$– $\mu$ Distribution: New Exact Analytical Formulations

Correlation among channels is a physical phenomenon that affects the performance of a wireless communication system and that cannot be neglected in a myriad of realistic fading scenarios. Providing computable mathematical means to better characterize the corresponding statistics is certainly of interest to any design engineer. In this context, this paper further extends the statistical correlation investigations of the α-μ fading model, presenting a new, exact, and easily computable series-type formulation for the multivariate α-μ joint cumulative distribution function (JCDF). Along with this general result and capitalizing on practical assumptions, an alternative, simpler formulation for the α -μ multivariate joint density function and its corresponding distribution function are also provided. These formulations are still general and yet compact, assuming arbitrary fading parameters and correlations among the marginal variates. An important feature of the series-type distribution is that any truncation version of it is a valid distribution. As an application example, the truncated series-based outage probability of the selection combining scheme is computed and compared with that obtained by means of numerical methods and simulations. The results show that a small number of terms of the series are sufficient to provide excellent agreement between approximate and exact results.