Generalized Gamma Fading Channels Research Articles

On Pre-Processing of Generalized Gamma Fading Channel Samples for Secret Key Generation

On Pre-Processing of Generalized Gamma Fading Channel Samples for Secret Key Generation

Ergodic capacity and error performance of spatial diversity UWOC systems over generalized gamma turbulence channels

In this paper, we study the ergodic capacity (EC) and average bit error rate (BER) of spatial diversity underwater wireless optical communications (UWOC) over the generalized gamma (GG) fading channels using quadrature amplitude modulation (QAM) direct current-biased optical orthogonal frequency division multiplexing (DCO-OFDM). We derive closed-form expressions of the EC and BER for the spatial diversity UWOC with the equal gain combining (EGC) at receivers based on the approximation of the sum of independent identical distributed (i.i.d) GG random variables (RVs). Numerical results of EC and BER for QAM DCO-OFDM spatial diversity systems over GG fading channels are presented. The numerical results are shown to be closely matched by the Monte Carlo simulations, verifying the analysis. The study clearly shows the adverse effect of turbulence on the EC & BER and advantage of EGC to overcome the turbulence effect.

A Closed-Form Approximation to the Distribution for the Sum of Independent Non-identically Generalized Gamma Variates and Applications

Evaluating the sum of independent and not necessarily identically distributed (i.n.i.d) random variables (RVs) is essential to study different variables linked to various scientific fields, particularly, in wireless communication channels. However, it is difficult to evaluate the distribution of this sum when the number of RVs increases. Consequently, the complex contour integral will be difficult to determine. Considering this issue, a more accurate approximation of the distribution function is required. By assuming the probability density function (PDF) of a generalized gamma (GG) RV evaluated in terms of a proper subset H1,0 1,1 class of Fox’s H-function (FHF) and the moment-based approximation to estimate the FHF parameters, a closed-form tight approximate expression for the distribution of the sum of i.n.i.d GG RVs and a sufficient condition for the convergence are investigated. The proposed approximate may be an analytical useful tool for analyzing the performance of certain numbers branch maximal-ratio combining receivers subject to GG fading channels. Hence, various closed-form performance metrics are derived and examined in terms of FHF. Numerical simulations are carried out to illustrate the theoretical results.

Average Contiguous Duration (ACD)-Based Quantization for Secret Key Generation in Generalized Gamma Fading Channels

The wireless channel-based Secret Key Generation (SKG) algorithms aim at securing the wireless link against unauthorized eavesdropping by exploiting the channel’s randomness for generating matching secret keys at the legitimate nodes for message encryption/decryption. To counter differences in hardware and noise conditions at the legitimate nodes, which can lead to key mismatch, the SKG algorithms typically include the intermediate steps of sampling, quantization, information reconciliation, and privacy amplification. These steps collectively aim to improve the performance trade-offs between Key Generation Rate (KGR), Key Agreement Probability (KAP), and Secret Key Randomness (SKR) properties. This paper derives a closed-form expression for the Average Contiguous Duration (ACD) of Generalized Gamma (GG) fading wireless channels. The ACD is a recently introduced novel quantifier for characterizing the second-order statistics of fading channels, which includes Average Fade Duration (AFD) as its special case. The proposed GG fading ACD expression is shown to include, as its special cases, the ACD for commonly observed fading distributions such as Gamma, Nakagami- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> , and Rayleigh. By exploiting the derived GG ACD expression, a multi-level quantization scheme for SKG is proposed that determines suitable quantization intervals for identical likelihood of an equal number of consecutive channel samples falling in each quantization interval. A comprehensive comparative analysis of the proposed ACD-based quantization for SKG is conducted in relation to conventional Uniform Quantization (UQ) and Cumulative Distribution Function (CDF)-based Non-Uniform Quantization (NUQ) schemes. The presented numerical results confirm the superior performance trade-off between KGR and KAP offered by the proposed ACD-based quantization in relation to that offered by UQ and CDF-based NUQ.

Average bit error rate performance of free-space optical systems over double generalized gamma fading channels based on avalanche photodiode detector

The performance of free-space optical (FSO) communication systems based on avalanche photodiodes (APDs) is investigated over the aggregated double generalized gamma (double GG) fading channels. The approximate average bit error rate (ABER) expression is theoretically derived in terms of the double GG distributions under moderate and strong turbulent atmospheric conditions considering thermal noise and shot noise. The union bound and Hermite polynomials are then used to estimate the ABER performance of M-ary pulse-position modulation (PPM)-based systems and orthogonal frequency division multiplexing scheme (OFDM)-based systems. The ABER performance is studied with different receiver noise temperatures, modulation orders, turbulence strengths, and average photon counts assuming plane wave and spherical wave propagations. The results show that adopting an optimal average APD gain affected by the receiver temperature minimizes the ABER value for both wave propagations. In addition, the present APD-based system offers better ABER performance than that of a PIN-based FSO system over the double GG fading channels at two receiver noise temperatures of 200 and 400 K for both the PPM and OFDM schemes. We provide a reference for FSO system design.

LDPC-Coded CAP with Spatial Diversity for UVLC Systems over Generalized-Gamma Fading Channel.

In this paper, low-density parity-check (LDPC)-coded carrierless amplitude and phase (CAP) modulation with spatial diversity is proposed to mitigate turbulence-induced fading in an underwater visible-light communication (UVLC) channel. Generalized-gamma (GG) distribution was used to model the fading, as this model is valid for weak- and strong-turbulence regimes. On the basis of the characteristic function (CHF) of GG random variables, we derived an approximated bit-error rate (BER) for the CAP modulation scheme with spatial diversity and equal-gain combining (EGC). Furthermore, we simulated the performance of the CAP system with diversity and LDPC for various turbulence conditions and validated the analysis. Obtained results showed that the combination of LDPC and spatial diversity is effective in mitigating turbulence-induced fading, especially when turbulence strength is strong.

Impact of temperature gradients on average bit error rate performance of low-density parity-check-coded multihop underwater wireless optical communication systems over the generalized gamma distribution

The impact of temperature gradients on the average bit error rate (ABER) performance of low-density parity-check (LDPC)-coded underwater wireless optical communication (UWOC) systems is investigated over the generalized gamma fading channels. The effects of absorption and scattering are also taken into account in our computation on the basis of the Monte Carlo (MC) ray-tracing method. The decoded-and-forward multihop communication is applied to extend the viable communication range of UWOC systems. In particular, using the generalized Gauss–Laguerre quadrature rule, the ABER analytical expressions of the multihop UWOC system with binary phase shift keying and multiple phase shift keying modulation schemes are mathematically derived under weak temperature-induced oceanic turbulence condition, respectively, which are also confirmed by MC simulation. In addition, LDPC codes are adopted to improve the UWOC system performance. The results reveal that the ABER performance of this multihop UWOC system degrades with increasing temperature gradients, hop numbers, and modulation orders, while it can be significantly enhanced by LDPC codes and the coding gains increase with the increase of temperature gradients and hop numbers. Our work will benefit the design and development of UWOC system.

Average secrecy rate and probability of non-zero secrecy capacity of wiretap generalised gamma fading channels

Average secrecy rate and probability of non-zero secrecy capacity of wiretap generalised gamma fading channels

Average secrecy rate and probability of non-zero secrecy capacity of wiretap generalised gamma fading channels

In this paper, secrecy performance is studied for the classic Wyner's wiretap channel which follows Generalised Gamma (GG) distribution. In order to evaluate the secrecy performance, we derived the exact Average Secrecy Rate (ASR) and closed form expression for the Probability of Non-Zero Secrecy Capacity (PNZSC) for different fading parameters corresponding to main and eavesdropper's channels. The results are then simulated and verified. It has been observed that the ASR of GG fading increases with the increase in the fading constant of the main channel.

Performance Analysis of a Secondary User in Cognitive Radio over Generalized-Gamma Fading Channels

DOI : 10.26650/electrica.2019.19017 In this paper, the performance of a secondary user (SU) in an underlay cognitive radio (CR) network over a generalized-gamma (GG) fading channel in terms of three performance metrics, namely, outage probability, ergodic capacity, and bit error rate (BER), is investigated. According to the underlay approach, the transmit power of the SU should be limited to avoid interference to primary users (PUs). The performance metrics of the SU in the underlay CR network are theoretically derived and also obtained with Monte Carlo simulations for a GG fading channel with different fading parameters. To demonstrate the effect of limited power on the performance metrics, three different maximum transmit power levels (Pmax), namely, 10, 20, and 30 dB, are used. The simulation results lead to three conclusions: First, when high values are chosen for the fading parameters (α, c), the fading channel gets less distorted and the performance metrics improve. The second conclusion is that the BER performance gets better as the limited power increases. The final conclusion is that the BER performance of SUs improves as the interference power that PUs can tolerate increases. Cite this article as : Aldirmaz Colak S. Performance Analysis of a Secondary User in Cognitive Radio over Generalized-Gamma Fading Channels. Electrica, 2019; 19(2): 166-172.

Performance analysis of wireless communication system over nonidentical cascaded generalised gamma fading channels

SummaryMultiplicative fading statistics usually encountered in different radio propagation environments. In this context, we evaluate and analyse the performance of a wireless communication system over the nonidentical cascaded generalised Gamma Fading Channels, also known as generalised Bessel‐K fading channel. To this end, the closed‐form expressions for the amount of fading (AOF), the outage probability (OP), the average symbol error probability (SEP), and the channel capacity are derived. In addition approximate expressions for the average SEP with maximal ratio combining (MRC) diversity are also provided. The low‐ and high‐power solutions for the channel capacity are also provided. Furthermore, simplified asymptotic average SEP expressions for MRC and selection combining (SC) are presented to gain the system performance with diversity. The proposed methodologies provide more flexibility to accommodate different radio propagation scenarios. To examine the accuracy of the proposed solutions, numerical and simulation results are compared and shown to fit for variety of fading parameters.

Outage and Diversity Analysis of Underlay Cognitive Mixed RF-FSO Cooperative Systems

We investigate the performance of asymmetric radio frequency (RF) and free-space optical (FSO) dual-hop cognitive amplify-and-forward relay networks where RF links are subject to independent and nonidentically distributed Nakagami-m fading. We consider that the RF link transmitter and receiver are secondary users of an underlay cognitive network. Specifically, the transmit power conditions of the proposed spectrum-sharing network are governed by either the combined power constraint of the interference on the primary network and the maximum transmission power at the secondary network, or the single power constraint of the interference on the primary network. Also, we consider a double generalized gamma fading channel with pointing error and both heterodyne and intensity modulation/direct detection methods in the FSO link. The closed-form and asymptotic expressions of outage probability for this system are calculated for fixed gain and channel-state-informationassisted relaying techniques. It is demonstrated that the diversity order is a function of the fading severity of the RF link, turbulence parameters of the FSO link, and pointing error, regardless of the interference channel parameter of the primary user. However, the coding gain is impressed by the interference link parameter and RF-FSO links parameters. The diversity-multiplexing trade-off analysis is done for this network, where we show that this trade-off is independent of the primary network.

On the Maximum and Minimum of Double Generalized Gamma Variates With Applications to the Performance of Free-Space Optical Communication Systems

In this paper, we derive the exact statistical characteristics of the maximum and the minimum of two modified double generalized gamma variates in closed form in terms of Meijer's G-function, Fox's H-function, the extended generalized bivariate Meijer's G-function, and H-function, in addition to simple closed-form asymptotic results in terms of elementary functions. Then, we rely on these new results to present the performance analysis of 1) a dual-branch free-space optical selection combining (FSO SC) diversity and 2) a dual-hop (DH) FSO relay transmission system over double generalized gamma fading channels with the impact of pointing errors. In addition, we provide asymptotic results of the bit error rate (BER) of the two systems at a high signal-to-noise ratio (SNR) regime. Computer-based Monte Carlo simulations verify our new analytical results.

On Physical Layer Security Over Generalized Gamma Fading Channels

In this letter, we study the secrecy performance of the classic Wyner's wiretap model over the generalized Gamma fading channels. The closed-form expressions for the probability of strictly positive secrecy capacity and the lower bound of secure outage probability are derived. Monte-Carlo simulations are performed to verify the derived analysis.

Best Neighbor Communication in a Poisson Field of Nodes

The communication channel power gain to the nearest neighbor of a node in a wireless communication network is not necessarily the largest among all neighbors due to fading. The probability that the $k$ th nearest neighbor of a node has the best communication channel with the highest power gain in a 2-D network with homogeneous Poisson distribution of nodes is derived for a general fading environment. The result is specialized to the case where the communication links are modeled as generalized-gamma fading channels. The analytical results are verified and illustrated by computer simulations and numerical results. Some applications of the new theory are also presented. A novel criterion that represents the fading severity, i.e., the generalized amount of fading (GAF) , is defined, and its value as an important measure for fading channels is justified.

Outage Probability Analysis of Dual-Hop Decode-and-Forward Relaying Over Mixed Rayleigh and Generalized Gamma Fading Channels

In this letter, outage probability of dual-hop decode-and-forward (DF) relaying scheme is analyzed over mixed Rayleigh and generalized Gamma fading channels. Cooperation model considered in this work consists of a source, a relay and a destination. It is assumed that source-relay and relay-destination channels experience Rayleigh fading and generalized Gamma fading, respectively. Exact outage probability expression is derived and outage performance is illustrated for both direct transmission and DF relaying scheme.

Performance analysis of lognormally shadowed generalized Gamma fading channels

AbstractA new composite channel model is proposed for the performance analysis of shadowed fading channels. This model is represented as a mixture of generalized Gamma (GG) multipath fading and lognormal shadowing. GG distribution includes the Rayleigh, Nakagami, and Weibull as special cases; hence the presented model, which is referred to as GG‐L, is a generic model that covers many well‐known composite fading models, including the Rayleigh–lognormal (R‐L), Nakagami–lognormal (N‐L), and Weibull–lognormal (W‐L). The main drawback of the lognormal‐based composite models is that the composite probability density function (PDF) is not in closed form, thereby making the performance evaluation of communication links in these channels cumbersome. To bypass this problem, an approximation method is developed which makes it possible to derive a closed‐form, analytical expression for GG‐L composite distribution. The proposed method only needs the mean and the variance of the underlying lognormal distribution, and hence, bypasses the required complicated integration needed to calculate the PDF of the received signal envelope in GG‐L channel. Based on this method, the most statistical characteristics, such as cumulative density function (CDF) and moments of the GG‐L composite distribution, are derived and used for the performance analysis of a single receiver operating over GG‐L fading channel. Copyright © 2010 John Wiley &amp; Sons, Ltd.

Performance evaluation of selection diversity receivers over arbitrarily correlated generalised Gamma fading channels

The performance of multibranch selection diversity (SD) receivers over L arbitrarily correlated generalised Gamma (GG) fading channels is analysed and evaluated. Following a statistical approach previously proposed for the multivariate Nakagami-m distribution, a closed-form upper bound for the joint GG probability density function (PDF) and an infinite series upper bound for the joint GG cumulative distribution function (CDF) are obtained. For the special case of the trivariate GG distribution (L=3), exact expressions in the form of infinite series for the PDF and CDF are presented. The derived bounds are used to obtain tight upper bounds for the distribution of the SD output signal-to-noise ratio (SNR). Furthermore, based on the derived analysis, novel analytical expressions that accurately approximate the distribution of the SD output SNR are presented. The bounds and approximations are used to study important performance criteria of SD receivers such as outage and average symbol error probability. The accuracy of the derived expressions has been verified, on the one hand, analytically for triple-branch (L=3) and, on the other hand, by means of computer simulations for multibranch (L&gt;3) SD receivers.

BER Performance of OFDM-BPSK and -QPSK Over Generalized Gamma Fading Channel

In this paper, the BER performance of OFDM-BPSK and -QPSK system over generalized gamma fading channel has been reported. This model is versatile enough to represent short-term fading such as Weibull, Nakagami-m, or Rayleigh as well as shadowing. The flexibility of this model is because of two fading parameters compared to only one in Nakagami-m fading model, which helps to analyze the severity of fading more deeply. Here, simulations of OFDM signals are carried with generalized gamma faded signal to understand the effect of channel fading.

Symbol Error Rate Performance of QS-CDMA over Frequency Selective Time Non-Selective Multipath Generalized Gamma Fading Channels

Quasisynchronous (QS) Code Division Multiple Access (CDMA) is currently being considered for a variety of wireless applications and services because QS-CDMA enables information transmission with a good quality of service. In this paper, for M-ary signaling, the Symbol Error Rate (SER) performance of QS-CDMA communication system with a maximal ratio combiner (MRC) over frequency-selective, time-nonselective multipath Generalized Gamma (GG3) fading channels is derived not only for any deterministic spreading sequences but also for any chip-limited chip waveforms, and it is investigated for Rectangular, Half-Sine, and Raised-Cosine chip waveforms by means of numerical and simulation results. Numerical and simulation results show that the performance of QS-CDMA is as good as or slightly better than synchronous CDMA (S-CDMA) when the maximum quasisynchronous delays do not need to be less than some specific values depending on the path power scattering. With this flexibility of quasisynchronous delays, both the transmitter and receiver complexities are reduced as quasisynchronous communication is a challenging task for researchers. Additionally, since not only the spreading sequences but also the partial autocorrelation functions of the chip waveform are influential on the performance of multipath QS-CDMA, a measure, Partial Power Ratio (PPR) is defined based on these partial autocorrelation functions in order to select or design a chip waveform for quasisynchronous communication. Furthermore, results show that QS-CDMA using the chip waveform whose PPR is greater has better performance.