Physical layer security for dual‐hop FSO/RF system using generalized ΓΓ/η−μ fading channels

We investigate the physical layer security of decode‐and‐forward–relayed free space optics (FSO)/radio frequency (RF) communication system. In this network, the eavesdropper exists after relay node and overhears RF transmission. Further, FSO being a line‐of‐sight transmission is assumed to be secure from eavesdroppers. Here, we have the Gamma‐Gamma (ΓΓ) distribution for FSO link and generalized η?μ distribution for RF link. The security for information transmission to the legitimate user in the presence of an eavesdropper is measured in terms of secrecy capacity and secrecy outage probability. Deriving the probability density function and cumulative distribution function of end‐to‐end signal‐to‐noise ratio, the closed‐form expressions for security parameters are achieved. The numerical analysis of the proposed system is done under the influence of atmospheric turbulence effects and various fading conditions. The results have been verified through simulation.     

Outage probability bound of decode and forward two‐way full‐duplex relay employing spatial modulation over cascaded α − μ channels

The system performance of mobile‐to‐mobile (D2D) cooperative communication has been improved by utilizing spatial modulation (SM) in this paper. The proposed system employs decode and forward (DF) relaying technique along with physical layer network coding (PLNC); hence, it has been named as SM‐based decode and forward two‐way relay (DFTWR). It enables full‐duplex communication thereby enhancing the system efficiency. Information bits are exchanged between the two bidirectional nodes. For two bits of information exchange, the antenna index is conveyed by the least significant bit (LSB) of the data symbol while the most significant bit (MSB) carries the message. The system performance has been investigated by analyzing certain performance metrics like lower and upper bounds of outage probability and average data rate for N‐α‐μ cascaded fading channels. The change in the system performance by varying certain parameters like relative geometrical gain, fading coefficients, and number of cascaded components has also been put forth in this paper.     

On the analysis of achievable rate for NOMA networks with cooperative users over κ‐μ shadowed fading channels

Cooperative nonorthogonal multiple access (NOMA) system is an effective solution for the fifth generation (5G) wireless mobile communications systems. In this work, the achievable rate analysis of a NOMA communication network with decode‐and‐forward (DF) relaying under κ‐μ shadowed fading conditions is investigated. First, we develop an analytical framework for cumulative distribution function (CDF) of the considered system model. Then, the average achievable rate expressions for two different information bits namely s₁ and s₂ are derived based on the derived CDF for NOMA with DF relaying over κ‐μ shadowed fading channels. Furthermore, we also propose simplified average achievable rate expressions for the special cases of κ‐μ shadowed fading channels in order to facilitate the evaluation of the derived expressions. Some numerical examples on the achievable rate of the considered system are shown for different scenarios. Moreover, our derived analytical average achievable rate expressions are confirmed by the simulations results.     

Impact of co‐channel interference on performance of dual‐hop wireless ad hoc networks over α−μ fading channels

In this work, we investigate the performance of a dual‐hop cooperative network over α?μ fading channels with the presence of co‐channel interference (CCI) at both the relay and destination nodes. Amplify‐and‐forward (AF) relaying is considered in the relay node. The upper bound of the signal‐to‐interference‐plus‐noise ratio (SINR) of the dual‐hop relay link is used to determine the system performance. The probability density function (PDF) and the cumulative distribution function (CDF) of the upper bound of the SINR are analyzed. The system performance is determined in terms of the outage and error probabilities. Numerical results are used to present the performance analysis of the system.     

Simplified approximations to the average of some useful forms of Gaussian Q functions with MRC diversity reception over Nakagami-q and Rician fading channels and their applications

In this paper, using an accurate exponential based approximation on the Gaussian Q function, the simplified novel approximations to the average of some useful forms of Gaussian Q functions, with maximal-ratio combining (MRC) diversity reception, over independent but not necessarily identical Nakagami-q (Hoyt) and Rician fading channels are proposed. The results proved to be useful in accurate estimation of the symbol error probability (SEP) for various digital modulation schemes like cross-QAM, triangular-QAM (TQAM), rectangular-QAM and square-QAM (SQAM), over the same fading statistics. Asymptotic expressions of the proposed approximations are also derived in this paper. Various simulation results are provided to verify the accuracy and significance of the proposed work.     

Closed‐form expressions for the average channel capacity of the α– μ fading model under different adaptive transmission protocols

In this paper,we consider a small‐scale multipath fading channel following the α– μ generalized fading model distribution.We first derive an expression for the amount of fading () for this channel model to show the generalization attribute of this fading model recently reported in the literature. Then, we derive closed‐form expressions for the average channel capacity considering this channel distribution under different adaptive transmission protocols, namely the simultaneous power and rate adaptation protocol, the optimal rate adaptation with fixed power protocol, and the channel inversion with fixed‐rate protocol. All the obtained expressions are in closed‐form and general expressions that can reduce to other channel capacity expressions that are well‐known and to some others that are not known for Rayleigh, Nakagami‐m, and Weibull, as special cases. The derived expressions in this paper are new and have not been previously reported in the literature. Copyright © 2012 John Wiley & Sons, Ltd.     

Unified analysis of EGC diversity over Weibull fading channels

In this paper, the performance analysis based on PDF approach of an L ‐branch equal gain combiner (EGC) over independent and not necessarily identical Weibull fading channels is presented. Several closed‐form approximate expressions are derived in terms of only one Fox H‐function as PDF, cumulative distribution function, and moments of the EGC output Signal‐to‐noise ratio (SNR), outage probability, amount of fading, channel capacity, and the average symbol error rate for various digital modulation schemes. All results are illustrated and verified by simulations using computer algebra systems.     

A comparative study on the performance of MIMO‐STBC subject to Weibull fading channels

In this paper, we investigate the analytical performance of the multiple‐input multiple‐output system (MIMO) with orthogonal space‐time block codes (STBCs) subject to Weibull fading channels (WFC). Space‐time block code technique provides an efficient pattern for wireless transmission over various fading channels using multiple transmit antennas. Two approximating methods of the sum of independent Weibull random variables are studied. For each approach, we derive accurate approximate expressions for several performance metrics of MIMO‐STBC system operating under independent and nonidentical WFC. The proposed approximations are expressed in terms of 2 generalized hypergeometric functions, namely, Fox's H and Meijer's G functions. All the derived approximate expressions prove high accuracy, while compared with the simulation results established via Monte Carlo method and Kolmogorov‐Smirnov test as well. Although the 2 approaches have approximately the same accuracy, the second method approximate expressions are much less complex than those of the first method.     

Error Performance of Digital Modulation Schemes with MRC Diversity Reception over η-μ Fading Channels

This paper provides exact-form expressions for the average symbol error probability (ASEP) of various digital modulation schemes with maximal ratio combining (MRC) diversity over L independent, not necessarily identically distributed (n.i.d.) eta-mu fading channels. The derived expressions are given in terms of the Lauricella and Appell hypergeometric functions and include several others available in the literature such as those for Nakagami-m and Hoyt. General asymptotic ASEP expressions are also derived for all the considered modulation schemes which provide useful insights regarding the factors affecting the performance of the considered system.     

BER performance of MQAM with L‐branch MRC diversity reception over correlated Nakagami‐m fading channels

Exact and closed form generalized expressions for bit error rate (BER) of M‐ary quadrature amplitude modulation (MQAM) with L‐branch maximal ratio combining (MRC) space diversity reception in fading channels are derived and analyzed. The fading channels are modeled as identical but correlated frequency‐nonselective slow Nakagami‐m fading channels corrupted by additive white Gaussian noise (AWGN). Analytical results obtained are in terms of few finite range integrals with an integrand composed of elementary functions. Because of their simple form, these analytical results readily allow numerical evaluation in cases of practical interest. The results are also general enough to include Nakagami‐m fading channels with and without correlation, no diversity system, Rayleigh fading channels with and without correlation, and AWGN as special cases. The numerical results for the case of 16QAM are shown graphically and also in tabular form in order to examine the effects of fading severity, order of diversity, and branch correlation on the BER performance. The two correlation models considered are constant correlation model and exponential correlation model. One may be interested to know how the BER of MQAM is related to symbol error rate (SER) of MQAM. Therefore, the BER results obtained in this paper are also compared with that obtained directly from the SER. It is expected that the analytical results presented in this paper will provide a convenient tool for design and analysis of a radio communication system with space diversity reception in uncorrelated and correlated fading environment. Copyright © 2002 John Wiley & Sons, Ltd.     

Bit error probability of the M‐QAM scheme under η‐μ fading and impulsive noise in a communication system using spatial diversity

This paper presents a new and exact expression for the bit error probability (BEP) of the square M‐ary quadrature amplitude modulation (M‐QAM) scheme, with the channel under double gated additive white Gaussian noise (G²AWGN) and η‐μ fading in a communication system using the spatial diversity technique. The expression for the BEP is written in terms of the Appell function. The BEP curves are presented under different values of the number of branches of the maximum ratio combining (MRC) receiver, order of the constellation M, and parameters that characterize mathematically the channel, corroborated by simulations performed with Monte Carlo method.     

Variable‐rate adaptive modulation with optimum switching thresholds for cooperative systems with relay selection

In this paper, the performance of variable‐rate adaptive modulation schemes in the amplify‐and‐forward cooperative systems with relay selection is analyzed over Rayleigh fading channels. We consider constant power and discrete‐rate adaptive multi‐level modulation techniques. The switching levels required for discrete‐rate adaptive modulation have been determined for two schemes, namely fixed switching levels and optimum switching levels, both respecting a target bit error rate requirements, where in the later scheme, the switching levels are optimally determined in a way that the average spectral efficiency of the system is maximized. Two M‐ary modulation schemes, namely quadrature amplitude modulation and phase shift keying, are considered. Closed‐form expressions are derived for three performance metrics, namely average spectral efficiency, outage probability, and average bit error rate, for two cases: independent and identically distributed fading relay links and independent and non‐identically distributed links. It is shown that, compared with using fixed switching levels, employing optimum switching levels provides a slight improvement in the spectral efficiency and moderate improvements in the signal‐to‐noise ratio gain and in the outage probability of the system. It is also shown that compared with the independent and identically distributed links, independent and non‐identically distributed relay links yield a slight increase in the signal‐to‐noise ratio gain and a slight decrease in the diversity order of the system. Copyright © 2011 John Wiley & Sons, Ltd.     

Outage Probability Analysis of Selection and Switch-and-Stay Combining Diversity Receivers Over the α−μ Fading Channel with Co-Channel Interference

In this paper, we evaluate the performance of two dual-branch diversity techniques operating over the α?μ fading channel in presence of a dominant co-channel interferer with a minimum desired signal power constraint. These two diversity schemes are selection combining and switch-and-stay combining. We derive expressions for the outage probability in both cases, which are very simple to calculate numerically using the commercially available mathematical packages. The obtained expressions are valid for integer values of the parameter μ and, in many special cases, they reduce to either a closed form or to expressions with finite-limit integrals that can also be easily evaluated. Also, our expressions reduce to previously published well-known results for the Rayleigh as well as the Weibull fading channels as special cases. We present a set of numerical results which show the effect of fading severity of both the desired signal and the interferer on the performance.     

Performance analysis of AF OFDM system using multiple relay in presence of nonlinear‐PA over inid Nakagami‐m fading

In this paper, performance of an orthogonal frequency division multiplexing–based variable‐gain amplify and forward cooperative system using multiple relay with relay selection is analyzed over independent but not necessarily identically distributed frequency selective Nakagami‐m fading channels. For the analysis, nonlinear power amplifier is considered at the relay, and selection combining is adopted at destination node. Closed‐form expressions of the outage probability for various threshold signal‐to‐noise ratio (SNR) values and average symbol error rate for M‐ary quadrature amplitude modulation techniques are derived for the considered system. Further, the outage probability analysis is performed in high SNR regime to obtain the diversity order. Furthermore, impact of different fading parameters, multiple relay, and nonlinear power amplifier is highlighted on the outage probability and asymptotic outage probability for various threshold SNRs and on the average symbol error rate for various quadrature amplitude modulation constellations. The derived analytical expressions are generalized for various fading environments while considering the integer‐valued fading parameters. Finally, all the analytical results are verified through the Monte Carlo simulations for various SNR levels and system configurations.     

Differential modulation for asynchronous two‐way relay systems over frequency‐selective fading channels

We propose two schemes for asynchronous multi‐relay two‐way relay (MR‐TWR) systems in which neither the users nor the relays know the channel state information. In an MR‐TWR system, two users exchange their messages with the help of N_R relays. Most of the existing works on MR‐TWR systems based on differential modulation assume perfect symbol‐level synchronization between all communicating nodes. However, this assumption is not valid in many practical systems, which makes the design of differentially modulated schemes more challenging. Therefore, we design differential modulation schemes that can tolerate timing misalignment under frequency‐selective fading. We investigate the performance of the proposed schemes in terms of either probability of bit error or pairwise error probability. Through numerical examples, we show that the proposed schemes outperform existing competing solutions in the literature, especially for high signal‐to‐noise ratio values. Copyright © 2016 John Wiley & Sons, Ltd.     

SEP calculations for coherent M‐ary FSK in different fading channels with MRC diversity

In this paper, the authors derive symbol error probability (SEP) expressions for coherent M‐ary frequency shift keying (MFSK) modulation schemes in multipath fading channels. The multipath or small‐scale fading process is assumed to be slow and frequency non‐selective. In addition, the channel is also subjected to the usual degradation caused by the additive white Gaussian noise (AWGN). Different small‐scale fading statistics such as Rayleigh, Rician (Nakagami‐n), Hoyt (Nakagami‐q), and Nakagami‐m have been considered to portray diverse wireless environments. Further, to mitigate fading effects through space diversity, the receiver front‐end is assumed to be equipped with multiple antennas. Independent and identically distributed (IID) as well as uncorrelated signal replicas received through all these antennas are combined with a linear combiner before successive demodulation. As the detection is coherent in nature and thus involves phase estimation, optimum phase‐coherent combining algorithms, such as predetection maximal ratio combining (MRC), may be used without any added complexity to the receiver. In the current text, utilizing the alternate expressions for integer powers (1≤n≤4) of Gaussian Q function, SEP values of coherent MFSK are obtained through moment generating function (MGF) approach for all the fading models (with or without MRC diversity) described above. The derived end expressions are composed of finite range integrals, which can be numerically computed with ease, dispenses with the need of individual expressions for different M, and gives exact values up to M=5. When the constellation size becomes bigger (M≥6), the same SEP expressions provide a quite realistic approximation, much tighter than the bounds found in previous literatures. Error probabilities are graphically displayed for each fading model with different values of constellation size M, diversity order L, and for corresponding fading parameters (K, q, or m). To validate the proposed approximation method extensive Monte‐Carlo simulations were also performed, which show a close match with the analytical results deduced in the paper. Both these theoretical and simulation results offer valuable insight to assess the efficacy of relatively less studied coherent MFSK in the context of the optimum modulation choice in wireless communication. Copyright © 2010 John Wiley & Sons, Ltd.     

SEP Performance of Cross QAM Signaling with MRC over Fading Channels and its Arbitrarily Tight Approximation

The exact average symbol error probability (SEP) of the cross quadrature amplitude modulation signal in a single-input multiple-output system over independent but not necessarily identical fading channels is derived. The maximal-ratio combining (MRC) is considered as the diversity technique, and the average SEP is obtained by using the moment generating function (MGF) method. The obtained closed-form SEP expression is presented in terms of a finite sum of single integrals with finite limits and an integrand composed of a finite product of elementary functions. In addition, the arbitrarily tight approximations with the form of a sum of constant coefficient exponential functions for Gaussian Q-function and the generalization of its Craig’s form are proposed by applying the composite rectangle and Simpson numerical integration rules, respectively. The proposed approximations are simple and accurate enough even with only a few terms of exponential functions, and they are particularly suitable for applications of averaging Q-function and the generalized Q-function over the fading distributions. As a result, the closed-form approximations of the SEP over the AWGN channel and fading multichannels are expressed as a finite sum of exponential functions and a finite sum of MGFs, respectively, such that it is convenient and rapid to evaluate the SEP performances. Both the simulation results and the approximations show excellent agreement with the exact analytical expressions.     

Cross‐layer design for MIMO systems over spatially correlated and keyhole Nakagami‐m fading channels

Cross‐layer design is a generic designation for a set of efficient adaptive transmission schemes, across multiple layers of the protocol stack, that are aimed at enhancing the spectral efficiency and increasing the transmission reliability of wireless communication systems. In this paper, one such cross‐layer design scheme that combines physical layer adaptive modulation and coding (AMC) with link layer truncated automatic repeat request (T‐ARQ) is proposed for multiple‐input multiple‐output (MIMO) systems employing orthogonal space‐‐time block coding (OSTBC). The performance of the proposed cross‐layer design is evaluated in terms of achievable average spectral efficiency (ASE), average packet loss rate (PLR) and outage probability, for which analytical expressions are derived, considering transmission over two types of MIMO fading channels, namely, spatially correlated Nakagami‐m fading channels and keyhole Nakagami‐m fading channels. Furthermore, the effects of the maximum number of ARQ retransmissions, numbers of transmit and receive antennas, Nakagami fading parameter and spatial correlation parameters, are studied and discussed based on numerical results and comparisons. Copyright © 2009 John Wiley & Sons, Ltd.     

On the Error Performance of <Emphasis Type="Italic">M</Emphasis>-ary Modulation Schemes on Rician–Nakagami Fading Channels

This paper presents exact expressions for the average error performance of various M-ary modulation schemes over Rician–Nakagami fading channels. The expressions for average symbol error probability (SEP) are given in terms of Lauricella’s multivariate hypergeometric function, which can be evaluated numerically using its integral or converging series representation. Furthermore, we show that the derived expressions include some previously published results for Rayleigh fading as special cases.     

Performance of dual-hop wireless communication systems over the α–μ fading channels

In this paper, we consider a dual-hop wireless communication system with non-regenerative relay node and we study its performance over the α–μ fading channels. Specifically, we derive a closed-form expression for the moment generating function (MGF) of the harmonic mean of end-to-end signal-to-noise ratio (SNR) assuming the α–μ fading models. We also derive closed-form expressions for the end-to-end outage probability and average bit error rate of coherent modulation techniques. The obtained expressions can be reduced to study the performance of dual-hop communication systems over other fading channel models by using the proper values for the α and μ parameters. Numerical results are provided and conclusion remarks are drawn.