A new closed-form of ASEP and channel capacity with MRC and selection combining over Inverse Gaussian shadowing

This paper analyse and investigate the performance of communication system with maximal ratio combining (MRC) and selection combining (SC) over Inverse Gaussian (IG) fading distribution. All formats of coherent and non-coherent modulation schemes are considered and novel analytical expressions of average symbol error probability (ASEP) with diversity are derived. Gamma and IG fading distributions are popularly used as a mathematically less complex solution to lognormal in the open literature. Hence, we provide a comparative analysis between IG and gamma fading with the aim to provide a quantitative measure of the difference between the two distributions in the context of ASEP. Moreover, the novel closed-form expressions of channel capacity under transmission schemes such as optimal rate adaptation (ORA) and channel inversion fixed rate (CIFR) are derived and analysed with MRC and SC diversity over IG fading. The analytical results have been validated with the Monte Carlo simulations and the exact numerical results.     

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

Multiplicative 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.     

New analytical expressions for the performance metrics of wireless communication system over Weibull/Lognormal composite fading

A realistic propagation scenario is more frequently characterized by a composite multipath/shadowed fading. In this work, a class of Weibull/Lognormal (W-LN) composite fading channel has been analysed and investigated. New analytical approximations to various important performance metrics of wireless communication systems such as the average symbol error probability (SEP), the outage probability, the amount of fading (AF), and the channel capacity are derived. Further, an asymptotic analysis of the composite fading channel is carried out and closed form expressions of the average SEP with and without maximal ratio combining (MRC) diversity along with the coding and diversity gain are presented. The solutions are presented in terms of Fox H-function and are valid for both the integer and non-integer values of the multipath and shadowing parameters. The results are validated via Monte-Carlo simulations and exact numerical results.     

Effect of Microdiversity and Macrodiversity on Average Bit Error Probability in Gamma‐Shadowed Rician Fading Channels

In this letter, we analyze the error performance of a mobile communication system with microdiversity and macrodiversity reception in gamma‐shadowed Rician fading channels for a binary differential phase‐shift keying modulation scheme. Analytical expressions for the probability density function (PDF) and moment‐generating function (MGF) are derived. The average bit error probability can be calculated by averaging the conditional bit error probability over the PDF or using the MGF‐based approach. Numerical results are graphically presented to show the effects of macrodiversity, correlation, number of diversity branches, and severity of both fading and shadowing.     

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).     

Unified performance analysis over Mckay–Meijer G shadowed fading channel

ABSTRACT

Composite fading models have been considered as the suitable fading models for scenarios such as indoor communication and free space optical. Most of the composite fading models are based on Nakagami-m fading distribution in which amount of fading parameter ranges from 0.5 (most severe fading) to infinity (no fading). However, using the McKay–Meijer G function, one of the recent article presents McKay shadowed fading distribution which shows that the fading severity may have values more than that of the most severe case of Nakagami-m fading. In this paper, using the conditional unified expression for conditional bit error rate (BER), a unified expression of the average bit error rate (ABER) over McKay–Meijer G shadowed fading model has been proposed. The proposed unified expression includes the ABER of almost all the modulation schemes. In addition, expression for ABER of binary phase shift keying modulation over McKay fading channel under generalised Gaussian distribution has been derived. Finally, analytical expressions of adaptive capacity under different adaptive schemes namely, COPRA, CORA, CCIFR and truncated CIFR have been presented. Through numerical analysis, different results have been compared with similar results available in the literature.     

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

Recently, 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.     

On the performance of underlay cognitive radio system with random mobility under imperfect channel state information

In this paper, the performance of an underlay cognitive radio system with random mobility and imperfect channel state information (CSI) is investigated. The mobile user (MU) utilises maximum ratio combining (MRC) and selection combining (SC) diversity techniques as signal reception to improve the quality of received signal‐to‐noise ratio (SNR). Under the Rayleigh fading, random waypoint mobility model is employed to characterised the effect of the MU random mobility on the system performance. Thus, novel probability density function (PDF) and cumulative distribution function (CDF) for the two considered diversity techniques are derived. Through these, the outage probability and average bit error rate (ABER) closed‐form analytical expressions are then obtained to quantify the system performance under the MRC and SC schemes. The results illustrate the effect of imperfect CSI, user mobility which is characterised by pathloss and the network topology on the system performance. Also, the results depict that MRC offers the system better performance compared with SC under the same system conditions. The accuracy of the derived analytical expressions is verified through Monte‐Carlo simulations.     

Composite Phase PDF in Gamma Shadowed Nakagami Fading Channel

This paper presents a new Fourier series form probability density function (PDF) for the phase of the received signal over gamma shadowed Nakagami-m fading channel with additive Gaussian noise. This PDF is further used to evaluate the average symbol-error probability of M-ary CPSK. An alternative new closed-form expression for bit error-rate of binary CPSK is also derived and numerically compared with the corresponding result based on the Fourier series form phase PDF. We show that the two expressions are indeed numerically equivalent.     

Performance analysis of lognormally shadowed generalized Gamma fading channels

A 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 & 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.     

Capacity analysis of M-SC receivers over TWDP fading channels

An expression for the probability distribution function (PDF) of the signal-to-noise ratio of a selection combining receiver in two-wave with diffuse power fading channel is derived. Using this PDF expression, the capacity for the different adaptive transmission techniques employing selection combining (SC) are obtained. The study presents the effects of the ratio of total dominant signal power to the scattered signal power on the system capacity. The change in the capacity of the system with the diversity order for a SC receiver in the fading channel is also presented.     

Performance analysis of a variable‐gain amplify‐and‐forward relayed mixed RF‐FSO system

In this work, an amplify‐and‐forward variable‐gain relayed mixed RF‐FSO system is studied. The considered dual‐hop system consists of a radio frequency (RF) link followed by a free space optical (FSO) channel. The RF link is affected by short‐term multipath fading and long‐term shadowing effects and is assumed to follow the generalized‐K fading distribution that approximates accurately several important distributions often used to model communication channels. The FSO channel experiences fading caused by atmospheric turbulence that is modeled by the gamma‐gamma distribution characterizing moderate and strong turbulence conditions. The FSO channel also suffers path loss and pointing error induced misalignment fading. The performance of the considered system is analyzed under the collective influence of distribution shaping parameters, pointing errors that result in misalignment fading, atmospheric turbulence, and path loss. The moment‐generating function of the Signal power to noise power ratio measured end‐to‐end for this system is derived. The cumulative distribution function for the Signal power to noise power ratio present between the source and destination receiver is also evaluated. Further, we investigate the error and outage performance and the average channel capacity for this system. The analytical expressions in closed form for the outage probability, symbol and bit error rate considering different modulation schemes and channel capacity are also derived. The mathematical expressions obtained are also demonstrated by numerical plots.     

Effects of pointing errors and channel fading on the performance of free‐space optically‐preamplified PPM systems

In this paper, we study the impact of pointing errors and channel fading on the performance of free‐space, optically preamplified, M ‐ary PPM systems. We consider two types of free‐space optical links: (i) inter‐satellite links and (ii) inter‐building links. For inter‐satellite links, only pointing error is considered. Starting with a Rayleigh model for the pointing error angle, we derive analytically the PDF for the pointing error parameter and for the signal‐to‐noise ratio (SNR) per bit. For inter‐building links, we derive the density function for the SNR per bit that includes the combined effects of pointing errors and channel fading, assuming Rayleigh‐distributed pointing errors. The channel fading models considered in this study for inter‐buildings links are the log‐normal and gamma–gamma models. We provide the error probability as a function of the average SNR per bit for both types of links. To cover systems with and without forward error correction, we compute the average SNR per bit required to achieve a bit error rate of 10^?4 and 10^?9. The corresponding power penalties are computed for different symbol sizes, scintillation indexes, and pointing jitters. Copyright © 2016 John Wiley & Sons, Ltd.     

Capacity limits of spectrum‐sharing systems over hyper‐fading channels

Cognitive radio (CR) with spectrum‐sharing feature is a promising technique to address the spectrum under‐utilization problem in dynamically changing environments. In this paper, the achievable capacity gain of spectrum‐sharing systems over dynamic fading environments is studied. To perform a general analysis, a theoretical fading model called hyper‐fading model that is suitable to the dynamic nature of CR channel is proposed. Closed‐form expressions of probability density function (PDF) and cumulative density function (CDF) of the signal‐to‐noise ratio (SNR) for secondary users (SUs) in spectrum‐sharing systems are derived. In addition, the capacity gains achievable with spectrum‐sharing systems in high and low power regions are obtained. The effects of different fading figures, average fading powers, interference temperatures, peak powers of secondary transmitters, and numbers of SUs on the achievable capacity are investigated. The analytical and simulation results show that the fading figure of the channel between SUs and primary base‐station (PBS), which describes the diversity of the channel, does not contribute significantly to the system performance gain. Copyright © 2011 John Wiley & Sons, Ltd.     

Performance analysis of multi-antenna relay networks with imperfect channel estimation

In this paper, we present the performance of multi-antenna selective combining decode-and-forward (SC-DF) relay networks over independent but non-identical Nakagami-m fading channels with imperfect channel estimation. The outage probability, moment generating function (MGF) and symbol error probability (SEP) will be derived in closed-form using the SNR statistical characteristics. To make the analysis trackable, we have derived the MGF and SEP for integer values of fading severity, m. Also, to make the relations more simple, we develop high signal to noise ratio (SNR) analysis for the performance metrics of our system. Subsequently, we propose optimal and adaptive power allocation algorithms along with the equal power allocation method. Finally, for comparison with analytical formulas, we perform some Monte-Carlo simulations.     

Performance analysis of cellular CDMA networks overfrequency-selective fading channel

An effect of multipath fading on the performance of a cellular code-division multiple-access (CDMA) system is analyzed in this paper. A wide-sense stationary uncorrelated scattering (WSSUS) channel model and the coherent binary phase-shift keying (BPSK) with asynchronous direct-sequence (DS) spreading signal are assumed in the analysis. The average error probability for both the forward link and reverse link of a cellular CDMA system over a frequency-selective fading channel using a conventional correlation-type receiver and RAKE receiver are derived. The impact of imperfect power control and channel capacity of a cellular CDMA system is also investigated. The closed forms of average error probability derived in the paper can save a lot of computation time to analyze the performance and channel capacity of a cellular CDMA system. The analytical results show that the performance and maximum transmission rate of cellular CDMA systems degrade with an increase in the number of simultaneous users and the number of interfering cells. The signal-to-interface ratio (SIR) for the reverse link derived in this paper can directly describe the interrelationships among a number of paths, number of users, number of interfering cells, fading factors, and maximum variation of a received unfaded signal     

Switched diversity receivers over generalized gamma fading channels

A versatile envelope distribution which generalizes several commonly used fading models is the generalized Gamma (GG) distribution. This letter deals with the performance analysis of switch and stay combining (SSC) receivers operating over not necessarily identical GG fading channels. For these receivers, novel analytical expressions for the moments of the output signal-to-noise ratio (SNR) (including average SNR and amount of fading), outage probability, average bit error probability (ABEP), and Shannon average spectral efficiency (ASE) are derived. Moreover, closed-form expressions are obtained for the optimal average SNR, ABEP, and ASE switching thresholds. Special cases of the derived expressions agree with known results.     

Double differential MPSK on the fast Rician fading channel

An analysis of adjacent and nonadjacent double differential M -ary PSK (M-ary D²PSK) on the fast Rician fading channel is presented. The probability density function (PDF) of the first-order phase error (FOPE) and the probability density functions of the second-order phase error (SOPE) for both adjacent and nonadjacent D²PSK on a fading channel have been derived. Asymptotic approximations for these PDFs are proposed in the case of channels with weak fading (including the additive white Gaussian noise (AWGN) channel) and high signal-to-noise ratio. For nonadjacent D²PSK with independent FOPEs a simplified PDF of SOPE has been obtained. The derived PDFs allow calculation of error performance of D²PSK, as well as of DPSK, on the Rician channel including the AWGN channel and the Rayleigh channel and verification of some results reported in the literature earlier. It is shown that nonadjacent D²PSK can be optimized by choosing a proper separation between the first-order phase differences     

The BER analysis of OFDMA and SC‐FDMA under pilot‐assisted channel estimation and pilot jamming in rayleigh slow‐fading channel

In this paper, the authors derived the analytical bit error rate expressions for orthogonal frequency division multiple access and single‐carrier frequency‐division multiple access (SC‐FDMA) in Rayleigh slow‐fading channel for binary phase‐shift keying/quadrature phase‐shift keying/16‐quadrature amplitude modulations under pilot jamming and pilot symbol‐assisted channel estimation. Beginning with the bit error rate analysis from the general case of pilot symbol‐assisted channel estimation technique in Rayleigh slow‐fading channel, the expressions are first modified for different modulations and then further customized to account for the Zero‐Forcing equalization in frequency or time direction with application respectively to orthogonal frequency division multiple access or SC‐FDMA without and with pilot jamming. Piecewise‐linear interpolation is used for its simplicity. The simulation results match perfectly with the theoretical predictions except for some discrepancies with SC‐FDMA, which imply that the generalized equations developed here have to be further modified to account for system‐specific features like discrete Fourier transform precoding for SC‐FDMA. Copyright © 2016 John Wiley & Sons, Ltd.