Equal-gain and maximal-ratio combining over nonidentical Weibull fading channels

We study the performance of L-branch equal-gain combining (EGC) and maximal-ratio combining (MRC) receivers operating over nonidentical Weibull-fading channels. Closed-form expressions are derived for the moments of the signal-to-noise ratio (SNR) at the output of the combiner and significant performance criteria, for both independent and correlative fading, such as average output SNR, amount of fading and spectral efficiency at the low power regime, are studied. We also evaluate the outage and the average symbol error probability (ASEP) for several coherent and noncoherent modulation schemes, using a closed-form expression for the moment-generating function (mgf) of the output SNR for MRC receivers and the Pade/spl acute/ approximation to the mgf for EGC receivers. The ASEP of dual-branch EGC and MRC receivers is also obtained in correlative fading. The proposed mathematical analysis is complimented by various numerical results, which point out the effects of fading severity and correlation on the overall system performance. Computer simulations are also performed to verify the validity and the accuracy of the proposed theoretical approach.     

Performance analysis of dual selection diversity in correlated Weibull fading channels

Ascertaining the importance of the dual selection combining (SC) receivers and the suitability of the Weibull model to describe mobile fading channels, we study the performance of a dual SC receiver over correlated Weibull fading channels with arbitrary parameters. Exact closed-form expressions are derived for the probability density function, the cumulative distribution function, and the moments of the output signal-to-noise ratio (SNR). Important performance criteria, such as average output SNR, amount of fading, outage probability, and average bit-error probability for several modulation schemes are studied. Furthermore, for these performance criteria, novel closed-form analytical expressions are derived. The proposed analysis is complemented by various performance evaluation results, including the effects of the input SNR's unbalancing, fading severity, and fading correlation on the overall system's performance. Computer simulation results have verified the validity and accuracy of the proposed analysis.     

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.     

Selection diversity receivers over nonidentical Weibull fading channels

The performance of selection combining (SC) receivers operating over independent, but not necessarily identically distributed, Weibull fading channels is studied. A novel closed form expression for the moments of the SC output signal-to-noise ratio (SNR) is derived, which is used to study the corresponding average output SNR and amount of fading. Second-order statistical parameters such as the average level crossing rate and average fade duration at the output of the SC are also obtained in closed form. Moreover, the average symbol error probability for several coherent and noncoherent modulations schemes as well as the Shannon capacity are extracted in terms of the tabulated Meijer's G-function. Simulations are also performed to validate the proposed formulation.     

The trivariate and quadrivariate weibull fading distributions with arbitrary correlation and their applications to diversity reception

The statistical characteristics of the trivariate and quadrivariate Weibull fading distribution with arbitrary correlation, non-identical fading parameters and average powers are analytically studied. Novel expressions for important joint statistics are derived using the Weibull power transformation. These expressions are used to evaluate the performance of selection combining (SC) and maximal ratio combining (MRC) diversity receivers in the presence of such fading channels.     

Performance analysis of three-branch selection combining over arbitrarily correlated Rayleigh-fading channels

The recent literature has thoroughly treated two-branch selection combining (SC) over correlated Rayleigh fading and three-branch SC over exponentially correlated Rayleigh fading. However, a long-standing open problem involves the three-branch SC performance over arbitrarily correlated Rayleigh fading. We solve this problem completely by deriving new infinite series expressions for the cumulative distribution function, the probability density function, and the moment generating function (mgf) of the three-branch SC output signal-to-noise ratio (SNR). The output mgf can be used to derive the average symbol-error rate for any two-dimensional digital modulations. The outage probability and the higher moments of the SC output SNR are also derived. These analytical results are canonical, in that the three-branch SC performance is now completely solved for arbitrary correlation. Some previous results are shown to be special cases of our new results.     

Effects of carrier phase error on EGC receivers in correlated Nakagami-m fading

The effects of incoherently combining on dual-branch equal-gain combining (EGC) receivers in the presence of correlated, but not necessarily identical, Nakagami-m fading and additive white Gaussian noise are studied. Novel closed-form expressions for the moments of the output signal-to-noise ratio (SNR) are derived. Based on these expressions, the average output SNR and the amount of fading are obtained in closed-form. Moreover, the outage and the average bit error probability for binary and quadrature phase-shift keying are also studied using the moments-based approach. Numerical and computer simulation results clearly depict the effect of the carrier phase error, correlation coefficient, and fading severity on the EGC performance. An interesting finding is that higher values of the correlation coefficient results to lower irreducible error floors.     

Performance evaluation of triple-branch GSC diversity receivers over generalized-K fading channels

In this letter, a detailed performance analysis of generalized selection combining GSC(2,3) receivers operating over independent but not necessarily identically distributed (n.i.d.) generalized-K (KG) fading channels is presented. For this class of receivers, a novel closed-form expression for the moments of the output signal-to-noise ratio (SNR) is derived. This result can be afterwards used to evaluate the outage probability and the average symbol error probability of different signal constellations. Various performance evaluation results are also presented and compared to equivalent simulation ones.     

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.     

Equal gain combining over Nakagami-n (rice) and Nakagami-q (Hoyt) generalized fading channels

Motivated by the importance of Nakagami-n (Rice) and Nakagami-q (Hoyt) statistical models to describe channel fading in land, mobile, terrestrial, and satellite telecommunications, we present an alternative moments-based approach to the performance analysis of equal-gain combining (EGC) receivers over independent, not necessarily identically distributed Rice- and Hoyt-fading channels. Exact closed-form expressions for the moments of the signal-to-noise ratio (SNR) at the output of the combiner are derived and significant performance criteria such as, the average output SNR, the amount of fading and the spectral efficiency at the low power regime, are studied. Moreover, using Pade rational approximation to the moment-generating function of the output SNR, the average symbol error probability and the outage probability are evaluated. We also study the suitability of modeling a Hoyt-fading environment by a properly chosen Nakagami-m model, as far as the error performance of the EGC is concerned.     

Diversity reception over generalized-K (KG) fading channels

A detailed performance analysis for the most important diversity receivers operating over a composite fading channel modeled by the generalized-K (Kg) distribution is presented. The Kg distribution has been recently considered as a generic and versatile distribution for the accurate modeling of a great variety of short term fading in conjunction with long term fading (shadowing) channel conditions. For this relatively new composite fading model, expressions for important statistical metrics of maximal ratio combining (MRC), equal gain combining (EGC), selection combining (SC) and switch and stay combining (SSC) diversity receivers are derived. Using these expressions and by considering independent but not necessarily identical distributed fading channel conditions, performance criteria, such as average output signal-to-noise ratio, amount of fading and outage probability are obtained in closed form. Moreover, following the moments generating function (MGF) based approach for MRC and SSC receivers, and the Pade approximants method for SC and EGC receivers, the average bit error probability is studied. The proposed mathematical analysis is complemented by various performance evaluation results which demonstrate the accuracy of the theoretical approach.     

The bivariate generalized-Κ (ΚG) distribution and its application to diversity receivers

The correlated bivariate generalized-K (K_G) distribution, with not necessarily identical shaping and scaling parameters, is introduced and studied. This composite distribution is convenient for modeling multipath/shadowing correlated fading environments when the correlations between the signal envelopes and their powers are different. Generic infinite series expressions are derived for the probability density function (PDF), the cumulative distribution function (CDF) and the joint moments. Assuming identical shaping parameters, simpler expressions for the PDF, CDF and the characteristic function (CF) are provided, while the joint moments are derived in closed form. Furthermore, the PDFs of the product and ratio of two correlated K_G random variables are obtained. Capitalizing on these theoretical expressions for the statistical characteristics of the correlated K_G distribution, the performance analysis of various diversity reception techniques, such as maximal ratio combining (MRC), equal gain combining (EGC) and selection diversity (SD), over bivariate K_G fading channels is presented. For the SD, the outage probability is studied, while for the MRC and EGC the average bit error probability is obtained. The proposed analysis is accompanied by numerical results, clearly demonstrating the usefulness of the theoretical approach as well as the appropriateness of the K_G distribution to model multipath/shadowing fading channels.     

Higher Order Capacity Statistics of Diversity Receivers

A statistical analysis for the channel capacity (CC) for several diversity receivers under optimal rate adaptation with constant transmit power is provided. Independent but not necessarily identically distributed Nakagami-m fading channels are considered. Specifically, the moments of the CC at the output of selection combining, maximal-ratio combining, and switched and stay combining are obtained, assuming integer-order fading parameters, while for the Rayleigh model the moments of the CC at the output of equal-gain combining and generalized-selection combining are derived in closed form. Using these formulas, a new performance criterion, namely as fading figure (FF) as well as the variance, skewness, and kurtosis, are studied. Our findings show that the FF improves with an increase of the signal-to-noise ratio (SNR), the fading parameters, and/or the diversity order. Also, unlike to the variance of the error probability, the variance of the CC is a monotonic function of the average input SNR.     

A New Approach to Bivariate Hoyt Distribution and its Application in Performance Analysis of Dual-Diversity Receivers

Novel infinite series based expressions for the bivariate Hoyt distribution are derived. More specifically, expressions for the joint probability density function (JPDF) and the joint cumulative distribution function (JCDF) of two Hoyt fading envelopes are derived, and proposed for use in performance analyses of dual-branch diversity receivers operating over correlated Hoyt fading channels. Using these reasonably simple and mathematically tractable expressions, we evaluate the performance of a dual-branch selection combining (SC) diversity receiver in terms of the outage probability (P _out ) and the average bit error probability (ABEP) criteria. The ABEP performance is evaluated for binary differential phase-shift-keying (BDPSK) and binary non-coherent frequency-shift keying (BNFSK) modulation schemes.     

The influence of mobile-to-mobile land communication channelspectrum on the error rate of binary DPSK and NFSK matched filterreceivers

The effect of a specific fading correlation function derived for a mobile-to-mobile land communication channel on the performance of differentially coherent PSK and noncoherent FSK matched filter receivers is investigated. The bit error probability, irreducible error rate, and the degradation in signal-to-noise ratio (SNR) are specifically derived for each system. The effect of the fading bandwidth on the performance of the system is also investigated     

Error analysis of generalized selection combining over relay channel

Cooperative communication is a recently popular concept which allows single-antenna devices to benefit from spatial diversity. The performance analysis of cooperative communication using generalized selection combining (GSC) over independent not necessarily identically distributed Nakagami-m fading channels is presented and compared with that of the conventional maximal ratio combining (MRC) and selection combining (SC) schemes. With the aid of Padé approximants theory, new closed-form expression is derived for the moment-generating function (MGF) of the GSC output signal-to-noise ratio (SNR). MGF is an important tool for researching the system performance. In this paper, the average bit-error probability is accurately approximated using the well-known MGF approach. Numerical results show that the proposed mathematical analysis is accurate and that for the more severe fading cases, the GSC receivers are closer to the optimum MRC receivers.     

Bivariate generalised gamma distribution with arbitrary fading parameters

The three-parameter generalised gamma distribution is a versatile fading model that generalises or accurately approximates many of the commonly used distributions for multipath, shadow, and composite fading. It is difficult to evaluate the performance(s) of closely spaced dual-diversity receivers operating in such a channel because an analytical expression is not yet available for the bivariate correlated generalised gamma distribution. This report studies the bivariate generalised gamma distribution with arbitrary parameters. Expressions for the joint distribution and joint central moments are derived, and are used to obtain the outage probability for a dual-branch selection combining receiver over a correlated generalised gamma fading channel.     

Correlated multivariate Weibull fading channels with selection diversity

The dependent multivariate Weibull distribution is modelled for correlated fading channels, where the probability density function of a Weibull fading factor is defined with two parameters (omega, beta), and the case of equal beta is considered. The joint cumulative distribution function and probability density function of the Weibull distribution are derived, and the outage probability of selection diversity is evaluated     

Predetection Switched Combining in Correlated Rician Fading

The performance of dual-branch predetection switch-and-stay combining (SSC) in correlated Rician fading is considered in conjunction with several modulation formats. Analytical expressions are derived for the average symbol error rate (SER) of predetection SSC in correlated Rician fading. Switching thresholds that minimize the average SER are obtained. The impact of fading factor and the fading correlation on the performance of predetection SSC is studied. Analytical expressions for the output average signal-to-noise ratio (SNR) and the outage probability are derived. The validity of the analytical expressions are verified using Monte Carlo simulation.     

Performance analysis of a class of GSC receivers over nonidentical Weibull fading channels

The performance of a class of generalized-selection combining (GSC) receivers operating over independent but nonidentically distributed Weibull fading channels is studied. We consider the case where the two branches with the largest instantaneous signal-to-noise ratio (SNR), from a total of L available, GSC(2, L) are selected. By introducing a novel property for the product of moments of ordered Weibull random variables, convenient closed form expressions for the moments of the GSC(2,L) output SNR are derived. Using these expressions, important performance criteria, such as average output SNR and amount of fading, are obtained in closed form. Furthermore, employing the Pade/spl acute/ approximants theory and the moment-generating function approach, outage and bit-error rate performance are studied. An attempt is also made to identify the equivalency between the Weibull and the Rice fading channel, which is typically used to model the mobile satellite channel. We present various numerical performance evaluation results for different modulation formats and channel conditions. These results are complemented by equivalent computer simulated results which validate the accuracy of the proposed analysis.