The authors reply to the comment by Simon (IEEE Trans. Commun., vol.54, no.8, p.1511-12, 2006 August) on their original paper (Zogas and Karagiannidis, IEEE Trans. Commun., vol.53, no.11, p.1970-4, 2005 November)

Analytical expressions for the evaluation of the bivariate Rician cumulative distribution function (CDF), the covariance, and the characteristic function (CHF) are not known, despite their usefulness in wireless communications systems analysis. In this letter, motivated by the ability of the Rician model to describe fading in wireless communications, we derive infinite-series representations for the probability density function, the CDF, the covariance, and the CHF of two correlated Rician random variables. It is shown that the presented infinite-series expressions converge rapidly, and can be efficiently used to study several performance criteria for dual-diversity receivers operating over correlated Rician 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.

In mobile radio systems, antenna diversity is used to combat fading and reduce the impact of cochannel interference. In this paper, we analyze the performance of L-branch equal-gain combining receivers over correlated nonidentically distributed Nakagami-m fading channels, in the presence of multiple identical cochannel interferers and additive white Gaussian noise. The performance criterion considered is the average output signal-to-interference-plus-noise ratio, which is obtained in closed form for both independent and correlative fading. Due to the simple form of the derived expressions, they readily allow numerical evaluation for cases of practical interest.

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.

Efficient performance bounds for multihop wireless communications systems with non-regenerative fixed-gain relays operating over non-identical generalized fading channels, are presented. More specifically, the end-to-end signal-to-noise ratio (SNR) is formulated and upper bounded by using the well-known inequality between harmonic and geometric mean of positive random variables. Based on this bound, the moments of the end-to-end SNR for Rayleigh, Nakagami-m, and Rice fading channels, are obtained in simple closed-forms. Furthermore, the outage performance and the average error probability for coherent and non-coherent modulation schemes are also studied using the moment-generating function (MGF) approach. The proposed method for the evaluation of the MGF is based on the Pade approximants theory. Moreover, new expressions are derived for the gain of previously proposed "semi-blind" relays. These expressions are used in numerical and computer simulations examples, to verify the accuracy and to show the tightness of the proposed bounds.

Motivated by the suitability of the Weibull distribution to model multipath fading channels, the performance of L-branch selection combining (SC) receivers, with non-identical statistics, is presented. Deriving a useful expression for the probability density function of the SC output signal-to-noise ratio (SNR), important performance metrics are studied. More specifically, a closed-form expression is derived for the moments of the combiner output SNR, which is used to study the average output SNR and the amount of fading. The average symbol error probability for several coherent and non-coherent, binary and multilevel modulation schemes is also obtained in closed-form.

The performance of dual-branch SC receivers over correlated Weibull fading channels is studied in this paper. Exact closed-form expressions are derived for the probability/cumulative density functions and the moments of the output signal-to-noise ratio (SNR). Important performance criteria, such as average output SNR, amount of fading (AoF), outage probability and average bit error probability (ABEP) for several modulation schemes, are studied and novel closed-form analytical expressions are derived. The proposed analysis is complemented by various performance evaluation results, including the effects of input SNRs unbalancing, fading severity and fading correlation on the overall system performance. Computer simulations results verify the validity and the accuracy of the proposed analysis.

Motivated by the suitability of the Weibull distribution to model multipath fading channels, the second order statistics and the spectral efficiency (SE) of L-branch SC receivers are studied. Deriving a novel closed-form expression for the probability density function (pdf) of the SC output SNR, the average level crossing rate (LCR), the average fade duration (AFD) and the Shannon's average SE, at the output of the SC, are derived in closed-forms. Our results are sufficiently general to handle arbitrary fading parameter and dissimilar branch powers.

In this letter, an approach to the evaluation of the error performance in dual predetection equal-gain combining (EGC) systems over correlated Nakagami-m fading channels is presented. Deriving an infinite series representation for the characteristic function of the sum of two correlated Nakagami-m variables, a closed-form formula is extracted for binary phase-shift keying and coherent binary frequency-shift keying, while several other modulation schemes are studied, capitalizing on a Parsevals's theorem-based approach, previously published. Numerical results and simulations are also presented to illustrate the proposed mathematical analysis and to point out the effect of the input signal-to-noise ratio unbalancing, the fading severity, and the fading correlation on the system's error performance.

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.

Previous studies have addressed with the performance analysis of L-branch equal gain combining (EGC) systems over independent Rayleigh- or Nakagami-m fading channels. In this paper, important statistical parameters, such as the /spl kappa/-moment, the /spl kappa/-central moment, the skewness, and the kurtosis of the output signal-to-noise ratio (SNR), in predetection EGC systems operating over correlated Nakagami-m fading channels are studied. Simple closed-form expressions for the mean and variance of the output SNR are presented and it is shown that our general results reduce to the specific noncorrelative fading case previously published. Moreover, significant performance criteria such as the amount of fading and the spectral efficiency in the low power regime, are investigated. Numerical results and simulations are presented to check the validity of the proposed mathematical analysis and to point out the impact of the fading correlation, the input SNRs unbalancing as well as the fading severity, on the EGC performance.

An exact and rapidly converging infinite series for the average output signal-to-noise ratio in a triple selection diversity system, over correlated Nakagami-m fading channels, is presented. Numerical results are presented to illustrate the proposed approach and to point out the effect of the fading correlation to the performance of the combiner, as well as the improvement achieved by the triple selection combining compared to the dual diversity case.

In this paper, important statistical parameters, such as the k-moment and the k-central moment, of the output signal-to-noise ratio (SNR), in predetection equal-gain combining (EGC) systems operating over correlated Nakagami-m fading channels are studied. Simple closed-form expressions for the mean and variance of the output SNR are presented. Furthermore, it is shown that our general results reduce to the specific noncorrelative fading case previously published. Moreover, significant performance criteria for the EGC such as amount of fading (AoF) and spectral efficiency in the low power regime are investigated. Numerical and simulation results are presented validating the proposed mathematical analysis. These results also point out the impact of the fading correlation, the input SNRs unbalancing as well as the fading severity, on the EGC performance.

Capitalizing on the proof of a theorem presented by L.E. Blumenson and K.S. Miller (see Ann. Math. Statist., vol.34, p.903-10, 1963), we propose a useful closed formula for the exponentially correlated n-variate Nakagami-m probability density function. Moreover, an infinite series approach for the corresponding cumulative distribution function is presented. Bounds on the error resulting from the truncation of the infinite series are also derived. Finally, in order to check the accuracy of the proposed formulation, numerical results are presented.

An approach to the performance analysis of a triple selection-diversity system over exponentially correlated Nakagami-m fading channels is presented. Closed-form expressions of converged sums for both outage and average error probabilities are derived. Numerical results are presented to point out the effect of the fading correlation, the fading severity, as well as the improvement achieved by the triple selection combining compared with the corresponding dual diversity case.

An efficient approach for the evaluation of the Nakagami-m (1960) multivariate probability density function (PDF) and cumulative distribution function (CDF) with arbitrary correlation is presented. Approximating the correlation matrix with a Green's matrix, useful closed formulas for the joint Nakagami-m PDF and CDF, are derived. The proposed approach is a significant theoretical tool that can be efficiently used in the performance analysis of wireless communications systems operating over correlative Nakagami-m fading channels.

A useful formulation for the multivariate Rayleigh probability density function (PDF) with an exponential form for its correlation matrix is presented. Furthermore, the corresponding multivariate Rayleigh cumulative distribution function (CDF) is derived in a nested infinite series representation, which converges rapidly and can be efficiently used in many wireless applications with diversity reception. Finally, bounds on the error resulting from truncation of the infinite series are also derived.