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.     

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.     

Moment analysis of the equal gain combiner output in equally correlated fading channels

Moments of the multibranch equal gain combiner (EGC) output signal-to-noise ratio (SNR) are only known for independent fading channels or exponentially correlated Nakagami-m fading channels. In this paper, we derive the moments of the EGC output SNR in equally correlated Rayleigh, Rician, and Nakagami-m fading channels. Our moment expressions can be used to evaluate the outage and the average error rate as well as purely moments-based measures such as the average output SNR and the amount of fading as functions of the fading correlation. Numerical results that illustrate the effect of fading correlation on the distribution of the EGC output SNR are also provided.     

Performance of cooperative diversity using Equal Gain Combining (EGC) over Nakagami-m fading channels

Cooperative diversity is a promising technology for future wireless networks. In this paper, we derive exact closed-form expressions for the average bit error rate (BER) and outage probability (Pout) for differential equal gain combining (EGC) in cooperative diversity networks. The considered network uses amplify-and-forward relaying over independent non-identical Nakagami-m fading channels. The performance metrics (BER and Pout) are derived using the moment generating function (MGF) method. Furthermore, we found (in terms of MGF) the SNR moments, the average signal-to-noise ratio (SNR) and amount of fading. Numerical results show that the differential EGC can bene?t from the path-loss reduction and outperform the traditional multiple-input single output (MISO) system. Also, numerical results show that the performance of the differential EGC is comparable to the maximum ratio combining (MRC) performance.     

Error Performance of DQPSK with EGC Diversity Reception over Fading Channels

This paper derives the average bit error probability (BEP) of differential quaternary phase shift keying (DQPSK) with postdetection equal gain combining (EGC) diversity reception over independent and arbitrarily correlated fading channels. First, using the associated Legendre functions, the average BEP of DQPSK is analyzed over independent Rayleigh, Nakagami-m, and Rician fading channels. Finite-series closed-form expressions for the average BEP of DQPSK over L-branch independent Rayleigh and Nakagami-m fading channels (for integer Lm) are presented. Besides, a finite-series closed-form expression is given for the average BEP of differential binary phase shift keying (DBPSK) with EGC over independent Rician fading channels. Second, an alternative approach is propounded to study the performance of DQPSK over arbitrarily correlated Nakagami-m and Rician fading channels. Relatively simple BEP expressions in terms of a finite sum of a finite-range integral are proposed. Moreover, the penalty in signal to noise ratio (SNR) due to arbitrarily correlated channel fading is also investigated. Finally, the accuracy of the results is verified by computer simulation.     

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.     

Moments-based approach to the performance analysis of equal gain diversity in Nakagami-m fading

In this letter, an alternative moments-based approach for the performance analysis of an L-branch predetection equal gain combiner (EGC) over independent or correlated Nakagami-m fading channels is presented. Exact closed-form expressions are derived for the moments of the EGC output signal-to-noise ratio (SNR), while the corresponding moment-generating function (MGF) is accurately approximated with the aid of Pade/spl acute/ approximants theory. Important performance criteria are studied; the average output SNR, which is expressed in closed form both for independent and correlative fading and for arbitrary system parameters, the average symbol-error probability for several coherent, noncoherent, and multilevel modulation schemes, and the outage probability, which are both accurately approximated using the well-known MGF approach. The proposed mathematical analysis is illustrated by various numerical results, and computer simulations have been performed to verify the validity and the accuracy of the theoretical approach.     

常见分集合并系统的性能分析

在移动通信中,分集技术是一种最有效的抗衰落技术。本文对3种常见的线性合并分集技术进行简要分析,给出它们的基带表示和合并器输出信噪比的概率密度函数(pdf),由此给出它们的合并增益。针对系统采用MPSK调制的情况,对瑞利衰落信道的3种合并分集系统的比特误码率(BER)性能进行理论研究,分别给出选择性合并(SC)和最大比率合并(MRC)系统的理论比特误码率表达式;对于等增益合并(EGC)分集,给出了一种近似的EGC系统的输出信噪比的pdf,由此导出EGC的一种近似的BER表达式,由蒙特卡罗仿真结果可以看出此近似的BER数值结果是准确的。数值结果显示:MRC性能最好,EGC性能稍差,而SC性能较差。文中给出的分析方法对于实际分集系统的理论研究具有普遍的指导意义。     

Closed-Form Analysis of Equal-Gain Diversity in Wireless Radio Networks

This paper deals with the performance of predetection equal-gain combining (EGC) receivers operating over multipath fading plus cochannel interference (CCI) and additive white Gaussian noise channels. The desired components of the received signals are considered to experience independent but not-necessarily identically distributed Nakagami-m fading, while the interferers are subject to independent Rayleigh fading. The analysis is not only limited to equal average fading power interferers, but the case of interferers with distinct average powers is also examined. By following the coherent interference power calculation, novel closed-form expressions for the moments of the EGC output signal-to-interference-plus-noise ratio (SINR) are derived, which are being used to study the performance of the average output SINR. Furthermore, by assuming an interference-limited fading scenario, novel closed-form union performance bounds are derived. More specifically, tight upper bounds for the outage and average symbol error probability for several constant envelope modulation schemes, and lower bounds for the Shannon average spectral efficiency, are provided. Numerical results demonstrate the effect of the number of interferers, the number of the receiver branches, and the severity of fading on the EGC receiver performance. Computer simulations have been also performed to verify the tightness of the proposed bounds and the correctness of the mathematical analysis. It is shown that the performance of cellular radio systems in the uplink is degraded mainly from the first-tier CCI of the adjacent cells     

Average SNR of dual selection combining over correlated Nakagami-mfading channels

We investigate the effect of fading correlation and branch gain imbalance on the average output signal-to-noise ratio (SNR) in conjunction with dual selection combining (SC). In particular, starting with the moment generating function of the dual SC output SNR, we derive a closed-form expression for the average output SNR in the general case of correlated unbalanced Nakagami-m fading channels. We then show that the generic result can be further simplified for the special cases of Rayleigh fading, uncorrelated branches, and/or equal average SNRs. Because of their simple form, the given expressions readily allow numerical evaluation for cases of practical interest     

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 of M-PSK with GSC and EGC with Gaussian weighting errors

Using a moment-generating function (MGF)-based approach, we study the performance of M-ary phase-shift keying (M-PSK) with generalized selection combining (GSC) and equal gain combining (EGC) in fading channels (including Rayleigh, Rician, Nakagami-m, and Nakagami-q fading) with independent and identically distributed (i.i.d) branches. Analytical expressions for the error and outage probabilities, the signal-to-noise-ratio (SNR) statistics, and the channel capacity of M-PSK diversity receivers are derived, taking into account the effects of Gaussian weighting errors and all relevant system and channel parameters. Unlike the case of perfect channel-state information (CSI), the outage probability for the case of imperfect channel estimation (ICE) is not only a function of the normalized SNR with respect to the SNR threshold, but also a function of the operating SNR itself. The SNR loss of the M-PSK GSC and EGC receivers due to ICE and the relation between the receiver input and output SNRs for ICE are derived. Our results show that, even with ICE, GSC and EGC are effective in improving the output SNR and significantly reduce the error floor and the channel-capacity loss caused by ICE.     

Performance analysis of coherent equal gain combining overNakagami-m fading channels

We study the exact average output signal-to-noise ratio (SNR) and symbol error rate (SER) of M-ary phaseshift-keying (PSK) signals with coherent equal gain combining reception. The analysis assumes independent Nakagami-m (1960) fading paths, which are not necessarily identically distributed. On one hand, we use geometric summations to obtain closed-form expressions for the average output SNR over diversity paths with an exponentially decaying power delay profile. On the other hand, capitalizing on an alternative integral representation of the conditional SER along with Gauss-Hermite quadrature integration, we derive an average SER expression in the form of a single finite-range integral and an integrand composed of tabulated functions. We also present a simpler but approximate approach for the closed-form evaluation of the SER of these signals over independent identically distributed Nakagami-m fading paths     

An MGF-based performance analysis of generalized selectioncombining over Rayleigh fading channels

Using the notion of the “spacing” between ordered exponential random variables, a performance analysis of the generalized selection combining (GSC) diversity scheme over Rayleigh fading channels is presented and compared with that of the conventional maximal-ratio combining and selection combining schemes. Starting with the moment generating function (MGF) of the GSC output signal-to-noise ratio (SNR), we derive closed-form expressions for the average combined SNR, outage probability, and average error probability of a wide variety of modulation schemes operating over independently, identically distributed (i.i.d.) diversity paths. Because of their simple form, these expressions readily allow numerical evaluation for cases of practical interest. The results are also extended to the case of non-i.i.d. diversity paths     

Equal-gain diversity receiver performance in wireless channels

Performance analysis of equal-gain combining (EGC) diversity systems is notoriously difficult only more so given that the closed-form probability density function (PDF) of the EGC output is only available for dual-diversity combining in Rayleigh fading. A powerful frequency-domain approach is therefore developed in which the average error-rate integral is transformed into the frequency domain, using Parseval's theorem. Such a transformation eliminates the need for computing (or approximating) the EGC output PDF (which is unknown), but instead requires the knowledge of the corresponding characteristic function (which is readily available). The frequency-domain method also circumvents the need to perform multiple-fold convolution integral operations, usually encountered in the calculation of the PDF of the sum of the received signal amplitudes. We then derive integral expressions for the average symbol-error rate of an arbitrary two-dimensional signaling scheme, with EGC reception in Rayleigh, Rician, Nakagami-m (1960), and Nakagami-q fading channels. For practically important cases of second- and third-order diversity systems in Nakagami fading, both coherent and noncoherent detection methods for binary signaling are analyzed using the Appell hypergeometric function. A number of closed-form solutions are derived in which the results put forward by Zhang (see ibid., vol.45, p.270-73, 1997) are shown to be special cases.     

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.     

Performance analysis of L-branch equal gain combiners in equally correlated Rayleigh fading channels

Theoretical performance results for L-branch (L/spl ges/3) coherent equal-gain combining (EGC) in correlated fading channels are not known. This letter develops a novel approach for performance analysis of L-branch EGC in equally correlated Rayleigh fading channels. Such channel gains can be transformed into a set of conditionally independent channel gains. The cumulative distribution function (cdf) of the EGC output signal-to-noise ratio (SNR) is, therefore, derived. The symbol error rate (SER) of different modulation schemes with EGC in equally correlated Rayleigh fading channels is evaluated. Numerical results that illustrate the effects of equally correlated fading on the SER performance of EGC are also provided.     

Performance analysis of dual MRC receiver in correlated hoyt fading channels

Performance of a dual maximal ratio combining receiver has been analyzed in correlated Hoyt fading channels. Analytical expressions for the probability density function of the receiver output signal-to-noise ratio (SNR), average SNR, outage probability and average bit error rate performance for binary, coherent and non-coherent modulations have been presented. Numerical results show that for coherent phase shit-keying and differential phase shift-keying modulations, to achieve an ABER of 10^?7, the required excess SNR is relatively small for correlation coefficient (?) less than 0.5 than it is for ? ≫ 0.5.     

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.