Gaussian class multivariate Weibull distributions: theory and applications in fading channels

Ascertaining on the suitability of the Weibull distribution to model fading channels, a theoretical framework for a class of multivariate Weibull distributions, originated from Gaussian random processes, is introduced and analyzed. Novel analytical expressions for the joint probability density function (pdf), moment-generating function (mgf), and cumulative distribution function (cdf) are derived for the bivariate distribution of this class with not necessarily identical fading parameters and average powers. Two specific distributions with arbitrary number of correlated variates are considered and studied: with exponential and with constant correlation where their pdfs are introduced. Both cases assume equal average fading powers, but not necessarily identical fading parameters. For the multivariate Weibull distribution with exponential correlation, useful corresponding formulas, as for the bivariate case, are derived. The presented theoretical results are applied to analyze the performance of several diversity receivers employed with selection, equal-gain, and maximal-ratio combining (MRC) techniques operating over correlated Weibull fading channels. For these diversity receivers, several useful performance criteria such as the moments of the output signal-to-noise ratio (SNR) (including average output SNR and amount of fading) and outage probability are analytically derived. Moreover, the average symbol error probability for several coherent and noncoherent modulation schemes is studied using the mgf approach. The proposed mathematical analysis is complemented by various evaluation results, showing the effects of the fading severity as well as the fading correlation on the diversity receivers performance.     

Asymptotic performance of hybrid-selection/maximal-ratio combining over fading channels

In this letter, we study the asymptotic performance of hybrid-selection/maximal-ratio combining (HS/MRC) and postdetection HS/equal-gain combining (HS/EGC) over generalized fading channels for large average signal-to-noise ratios (ASNRs). By evaluating the asymptotic moment generating function of the HS/MRC output SNR at high ASNR, we derive the diversity and coding gains for HS/MRC for a large class of modulation formats and versatile fading conditions, including different types of fading channels and nonidentical SNR statistics across diversity branches. Our analytical results reveal that the diversity gains of HS/MRC and HS/EGC are equivalent to that of MRC, and the difference in the coding gains for different modulation formats is manifested in terms of a modulation factor defined in this letter. Some new analytical results about effects of the number of combined branches for HS/MRC and noncoherent combining loss of HS/EGC are also provided.     

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.     

A Hybrid Selection/Equal-Gain Combining over Correlated Nakagami-m Fading Channels

A new type of hybrid selection/equal-gain combining (HS/EGC) scheme is proposed and analyzed. This scheme dynamically selects the best combination of branches by a simple test and combines them in equal-gain combining (EGC) manner. As a result, the scheme always shows better performance than conventional EGC and selection diversity (SD), and close to maximal-ratio combining (MRC). As an exemplary performance indicator, its average output SNR for dual correlated Nakagami-m fading channels is calculated and demonstrated in comparison with other diversity schemes     

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.     

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 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.     

Blind Ratio Combining (BRC): An Optimum Diversity Receiver for Coherent Detection With Unknown Fading Amplitudes

We present an optimum diversity receiver called blind ratio combining (BRC) that minimizes the average symbol error probability or maximizes the average output SNR, where the channels' time delays and the random phases are known, while the fading amplitudes are unknown. In contrast to previous works, where efforts were made to find a posteriori probabilities at the receiver, the BRC simply calculates the optimum weights, which depend on the channel's statistics, avoiding continuous channel estimation, and thus, it significantly reduces the system's complexity. In nonidentical multipath fading channels with power delay profile (PDP), the BRC receiver performs between maximal ratio combining (MRC) and equal gain combining (EGC), and keeps its performance comparable - and in some cases superior - to that of generalized selection combining, while for large values of the decay factor, it approaches MRC. Moreover, in the important practical case of exponential PDP - common in RAKE receivers modeling and adopted for the Universal Mobile Telecommunications System spatial channel modeling by the European Telecommunications Standards Institute-3GPP - the optimum weights can be accurately approximated by simple elementary functions. Furthermore, it is proved that the utilization of these weights ensures an error performance improvement over EGC for arbitrary PDPs. The proposed BRC receiver can be efficiently applied in wireless wideband communication systems, where a large number of diversity branches exists, due to the strong multipath effects.     

Optical Wireless Systems Employing Adaptive Collaborative Transmitters in an Indoor Channel

We propose a novel optical wireless (OW) system based on a power adaptive multibeam spot-diffusing transmitter serving multiple seven-segment maximum ratio combining (MRC) angle diversity receivers. A feedback link is assumed between the transceivers so that each receiver conveys to the multibeam transmitter the new beams transmit power weights to be used to achieve the best signal quality at a given receiver location. Two cases involving three and five receivers are considered. Four different configurations for the placement of the three-receiver case in the room are also examined. The system's performance in each case is evaluated in terms of signal-to-noise ratio (SNR) and is compared with the single receiver scenario with and without power adaptation. In the presence of one receiver, the transmit spot powers can be adjusted for optimum performance at that receiver location. For multiple receivers, there is conflict, and we propose spot power adaptation based on the average requirements (power distribution in spots), i.e., transmit equal gain combining (EGC) of spot power or MRC of transmit spot powers. The results show that the three receivers benefit most from an adaptive transmitter when each is placed at a corner of the room. In this case, an SNR increase of as much as 2.6 dB is achieved for all three receivers at the corners by both MRC and EGC. Moreover, when all receivers are placed away from the line of diffusing spots, our proposed MRC collaborative approach is 1 dB better than the noncollaborative system. This gain reduces the difference from the upper bound set by the single receiver adaptation, which is 3 dB. For a mobile transmitter, MRC also significantly improved the SNR for the farthest receivers at the opposite end from the transmitter located near one room corner.      

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.     

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.     

Performance comparison of MRC and EGC on a MC-CDMA system with synchronization errors over fading channels

This work derives the average bit error rate (BER) of the uplink and downlink multicarrier code division multiple access (MC-CDMA) systems using maximum ratio combining (MRC) and equal gain combining (EGC) with synchronization errors over fading channels. The derived equation can simultaneously incorporate the parameters of the fading channel and all of the synchronization errors, including frequency offset, carrier phase jitter, and timing jitter. Numerical results indicate that those two combining schemes on the uplink and downlink MC-CDMA systems are degraded by all of the normalized synchronization errors over 10⁻². The comparison outcomes between MRC and EGC reveal that the MRC generally outperforms EGC in the uplink MC-CDMA system. However, EGC achieves better performance when the number of users is small, the normalized synchronization errors are low and the signal to noise ratio (SNR) is high. In the downlink system, EGC mainly outperforms MRC when the SNR and the number of users are gradually increased and the normalized synchronization errors are low. Therefore, the selection of MRC or EGC depends on the SNR, the synchronization errors and the number of users in uplink and downlink MC-CDMA systems.     

Performance of Up-link MC-CDMA System with Frequency Offset and Imperfect Channel Estimation Simultaneously over Nakagami Fading Channels

In this paper, effects of carrier frequency offset on performance of uplink MC-CDMA (Multi-Carrier Code Division Multiple Access) system in Nakagami fading channel are investigated through the theoretical analysis and Monte Carlo computer simulations. Both perfect maximal-ratio combining (MRC) and equal gain combining (EGC) receivers are analyzed; the impact of imperfect channel fading estimation on the performance of MRC is also explored. The performance of MC-CDMA system is also compared with that of the conventional single-carrier DS-CDMA system. Our results indicate that the performance of MC-CDMA system is sensitive to even small values of carrier frequency offset and that the performance of MC-CDMA system improves as number of subcarriers increases. In perfect channel fading estimation, the overall performance of MRC is superior to EGC. However, when imperfect or inaccurate channel fading estimation exists, which leads to serious performance degradation, EGC becomes superior to MRC. This revised version was published online in July 2006 with corrections to the Cover Date.     

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。     

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.     

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.     

Performance of coherent receivers with hybrid SC/MRC overNakagami-m fading channels

A performance analysis of two hybrid selective combining/maximal ratio combining (SC/MRC) diversity receivers over Nakagami-m (1960) fading channels with a flat multipath intensity profile is presented and numerically compared with that of the conventional SC and MRC schemes. Numerical results for particular cases of interest show that the bit error rate (BER) degradation arising from the use of hybrid SC/MRC instead of MRC is independent of the average signal-to-noise ratio (SNR) regardless of the severity of the fading and that MRC provides a higher rate of improvement than the hybrid SC/MRC as the severity of fading decreases     

Performance analysis of predetection EGC receiver in Weibull fading channel

The predetection equal gain combining (EGC) receiver is generally known to have a performance that is close to the maximal ratio combining (MRC) receiver while having relatively less implementation complexity. The bit error rate (BER) of an EGC receiver for binary, coherent and noncoherent modulations has been analysed for an independent Weibull fading channel. Numerical results have been compared with the available results for selection combining (SC) and MRC diversity receivers.     

Micro- and macrodiversity NCFSK (DPSK) on shadowed Nakagami-fadingchannels

The improvements achievable using diversity with matched filter NCFSK (and DPSK) receivers operating on log-normal shadowed Nakagami-fading channels are analyzed. Three microdiversity techniques, equal gain combining (EGC), maximal ratio combining (MRC) and selection combining (SC) are compared. The system performances are assessed by considering two measures of coverage; one well suited for mobile users and one well suited for portable users. The detrimental effects of multipath fading in cellular mobile radio systems can be mitigated by using a number of microdiversity paths at the receiver. The effects of shadowing can be mitigated by using a number K of macrodiversity radio ports to serve each cell. The improvements gained by using microdiversity to combat multipath fading and macrodiversity to combat shadowing are investigated. The effects of the fading severity, the number of microdiversity branches at each port L and the number of macrodiversity ports K on the system performance are investigated in detail. The results, in most cases, are obtained by carrying out a single numerical integration (for any order of diversity). The results show that although MRC gives the best performance, EGC and SC perform nearly as well for dual (L=2) diversity. For larger L, i.e., L⩾4, the relative performance of SC deteriorates substantially whereas the performance of EGC remains close to that of MRC. Also, our results show that as the fading gets less severe, the performance of EGC gets closer to that of MRC, while the performance of SC worsens compared to that of MRC     

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.