Exact evaluation of maximal-ratio and equal-gain diversityreceivers for M-ary QAM on Nakagami fading channels

Exact integral expressions are derived for calculating the symbol-error rate (SER) of multilevel quadrature amplitude modulation (MQAM) in conjunction with L-fold antenna diversity on arbitrary Nakagami fading channel. Both maximal-ratio combining (MRC) (in independent and correlated fading) and equal-gain combining (EGC) predetection (in independent fading) diversity techniques have been considered. Exact closed-form SER expressions for two restricted Nakagami fading cases (MRC reception) are also derived. An exact analysis of EGC for MQAM has not been reported previously, despite its practical interest. Remarkably, the exact SER integrals can also be replaced by a finite-series approximation formula. A useful procedure for computing the confluent hypergeometric series is also presented     

Ordered Statistic Analysis for Diversity Combining Schemes over Nakagami-m Fading Channel

Order diversity combining technique is one of efficient methods to lower the complexity but not to significantly degrade performance. Recently, Eng and Milstein [1] proposed a novel order-combining technique, called the second order diversity combining (SC2) and third order diversity combining (SC3) and applied to Rayleigh fading channel. SC2 and SC3 schemes mean that the two (three) signals with the first two (three) largest amplitudes among the branches are chosen and coherently combined. However, when compared to Rayleigh distribution, the Nakagami-m distribution [10] provides a more general and versatile way to model wireless channel. For the reason, the bit error rate (BER) performance of proposed schemes were then analyzed with order statistic method and compared to the traditional diversity technique over Nakagami fading environment in this paper. The results are compared to maximal ratio combining (MRC), and conventional selection combining (SC) in coherent reception and to equal gain combining (EGC) in noncoherent reception. The results show that SC is in performance the worst for either in coherent or in noncoherent schemes, as expected. The performance differences between SC2 (SC3) and MRC (EGC) are not significant when the diversity order L 3, but the difference will increase when L 5. It is worth noting that the result of [1] is a special case with fading figure, m = 1. It is also observed the performance is much affected by the number of diversity branches L, the fading figure m, and the signal-to-noise ratio (SNR).     

Nakagami衰落上DE-QPSK在联合收发分集下的性能分析

利用高斯Q函数的高阶次幂在最大比合并（MRC）分集接收瑞利衰落信道上统计平均的结果,推导了Nakagami 衰落信道上采用组合发射选择合并（SC）/接收 MRC 天线分集的相干检测差分编码四相相移键控（DE-QPSK）的平均误符号率（ASER）精确表达式。利用高斯Q函数的近似表达式和矩生成函数（MGF）方法,推导了Nakagami衰落信道上采用组合SC/MRC天线分集的相干检测DE-QPSK 的ASER近似表达式。通过数值计算和仿真,验证了DE-QPSK的ASER精确表达式的正确性以及近似表达式的准确性。利用精确表达式和近似表达式可研究收发天线数目和衰落参数对DE-QPSK的ASER性能的影响,为实际SC/MRC天线分集方案的设计提供了理论指导。     

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。     

Error Probabilities for MRC Diversity Reception of MDPSK in Slow Nakagami Fading

New closed form error probability expressions for M-arydifferential-phase-shift-keying (MDPSK) with maximal ratio combining (MRC)diversity reception in Nakagami fading, are derived. These expressions involveeasily computable Legendre polynomials and Associated Legendre functions. Bysetting the fading severity parameter m to unity, the new general errorprobability formula reduces to the known results for MDPSK systems in slowRayleigh fading. For binary DPSK, the bit error rate (BER) performance withMRC is compared with known results for selection diversity combining (SDC).It is shown that MRC is more effective than SDC in improving BER performancefor the Nakagami channels, as expected. We also discuss the ranges of thefading severity parameter and diversity order, within which the errorprobability expressions can be computed efficiently.     

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.     

弱湍流中紫外光非直视分集接收技术的研究

根据弱湍流信道中对数正态分布模型,建立了紫外光非直视分集接收系统。采用开关键控（OOK）调制,在不同闪烁指数和接收天线数下,分别对比分析了最大比合并（MRC）、等增益合并（EGC）和选择性合并（SC）的误码性能。仿真结果表明,相比于无分集情况,采用三种合并方式的误码率性能有明显提升。在接收天线数相同的情况下,三种合并方式中,MRC的性能最优,其次是EGC,SC的性能最差。对比分析了不同接收天线数时的误码率性能,随着接收天线数的增加,三种合并方式的误码性能得到了较大改善。在弱湍流信道中,采用分集接收技术能够减轻衰落的影响,提高分集增益。     

Comparison of diversity combining techniques for Rayleigh-fadingchannels

Several methods of diversity combining for a Rayleigh-faded channel are evaluated and compared. The methods considered are, for coherent reception, maximal ratio combining (MRC), selection combining (SC), and a generalization of SC, whereby the two (three) signals with the two (three) largest amplitudes are coherently combined. We will call this method second (third) order SC, and denote it SC2 (SC3). Similar techniques are also investigated for noncoherent reception, with equal gain combining (EGC) replacing MRC, and noncoherent versions of SC2 and SC3. Numerical results indicate that SC2 and SC3 significantly enhances the bit-error rate (BER) performance relative to that achievable with SC, and under certain conditions approaches the performance achieved by MRC or EGG. The performance enhancement of SC2 and SC3 is especially noticable for noncoherent reception, where EGC is seen to provide the best performance only for low BER values. In fact, when the BER is 10 ^-3 or greater, SC2 and SC3 performed comparably to EGG, and in some cases performed better than EGC     

采用两条支路分集接收的相关瑞利衰落信道容量

本文研究采用两条支路最大比合并(MRC)或选择合并(SC)分集接收的相关瑞利衰落信道理论容量推导恒定发射功率自适应M进制正交幅度调制(M-QAM)的频谱效率,并将它们与独立同分布瑞利信道理论容量进行比较,其结果对收发信机之间无视距分量路径、接收机上分集天线之间的距离小于半个波长的无线通信系统设计具有指导作用.     

Linear Diversity Analysis for M‐ary Square Quadrature Amplitude Modulation over Nakagami Fading Channels

We derive and analyze the exact closed‐form expression for the average bit error probability (BEP) of M‐ary square quadrature amplitude modulation (QAM) for diversity reception in frequency‐nonselective Nakagami fading. A maximal ratio combining (MRC) diversity technique with independent or correlated fading cases are considered. Numerical results demonstrate error performance improvement with the use of MRC diversity reception. The presented new expressions offer a convenient way to evaluate the performance of M‐ary square QAM with an MRC diversity combiner for various cases of practical interest.     

Average probability of packet error with diversity reception over arbitrarily correlated fading channels

Closed form expressions for the average probability of packet error (PPE) are presented for no diversity, maximum ratio combining (MRC), selection combining (SC) and switch and stay combining (SSC) diversity schemes. The average PPE for the no diversity case is obtained in two alternative expressions assuming arbitrarily correlated Nakagami and Rician fading channels. For the MRC case, L diversity branches are considered and the channel samples are assumed to follow Nakagami distribution and to be arbitrarily correlated in both time and space. For the SC diversity scheme with L diversity branches, two bounds on the average PPE are derived for both slow and fast fading channels. The average PPE in this case is obtained in an infinite integral form for Nakagami channels while it is reduced to a closed form expression for the Rayleigh case. The average PPE is also derived in the case of SSC diversity with dual branches for both slow and fast Rayleigh fading channels. The new formulas are applicable for all modulation schemes where the conditional probability of error has an exponential dependence on the signal‐to‐noise ratio. The average PPE is then used to obtain a modified expression for the throughput for network protocols. In general, the diversity gain exhibits a little diminishing effect as the number of diversity branches increases. In addition, the system is found to be more sensitive to the space correlation than to the time correlation. The effects of different system parameters and diversity schemes are studied and discussed. Specific figures about the system performance are also provided. Copyright © 2004 John Wiley & Sons, Ltd.     

Second-order statistics for diversity-combining techniques inNakagami-fading channels

Exact and closed-form expressions for the level crossing rate and average fade duration are presented for the M branch pure selection combining (PSC), equal gain combining (EGC), and maximal ratio combining (MRC), techniques, assuming independent branches in a Nakagami (1960) environment. The analytical results are thoroughly validated by reducing the general case to some special cases, for which the solutions are known, and by means of simulation for the more general case. The model developed here is general and can be easily applied to other fading statistics (e.g., Rice)     

无线相干光通信空间分集接收合并技术

空间分集接收能补偿大气湍流造成的信道衰落。在给出相干检测分集接收的系统模型和晴朗大气信道模型的基础上,考虑子孔径间信号相关性,分析了等增益合并分集和最大比合并分集的误码率性能,并就中断概率与选择分集进行了比较。分析结果表明,空间分集接收能够明显改善相干光通信系统的性能,并且接收信号间的空间相关性越小分集接收的性能越好,其中最大比合并分集性能相对其他两种合并方式优势明显,选择分集性能最差,但它与等增益合并分集的差距不大,同时选择分集实现相对容易,在工程应用中要综合考虑实现的难易程度和性能。     

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.     

A Unified Capacity Analysis for Wireless Systems With Joint Multiuser Scheduling and Antenna Diversity in Nakagami Fading Channels

A Unified Capacity Analysis for Wireless Systems With Joint Multiuser Scheduling and Antenna Diversity in Nakagami Fading Channels In this paper, we present a cross-layer analytical framework to jointly investigate antenna diversity and multiuser scheduling under the generalized Nakagami fading channels. We derive a unified capacity formula for the multiuser scheduling system with different multiple-input multiple-output antenna schemes, including: 1) selective transmission/selective combining (ST/SC); (2) maximum ratio transmission/maximum ratio combining (MRT/MRC); 3) ST/MRC; and 4) space–time block codes (STBC). Our analytical results lead to the following four observations regarding the interplay of multiuser scheduling and antenna diversity. First, the higher the Nakagami fading parameter, the lower the multiuser diversity gain for all the considered antenna schemes. Second, from the standpoint of multiuser scheduling, the multiple antennas with the ST/SC method can be viewed as virtual users to amplify multiuser diversity order. Third, the boosted array gain of the MRT/MRC scheme can compensate the detrimental impact of the reduced amount of fading gain on multiuser scheduling, thereby resulting in greater capacity than the ST/SC method. Last, employing the STBC scheme together with multiuser diversity may cause capacity loss due to the reduced amount of fading gain, but without the supplement of array gain.     

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.     

Error probability performance of L-branch diversity reception ofMQAM in Rayleigh fading

New exact expressions involving hypergeometric functions are derived for the symbol-error rate (SER) of M-ary quadrature amplitude modulation (MQAM) for L branch diversity reception in Rayleigh fading and additive white Gaussian noise (AWGN). The diversity combining techniques considered are maximum ratio combining (MRC) and selection combining (SC). MRC with identical channels and dissimilar channels are analyzed     

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.     

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.     

Dual MRC diversity reception of TCM-MPSK signals over Nakagamifading channels

Space diversity reception and forward error correction coding are powerful techniques for combating the multipath fading encountered in mobile radio communications. In this Letter, the authors analyse the performance of a dual maximal ratio combining (MRC) diversity system using trellis coded modulation-multiple phase shift keying (TCM-MPSK) on slow, nonselective correlated Nakagami fading channels. An alternative exact derivation is introduced for the pairwise error probability, used in calculating average bit error rate analytical upper bounds