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。     

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.     

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.     

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。     

Carrier Frequency Offset in VSF-OFCDM Systems with Subcarrier Grouping: Analysis,Estimation and Correction

We investigate the effect of carrier frequency offset (CFO) on the performance of downlink variable spreading factor (VSF) orthogonal frequency and code division multiple access (OFCDM) systems when subcarrier grouping is used. An analytic expression of the signal to interference and noise ratio (SINR) is derived for the VSF-OFCDM with CFO for the case of maximal ratio combining (MRC) and equal gain combining (EGC) receivers. Numerical results show that, when the total spreading factor is fixed, a system with higher frequency domain spreading factor is more sensitive to CFO than that with lower frequency domain spreading factor. Also, for high E _b /N _o , EGC has better bit error rate performance than MRC due to the greater interference amplification present in MRC which compounds the effect of the loss of orthogonality. Due to the adverse impact of the CFO on VSF-OFCDM systems, we propose a correction scheme based on the maximum likelihood principle. We then use a gradient algorithm to estimate and minimize the effect of CFO in a tracking mode. Our results show that the BER performance in the low SINR environment can be improved significantly with few number of iterations for different spreading factors.     

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     

On the Effect of Imperfect Cophasing in MRC and EGC Receivers Over Correlated Weibull Fading

This paper presents a comparative analysis of dual-branch maximal-ratio combining (MRC) and equal-gain combining (EGC) receivers with coherent modulations over correlated Weibull fading channels. The numerical and simulations results show the influence of imperfect cophasing, branch unbalancing and correlation on the error performance. It is interestingly shown that EGC has lower irreducible error floor than MRC in the presence of incoherent combining, while the higher value of the correlation coefficient results to lower irreducible error floor. Furthermore, the unbalance parameter has practically no influence on the irreducible error floor.     

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     

Outage probability of diversity systems over generalized fading channels

Outage probability is an important performance measure of communication systems operating over fading channels. Relying on a simple and accurate algorithm for the numerical inversion of the Laplace transforms of cumulative distribution functions, we develop a moment generating function-based numerical technique for the outage probability evaluation of maximal-ratio combining (MRC) and postdetection equal-gain combining (EGC) in generalized fading channels for which the fading in each diversity path need not be independent, identically distributed, nor even distributed according to the same family of distributions. The method is then extended to coherent EGC but only for the case of Nakagami-m fading channels. The mathematical formalism is illustrated by applying the method to some selected numerical examples of interest showing the impact of the power delay profile and the fading correlation on the outage probability of MRC and EGC systems.     

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)     

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.     

Analytical level crossing rates and average fade durations for diversity techniques in Nakagami fading channels

The level crossing rates (LCRs) and average fade durations (AFDs) of a fading channel find diverse applications in the evaluation and design of wireless communication systems. Analytical expressions for these quantities are available in the literature for certain diversity reception techniques, but are generally limited to the Rayleigh fading channel, with few exceptions. Moreover, the methods employed are usually specific to a certain channel/diversity pair, and thus cannot be applied to all cases of interest. Using a unified methodology, we derive analytical expressions for the LCRs and AFDs for three diversity reception techniques and a general Nakagami (1960) fading channel. We provide novel analytical expressions for selection combining (SC) and equal-gain combining (EGC), and rederive in a more general manner the case of maximal-ratio combining (MRC). It is shown that our general results reduce to some specific cases previously published. These results are used to examine the effects of the diversity technique, the number of receiving branches and severity of the fading on the concerned quantities. It is observed that as the Nakagami m-parameter and the diversity order increase, the behavior of the combined received envelope for EGC follows closely the one for MRC, and distances itself from SC.     

弱湍流信道无线光通信分集接收合并技术

为了克服大气湍流所造成的信道衰落效应,分析了在弱湍流信道模型下基于强度检测脉冲位置调制方式的自由空间光通信空间（FSO）分集接收系统模型,推导了无分集系统的误时隙率计算公式。然后以此作为参考,在独立同分布的情况下,采用数值仿真的方法,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）的误时隙率性能。结果表明,3种合并技术中,误时隙率性能改善最优的是MRC,其次是EGC,而SC的改善性能最差,但是SC实现相对容易。利用分集接收合并技术可以有效改善FSO系统的性能,并且具有较好的抗大气信道衰落能力,在无线光通信中将有一定的应用前景。     

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.      

Postdetection diversity receiver for DAPSK signals on the Rayleigh and Rician-fading channel

In this paper, the optimum decision boundaries for (N, M) differential amplitude phase-shift keying on the Rayleigh-fading channel are analyzed. A postdetection maximal ratio combining (MRC) and weighted maximal ratio combining (WMRC) diversity receivers are proposed. In the Rayleigh-fading channel, assuming a high signal-to-noise ratio and a small normalized Doppler frequency, the analytical optimum decision boundaries are obtained. In addition, it is shown that an outer optimum decision boundary is the inverse of the inner optimum decision boundary. In the proposed MRC receiver, the decision at each branch is made based on the minimum distance criterion. The performance of the MRC receiver is analyzed, in terms of the union bound for bit error probability. The proposed WMRC receiver assigns weighting factors to the decision variable at each branch, based on the optimum decision boundaries. The performance of the WMRC is investigated through computer simulation and compared with those of MRC and equal gain combining (EGC). From the results, the performances of MRC and WMRC are found to be better than those of the EGC receiver on both the Rayleigh- and Rician-fading channels. It is also found that the performance improvement of WMRC over MRC is more pronounced as the number of diversity branches increases     

Research on diversity receive technology for wireless optical communication using PPM in weak turbulence atmosphere channel

In order to mitigate atmospheric turbulence, the free space optical （FSO） system model with spatial diversity is ana- lyzed based on intensity detection pulse position modulation （PPM） in the weak turbulence atmosphere. The slot error rate （SER） calculating formula of the system without diversity is derived under pulse position modulation firstly. Then as a benchmark, independent of identical distribution, the average slot error rates of the three linear combining tech- nologies, which are the maximal ratio combining （MRC）, equal gain combining （EGC） and selection combining （SelC）, are compared. Simulation results show that the performance of system is the best improved by MRC, followed by EGC, and is poor by SelC, but SelC is simpler and more convenient. Spatial diversity is efficient to improve the performance and has strong ability on resistance to atmospheric channel decline. The above scheme is more suitable for optical wire- less communication systems.     

Diversity combining for coherent and differential M-PSK in fading and class-A impulsive noise

In this paper, optimum and suboptimum diversity combining schemes for coherent and differential M-ary phase-shift keying (M-PSK) transmission impaired by general Ricean fading and impulsive Class-A noise are derived and analyzed. The proposed suboptimum coherent combining (SCC) and suboptimum noncoherent combining (SNC) schemes yield similar performance as the corresponding optimum combining schemes but require a lower computational complexity. In addition, the novel SCC and SNC strategies achieve large performance gains over conventional maximum ratio combining (MRC) and equal gain combining (EGC), respectively. For MRC and EGC, respectively, we also provide a performance analysis for coherent and differential M-PSK transmissions over general Ricean fading channels with Class-A noise. Furthermore, tight performance upper bounds for the proposed optimum and suboptimum combining schemes are derived.     

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