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.     

The performance of MT-CDMA system in the presence of carrier frequency offset

In this letter, the sensitivity of an uplink Multi-Tone Code-Division Multiple Access （MT-CDMA） system to the Carrier Frequency Offset （CFO） is investigated. The analytical expression for the Bit Error Rate （BER） of uplink MT-CDMA in the presence of CFO is derived in a multipath Rayleigh fading channel which is verified through simulations. Both Maximal Ratio Combining （MRC） and Equal Gain Combining （EGC） are considered in combining multipath signals in the analysis. It is found that the BER performance can be improved with the number of multipath increasing in the presence of CFO.     

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.     

Accurate bit-error rate evaluation for synchronous MC-CDMA over Nakagami-m-fading channels using moment generating functions

In the bit-error rate (BER) analysis of code-division multiple-access (CDMA) systems, a Gaussian approximation is widely used to tackle the multiple access interference (MAI), although it does not always offer satisfactory accuracy. This paper investigates the BER performance of synchronous multicarrier (MC) CDMA systems over Nakagami-m-fading channels in a different way. We present an accurate and unified BER analysis for synchronous MC-CDMA systems. To facilitate our analysis, we assume a synchronous uplink, whose BER performance can be intuitively viewed as a lower BER bound of the more realistic asynchronous MC-CDMA. The basic idea is that, by using the Gauss-Chebyshev quadrature (GCQ) rule to perform inverse Laplace transform, an accurate BER can be numerically obtained from the moment generating function (MAG) of the output decision variable at a receiver, without any assumption about the MAI distribution. First, signals on all subcarriers of MC-CDMA systems are assumed to experience independent fading. Two standard diversity combining techniques, equal gain combining (EGC) and maximal ratio combining (MRC), are employed. The BER performance in both downlink and synchronous uplink is analyzed. We then consider a more general system model, in which signals on different subcarriers undergo correlated fading. The asymptotic (error floor) performance of downlink MC-CDMA with MRC is studied. In particular, we investigate the effects of spreading sequences and the delay spread of the channel on the system performance. Numerical examples are provided to show the main results of this paper. The accuracy of the GCQ and MGF based solution is verified by different approaches such as Monte Carlo integration and the exact residue method. In addition, the accuracy of the commonly used Gaussian approximation is also examined.     

空时分组码多音调制CDMA系统性能分析

提出了一种空时分组码（STBC,space-time block-code）多音调制CDMA（MT-CDMA）系统结构。对系统上行链路误码率（BER）性能进行了理论分析,推导出了在多径衰落信道下采用最大比合并时系统的BER表达式,并通过计算机仿真进行了验证。数值结果表明由于联合的空时与多径分集增益,使系统的BER性能、差错地板和容量都得到了显著地改善。     

BER of MC-CDMA systems with MRC in correlated Nakagami-m fading

Based on the characteristic function of the sum of correlated gamma random variables and an alternative expression of Q-function, a simple bit error rate (BER) expression is derived for the multicarrier code division multiple access (MC-CDMA) systems with maximal ratio combining (MRC) in correlated Nakagami-m fading channels. The much simpler approximate average BER expression using exponential approximation of the Q-function is also derived.     

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。     

A MC-CDMA system based on orthogonal filter banks of wavelet transforms and partial combining

Multi Carrier Code Division Multiple Access (MC-CDMA) is an appropriate modulation technique for high data rates. In this modulation scheme, employing of combining techniques are unavoidable for restoring orthogonality between different user signals. In this paper, the combining techniques of a MC-CDMA based on wavelet transform are studied. The partial combining of the wavelet based MC-CDMA system is suggested and its performance is compared with the maximum ratio combining (MRC), equal gain combining (EGC), orthogonality restoring combining (ORC) and the minimum mean square error (MMSE) techniques. Orthogonal filter banks of the wavelet transforms provide orthogonality between the wavelets and scaling functions, subcarriers and spreading sequences. Therefore, they provide new dimensions in combatting multipath fading, inter carrier interference (ICI) and narrowband interference in MC-CDMA systems. Furthermore, analysis of partial combining shows that coefficients of this technique can be computed in a simple manner. Simulations results indicate that the bit error rate (BER) performance of the proposed scheme is almost comparable with the MMSE combining scheme and the proposed system has a proper performance in terms of BER versus the signal to noise ratio (SNR) in frequency selective fading channels.     

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     

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.     

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.     

BER performance evaluation for MC-CDMA systems in Nakagami-m fading

Based on the approximation of the sum of several Nakagami-m variables and an alternative expression of the Q-function, an efficient bit error rate (BER) expression is described. The closed BER form is applicable to multicarrier code-division multiple-access (MC-CDMA) systems with equal gain combining (EGC) in frequency selective Nakagami (1960) fading channels.     

最大比合并分集接收性能的新的分析方法

对Rayleigh衰落信道中最大比合并分集系统的性能进行了分析.基于泊松分布,提出了一种新的误比特率计算式,并提出了一个新的性能上界,去除了级数和运算,进一步简化了性能分析.数值分析表明,提出的误码率计算式与原分析式一致,且性能上界与误码率的准确值近乎重合.运用仿真对理论分析进行了验证,数值和仿真结果表明,提出的性能分析式简单准确有效,可更为迅速的评估最大比分集合并系统的性能.     

MC-CDMA系统迭代检测中的均衡

本文研究在同步MC- CDMA系统中的上行链路中的均衡技术。接收机采用多用户检测和译码相结合的迭代检测技术;其中,串行干扰消除用于多用户检测,一个SISO译码器用于信道译码。仿真给出在不同的均衡策略下如ORC、EGC、MRC、MMSE,迭代检测接收机的性能     

Capacity of multiuser diversity systems with adaptive transmission and different MIMO schemes

In this paper, we present a comprehensive capacity analysis of the downlink of multiuser diversity (MD) systems with adaptive transmission over Rayleigh fading channels. First, the exact capacity of the single‐input single‐output (SISO) systems with MD and adaptive transmission technique is derived. The optimal power allocation scheme for such a system is shown to be a water‐filling algorithm. Next, we derive the exact closed‐form capacity expressions for different multiple‐input multiple‐output (MIMO) schemes, including the selective combining (SC), maximum ratio combining (MRC) and space‐time block codes (STBC). In order to avoid the cumbersome numerical root finding techniques in solving the optimal cutoff SNR level below which the channel is not used, we also provide the approximate expressions for the cutoff level. For the MD MIMO systems, it is observed that the optimal power allocation strategy is to focus transmit power on a single transmit antenna (e.g. Tx‐MRC/Rx‐MRC scheme) or selecting the best transmit antennas (e.g. Tx‐SC/Rx‐MRC scheme). Copyright © 2007 John Wiley & Sons, Ltd.     

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.     

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     

Error rates of M-ary signals with. Multichannel reception in Nakagami-m fading channels

In this letter, we present closed. form expressions for the exact average symbol-error rate (SER) of M-ary modulations with multichannel reception over Nakagami-m fading channels. The derived expressions extend already available results for the nondiversity case, to maximal-ratio combining-(MRC) and postdetection equal-gain combining (EGC) diversity systems. The average SERs are given in terms of Lauricella's multivariate hypergeometric function F/sub D//sup (n)/. This function exhibits a finite integral representation that can be used for fast and accurate numerical computation of the derived expressions.     

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     

Performance analysis of MIMO systems with multiuser diversity

In this paper, we present a comprehensive performance analysis for multiple‐input multiple‐output (MIMO) systems with multiuser diversity over Rayleigh fading channels. We derive exact closed‐form expressions of the outage probability and the average bit error rate (BER) for different MIMO schemes, including the selective combining (SC), maximum ratio combining (MRC) and space‐time block codes (STBC). We also provide the explicit upper bounds on the BER performance. Finally, the mathematical formalism is verified by numeric results that study the interaction between the antenna diversity and the multiuser diversity. It is observed that the system performance is deteriorated as the number of transmit antennas increases in multiuser scenario, which is unlike the case in single‐user systems. Copyright © 2007 John Wiley & Sons, Ltd.