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.     

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.     

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.     

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.     

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     

On the performance and capacity of an asynchronous space-time block-coded MC-CDMA system in the presence of carrier frequency offset

In this paper, the bit-error rate (BER) performance and capacity of asynchronous space-time block-coded (STBC) multicarrier code-division multiple-access (MC-CDMA) systems in the presence of carrier frequency offset (CFO) between the transmitter and receiver oscillators are analyzed. The exact BER expression when using equal gain combining (EGC) and the approximate BER expression when using maximum ratio combining (MRC) are derived. These BER expressions are verified through simulations. Using these derived expressions, the achievable system capacity satisfying a minimum BER requirement can be studied for the two cases when EGC and MRC are used and, hence, it is possible to compare the achievable capacity of STBC MC-CDMA systems with that of MC-CDMA systems. It is concluded that small CFO has an insignificant effect on the BER and capacity of STBC MC-CDMA systems and that this range of CFO is important in transceiver design. Besides, STBC MC-CDMA systems with multiple receive antennas can achieve higher capacity than that of the MC-CDMA systems; this amount can be obtained analytically using the theoretical BER expressions derived.     

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.     

基于空时分组编码的MC-CDMA下行链路合并方案

基于空时分组编码的发射分集技术利用空间和时间分集 ,能有效抗多径 ,增强信道可靠性。将空时分组编码应用到MC -CDMA下行链路中 ,构建了一种新的多载波CDMA系统 (ST -MC -CD MA) ,通过在每个子载波信道中获得空间分集增益来提高系统性能。具体实现时 ,依据传统MC -CDMA信号合并方案 ,提出了ST -MC -CDMA空时译码后相应的四种合并方案。仿真结果验证了这 4种合并方案的优、缺点 ;并进一步证明 :在频率选择性瑞利衰落信道中 ,该系统比采用相同合并方案的传统MC -CDMA有明显的性能改善。     

Spectral efficiency of multicarrier CDMA

We analyze the spectral efficiency (sum-rate per subcarrier) of randomly spread synchronous multicarrier code-division multiple access (MC-CDMA) subject to frequency-selective fading in the asymptotic regime of number of users and bandwidth going to infinity with a constant ratio. Both uplink and downlink are considered, either conditioned on the subcarrier fading coefficients (for nonergodic channels) or unconditioned thereon (for ergodic channels). The following receivers are analyzed: a) jointly optimum receiver, b) linear minimum mean-square error (MMSE) receiver, c) decorrelator, and d) single-user matched filter.     

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。     

Sensitivity to timing errors in EGC and MRC techniques

The effect of imperfect timing is analyzed in equal gain combining (EGC) and maximal ratio combining (MRC) techniques over Rayleigh and Nakagami-m fading channels with binary phase-shift keying modulation. In the case of EGC, the bit-error probability is derived, while in the case of MRC, error rate bounds are presented. Theoretical results are justified by computer simulation. Numerical results demonstrate that both EGC and MRC are fairly sensitive to timing errors, and comparatively, MRC is more sensitive.     

用复合正交换频码进行调制的M—ary MC—CDMA方法

本文提出了一种用复合正交扩频码进行调制的M－ary MC-CDMA方法,在频率选择性慢衰落信道,用等增益合成和最大化率合成分析了系统下行链的性能,并与单扩频码系统进行了比较,最后给出了保护时隙对系统的影响。     

Analytical modelling of multiservice switching networks with multiservice sources and resource management mechanisms

In this paper, we presents an analytical link capacity and outage performance analysis of downlink multiuser diversity (MUD) in multiple-input multiple-output (MIMO) system employing maximal-ratio combining (MRC) with transmit antenna selection (TAS) in the presence of imperfect channel state information (CSI) due to feedback delay over Rayleigh fading channels. The unified achievable analysis is appropriate for MUD–MIMO with TAS/MRC systems in which effective output signal-to-noise ratio (SNR) is specified as highest order statistic of chi-square distribution. Based on this framework, the closed-form channel capacity and outage probability expressions are examined for the MUD–MIMO exploiting TAS/MRC with normalized SNR based scheduling in heterogeneous wireless networks. Further, we derive approximate upper bound capacity as well as capacity at high SNR and low SNR region under delayed feedback CSI. The upper and lower bound of outage probability under delayed feedback CSI is also evaluated. Thereafter the impact of feedback delay and antenna structures with significance on the consideration of MUD on the performance of the system has been analyzed.     

Exact analysis for downlink MC-CDMA in Rayleigh fading channels

In this letter, downlink multicarrier code-division multiple access (MC-CDMA) systems with maximal ratio combining (MRC) in frequency-selective Rayleigh fading channels is considered. An exact bit error rate (BER) is provided based on the characteristic function (CF) and residue calculation method. The BER performance is evaluated in the time domain instead of the frequency domain. This method does not require any assumption regarding the statistical or spectral behavior of multiple access interference (MAI).     

Performance analysis for OFDM-CDMA with joint frequency-time spreading

In this paper, a novel OFDM-CDMA system with joint time-frequency spreading methods is proposed. The average bit error probability of the proposed system using maximum-ratio combining (MRC) is derived for a frequency-selective fading channel and that of conventional MC-CDMA is also presented for comparison. Numerical analysis and simulation results indicate that the proposed system outperforms MC-CDMA system.     

应用于MC-CDMA系统的块最小均方自适应合并技术

提出了一种使用块最小均方自适应滤波器进行信号合并的方案，适用于多载波码分多址（MC-CDMA）系统。在瑞利慢衰落信道下，只需要少量的训练符号就可以最大限度地消除信道噪声干扰和多址接入干扰。仿真结果表明，在一个满负荷的下行链路中，块最小均方自适应合并的性能接近非自适应的最小均方误差合并（MMSEC）；而在轻负荷（由激活用户数衡量）的情况下，性能优于MMSEC。     

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.     

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.     

Frequency acquisition synchronization for multiple antenna systems

In this paper, we consider the problem of frequency acquisition synchronization by using multiple antennas over wireless fading channels. We introduce frequency synchronization with different combining schemes including space diversity and time diversity. Their performance is estimated for a Rayleigh fading channel with an analysis both theoretically and by simulation. We investigate the relationship between the mean squared error (MSE) and the average signal‐to‐noise ratio (SNR) for combining of different blocks and antennas. Both the carrier frequency offset and the sampling frequency offset are estimated when multiple antennas are utilized for signal transmission. The estimation with maximum ratio combining (MRC) scheme is presented in detail, and the estimation with selection combining scheme and equal gain combining scheme are introduced briefly. The simulation results explicitly show that the performance of the frequency acquisition synchronization with MRC scheme is better than that of others and that the MSE at low SNR is not very close to the Cramér–Rao low bound in multiblock combining frequency synchronization. Furthermore, the results address that in order to improve the performance, the total number of receive antennas will be increased exponentially. Copyright © 2013 John Wiley & Sons, Ltd.     

空时编码多载波码分多址MIMO系统下行频率选择性信道盲估计

基于子空间方法的无线信道盲估计由于其算法的固有特性,使得估计结果与实际信道之间存在一个不确定复系数,无法得到无线信道的精确估计。在利用子空间分解方法对空时编码多输入多输出MC-CDMA系统下行频率选择性信道盲估计的基础上,利用发射符号的有限码集特性,将单载波系统下的模糊复系数盲辨识方法推广到多载波多输入多输出系统,从而得到信道的精确估计。Monte-Carlo仿真表明,在信噪比较低的情况下,本方法的信道估计误差仍然较小。