General Order Selection Combining for Nakagami and Weibull Fading Channels

In this paper, some analytical results for general order selection (GOS) over independent but not necessarily identically distributed (i.n.d.) Weibull and Nakagami fading channels are presented. The Weibull fading parameters are assumed to be equal whereas the Nakagami fading parameters are assumed to be integer-valued. It is shown that the pdf of the q-th order statistic can be expressed as a linear combination of Weibull and Nakagami pdf's respectively. Closed-form expressions for the moment generating functions and general moments are derived. In addition, exact closed-form expressions for the symbol error rate are obtained for a number of modulation schemes. Numerical results show that for the same average channel gains, the performance on i.n.d. channels may be better or worse than on i.i.d. channels.     

Nakagami衰落环境下合并接收的平均错误概率

本文对最大比值合并,等增益合并及选择性合并等合并技术进行了归纳与总结,给出了各种调制方法在Nakagami信道下的错误概率的精确表达式或近似表达式。同时还给出了相应的计算方法。对这类问题研究中的主要理论工具进行了总结与分析。本文最后还讨论了这方面值得进一步研究的一些问题。     

选择性放大传送协同通信在Nakagami信道中的性能分析

该文根据两个统计独立非负随机变量的调和平均值的概率密度函数在零点的变化特性,分析了选择性放大传送协同协议在Nakagami衰落信道中的性能,得出了高信噪比时系统误符号率的闭合表达式。理论分析和数值仿真结果表明,在Nakagami信道中选择性放大传送协同协议可获得和传统放大传送协同协议一样的分集阶数,并且具有更优的误符号率性能。     

Error Probability Distribution and Density Functions for Weibull Fading Channels With and Without Diversity Combining

In this letter, a detailed theoretical analysis of probability distribution and density functions of probability of error in a wireless system is considered. Closed form expressions for distribution and density functions of the probability of error are derived for Weibull fading channels for the cases of (i) No Diversity (ND), (ii) Selection Combining (SC) diversity, and (iii) Switch and Stay Combining (SSC) diversity. Numerical results are plotted and discussed in detail for the various cases.     

Adaptive Modulation over Nakagami Fading Channels

We first study the capacity of Nakagami multipath fading (NMF) channels with an average power constraint for three power and rate adaptation policies. We obtain closed-form solutions for NMF channel capacity for each power and rate adaptation strategy. Results show that rate adaptation is the key to increasing link spectral efficiency. We then analyze the performance of practical constant-power variable-rate M-QAM schemes over NMF channels. We obtain closed-form expressions for the outage probability, spectral efficiency and average bit-error-rate (BER) assuming perfect channel estimation and negligible time delay between channel estimation and signal set adaptation. We also analyze the impact of time delay on the BER of adaptive M-QAM.     

Level Crossing Rate and Average Fade Duration of Dual Selection Combining With Cochannel Interference and Nakagami Fading

This letter provides closed-form expressions for the outage probability, the average level crossing rate (LCR) and the average fade duration (AFD) of a dual diversity selection combining (SC) system exposed to the combined influence of the cochannel interference (CCI) and the thermal noise (AWGN) in Nakagami fading channel. The branch selection is based on the desired signal power SC algorithm with all input signals assumed to be independent, while the powers of the desired signals in all diversity branches are mutually equal but distinct from the power of the interference signals. The analytical results reduce to known solutions in the cases of an interference-limited system in Rayleigh fading and an AWGN-limited system in Nakagami fading. The average LCR is determined by an original approach that does not require explicit knowledge of the joint PDF of the envelope and its time derivative, which also paves the way for similar analysis of other diversity systems.     

Capacity and Error Probability for Maximal Ratio Combining Reception over Correlated Nakagami Fading Channels

In this paper, the capacity and error probability of maximal ratio combining (MRC) reception are considered for different modulation schemes over correlated Nakagami fading channels. Based on an equivalent scalar additive white Gaussian noise (AWGN) channel, we derive the characteristic function (CF) and the probability density function (PDF) of the signal to noise ratio for MRC reception over Nakagami fading channels. Using these CF and PDF results, closed form error probability and capacity expressions are obtained for PSK, PAM and QAM modulation. Wei Li received his Ph.D. degree in Electrical and Computer Engineering from the University of Victoria in 2004. He is now a Post-doctoral Research Fellow in the Department of Electrical and Computer Engineering at the University of Victoria. He is a Member of the IEEE. His research interests include ultra-wideband system, spread spectrum communications, diversity for wireless communications, and cellular communication systems. Hao Zhang was born in Jiangsu, China, in 1975. He received his Bachelor Degree in Telecom Engineering and Industrial Management from Shanghai Jiaotong University, China in 1994, his MBA from New York Institute of Technology, USA in 2001, and his Ph.D. in Electrical and Computer Engineering from the University of Victoria, Canada in 2004. His research interests include ultra-wideband radio systems, MIMO wireless systems, and spectrum communications. From 1994 to 1997, he was the Assistant President of ICO(China) Global Communication Company. He was the Founder and CEO of Beijing Parco Co., Ltd. from 1998 to 2000. In 2000, he joined Microsoft Canada as a Software Engineer, and was Chief Engineer at Dream Access Information Technology, Canada from 2001 to 2002. He is currently an Adjunct Assistant Professor in the Department of Electrical and Computer Engineering at the University of Victoria. T. Aaron Gulliver received the Ph.D. degree in Electrical and Computer Engineering from the University of Victoria, Victoria, BC, Canada in 1989. From 1989 to 1991 he was employed as a Defence Scientist at Defence Research Establishment Ottawa, Ottawa, ON, Canada. He has held academic positions at Carleton University, Ottawa, and the University of Canterbury, Christchurch, New Zealand. He joined the University of Victoria in 1999 and is a Professor in the Department of Electrical and Computer Engineering. He is a Senior Member of the IEEE and a member of the Association of Professional Engineers of Ontario, Canada. In 2002, he became a Fellow of the Engineering Institute of Canada. His research interests include information theory and communication theory, algebraic coding theory, cryptography, construction of optimal codes, turbo codes, spread spectrum communications, space-time coding and ultra wideband communications.     

On Joint Order Statistics in Correlated Nakagami Fading Channels

In this letter, the joint probability density function (pdf) of the order statistics for a set of correlated Nakagami-m fading channels is derived. This result is useful in analyzing the performance of a variety of diversity schemes which involve branch selection. The derivation also yields a computationally efficient method for obtaining the marginal pdf of the p-th order statistic for a set of correlated Nakagami-m fading channels.     

Reception Through Nakagami Fading Multipath Channels with Random Delays

The Nakagami fading distribution is shown to fit empirical results more generally than other distributions. A statistical model for a noisy, Nakagami fading multipath channel is given, following Turin's delay-line model. Optimal receivers are derived for two states of knowledge of the channel-known path delays and random path delays. Upper bounds on the probability of error are computed, for binary, equal-energy, equiprobable signals, which are uniformly orthogonal and have equal, triangular, autocorrelation moduli. Results are graphically displayed and show the dependence of error probability on number of paths, amount of fading and spread of path delays.     

空时码在Nakagami衰落信道下性能分析

基于Alamouti提出的BPSK调制下空时分组码在Rayleigh衰落信道中的简单分集方案。推导出多发射和多接收天线系统中正交空时分组码在Nakagami衰落信道的BPSK调制下的比特差错率的最小距离球界,并推广到在高阶调制下衰落信道中系统符号差错率的性能。仿真分析和比较了空时分组码的多天线系统中发射和接收天线分集增益,以及信道相关参数的变化对系统误比特性能的影响。     

Effect of Channel Estimation Errors on M -QAM With MRC and EGC in Nakagami Fading Channels

We study the effect of imperfect channel estimation (ICE) on the error probability performance of M-level quadrature amplitude modulation ( M-QAM) with maximal-ratio combining and equal-gain combining diversity formats in Nakagami fading channels. We provide a novel formulation of the bit-error rate (BER) of M-QAM with ICE in terms of the signal constellation-dependent effective signal-to-noise ratios (SNRs) or amplitudes, which allows us to derive the general, accurate, and easy-to-evaluate BER formulas for square and rectangular diversity M-QAM with channel estimation errors. Our result shows that the performance loss caused by ICE may be manifested by the signal decision space distortion and a scaling of the effective SNR. Using our analytical result, we evaluate the performance of M-QAM with pilot-symbol assisted modulation and present some insightful findings     

Diversity Analysis of Peaky FSK Signaling in Fading Channels

Error performance of noncoherent detection of on-off frequency shift keying (OOFSK) modulation over fading channels is analyzed when the receiver is equipped with multiple antennas. The analysis is conducted for two cases: 1) the case in which the receiver has the channel distribution knowledge only; and 2) the case in which the receiver perfectly knows the fading magnitudes. For both cases, the maximum a posteriori probability (MAP) detection rule is derived and analytical probability of error expressions are obtained. Numerical and simulation results indicate that for sufficiently low duty cycle values, lower error probabilities with respect to FSK signaling are achieved. Equivalently, when compared to FSK modulation, OOFSK with low duty cycle requires less energy to achieve the same probability of error, which renders this modulation a more energy efficient transmission technique. Also, through numerical results, the impact of number of antennas, antenna correlation, duty cycle values, and unknown channel fading on the performance are investigated.     

Scaled Selection Combining for Adaptive Decode-and-Forward Relaying in Dissimilar Rayleigh Fading Channels

This paper enhances the conventional scaled selection combiner (SSC) for decode-and-forward (DF) relay networks using adaptive M-ary quadrature amplitude modulation (M-QAM) to improve the spectral efficiency. Compared with the conventional SSC designed for the combining of identically distributed diversity branches using the same modulation level, the improved SSC allows all diversity branches to choose different modulation levels according to the dissimilar channel conditions. Different scale factors are used for all diversity branches to reflect not only the performance degradation caused by possible erroneous relaying but also different error-resistance abilities of different levels QAM. We derive the bit-error-rate (BER) expressions for DF relay networks using SSC in a recursive way, with all channels conforming to independently and non-identically distributed (i.ni.d.) Rayleigh fading. Newton’s method is employed to obtain the numerical solutions of the optimal scale factors minimizing the BER, and the approximations of the optimal scale factors are derived in closed form for high SNRs. Theoretical analysis and simulation results show that the improved SSC can effectively combine diversity branches with different modulation levels, and for a DF cooperative network with N relay nodes, SSC achieves the full diversity gain of N+1 if for each branch its source-to-relay SNR is proportional to the (N+1)th power of its relay-to-destination SNR.     

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     

Analysis of Transmit Antenna Selection/Maximal-Ratio Combining in Rayleigh Fading Channels

In this paper, we investigate a multiple-input-multiple-output (MIMO) scheme combining transmit antenna selection and receiver maximal-ratio combining (the TAS/MRC scheme). In this scheme, a single transmit antenna, which maximizes the total received signal power at the receiver, is selected for uncoded transmission. The closed-form outage probability of the system with transmit antenna selection is presented. The bit error rate (BER) of the TAS/MRC scheme is derived for binary phase-shift keying (BPSK) in flat Rayleigh fading channels. The BER analysis demonstrates that the TAS/MRC scheme can achieve a full diversity order at high signal-to-noise ratios (SNRs), as if all the transmit antennas were used. The average SNR gain of the TAS/MRC is quantified and compared with those of uncoded receiver MRC and space-time block codes (STBCs). The analytical results are verified by simulation. It is shown that the TAS/MRC scheme outperforms some more complex space-time codes of the same spectral efficiency. The cost of the improved performance is a low-rate feedback channel. We also show that channel estimation errors based on pilot symbols have no impact on the diversity order over quasi-static fading channels.     

SER of M-ary NCFSK with S + N Selection Combining in Nakagami Fading for Integer m

The performance of M-ary orthogonal noncoherent frequency-shift keying (NCFSK) with N branch signal-plus-noise (S + N) selection combining (SC) in Nakagami-m fading (m, integer) is studied. Both independent, identically distributed (i.i.d) and independent, nonidentically distributed (i.n.d) diversity branches are considered and two S + N SC receiver structures are examined. The performances of the S + N SC receivers are compared to those of classical SC and square-law combining (SLC) receivers. The effects of modulation order, fading parameter and the number of diversity branches on the performance of S + N SC are compared to the effects on the performances of classical SC and SLC. For example, it is shown that in an i.n.d fading channel, the value of signal-to-noise ratio (SNR) at which the error rate curves of classical SC and S + N SC cross, decreases as the modulation order, M, increases. Our results indicate that in i.n.d fading channels classical SC outperforms S + N SC for small ranges of SNR, while for moderate to large SNR values S + N SC has superior performance over classical SC. It is also shown that increasing the diversity order will increase the performance gap of S 4N SC over classical SC and over SLC in both i.i.d and i.n.d Nakagami-m fading channels     

Spectrum Efficiency of Weibull Fading Channels for Various Adaptation Policies with and Without Diversity Combining

In this paper, closed-form expressions for the capacities per unit bandwidth (spectrum efficiency) of Weibull fading channels are derived and plotted for (a) Switch and Stay Combining diversity case and (b) no diversity case for adaptation policies like: (i) Optimal Power and Rate Adaptation policy, (ii) Optimal Rate Adaptation with constant transmit power policy, (iii) Channel Inversion with Fixed Rate policy, and (iv) Truncated Channel Inversion policy. In addition, spectrum efficiency expressions for asymptotic approximations, upper bounds, approximations for low and high SNR cases are derived for the cases with and without diversity. The probability density function of capacity, and the complementary cumulative distribution function of capacity are derived and plotted from the moment generating function for the cases with and without diversity. Optimal power and rate adaptation policy provides the highest capacity and optimal rate adaptation with constant transmit power policy provides the highest capacity penalty over other policies for the no diversity and SSC diversity cases. Numerical results for spectrum efficiency are plotted for all adaptation policies with and without diversity.     

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.     

自适应Turbo-QAM编码调制及其在 平坦Nakagami衰落信道的吞吐量性能

本文提出了一种通用的自适应编码调制系统吞吐量性能分析方法.基于各固定编码调制方式的误码率(BER)性能,使每种编码调制方案对应于一个信道平均信噪比(SNR)范围,再应用拉格朗日函数法得到使自适应编码调制系统吞吐量性能最大的信噪比转换门限,可得到系统的平均吞吐量性能.数值分析结果表明,相对于自适应M进制正交幅度调制(MQAM),自适应Turbo编码MQAM系统吞吐量性能有显著提高,并且该性能受瞬时误码率要求的影响较小.Nakagami信道中,在相同平均信道信噪比条件下,随着m的增大,系统吞吐量性能提高缓慢.     

Nakagami衰落信道上MIMO WCDMA系统的MQAM性能分析

日益增长的无线业务需求要求提高衰落信道上无线通信的频谱利用率。本文利用Q2(x)的另一种数学表达式和矩生成函数推导了Nakagami-m衰落信道上多输入多输出(MI-MO)WCDMA系统采用M进制正交幅度调制(MQAM)的平均误符号率(ASER)表达式,分析框架可以推广到开环和闭环系统发射和接收天线为任意数目的应用场合,研究了存在多址干扰下MIMOWCDMA系统的平均误符号率性能,数值计算结果表明组合发送分集和接收分集可以显著改善系统的性能。