Statistical Models for Fading and Shadowed Fading Channels in Wireless Systems: A Pedagogical Perspective

A unified analysis of statistical models for describing fading, shadowing, and shadowed fading channels is presented from a pedagogical viewpoint. The different probability density functions such the Rayleigh, Nakagami, gamma, generalized gamma, Weibull, lognormal, Nakagami-lognormal, K distribution, generalized K distribution, and Nakagami inverse Gaussian distribution are presented and the relationships among them are detailed. These density functions are compared in terms of two quantitative measures, namely the amount of fading and outage probability. A general approach to fading and shadowed fading channels using a cluster based approach is also presented to link several of the distributions. It is expected that this overview will be very helpful to students and educators who are engaged in the study of wireless systems and the adverse impact of fading and shadowing in wireless data transmission.     

Novel Approach for Modeling Wireless Fading Channels Using a Finite State Markov Chain

Empirical modeling of wireless fading channels using common schemes such as autoregression and the finite state Markov chain (FSMC) is investigated. The conceptual background of both channel structures and the establishment of their mutual dependence in a confined manner are presented. The novel contribution lies in the proposal of a new approach for deriving the state transition probabilities borrowed from economic disciplines, which has not been studied so far with respect to the modeling of FSMC wireless fading channels. The proposed approach is based on equal portioning of the received signal‐to‐noise ratio, realized by using an alternative probability construction that was initially highlighted by Tauchen. The associated statistical procedure shows that a first‐order FSMC with a limited number of channel states can satisfactorily approximate fading. The computational overheads of the proposed technique are analyzed and proven to be less demanding compared to the conventional FSMC approach based on the level crossing rate. Simulations confirm the analytical results and promising performance of the new channel model based on the Tauchen approach without extra complexity costs.     

无线衰落信道中H.264视频流的可靠传输

本文提出了一种无线衰落信道中进行H.264视频传输的不等差错保护方案.这种方案通过对视频流的不同重要性的部分进行不同码率的删余卷积信道编码和一种特殊的重传机制来实现不等差错保护机制.仿真结果显示,该方案可以有效改善视频传输的性能,提高视频传输的鲁棒性.     

噪声功率时变的瑞利慢衰落信道有限状态Markov模型

对衰落信道的准确建模对于自适应无线通信、认知无线电等应用中的信道预测具有重要意义。针对噪声功率存在时变特性的无线通信应用环境,提出了一种新的瑞利衰落信道的有限状态Markov模型。通过将接收信号的衰落电平进行离散化处理,建立了衰落电平区间与Markov模型状态之间的一一对应关系,推导了门限电平与状态转移概率和状态分布概率之间的理论关系式,并在此基础上提出了一种易于实现的基于等概率的信道模型。理论分析与仿真结果表明:在噪声功率时变的条件下,已有的基于信噪比的模型失效,而该模型能准确反映信道的衰落特性,最大相对误差小于7%。      

Turbo乘积码在衰落信道中的应用

基于Turbo乘积码的编译码原理,利用Matlab仿真工具,对以(64,57,4)扩展汉明码为子码的Turbo乘积码进行迭代次数、量化比特数等不同参数的性能仿真,根据仿真结果选取最佳的设计参数,同时通过仿真给出了Turbo乘积码在衰落信道中的应用效果。结合Matlab仿真,在Quartus环境中完成编译码算法的硬件设计与调试,并将其应用到无线通信调制解调器中。测试结果表明,Turbo乘积码显著改善了调制解调器在衰落信道中的误码性能。     

Performance of a Predetection EGC Receiver in Hoyt Fading Channels for Arbitrary Number of Branches

Simple and accurate expressions for the performance of an L branch equal gain combining receiver in independent Hoyt fading channels are presented. Using an approximate but highly accurate probability density function of the sum of Hoyt random variables, expressions for the average bit error rate for binary, coherent and noncoherent modulations have been obtained. The effect of the number of diversity branches on the normalized average output SNR is examined. The results have been verified against available results.     

MIMO-OFDM系统无线衰落信道容量分析

推导了MIMO-OFDM系统在衰落信道下的各态历经容量、最优发送策略、使用等功率分配时的容量上界以及相对于单天线OFDM系统的容量增益。结果表明：天线数和平均接收信噪比是决定MIMO-OFDM系统信道容量的关键因素。天线数越多或者接收信噪比越大,信道的容量越大,信道容量几乎不受多径时延扩展的影响。慢衰落信道下的最大信道容量可以使用空-频两维注水算法得到,当接收信噪比足够大时,最大信道容量也可以用平均分配发送功率的方法逼近。     

Statistical Modeling and Analysis of Mobile-to-Mobile Fading Channels in Cooperative Networks Under Line-of-Sight Conditions

Recently, mobile-to-mobile (M2M) cooperative network technology has gained considerable attention for its promise of enhanced system performance with increased mobility support. As this is a new research field, little is known about the statistical properties of M2M fading channels in cooperative networks. So far, M2M fading channels have mainly been modeled under the assumption of non-line-of-sight (NLOS) conditions. In this paper, we propose a new model for M2M fading channels in amplify-and-forward relay links, where it is assumed that a line-of-sight (LOS) component exists in the direct link between the source mobile station and the destination mobile station. Analytical expressions will be derived for the main statistical quantities of the channel envelope, such as the mean value, variance, probability density function (PDF), level-crossing rate (LCR), and average duration of fades (ADF) as well as the channel phase. Our results show that the statistical properties of the proposed M2M channel are quite different from those of double Rayleigh and double Rice channels. In addition, a high-performance channel simulator will be presented for the new M2M channel model. The developed channel simulator is used to confirm the correctness of all obtained theoretical results by simulations.     

The Criterions with LCR and AFD of Dual-Branch SC Diversity over Specified Wireless Radio Fading Channels

In this paper we proposed the results of average LCR (level crossing rate) and AFD (average fading duration) criterions applied to evaluate the performance of dual-branch SC (selection combining) reception in the specified fading channels characterized as statistical distributions with correlated-Rayleigh and correlated-Rice models. Moreover, in order to unify and clarify the criterions of performance formulas with average LCR and AFD for SC diversity over different kinds of fading models, include such as Rayleigh, Rice, Nakagami-m, and Weibull distributions etc., almost all of the ever researched and published results from discussing about the LCR and AFD of SC diversity are comprehensively collected in this report. On the other hand, for the purpose of comparison, there are a large number of LCR and AFD performance formulas for SC diversity and the generalized fading statistic models are extracted and tabulated together, in which the cases of correlated and independent proprieties between diversity branches are taken into consideration too (some of the formulas are illustrated by the assumption of dual-branch SC diversity).

Performance of a Multicarrier CDMA System with Rayleigh Fading Multipath Channels

This paper examines the performance of a multicarrier CDMA system in a Rayleigh fading channel without a RAKE receiver. Since the multicarrier technique is a diversity reception technique used in the frequency domain, the signal is transmitted at different frequency bands and undergoes different fading. The superimposed signal of the multipath components after going through the mobile channel will be processed by an Fourier Transform to enter the frequency domain, where the time delays in various paths are converted to the phase shifts in the compound signal. In this paper, we use sounding bits to extract the characteristics of the mobile channel and to partly remove the multipath effect. From the simulation, it is found that the multicarrier technique is simpler than the technique used in the single carrier system with a RAKE receiver while producing a better performance than that of the RAKE receiver.     

Packet-Based Modeling of Reed–Solomon Block-Coded Correlated Fading Channels Via a Markov Finite Queue Model

We consider the transmission of a Reed–Solomon (RS) code over a binary modulated time-correlated flat Rician fading channel with hard-decision demodulation. We define a binary packet (symbol) error sequence that indicates whether an RS symbol is successfully transmitted across the discrete (fading) channel whose input enters the modulator and whose output exits the demodulator. We then approximate the packet error sequence of the discrete channel (DC) using the recently developed queue-based channel (QBC), which is a simple finite-state Markov channel model with $M$th-order Markovian additive noise. In other words, we use the QBC to model the binary DC at the packet level. We propose a general framework for determining the probability of codeword error (PCE) for QBC models. We evaluate the modeling accuracy by comparing the simulated PCE for the DC with the numerically evaluated PCE for the QBC. Modeling results identify accurate low-order QBC models for a wide range of fading conditions and reveal that modeling the DC at the packet level is an efficient tool for nonbinary coding performance evaluation over binary channels with memory.      

IGCC for PAPR Reduction in OFDM Systems Over the Nonlinearity of SSPA and Wireless Fading Channels

High peak-to-average power ratio (PAPR) in orthogonal frequency division multiplexing (OFDM) systems seriously impacts power efficiency in radio frequency section due to the nonlinearity of high-power amplifiers. In this article, an improved gamma correction companding (IGCC) is proposed for PAPR reduction and investigated under multipath fading channels. It is shown that the proposed IGCC provides a significant PAPR reduction while improving power spectral levels and error performances when compared with the previous gamma correction companding. IGCC outperforms existing companding methods when a nonlinear solid-state power amplifier (SSPA) is considered. Additionally, with the introduction of \(\alpha , \beta , \gamma \), and \(\varDelta \) parameters, the improved companding can offer more flexibility in the PAPR reduction and therefore achieves a better trade-off among the PAPR gain, bit error rate (BER), and power spectral density (PSD) performance. Moreover, IGCC improves the BER and PSD performances by minimizing the nonlinear companding distortion. Further, IGCC improves signal-to-noise ratio (SNR) degradation (\(\varDelta _{\mathrm{SNR}}\)) and total degradation performances by 12.2 and 12.8 dB, respectively, considering an SSPA with input power back-off of 3.0 dB. Computer simulation reveals that the performances of IGCC are independent of the modulation schemes and works with arbitrary number of subcarriers (N), while it does not increase computational complexity when compared with the existing companding schemes used for PAPR reduction in OFDM systems.     

Delay Spread Statistics in a Two-Path Distributed Antenna System with Gamma-Lognormal Fading Channels

This letter analyzes the statistical properties of the root-mean-square (RMS) delay spread in a two-path distributed antenna system, where the received signal power from each path is subject to composite gamma fading and lognormal shadowing. The channel power delay profile considered consists of two delta functions with correlated power levels. We present analytical expressions for the probability density function of the RMS delay spread, as well as the cumulative distribution function, mean value and standard deviation. These analyses are validated through comparison with Monte-Carlo simulation results.     

SER Analysis of QAM with Space Diversity in Rayleigh Fading Channels

This paper derives the symbol error probability for quadrature amplitude modulation(QAM) with L-fold space diversity in Rayleigh fading channels. Two combining techniques, maximal ratio combining(MRC) and selection combining(SC), are considered. The formula for MRC space diversity is obtained by averaging the symbol error probability of M-ary QAM in an additive white Gaussian noise(AWGN) channel over a chi-square distribution with 2L degrees of freedom. The obtained formula overcomes the limitations of the earlier work, which has been limited only to deriving the symbol error rate(SER) of QAM with two branch MRC space diversity. The formula for SC space diversity is obtained by averaging the symbol error probability of M-ary QAM in an AWGN channel over the distribution of the maximum signal-to-noise ratio among all of the diversity channels for SC space diversity. No analysis for QAM with SC space diversity has been reported yet. Analytical results show that the probability of error decreases with the order of diversity. We can also see that the incremental diversity gain per additional branch decreases as the number of branches becomes larger. On the other hand, the performance of 16 QAM with MRC becomes much better than that of SC as the number of branches becomes larger. By giving the order of diversity, L, and the number of signal points, M, we have been able to obtain the SER performance of QAM with general space diversity. These results can be used to determine the order of diversity to achieve the desired SER in land mobile communication system employing QAM modulation.     

Connectivity of Wireless Multihop Networks in a Shadow Fading Environment

This article analyzes the connectivity of multihop radio networks in a log-normal shadow fading environment. Assuming the nodes have equal transmission capabilities and are randomly distributed according to a homogeneous Poisson process, we give a tight lower bound for the minimum node density that is necessary to obtain an almost surely connected subnetwork on a bounded area of given size. We derive an explicit expression for this bound, compute it in a variety of scenarios, and verify its tightness by simulation. The numerical results can be used for the practical design and simulation of wireless sensor and ad hoc networks. In addition, they give insight into how fading affects the topology of multihop networks. It is explained why a high fading variance helps the network to become connected.Christian Bettstetter is a senior researcher in the Future Networking Lab at DoCoMo Euro-Labs. His current research interests are in the area of self-organized networking, especially, in wireless ad hoc and sensor networks. He published several technical articles in this area and co-authored the Wiley book ‘GSM: Switching, services and protocols.’ From 1998 to 2003, he was with the Institute of Communication Networks at the Technische Universität München (TUM), where he did research and teaching on mobile communication networks, and managed a new international graduate program. Christian received the Dr.-Ing. degree (summa cum laude) and the Dipl.-Ing. degree in electrical engineering and information technology from TUM in 2004 and 1998, respectively. During his graduate studies, he worked for Wacker Siltronic, Portland, OR, USA, and wrote his master thesis on turbo decoding at the University of Notre Dame, IN, USA. He is a member of the IEEE and ACM SIGMOBILE.Christian Hartmann studied electrical engineering at the University of Karlsruhe (TH), where he received the Dipl.-Ing. degree in 1996. In 1997 he joined the Institute of Communication Networks at the Technische Universität München (TUM), where he earned the Dr.-Ing. degree (summa cum laude) in 2003. He is currently a senior researcher and member of the teaching staff at the same institution. During a research leave in the winter of 2000/2001 Christian was with the Wireless Research Lab of Lucent Bell Labs, Crawford Hill, NJ. His main research interests are in the area of mobile and wireless networks, including capacity and performance evaluation, radio resource management, modeling and simulation. He is a member of the IEEE.     

Dominant and Second-Order Mode Cutoff Frequencies in Fin Lines Calculated with a Two-Dimensional TLM Program

This paper presents the dominant and second-order mode cutoff frequencies in unilateral, bilateral, and insulated fin lines as calcuIated with a two-dimensional TLM program. Through careful correction of errors associated with this method, an overall accuracy better than +-1 percent has heen achieved. This TLM program therefore provides an excellent reference for verifying other existing methods.