A decomposition technique for efficient generation of correlatedNakagami fading channels

Correlated Nakagami m-fading is commonly encountered in wireless communications. Its generation in a laboratory environment is therefore of theoretical and practical importance. However, no generic technique for this purpose is available in the literature. Correlated Rayleigh fading is easy to simulate since it has a simple relationship with a complex Gaussian process. Unfortunately, this is not the case for Nakagami fading. The difficulty lies in that the fading parameter can be a real number and there is no general theory linking a Nakagami vector to a finite set of correlated Gaussian vectors. In this paper, by introducing a direct-sum decomposition principle and determining the statistical mapping between the correlated Nakagami process and a set of Gaussian vectors for its generation, a simple general procedure is derived for the generation of correlated Nakagami channels with arbitrary parameters. A key parameter in the statistical mapping can be determined by using an iterative method. The validity of the new technique is examined through the generation of a correlated Nakagami sequence, as encountered in U.S. digital cellular, and a multibranch vector channel as encountered in diversity reception     

Accurate Simulation of multiple cross-correlated Rician fading channels

The computer generation of multiple cross-correlated Rician fading channels is investigated. We prove that the output sequences of existing multichannel fading simulators are restricted to have cross-correlation statistics that have the same functional form as the component autocorrelation functions. To overcome this limitation, vector autoregressive stochastic models are proposed for the generation of multiple Rician fading processes with specified realizable autocorrelation and cross-correlation statistics. This capability is desirable, for example, to permit realistic performance assessments of space-time modem designs by enabling the simulation of space-time-selective wireless channel models. The utility of the simulation approach is demonstrated by the accurate synthesis of some bandlimited multichannel Rayleigh and Rician processes.     

Nakagami衰落信道的仿真方法研究

Nakagami衰落能够描述实际中所遇到的大多数衰落环境。文章提出了一个新的Nakagami衰落信道的仿真方法,用它仿真了Nakagami衰落信道的一阶、二阶统计特性并通过与其理论值进行比较验证了该方法的可靠性。该仿真方法直接基于瑞利衰落信道仿真基础之上,是对Nakagami衰落信道的一种新的研究探讨。     

On the generation of correlated Rayleigh fading envelopes for accurate simulation of diversity channels

The generation of correlated Rayleigh fading envelopes based on mobile radio channel characteristics for realistic simulation of diversity systems was documented in 1974 by Jakes. In this letter, a survey of recent algorithms which draw upon Jakes' work will be given, as well as an illustration of their shortcomings. Subsequently, a procedure is presented for the generation of multiple equal-power correlated Rayleigh fading envelopes, with desired cross-correlations and autocorrelation functions specified so as to model channel conditions under the general assumption of isotropic scattering. The algorithm presented will enable accurate simulation and investigation of the effect of correlated fading on diversity schemes.     

Nakagami衰落上DE-QPSK在联合收发分集下的性能分析

利用高斯Q函数的高阶次幂在最大比合并（MRC）分集接收瑞利衰落信道上统计平均的结果,推导了Nakagami 衰落信道上采用组合发射选择合并（SC）/接收 MRC 天线分集的相干检测差分编码四相相移键控（DE-QPSK）的平均误符号率（ASER）精确表达式。利用高斯Q函数的近似表达式和矩生成函数（MGF）方法,推导了Nakagami衰落信道上采用组合SC/MRC天线分集的相干检测DE-QPSK 的ASER近似表达式。通过数值计算和仿真,验证了DE-QPSK的ASER精确表达式的正确性以及近似表达式的准确性。利用精确表达式和近似表达式可研究收发天线数目和衰落参数对DE-QPSK的ASER性能的影响,为实际SC/MRC天线分集方案的设计提供了理论指导。     

Effective capacity of a correlated Nakagami‐m fading channel

The grail of next‐generation wireless networks is providing real‐time services for delay‐sensitive applications, which require that the wireless networks provide QoS guarantees. The effective capacity (EC) proposed by Wu and Negi provides a powerful tool for design of QoS provisioning mechanisms. In this paper, we intend to generalize their formula for the effective capacity of a correlated Rayleigh fading channel; specifically, we derive a closed form approximate EC formula for a special correlated Nakagami‐m fading channel, for which the inverse of the correlation coefficient matrix is tridiagonal. To verify its accuracy via simulation, we develop a Green‐matrix based approach, which allows us to analytically obtain the effective capacity (given the joint probability density function of a correlated Nakagami‐m fading channel) while being able to simulate the corresponding channel gain process. Simulation results show that our EC formula is accurate. Furthermore, to facilitate the application of the EC theory to the design of practical QoS provisioning mechanisms, we propose a simple algorithm for estimating the EC of an arbitrary correlated Nakagami‐m fading channel, given channel measurements; simulation results demonstrate the accuracy of our proposed EC estimation algorithm showing its suitability in practice. Copyright © 2011 John Wiley & Sons, Ltd.     

On the Analysis of Envelope Correlation and Spectra for Rician Fading Channel

Physical fading radio channels encountered in wireless mobile communication are often modeled as a complex Gaussian process whose envelope is statistically described by Rayleigh or Rician probability distribution function (PDF). In most of the literature, the accuracy of the simulation model is estimated by comparing the simulated autocorrelation function (ACF) of inphase (or quadrature phase) component of the fading process and ACF of squared envelope with the analytical ones. In this paper, we examine the performance of a sum of sinusoid (SOS) based Rician fading channel simulator on the basis of the ACF and power spectral density (PSD) of the fading envelope. We obtained simplified approximate expressions for the autocorrelation and mean value of the fading envelope which become more accurate as the value of Rice factor increases. In the simulation, the line-of-sight (LOS) component is modeled as a zero-mean random variable with pre-chosen angle of arrival (AOA) and random initial phase. We showed that the AOA of the LOS component significantly affects the level crossing rate (LCR) and average fade duration (AFD) of the fading envelope. All simulation results are compared with the analytical results and a very good agreement between them is found.

An iterative algorithm for Doppler spread estimation in LOS environments

An iterative algorithm is proposed to estimate the maximum Doppler frequency in a line-of-sight (LOS) environment. While the autocorrelation function of a Rayleigh fading signal depends only on the maximum Doppler frequency, that of a Rician fading signal is also related to the K factor and the angle of arrival (AOA) of the LOS component. The performance of conventional Doppler spread estimators based on the Rayleigh fading assumption degrades in LOS environments due to the autocorrelation function mismatch. The proposed estimator estimates the Rician K factor first, then iteratively estimates the Doppler spread and the AOA of the LOS component. The performance degradation due to channel parameter variations is investigated by means of matching the autocorrelation functions. The simulation results indicate that the proposed estimator is not only superior to the conventional autocorrelation-based Doppler spread estimator but also robust to the channel parameter variation in both LOS and non-LOS environments.     

A New Design Concept for High-Performance Fading Channel Simulators Using Set Partitioning

In this paper, we introduce a new technique for the design of high-performance Rayleigh fading channel simulators. The proposed design method uses set partitioning – a technique, which plays a key role in the design of trellis-coded modulation schemes. We show how set partitioning can be used to design multiple uncorrelated fading waveforms enabling the simulation of Rayleigh fading channels. For the important case of isotropic scattering, we show that the sample average of the generated waveforms results in a deterministic process, the autocorrelation function (ACF) of which tends to the zeroth-order Bessel function of the first kind as the number of sample functions increases. The proposed procedure is completely deterministic. The comparison with a stochastic procedure using Monte Carlo techniques will be made. A study of the performance shows clearly that the new technique using set partitioning outperforms by far existing Monte Carlo methods.     

Approximation of envelope statistics with Nakagami distribution foroutput of noncoherent diversity combiners

A simple relationship for estimating the fading parameter m of the Nakagami distribution is obtained for the output of L-branch noncoherent diversity combiners when the branch signals of unequal mean powers are independently Rayleigh faded. Comparisons between the exact distributions and the Nakagami distribution with approximated ms for L=2 and L=3 show good agreement over wide ranges of relative mean powers between the branch signals     

Closed-form approximation for the outage capacity of orthogonal STBC

In this letter we derive a tight analytical approximation for the outage capacity of orthogonal space-time block codes (STBC's). The proposed expression is a simple closed-form function of the power covariance matrix of the channel. In the case of uncorrelated channels, the expression only depends on the variances of the channel power gains that can be expressed analytically for the most common fading distributions: Rayleigh, Rice, Nakagami, Weibull, etc. Furthermore, the approximation encompasses different fading distributions and gains between different pairs of transmit and receive antennas, which can occur in distributed STBC networks.     

基于MATLAB的Nakagami衰落信道仿真与分析

由于Nakagami衰落能够准确地表示实际中所遇到的大多数衰落环境，因而本文基于MATLAB针对Nakagami衰落信道仿真了它的统计特性，包括接收信号的复包络模拟和在具有最大比合并分集下的电平通过率及平均衰落持续时间的性能分析。重点在于理解和建立采用MATLAB进行信道信真的方法及对Nakagami衰落信道本身统计特性的理解。     

Performance analysis of κ-μ/gamma shadowed fading model over indoor off body communication channel

The κ-µ/gamma distribution has an importance role to model the small scale fading and shadowing over human off body indoor communication channel. This composite fading model has various special cases like κ-µ, Rician, Nakagami-m, Rayleigh, Rayleigh/gamma, Nakagami/gamma and Rice/logormal. In this paper, the expression for bit error rate (BER) using various modulation schemes, average channel capacity (ACC) and outage probability (OP) over κ-µ/gamma shadowed fading channel are derived. All the derived expressions are novel and presented in analytical form. The expression for BER and channel capacity are in form of well-known Meijer G function, whereas the outage probability expression is obtained from cumulative distribution function (CDF) proposed in previous literature. The derived expressions of BER (BPSK), average channel capacity and outage probability reduces to special cases for validation purpose. The study shows that binary phase shift keying (BPSK) modulation technique has better BER performance as compare to other modulation techniques. Moreover, on increasing α and β while κ and µ kept constant and vice versa, the ACC get increases but below the Additive white Gaussian Noise (AWGN) channel capacity as expected. Also, better outage probability performance is obtained at lowest threshold signal to noise ratio (5 dB).     

Error rate of asynchronous DS-CDMA in Nakagami fading

An accurate bit-error-rate (BER) calculation method is derived for a binary direct-sequence (DS) spread-spectrum multiple-access (SSMA) system using conventional matched filter receivers and random sequences on flat-fading Nakagami channels. A closed-form expression for the characteristic function of a sum of multiple Nakagami interfering signals is found. The accuracy of the standard Gaussian approximation (SGA) is assessed for DS code-division multiple-access (CDMA) systems operating on Nakagami fading channels.     

Multipath effects and adaptive transmission in presence of indoor power line background noise

The paper studies the background noise characteristics of a typical indoor power line (PL) in India. The noise decreases rapidly with frequency and can be considered as white beyond 5 MHz. The time variation of the background noise at every frequency in the non‐white region is modeled and compared in different environments which include laboratory and factory setups. In all cases, the background noise can be modeled by density functions related to multipath fading i.e. Nakagami‐m, Rayleigh and Rician. Fading is worse than the Rayleigh fading when the PL network has more connected loads and impedance discontinuities. Single frequency noise shows Rician fading when the background noise is narrowband Gaussian. The results are compared with those obtained in other countries in an attempt to check the validity of the model worldwide. A PL channel noise simulator is developed using the density functions to simulate the background noise. A technique is proposed that adapts the carrier frequency according to the channel property at a particular instant. The performance of such a system is tested in a simulated environment and shows that the method enables transmission of signals at very low transmission power compared with that in the AWGN channel. Copyright © 2009 John Wiley & Sons, Ltd.     

Forward-link BER analysis of asynchronous cellular DS-CDMA overNakagami-faded channels using combined PDF approach

A closed-form conditional probability density function (PDF) of the Nakagami-faded-interference-to-signal power ratio, given the exact location of the tagged mobile, is derived for integer values of Nakagami (1960) fade parameter m. The conditional PDF, whose coefficients can be computed efficiently in a recursive manner, significantly reduces the computational complexity of forward-link bit error rate (BER) evaluation of a direct-sequence code-division multiple-access (DS-CDMA) cellular system over a fading channel, BER curves reveal that the performance improvement of increasing m is not significant for m>4. Performance results for noninteger values of m can be estimated using the linear interpolation technique. With the derived BER expressions, a more realistic cellular model that takes into account the effects of nonidentical m and path-loss exponent is proposed and analyzed. By substituting appropriate values of m, the BER performance for a class of fading distributions such as Rayleigh and Ricean fading can be evaluated or approximated. In particular, the Nakagami approximation may be treated as a tight lower bound to the corresponding mathematically involved Ricean case     

A general moment generating function for MRC diversity over fading channels with Gaussian channel gains

For maximal ratio combining (MRC) diversity over correlated fading channels with Gaussian channel gains, we utilize unitary diagonalization of the channel covariance matrix to decorrelate the physical channels into uncorrelated virtual channels to obtain the moment generating function (MGF) of the received signal‐to‐noise ratio (SNR). The MGF thus obtained has a compact form and can be universally applied to various popular fading models. In addition to the advantage of simple derivation procedure, this general MGF can be readily modified to express various scenarios of channel power distributions as well as joint fading models. To demonstrate these advantages, we use the generalized Ricean fading as a specific example to compare our derivation and our MGF expression with an existing work in the literature. Again, we present numerical simulations for MRC reception of binary phase shift keying (BPSK) signals over Nakagami fading to compare with existing results appearing in the literature. Copyright © 2006 John Wiley & Sons, Ltd.     

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.     

Ordered Statistic Analysis for Diversity Combining Schemes over Nakagami-m Fading Channel

Order diversity combining technique is one of efficient methods to lower the complexity but not to significantly degrade performance. Recently, Eng and Milstein [1] proposed a novel order-combining technique, called the second order diversity combining (SC2) and third order diversity combining (SC3) and applied to Rayleigh fading channel. SC2 and SC3 schemes mean that the two (three) signals with the first two (three) largest amplitudes among the branches are chosen and coherently combined. However, when compared to Rayleigh distribution, the Nakagami-m distribution [10] provides a more general and versatile way to model wireless channel. For the reason, the bit error rate (BER) performance of proposed schemes were then analyzed with order statistic method and compared to the traditional diversity technique over Nakagami fading environment in this paper. The results are compared to maximal ratio combining (MRC), and conventional selection combining (SC) in coherent reception and to equal gain combining (EGC) in noncoherent reception. The results show that SC is in performance the worst for either in coherent or in noncoherent schemes, as expected. The performance differences between SC2 (SC3) and MRC (EGC) are not significant when the diversity order L 3, but the difference will increase when L 5. It is worth noting that the result of [1] is a special case with fading figure, m = 1. It is also observed the performance is much affected by the number of diversity branches L, the fading figure m, and the signal-to-noise ratio (SNR).