Efficient Nakagami-m fading channel Simulation

An efficient method for generating correlated Nakagami-m fading envelope samples is presented; this method is applicable for arbitrary values of the fading parameter m. The new method is compared to other methods used to generate Nakagami-m random variates. An accurate approximation to the inverse Nakagami-m cumulative distribution function, valid for all values of m, is derived. Uncertainties regarding the autocorrelation of the Nakagami-m fading process are discussed. The fading envelope autocorrelation is determined by simulation and asymptotic analysis.     

Unified performance analysis over Mckay–Meijer G shadowed fading channel

ABSTRACT

Composite fading models have been considered as the suitable fading models for scenarios such as indoor communication and free space optical. Most of the composite fading models are based on Nakagami-m fading distribution in which amount of fading parameter ranges from 0.5 (most severe fading) to infinity (no fading). However, using the McKay–Meijer G function, one of the recent article presents McKay shadowed fading distribution which shows that the fading severity may have values more than that of the most severe case of Nakagami-m fading. In this paper, using the conditional unified expression for conditional bit error rate (BER), a unified expression of the average bit error rate (ABER) over McKay–Meijer G shadowed fading model has been proposed. The proposed unified expression includes the ABER of almost all the modulation schemes. In addition, expression for ABER of binary phase shift keying modulation over McKay fading channel under generalised Gaussian distribution has been derived. Finally, analytical expressions of adaptive capacity under different adaptive schemes namely, COPRA, CORA, CCIFR and truncated CIFR have been presented. Through numerical analysis, different results have been compared with similar results available in the literature.     

A Simple Accurate Method for Generating Autocorrelated Nakagami-m Envelope Sequences

We propose a simple accurate method for generating autocorrelated Nakagami-m envelope sequences. The method allows for arbitrary values of fading parameter and nonisotropic fading scenarios. In essence, Nakagami-m samples are first drawn and then rearranged to match the Nakagami-m autocorrelation. The rearrangement is made in accordance with the rank statistics of an underlying Rayleigh reference sequence with the desired autocorrelation. Examples illustrate the excellent performance of the new method     

On higher order statistics of the Nakagami-m distribution

This paper proposes a fading model that leads to a formal, but simple method to obtain the exact formula of the Nakagami-m published in 1960 distribution for m=n/2, with n a nonzero integer number. Based on such a model, the joint distribution of the envelope and its time derivative are accomplished, and exact formulas for the level crossing rate (closed-form formula) and for the average fade duration are derived. Simulation curves and exact formulas are checked against each other and a very good agreement between them is attained. Although derived for discrete values of m (m being an integer multiple of 1/2), there are no mathematical constraints for these expressions to be used for any real value of m⩾1/2     

An Empirical Model for Nonstationary Ricean Fading

Ricean fading is common in dense urban cellular networks and, as a mobile moves through that environment, the K-factor of the Ricean fading will change. This paper presents a statistical model for dense urban vehicular nonstationary Ricean fading, where the K-factor gradually changes due to movement through changing surroundings. This model is empirical and is based on K-factor fluctuations that are observed in dense urban cellular radio channel measurements. The K -factor is modeled using a random process with a distribution that is fit to the measured K-factor values. An autoregressive (AR) model is also used to ensure that the autocorrelation of the simulated K-factor process matches the empirical data. The nonstationary Ricean fading envelope that is generated using this model is verified by comparing it with the fading envelope that is observed in the measurements.     

Generalized Nakagami-m phase crossing rate

This paper provides simple, exact, new closed-form expressions for the generalized phase crossing rate of Nakagami-m fading channels. Sample numerical results obtained by simulation are presented that validate the formulations developed here. A special case of this formulation is the Rayleigh case, whose result agrees with that obtained elsewhere in the literature. In passing, several new closed-form results concerning the statistics of the envelope, its in-phase and quadrature components, phase, and their time derivatives are obtained.     

Estimators of the Nakagami-m parameter and performance analysis

The Nakagami-m parameter is known to capture the envelope distribution of various fading channel conditions in wireless communications. The value of m is indicative of the severity of fading, and is a measure of channel quality, making its estimation necessary in many applications. In this paper, we summarize the existing estimators for the Nakagami-m parameter and propose a new class of estimators, whose performance is analyzed by deriving the asymptotic variance and comparing with the Cramer-Rao bound (CRB). Moreover, we develop a novel estimator robust to the presence of additive white Gaussian noise (AWGN) or any other additive noise with a symmetrical distribution. We also discuss practical issues not previously addressed in the literature including adaptation and computational complexity of these estimators. We conclude that our novel integer-moment based estimators are the best choice from a computational complexity and performance point of view. Simulation results corroborate our analysis.     

The κ-μ distribution and the η-μ distribution

This paper presents two general fading distributions, the κ-μ and the η-μ distribution, for which fading models are proposed. These distributions are fully characterized in terms of measurable physical parameters. The κ-μ distribution includes the Rice (Nakagami-n), the Nakagami-m, the Rayleigh, and the one-sided Gaussian distributions as special cases. The eta-mu distribution includes the Hoyt (Nakagami-q), the Nakagami-m, the Rayleigh, and the one-sided Gaussian distributions as special cases. Field measurement campaigns were used to validate these distributions. It was observed that their fit to experimental data outperformed that provided by the widely known fading distributions, such as the Rayleigh, Rice, and Nakagami-m. In particular, the κ-μ distribution is better suited for line-of-sight applications, whereas the η-μ distribution gives better results for non-line-of-sight applications     

Performance analysis of equal-gain diversity receivers over generalized Gamma fading channels

Generalized Gamma (GG) distribution is a generic model that covers many well-known fading distributions as special cases. This paper deals with the performance analysis of L-branch equal gain combining (EGC) receivers operating over GG fading channels. For these receivers and by using convergent infinite series approach, the probability of error (P_e) can be formulated in the form of an infinite series. The coefficients of P_e series can be derived by calculating complicated integrations over the fading envelope distribution. In this paper, it is shown that the required integrations for the case of GG distribution have a complex closed-form in terms of Meijer's G function, and then, a new approximation method is developed for computation of them. The proposed method only needs mean and variance of the fading envelope; hence it has low complexity and eliminates the need for calculation of complex functions. The presented numerical examples show that the developed method can approximate the required parameters and also the individual coefficients accurately and this accuracy increases with the increase of L. The proposed method is applied to analyze the probability of error performance of the L-branch EGC receiver with both coherent phase shift keying (CPSK) and frequency shift keying (CFSK) modulation schemes under different GG channel conditions. Also the effect of gain unbalance between diversity branches on the probability of error is investigated.     

Phase-Jitter based SER of MPSK Scheme over Generalised Mixture Gamma Fading

ABSTRACT

Extensive literature exists for simple and exact expressions of symbol error rate (SER) over fading channels under different modulation schemes whose boundaries meet at right angles. In cases where boundaries do not meet at right angles, integrals of special function in the expressions make the exact calculation most complex. In such cases only approximate solutions are possible. Also, it is noteworthy to mention that when detection is performed with proper use of the phase (phase-jitter-based approach), noise performance of the receiver improves significantly. This paper applies phase-jitter PDF-based approach to present exact and closed-form SER expression of MPSK scheme over Mixture Gamma (MG) distribution for an arbitrary array of signal points. The proposed expression is generic as MG distribution can be approximated in almost all fading/shadowed fading channel models. As a proof to the authenticity, SERs of MPSK scheme over Rayleigh and Nakagami-m fading channels are deduced from the proposed SER over generalised MG distribution. Further, a significant improvement in SER has been achieved with phase-jitter-based approach as compared to conventional (non-phase-jitter-based) approach. Finally, to confirm the correctness of the proposed expression, results are validated through comparison with the existing results and Monte Carlo simulation.     

The k-μ phase-envelope joint distribution

This paper derives an exact closed-form expression for the phase-envelope joint distribution of the k-μ fading environment, a general fading model that includes the Rice and the Nakagami-m models as special cases. The derived joint statistics are obtained so that compatibility with both Rice as well as Nakagami-m cases are kept. Monte Carlo simulation plots are presented that are in accordance with the formulations developed here. As a consequence of the derivation of the required PDF, an interesting solution to a very general probability problem is proposed, namely, given the PDF of the modulus of a variate, find the PDF of the variate. Additionally, several new integral relations of the modified Bessel function are given.     

Novel distribution model of transformed coefficients in video coding using quad-tree structured block partitioning

Today’s video coding standard such as high efficiency video coding uses a full quad-tree structured block partitioning, so the underlying statistics of transformed coefficients becomes more complicated to estimate than the previous standards due to the coding structure. However, a statistical distribution of transformed residue is important for a design of a smart encoder. Thus, in this paper, we present a theoretic analysis of a distribution of transformed coefficients produced from an encoder using different transform sizes, and derive a probability density function (pdf) for the estimation. The proposed density model provides a more accurate distribution model than the conventional pdfs. Parameters are theoretically estimated, and rate-distortion model is established from the proposed pdf. We also apply the proposed method to a rate control problem to show the efficiency of the proposed density model. Our experimental results show that the proposed method is better capable of modeling the mixed sources of multiple-type transform coefficients occurred from the quad-tree coding structure of transform and provides an accurate estimate in rate control.

     

A simulation model for Nakagami-m fading channels, m<1

This paper proposes a mathematical model for simulating a Nakagami-m (1960) fading channel, m<1. It is shown that the m fading process can be expressed as a product of a square-root-beta process and a complex Gaussian process. Extension of the proposed model to simulate correlated diversity channels is also given. Numerical results demonstrate that the statistical properties of the samples generated from the proposed model are close to the required ones     

Nakagami-m approximation to the sum of M non-identical independent Nakagami-m variates

A Nakagami-m approximate distribution to the sum of M non-identical independent Nakagami-m variates is derived. Comparisons between exact and approximate sum distributions show excellent agreement. This new approach finds applicability in important communications issues such as equal-gain combining, signal detection, linear equalisers, outage probability, intersymbol interference and phase jitter.     

BER Evaluation of IEEE 802.15.4 Compliant Wireless Sensor Networks Under Various Fading Channels

This paper presents bit error rate (BER) analysis of wireless sensor networks (WSNs) consisting of sensor nodes based on an IEEE 802.15.4 RF transceiver. Closed-form expressions for BER are obtained for WSNs operating over AWGN, Rayleigh and Nakagami-m fading channels. For the purpose of analysis, we consider an IEEE 802.15.4 RF transceiver using direct sequence spread spectrum-offset quadrature phase shift keying (DSSS-OQPSK) modulation under 2.4 GHz frequency band in a WSN. Analytical expressions for BER are derived for a wireless link between sensor nodes that act as a transmitter unit and a base station without considering the effect of interferers in the wireless environment. Numerical results for BER are obtained by varying the IEEE 802.15.4 standard specific physical layer parameters, such as number of bits used to represent a Zigbee symbol, number of modulation levels used in an OQPSK modulator, and various values of Rayleigh and Nakagami-m fading parameters, denoted as \(\alpha \) and \(m\) , respectively. Moreover, optimum values of physical layer parameters are identified for improved system performance. It is found that error performance analysis of WSN shows improvement when lower number of bits is used to represent a Zigbee symbol. Specifically, under a Rayleigh fading channel which reflects a real-time WSN environment, the network exhibits better performance only when it is operated at high SNR values, i.e., BER of order \(10^{-2}\) is achieved when SNR lies in the range 5–15 dB. Also, the effect of fading parameters on network performance shows that better results are obtained for higher values of \(\alpha \) and \(m\) for Rayleigh and Nakagami-m fading channels, respectively.     

Effects of Hardware Impairment on the Cooperative NOMA EH Relaying Network Over Nakagami-m Fading Channels

In this paper, we analyze the performance of Non Orthogonal Multiple Access (NOMA) Energy harvesting relaying system in presence of hardware impairments at both the transmitter and receiver over a Nakagami-m fading channel. The proposed system with destinations are allocated different power levels in which the source node communicates with the destinations via an energy harvesting (EH) relay employing a power-splitting relaying architecture and a direct link to the near destination. Moreover, the amplify-and-forward protocol at the EH relay is investigated to evaluate the performance of system. Additionally, the expressions for outage probability are derived, and these analyses are verified by a Monte Carlo simulation. Furthermore, these results are also compared to an orthogonal multiple access (OMA) system. Finally, the effects of various parameters, such as power allocation levels, position of EH relay node, channel coefficients, and hardware impairment levels on the outage performance and throughput of proposed NOMA-EH system and OMA system are investigated. These results demonstrate the advantage of NOMA-EH system as user fairness since multiple destinations compared to the OMA-EH system.

     

A Nakagami-N-gamma Model for Shadowed Fading Channels

Wireless channels are subject to short term fading and shadowing. Such shadowed fading channels are described using a Nakagami-lognormal process, with the Nakagami-m (short term fading) and lognormal distributions (shadowing). This approach does not result in a closed form solution for the density function of the signal-to-noise ratio (SNR) making wireless systems analysis difficult. It was suggested that a gamma or an inverse Gaussian distribution can be used in place of the lognormal distribution providing an analytical framework. The match of these two distributions to the lognormal was less than ideal. Invoking shadowing as multiplicative process, the distribution of the product of N gamma variables is proposed in place of the lognormal pdf resulting in the Nakagami-N-gamma model. It is shown that this model leads to simple solutions to the density and distribution functions as well as error rates for coherent phase shift keying modems. The outage probabilities and error rates based on the Nakagami-lognormal (NL) and Nakagami-N-gamma (NNG) models were compared. Results showed excellent match at levels of shadowing generally observed in wireless systems. While values of N as low as 3 was sufficient for low values of m and weak to moderate shadowing, values of N in the range of 7–9 provided better match for higher levels of shadowing and higher values of m. By varying N, it is also possible to get the NNG pdf to move closer to the NL pdf making the new model an ideal one for the shadowed fading channels with its flexibility and availability of analytical expressions.     

Asymptotic SEP for M-PSK Signals overα-μFading Channels

The α-μfading is a general physical model recently rewritten from the Stacy (or generalized gamma) distribution, encompassing a variety of fading environments such as Rayleigh, Nakagami-m, and Weibull fading. We characterize the asymptotic average symbol error probability (SEP) at a high signalto- noise ratio (SNR)?specifically, the high-SNR slope and power gain?in terms of two physical fading parametersαandμ. We further extend the asymptotic SEP analysis to a multiple-input multiple-output diversity system employing orthogonal space? time block codes inα-μfading channels.     

外形包络面的尾焰红外图像仿真

基于粒子系统的尾焰红外图像仿真计算量大,难以与红外辐射的计算模型相结合。为了解决这个问题,首先提出了基于化学反应式的航空发动机尾焰气体组分计算模型,改进现有的尾焰流场工程计算方法;然后提出了基于外形包络面的尾焰红外图像仿真模型,研究了包络面的建立、包络面模型与流场计算模型以及气体辐射计算模型的结合、包络面模型对尾焰红外图像影响三个相关问题;最后通过数值仿真得到了尾焰的红外图像。结果表明:尾焰的红外图像主要由其核心区的高温气体决定;当包络范围增大到一定程度后,尾焰图像与选用的包络面的外形无关;选择一个易于划分面元的包络面模型,并划定能全面反映尾焰辐射分布特征的小包络面范围,可使尾焰图像的生成更加高效准确。     

Accurate error-rate performance analysis of OFDM on frequency-selective Nakagami-m fading channels

Error rates of orthogonal frequency-division multiplexing (OFDM) signals in multipath slow fading Nakagami-m fading channels are considered. The exact probability density function of a sum of Nakagami-m random phase vectors is used to derive a closed-form expression for the error rates of OFDM signals. The precise error-rate analysis is extended to a system using multichannel reception with maximal ratio combining. An asymptotic error-rate analysis is also provided. For a two-tap channel with finite values of Nakagami-m fading parameters, our analysis and numerical results show that the asymptotic error-rate performance of an OFDM signal is similar to that of a single carrier signal transmitted over a Rayleigh fading channel. On the other hand, our analysis further shows that a frequency-selective channel that can be represented by two constant taps has similar asymptotic error-rate performance to that of a one-sided Gaussian fading channel. It is observed that, depending on the number of channel taps, the error-rate performance does not necessarily improve with increasing Nakagami-m fading parameters.