Spectral efficiency evaluation for selection combining diversity (SCD) scheme over slow fading

In this paper we derive closed-form expressions for the single-user capacity of selection combining diversity (SCD) system, taking into account the effect of imperfect channel estimation at the receiver. The channel considered is a slowly varying spatially independent flat Rayleigh fading channel. The complex channel estimate and the actual channel are modelled as jointly Gaussian random variables with a correlation that depends on the estimation quality. Three adaptive transmission schemes are analysed: 1) optimal power and rate adaptation opra; 2) constant power with optimal rate adaptation ora; and 3) channel inversion with fixed rate cifr. Furthermore, we derive in this paper analytical results for capacity statistics including moment generating function (MGF), complementary cumulative distribution function (CDF) and probability density function (PDF). These statistics are valid for arbitrary number of receive antennas. Our numerical results show the effect of Gaussian channel estimation error on the achievable spectral efficiency.     

Performance of binary DS‐SSMA communications through Nakagami fading channel

Abstract

A binary asynchronous direct sequence spread spectrum multiple access system through Nakagami's m‐distributed channel is considered for non‐diversity receptions. Effects of fading and multiple access interferences on the average error probability are investigated. Approximation method to the average error probability is evaluated in two steps based on the moments of multiple access interferences and Nakagami distributions. Gauss quadrature rule is applied to evaluate the conditional probability conditioned on a fixed m‐distributed fading amplitude of the desired signal. Average error probability is then evaluated by the trapezoidal integration which integrates the conditional probability and the m‐distributed probability density function of the desired signal. This method provides a good approximation to the average error probability when the number of simultaneous users is large. Numerical results for the pseudorandom codes of code length 31 and Gold codes of code length 31 and 127 are presented.     

Performance analysis of rectangular quadrature amplitude modulation with combined arbitrary transmit antenna selection and receive maximal ratio combining in nakagami-m fading

The average symbol error probability (SEP) performance of arbitrary rectangular quadrature amplitude modulation in the context of arbitrarily ordered transmit antenna selection and receive maximal ratio combining diversity system is analysed. The channel gains are assumed to follow Nakagami-m fading distribution with in general arbitrary fading parameters. Exact expressions for the average SEP performance are derived for the general case of unequal in-phase and quadrature decision distances as well as distinct in-phase and quadrature modulation orders. The results generalise many previous case studies, and can be used to investigate the impact of various diversity-combining schemes and different modulation and channel parameters on the system average SEP performance.     

Chain Sampling Scheme under Constant Inspection Errors

The primary aim of this paper is to extend the inspection error consideration to chain sampling schemes, an area that has not been dealt with in the literature. A mathematical model is developed to investigate the performance of chain sampling schemes under constant inspection errors. Expressions of performance measures, such as operating characteristic function, average total inspection and average outgoing quality, are derived to aid the analysis of a general chain sampling scheme, ChSP‐4A ( ) r, developed by Frishman. This study reveals that as Type I inspection error increases the probability of acceptance will decrease and as Type II inspection error increases the acceptance probability will increase. The effect of Type II error on the probability of acceptance is very marginal compared with that of Type I error, especially when the true fraction non‐conforming is small. In addition, the effects of inspection errors can be ‘eliminated’ by transforming to its equivalent perfect inspection counterpart, hence greatly reducing the complexity of the analysis. The effects of other sampling parameters are also studied to serve as a foundation for future plan designing purposes. Copyright © 2006 John Wiley & Sons, Ltd.     

Outage capacity and outage rate performance of MIMO free-space optical system over strong turbulence channel

Abstract

In this paper, we investigate outage capacity, outage probability, and outage rate performance of multiple-input multiple-output (MIMO) free-space optical system operating over strong turbulence channels. The MIMO optical system employs intensity modulation direct detection with on-off signaling, and equal gain combining technique at the receiver. We derived novel closed-form expressions for three system metrics, namely, outage capacity, outage probability, and outage rate. Expressions derived here are based on the generalized Gamma–Gamma channel model, which is based on scintillation theory that assumes that the irradiance of the received optical wave is modeled as the product of small-scale and large-scale turbulence eddies. The results are evaluated for different values of received signal-to-noise ratios, strong turbulence conditions, and several values of transmit/receive diversity.     

Quantum authentication with unitary coding sets

Abstract

A general class of authentication schemes for arbitrary quantum messages is proposed. The class is based on the use of sets of unitary quantum operations in both transmission and reception, and on appending a quantum tag to the quantum message used in transmission. The previous secret between partners required for any authentication is a classical key. We obtain the minimal requirements on the unitary operations that lead to a probability of failure of the scheme less than one. This failure may be caused by someone performing a unitary operation on the message in the channel between the communicating partners, or by a potential forger impersonating the transmitter.     

New minimum error rate algorithms for DFE

Abstract

We propose new adaptive minimum symbol error rate algorithms (MSER) for decision feedback equalization over M‐ary PAM channels. In addition, we take into consideration biased as well as unbiased estimates leading to two major versions respectively called biased MSER (BMSER) and unbiased MSER (UMSER). The exact forms of these algorithms are computationally complex and require channel parameter information and thus must be processed off‐line. We thus modify the exact forms into stochastic and simplified versions to reduce computation load. The stochastic version requires no channel information and hence can be processed on‐line, but at the cost of convergence rate. Merits and characteristics of various versions are discussed and compared.     

Effect of error in channel state information on the channel capacity with QAM signalling and the design of robust signal constellations

The effects of channel estimation errors on the channel capacity of a discrete time, discrete input, infinite output Rayleigh fading channel are investigated. The case of conventional modulation methods such as phase shift keying (PSK) and quatrature amplitude modulation (QAM) is investigated at first where it was observed that the capacity degrades rapidly with increasing channel estimation errors. The effect of error in the channel estimation is similar to the effect of higher noise in the channel that depends on the transmitted signal. A genetic algorithm is used to optimise the signal constellation in order to maximise the capacity for a given finite number of signal points. The aim of trying to maximise the capacity is to estimate the remaining gap in performance between a traditional modulation scheme such as QAM and the best possible constellation that is optimised for the channel. The constellations obtained from the genetic algorithm are, in general, not directly implementable. A method to design practical robust signal constellations that overcome the effect of channel state information (CSI) error is presented. The robust signal constellations obtained show a performance that is very close to the optimal constellations. In this work, the probability distribution of the error in CSI is assumed to be known.     

Asymptotic Lyapunov stability with probability one of Duffing oscillator subject to time-delayed feedback control and bounded noise excitation

The asymptotic Lyapunov stability with probability one of a Duffing system with time-delayed feedback control under bounded noise parametric excitation is studied. First, the time-delayed feedback control force is expressed approximately in terms of the system state variables without time delay. Then, the averaged Itô stochastic differential equations for the system are derived by using the stochastic averaging method and the expression for the Lyapunov exponent of the linearized averaged Itô equations is derived. It is inferred that the Lyapunov exponent so obtained is the first approximation of the largest Lyapunov exponent of the original system, and the asymptotic Lyapunov stability with probability one of the original system can be determined approximately by using the Lyapunov exponent. Finally, the effects of time delay in feedback control on the Lyapunov exponent and the stability of the system are analyzed. The theoretical results are well verified through digital simulation.     

Statistical Monitoring of Time‐to‐Failure Data Using Rank Tests

A common type of reliability data is the right censored time‐to‐failure data. In this article, we developed a control chart to monitor the time‐to‐failure data in the presence of right censoring using weighted rank tests. On the basis of the asymptotic properties of the rank statistics, we derived the generic formulae for the operating characteristic functions of the control chart to show the relationship between type I error probability, type II error probability, sample size, and hazard rate change. We presented case studies to illustrate the design procedure and the effectiveness of the proposed control chart system. We also investigated and compared the performance of the proposed monitoring procedure with some available monitoring techniques for nonconformities. Copyright © 2011 John Wiley & Sons, Ltd.     

Average symbol error probability of arbitrary rectangular quadrature amplitude modulation in generalised shadowed fading channels

A closed-form approximation of average symbol error probability of arbitrary rectangular quadrature amplitude modulation in a gamma-shadowed Nakagami fading radio channel is derived. The final result is obtained on the basis of an exponential approximation of the Gaussian Q-function. It is shown that the derived formula can also be used for error probability estimation in Nakagami-log-normal radio channels for a wide range of shadowing spread values. The numerical aspects of calculation are discussed.     

c‐Type method of unified CAMG and FEA. Part 1: Beam and arch mega‐elements—3D linear and 2D non‐linear

Computer‐aided mesh generation (CAMG) dictated solely by the minimal key set of requirements of geometry, material, loading and support condition can produce ‘mega‐sized’, arbitrary‐shaped distorted elements. However, this may result in substantial cost saving and reduced bookkeeping for the subsequent finite element analysis (FEA) and reduced engineering manpower requirement for final quality assurance. A method, denoted as c‐type, has been proposed by constructively defining a finite element space whereby the above hurdles may be overcome with a minimal number of hyper‐sized elements. Bezier (and de Boor) control vectors are used as the generalized displacements and the Bernstein polynomials (and B‐splines) as the elemental basis functions. A concomitant idea of coerced parametry and inter‐element continuity on demand unifies modelling and finite element method. The c‐type method may introduce additional control, namely, an inter‐element continuity condition to the existing h‐type and p‐type methods. Adaptation of the c‐type method to existing commercial and general‐purpose computer programs based on a conventional displacement‐based finite element method is straightforward. The c‐type method with associated subdivision technique can be easily made into a hierarchic adaptive computer method with a suitable a posteriori error analysis. In this context, a summary of a geometrically exact non‐linear formulation for the two‐dimensional curved beams/arches is presented. Several beam problems ranging from truly three‐dimensional tortuous linear curved beams to geometrically extremely non‐linear two‐dimensional arches are solved to establish numerical efficiency of the method. Incremental Lagrangian curvilinear formulation may be extended to overcome rotational singularity in 3D geometric non‐linearity and to treat general material non‐linearity. Copyright © 2003 John Wiley & Sons, Ltd.     

Selecting Significant Effects in Factorial Designs Taking Type II Errors into Account

When analysing the effects of a factorial design, it is customary to take into account the probability of making a Type I error (the probability of considering an effect significant when it is non‐significant), but not to consider the probability of making a Type II error (the probability of considering an effect as non‐significant when it is significant). Making a Type II error, however, may lead to incorrect decisions regarding the values that the factors should take or how subsequent experiments should be conducted. In this paper, we introduce the concept of minimum effect size of interest and present a visualization method for selecting the critical value of the effects, the threshold value above which an effect should be considered significant, which takes into account the probability of Type I and Type II errors. Copyright © 2006 John Wiley & Sons, Ltd.     

Roughness effect on flow and thermal boundaries in microchannel/nanochannel flow using molecular dynamics‐continuum hybrid simulation

Our molecular dynamics‐continuum hybrid simulation method is further validated in terms of flexibility in domain decomposition. The roughness effects on the flow and thermal boundaries in liquid channel flow is studied. The results indicate that the molecules in the wall‐neighboring area can be firmly confined in the concaves due to geometric structure and strong liquid–solid interaction and cause locking boundary in the velocity profile and linear gradient in the temperature profile. The locking boundary can further lead to negative slip length, which varies in power law with channel height. The linear temperature gradient, as well as nearly constant temperature jump, can lead to obviously increasing Kapitza length versus channel height. Analysis on flow friction shows that the confinement on the molecules will equivalently narrow the channel, where larger pressure gradient is needed. Therefore, the roughness should be strictly restricted within a range shrinking correspondingly with channel height if the flow condition is supposed to be maintained unchanged. Finally, our hybrid simulation is compared with full molecular dynamics simulation in terms of computational efficiency. Great advantages of the hybrid simulation, such as exclusively flexibility and combination characteristics, demonstrate its potential values and promising applications in the field of microfluidics/nanofluidics. Copyright © 2011 John Wiley & Sons, Ltd.     

Field singularities at lossless metal-dielectric arbitrary-angle edges and their ramifications to the numerical modeling of gratings

I extend a previous work [J. Opt. Soc. Am. A, 738 (2011)] on field singularities at lossless metal-dielectric right-angle edges and their ramifications to the numerical modeling of gratings to the case of arbitrary metallic wedge angles. Simple criteria are given that allow one knowing the lossless permittivities and the arbitrary wedge angles to determine if the electric field at the edges is nonsingular, can be regularly singular, or can be irregularly singular without calculating the singularity exponent. Furthermore, the knowledge of the singularity type enables one to predict immediately if a numerical method that uses Fourier expansions of the transverse electric field components at the edges will converge or not without making any numerical tests. All conclusions of the previous work about the general relationships between field singularities, Fourier representation of singular fields, and convergence of numerical methods for modeling lossless metal-dielectric gratings have been reconfirmed.     

On the convergence of the lp ‐norm algorithm for polynomial perceptron having different error signal distributions

Abstract

The convergence property of the l_p ‐norm algorithm for polynomial‐perceptron having different error signal distributions will be analyzed in this paper. To see the effect of error signal on the convergence rate, two types of activation functions are considered in the analysis: one is of a linear type and the other is of a sigmoidal type. Different activation functions yield different ranges of output signal and, in turn, yield different error signal distributions. Linear activation function causes the error signal to be distributed in an uncertain way, while sigmoidal activation function causes it to be distributed in a tightly bounded region. Based on this difference the convergence property of the l_p ‐norm algorithm, 1 ≤ p ≤ 2, is investigated in this paper. Expressions of average learning gains are obtained in terms of the power metric p, the error probability, and the upper bound of the error signal distribution. Analytic results indicate that it is of particular value in using the l_p ‐norm algorithm for the perceptron using sigmoidal activation functions. Computer simulation of an adaptive equalizer using this algorithm confirms the theoretical analysis.     

Analysis of an automatic sinusoidal detector with FFT and cell‐averaging processor

Abstract

A sinusoidal detector with adaptive thresholding CFAR (constant‐false‐alarm‐rate) processor operating in noise of changing statistics is analyzed for some very general situations. The detector contains FFT and a cell‐averaging processor, which can be easily implemented for real time applications, such as in pulse doppler radar. For signals in stationary noise in particular, the second‐order statistics of the FFT‐based periodogram of the windowed data are derived. In the AWGN case, this detector possesses the desired CFAR characteristics. For Gaussian colored noise, the detector performance is derived analytically with certain reasonable approximations. It is shown from some numerical examples that in this case the variation of the false alarm probability with respect to the unknown sinusoidal frequency and noise spectrum is not significant, which reveals the property of robustness. Moreover, the detection probability is satisfactory for most cases.     

Concatenated coded modulation techniques and orthogonal space-time block codes in the presence of fading channel estimation errors

Performance of coding and modulation systems in fading channels is usually analysed under the assumption that the receiver has perfect knowledge of channel condition. However, various shortcomings in practical channel estimation techniques lead to imperfections, resulting in channel estimation errors. The authors analyse a practical coding and modulation scheme for multiple-antenna systems considering channel estimation errors. The novelty of this study resides in providing error probability bounds for concatenated trellis coded modulation (TCM) or bit-interleaved coded modulation (BICM) schemes with orthogonal space--time block codes (OSTBC) under imperfect channel estimation assumption. Moreover, our analytical results quantify the performance degradation associated with various levels of channel estimation error variance. The authors also show that if channel estimation quality does not improve sufficiently with SNR, there would be error floor in performance, such that the coded system could get outperformed by a system with differential signalling that requires no channel estimation. Simulation results are presented, which confirm the validity of the analytical results.     

Approproximate Photocounting Statistics of Shot-noise Light with Arbitrary Spectrum

Abstract

The photocounting statistics of shot-noise light have been studied extensively. Light exhibiting such statistical properties arises in photon-generation processes that involve a two-stage cascade of Poisson-based events, such as cathodoluminescence. Expressions for the photocounting distributions are complex because they depend on the overall mean of the distribution, the photodetector counting time, and the spectrum of the light. A simple two-parameter distribution, the Neyman Type-A (NTA), is shown to provide an excellent approximation to the photocounting statistics of shot-noise light with arbitrary spectral properties. The NTA distribution therefore plays the same role for shot-noise light that the negative-binomial distribution plays for chaotic light.     

Performance analysis of decision-feedback equalisation for cellular mobile radio with cochannel interference and fading

The error probability of minimum-mean-square-error decision-feedback equalisation (MMSE-DFE) is evaluated for digital cellular mobile radio systems in the presence of cochannel interference (CCI) and is compared with linear equalisation (LE). The main contribution of the paper is that this analysis accounts for pulse waveform, modulation and fading of the signal of interest, as well as the CCI. Quadrature-amplitude modulation (QAM) signalling in frequency-selective and quasi-static channels is considered. The CCI is treated as a stationary process, when caused by random phase and symbol-timing offsets relative to the signal of interest. Analysis includes techniques combining antenna diversity. The performance improvement as a function of taps in both feedforward and feedback filters is quantified. Owing to residual intersymbol interference (ISI) and CCI, the evaluation of the error probability is extremely complicated and time consuming in simulation. To overcome this issue, an efficient method based upon Gauss quadrature rules (GQR) is presented to compute the error probability. The method is not limited due to interference statistics and it yields remarkable advantages compared with other methods. The convergence of finite-length results to their infinite-length counterparts is also provided. Unlike the case of white noise, the simulations reveal that with the same finite length the DFE is unable to outperform the linear equaliser in a CCI-dominated channel if the feedback filter is of insufficient length.