On the approximation of the output process of multiuserrandom-access communication networks

Bernoulli and first-order Markov processes are used to approximate the output process of a class of slotted multiuser random-access communication networks. The output process is defined as the process of the successfully transmitted packets within the network. The parameters of the approximating processes are analytically calculated for a network operating under a specific random access algorithm. The applied methods are general and can be used to calculate these parameters in the case of any random access algorithm within a class. To evaluate the accuracy of the approximations, a star topology of interconnected multiuser random-access communication networks is considered. The mean time that a packet spends in the central node of the star topology is calculated under the proposed approximations of the output processes of the interconnected networks. The results are compared to simulation results of the actual system. It turns out that the memoryless approximation gives satisfactory results up to a certain per network traffic load. Beyond that per network traffic load, the first-order Markov process performs better     

Real-time digital simulation for systems control

This paper discusses techniques employed in the discrete modeling of physical systems for digital simulation and control applications. Traditional numerical integration techniques provide accurate means of model making but prove too slow for real-time simulation of complex systems or systems with fast response. For rapid digital simulation, a simplified discrete approximation is sought for the linear integro-differential operators of a continuous system. This discrete operator, a digitized transfer function, yields difference equations hopefully permitting real-time approximation of continuous system performance on a digital computer. Determination of the discrete operator is the essential goal of each of the simulation schemes described herein, though differing initial assumptions and approximations alter the resulting forms. After a brief review of these approaches to simulation, techniques for improved approximations for linear system transforms and for discrete parameter optimization and identification are developed. The optimum discrete transfer function which minimizes the sum of error squared between a linear continuous system output and a linear discrete system output is obtained. By adjusting gain parameters in the discrete transfer function, the simulation result is shown to be improved for various inputs and system nonlinearities. Application of standard variational methods to optimize the desired parameters leads to a two-point nonlinear boundary-value problem which is resolved via the techniques of quasilinearization and differential approximation. The procedure for application of various simulation methods is summarized, and the effectiveness of the methods is shown by the simulation of a second-order, nonlinear system for various inputs and sample intervals.     

Approximating filtered scale-variant signals.

We develop theorems that place limits on the point-wise approximation of the responses of filters, both linear shift invariant (LSI) and linear shift variant (LSV), to input signals and images that are LSV in the following sense: they can be expressed as the outputs of systems with LSV impulse responses, where the shift variance is with respect to the filter scale of a single-prototype fillter. The approximations take the form of LSI approximations to the responses. We develop tight bounds on the approximation errors expressed in terms of filter durations and derivative (Sobolev) norms. Finally, we find application of the developed theory to defoveation of images, deblurring of shift-variant blurs, and shift-variant edge detection.     

State learning and mixing in entropy of hidden Markov processes andthe Gilbert-Elliott channel

Hidden Markov processes such as the Gilbert-Elliott (1960) channel have an infinite dependency structure. Therefore, entropy and channel capacity calculations require knowledge of the infinite past. In practice, such calculations are often approximated with a finite past. It is commonly assumed that the approximations require an unbounded amount of the past as the memory in the underlying Markov chain increases. We show that this is not necessarily true. We derive an exponentially decreasing upper bound on the accuracy of the finite-past approximation that is much tighter than existing upper hounds when the Markov chain mixes well. We also derive an exponentially decreasing upper bound that applies when the Markov chain does not mix at all. Our methods are demonstrated on the Gilbert-Elliott channel, where we prove that a prescribed finite-past accuracy is quickly reached, independently of the Markovian memory. We conclude that the past can be used either to learn the channel state when the memory is high, or wait until the states mix when the memory is low. Implications fur computing and achieving capacity on the Gilbert-Elliott channel are discussed     

Mathematical Models for Cochannel Interference in FH/MFSK Multiple-Access Systems

FH/MFSK has been Proposed for a multiuser spread spectrum digital communication system to combat both self-jamming and intentional jamming. An independence assumption at the energy detector outputs is used to evaluate such a system for a digitized voice mobile radio system [11]. This paper presents a correlated model and compares its performance to an independence model under the symbol error probability criterion. A Gaussian process model is also developed for comparison. It is found that the conventional Gaussian approximation is inadequate in predicting the number of users that can be accommodated by an FH/MFSK system using the conventional receiver. Furthermore, for the cases we evaluated, the independence model provides an excellent approximation to the correlated model. Additionally, a conditional Chernoff bound is presented for the more general case of frequency-hopping systems with multiple hops per symbol.     

Reduced-complexity filtering for partially observed nearly completely decomposable Markov chains

This paper provides a systematic method of obtaining reduced-complexity approximations to aggregate filters for a class of partially observed nearly completely decomposable Markov chains. It is also shown why an aggregate filter adapted from Courtois' (1977) aggregation scheme has the same order of approximation as achieved by the algorithm proposed in this paper. This algorithm can also be used systematically to obtain reduced-complexity approximations to the full-order fitter as opposed to algorithms adapted from other aggregation schemes. However, the computational savings in computing the full-order filters are substantial only when the large scale Markov chain has a large number of weakly interacting blocks or "superstates" with small individual dimensions. Some simulations are carried out to compare the performance of our algorithm with algorithms adapted from various other aggregation schemes on the basis of an average approximation error criterion in aggregate (slow) filtering. These studies indicate that the algorithms adapted from other aggregation schemes may become ad hoc under certain circumstances. The algorithm proposed in this paper however, always yields reduced-complexity filters with a guaranteed order of approximation by appropriately exploiting the special structures of the system matrices.     

Strong diffusion approximations for recursive stochastic algorithms

Lai and Robbins (1978) prove strong diffusion approximations for the Robbins-Monro stochastic approximation algorithm. We show that similar strong approximations hold for stochastic algorithms at the level of generality proposed in the monograph of Benveniste, Metivier and Priouret (1990), wherein algorithms with generally discontinous right-hand sides driven by conditionally Markovian data are considered. The relevance of our result is demonstrated on an estimation algorithm with a discontinuous right-hand side which is used in data communication. The technique of adaptive delta modulation used in digital communication is considered     

Reduced-complexity estimation for large-scale hidden Markov models

In this paper, we address the problem of reduced-complexity estimation of general large-scale hidden Markov models (HMMs) with underlying nearly completely decomposable discrete-time Markov chains and finite-state outputs. An algorithm is presented that computes O(/spl epsi/) (where /spl epsi/ is the related weak coupling parameter) approximations to the aggregate and full-order filtered estimates with substantial computational savings. These savings are shown to be quite large when the chains have blocks with small individual dimensions. Some simulation studies are presented to demonstrate the performance of the algorithm.     

Performance analysis of a star topology of interconnected networksunder 2nd-order Markov network output processes

The concept of approximating the output process of slotted multiuser random-access communication networks (i.e. the process of the successfully transmitted packets within the networks) by a second-order Markov process is introduced. A method is developed for analytically calculating the parameters of the approximating process for a class of random-access algorithms. The method is illustrated by considering a specific random-access algorithm from that class. The mean time that a packet spends in the central node of a star topology of interconnected networks is incorporated in the evaluation of the accuracy of the proposed approximation. This quantity is calculated under the proposed approximation on the output processes of the interconnected networks and is compared to simulation results from the actual system. Results showing the accuracy of the proposed approximation for networks operating under a specific random-access algorithm are presented     

Blind identification of multiuser nonlinear channels using tensor decomposition and precoding

This paper presents two blind identification methods for nonlinear memoryless channels in multiuser communication systems. These methods are based on the parallel factor (PARAFAC) decomposition of a tensor composed of channel output covariances. Such a decomposition is possible owing to a new precoding scheme developed for phase-shift keying (PSK) signals modeled as Markov chains. Some conditions on the transition probability matrices (TPM) of the Markov chains are established to introduce temporal correlation and satisfy statistical correlation constraints inducing the PARAFAC decomposition of the considered tensor. The proposed blind channel estimation algorithms are evaluated by means of computer simulations.     

Solution for M/G/1 queues

M/G/1 type queueing systems are frequently found in the performance evaluation of communication systems. The authors develop a new solution method for these queues: their results are an alternative to both standard forms of exact analysis, and to diffusion approximations, while offering comparable computational complexity to the latter     

System Penalty From Second-Order PMD Approximation: Reference Frame Implication

In this paper, we show that second-order PMD approximations, when derived using the input frame and output frame of an optical link, result in two different PMD systems represented by two distinct Jones matrices. In contrast to an all-order representation of a system, which is independent of reference frame, it is found that a finite second-order approximation cannot be obtained simultaneously in both input and output reference frames, except in some limited special cases. The consequences of this are illustrated by analyzing the difference between these two approximations in pulsewidth distortion. It is shown that the second-order PMD approximation in the input frame corresponds to a truncated second-order expansion of the pulse distortion, whereas the second-order PMD approximation in the output frame leads to an infinite-order pulse distortion     

Tensor splines for interpolation and approximation of DT-MRI with applications to segmentation of isolated rat hippocampi

In this paper, we present novel algorithms for statistically robust interpolation and approximation of diffusion tensors-which are symmetric positive definite (SPD) matrices-and use them in developing a significant extension to an existing probabilistic algorithm for scalar field segmentation, in order to segment diffusion tensor magnetic resonance imaging (DT-MRI) datasets. Using the Riemannian metric on the space of SPD matrices, we present a novel and robust higher order (cubic) continuous tensor product of B-splines algorithm to approximate the SPD diffusion tensor fields. The resulting approximations are appropriately dubbed tensor splines. Next, we segment the diffusion tensor field by jointly estimating the label (assigned to each voxel) field, which is modeled by a Gauss Markov measure field (GMMF) and the parameters of each smooth tensor spline model representing the labeled regions. Results of interpolation, approximation, and segmentation are presented for synthetic data and real diffusion tensor fields from an isolated rat hippocampus, along with validation. We also present comparisons of our algorithms with existing methods and show significantly improved results in the presence of noise as well as outliers.     

Markov-modulated flow model for the output queues of a packetswitch

The output queues of an M×N packet switch are studied using a Markov-modulated flow model. The switching element is a central server which sequentially routes packets from the inputs to the outputs. The focus is on systems in which the server speed is such that the bulk of the queuing takes place in the output queues. The conventional point process approach neglects the impact of switching and transmission time. An attempt is made to account for these finite system speeds by using a Markov-modulated continuous flow to approximate the arrival process to an output queue. This model captures the dependency between arrivals at different outputs and reflects the fact that packet arrivals and departures are not instantaneous. The output queue content distribution is obtained, for both infinite and finite buffer systems, from the spectral expansion of the solution of a system of differential equations. Numerical examples and comparisons with the results of an M/M/1 approximation are presented     

FSO MIMO系统中迭代译码算法的研究

自由空间光通信（FSO）系统是一种新型的宽带接入系统,结合了光纤通信与微波通信的优点。但是FSO系统容易受到环境和天气状态的影响,把多输入多输出（MIMO）技术应用于FSO系统中可以有效改善大气对激光波束的影响,提高系统性能。文中主要研究了FSO-MIMO系统的空时译码问题,结合传统的一些译码算法,把Turbo码的迭代译码思想应用于FSO MIMO的空时译码中,分析了一种基于马尔科夫链蒙特卡洛（MCMC）算法的迭代译码方法。     

Complete Characterization of Stable Bandlimited Systems Under Quantization and Thresholding

In this paper, we analyze the approximation behavior of sampling series, where the sample values—taken equidistantly at Nyquist rate—are disturbed either by the nonlinear threshold operator or the nonlinear quantization operator. We perform the analysis for several spaces of bandlimited signals and completely characterize the spaces for which an approximation is possible. Additionally, we study the approximation of outputs of stable linear time-invariant systems by sampling series with disturbed samples for signals in ${cal PW}_{pi}^{1}$. We show that there exist stable systems that become unstable under thresholding and quantization and that the approximation error is unbounded irrespective of how small the quantization step size is chosen. Further, we give a necessary and sufficient condition for the pointwise and the uniform convergence of the series. Surprisingly, this condition is the well-known condition for bounded-input bounded-output (BIBO) stability. Finally, we discuss the special case of finite-impulse-response (FIR) filters and give an upper bound for the approximation error.      

Wavelet domain statistical hyperspectral soil texture classification

This communication presents an automatic soil texture classification system using hyperspectral soil signatures and wavelet-based statistical models. Previous soil texture classification systems are closely related to texture classification methods, where images are used for training and testing. In this study, we develop a novel system using hyperspectral soil textures, which provide rich information and intrinsic properties about soil textures, where two wavelet-domain statistical models, namely, the maximum-likelihood and hidden Markov models, are incorporated for the classification task. Experimental results show that these methods are both reliable and robust.     

A Functional Analysis Approach to Subband System Approximation and Identification

The subband system identification method consists of identifying a linear system in the time-frequency domain. This technique can be also used to approximate a linear system in the same domain. In both cases, it has the advantage of having a very high numerical efficiency; however, analyzing such a technique is not trivial, and the best setup for subband system approximation and identification is not clear. In this paper, we propose a functional analysis setting to the analysis of the subband technique, which leads us to some results on both subband system approximation and identification. Concerning system approximation, we provide an analytical expression to calculate the optimal subband approximation of a given full-band system, when the quality of the approximation is measured by the power of the output error signal, assuming a white input signal. We also provide a tight approximation error bound, for a given subband configuration, which applies in the case where the unknown system to be approximated is known to be the finite-impulse response (FIR) of a given order. Concerning system identification, we provide a novel identification strategy that consists of identifying a "low quality" subband model and use it to build the required model for either subband or delayless reconstruction. This identification strategy reduces the computational complexity of the identification process and yields significantly smaller asymptotic residual errors, when compared with the existing methods     

Availability formulae for standby systems of similar units that arepreventively maintained

Some simple approximation formulae for the availability of standby redundant systems comprising similar units that are preventively maintained are presented. The formulae are established using standard Markov theory. A number of simulations have been performed in order to evaluate the formulae. The simulations show that the formulae give very good approximations for various preventive maintenance regimes. These formulae have been used to model the performance of standby systems on offshore platforms     

BCI2000: a general-purpose brain-computer interface (BCI) system

Many laboratories have begun to develop brain-computer interface (BCI) systems that provide communication and control capabilities to people with severe motor disabilities. Further progress and realization of practical applications depends on systematic evaluations and comparisons of different brain signals, recording methods, processing algorithms, output formats, and operating protocols. However, the typical BCI system is designed specifically for one particular BCI method and is, therefore, not suited to the systematic studies that are essential for continued progress. In response to this problem, we have developed a documented general-purpose BCI research and development platform called BCI2000. BCI2000 can incorporate alone or in combination any brain signals, signal processing methods, output devices, and operating protocols. This report is intended to describe to investigators, biomedical engineers, and computer scientists the concepts that the BC12000 system is based upon and gives examples of successful BCI implementations using this system. To date, we have used BCI2000 to create BCI systems for a variety of brain signals, processing methods, and applications. The data show that these systems function well in online operation and that BCI2000 satisfies the stringent real-time requirements of BCI systems. By substantially reducing labor and cost, BCI2000 facilitates the implementation of different BCI systems and other psychophysiological experiments. It is available with full documentation and free of charge for research or educational purposes and is currently being used in a variety of studies by many research groups.