Stochastic Interference Research Articles

An Investigation of Stochastic Market Equilibrium in Cognitive Radio Networks

In this letter, we model a cognitive radio network as an interference market where each primary user (PU) and secondary user (SU) are price-taking interference offerers and purchasers, respectively. We consider stochastic interference demands of SUs and the existence of random disturbances in PUs' interference observations. Exploiting the fact that the dB value of the uplink inter-cell interference in CDMA networks is modeled as a Gaussian normal distribution, the price-demand decision process in each PU is given by a pair of stochastic differential equations. Then, we investigate an equilibrium of the interference market and its convergence in the context of asymptotic stability in the mean. Numerical results illustrate the convergence of the price-demand decision process to the equilibrium.

A method for identifying a spacewise-dependent heat source under stochastic noise interference

We consider an inverse problem of determining a spacewise-dependent heat source in the time-dependent heat equation using the usual conditions of the direct problem and information from temperature measurements at a given single instant of time. This spacewise-dependent temperature measurement ensures that the inverse problem has a unique solution, but the solution is unstable and hence the problem is ill-posed. Furthermore, it is assumed that information about this temperature measurement is available only at a finite number of points, and moreover, these measurements are blurred by a stochastic noise. The continuous problem is discretized using a finite element method and for the discrete model an estimate of the heat source is obtained by a Tikhonov regularization. It is proved that increasing the number of measurements and decreasing the mesh size produces a sequence of solutions which under appropriate conditions converge to the continuous heat source.

Adaptive Reception of Signals in Channels with Stochastic Narrowband Interference

Adaptive Reception of Signals in Channels with Stochastic Narrowband Interference

Particle filter based stochastic interference cancellation for frequency-selective MIMO channel equalization

To mitigate the effects of the previous symbol decision errors of a decision-feedback (DF) equalizer on the current decision, a particle filter (PF) based DF equalizer for frequency selective multiple-input-multiple-output (MIMO) channel is proposed. On the basis of the analyses of DF equalization for the MIMO wireless system, it is found that a stochastic interference cancellation (IC) scheme can be employed to prevent the error propagation in a severe space-time interference scenario. This is because the random rather than the deterministic scheme can reduce the probability of an error decision even if an error decision occurs. Besides, the signal-to-interference-plus-noise ratio (SINR) based IC order, which is obtained via pilot, can guarantee the optimality of the cancellation. The bit error rate (BER) performance of the proposed scheme is verified through simulation experiments under different multipath interference environment.

Some application cases and related manufacturing techniques for optically functional microstructures on large areas

With surface-relief structures, optical functions that are required for radiation power management such as antireflection, light trapping, or light distribution and redirection can be obtained for new applications in solar energy systems and in displays. There, structures with submicrometer features must be distributed over large areas homogeneously. We address the design and the whole experimental process chain from the microstructure origination on large areas to the replication and the system integration in the specific application. Topics are antireflective surfaces for solar systems and displays, light trapping in polymer solar cells, sun protection systems for facades, and diffusers for projection displays and in glazing. For the microstructure origination we investigate the suitability of holographic recording in photoresist using a large-scale interferometer. We use an argon ion laser as a coherent light source at a wavelength of 364 nm. Periodic and stochastic interference patterns are recorded in positive photoresist with the interferometer setup. In the case of periodic structures, grating periods between 200 nm and 20 µm are realized. By carefully modeling the resulting resist profiles it is possible to originate even prismatic surface-relief profiles. Structures with good homogeneity are originated on areas of up to 4800 cm2 by optimizing the interferometer setup and the photoresist processing.

Computer-generated holograms in interferometric testing

With surface-relief structures, optical functions that are required for radiation power management such as antireflection, light trapping, or light distribution and redirection can be obtained for new applications in solar energy systems and in displays. There, structures with submicrometer features must be distributed over large areas homogeneously. We address the design and the whole experimental process chain from the microstructure origination on large areas to the replication and the system integration in the specific application. Topics are antireflective surfaces for solar systems and displays, light trapping in polymer solar cells, sun protection systems for facades, and diffusers for projection displays and in glazing. For the microstructure origination we investigate the suitability of holographic recording in photoresist using a large-scale interferometer. We use an argon ion laser as a coherent light source at a wavelength of 364 nm. Periodic and stochastic interference patterns are recorded in positive photoresist with the interferometer setup. In the case of periodic structures, grating periods between 200 nm and 20 µm are realized. By carefully modeling the resulting resist profiles it is possible to originate even prismatic surface-relief profiles. Structures with good homogeneity are originated on areas of up to 4800 cm2 by optimizing the interferometer setup and the photoresist processing.

Modeling and on-line recognition of PD signal buried in excessive noise

The problem of on-line recognition and retrieval of relatively weak industrial signal such as partial discharges (PD), buried in excessive noise has been addressed in this paper. The major bottleneck being the recognition and suppression of stochastic pulsive interference (PI), due to, overlapping broadband frequency spectrum of PI and PD pulses. Therefore, on-line, on-site, PD measurement is hardly possible in conventional frequency-based DSP techniques. We provide new methods to detect, estimate and classify the PD signal. The observed PD signal is modeled as linear combination of systematic and random components employing probabilistic principal component analysis (PPCA) and pdf of the underlying stochastic process is obtained. The PD/PI pulses are assumed as the mean of the process and modeled using both parametric and non-parametric methods. A Gaussian model is incorporated in parametric modeling and smooth FIR filter method is used in non-parametric modeling and the parameters of the models are estimated using maximum-likelihood (ML) estimation technique. The methods proposed by the authors are able to recognize and retrieve the PD pulses, completely automatic without any user interference.

Assessment of the GA‐based adaptive array control strategy: The case of stochastic life‐time co‐channel interferences

AbstractIn this paper, the performances of an adaptive antenna array control strategy, based on an improved genetic algorithm, are evaluated in terms of signal‐to‐interference‐noise ratio (SINR). The working case considered deals with the presence of co‐channel interfering signals characterized by stochastic arrivals, phases, and lifetime. This scenario provides a reliable testing benchmark for such array control methodologies. The simulation results prove the robustness of the learned real‐time genetic algorithm (LRTGA) in the presence of non‐deterministic interferences as well. © 2003 Wiley Periodicals, Inc. Microwave Opt Technol Lett 37: 198–201, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10867

Amplification by stochastic interference

A new method is introduced to obtain a strong signal by the interference of weak signals in noisy channels. The method is based on the interference of 1/f noise from parallel channels. One realization of stochastic interference is the auditory nervous system. Stochastic interference may have broad potential applications in the information transmission by parallel noisy channels.

Production Lot Sizing with Machine Breakdowns

Economic lot sizing and batching models often assume reliable manufacturing facilities. In this research, we focus on the effects of machine breakdowns and corrective maintenance on the economic lot sizing decisions. Two production control policies are proposed for coping with these stochastic interferences. The first policy assumes that production of the interrupted lots is not resumed after a breakdown. Instead, the on-hand inventory is depleted before a new cycle is initiated. Under the second policy studied here, production is immediately resumed after a breakdown, if the current on-hand inventory is below a certain threshold level. It is shown that this control structure is optimal among all stationary policies. We show that under both policies the optimal lot sizes will always be bigger than the ones in a corresponding deterministic case, and that the optimal lot size increases with the failure rate. We also provide exact optimal and closed form approximate lot sizing formulas and derive tight bounds on the average cost per unit time for the approximations. In addition, we present various structural properties for these policies and operational insights relevant to such management decisions as machine replacement or maintenance schedules.

Adaptive processing techniques based on Hidden Markov Models for characterizing very small channel currents buried in noise and deterministic interferences

Techniques for characterizing very small single-channel currents buried in background noise are described and tested on simulated data to give confidence when applied to real data. Single channel currents are represented as a discrete-time, finite-state, homogeneous, Markov process, and the noise that obscures the signal is assumed to be white and Gaussian. The various signal model parameters, such as the Markov state levels and transition probabilities, are unknown. In addition to white Gaussian noise, the signal can be corrupted by deterministic interferences of known form but unknown parameters, such as the sinusoidal disturbance stemming from AC interference and a drift of the base line owing to a slow development of liquid-junction potentials. To characterize the signal buried in such stochastic and deterministic interferences, the problem is first formulated in the framework of a Hidden Markov Model and then the Expectation Maximization algorithm is applied to obtain the maximum likelihood estimates of the model parameters (state levels, transition probabilities), signals, and the parameters of the deterministic disturbances. Using fictitious channel currents embedded in the idealized noise, we first show that the signal processing technique is capable of characterizing the signal characteristics quite accurately even when the amplitude of currents is as small as 5-10 fA. The statistics of the signal estimated from the processing technique include the amplitude, mean open and closed duration, open-time and closed-time histograms, probability of dwell-time and the transition probability matrix. With a periodic interference composed, for example, of 50 Hz and 100 Hz components, or a linear drift of the baseline added to the segment containing channel currents and white noise, the parameters of the deterministic interference, such as the amplitude and phase of the sinusoidal wave, or the rate of linear drift, as well as all the relevant statistics of the signal, are accurately estimated with the algorithm we propose. Also, if the frequencies of the periodic interference are unknown, they can be accurately estimated. Finally, we provide a technique by which channel currents originating from the sum of two or more independent single channels are decomposed so that each process can be separately characterized. This process is also formulated as a Hidden Markov Model problem and solved by applying the Expectation Maximization algorithm. The scheme relies on the fact that the transition matrix of the summed Markov process can be construed as a tensor product of the transition matrices of individual processes.

Stochastic mechanics and quantum interference

It is shown that in the framework of the stochastic interpretation of quantum mechanics it is always possible to determine correct real positive transition probabilities that can be added together to obtain the quantum interference patterns. The implication of this fact on the possibility that quantum micro-objects follow trajectories in space and time is discussed. A derivation is given of a path integral formula yielding these transition probabilities.

Product Forms for Stochastic Interference Systems

Systems are studied that consist of interfering components which are alternatively active (busy) and passive (idle) for random periods. Such systems naturally arise from the performance evaluation of computer models. A concrete invariance condition is imposed on the interferences allowed. Under this condition, the steady-state vector of active components is shown to be of product form as well as to be robust to distributional forms of active and passive periods. The proof is simple and self-contained. A number of concrete and generic examples is provided. These include resource sharing mechanisms, hierarchical circuit switchings, parallel processing, priorities, and breakdowns.

Non-Normality of Probability Density Function of Total Second Order Responses of Moored Vessels in Random Seas

This paper is concerned with statistical estimation of total second order responses including the slow drift oscillation of a moored floating offshore structure in random seas. Stochastic interference between a wave frequency response and the slow drift oscillation affecting on the probability distribution is discussed.Assuming that the responses are represented in the form of two term Volterra functional series, an extended theory of probability density functions of an instantaneous response and its maxima are developed from the previous paper. It is applied to sway of moored floating semi-circular and rectangular cylinders, and confirmed its accuracy comparing with the exact solution in case of a pure second order motion at first. Next, non-normality of the total second order motion is investigated. It is shown that it is significant especially in case of heavy damping of the system and totally different from non-normality of the pure second order motion. The interference between the first and second order responses plays important roles on the probability density and the extreme value of the total response.

Array processors for simultaneous noise and interference suppression or simultaneous signal-to-noise and resolution enhancement

A symmetrical treatment is described of signal and interference arrivals, both spatially coherent across the aperture of a receiving array and appearing in a generalized ambient-noise background. By separating the coherent interference from the rest of the noise background, it is possible to implement a simple form of adaptive suppression of the interference, particularly when the latter is time varying and the remainder of the noise is stationary. Optimal processors are derived for simultaneous suppression of noise and interference, and for enhancement of the signal-to-noise ratio after elimination of interference. The processor for the latter case is shown to be a suboptimum version of the former. Both deterministic and stochastic interference are considered, as well as interference whose arrival time is synchronized with that of the desired signal (e.g., unwanted signal multipath arrivals, reverberation, etc.). Processors for two or more simultaneous and independent interference sources are described. Finally, the interference descriptor can be reinterpreted as a generalized resolution measure, so as to describe processors that simultaneously maximize the signal-to-noise ratio and the signal time resolution, or the signal-to-noise ratio and a combination of arrival angle and time resolution. Subject Classification: [43]60.30.

Interpulse Interval Distribution in the Environment of N Periodic Radars

This paper is concerned with an environment consisting of N periodic radars, each emitting a periodic pulse train. The number of radars and their periodicities are assumed known but the epoch of each pulse train is a random variable with a uniform distribution. The principal result of this paper is the expression for the probability density function of interpulse intervals of the sum of all the N pulse trains. Only absence or presence of a pulse is considered, and the amplitude distribution is not treated; i.e., any pulse emitted by any of the N radars is considered capable of initiating a new interpulse interval. The obtained result is useful in establishing the control function for the interpulse interval generator of a stochastic interference simulator.